Techniques of Physics
Editor
N.H. M A R C H
Department
of
Oxford,
England
Theoretical
Chemistry:
University
of
Oxford,
Techniques of physics find wide application in biology, medicine, engineering and
technology generally. This series is devoted to techniques which have found and are
finding application. The aim is to clarify the principles of each technique, to emphasize
and illustrate the applications, and to draw attention to new fields of possible
employment.
1.
D.C. Champeney: Fourier Transforms and their Political
Applications
2.
J.B. Pendry: Low Energy Electron Diffraction
3.
K.G. Beauchamp: Walsh Functions and their Applications
4.
V. Cappellini, A.G. Constantinides and P. Emiliani: Digital Filters and their
Applications
5.
G. Rickayzen: Green's Functions and Condensed Matter
6.
M. C. Hutley: Diffraction Gratings
7.
J.F. Cornwell: Group Theory in Physics, Vols I and II
8.
N.H. March and B.M. Deb: The Single-Particle Density in Physics and Chemistry
9.
D.B. Pearson: Quantum Scattering and Spectral Theory
10.
J.F. Cornwell: Group Theory in Physics, Vol III: Supersymmetries and InfiniteDimensional Algebras
11.
J.M. Blackledge: Quantitative Coherent Imaging
12.
D.B. Holt and D.C. Joy: SEM Microcharacterization of
Semiconductors
SEM Microcharacterization
of Semiconductors
Edited by
D.B. HOLT
Department
of Materials,
London,
UK
Imperial
College
of Science
and
Technology,
of Tennessee,
Division,
Tennessee
Knoxvifle,
D.C. JOY
Electron Microscope
Facility,
The University
Tennessee,
USA and Metals and Ceramics
Oak Ridge National Laboratory,
Oak Ridge,
ACADEMIC
PRESS
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Copyright © 1989 by
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No part of this book may be reproduced in any form
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British Library Cataloguing in Publication Data
S E M microcharacterization of semiconductors
1. Semiconductor devices
I. Title II. Holt, D.B. (David Basil),
1928621.3815'2
I S B N 0-12-353855-6
Phototypeset by Thomson Press (India) Limited, New Delhi
and Printed in Great Britain by The University Press, Cambridge
Contributors
L.J. Balk, Universitat Duisburg, Fachgebiet Werkstoffe der Elektrotechnik,
Kommandantenstrasse 60, 4100 Duisburg 1, Federal Republic of G e r m a n y
O. Breitenstein, Institut fur Festkorperphysik und Elektronenmikroskopie,
Academie der Wissenschaften der D D R , Postfach 250, DDR-4020 Halle,
G e r m a n Democratic Republic
S.M. Davidson, Deben Research, 5 Friars Courtyard, Princes Street, Ipswich,
IP1 1RJ, U K
J. Heydenreich, Institut fur Festkorperphysik und Elektronenmikroskopie,
Academie der Wissenschaften der D D R , Postfach 250, DDR-4020 Halle,
G e r m a n Democratic Republic
D.B. Holt, Department of Materials, Imperial College of Science and
Technology, Prince Consort Road, L o n d o n SW7 2BP, U K
D.C. Joy, Electron Microscope Facility, The University of Tennessee, F239
Walters Life Sciences Building, Knoxville, T N 37996-0810, USA and Metals
and Ceramics Division, O a k Ridge National Laboratory, O a k Ridge, Tennessee 37831-6376, USA
D.E. Newbury, Center for Analytical Chemistry, National Institute of
Standards and Technology, Gaithersburg, M D 20899, USA
B.G. Yacobi, Microscience Research, P.O. Box 67034, Newton, Massachusetts 02167, USA
Preface
It is over a decade since Quantitative Scanning Electron Microscopy appeared
and a number of people have suggested that it is overdue for replacement. The
fundamental principles involved have not changed and the accounts of the
basic topics in the earlier m o n o g r a p h have, on the whole, stood the test of time
well. However, a number of topics such as Kossel patterns are now seen to be
of limited value and others are no longer novel while new techniques have
appeared such as the electroacoustic mode, scanning deep level transient
spectroscopy and S O M S E M . Others have grown to maturity and great
practical importance such as stroboscopic voltage contrast. Most strikingly,
the applications of S E M techniques of microcharacterization have proliferated to cover every type of material and virtually every branch of science and
technology and microcomputers have become all pervasive.
We have therefore tried to follow the basic format of the earlier volume with
an introductory section and a section on the interpretation of the information
obtained in the main modes of the SEM. The emphasis again is on
fundamental physical principles. Those needing guidance on the operation
and maintenance of SEMs will find their needs met elsewhere. O n consideration we felt that it was better to try to produce a fairly concise book
concentrating on the field of application, semiconductors and electronic
materials, which is the seed bed of most advances than to attempt to cover all
fields or to try to be abstractly theoretical.
We hope that you will find this book useful.
D . B . HOLT
D . C . JOY
Foreword
The scanning electron microscope (SEM) can be applied to semiconductor
science in many ways. M e t h o d s based on the injection of charge carriers by the
electron beam in the S E M can be very useful for measuring the properties of a
semiconducting material (such as the carrier lifetime or diffusion length, for
example). O r alternatively, the surface potentials can be measured by the
'voltage contrast' method. Surface topography can be studied by either the
secondary or backscattered electron imaging methods. Thus, the position of a
crystal defect or a p - n junction can be correlated with the surface topography
by comparing the images obtained by different methods. The crystal perfection
of a surface can be studied by electron channelling contrast. Other techniques
have also been developed.
The original demonstration of electron beam induced conductivity (EBIC)
was of the 'beta-conductivity' that is found when there is no barrier present.
Thus, Becker (1904) found that a current can be induced in an insulator if it is
bombarded with electrons. The same effect was found in selenium by Kronig
(1924), in diamond by M c K a y (1948), and with the insulating thin films by
Pensak (1949). M c K a y wrote:
'Although the results have a considerable bearing on [diamond's] use as a solid
counter, it is of more significance that a new method of investigating certain of the
solid state properties of insulators and semiconductors is described.'
The earliest apparatus to resemble any S E M was built by Knoll (1936 and
1940) in order to measure the potentials to which objects are charged by an
electron beam. M a n y of the concepts that are familiar to present-day users of
the low voltage S E M were described by him.
The use of the S E M to study surface topography was investigated by von
Ardenne (1940), by Zworykin, Hillier and Spy der (1940) and in more detail by
students supervised by C.W. Oatley in the Engineering Laboratory at
Cambridge University in England (McMullan 1953, Oatley 1982). The
secondary electron imaging method was developed in its modern form by
K.C.A. Smith and T.E. Everhart, and this set the stage for generations of
spectacular micrographs that are now the standard of the industry (Smith and
Oatley 1955, Smith 1959, Everhart and Thornley 1960). Voltage contrast at a
reverse-biased p - n junction in germanium was described by Oatley and
Everhart (1957).
xii
Foreword
Induced signals were obtained from p - n sections by Ehrenberg, et al (1951)
and by R a p p a p o r t (1954). The use of finely focused electron beams in
semiconductor science began when Ever hart (1958) obtained an induced
waveform by scanning in a line across a p - n junction in germanium. The E B I C
image from a semiconductor device was obtained in a closely run race as a
method for locating the structure during E B fabrication (Wells et al, 1963), as
a method for showing the geometry of integrated circuits (Everhart et al, 1963)
and a method for showing defects in a diffused p - n junction (Lander et al
1963).
I m p o r t a n t work with the S E M (and this includes the above) took place in
the early 1960's at the Westinghouse Research Laboratories in Pittsburgh, PA,
at the I B M Research Laboratories at Yorktown Heights, NY, in the Electrical
Engineering D e p a r t m e n t of the University of California at Berkeley, and at
Bell Telephone Laboratories at M u r r a y Hill, NJ. The situation was, of course,
totally transformed when commercial S E M s became available in 1965.
In this book, the available techniques are described in detail by workers who
in many cases took part in the original development of the S E M , and who in all
cases have had extensive theoretical and practical experience with the methods
that they describe. As things stand now, the development and improvement of
commercial S E M s and the associated computer systems to control the
instruments and to record and process the data are proceeding at a rapid pace.
It is therefore very timely that this b o o k has been written for those who either
wish to study these procedures in detail, or who might wish to apply these
methods in the course of their work.
9
References
Ardenne, M. von. (1940). Elektronen-Ubermikroskopie, Springer, Berlin (1940);
Edwards, Ann Arbor (1943).
Becker, (1904). Concerning the effect of cathode rays on solid insulators (in German),
Ann. d. Physik, 13, 394-421.
Ehrenberg, W., Lang, C.S. and West, R. (1951). The electron voltaic effect. Proc. Phys.
Soc. A. 64, p. 424 only.
Everhart, T.E. (1958). Contrast formation in the scanning electron microscope. Ph.D.
Diss., Cambridge Univ., England.
Everhart, T.E., and Thornley, R.F.M. (1960). Wide-band detector for micromicroampere low-energy electron currents. J. Sci. Instrum., 37, 246-248.
Everhart, T.E., Wells, O.C. and Matta, R.K. (1963). Evaluation of passivated integrated
circuits using the scanning electron microscope. (Extended Abstract), Electrochemical Society, Electronics Division 12, no. 2,2-4. (New York meeting, Oct. 1963).
Knoll, M. (1935). Static potential and secondary emission of bodies under electron
irradiation (in German). Z. Tech. Physik, 11, 467-475.
Knoll, M. (1940). Deflecting action of a charged particle in the electric field of a
secondary emitting cathode (in German). Naturwiss, 29, 335-336.
Foreword
xiii
Kronig, R. de L. (1924). Change of conductance of selenium due to electronic
bombardment. Phys. Rev., 24, 377-382.
Lander, J.J., Schreiber, H., Buck, T.M. and Mathews, J.R. (1963). Microscopy of
internal crystal imperfections in Si p - n junction diodes by use of electron beams.
Appl. Phys. Lett., 3, 206-207.
McKay (1948). Electron bombardment conductivity in diamond. Phys. Rev., 74,16061621.
McMullan, D. (1953). An improved scanning electron microscope for opaque
specimens. Proc. IEE Pt. II, 100, 245-259.
Oatley, C.W. and Everhart, T.E. (1957). The examination of p - n junctions with the
scanning electron microscope. J. Electronics, 2, 568-570.
Oatley, C.W. (1982). The early history of the scanning electron microscope. J. Appl.
Phys., 53, R1-R13.
Pensak, L. (1949). Conductivity induced by electron bombardment in thin insulating
films. Phys. Rev., 75, 472-478.
Rappaport, P. (1954). The electron-voltaic effect in p - n junctions induced by betaparticle bombardment. Phys. Rev., 93, 246-247.
Smith, K.C.A. and Oatley, C.W. (1955). The scanning electron microscope and its fields
of application. Brit. J. Appl. Phys., 6, 391-399.
Smith, K.C.A. (1959). Scanning electron microscopy in pulp and paper research. Pulp
Paper Mag. Canada, 60, T366-T371.
Wells, O.C., Everhart, T.E., and Matta, R.K. (1963). Automatic positioning of device
electrodes using the scanning electron microscope. (Extended Abstract), Electrochemical Society, Electronics Division, 12, no. 2, 5-12. (New York meeting, Oct.
1963.)
Zworykin, V.K., Hillier, J. and Snyder, R.L. (1942). A scanning electron microscope.
ASTM Bull. no. 117, pp. 15-23.
Yorktown Heights, N Y
March 1989
Oliver Wells
1 An Introduction to Multimode Scanning
Electron Microscopy
D.B. HOLT
Department
Prince
of Materials,
Consort
Road,
Imperial
London
College
of Science
and
Technology,
SW7 2BP, UK
List of symbols
1.1 The SEM as a two-component system: signals, modes and contrast . .
1.2 Resolution: the specification of instrumental capabilities
1.2.1 Spatial resolution and contrast
1.2.2 Spatial resolution and magnification
1.2.3 Signal (spectral) resolution and contrast
1.3 Instrumentation
1.3.1 Electron beam diameter and current
1.3.2 The minimum attainable spot size: the limitation due to diffraction
and aberrations
1.3.3 Beam voltage
1.3.4 Detector system limiting factors
1.3.5 Computerization
1.4 Types of electron beam instruments
1.4.1 General purpose SEMs
1.4.2 MiniSEMs
1.4.3 Dedicated STEMs
1.4.4 Dedicated EPMAs
1.4.5 Combined transmission and scanning instruments (TEMSCANS)
1.4.6 E-beam testers
1.4.7 E-beam lithography systems
References
3
5
8
10
15
15
16
17
22
23
24
24
25
25
25
26
26
27
27
27
27
List of s y m b o l s
B
B'
B'
C
brightness of the electron beam (defined by eqn (1.7)
brightness (of a pixel)
average brightness
contrast
SEM Microcharacterization of Semiconductors
ISBN 0-12-353855-6
Copyright © 1989 Academic Press Limited
All rights of reproduction in any form reserved
4
D.B. Holt
c.
c
s
d
d
d
0
c
d
d
d
A
t
s
^total
D
J
Jo
k
I
L
L
M
M
M
u
l,2,3
q
T
v
b
AV
a
X
P
chromatic aberration coefficient
spherical aberration coefficient
beam spot (probe) diameter
diameter of the crossover in a thermionic gun
chromatic aberration limited spot diameter
Airey's (diffraction limited) disc diameter
aberration and diffraction limited beam diameter
spherical aberration limited spot diameter
beam (probe) diameter due to all the effects involved
diameter of the final (objective) aperture
beam current
maximum current density that can be focused into a probe from a
thermionic cathode (Langmuir's Law)
density of current emitted from the surface of a thermionic cathode
Boltzmann's constant
side of area raster scanned on the specimen
side of area raster scanned on the C R O screen
working distance (objective aperture to specimen)
magnification
useful magnification
(de)magnifications of the three lenses
charge on the electron
temperature in degrees Kelvin
beam accelerating potential difference (voltage)
spread of voltage corresponding to the range of velocities a m o n g the
beam electrons
semi-angle of convergence of the beam at the specimen
wavelength of the beam electrons
point resolution in millimetres
In 1984 it was estimated that scanning electron microscopes (SEMs) outsold
transmission electron microscopes (TEMs) by three to one, that a thousand
SEMs were being manufactured per a n n u m and that 15,000 were in use
worldwide.* Yet when, in 1964, it was first proposed that S E M s should be
manufactured commercially, Cambridge Instruments made a first batch of
only five. The most optimistic forecast then was that twenty SEMs might be
sold per year. The reason for this underestimation of the new instrument was
that only its (then modest) spatial resolution for secondary electron, emissive
*T.H.P. Chang, paper presented at the Oatley commemoration meeting, Cambridge (UK), 25
June 1984.
An introduction to multimode scanning electron microscopy
5
mode use was considered. It was seen as a competitor to the T E M surface
replica technique. (For historical accounts of the emergence of the S E M from
an academic laboratory development into an industrial product see Oatley
(1982), McMullan (1985), and Stewart (1985). The industrial history is
reviewed by Jervis (1971/72).)
The main attractions of the S E M were found to be its versatility,
information output rate and convenience. Perhaps the earliest clear statement
of the importance of the unique "information-encoding mechanism" of the
S E M is that of Everhart (1968). The S E M is now recognized as not only a
microscope, but a family of modular, computer-based microcharacterization
instruments.
Here we will try to cover the fundamentals of the system from this point of
view, together with the advantages and disadvantages of the different types of
scanning electron beam instruments now available for use in semiconductor
microcharacterization. The basic principles of the individual modes and
techniques of special interest in semiconductor microcharacterization will be
treated in the second section of this book.
1.1
The S E M as a two-component system: signals, modes
and contrast
The S E M consists of two subsystems (Fig. 1.1). These are (i) an electron optical
column that produces a finely focused electron probe which can be raster
scanned over the specimen surface and (ii) a detection system which includes
some signal processing and output facilities. The third essential element is the
specimen, together with the necessary stage facilities. The three constituents
together determine the performance of the system. The microscope has a
certain spatial and signal (spectroscopic) resolution but the results attainable
are specimen limited so the most important results are often only achievable
on unusual or specially prepared samples.
The incident beam electrons dissipate their kinetic energy into other forms
in a large dissipation (generation or cascade) volume. Any one of six types of
resultant energy may be detected, i.e. transduced into electrical signals. These
six types of signal are (Fig. 1.2), in the approximate chronological order of their
exploitation: (1) X-rays, (2) emitted electrons, (3) charge collection (CC) or
conductive mode signals, (4) cathodoluminescence (CL) light, (5) transmitted
electrons and (6) acoustic (ultrasonic) waves. These form the bases of the
modes of operation generally known, respectively, as (1) E P M A (electron
probe microanalysis or the X-ray mode), (2) the emissive mode, (3) the C C and
(4) the C L modes, (5) S T E M (scanning transmission electron microscopy) and
(6) the electroacoustic mode. Contrast arises from spatial variations of those
6
D.B. Holt
5- 30 k V negotivc
Electron gun
Electron optical column
J
L
Scon
generator
gnd
iB H i
Condenser
lenses
Magnification
control
.Objective lens containing
-scanning coils
Video
signal
Detector
Signal
Specimen
Amplifier
Synchronously
scanned
~CR.O
Display system
To vacuum
pumps
F i g . 1.1 Schematic diagram of the components of a simple scanning electron
microscope.
properties that affect the strength (intensity) of the signal so in each mode
information is obtainable concerning a group of properties. These different
detectable properties give rise to forms of contrast. Thus, using the secondary
electron signals of the emissive mode, it is possible to observe topographic,
voltage and magnetic contrast. By using the EBIC (electron beam-induced
current) signals in the C C mode it is possible to observe electrical barrier
contrast at p - n junctions, Schottky barriers and heterojunctions and bulk
contrast at, for example, impurity growth striations.
The minimal detection (including processing and output) system is that
supplied by the manufacturers of SEMs and intended for simple pictorial
microscopy. This system consists of an electron detector, video amplifier and
synchronously scanned cathode ray oscilloscopes (CROs) for viewing and
photography (Fig. 1.1). M o r e generally, the detection system can transduce to
electrical signals energy corresponding to any one of the six modes, computer
process and output the results on any form of computer peripheral. The energy
dispersive X-ray spectroscopy systems available from a number of manufacturers provide such computer-based processing and output systems and
these can readily be adapted to handle the signals of the other modes. General
purpose SEM frame store and image (signal) processing systems are also
available from several manufacturers.
S O M S E M (scanning optical microscopy in an SEM) does not readily fit
into the scheme outlined above. S O M S E M uses a phosphor layer or
An introduction to multimode scanning electron microscopy
7
(a )
Emitted
electrons
Charge
collection
Specimen
Transmitted
electrons
==D>
dc
amplifier
Current
i
Specimen
current
-
electron beam
energy dissipation
volume
0
T
-d
'z
F i g . 1.2 The signals used in the six modes of scanning electron microscopy: (a) the
five signals available with continuous bombardment and (b) the generation of decaying
thermal waves and ultrasonic waves by a beam chopped at a high frequency. (After
Balk, 1988.)
luminescent crystal under the beam to create a scanning light spot. A system of
lenses focuses this light onto the surface of a specimen (Fig. 1.3). Analogues of
several modes of the S E M then arise: O B I C (optical beam-induced current),
P L (photoluminescence), etc. It is too early to assess its value. However, in view
8
D.B. Holt
Phosphor
screen
Lens —#
Specimen —
F i g . 1.3 Principles of scanning optical microscopy in a scanning electron microscope (SOMSEM). (After Battistella et aU 1987).
of the destructive effect of electron b o m b a r d m e n t on M O S (metal-oxidesemiconductor) devices (and all VLSI circuits are M O S devices), O B I C
appears to be worth developing. The same effects can be produced without an
S E M by using, for example, a confocal scanning laser optical microscope. This
competing (expensive) instrument is now commercially available also
(Fig. 1.4). An obvious advantage of the S O M S E M technique is that the
information so obtained can be compared with that obtained by means of the
various modes of the SEM. An apparent disadvantage is the more limited
optical power available in the S O M S E M light spot.
Scanning deep level trap spectroscopy (SDLTS) also does not fit neatly into
the scheme of six modes of scanning electron microscopy. It could be argued
that S D L T S detects specialized forms of charge collection signal. However, the
technique is new, important and requires specialized detection systems so
S D L T S is treated in Chapter 7 by D r O. Breitenstein and Professor J.
Heydenreich.
1.2
Resolution: the specification of instrumental capabilities
There are two essentially different types of resolution involved in the operation
of multimode quantitative SEMs. There is spatial resolution and, for each
mode, some form of spectroscopic resolution provided by the capacity of the
detection system to discriminate between the components of the particular
An introduction to multimode scanning electron microscopy
9
(a)
Obftclwt
Coil rc tor
0bf«cl
Video
[mentor!
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F i g . 1.4 Schematic diagrams of (a) a confocal scanning laser transmission microscope (after Sheppard, 1986) and (b) a commercial reflection instrument of this type (the
Bio-Rad "Lasersharp" microscope).
signal involved. In several cases this signal resolution is provided by actual
spectrometers:
(1) F o r the X-ray mode (EPMA) either energy dispersive or wavelength
dispersive X-ray spectrometers are used.
(2) F o r the emissive and S T E M modes, E E L S (electron energy loss spectroscopy) and SAM (scanning Auger microscopy) electron spectrometers
of various resolutions are necessary. Even within the emissive mode, to
detect voltage contrast quantitatively, with linear sensitivity to small
potential differences, electron detectors of special design are used.
(3) F o r the C L m o d e m o n o c h r o m a t o r s and Fourier transform spectrometers
are used.
10
D.B. Holt
For the C C and electroacoustic modes the fact that signal discrimination is
possible and desirable is less widely recognized perhaps. The latter mode is
new and is discussed by D r P. Balk in Chapter 9. In the C C mode it is necessary
to distinguish /J-conductive from electron voltaic effect signals, and in the
latter case, to record either the short-circuit current (true EBIC) or opencircuit voltage (true EBIV) reliably (Chapter 6).
1.2.1
S p a t i a l resolution a n d contrast
The spatial detection limit is the diameter of the smallest area or volume from
which sufficient intensity can be obtained to satisfy the signal/noise ratio
requirements of the detection system. This is, of course, determined by all three
system elements. The electron optical column determines the spot diameter
into which a given beam power can be focused. The detection, amplification
and processing system sets the minimum signal intensity requirement. The
specimen has an efficiency of signal generation which determines how great a
beam power will be needed to generate the necessary intensity of signal.
(Unlike light optical microscopes (LOMs) and transmission electron
microscopes (TEMs), S E M s do not form optical images and so are not
basically diffraction limited. Therefore the Rayleigh criterion cannot define
SEM resolution nor can the Abbe theory of resolution be applied to calculate
an SEM limit of resolution or resolving power. T o avoid confusion, therefore,
the terms limit of resolution and resolving power are not used in relation to
SEMs.)
The diameter of the energy dissipation (generation or cascade) volume is
determined by electron scattering processes inside the solid. These can now be
rapidly simulated on a microcomputer to give the size and shape of the energy
dissipation volume and the depth and lateral "dose" functions, i.e. the
distribution of the energy deposited in the material including the electronhole pair distribution (Fig. 1.5). The energy dissipation volume is often
approximated, for simple modelling of Si at beam voltages of tens of kilovolts,
by a uniform energy-density sphere tangential to the surface, as shown in
Fig. 1.5b, of the order of 1 /im in diameter. There can be seen to be a basic
difference in spatial resolution between S T E M , which requires such thin
specimens that there is virtually no beam spreading (Fig. 1.5c), the emissive
mode in which beam spreading results in roughly a two-fold increase in the
resolution as compared with the beam diameter and the "bulk modes", X-ray,
C L and C C in which the signal is obtained from the whole energy dissipation
volume. In the bulk modes the energy dissipation volume diameter, D, is the
resolution, almost independently of beam diameter, d, for small values of the
latter.
HONTC CARLO SIMULATION
HONTC CARLO SIMULATION
A c c . V o l t a s * <kaV> : 3B.BB
• •loctrons: M M
B a c k s e a t , -fraction:
9.19
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silicon susstrats
silicon susstrats
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K
D
(b)
H
l
c
J
F i g . 1.5 (a) Electron trajectories and energy deposited at different depths (depthdose function) for silicon and a 30 kV beam, obtained by Monte Carlo simulation on a
microcomputer (E. Napchan, private communication) and schematic diagrams showing
the regions from which the signals are obtained in (b) bulk and (c) thin specimens.
12
D.B. Holt
B
A
B
C
0 £
Distance
Two points ore resolved when
BM,- AB *
or
AB *
075 BM,
0.25 B M ,
F i g . 1.6 Schematic diagram (after Everhart, 1970, quoting Leisegang) illustrating
point resolution. The points at the lettered positions along a line scan all produce the
form of signal amplitude versus distance distribution shown at A. The points at B and C
are just resolved on Leisegang's criterion, stated below the graph, whereas D and E are
not.
The spatial detection limit is thus the size of the smallest "point" that can be
observed. Point resolution depends on contrast and the signal-to-noise ratio.
The enlightening account of these points due to Everhart (1970) will be
followed here. Contrast on the C R O screens of SEMs is defined as in television
(Zworykin and M o r t o n , 1954) to be
(i.i)
where B' is the average brightness and B' is that of the point in question. This
will only be detectable if it exceeds some threshold value. F o r the h u m a n eye
this is 0.02-0.05, for example. F o r photographic recording it will depend on
the film and developer used, etc. Everhart adopted the arbitrary criterion for
point resolution, due to Leisegang, that two points are resolved when the
intensity at the minimum between them is 75% or less of the maximum
intensity (Fig. 1.6). Thus the minimum point resolution is the smallest
separation of object points of equal brightness, between which the screen
brightness falls by a quarter. This is affected by the signal-to-noise ratio
(Fig. 1.7). F o r high noise levels a fall of a quarter will not be reliably detectable
and the minimum separation of points that can just be resolved will be
increased.
Clearly the minimum value of the point resolution cannot be less than the
spatial detection limit. Figure 1.8 shows that, even if the point brightness peak
is of square wave form, for a point separation equal to the point size (spatial
detection limit) there is then zero contrast. Thus the spatial detection limit as
An introduction to multimode scanning electron microscopy
13
(a)
^^^^
^wWPw
B = 0.5 B ax
B --0
AB = O . I 5 B
AB-0.3B
m
m Q X
C,=0.l
C, --0.2
gain = G
gain = 2G
m o x
F i g . 1.7 Schematic diagram of a signal line scan trace (a) without back-off and (b)
with back-off and increased amplifier gain. Although in (b) B' is reduced producing an
increase in gain (eqn (1.1)) this is at the price of an increase in the (amplified) noise (after
Everhart, 1970).
AS
<-d ->
<
(a)
(b)
(c)
F i g . 1.8 (a) If the spatial detection limit is d and the point brightness peak is of square
waveform, the contrast minimum between adjacent bright points rises suddenly from
(b) zero for a point separation = d to (c) a finite value for point separations > d.
defined above gives a minimal value for the point resolution which will
increase for line scan peak shapes of greater half-width. Moreover resolution,
like contrast, on any definition is degraded by noise.
S E M spatial resolution is different for each mode since the volume of the
specimen from which the different types of signal are obtained varies (Fig. 1.5)
as do the sensitivities (detection limits and noise levels) of the different types of
14
D.B. Holt
detectors (transducers) available. Spatial resolution can also vary within a
mode from one form of contrast to another since the form of the point
brightness peaks will vary with the physical contrast mechanism. The spatial
resolution of S E M s tends to improve with the passage of the years, since the
technology has hardly begun to approach inherent physical limitations in
most cases.
In addition to the (horizontal) spatial resolution, a degree of (vertical) depth
resolution is obtainable in the bulk modes (X-ray, C C and CL) by varying the
beam voltage, V , to vary the penetration range of the electrons. A minimum
value is set by the sensitivity of the detector and the associated value of beam
power, V I , to produce a signal above noise level. As V is increased above this
threshold the effective depth from which the signal is obtained increases. The
upper limit is set by the maximum beam voltage of the S E M and the (average)
atomic number (stopping power) of the material under examination. Of course
the horizontal resolution becomes worse (larger) as the depth penetration is
increased. S E M bulk microcharacterization techniques for semiconductors
fortunately have depth resolutions that readily suffice for examining the entire
active device thickness in most cases.
h
b
b
b
The approximate values of the spatial resolution of the six modes of the
SEM in the late-1980s are as follows.
The emissive mode has available sensitive electron detectors so beam
currents down to 1 0
A suffice to give acceptable secondary electron
currents. Currently thermionic-electron-gun, high-vacuum instruments can
focus such a current into a spot of a diameter of a few nanometres (a few tens of
angstroms). The secondary electrons only escape from a small depth so the
beam has not spread much (Fig. 1.5). Some increase in the signal-producing
area also arises from high-energy backscattered electrons giving rise to
secondary electrons further away from the beam impact point. Current
manufacturers claims for secondary electron resolution range down to 3 or
even 1.5 nm. Certainly 5 n m is readily and routinely attainable on a heavily
used instrument by an operator of modest skill.
The bulk modes (X-ray, CL and CC) obtain their signals from the entire
energy dispersion volume (Fig. 1.5b). The detector sensitivities are such that
the X-ray and C L modes generally use tens of kilo volts accelerating potentials
and up to 1 mA of beam current. Consequently the penetration range and the
dissipation volume diameter are a micrometre or more. In the C C mode, EBIC
signals from Si devices are relatively large, so the resolution can be better.
However, most operators use 2 0 - 3 0 kV beams to probe the full depth of the
planar device volume, and so obtain similar resolutions.
STEM is only possible if the specimen is thin. Beam spreading is therefore
negligible. Dedicated (Crewe-type) S T E M microscopes which use field
emission guns in ultrahigh vacuum can focus the necessary 10 ~ A into about
- 1 1
1 1
An introduction to multimode scanning electron microscopy
15
0.5 nm (5 A) which is the resolution. Atomic resolution is just possible.
Electroacoustic mode resolution is set by the wavelength generated. This is
determined by the beam-chopping frequency. It is improving rapidly and is
currently of the order of 0.1 /mi.
1.2.2
S p a t i a l resolution a n d magnification
Magnification in the S E M is obtained by tapping off a variable fraction of the
scan voltage, driving the synchronously scanned C R O viewing and p h o t o graphic recording screens, to drive the scan coils in the bore of the objective
lens (Fig. 1.1). The raster scanned on the specimen surface is of variable side /,
therefore, while that on the C R O is of constant side L. The magnification is
simply given by
M = L/l
(1.2)
To give an objective criterion, the "standard eye" is capable of resolving
0.1 m m at the least distance of distinct vision of 25 cm. It is useful to magnify
the micrograph so the minimum distance between resolved points on the
specimen is enlarged to this figure. The useful magnification M is thus
u
M
u
= 0A/p
(1.3)
where p is the point resolution in millimetres. F o r photographic recording of a
high resolution screen the pixel size of the C R O screen should be substituted
for the visual value of 0.1 mm. Any larger magnification is "empty" and does
not reveal any additional reliable detail. A value a few times greater than M is
usually convenient for strain-free viewing.
u
1.2.3
S i g n a l (spectral) resolution a n d contrast
Signal resolution specifies the capacity of the system to resolve detail in signal
spectra recorded at a point (point analyses in the terminology of E P M A ) or in,
for example, curves of EBIC current or contrast versus temperature or reverse
bias voltage. It does not apply directly to micrographs. However, it limits the
ability of the system to produce observably different spatial contrast in
micrographs using different signal-producing mechanisms.
M o r e information can be obtained than was originally realized, by using
"modulation spectroscopy". T h a t is, by measuring signals such as EBIC
currents as functions of specimen or device operating variables such as reverse
bias and S E M operating parameters like beam voltage and hence penetration
depth. In the C L mode, for example, "depth-resolved" (beam voltage
16
D.B. Holt
dependent) and "time-resolved" (rate of intensity decay after beam chopping)
C L (spectroscopy) are well known. Each mode will have analogous energetic,
depth, etc. signal resolution.
Signal (spectral) resolution is the smallest difference in some physical
variable between signal peaks (or other features) that can just be distinguished.
That is, signal resolution is defined as in Fig. 1.6, except that the vertical
ordinate is not (screen) brightness but the intensity or strength of the signal
detected while the horizontal abcissa is not spatial distance but a physical
parameter such as wavelength. Signal resolution will vary in magnitude and
significance with the mode (type of signal), the resolution variable (abcissa), the
mechanism producing signal strength variation and specimen condition
parameters such as temperature. Signal resolution determines the sensitivity of
measurements of materials properties and device parameters in the SEM. The
fact that such properties and parameters can be measured with a high spatial
resolution as well, is what makes possible S E M microcharacterization, the
subject matter of this book.
The availability of two types of resolution is an important advantage of the
SEM. F o r example, using the C L mode, it is readily possible to resolve the
emission from epitaxial layers of semiconducting compounds and alloys
although the layer thickness is well below the spatial resolution of the
technique. Then, by scanning over the area of the layers, detecting a
wavelength characteristic of one material, inhomogeneities in composition or
doping may also be detected in the directions parallel to the layers.
The availability of six modes, each giving several forms of contrast and
signal resolution and the general simplicity of specimen preparation (compared, for example, with the thinning necessary for transmission electron
microscopy) are important advantages of the family of techniques that
scanning electron beam instruments represent.
1.3
Instrumentation
The overall performance of the instrument is determined by the physical
characteristics of the two subsystems of which it consists. A grasp of the
principles of operation of the electron optical column and the signal detection,
processing and read-out system is, therefore, needed both to understand the
limitations of the techniques and the advantages and disadvantages of
alternative instruments. The electron optics of the column imposes interrelated limits on the attainable values of beam current, beam voltage and probe
size. These will be discussed here, and the detection system limitations for each
mode will be dealt with in the chapters that follow.
An introduction to multimode scanning electron microscopy
17
Grid
1
h
T
Anode
F i g . 1.9 Diagram of a triode gun with a tungsten hairpin filament, d is the aperture in
the Wehnelt electrode or grid and h is the height of the filament above the Wehnelt.
(After Haine and Einstein, 1952.)
1.3.1
Electron beam diameter a n d current
The standard form of triode thermionic-emission, tungsten-hairpin electron
gun is shown in Fig. 1.9. The potential differences between the filament at a
negative "accelerating voltage" and the earthed anode with the Wehnelt (grid)
at an intermediate value, produces a lens-like focusing action as shown in
Fig. 1.10. The crossover is the smallest diameter beam in the gun. A
demagnified image of the crossover is projected onto the specimen surface to
act as the electron probe. The usual design of general purpose ("conventional")
SEMs has three lenses as shown in Fig. 1.11. The effective electron source is the
crossover of diameter d and the resultant probe is of diameter
0
d=
MMMd.
1
2
3
0
(1.4)
All the lenses are demagnifying so the M s are < 1. Thjs equation gives the socalled Gaussian spot size, obtained neglecting the aberrations and diffraction
effects, to be dealt with below.
All the lenses are operated to produce demagnification so, as shown in
Fig. 1.12, for the case of a two-lens design, many electrons from the gun d o not
get through the aperture at lens 1. M a n y of those that do, in turn do not get
through the aperture of lens 2. This is because the (semi)angular aperture of
lens 2 is smaller than the (semi)angle of convergence of the electron trajectories
from lens 1 to the intermediate image. As the current through lens 1 is
F i g . 1.10 Electron trajectories illustrating the lens-like action of a triode gun
producing a diffraction pattern, the crossover, in the back focal plane and an image of
the emitter surface in the conjugate plane. C is the cathode surface, G the grid (Wehnelt
cylinder), A the anode. Points at S, O and Q are imaged at T, P and R respectively.
(After Oatley, 1972.)
SOURCE
LENS 1
IMAGE 1
LENS 2
2
IMAGE 2
LENS
3
SPECIMEN
F i g . 1.11 Schematic electron ray diagram illustrating the focusing of a reduced real
image, of diameter d, of the gun crossover of diameter d on the specimen surface. (After
Booker, 1970.)
0
An introduction to multimode scanning electron microscopy
19
B Lt
t
Crossover
F i g . 1.12 Schematic diagram showing the formation, in a two-lens system of the
probe on the specimen surface S from the demagnified image of the crossover in the gun.
Many electrons following paths like b and c do not get through the spray aperture at B
of the first lens. Further electrons, e.g. h and k, do not get through the aperture B . (After
Oatley, 1972.)
x
2
increased to produce greater demagnification, the image moves nearer lens 1,
and the mismatch of these angles increases. Hence the fraction of the electrons
lost becomes greater. This happens again between lenses 2 a n d 3, in three-lens
designs. Thus as the first and second (condenser) lens currents increase, the
final beam current, J , bombarding the specimen decreases. Appropriately
named "spray apertures" are placed in the column to stop the lost electrons
striking the pole-pieces and causing contamination.
A final objective aperture, placed in the third, objective lens, is used to
control the beam convergence (semi)angle at the specimen, as shown in
Fig. 1.13. That is, the beam is focused on the specimen, and this requires a
convergence angle that depends on b o t h the aperture diameter and working
b
APERTURE
F i g . 1.13 The convergence (semi)angle of the focused beam at the specimen surface
is determined by the diameter D of the final aperture and the working distance L used.
(After Booker, 1970.)
D.B. Holt
r
SIZE -
d
20
BEAM
DIVERGENCE - *
- RADIANS
F i g . 1.14 Graphic presentation of relation (1.8) between probe spot size, d, and beam
convergence semi-angle a for a range of beam currents I for B = 4 x 10 A cm ~ sr~
(After Booker, 1970.)
4
2
h
distance in use. It can be seen that, by geometry,
a = D/2L
(1.5)
The relations between these parameters is shown in Fig. 1.14. The final beam
current reaching the specimen also depends on the size of the objective
aperture, i.e. I is proportional to a and so to D .
The aberrations of electron lenses are large compared with those of glass
lenses for light. The spherical aberration values are such that the beam
convergence angles must be kept down to 1 0 " - 1 0 " rad whereas they range
up to about 1 rad for light lenses. Fortunately, these small convergence angles
result in theoretical simplifications as we shall see. They are also responsible
for the much larger depths of field of the emissive mode than those obtained in
light microscopy.
Langmuir's law for the maximum density of current, that can be focused
into an electron probe from a thermionic cathode can be simplified, due to the
small value of the convergence angle (Oatley, 1972, pp. 14, 15) to:
2
2
h
2
J=JoqV * /kT
2
b
3
(1.6)
where j is the density of the current emitted from the surface of the thermionic
cathode, V is the (beam accelerating) potential difference between the emitter
and the image point, and T and k have their usual meanings.
0
21
An introduction to multimode scanning electron microscopy
The brightness of an electron beam is defined as the electron current per unit
area per unit solid angle. Hence:
B=j/oi
(1.7)
= (q/k)(j /T)V
2
0
b
The second term depends on the work function of the material of the source
(tungsten or l a n t h a n u m hexaboride). The emission current density, ; , then
depends on the filament temperature (heating current). This is set by the
standard filament saturation procedure which is designed to give the highest
emission current consistent with an acceptable filament operating life.
The brightness is constant for successive images in the microscope. Hence
the beam current can be found in terms of the brightness of the gun. By
definition, for the spot on the specimen surface
0
B = I /n(d/2) 7i(x
2
b
2
(1.8)
= QAI /d (x
2
2
b
Substituting typical values into eqn (1.7) it is found (Booker, 1970) that gun
(crossover) brightnesses tend to be a r o u n d 4 x 1 0 A cm ~ sr ~ . Equating this
value to the left-hand side of eqn (1.8) gives the relation between I , d and a
plotted in Fig. 1.14.
Thus the facts of electron optics mean that the beam current and power fall
as the spot size is reduced. The diameters of spot into which the smallest
currents can be concentrated vary with the type of source: thermionic emission
from tungsten filaments or lanthanum hexaboride crystals or field emission
from tungsten tips. It is not always recognized that for the larger currents,
needed for the X-ray and C L modes, there is no difference in the total output of
the three types of emitter. Consequently all give similar maximum currents
into large electron probes (greater than, say, 5 x 1 0 " A and 50nm). This
behaviour is illustrated in Fig. 1.15.
4
2
1
b
9
LaB
6
guns
These now generally consist of a pointed L a B tip attached to a tungsten
filament in such a way as to be interchangeable for a standard tungsten
emitter. The advantages are that, if the operating conditions and gun vacuum
are correct, the operating life is many months rather than tens or hundreds of
hours, and that the source brightness is higher than for a tungsten thermionic
filament. Hence the necessary beam current ( > 1 0 " A for the emissive mode)
can be got into smaller spots, giving better spatial resolutions.
6
1 1
Field-emission
guns
Such guns are used in dedicated S T E M instruments, of the type pioneered by
Crewe. Again, if the necessary clean ultrahigh-vacuum environment is
22
D.B. Holt
3
Electron probe diameter, (nm)
I0
Field emission
(Tetrode)
i
10"r»2
i i mil
1—i
i i MIII
i
•10
10
10 r l l
i i IIIIII
10"
•
• »
in
10"
Electron probe current, ( A )
F i g . 1.15 Relations between probe diameter and beam current for tungsten and
lanthanum hexaboride thermionic guns and a tetrode field emission gun. (After Cleaver
and Smith, 1973.)
provided, the operating life is many m o n t h s and the source brightness is still
higher, so the necessary current can be got into still smaller spots (Fig. 1.15).
This is the basis for the attainment of spatial resolutions down to 0.5 nm in
commercial "dedicated" (ultrahigh vacuum throughout) S T E M s . Differentially pumped field emission guns can also be fitted to high-vacuum SEMs and
Hitachi high-resolution S E M s are so equipped.
1.3.2
T h e m i n i m u m attainable spot size: the limitation d u e to
diffraction a n d aberrations
The Gaussian spot diameter, d, given by eqn (1.4) is the effective value for
diameters more than a few tens of nanometres. F o r smaller probes the circle of
confusion due to lens aberrations and the Airey's disc pattern due to the
diffraction effect of a circular aperture on the image of a bright point object,
become significant. Because all the lenses are demagnifying, the aberrations of
the final (objective) lens are the important ones.
The effect of spherical aberration is to produce, from a bright point object, a
disc of diameter
rf = C a
s
where C
s
s
3
(1.9)
is the spherical aberration coefficient. The effect of chromatic
An introduction to multimode scanning electron microscopy
23
aberration, due, for example, to the spread of velocities in the electrons emitted
thermally, is a disc of diameter
(1.10)
d = C (AV/V )a
c
c
h
where C is the chromatic aberration coefficient, AV is the spread of voltage
corresponding to the range of velocities in the beam of nominal accelerating
potential V . The diffraction effect is to produce a disc of diameter (to the first
dark ring) as Airey showed:
c
h
d =1.22A/a
(1.11)
d
where X is the wavelength of the electrons and decreases with increasing
voltage (as V ). (The effects of the astigmatism of the objective lens can be
made negligible by applying the usual astigmatism correction.)
It is customary to obtain the resultant effect by combining these diameters
"in quadrature", i.e. to write
1/2
(1.12)
d = d + d +d
2
2
2
2
c
This equation is a polynomial in a, the first term being to the sixth power, the
second squared and the third to the reciprocal second power. There will,
therefore, be an optimum value of a which gives the minimum resultant
diameter.
If the lenses are set to give a Gaussian spot (eqn (1.4)) of diameter d the
combined effect is similarly written:
v
dl«
t
(1.13)
= dl+d?
The effects of lens aberrations and diffraction can be neglected, therefore,
when the Gaussian diameter is more than, say, four or five times this resolution
figure. The resolutions quoted by S E M manufacturers for their products
should be experimentally demonstrable values of d .
This is a simplified account. F o r critical accounts of the limitations to the
model (assumptions) involved see Oatley (1972) or Booker (1970).
total
1.3.3
Beam voltage
The electron optical difficulties involved in producing good quality micrographs for both low (hundreds of volts) and high (many tens of kilovolts)
beams are severe. Consequently it is customary for manufacturers to offer
instruments providing low beam voltages to minimize surface oxide charging
(hundreds of volts up to say 30 kV) for the semiconductor and non-metallic
materials market, and higher voltage (up to say 50 kV) instruments. The latter
are used, for example, for metallurgical work in which the extra beam power is
D.B. Holt
24
needed for the excitation of the characteristic X-ray spectra of the heavier
elements of the periodic table for electron probe microanalysis. Electrical
damage is not a problem in metal specimens.
1.3.4
Detector system limiting factors
The essential parameters are (i) the sensitivity or detectivity and gain or
amplification of the detector (transducer) and (ii) the noise level of the complete
detection, processing and output system. The first determines the minimum
power of a signal from the specimen that can be detected above background
physical noise and the magnitude of the amplified video signal strength output
by the detector. The second determines this initial level of the video signal
strength necessary to be seen, in any form of read-out, above system noise.
Together they help determine the spatial resolution of the mode.
The characteristics of the detection systems for each mode are different.
Several modes have more than one type of detector available. Well-known
examples include the X-ray mode for which there are both energy dispersive
spectrometers (EDS) which are fast and used for semiquantitative work and
wavelength dispersive spectrometers (WDS) which are used for quantitative
analyses. F o r the C L mode there are grating m o n o c h r o m a t o r s for the visible
range and Fourier transform spectrometers for the infrared. Each type of
detector for any mode will have different characteristics, give a different
performance envelope and be better for some purposes, worse for others.
Better detectors are still appearing at intervals.
1.3.5
Computerization
The incorporation of microcomputers into microscopes and analytical
instruments is becoming universal. It is necessary in order to overcome the
disadvantage of the S E M that the picture is formed sequentially so the "image"
cannot be seen until the scan is completed. This can make focusing and
optimizing operating conditions not only tedious but also harmful or
destructive of the specimen. The use of frame stores with signal averaging
facilities or computer image processing systems means that images can be
stored, studied and processed at leisure, without further b o m b a r d m e n t of the
specimen.
In addition to thus transforming the convenience and power of S E M
techniques, with microcomputers simulation techniques can be used for the
interpretation of results as can semi-empirical iterative correction procedures.
The best-known example of the latter are the Z A F corrections of E P M A .
An introduction to multimode scanning electron microscopy
25
These developments are essential to enable full use to be made of the flood of
information available from the six modes of S E M and microcharacterization.
Computerization will be found to be a red thread running through this
book.
1.4
Types of electron beam instruments
Instrument design is continuing to advance and innovations still occur
frequently. Consequently there are now available a wide range of scanning
electron beam instruments. These will be outlined here to provide the
background for an appreciation of their advantages and disadvantages. They
will not be described in detail as they are constantly evolving.
1.4.1
General purpose S E M s
These are the descendants of the original commercial "Stereoscans" and have
conventional vacuum systems, thermionic emission guns and a column
containing two or three lens as indicated in Figs 1.1, 1.11 and 1.12. They are
provided with an emissive mode detection, amplification and video display
system. Several ports are available r o u n d the specimen chamber so detection
systems for additional modes can be attached and X-ray energy dispersive
spectrometer, microcomputer output systems are available through the S E M
manufacturers.
The basic S E M s themselves, at least the "top of the range" (expensive)
models, are increasingly microprocessor controlled and, at the time of writing,
at least one (the Stereoscan 360 from Cambridge Scientific Instruments) is
completely digital in operation. This will make the computer processing of the
output and computer feedback control of operation increasingly simple and
logical. We can therefore expect to see this trend accelerate in the next few
years.
1.4.2
MiniSEMs
The large S E M manufacturers all offer smaller instruments of the same kind, at
prices similar to those of good-quality light microscopes. These should not be
underestimated. They have resolutions, beam current and voltage ranges,
ports for mounting X-ray analytical systems, etc. as good as the best
instruments available not many years ago. In many university departments
such small microscopes take the bulk of the load, being preferred to the more
D.B. Holt
26
expensive instruments for their simplicity of operation for the standard
emissive and X-ray mode work of a qualitative and semiquantitative nature
(materials identification rather than quantitative analysis).
F o r the bulk modes, X-ray, C L and C C (EBIC etc.), the resolution is of the
order of a micrometre due to beam spreading in the specimen, so the better
resolution available at lower beam currents in the more expensive instruments
is of little interest. M u c h money can be invested in facilities that are little used.
1.4.3
Dedicated S T E M s
A completely different type of instrument was developed by Professor A.V.
Crewe (Crewe et ai, 1970; Crewe and Wall, 1970) and is now commercially
available as the HB-5 from Vacuum Generators. It is an ultrahigh-vacuum
instrument employing a field emission gun and gives a resolution of 5 A
(0.5 nm) in the S T E M mode. The micrographs and diffraction patterns
produced are closely analogous to those of T E M s . In addition, the clean
vacuum environment means that surface analytical instruments can be
incorporated. F o r example, the HB-50A (Vacuum Generators) produces a
spatial resolution of only 50 A (5 nm) but incorporates Auger spectroscopic
detection, so scanning Auger microscopy (SAM) as well as S T E M is available.
P. Petroff combined a S T E M instrument with an M B E (molecular beam
epitaxy) growth (specimen) chamber to make in situ studies of M B E growth of
multiquantum well ( M Q W ) materials possible (Petroff, Private communication). The incorporation of electron spectrometer detection systems is
customary. E E L S (electron energy loss spectrometry) is therefore possible.
1.4.4
Dedicated E P M A s
The first type of scanning electron beam instrument available was of this type,
designed for large beam currents up to 10 pA or more, and beam voltages up
to 50 kV or more to give the power desirable for X-ray microanalyses. They are
usually available with two or more wavelength dispersive X-ray spectrometers. D u e to the restricted demand for such instruments there is now a
limited range of models available. It should not be forgotten that they are ideal
for the bulk modes, so C L and some C C techniques are better used on such
instruments, if available. That is, if specimens are to be investigated that will
withstand such high-power b o m b a r d m e n t but give weak C L or EBIC, EBIV
or ^-conductivity signals, better results will be obtained on a microanalyser
than on an SEM. Needless to say, they also give far faster quantitative
microanalyses than SEMs.
An introduction to multimode scanning electron microscopy
1.4.5
27
C o m b i n e d transmission a n d s c a n n i n g instruments ( T E M S C A N S )
An impressive development of recent years is the incorporation of scanning
facilities into T E M s . Such instruments were termed T E M S C A N S by the
original manufacturer ( J E O L Ltd). They provide T E M , S E M emissive mode,
S E M energy-dispersive X-ray microanalytical facilities and S T E M facilities in
a single instrument, each with an impressive performance. Again the
installation of E E L S facilities is possible to give an additional analytical
technique.
Particularly valuable is the ability of these instruments to locate, for
example, small precipitates in T E M images, obtain their electron diffraction
patterns and, at least in favourable cases, to carry out E D S microanalyses of
the material.
1.4.6
E - b e a m testers
These instruments are the newest arrivals on the market and are, in effect,
stroboscopic voltage constrast instruments with the electron optical column
and specimen chamber as an "attachment". F o r integrated circuit studies they
have the advantage of purpose-built stages, multilead electrical feedthroughs,
etc.
1.4.7
E - b e a m lithography systems
Also relatively recent, these instruments are relatively rare owing to their high
cost (of the order of a megaquid, £ 1 million). They are designed for writing
lithographic patterns on resist-coated masks or wafers and so incorporate
elaborate computer-controlled scan drives and beam blanking facilities. It is
unlikely that they will be available for microscopic work, but can be used for
this purpose, e.g. to check the results of the lithography produced.
References
Balk, L.J. (1988). Adv. Electron. Electron Phys., 71, 1-73.
Battistella, F., Berger, S. and Makintosh, A. (1987). J. Electron. Microsc. Technique, 6,
377-384.
Booker, G.R. (1970). In Modern Diffraction and Imaging Techniques in Material
Science, eds Amelinckx, S., Gevers, R., Remaut, G., and van Landuyt, J., NorthHolland, Amsterdam, pp. 553-595.
Cleaver, J.R.A. and Smith, K.C.A. (1973). Scanning Electron Microsc, 49-56.
28
D.B. Holt
Crewe, A.V. and Wall, J. (1970). Optik, 30, 461-474.
Crewe, A.V, Wall, J. and Langmore, J. (1970). Science, JV.Y, 168, 1338-1340.
Everhart, T.E. (1968). Scanning Electron Microsc, I, 3-12.
Everhart, T.E. (1970). Proc. 3rd Ann. Stereoscan Colloquium, Kent Cambridge
Scientific, Morton Grove, 111, pp. 1-8.
Haine, M.E. and Einstein, P.A. (1952). Br. J. Appl. Phys., 3, 40-46.
Jervis, P. (1971/72). Res. Policy, 1, 174-207.
McMullan, D. (1985). J. Microscopy, 139, 129-138.
Maher, E.F. (1985). Scanning, 7, 61-65.
Oatley, C.W. (1972). The Scanning Electron Microscope Part I. The Instrument,
Cambridge University Press, Cambridge.
Oatley, C.W. (1982). J. Appl Phys., 53, R1-R13.
Sheppard, C.J.R. (1986). Endeavour, 10, 17-19.
Stewart, A.D.G. (1985). J. Microscopy, 139, 121-127.
Zworykin, V.K. and Morton, G.A. (1954). Television, Wiley, New York.
2 Modeling Electron Beam Interactions in
Semiconductors
D.E. NEWBURY
Center
for Analytical
Technology,
Chemistry,
Gaithersburg,
National
MD 20899,
Institute
of Standards
and
USA
List of symbols
2.1 Introduction
2.2 Electron scattering
2.2.1 Scattering processes
2.2.2 Cross sections
2.2.3 Elastic scattering
2.2.4 Inelastic scattering
2.3 Monte Carlo electron trajectory simulation
2.3.1 General principles
2.3.2 Formulation
2.3.3 Practical aspects of Monte Carlo calculations
2.3.4 Applications to semiconductors
2.4 Summary
References
Appendix
29
31
31
31
33
34
38
45
45
46
48
52
61
62
63
List of s y m b o l s
a
A
b
c
E
AE
E
£
£
0
s
s
c
e h
F S E
Bohr radius for an a t o m
atomic weight
constant for shell s in X-ray cross-section
constant for shell s in X-ray cross-section
electron energy
energy loss
critical ionization energy
energy to create one electron-hole pair
energy of fast secondary electrons
SEM Microcharacterization of Semiconductors
ISBN 0-12-353855-6
Copyright © 1989 Academic Press Limited
All rights of reproduction in any form reserved
30
D.E. Newbury
^SE
h
I
1(E)
J
k
L
m*
m
0
"t
N
N
N
N
A
at
eh
Q
R
s
t
u
v
n
?d
z
Z
»
8
incident electron energy
plasmon energy
secondary electron energy
Planck's constant
Intensity of incident beam
Intensity of transmitted electrons with energy E
mean ionization potential
wave vector k = 1/A
minority carrier diffusion length
effective electron mass
electron rest mass
number of conduction band electrons per a t o m
number of free electrons
number of incident particles
number of atoms per unit volume
number of target sites
number of events per unit volume
Avagadro's number
Projected number of atoms per unit area
number of electron-hole pairs
cross-section
nth r a n d o m number
step length
thickness
over-voltage ratio
velocity
depletion depth
depth coordinate
atomic number
scattering angle for fast secondary electron
complex dielectric constant
real component of complex dielectric constant
imaginary component of complex dielectric constant
ratio of
E /E
plasmon scattering angle
azimuthal scattering angle
mean free path
electron wavelength
solid angle
scattering angle
characteristic inelastic scattering angle at energy E
differential inelastic scattering cross-section
FSE
</>
*p
P
x
A
n
e
e
E
G
Modeling electron beam interactions in semiconductors
p
S
rj
co
co
pl
2.1
31
density
screening parameter
backscattering coefficient
fluorescent yield
plasmon oscillation frequency
Introduction
Scanning electron microscopy is rapidly maturing from a qualitative "looksee" imaging technique to a level of understanding in which quantitative
information can be derived from images and associated measurements
performed in situ on semiconductor materials and working semiconductor
devices. A major source of this maturation is a developing understanding of
the interaction of the primary electron beam with the solid and of the
secondary radiation products which result from that interaction. This
understanding has now reached a level of sophistication such that it is possible
to develop models for the interactions which can predict the images which are
observed with the SEM. These models can thus serve to aid in the
interpretation of images to yield a better understanding of the structures
which produce those images, which is the ultimate goal of the microscopist.
This chapter will provide a survey of the electron beam-specimen
interactions of particular interest to the microscopist who is studying
semiconductor materials. A catalog will be given of the elastic and inelastic
scattering processes with equations describing the appropriate cross sections.
F r o m this physical basis, the M o n t e Carlo electron trajectory simulation
technique will be developed. Selected applications will illustrate the use of
M o n t e Carlo calculations for characterization of semiconductors through
improved understanding of S E M imaging processes by modeling electron
beam-specimen interactions in order to interpret image characteristics.
2.2
Electron scattering
2.2.1
Scattering processes
The S E M is designed to provide the microscopist with a high degree of control
of a wide range of properties of the primary beam: beam energy, typically over
a range of 0.5-30 keV or more; beam current from picoamperes to microamperes; beam divergence from 5 to 100 mrad; and beam diameter from 1 to
1000 nm (Goldstein et a/., 1981; Newbury et a\., 1986). The reason for choosing
32
D.E. Newbury
a particular set of beam conditions from the available ranges of these
properties is usually determined by the characteristics of the image contrast
mechanism or other type of information which we are seeking from the
specimen, and this information in turn is determined by the characteristics of
the electron beam-specimen interaction with the specimen. The electron beam
entering the specimen can be considered to consist of nearly monoenergetic
particles with a kinetic energy spread of only 0.5-3 eV, depending on the type
of electron source which is utilized, and traveling along nearly parallel
trajectories. The interaction of the beam with the specimen results in five major
effects: (1) The trajectories of the beam electrons rapidly deviate from the
incident trajectory due to the effects of elastic scattering. (2) This angular
deviation can alter the trajectories so greatly that as a result of single or
cumulative events, a significant fraction of the beam electrons actually reemerge from the specimen, forming the class of interaction product called
backscattered electrons. (3) The diameter of the incident beam, which may be
initially as small as nanometers, is degraded by scattering to an effective value
of micrometers laterally. The degree of the broadening depends on the incident
beam energy. (4) The energy of the beam electron is rapidly diminished with
passage through the solid at a rate of the order of l - 1 0 e V / n m or more as a
result of inelastic scattering processes, setting an eventual limit on the range of
the electrons in the target; this range has a value of the order of micrometers
and is again dependent on the incident energy. (5) As a result of inelastic
scattering, energy is transferred to the electrons and atom cores of the solid
with the subsequent emission of some or all of a wide range of secondary
radiation products, depending on the composition of the target: low and high
energy secondary electrons, characteristic and bremsstrahlung X-rays, long
wavelength photons in the ultraviolet, visible and infrared wavelengths,
phonons and plasmons.
The key to understanding these effects lies in an understanding of the variety
of scattering processes which can take place. A scattering process is an
interaction of the beam electron with the atoms of the target which results in a
change of trajectory direction and/or energy of the incident particle. Two
broad classes of scattering are recognized. Elastic scattering alters the
trajectory of the beam electron, generally by an average value of about 5°, but
ranging from 0 to 180° deviation in a single event, while the energy of the beam
electron is essentially unchanged by the event, varying by only a few
electron volts. Inelastic scattering decreases the energy of the beam electron by
an a m o u n t ranging from 1 eV up to many kiloelectronvolts, depending on the
particular inelastic scattering process which takes place, while the trajectory of
the electron is deviated only slightly, generally by an angular value in the range
of tens of milliradians.
Modeling electron beam interactions in semiconductors
2.2.2
33
Cross sections
The mathematical description of a scattering process is k n o w n as a scattering
cross section, which is a measure of the probability that a process will occur. In
order to employ cross sections in useful calculations, it is important to note the
dimensions of a cross section expression. When a reference to a cross section is
encountered, the dimensions of the cross section are often given as area, e.g.
c m , and this area is usually thought of as the effective "size" presented by the
target atom to the incident particle. It should be recognized that this area is
actually a reduced dimension, and that the proper definition of a cross section,
<2, includes some "dimensionless terms" and its complete description is:
2
(2.1)
Q = N/n n
{
t
where N is the number of events of a certain type, e.g. elastic scattering events,
which occur per unit volume of the target (events/cm ) n is the number of
incident particles, e.g. electrons in the cases in which we are interested in this
chapter, per unit area (electrons/cm ) and n is the number of target sites, e.g.
atoms, per unit volume (atoms/cm ). The complete dimensions of a cross
section are thus:
3
x
2
t
3
(events/cm )/[(electrons/cm )(atoms/cm )]
3
2
3
which reduces to
events/[e ~ / ( a t o m / c m ) ]
2
The complete definition of the dimensions of the cross section forms the
basis for the derivation of two other useful parameters which describe the
beam interaction: (1) the mean free path and (2) the probability of scattering.
The mean free path, A , is the average distance which an electron must travel
through the specimen to experience one event of a specified type and has
dimensions of (cm/event). The cross section can be converted into a mean free
path by means of the following dimensional argument:
g ( e v e n t s / c m ) / [ ( e l e c t r o n s / c m ) ( a t o m s / c m ) ] x iV (atoms/mol)
3
2
3
A
x l / ^ ( m o l / g ) x p ( g / c m ) = \ jk(events/cm)
3
(2.2)
or
X = A/QN
A
p (cm/event)
(2.3)
where N is Avogadro's number, A is the atomic weight, and p is the density.
When a variety of different scattering processes can occur, it is possible to
define a series of cross sections Q for the various processes, and to calculate a
corresponding series of mean free paths, X . F r o m these individual values, a
A
t
t
34
D.E. Newbury
total mean free path, A , can be calculated by the equation:
T
1At=I1M,
i
(2.4)
The probability of scattering, P (events/electron), gives the number of
scattering events per electron as it travels through a specimen of thickness t.
For small numbers of events, the number will be proportional to the thickness
divided by the mean free path, t/X, or:
p = QN pt/A
k
(events/electron)
(2.5)
Cross sections generally depend on a number of parameters, including
properties of the beam electrons such as energy and the angle of scattering, properties of the secondary products such as energy and angle of emission,
and properties of the specimen, such as atomic number and binding energy.
Cross sections can be described which include all possible parameters and
their complete ranges (total cross sections) or a differential or partial cross
section can be used which is resolved in one or more parameters, such as the
scattering angle. In constructing simulations such as the M o n t e Carlo
technique, both total and partial cross sections are employed.
2.2.3
Elastic scattering
Elastic scattering results from the deflection of the beam electron by the
positive charge of the nucleus of the atom, as screened or reduced in value by
the orbital electrons. The Rutherford differential cross section for elastic
scattering as a function of the scattering angle 9 for a constant value of the
electron energy E is given by:
(2.6)
where d Q = In sin 9 d9 is the element of solid angle Q into which the electron
of energy E is scattered at an angle 9 from its incident direction, e is the electron
charge, Z is the atomic number of the scattering atom, £ is the dielectric
constant, and 9^/4 is the screening parameter S and is numerically equal to
0
S = 9 /4 = 3.4 x 1 0 " Z
2
3
0
0 6 7
/£
(E in keV)
(2.7)
A full derivation of eqn (2.6) from first principles has been given by Henoc and
Maurice (1976).
Equation (2.6) can be integrated over all possible scattering angles from 0 to
Modeling electron beam interactions in semiconductors
35
180° to give a total elastic scattering cross section:
(2.8)
U p to energies of approximately 50keV, relativistic effects of the electron
velocity can be safely ignored, representing a correction of approximately 1%
to the cross section at 50keV. Above this energy, a relativistic correction
should be applied. Equation (2.6) can be corrected for relativistic effects by the
following procedure: Equation (2.6) is altered by means of first substituting the
Bohr radius, a , where
0
a = ^ _
nm e
= 5.29 x 1 0 " c m
(2.9)
9
0
0
where h is Planck's constant, m is the electron rest mass. The electron
wavelength A is also substituted in eqn (2.6), where A = h/(2mE) .
The
transformed equation is thus:
0
1/2
(2.10)
The relativistic correction is then m a d e by substituting the relativistically
corrected wavelength A into eqn (2.10) where
R
A = h/[2m E(\
R
0
+ £/2m c )]
2
1 / 2
0
A = 3.87 x 1 0 " / [ £
9
R
1 / 2
( 1 +9.79 x 1 0 ' £ )
4
1 / 2
] (cm)
(2.11)
The probability for elastic scattering from 0 to a given angle can be found by
integrating the cross section differential in scattering angle as normalized by
the total elastic scattering cross section:
P(6) =
VQ{d)IQ]
dQ=
[\lK
sin
6Q(9)/Qld9
P(0) = (l + S) {1 - [25/(1 - cos 6 + 26)-]}
(2.12)
The Rutherford elastic scattering cross section has been found to be
reasonably accurate for intermediate beam energies, e.g. 2 0 - 5 0 keV, and for
targets of low to intermediate atomic number, e.g. Cu. It has been demonstrated that the exact q u a n t u m mechanical formulation of the elastic
scattering cross section should be employed at low beam energies and for high
atomic number targets (Reimer and Krefting, 1976). Unfortunately, the exact
elastic cross section (see M o t t and Massey, 1965) cannot be expressed in a
simple analytic form such as eqn (2.8) for the Rutherford cross section. Reimer
and Krefting (1976) have provided graphical comparisons of the Rutherford
—•
ML/ML
0
3d*
60*
90*
—
6(f
12(f
15d*
tf0>
Streuwinkei
&
1
120°
150°
160°
Tietz
90°
37
ML/ ML
Modeling electron beam interactions in semiconductors
F i g . 2.1 Comparison of the exact Mott cross section for elastic scattering with the
Rutherford cross section as a function of the scattering angle 6 for: (a) aluminum; (b)
germanium; and (c) gold. (From Reimer and Krefting, 1976.)
and M o t t cross sections, and Fig. 2.1, which shows the comparison for G e and
Au, is taken from their work.
Elastic scattering plays a critical role in scanning electron microscopy. The
cumulative effect of elastic scattering leads to the phenomenon of backscattering, in which the beam electrons undergo sufficient deviation from their initial
trajectory to re-emerge through the entrance surface. The strong dependence
of the cross section on the atomic number of the scattering atom, entering as a
squared term in eqn (2.8), manifests itself in the contrast mechanism k n o w n as
"atomic n u m b e r " contrast (also referred to as "compositional contrast" or " Z
contrast") in the backscattered electron signal. The electron backscattering
coefficient, Y\, is defined as the fraction of the beam electrons which re-emerge
through the original entrance surface as a result of single or multiple elastic
scattering events. A plot of the backscattering coefficient as a function of
38
D.E. Newbury
Bockscotter Coefficient
0.6
0
20
40
60
80
100
)
Atomic number
F i g . 2.2 Dependence of the backscattered electron coefficient on the atomic number
of the target, E = 20keV. Monte Carlo calculations (Newbury and Myklebust, 1984)
compared with the experimental data of Heinrich (1981).
atomic number is shown in Fig. 2.2 a n d reveals a relatively smooth monotonic
behavior, which of course forms the basis for an easily interpreted contrast
mechanism. The increase in backscattering with atomic number is very much
less than the squared atomic number term in the elastic scattering cross section
would suggest, reflecting the influence of other factors, such as multiple
scattering and energy loss due to inelastic scattering, on the overall interaction
process.
2.2.4
Inelastic scattering
Inelastic scattering occurs through a variety of interactions of the beam
electron with the electrons a n d atoms of the sample. The type of interaction
and the a m o u n t of energy loss depend on whether the specimen electrons are
39
Modeling electron beam interactions in semiconductors
excited singly or collectively and on the binding energy of the electron to the
atom. The excitation of the specimen electrons leads to the generation of
secondary products which can be used to image or analyse the sample.
Separate cross sections can be described for the processes of low energy
("slow") and high energy ("fast") secondary electrons, inner shell ionization,
which leads to the emission of X-rays and Auger electrons, bremsstrahlung Xrays, plasmon scattering and thermal diffuse scattering (phonons).
Single electron
excitations
Low-energy secondary electrons.
Secondary electrons are generated by
the beam electron interacting with the loosely b o u n d conduction-band
electrons of the solid. The energy transferred to the conduction-band electron
is relatively small and in the range of l - 5 0 e V . Because of the low energy of the
secondary electrons, their range in the solid is only of the order of 5 nm.
Although secondary electrons are generated along the entire trajectory of the
beam electron within the target, only those secondaries generated when the
beam electron is near the surface of the solid have a significant probability of
escape.
The differential cross section with respect to secondary electron energy is
given by (Streitwolf, 1959):
QSE^SE) = n e*k A/[3nEpN (E
c
F
A
- £ ) ]
(2.13)
2
F
SE
where the cross section is expressed in terms of secondary electrons per unit
energy interval per incident electron per (atom/cm ). In eqn (2.13) n is the
n u m b e r of conduction-band electrons per atom, A is the atomic weight, k is
the magnitude of the wave vector (fc = 1/A ), which corresponds to the Fermi
energy £ , £ is the secondary electron energy, and E is the beam energy, with
all energies in kiloelectronvolts. A total cross section can be obtained by
integrating eqn (2.13) over the practical range of secondary electron energies.
Since the cross section in eqn (2.13) is undefined at E = E the lower limit of
integration can be arbitrarily set at £ = E + 1 eV. The upper limit of
integration is also set arbitrarily at a value of 50 eV, which defines an energy
range which covers the practical extent of secondary electron energies:
2
c
F
F
F
F
S E
SE
S E
Q
SE
- 0.050 keV) + 1/(0.001 keV)]/(37r£pJV )
= e*k An [l/(E
F
c
F
F
A
F
(2.14)
Fast secondary electrons.
Although the most numerous secondary electrons
are those of low energy, E < 50 eV, it is possible for the beam electron to
interact with more tightly b o u n d electrons and transfer larger a m o u n t s of
energy, creating so-called "fast secondary electrons". Fast secondary electrons
SE
40
D.E. Newbury
are of interest because their range is greater than that of low-energy
secondaries and their angle of emission is nearly at right-angles to the beam
electron trajectory. M u r a t a et al (1981) have demonstrated that fast secondary electrons play a significant role in the degradation of lateral spatial
resolution in the exposure of electron beam resists.
Fast secondary electrons can be generated with energies up to that of the
incident electron. Since the primary and secondary electrons cannot be
distinguished after the collision, the cross sections for the two electrons are
added, and the maximum possible energy loss is restricted to AE < 0.5E. The
cross section differential in secondary electron energy has been given by
Moller(1931)as:
Q(E )
+ 1/(1 - £ ) ] / £
= ne Zl(\/s)
4
FSE
2
2
(2.15)
2
where £ is the energy transferred to the fast secondary electron normalized by
the beam electron energy, £ = E /E, and Z, is the number of atomic electrons.
This equation can be integrated over the range of fast secondary electron
energies, with the lower limit of integration set at E
= 0.050 keV and the
upper limit set at £
= 0.5£. The result is given by:
FSE
FSE
F S E
6
FSE
= ne^id/s^)
- [1/(1 - e
m i n
)]}/£
(2.16)
2
The scattering angle 6 of the primary electron after the collision relative to its
incident direction is given by:
s i n 0 = 26/(2 + E' - E'e)
(2.17)
2
where E' = E/5W keV. The scattering angle /? of the fast secondary electron
relative to the incident primary is given by:
s i n j ? = 2(l - e ) / ( 2 + £'£)
(2.18)
2
F o r a beam electron energy of 20 keV and a fast secondary electron energy of
1 keV, the fast secondary electron is scattered at an angle of 77° from the
incident beam electron trajectory.
Inner-shell ionization.
Inner-shell ionization occurs when the beam electron
transfers sufficient energy to a tightly b o u n d inner-shell electron to eject it
from the atom. The atom is left in an excited state and subsequently undergoes
de-excitation by means of electron transitions from outer shells. The energy
released during these transitions can manifest itself as either a characteristic Xray or an Auger electron. The fraction of ionizations which leads to X-ray
emission is given by the fluorescence yield, co. The fraction of Auger electrons
produced is given by 1 — co. The total cross section for inner-shell ionization is
given by the formula (Bethe, 1930):
ft = ne n b
s
log [ c ( m i ; / 2 ) / £ ] / [ ( m i ; / 2 ) £ ]
2
4
s
s
0
2
c
0
c
(2.19)
Modeling electron beam interactions in semiconductors
41
where n is the n u m b e r of electrons in the shell, b and c are constants
appropriate to the shell, E is the critical excitation energy, m is the rest mass
of the electron and v is the velocity. At the low beam energies appropriate to
most scanning electron microscopy and X-ray microanalysis, the mass of the
moving electron is very nearly that of the rest mass, so that the term (m v /2)
can be set equal with little error to the kinetic energy of the electron, which is
the energy imparted to the electron as a result of its acceleration through the
potential d r o p V (kinetic energy = eV where e is the electronic charge):
s
s
s
0
c
2
0
9
Low V(< 50kV){m v /2)
(2.20)
= eV= E
2
o
With this substitution, eqn (2.19) thus becomes:
Q = ne\b
{
s
log (c E/E )/(E E)
s
c
(2.21)
c
where E is the beam energy. Equation (2.21) is often expressed in terms of the
overvoltage, U = E/E , and also expressing the constant ne* for E in keV:
c
Q, = 6.51 x 10- »Alog(c s C/)/(l/£ c )
20
2
(2.22)
where the dimensions are ionizations/(e~ a t o m / c m ) .
The constants b and c depend on the shell which is excited and have been
assigned a range of values by different authors. Thus, for K-shell ionization,
M o t t and Massey (1965) gave £> = 0.35 and c = 2.42. In an extensive
examination of available experimental data, Powell (1976) deduced that for
the overvoltage range 4 < U < 25 the constants have the values b = 0.9 and
c = 0.65.
N o t e that the Powell constants should not be applied at low overvoltages,
since with the choice of c = 0.65, the cross section becomes negative due to
the log term below U = 1.55. Moreover, the data upon which these constants
were based were derived only from low atomic number elements and
from overvoltages below 5. In the analysis of solid specimens, we are frequently
interested in inner-shell ionization from the incident beam energy down to
E = £ , since a significant fraction of the electrons lose all their energy in the
solid. F o r calculations in solid specimens, the constants given by Brown (1974)
are useful:
2
s
s
K
K
K
K
K
c
K-shell
L-shell
c = 1
K
c
L 2 3
= 1
b = 0.52 + 0.0029 Z
(2.23)
= 0.44 + 0.0020 Z
(2.24)
K
b
L23
where Z is the atomic number. With c = c
positive down to (7=1.
K
Multiple
electron
L 2 3
~ 1, the cross section remains
excitations
Bremsstrahlung.
As the beam electron passes through the coulomb field of
the atom, it can undergo deceleration which decreases the magnitude of the
42
D.E. Newbury
velocity and, hence, the kinetic energy. The energy lost by the beam electron is
emitted as a p h o t o n of electromagnetic radiation. This radiation is known as
"bremsstrahlung" or "braking radiation" and since any deceleration is
possible from no loss up to total loss of the kinetic energy of the electron, the
bremsstrahlung forms a continuous spectrum from zero energy to the incident
beam energy. The intensity of bremsstrahlung emission depends on the angle
relative to the beam electron trajectory.
Kirkpatrick and Wiedmann (1945) described algebraic equations which
provided a fit to the Sommerfeld (1931) theory for bremsstrahlung production.
These equations give the components of the cross section for bremsstrahlung
production of energy E along axes x, y, z oriented such that x lies along the
beam electron trajectory and y and z lie in a plane orthogonal to x. Following
Statham (1976), the units of these cross sections are given in terms of (keV
p h o t o n energy/keV energy interval/steradian/(atom/cm ):
b
2
Q = 4.5 x 1 0 - Z { 0 . 2 5 2 + « [ ( £ / £ ) - 0 . 1 3 5 ]
25
2
b
x
b
-fe [(£ /£)-0.135] }/£
(2.25)
2
b
b
a = 1.47 B - 0.507 A - 0.833
h
b
b = 1.70 B
h
b
h
- 1.09 A
h
- 0.627
A = exp ( - 0.223 £/0.2998 Z ) - exp ( - 57 E/0.2998 Z )
2
2
h
B = exp ( - 0.0828 E/0.2998 Z ) - exp ( - 84.9 £/0.2998 Z )
2
2
b
4.5 x \0- Z l-j
25
Q y
=
Q
z
=
+ {k /[(E /E)
2
b
b
+ h -]}/El
b
b
(2.26)
h = ( - 0.214yl + 1.21 y2 - y3)/(1.43yl - 2 . 4 3 y l + y3)
b
j =
b
k =
h
(l+2h )y2-2(l+h )y3
b
b
(l+h )(y3+j )
b
b
yl = 0 . 2 2 0 [ 1 - 0 . 3 9 0 exp ( - 2 6 . 9 £ / 0 . 2 9 9 8 Z ) ]
2
y2 = 0.067 4- 0.023/[(£/0.2998 Z ) + 0.75]
2
y3 = - 0.00259 + 0.00776/[(£/0.2998 Z ) + 0.116]
2
These components resolved along the three axes of the coordinate system can
be combined to give the cross section at a particular angle \jj in the x-z plane
which contains the beam direction:
Q = Q s i n iA + Q + Q c o s (A
2
b
2
x
y
z
(2.27)
The total cross section is found by integrating over 4n steradians:
Q = Sn(Q + Q + Q )/3
B
Plasmon scattering.
x
y
z
(2.28)
The coulomb field of the beam electron can perturb the
Modeling electron beam interactions in semiconductors
43
free electron gas of conduction-band electrons of a metal at long range. The
beam electron excites oscillations or "plasmons" in this free electron gas. The
cross section differential in scattering angle per conduction band electron per
unit volume is given by (Ferrel, 1956):
Q((j>) = <j>J[2na {<t> + 0 ) ] = 3 x 10 c6 /((/> + </> )
2
2
7
2
2
p
0
P
(2-29)
where a is the Bohr radius and c/> = A £ / 2 £ , where A £ is the energy
transferred to the plasmon wave. Plasmon scattering results typically in an
energy transfer A £ in the range 3-30 eV, depending on the atomic number.
F o r an aluminum target, A £ = 15 eV, hence for a beam energy of 10 keV, the
plasmon scattering angle 0 = 1.5 x 1 0 " r a d . Plasmon scattering is peaked
so sharply forward that the total plasmon scattering cross section can be found
by setting d Q = 2n sin (j> dcf) = 2n(j) dc/>:
p
0
p
p
p
p
3
P
<2 =
P
Q((t>)dQ =
((t) /2na )
p
0
o
Taking the upper integration limit as
= 0 . 1 7 5 rad, where (/> = sin</> and
incorporating the factor (n A/pN )
to put the cross section on the basis
(atom/cm ) gives the total cross section as:
c
A
2
6 = M</>pPog (</> + 0.175 ) - log (<j> )y2N p a
2
P
Comparison
of cross
2
2
p
p
A
A
0
(2.31)
sections
Figure 2.3 contains plots of the elastic, plasmon, slow secondary electron
( < 50 eV), fast secondary electron ( > 50 eV), L-shell ionization, a n d K-shell
ionization cross sections for silicon (Fig. 2.3a) and germanium (Fig. 2.3b) over
the energy range 1-50 keV. F o r these elements, the largest cross section is that
for plasmon scattering, followed by the cross section for slow secondary
electron formation. F o r elements of high atomic number, such as gold, the
elastic cross section increases relative to the inelastic cross sections, so that
elastic scattering dominates.
Continuous
energy loss
approximation
The energy loss rate due to all of the inelastic scattering processes can be
estimated from the continuous energy loss approximation of Bethe (1933). The
energy loss d £ per unit of distance ds traveled in the solid is given by:
d£/ds =
(-2ne*N Zp/AEJlog(U66EJJ)
A
= - 7 . 8 5 x 10 (Zp/yl£ )log(1.166£ /J)
4
m
m
(keV/cm)
(2.32)
44
2
Cross section [ events/e/(atom/cm )]
D.E. Newbury
20
30
Energy ( k e V )
-214
0
10
(a)
20
30
Energy (keV)
40
50
F i g . 2.3 Elastic and inelastic scattering cross sections for (a) silicon and (b)
germanium over the range l-50keV. • Slow SE; • Fast SE; • Plasmon; O K-Shell;
• L-Shell; + Elastic.
where E is the mean energy across the distance interval ds. J is the mean
ionization potential, which is the average energy loss per interaction
considering all possible energy loss processes. J has been given as (Berger and
Seltzer, 1964):
m
J = (9.76Z + 5 8 . 5 Z "
0 1 9
) x 1(T
3
(keV)
(2.33)
A plot of the Bethe expression as a function of energy is shown in Fig. 2.4 for
silicon and germanium, where the dependence of the energy loss rate upon the
energy can be readily seen.
Modeling electron beam interactions in semiconductors
45
40
• SidE/dseV/nm
• GedE/ds
O
dE/ds( Bethe) eV/nm
30
10
0
10
20
30
40
50
Energy (keV)
F i g . 2.4 Bethe energy loss per unit distance as a function of electron energy for
silicon and germanium.
2.3
2.3.1
Monte Carlo electron trajectory simulation
General principles
The development of purely analytic models for electron beam-specimen
interactions becomes difficult when conditions of multiple scattering are
encountered. When the specimen dimensions exceed several mean free paths,
or when several competing scattering processes are possible, a mathematical
solution in closed form may not be possible. The complex dependence of the
cross sections for the various elastic and inelastic scattering processes on
electron energy and the complex dependence of the rate of energy loss on
electron energy (d£/ds ~ ( l / £ ) l o g E) lead to functional expressions which are
difficult to solve analytically. Moreover, even when such expressions can be
derived, their application to the configurations of real samples encountered in
46
D.E. Newbury
scanning electron microscopy may be severely limited due to the need to
incorporate specific boundary conditions of size, shape, and differing compositions across interfaces. F o r such applications, a more flexible approach to
modeling electron scattering is needed. Such an approach is obtained by
means of M o n t e Carlo electron trajectory simulation. The extensive development of M o n t e Carlo calculations has provided a major tool of great utility in
the field of scanning electron microscopy and X-ray microanalysis analogous
to the use of mathematical formulations of diffraction theory for the
interpretation of images in the transmission electron microscopy of crystalline
materials. F o r example, M o n t e Carlo calculations have been applied to the
study of magnetic contrast (Newbury et al, 1973), X-ray emissions from
particles (Yakowitz et al, 1975), X-ray emissions from thin films (Kyser and
M u r a t a , 1974), and the resolution of signals in high-resolution images
(Hembree et al, 1981).
2.3.2
Formulation
The technique of M o n t e Carlo electron trajectory simulation provides a "first
principles" approach for the calculation of electron beam-specimen interactions which gives detailed information on the spatial distribution of scattering
events. In the M o n t e Carlo technique, the beam electron is considered as a
discrete particle which undergoes elastic and inelastic scattering with the
atoms of the sample, which is considered a m o r p h o u s . The trajectory is
calculated in discrete steps, an example of which is shown in Fig. 2.5, and at
F i g . 2.5 Schematic diagram of fundamental repetitive calculation step in a Monte
Carlo electron trajectory simulation.
Modeling electron beam interactions in semiconductors
47
every step in the simulation, the characteristics of the electron are known:
position (x, y, z), energy and m o m e n t u m . The electron undergoes a scattering
interaction at location P which causes it to deviate by an angle 9 from its
previous path. It travels a distance S along the new path, where S is the step
length of the calculation, until it undergoes another scattering event at point
P .
The selection of the scattering angles and step lengths is made from the
elastic scattering cross sections given above. F o r the energy range of interest,
l - 5 0 k e V , significant angular deviations result mainly from elastic scattering
events. It is c o m m o n practice in M o n t e Carlo simulations to consider only
elastic scattering when calculating the scattering angle, 9. Since the elastic
scattering can take on any value from 0 to 180° for a particular scattering
event, with an average value for the energy range of interest of the order of 5°,
the scattering angle must be chosen from the possible range in a statistically
meaningful manner. The scattering angle distribution is found from eqn (2.12)
re-expressed in terms of a r a n d o m number:
N
N+l
cos 9 = 1 - [25/11/(1 + S - Rl)-]
(2.34)
where Rl is a r a n d o m number such that 0 ^ Rl ^ 1. Substitution in eqn (2.34)
of r a n d o m numbers linearly distributed across this range produces a
distribution of scattering angles. (The use of randomly selected numbers at
several points in the calculation sequence of the simulation gives the basis of
the name " M o n t e Carlo".) The azimuthal angle \jt in the base of the scattering
cone shown in Fig. 2.5 can take on any value in the range 0-360° selected by a
different r a n d o m number:
(2.35)
ijj = 2nRl
Since only elastic scattering events are presumed to contribute to significant
angular deviations, the step length between scattering events is determined
from the mean free parh for elastic scattering, which is found from eqn (2.3)
with the total elastic scattering cross section from eqn (2.8). Because the mean
free path is the value of the average distance between scattering events, a
distribution is obtained by means of the equation:
(2.36)
S= -k\ogR3
where X is the elastic mean free path. F r o m the scattering angles 9 and i//, and
the step length S, the x, y, z coordinates of point P
can be calculated from
the coordinates of point P :
N
+ 1
N
x =x -\-SA cos9-^-ScosA
N+1
N
e
sin 9 cos \// + SB cos V sin 9 sim//
(2.37a)
*jv + i = YN + SB cos 9 + S sin \jj(C cos A — A cos F)
(2.37b)
= z + SC cos 9 + S cos r cos ijt + S sin
(2.37c)
C
z
N
+ 1
N
e
- B cos A)
D.E. Newbury
48
where A , B , C are the direction cosines of the trajectory segment preceding
the scattering event being calculated, A = arctan (-AJC )
and T = a r c t a n
(-CJA ).
Although inelastic scattering is neglected as far as angular deviations and the
path length are concerned, energy loss due to inelastic scattering must be
considered. Because of the plethora of possible inelastic scattering processes,
and the lack of accurate inelastic scattering cross section data for many
elements, it has become c o m m o n in most M o n t e Carlo simulations to account
for the effects of inelastic scattering by means of the Bethe continuous energy
loss approximation, eqn (2.32). The energy loss AE along a segment of path of
length 5 is approximated as
e
e
e
e
t
AE = S(dE/ds)
(2.38)
The trajectory of the electron is thus followed incrementally through the
target, with constant knowledge of the electron coordinates, energy, direction
of flight, and production of secondary radiation. The progressive loss of energy
from the beam electron eventually reduces its energy below the level necessary
to excite secondary processes and the trajectory is terminated as an "absorbed
electron." Alternatively, the trajectory may interesect a surface of the target,
leading to electron escape as a "backscattered electron", and the final energy,
position of intersection with the surface, and direction of emission from the
target can be recorded. An example of electron trajectories calculated for an
aluminum target at a beam energy of 20 keV is shown in Fig. 2.6. Such a plot,
consisting of 100-200 individual trajectories, gives a good visualization of the
"interaction volume" of the beam electrons. In viewing such plots, it should be
recognized that the three-dimensional trajectories are projected onto a plane
to give a two-dimensional representation. The true nature of the threedimensional character of the interaction volume can be seen in stereo pair
plots which can be synthesized from the trajectory data (Bright et al, 1984).
2.3.3
Practical a s p e c t s of M o n t e C a r l o c a l c u l a t i o n s
The formulation described in the previous section can be thought of as a
"zeroth" order M o n t e Carlo calculation, a simple skeleton upon which the
user can design a simulation appropriate to specific needs. In order to
implement a successful M o n t e Carlo simulation, several practical aspects must
be considered.
Incorporating
secondary
processes
The production of secondary radiation along the electron path can be
calculated from the appropriate cross section, the specimen atom species
M o d e l i n g e l e c t r o n b e a m i n t e r a c t i o n s in s e m i c o n d u c t o r s
49
Al, E„=20keV
F i g . 2.6 Plot of 100 electron trajectories calculated for aluminum at an incident
beam energy of 20 keV.
parameters (concentration, atomic number, atomic weight and density), and
the path length. As an example of a calculation of a secondary radiation
process, consider the production of inner shell ionization events. The cross
section given in eqn (2.21) specifies the cross section in terms of ionizations per
electron per atom per c m . During travel along a segment of path t, the
production of ionization can be calculated as:
2
g [ i o n i z a t i o n s / e ( a t o m / c m ) ] x N ( a t o m s / m o l ) x (l/v4)(mol/g)
x p(g/cm ) x t(cm) = QN pt/A = ionizations/e
2
A
3
A
(2.39)
In the M o n t e Carlo calculation, the step lengths of the calculation are
sufficiently short so that the energy change along the step is small. The energy
dependence of the ionization cross section, or for the cross sections of other
processes, can be safely ignored along a single step so that a constant value can
be assumed, based on the mean energy of the beginning and endpoints of the
step. The step length S is substituted for t into eqn (2.39), and the ionization per
electron is calculated.
Testing
A M o n t e Carlo simulation must be tested to determine the accuracy of the
calculated results. Such tests usually involve comparison with published
50
D.E. Newbury
experimental data on electron interactions with solids (Newbury and
Myklebust, 1984). A useful selection of experimental data includes the backscattering coefficient as a function of the atomic number of the target and as a
function of specimen tilt, and the angular and the energy distributions of
backscattered electrons. The transmission of electrons through thin foils has
been identified by Reimer and Krefting (1976) as especially sensitive to the
choice of scattering models. A good procedure to follow in testing a M o n t e
Carlo procedure is first to compare the calculated backscatter coefficients at
normal beam incidence with experimental values. The accuracy of the
calculated results is dependent on the accuracy of the elastic cross section used
for calculation of the scattering angles and the mean free path and of the Bethe
expression for calculating energy loss. The screened Rutherford cross section
for elastic scattering, while convenient to calculate, introduces a bias in the
calculated backscatter coefficients such that the calculated coefficients are
about 15% too high for heavy elements. To compensate for the inaccuracy of
the cross section, it is necessary to apply a correction term to the mean free
path calculated from the Rutherford elastic cross section. F o r example, Kyser
and M u r a t a (1974) suggested modifying the Rutherford elastic mean free path
with an atomic number-dependent correction of the form X = 1(1 + Z/C),
where C had a value of 300. The correspondence between the modified Monte
Carlo calculation and the experimental values of the backscattering coefficients is shown in Fig. 2.2. The need for this empirical correction can be
understood in terms of the deviation of the exact cross section from the
Rutherford cross section illustrated in Fig. 2.1. With this empirical adjustment
to the mean free path, the M o n t e Carlo simulation is found to be capable of
calculating other experimentally measured parameters, such as the backscatter coefficient as a function of tilt, as shown in Fig. 2.7, with considerable
accuracy. Detailed testing of the results of Monte Carlo simulations has
demonstrated their considerable utility in accurately calculating values of
electron beam-specimen interaction parameters (Newbury and Myklebust,
1984).
Statistics
The principal weakness of the M o n t e Carlo calculation is the need to calculate
many trajectories in order to obtain statistical significance. Examination of the
individual trajectories in Fig. 2.6 reveals that each trajectory varies greatly
from any of the others because of the random selections from the range of
scattering parameters. In order to calculate results which are representative of
the overall interaction a statistically significant number of trajectories must be
calculated. The precision of a M o n t e Carlo calculation depends on the number
of events calculated, with the standard deviation of the calculation given by the
51
M o d e l i n g e l e c t r o n b e a m i n t e r a c t i o n s in s e m i c o n d u c t o r s
I.O,
»
K Measured for Fe-3.2 2 Si
O-——O Calculated for Iron
0.2
10
20
30
40
50
60
70
80
90
Tilt, 9 (Degrees)
F i g . 2.7 Calculation of the behavior of the backscattered electron coefficient as a
function of specimen tilt and compared to experimental measurements. (From
Newbury et al, 1973.)
expression:
SD = n\
(2.40)
12
where n is the number of trajectories which contribute to an event of type "i".
The relative standard deviation is then given by
{
R S D = w /n = n "
1/2
i
i
i
1 / 2
(2.41)
Thus in a calculation of a backscattering coefficient, the precision of the
calculation is not determined by the total number of electrons calculated, N,
but by the number of electrons which backscatter:
n, = t]N
(2.42)
In the same simulation, the calculation of characteristic X-ray production
would be obtained with greater precision, since all of the incident electrons
contribute to the generation of X-rays.
Targets with special
geometry
The great strength of the Monte Carlo simulation is the capability for
continually following the position of the beam electron through the target. The
calculation of spatial distributions of primary and secondary products is
52
D.E. Newbury
>—
1
1 pm
F i g . 2.8 Interaction of beams of various energies with spherical aluminum particles
2 fim in diameter.
straightforward. An example of a calculation of the interaction volume in a
flat, semi-infinite target is shown in Fig. 2.6. When the target has a complex
shape, the boundary can be considered by means of an appropriate equation,
or else an array of points defining the boundary can be stored, with
interpolation used to obtain intermediate points for comparison with the
position of the electron to determine the escape of electrons from the target. An
example of the utility of the M o n t e Carlo calculation for the simulation of
electron interactions in complex targets is shown in Fig. 2,8, where beams of
various energies are shown interacting with spherical aluminum particles with
a diameter of 2 fim. Complete containment of the beam within the target is
obtained at 5 keV, while at higher beam energy penetration through the sides
and bottom of the particle occurs.
2.34.
A p p l i c a t i o n s to s e m i c o n d u c t o r s
Calculation of line width
The fabrication of high-density devices requires accurate positioning of
substrates and patterns and frequently involves many steps of re-registration
in order to build up complicated layered structures. The problem of
positioning becomes more acute as the dimensions of the structure to be
fabricated are reduced. Electron beams from high-brightness electron optical
systems can be focused to nanometer dimensions, which appears to offer an
ideal probe for locating the edge of fine features in a high-density structure.
Unfortunately, the finite size of the interaction volume results in a substantial
53
r—i—i—i—i—I—i—i—i—i—I—i—i—i—r—i—i—i—i—i—i
ru
U)
i
.
1 . 1 < « « 1 1 « « rl 20000 T r a j e c t o r i es/Pt,
70 Degree L i n e
Edge
|- C R L i n e O n S I
I
0 . 5 p m L i new i d t h
0.14 pm Line
Thickness
1
i
i
i
I
»
i—i—i
0
r\>
—
BSE
COEFFICIENT
M o d e l i n g e l e c t r o n beam interactions in s e m i c o n d u c t o r s
X
I
.25
RXIS
i
i
± 3o-
i—i
.5
.75
(MICROMETERS)
F i g . 2.9 Monte Carlo calculation of the backscattered electron signal response from
a strip of chromium (thickness 0.14 jum, width 0.5 fim) on a silicon substrate scanned
with a 10 nm diameter 20keV beam. (From Hembree etai, 1981.)
broadening of the backscattered electron signal response profile as the beam is
scanned across an edge. Hembree et al. (1981) have made use of a M o n t e Carlo
simulation to study the nature of the backscattered electron signal response for
beams of various energies scanned across structures consisting of "lines" of
various metals (aluminum, chromium and gold) with a range of thicknesses
placed on top of a semi-infinite silicon substrate. Figure 2.9 taken from this
work shows a calculated response curve for a chromium line with a width of
0.5 jum and a thickness of 0.14 /mi on silicon scanned with a 10 nm, 20keV
beam. The resulting BSE profile shows a 70 nm width for the signal to rise from
the BSE coefficient of Si to the BSE coefficient of Cr.
A second calculation by these authors, shown in Fig. 2.10, tested the effect of
changing the line material. Although the use of gold produced a larger change
in the BSE signal across the edge, the width of the response curve was similar
for Cr and Au. Finally, the authors calculated the effect of beam energy on the
edge response, shown in Fig. 2.11. Decreasing the beam energy from 20keV to
5 keV produced a substantially sharper rise in the signal profile.
Exposure of photoresists
Inelastic scattering of beam electrons in photoresists leads to the transfer of
energy to the atoms of the target resulting in a n alteration in the chemical
bonding structure of these compounds which renders them susceptible to
selective chemical etching. The rate of chemical attack depends on the a m o u n t
of energy deposited per unit volume. Shimizu et al. (1975) employed a M o n t e
BSE
Coefficient
. 6
0
L_J
-50
I
I
I
1 1
1
1
1
-25
X
1 1
0
R x i s
I
I
I
I
I
I
I
I
25
I
50
I
I
I
L_J
75
(Nanometers)
BSE
Coefficient
Fig. 2.10 Effect of atomic number on the backscattered electron signal response
from metallic strips on a silicon substrate (thickness 0.14 /im, width 0.5 fim; beam 10 nm
diameter, 20keV). (From Hembree et a/., 1981.)
X
R x i s
(Nanometers)
F i g . 2.11 Effect of beam energy on the backscattered electron signal response from a
chromium strip on a silicon substrate (thickness 0 . 1 4 j i m , width 0.5 [im; beam 10 nm
diameter). (From Hembree et al, 1981.)
M o d e l i n g e l e c t r o n b e a m i n t e r a c t i o n s in s e m i c o n d u c t o r s
Experiment
Incident
electron
55
Monte Carlo
F i g . 2.12 Comparison between experimental measurements and Monte Carlo
electron trajectory calculations of energy deposition in polymethylmethacrylate.
(From Shimizu et al, 1975.)
Carlo simulation to calculate the energy deposited per unit volume in
polymethylmethacrylate and compared the results of the calculation with
careful experiments in which the damage contours were directly revealed by
quantitative etching experiments. The results of the calculation and experiment, which are compared in Fig. 2.12, show remarkably good agreement in
view of the difficulty of the experimental measurement.
Effect of fast secondary electrons on photoresist
resolution
The calculation of the deposition of the beam energy to expose photoresist
materials illustrated in the previous section is based entirely on the trajectories
of the beam electrons. This approach is adequate when resolution on the scale
of the full interaction volume is considered. However, in exploring the limits of
spatial resolution which could be achieved with finely focused beams and thin
resist layers, M u r a t a et al (1981) and Joy (1983) recognized the need to
incorporate fast secondary electrons into the simulation. Figure 2.13a shows
primary trajectories in an unsupported resist layer 100 nm thick with a 1 nm
diameter, 100 keV beam incident normal to the surface. The trajectories are
nearly parallel below the entrance surface, with a conical interaction volume
developing near the exit surface. When a high energy primary beam electron
generates a fast secondary electron, the scattering angle of the fast secondary
electron is approximately 90° relative to the beam electron trajectory. When
the primary electron trajectories are unscattered and nearly parallel near the
56
D.E. Newbury
,
{
.
Q
)
BEAM
AXIS
Top
( b
Top
Fig. 2.13 Interaction volume in photoresist as calculated by Monte Carlo electron
trajectory simulation. Thickness: lOOnm; beam energy lOOkeV; (a) primary electron
trajectories; (b) fast secondary electron trajectories generated by primaries in (a). (From
Joy, 1983.)
entrance surface most fast secondary electrons which are generated will tend
initially to propagate parallel to the specimen surface. Since the energy of the
beam electron is essentially unchanged while passing through the thin film, the
rate of fast secondary electron production is constant along the primary
trajectory. The fast secondary electrons are produced with low energy relative
to the primary electron, so that the energy loss rate will be much greater,
resulting in an efficient transfer of energy to the target, and the elastic
scattering of the fast secondary electrons will be high, resulting in rapidly
curling trajectories.
A "double" M o n t e Carlo procedure is used to calculate the behavior of fast
Modeling electron beam interactions in semiconductors
57
secondary electrons. A primary trajectory is followed until a fast secondary
electron is generated, and then the trajectory of the fast secondary electron is
calculated from the point of generation. After the fast secondary electron
trajectory terminates due to complete energy loss or escape from the target,
the primary electron is resumed from the point of interruption. The paths of
the fast secondary electrons calculated with a double M o n t e Carlo procedure
are shown in Fig. 2.13b, forming a cylindrically shaped interaction volume
with approximately the same radial density near both the entrance and exit
surfaces of the target. The net effect of fast secondary electron generation is to
deposit energy in the target in regions not directly reached by the primary
electrons and thus to set a limit to the spatial resolution of electron
lithography which is independent of the resist thickness and the energy of the
incident beam.
Calculation of charge collection microscopy
images
Charge collection scanning electron microscopy or electron beam induced
conductivity (EBIC) is an important mode of operation for semiconductor
characterization. The incident high-energy electron deposits its energy in the
semiconductor target in a cascade process which eventually leads to the
formation of mobile charge carriers. Electrons are promoted from the filled
valence band to the conduction band, where they are free to move under an
applied electric field, and a corresponding positively charged hole is left in the
valence band, which is also mobile, forming a so-called electron-hole pair.
These electron-hole pairs are created throughout the interaction volume of
the primary electrons. The electrons and holes tend to mutually attract and
annihilate (recombination). However, if an electric field due to a p - n junction
or a Schottky barrier exists across the volume in which the electron-hole pairs
are produced, the charge carriers can be swept apart before recombination
occurs. The internal motion of this charge will cause an equal a m o u n t of
charge to flow in an external circuit connected to electrodes on the front and
back surfaces of the specimen. This external current is used to provide the
signal for S E M imaging. Contrast arises at defects where the local recombination rate differs from the bulk rate for perfect material.
M o n t e Carlo simulation techniques have been applied to the calculation of
charge collection images to aid in the interpretation of defect images by Joy
(1986) with the following procedure. The information necessary to calculate an
EBIC image is firstly the volume density of production of electron-hole pairs.
This calculation can be made in a straightforward fashion by first calculating
the total energy loss AE in a step of the calculation by means of the Bethe
expression (eqn (2.32)). The energy £ necessary to create an electron-hole
pair is typically three times the bandgap energy for the semiconductor (Klein,
e h
58
D.E. Newbury
r/r
E
F i g . 2.14 Distribution of electron-hole pairs in silicon as calculated with a Monte
Carlo electron trajectory simulation. The horizontal and vertical scales are plotted in
terms of the electron beam range, r . (From Joy, 1986.)
E
1968); for silicon, £ is 3.6 eV. The total number N
produced along a step is then:
e h
eh
N
eh
= E/E
eh
of electron-hole pairs
(2.43)
The distribution of carrier pair generation in a silicon target is shown in
Fig. 2.14, where relative contours of equal density are plotted as a function of
the depth and lateral distances from the beam impact point.
With this distribution of carrier pairs as a starting point, the next step is to
calculate the current gain of the external circuit. In the simple case of a planar
Schottky barrier, the in-built potential of the barrier collects all carriers with
unit efficiency down to a depth Z , the depletion depth. The gain for this region
is the average number of electron-hole pairs per beam electron,
E /E .
However, the effect of backscattering is to reduce this gain, since part of the
incident energy is effectively lost. The M o n t e Carlo calculation directly
accounts for this loss in the calculation of the original distribution of
D
0
eh
CURRENT GAIN
10
0 1
-J
0 5
I
I
2.0
l.O
I
50
1 _
100
DEPLETION DEPTH (/xm)
Fig . 2 . 1 5 Monte Carlo computed current gain as a function of depletion depth for a
Schottky barrier on silicon. Beam energy 30 keV. Diffusion lengths from 0.1'to 5 fim are
plotted. (From Joy, 1986.)
5000
r
4000
II
12
13
BEAM ENERGY (keV)
F i g . 2.16 Effect of various metal thicknesses on the gain of a Schottky barrier on
indium phosphide. (From Joy, 1986.)
60
D.E. Newbury
3800
• *
25
W
\\
\\
CURRENT GAIN
3700
s
/
s
/
i
*\
i
\
3600 -
i
'20
V
1
I
15
3500 -
no
S i 15 kev
1000 ii-CM
L=i/IM
J
ZERO BIAS
3400
0.51
1
5
i
4
l
I
3
2
1
1
1 0
1
1
I
1
2
3
i
4
5
DISTANCE (/XM)
Fig .2.17 Monte Carlo calculation of the width of an image of a single dislocation in
silicon lying parallel to the surface at various depths and with a diffusion length of 1 //m.
Beam energy 15keV. (From Joy, 1986.)
generation of electron-hole pairs, since each trajectory is followed to
completion, whether it is fully absorbed or backscatters. For carriers produced
beyond the depletion depth, recombination will occur, except for a fraction, y,
which diffuses back to the depleted region. This fraction is determined by the
depth, Z, relative to the depletion depth, and the minority carrier diffusion
length, L (Wittry and Kyser, 1964):
7
= exp[-(Z-Z )/L]
D
(2.44)
The gain computed by the M o n t e Carlo for a Schottky barrier as a function of
depletion depth with an incident beam energy of 30 keV is shown in Fig. 2.15.
A second advantage of the Monte Carlo simulation is the ability to directly
account for the influence of the thickness of the metal electrode of the Schottky
barrier. The effect of varying the electrode thickness is shown as a function of
incident beam energy in Fig. 2.16 for indium phosphide.
In order to calculate the contrast which arises from a defect, the diffusion of
carriers from the point of generation in the interaction volume to the position
of the defect must be determined. Joy (1986) has described modifications to the
expression for defect contrast of D o n o l a t o (1978) to adapt it to the M o n t e
Carlo simulation. Two examples of calculations of the image width for a
dislocation lying parallel to the specimen surface are shown in Figs. 2.17 and
Modeling electron beam interactions in semiconductors
A SIGNAL (ARBITRARY UNITS)
61
OQQ
O
U
1 I
U
1
5
I
4
I
3
I
2
I
I
I
O
I
DISTANCE (/xm)
1
2
1
1
3
4
1
5
F i g . 2.18 Monte Carlo calculation of the width of the image of a horizontal
dislocation at a depth of 0.5 /mi in silicon as a function of beam energy. (From Joy,
1986.)
2.18. In the case of Fig. 2.17, the depth of the defect below the surface has been
varied, demonstrating the loss in contrast as the defect is placed further down
into the specimen. In Fig. 2.18, the effect of varying the incident beam energy
on the image width of a dislocation located 1 /im below the surface is
calculated. A complex behavior is observed. At 5 keV, the defect produces only
a slight modulation, since it lies below the interaction volume. At lOkeV the
modulation of the signal increases greatly, since the defect now lies within the
interaction volume. Further increases in the beam energy actually cause the
contrast to decrease, since the charge carriers are generated further away from
the site of the defect.
2.4
Summary
M o n t e Carlo electron trajectory simulation can provide a powerful tool to the
semiconductor microscopist. A wide variety of electron beam-specimen
interactions can be simulated with sufficient accuracy to be of value in
elucidating the details of S E M images. The particular strength of the
procedure is the ability to adapt the simulation to accommodate unusual
specimen geometries, especially the presence of defects in a structure. The
D.E. Newbury
62
major weakness of the approach is the statistical nature of the calculation with
the resulting need to simulate large numbers of trajectories for each choice of
experimental conditions.
References
Berger, M. and Seltzer, S. (1964). National Academy of Science/National Research
Council Publ. 1133, Washington, p. 205.
Bethe, H. (1930). Ann. Physik, 5, 325.
Bethe, H. (1933). Handbook of Physics, Vol. 24, Springer Verlag, Berlin, p. 273.
Bright, D.S., Myklebust, R.L. and Newbury, D.E. (1984). J. Micros., 136, 113.
Brown, D.B. (1974). In 'Handbook of Spectroscopy' (J.W. Robinson, Ed.), p. 248. CRC
Press, Cleveland.
Donolato, C. (1978). Optik, 52, 19.
Everhart, T.E, Herzog, R.F, Chang, M.S. and Devore, W.J. (1972). Proc. 6th Int. Conf.
on X-ray Optics and Microanalysis, eds Shinoda, G , Kohra, K. and Ichinokawa, T ,
University of Tokyo Press, Tokyo, p. 81.
Ferrel, C. (1956). Phys. Rev., 101, 554.
Goldstein, J. I , Newbury, D.E, Echlin, P., Fiori, C.E. and Lifshin, E. (1981). Scanning
Electron Microscopy and X-ray Microanalysis, Plenum Press, New York.
Heinrich, K.F.J. (1981). Electron Beam Microanalysis, Van Nostrand, New York,
p. 245.
Hembree, G.G, Jensen, S.W. and Marchiando, J.F. (1981). Microbeam Analysis, San
Francisco Press, p. 123.
Henoc, J. and Maurice, F. (1976). In Use of Monte Carlo Calculations in Electron Probe
Microanalysis and Scanning Electron Microscopy, National Bureau of Standard
Special Publication 460, Washington, p. 61.
Joy, D.C. (1983). Microelectronic
Engr., 1, 103.
Joy, D.C. (1986). J. Microscopy, 143, 233.
Kirkpatrick, P. and Wiedmann, L. (1945). Phys. Rev., 67, 321.
Klein, C.A. (1968). J. Appl. Phys., 39, 2029.
Kyser, D.F. and Murata, K. (1974). IBM J. Res. Dev., 18, 352.
Moller, C. (1931). Z. Phys., 70, 786.
Mott, N.F. and Massey, H.S.W. (1965). The Theory of Atomic Collisions (3rd edn),
Oxford University Press, Oxford.
Murata, K , Kyser, D.F. and Ting, C.H. (1981). J. Appl. Phys., 52, 4396.
Newbury, D.E. and Myklebust, R.L. (1984). In Electron Beam Interactions with Solids,
SEM, Inc., Chicago, pp. 153-163.
Newbury, D.E, Yakowitz, H. and Myklebust, R.L. (1973). Appl. Phys. Lett., 23, 448.
Newbury, D.E, Joy, D.C, Echlin, P , Fiori, C.E. and Goldstein, J.I. (1986). Advanced
Scanning Electron Microscopy and X-ray Microanalysis, Plenum Press, New York.
Reimer, L. and Krefting, E.R. (1976). In Use of Monte Carlo Calculations in Electron
Probe Microanalysis and Scanning Electron Microscopy, National Bureau of
Standards Special Publication 460, Washington, p. 45.
Shimizu, R, Ikuta, T , Everhart, T.E. and Devore, W.J. (1975). J. Appl. Phys., 46,15811584.
Sommerfeld, A. (1931). Ann. Phys. (Leipzig), 11, 257.
Statham, P.J. (1976). X-ray Spectrom., 5, 154.
63
Modeling electron beam interactions in semiconductors
Streitwolf, H.W. (1959). Ann. Phys. (Leipzig), 3, 183.
Wittry, D.B. and Kyser, D.F. (1964). J. Appl. Phys., 35, 2439.
Yakowitz, H., Newbury, D.E. and Myklebust, R.L. (1975). In Scanning
Microscopy,
Electron
1975, Vol. I, p. 93.
A p p e n d i x by D . C . J o y
S e m i - e m p i r i c a l d e p t h - a n d lateral-dose f u n c t i o n s a n d electron energy
loss s p e c t r o s c o p y
Monte Carlo simulation is the most important method available for treating the
interactions of the electron beam with solid specimens and it will be increasingly widely
applied in the future. However, in earlier theoretical papers the use of semi-empirical
analytical expressions for the distribution of energy deposited in the specimen was
widespread. Such expressions are likely to continue to be used for such purposes to
some extent. A brief outline of these expressions with refereneces to the original
literature will be found in Section 6.1.5 of Chapter 6.
Electron energy loss spectroscopy ( E E L S )
The details of electron-solid interactions can be directly observed by the technique of
electron energy loss spectroscopy (EELS). Two possible experimental arrangements
are shown in Figs. 2.Ala and b. In Fig. 2.Ala, electrons which have been transmitted
through a thinned portion of the sample are passed through a magnetic prism, or
electron spectrometer, which disperses them according to their energy. By placing a
photograph film in the dispersion plane, or by magnetically or electrostatically
scanning the dispersion across a selection slit placed in front of a suitable electron
detector, the energy loss spectrum can be measured. In Fig. 2. A lb the same
spectrometer system is used but the incident electrons are observed after specular
reflection from a solid (i.e. not electron-transparent) material, so permitting a spectrum
to be obtained from the near-surface region of the target.
Figure 2.A2 shows a transmission EELS spectrum from silicon, obtained at 100 keV
incident electron energy from a sample about 1200 A thick. The spectrum is plotted
with relative signal intensity at energy loss 1(E), on the vertical axis and energy loss AE
on the horizontal axis. Energy loss increases in the positive x direction. In the EELS
experiment we measure 1(E) over some solid angle dQ (i.e. the angle subtended by the
spectrometer) about some angle 6 from their original incident direction. If the intensity
of the incident beam is /, then I(E/6)/I is the fraction of electrons losing energy E while
being scattered through an angle 0. This fraction is directly proportional to the doubly
differential cross section d <r/d£dQ. The constant of proportionality is JV , the
projected number of atoms per unit area in the volume examined, thus:
2
at
I(E,0)
at
(2.A1)
This cross section, which is the quantity effectively measured in an EELS experiment,
can be related to the properties of the sample in two different but equivalent ways.
64
D.E. Newbury
Incident Beam
Energy Eo
Thin sample
Electron Spectrometer
(Magnetic Prism)
Energy Eo
Slit
I Scintillator and
I
ip
P n o t o m u l t
n e r
F i g . 2.A1 Experimental arrangements for the observation of electron energy loss
spectra (a) from a thin (electron transparent) specimen and (b) from a solid sample.
The first of these is the "macroscopic" approach, which ignores all the microscopic
detail of the sample such as its chemistry and crystallography, and described the
material instead in terms of its complex dielectric constant £ . The "real" part of the
dielectric constant, e describes the refraction of the electron or electromagnetic wave
by the specimen while the "imaginary" part, e , describes the absorption or energy loss
of the electron or wave. It can be shown (Egerton, 1986) that
0
l5
2
(2.A2)
where a is the Bohr atomic radius, n is the number of atoms/cm , 6 is the
3
0
n
E
65
Modeling electron beam interactions in semiconductors
F i g . 2. A 2 Transmission electron energy loss spectrum from sample of silicon, about
1200 A thick, observed at an incident energy of 100 keV. Note the zero loss peak, the
three plasmon loss peaks (labelled 1,2 and 3), the 100 x change in the recording gain to
make the higher energy loss data visible, and the silicon L ionization edge at 99 eV
energy loss.
2 3
characteristic inelastic scattering angle defined as
AE
(2. A3)
0 = —
E
where, as above, AE is the energy loss relative to the incident energy E .
The EELs experiment therefore provides a direct measure of Im( — \/e ). While this
is not in itself particularly useful, if it can be assumed that essentially all of the
transmitted electrons have been accepted by the spectrometer, then the real part Re
(l/£ ) of the dielectric function can also be obtained through a Kramer-Kronig
transformation (e.g. Daniels et al, 1970) of the spectrum, to give the complete dielectric
response. In the case of semiconductor materials the ability to obtain this function is
valuable because it provides a detailed look at the electronic structure of the specimen
that would not be possible from the spectrum alone. For example, since
0
0
0
e = e -\- is
0
l
(2.A4)
2
then interband transitions will cause a variation in s with energy. In the EEL spectrum
the signal will vary, as before, as
2
(2.A5)
so the result of any variation in c will be damped out, but by transforming the spectrum
and deriving e and E separately their true variation can be observed.
The second way of relating the energy loss spectrum to the electron-solid interaction
is through a "microscopic" model, which considers how each feature in the spectrum
2
t
2
66
ARBITRARY UNITS
D.E. Newbury
l 23
! 1
L
100
L
120
140
160
180
200
ENERGY LOSS E (eV)
F i g . 2.A3 Transmission electron energy loss spectrum showing the silicon L
ionization edge in (a) amorphous silicon, (b) from the silicon in silicon carbide and (c)
from crystalline silicon of (111) orientation.
2 3
can be associated with a specific physical process. For example, the most prominent
feature of the spectrum shown in Fig. 2.A2 is the peak identified as "zero-loss". This
includes those electrons which have not interacted at all with the specimen, and so are
unscattered, electrons which have been elastically scattered, and finally electrons which
have inelastically interacted with the sample through the phonon excitations, but have
lost so little energy (typically 0.1 eV or less) that the spectrometer cannot distinguish
them from electrons that have lost no energy. In a typical spectrum 70% or more of the
electrons fall into one of these three categories so a majority of the signal intensity
appears in the zero-loss peak. This peak is of little analytical value, but does define the
reference energy position.
67
Modeling electron beam interactions in semiconductors
The features labeled 1,2 and 3 in the spectrum, to the right of the zero-loss peak, are
plasmon excitations. In metals, and other materials containing 'free" electrons, the
equilibrium of the conduction electrons is disturbed by the passage of a fast incident
electron. This sets the electron gas into oscillation with a frequency co which is
proportional to ( « ) where n is the number of free electrons per unit volume. To
produce this oscillation requires an energy
pi
1/2
e
e
(2.A6)
E = hco
p
pl
so that an incident electron producing a plasmon suffers an energy loss E . Since
co ~ 1 0 r a d / s £ ~ 20eV. In the example here the sample is sufficiently thick that
many electrons generate more than one plasmon so finishing with energy losses of E ,
2£ , 3 £ and so on.
All materials that give good plasmon loss peaks have E in the range 10-20 eV, so an
unambiguous chemical identification from a measurement of E is not possible. But
changes in chemistry caused by the addition of another element, for example SiS i O - S i 0 , produce monotonic plasmon energy shifts which, once calibrated on
standards of known composition, can be used to find the percentage of the addition in
some sample of the mixture. Because the plasmon signals are relatively strong this
provides a rapid way of performing quantitative chemical microanalysis in a well
characterized sample (Williams and Eddington, 1976). It should be noted that E also
varies with the effective electron mass m*, so variations in this due to various effects will
similarly be manifested as shifts in the plasmon energy loss. The width of the plasmon
peaks is a measure of the damping that the oscillation experiences and in some cases, for
example the icosahedral quasi-crystalline materials, anomalously high values can be
observed (Chen et al, 1986) and associated with the detailed band structure of the
sample.
The final portion of the spectrum is at higher energy losses than the plasmon peaks
and, since the average value of 1(E) falls at about E~ , much weaker. As seen from
Fig. 2.A2 a gain increment of 100 x is required to make the detail in this portion of the
spectrum visible. Superimposed on the £ ~ "background" are evidences of inner shell
ionization events. If the critical ionization energy is E then
p
16
p
pl
p
p
p
p
p
2
p
4
4
c
=0
for E < E
>0
for£^£
c
(2.A7)
c
so, from eqn (2.A1), the spectrum will show a discontinuity or "edge" at E = E . Thus in
Fig. 2.A2 the edge at E = 99 eV loss is the L ionization of silicon. Since this energy is
unique to the element a measurement of the edge energy loss unambiguously defines
the element as being present in the material. EELS therefore provides a means of
chemical microanalysis.
The onset of the edge is not abrupt, as might be supposed from eqn 2.A7, but instead
shows some structure in the vicinity of E . This structure reflects the available density of
states into which the ionized electron can be promoted convoluted with the relevant
transition probability. This "fine structure" or "pre-edge structure" is therefore a
sensitive indicator of the bonding state of the atom concerned. Figure 2.A3, shows
the silicon L edge when (a) the silicon is amorphous, (b) the silicon is in silicon
carbide and (c) the silicon is crystalline. The differences are both reproducible and
c
2 3
c
2 3
68
D.E. Newbury
unmistakable. EELS therefore permits both the chemical state and electronic nature of
the bonding to be determined.
References
Chen, C.H., Joy, D.C, Chen, H.S. and Hauser, J.J. (1986). Phys. Rev. Lett. 57, 743.
Daniels, J. Festenberg, C.V., Raether, H. and Zeppenfeld, D. (1970). Optical Constants
of Solids by Electron Spectroscopy, Springer Tracts in Modern Physics 54, SpringerVerlag, Berlin.
Egerton, R.F. (1986). Electron Energy Loss Spectroscopy
in the Electron
Plenum Press, New York.
Williams, D.B. and Edington, J.W. (1976). J. of Microsc,
108, (2), 113.
Microscope,
3
Electron Channeling Patterns
D.C. JOY
Electron Microscope
Facility, The University of Tennessee, F239
Walters
Life Sciences Building, Knoxville,
TN 37996-0810,
USA and Metals and
Ceramics Division,
ORNL, Oak Ridge TN
37831-6376
List of symbols
3.1 Introduction
3.2 ECP contrast
3.2.1 Theory
3.2.2 Practical conditions for obtaining channeling patterns
3.3 Information in channeling patterns
3.3.1 Orientation
3.3.2 Lattice parameter determinations
3.3.3 Microanalysis
3.3.4 Crystal perfection
3.4 Channeling micrographs
3.5 Selected area channeling patterns (SACP)
3.6 Using selected area channeling pattern
3.6.1 Application to microcrystalline orientation
3.6.2 Studies of crystalline perfection
3.7 Other techniques for SEM crystallography
3.7.1 Electron backscattering patterns
3.7.2 Kossel patterns
References
Appendix
. . . .
69
70
71
71
76
83
83
93
95
95
98
100
105
105
108
113
113
115
116
118
List o f s y m b o l s
A
B
C
C
d
d
d
2
s
hkl
min
0
linear dimension of display screen
gun brightness (amp/cm /str)
contrast level
spherical aberration coefficient
lattice spacing for Miller planes hkl
minimum selected area size
spot size of electron beam
SEM Microcharacterization of Semiconductors
ISBN 0-12-353855-6
Copyright © 1989 Academic Press Limited
All rights of reproduction in any form reserved
70
D
E
/
hkl
HKL
/
I
I
I
J
7
J
I(x)
L
n
p
R
s
t
u
WD
x
9
9
X
fi
0
\j/
$
B
BS
F
m a x
m i n
X H
B
3.1
D.C. Joy
diameter of limiting aperture
electron energy
focal length of probe forming lens
Miller indices of lattice planes
normalized Miller indices
incident beam current
backward intensity of beam
total backscatter intensity
forward intensity of beam
maximum signal intensity
minimum signal intensity
threshold current for imaging
intensity of xth Bloch wave
diameter of the filament crossover image
order of diffraction 1,2,3 etc
mean backscattering coefficient
radius of constructed stereogram
distance of specimen from lens
sample thickness
distance of image from final lens
working distance in SEM
depth beneath surface
incident angle
Bragg angle
electron wavelength
mean absorption coefficient
probe convergence contribution from lens focusing
probe covergence contribution from finite source size
scanned semi-angle
Introduction
A knowledge of the crystalline state of the material being studied is of great
importance in all aspects of semiconductor physics. The technique of electron
channeling discussed in this chapter permits a rapid determination in the
scanning electron microscope of whether a given specimen is a m o r p h o u s or
crystalline and, if crystalline, the type, orientation, spacing, and quality of its
lattice. Electron channeling patterns (ECP), in the form of bands of contrast in
the backscattered electron signal showing the three-fold symmetry of the (111)
face of the silicon crystal being examined, were first observed by Coates (1967)
and subsequently explained by Booker et al (1967) and play a similar role in
Electron channeling patterns
71
the S E M to that of diffraction and Kikuchi patterns in the transmission
electron microscope, but have the additional advantage that no thinning of the
specimen is required. The necessary electron optical conditions to utilize this
technique are now available on nearly all modern SEMs so that nothing other
than a clean specimen is required for its application. F o r a comprehensive
bibliography of electron channeling patterns and their applications see Joy
et al (mi);
see also Wells (1974), Schulson (1977), Newbury et al (1986).
3.2
3.2.1
E C P contrast
Theory
The probability that an incident electron will be backscattered (that is
scattered through an angle of greater than 90°) depends on how closely it
approaches the nucleus of the a t o m that is deflecting it. If a beam of electrons is
F i g . 3.1 The origin of electron channeling. In an amorphous material (a) the
projected atom density is the same in all incident directions, but in a crystal lattice (b)
some symmetry directions provide channels of low atom density and hence low
backscattering.
D.C. Joy
72
incident on an a m o r p h o u s material then, irrespective of the direction of the
beam relative to the surface normal, the packing density of the atoms will look
the same, and so the backscattering probability will be constant. In the case of
a crystalline material, however, the apparent packing density of the atoms
varies with the angle of incidence (Fig. 3.1). In particular, for certain directions
such that the electrons are moving parallel to the crystal lattice planes the
packing density appears to be low because all the atoms are aligned. The
electron therefore has a high probability of penetrating deeply, i.e. channeling,
into the sample before it is scattered, and consequently a lower probability of
being backscattered. We would thus expect that the backscattering coefficient
for a beam of electrons incident on a crystal surface would show modulations
at angles related to the symmetry of the lattice.
Although the prediction made by this particle model is correct, it is more
useful to think instead of the electron, particularly at low beam energies, as a
wave. In this case the channeling can be considered as diffraction of the
electron by the lattice. A convenient mathematical representation of the
electron wave interaction with a crystal is in terms of the so-called Bloch waves
(Hirsch et al 1978), each of which is a standing plane wave with the periodicity
of the lattice and directed normal to the incident surface. The square of the
amplitude of a Bloch wave at any point represents the probability of finding an
electron there or, in a macroscopic sense, the local current density. In the
simplest case the current flow in the specimen can be resolved into just two
Bloch waves. The first, type I, has its maximum intensity on the line of atom
centers making up the lattice planes, while the second, type II, has its maxima
midway between the lattice planes (Fig. 3.2). Electrons in the type I wave are
most likely to be found close to an atom center and will therefore interact
strongly and have a relatively high chance of being backscattered, while
electrons in the type II wave are comparatively far from the atom centers and
so are only weakly scattered.
The ratio of Bloch wave II to Bloch wave I depends on the angle of the
incident beam to the lattice. Since the incident current is constant, the sum of
the intensities in the two Bloch waves must also be constant, but the ratio of
their intensities can vary, and when this happens the backscattering probability will also change. When the incident angle 9 is such that Bragg's condition
is satisfied, 9 = # , i.e.
B
2dsin(9)
= nX
(3.1)
where d is the lattice spacing, n is an integer, here taken to be 1, and X is the de
Broglie electron wavelength, then the intensity of the two waves is equal. When
9 is less then 9 then the intensity of Bloch wave I is greater than that of Bloch
wave II and the total backscattered intensity will increase, while for 9 greater
than 9 then the intensity of I is less than that of II and the backscatter yield
B
B
73
Electron channeling patterns
TYPE I
TYPE
H
II AAA V W
LATTICE
PLANES
F i g . 3.2 The Bloch wave representation of standing currents in a crystal. For
simplicity only two Bloch waves are shown.
will correspondingly fall (Hirsch and Humphreys, 1970; Spencer et al., 1972).
Using this description then it can be predicted that if a beam of electrons is
scanned over a crystal as shown in Fig. 3.3 then the backscatter signal profile
would show a band of enhanced yield between the points where the incident
angle 6 equalled the Bragg angle 9 , with reduced backscattering in the regions
where 9 > 9 . Since the Bloch wave intensities are again equal at the secondorder Bragg condition (i.e. n = 2 in eqn (3.1)) then this form of signal variation
will repeat giving the profile shown in Fig. 3.3.
B
B
While the discussion of the Bloch wave model given above is adequately
detailed for most purposes, a brief outline of the full mathematical theory
(Spencer et al, 1972) does add some useful points. This analysis considers the
electrons in the sample to be of two classes, those which are in the Bloch waves
and those which have inelastically scattered out of the Bloch waves in either
the forward or backwards direction. These scattered electrons are distributed
isotropically, and their transport through the crystal can be described in terms
of a mean absorption coefficient ju , and a mean backscattering coefficient
p . Similarly for electrons in each of the Bloch waves j we have an absorption
coefficient
and a backscattering coefficient p . Considering some slice of
the crystal dx thick and at a depth x beneath the surface the scattering will
change the intensity I(x) of the jth Bloch wave as well as of the forward, J , and
{0)
{0)
ij)
F
D.C. Joy
BACKSCATTER
SIGNAL
74
SCAN
ANGLE
F i g . 3.3 The predicted variation of the backscattering signal with incident beam
angle.
backward, 7 , scattered components, i.e.
B
= I>
dI
B
(
0
)
' B «
-
- P / ( x ) ] dx
P I(x)
( 0 )
iJ)
F
d / = [ ( / * " P)l(x) + P / ( x ) - P / ( x ) ] dx
(0)
F
( 0 )
B
d/(x) = - ^
F
7(0) exp ( - fi x) dx
(3.2)
(3.3)
(3.4)
iS)
where 1(0) is the intensity of the jth Bloch wave at the entrance surface. F o r a
perfect crystal (i.e. no defects) of the thickness t the backscattered intensity at
the entrance surface of the crystal due to Bloch wave j is then
h = [V(l + P
( 0 )
0 ] lP tI(0)
+ (p<» - p™)I{x) d x ]
iO)
(3.5)
and since
7(x) = / ( 0 ) e x p ( - / i x )
(3.6)
O )
from the definitions above, the backscattered intensity at the entrance surface
from the j t h wave becomes
/B(0) = [/(0)/(l + P
( O )
0 ] {p t
(0)
+ (P ~ P )CI " e x p ( - i P t ) l i i \ }
(0)
U)
Summing over all the Bloch waves then gives the total backscatter signal /
' n s = i > / ( i + p t n + [ i / ( i + pt)i I {mi(p
j
- p )/^
0
(3.7)
B S
as
[ i - exp ( (3.8)
This expression consists of two terms, the first of which \_pt/(\ + pr)] is
Electron channeling patterns
75
constant and represents the background produced by the backscattered
electrons, and the second consisting of the terms summed over j which is the
desired signal contrast. A comparison of profiles predicted by this expression
and experimental data shows very good agreement (e.g. Joy et al, 1982). Two
general deductions can also be made from eqn (3.8):
(a) Channeling contrast is a function of the specimen thickness t. When the
sample is so thin that it is electron transparent (e.g. a few tens of nanometers at
20keV) then the backscattering (represented by the first term of eqn (3.8)) is
small and the contrast, defined as ( 7 — / ) / / , can approach 100%. As the
sample thickness is increased the contrast falls because the backscattering
component rises; however, it never falls to zero because electrons have only a
finite range of travel. Once the specimen thickness is greater than about 0.4 of
the Bethe range then the backscatter component is constant, and the
channeling contrast reaches a steady value of about 5%. This shows that
channeling contrast will be visible from solid specimens, but that the majority
of the contrast will come from a thin-layer region near the crystal surface.
(b) Channeling contrast varies with the incident beam energy. Although the
backscattering coefficient, and hence the background, is independent of beam
energy for a bulk specimen the contrast term varies as p/ja. p varies as l / £ ,
where E is the electron energy, while ft varies as l/E (Hall and Hirsch, 1965),
giving a combined variation of l/E. Hence channeling contrast falls with
increasing beam energy.
m a x
m i n
m a x
2
F i g . 3.4
A channeling pattern from the (111) pole of silicon.
76
D.C. Joy
In a real crystal there are many intersecting sets of lattice planes. Therefore,
if the beam is deflected so that it varies its angle of incidence in both the X and
Y directions, then the other lattice planes will also contribute to the signal
profile. An image formed from these electrons will now show contrast bands
from all sets of planes normal, or nearly normal, to the surface (Fig. 3.4). In
each case the angular width of the band will be twice the appropriate Bragg
angle for the set of lattice planes from which it comes, and the angle between
the bands will be the same as the angle between the corresponding sets of
planes. If the crystal is tilted, or rotated, the bands will appear to move as if
fixed to the lattice. However, a lateral motion of the sample would not change
the pattern because the symmetry of the crystal is unaffected by translations.
3.2.2
Practical c o n d i t i o n s for obtaining c h a n n e l i n g patterns
N o w that the basic theory of channeling patterns has been developed the
conditions necessary to produce them in the SEM can readily be determined.
Three basic electron optical conditions must be satisfied:
Angle of scan
It has been shown above that the channeling contrast comes about from
changes in angle of incidence between the beam and the crystal lattice. In order
for the pattern to be easily recognizable it is necessary to scan the beam
through at least twice the Bragg angle 6 of the lattice plane whose channeling
band it is desired to observe. A list of the values of the Bragg angle 6 for
important low Miller index planes in some c o m m o n materials of interest is
given in the Appendix. It can be seen that the Bragg angle is typically of the
order of one to two degrees, at 20 keV, so in order to produce a pattern such as
that shown in Fig. 3.4, which displays the (220) bands passing through the
(111) pole of silicon, it is necessary to change the angle of beam incidence
through a total angle of at least 8-10°.
For the SEM the magnification M is given by
B
B
M = >l/[2W Dtan($)]
r
(3.9)
where A is the linear dimension of the display screen, WD is the working
distance (i.e. the distance from the scan pivot to the specimen), and $ is the
scanned semi-angle. Thus an instrument with 10 cm size screen, a working
distance of 10 mm, and operating at x 20 magnification scans the beam
through ± 8 ° .
One basic condition for generating a channeling pattern can therefore be
obtained by operating the S E M at its lowest magnification setting. O n most
77
Electron channeling patterns
SEMs the magnification is kept constant when the instrument is switched
between different accelerating voltages so the total scanned angle will remain
the same. Since, however, the Bragg angle varies as the electron wavelength the
apparent width of the bands on the screen will fall as E~ , where E is the
beam energy. A necessary consequence of operating at such a low magnification is that a large area of the specimen is scanned, and the whole area
observed (typically several millimeters on a side) must be a single crystal.
1/2
Beam
collimation
We have seen that the contrast in the channeling pattern is a function of the
angle of incidence of the electron beam to the crystal lattice. If the beam at any
instant is striking the specimen over a range of incident angles (i.e. the beam is
convergent) then the angular width of the transitions in the pattern will be
increased, and the contrast will be decreased, by the integration over the beam
convergence angle a. In order to avoid this it is necessary to ensure that the
beam is nearly collimated, that is that a is small enough not to cause any
degradation of the pattern. Experimentally it is found that this means that a
should not exceed about 0.3 x 9 .
The convergence angle a is the sum of two contributions (Schulson and van
Essen, 1969), one due to the operation of the probe-forming lens and
depending on the size of the limiting aperture in the column and the other due
to the finite source size of the electron gun. Figure 3.5 shows the variation of
these quantities for three different lens conditions: (a) the normal micrograph
B
F i g . 3.5 Electron optical contributions to the incident beam convergence: (a) normal
imaging, (b) final lens switched off and (c) final lens weakly excited to produce a
collimated beam.
D.C. Joy
78
case where the beam is focused on to the specimen surface by the final
probe-forming lens; (b) the case where the beam is not focused because the
final lens has been switched off; and (c) the case where the beam is collimated
by setting the focal length of the final lens equal to the object distance.
Calling the contribution from the lens </>, and from the finite source size i//, we
get
Case (a)
Case (b)
Case(c)
0 = D/s and \j/ = L/u
<\> = D/u and ij/ = L/(u + s)
0 = 0
and il/ = L/u = L/f
where D is the diameter of the final aperture, L is the diameter of the filament
crossover image before the final lens, u is the distance of the image from the
final lens, s is the distance of the specimen from the final lens, and / is the focal
length of the final lens.
In case (a) the microscope is set up for normal high-resolution microscopy.
The source image L is therefore small after demagnification by the previous
lenses so ij/ is negligible, typically a few microradians. However, the
contribution from the lens will be large because the final aperture will have
been selected to optimize the imaging performance of the microscope.
Typically D will be about 100 fim for s of about 1 cm, so that <j> will be 10" rad
(i.e. about 1/2 degree). Under such conditions only a poor pattern would be
achieved. In case (b) the final lens has been switched off. The beam convergence
will now be considerably less than in case (a) since u » s, allowing a value of
1 0 " rad to be achieved. The contribution from the finite source size will still
be negligible in comparison with that due to the lens action. This technique for
producing E C P s is a useful one as it is simple to apply and gives patterns of
excellent quality; however, the probe size obtained will be approximately the
diameter of the final aperture and hence little or no surface detail will be
imaged.
The optimum technique is that of Fig. 3.5c where the beam has been
collimated by the final lens. The limit on the minimum beam convergence is
now set by the source size only. Using a L a B source a value of below 10" rad
is obtainable in this way, with adequate beam current. Once again, however,
the probe size will be comparable with the diameter of the final aperture.
In a three-lens SEM the most convenient way to obtain high-quality
channeling patterns, without surface detail, is technique (c) with the final lens
weakly excited. O n many modern instruments, unfortunately, the user is
prevented from lowering the excitation current sufficiently to achieve the
desired condition. In that case, or when a two-lens SEM is in use, technique (b)
with the lens switched off is the most useful. The only problem with this mode
of operation is that any slight misalignment in the column will tend to give
uneven illumination of the specimen.
2
3
4
6
Electron channeling patterns
Beam
79
current
Although the contrast from an electron-transparent material is high, 50% or
more, for the usual bulk S E M sample the maximum channeling contrast is 5%
or less. In order to see a level of contrast as small as this above the inherent
noise of the signal a minimum beam current 7 equal to
X H
I
TH
= 4 x 10
_ 1 2
/(C Oamps
(3.10)
2
is required (e.g. Goldstein et al, 1981), where C is the fractional contrast and t
is the time (in seconds) to record the image. Thus for an E C P with 5% contrast,
C = 0.05, and for recording in 1 s an incident current of about 1.5-2 nA is
required for a minimum quality image. The production of a good-quality E C P
therefore requires a relatively high incident beam current compared to that
used for high-resolution imaging. This fact also influences the way in which the
instrument can be set up for channeling use. The incident current on to the
specimen is given (Goldstein et al, 1981) by the formula
/ = 2.5d oi B
2
2
amps
(3.11)
where d is the spot size (in centimeters), a is the beam convergence angle (in
radians), and B is the gun brightness (in amps/cm /steradian). Once the
accelerating voltage of the microscope has been fixed and the gun has been
properly saturated, B is a fixed quantity. As a consequence, the three quantities
in eqn (3.11), l,d and a, are not independent. Once two of them have been
selected the third is automatically fixed. In particular, since / must be at
least the minimum value determined from eqn (3.11) this means that once /
has been selected the product (da) is constant, so that improved angular
resolution in the channeling pattern (i.e. a small) can only be achieved at the
expense of degraded spatial resolution (i.e. d large), and vice versa. This is
illustrated in Fig. 3.6 where the microscope has been adjusted to keep the
incident beam current fixed at lOnA while the probe size and convergence
angle are varied. In Fig. 3.6a the instrument is in a standard imaging mode
where d= 1 /mi and a= 1 0 r a d . Although surface features on the sample
are readily seen the channeling band is barely discernible. If the probe size
is increased to 2 /im while the convergence is improved to 5 x 1 0 " rad then
(Fig. 3.6b) the surface detail is degraded but the pattern is more clearly
evident. At a probe diameter of 10/mi and a convergence of 1 0 " rad
(Fig. 3.6c) a good-quality pattern is visible accompanied by weak surface
details. Finally, with the lens set to produce collimation such that
a = 2 x 1 0 ~ r a d while d is 50/im, a high-resolution pattern is visible, and
the surface detail has essentially disappeared.
2
_ 2
3
3
4
To summarize, therefore, three conditions are necessary to generate
channeling patterns from a large single crystal: a suitably wide angle of scan,
80
D.C. Joy
PROBE urn
a
'
CONVERGENCE m.rad
1
10
2
5
10
1
50
0-2
F i g . 3.6 The consequences of the brightness equation on electron channeling
patterns. In the (a)-(d) the angular resolution of the pattern, set by the beam
convergence a, and the spatial resolution, set by the probe size d, are varied while
keeping the incident beam current constant.
low beam convergence, and adequate beam current. O n most SEMs these
conditions can be obtained most simply by operating at the lowest possible
magnification and switching off the final lens.
Signal
collection
A topic that requires some discussion is the mode of signal collection for
electron channeling. The theory of this effect shows that the majority of the
contrast is carried by the backscattered electrons whose energy lies closest to
the incident beam energy. Experimental (Wells, 1971) and computed (Sandstrom et al, 1974) data for copper at 20 keV demonstrate that while the E C P
contrast is only 1.6% when collecting all backscattered electrons regardless of
their energy, if collection is restricted to those backscattered electrons lying
within 100 eV of the beam energy (i.e. 19.9-20 keV) the contrast is in excess of
40%. Because of this fact solid-state backscattered detectors are to be preferred
for electron channeling studies since their output signal is linearly proportional to the energy of the electron striking them. The detected signal is thus
Electron channeling patterns
81
weighted preferentially towards the highest energy electrons. M o d e r n backscatter detectors of this type are also advantageous in that their typical
mounting position, directly above the sample and concentric about the beam,
minimizes unevenness in the image illumination.
Channeling effects can also be observed in most other signal modes of the
SEM, although at lower contrast. The secondary signal will usually carry the
channeling contrast because a significant fraction of the secondaries are
generated by the exiting backscattered electrons. The contrast is weak,
however, and readily masked by other stronger secondary contrast effects. As
a practical point it can also be noted that the use of the conventional E v e r h a r t Thornley (ET) secondary electron detector is undesirable when using beam
currents as high as those needed for electron channeling because of the rapid
rate of damage of the scintillator. Unless access to the secondary signal is
essential it is good procedure to place a negative bias on the E T detector cage
to eliminate the secondaries striking the scintillator.
Signal
processing
Once the current electron optical conditions have been set up so that the
desired channeling information is present in the signal coming from the
specimen, it is invariably necessary to process this in order to ensure its
visibility when displayed on the S E M screen. This is because, as noted above,
the maximum contrast in a channeling pattern is only of the order of 5% and
this is too low to provide satisfying or useful visual information (see Fig. 3.7a).
In order to provide an image that properly displays the detail in the pattern the
image must be enhanced in some way. The most convenient way is with
differential signal amplification, sometimes also known as black level correction or contrast expansion, since all SEMs offer this capability. In this
technique (Goldstein et al, 1981) the unvarying component of the signal which
contains no information is subtracted away, and the residual signal then
amplified to fill the dynamic range of the display system. As shown in Fig. 3.7b
this now makes all of the features of the E C P readily visible, provided that the
incident beam current is high enough to ensure an adequate signal-to-noise
ratio. O n SEMs equipped with digital image storage and display ability other
more sophisticated options for improving the image, such as histogram
equalization and edge sharpening, are also available and can be used with
benefit on channeling patterns.
Sample
preparation
Although sample preparation techniques for scanning microscopy are less
demanding in general than those for transmission microscopy special care is
82
D.C. Joy
•
F i g . 3.7 Signal processing for ECP observation. In (a) the signal is viewed direct,
while in (b) black level correction has been applied.
required for E C P work. Because the contrast comes mainly from a thin surface
layer only 500-1000 A thick the specimen to be observed must have a surface
that is both clean, e.g. free from hydrocarbons, oxides, etc., and undamaged.
This means that conventional mechanical means of surface preparation are
unsuitable because they cause both chemical contamination, and leave
sufficient plastic damage to most crystals to eliminate channeling contrast (Joy
et al, 1972). The most suitable approach is usually to chemically, or
electrochemically polish the crystal to be observed. Because of their brittle
nature and low oxidation rate at room temperature, silicon wafers will usually
give adequate patterns without much effort, but material that has been
processed will require a light etch (such as 2% H F in nitric acid) for a few
seconds to remove the oxide. Other materials will require other polishes,
details of which can be found in standard references (e.g. Hirsch et al, 1978;
Electron channeling patterns
83
Goodhew, 1984). In all cases it is desirable to wash the surface before
observation with electronic grade ethanol (stored in glass not in a squeeze
bottle) to remove any traces of finger or vacuum grease.
3.3
I n f o r m a t i o n in c h a n n e l i n g p a t t e r n s
The discussion above has shown that, with suitable electron optical conditions, an electron channeling pattern from a large single crystal can be
generated on almost any SEM. A considerable variety of information can be
derived from this pattern, and we shall now discuss the ways in which this can
be done.
3.3.1
Orientation
A channeling pattern provides a view of the symmetry of the crystal lattice
from which it is obtained. Consider, for example, the pattern shown in Fig. 3.8.
It is conventional to describe the detail as being made up of two or more bands
of contrast which intersect at poles. As discussed in the theory section these
bands represent the beam positions at + 6 and — 0 relative to the lattice
plane giving rise to the reflection. If this lattice plane has Miller indices [hkl\
then the band is also called an {hkl) band. The trace of the lattice planes (i.e.
B
B
F i g . 3.8 An electron channeling pattern from the (001) face of GaAs recorded in
backscattered mode at 30 keV.
D.C. Joy
84
their apparent intersection with the plane of the ECP) is parallel to the
direction of the band, and midway between the edges. Consider now another
set of lattice planes with indices (pqr). The angle 0 between the lattice planes
is given for cubic crystals as
1 2
(3.12)
and since the bands are parallel to the traces of the planes from which they
come, this will also be the angle between the bands. The pole defined by the
intersection of the bands has the indices (abc) such that
a*h + b*k + c*/ = a*p + b*q + c*r = 0
(3.13)
The simplest case occurs when the pole is a major symmetry pole, such as that
in Fig. 3.8, which shows the {001} pole of GaAs. This is a four-fold symmetric
pole, and lies at the intersection of two families of bands, each of which shows
four-fold symmetry but lying at 45° to each other. In general a high symmetry
pole will lie at the intersection of low index planes. By inspection the lowest
Miller indices satisfying eqns (3.13) for a {001} pole are (100) and (011) types,
and since from eqn (3.12) the angle between (100) and (110) is 45° this would
appear to support this identification. However, electron channeling patterns
obey the same rules as X-ray diffraction in that not all possible Miller indices
are "allowed reflections". Strong electron diffraction from a lattice only occurs
when the Miller indices satisfy certain conditions which are given in Table 3.1.
It should be noted that while the rules of Table 3.1 are a useful guide, they
are not infallible. In particular, some otherwise "allowed" reflection, such as
the (111) in silicon, the (222) in gold, or the (lOlO) in cobalt, are actually so
weak as to be effectively absent because of dynamical structure factor
considerations. As discussed later this fact can sometimes be used to
distinguish between materials.
Using these rules for G a A s which has an F C C lattice, we can therefore index
the families of bands in Fig. 3.8 as being (200) and (220) type.. The
corresponding 2nd- and 3rd-order reflections will therefore be (400), (600),
T a b l e 3.1
Lattice
Rules for allowed reflections
type
Simple cubic
Body centered cubic
Face centered cubic
Diamond cubic
Reflections
allowed
All
h + k + / = 2n
h, k, I all odd or all even
h, k, I all odd or all even
except /j + fc + / = 4 + 2n
85
Electron channeling patterns
etc. or (440), (660). Which of the bands is which can be distinguished easily
since
2 sin(0 ) = X/d
B
= Wa )V(/i + k + I )
2
hkl
2
2
0
(3.14)
where X is the electron wavelength, d is the spacing of the (hkl) lattice planes,
and a is the unit cell size, so the width of the band (i.e. 26 ) is proportional to
{h + k + I ), thus (220) is wider than (200).
When the orientation is known, as was the case here, then indexing the
pattern is straightforward. In general, however, the orientation is not known
and so a procedure is required which will allow bands and poles to be
identified and the orientation deduced. F o r an arbitrarily chosen orientation
the E C P obtained may have no prominent symmetry feature, or even any clear
band. But if the crystal is tilted or rotated the pattern will change and by
appropriate adjustment of the specimen stage controls it will be possible to
move through the pattern, or follow any chosen line or band. If a large number
of patterns are recorded as the sample is successively tilted then a " m a p " can be
constructed. Starting from a major symmetry pole, such as (100) it will be
found possible only to obtain unique patterns from a triangle bounded by the
orientations (100), (110), (111). Once the patterns within this triangle are
obtained, the pattern from any orientation recorded at the same beam energy
will be found within the triangle, either directly or as a mirror image.
hkl
0
2
B
2
2
This triangle is known as the "unit triangle" and comprises 1/48 of the
stereographic projection of the crystal. All of the symmetry elements of the
crystal appear once inside the unit triangle, which is therefore characteristic of
the crystal. The interplanar angles, and hence the angles between poles, are the
same for all cubic crystals so the dimensions of the unit triangle are constant.
However, because of the operation of the reflection rules given above the poles
which are prominent inside the triangle, and the major bands visible, will
depend on whether the crystal is simple cubic, F C C , BCC or diamond cubic.
Figures 3.9 and 3.10 show experimental maps, together with indexed drawings, for the two most c o m m o n cubic systems encountered in semiconductor
materials. Although the angles between the poles are constant the detailed
appearance of the m a p will depend both on the accelerating voltage and the
lattice parameter of the crystal from which the m a p was made. An increase in
either the accelerating voltage or the lattice parameter will make all the bands
narrower and this has the effect of altering the m a p at all the places where lines
and bands intersect. The maps of two materials of the same lattice type but
different lattice parameter can be made identical by choosing an accelerating
voltage such that (X/a) is the same in both cases. F o r example iron (a = 2.867 A)
recorded at 20keV has a m a p identical to that from niobium (a = 3.33 A) at
15 keV. Since small changes in the lattice parameter do not markedly alter the
m a p this correspondence makes it possible to cover most c o m m o n lattice
F i g . 3.9 A channeling map from copper, an FCC crystal, at 20 keV, together with
corresponding indexed drawing of the map. (Map courtesy of C. van Essen.)
F i g . 3.10 A channeling map from molybdenum, a BCC crystal, at 20keV, together
with the corresponding indexed drawing of the map. (Map courtesy of C. van Essen.)
D.C. Joy
88
parameters with a limited number of maps and an appropriate choice of
accelerating voltage.
Ideally, channeling maps for the materials of interest, and for a range of
beam energies, would be available for use. However, the experimental
generation of maps is a tedious and time-consuming business. Because the
angular range covered by a unit triangle is large (45 x 54°) compared to the
angular width of a typical pattern, many individual exposures must be taken
and montaged to form the final map. The cumulative effect of non-linearities in
the scan and display optics also makes tidy assembly of the m a p a difficult
process. Finally obtaining all the required orientations from a single crystal
can lead to problems with uneven illumination at high tilt angles unless a
hemispherical crystal can be fabricated. Hence the number of good maps
available is low, and for most materials it is necessary instead to resort to a
constructed map.
The electron channeling pattern can be regarded as being essentially the
stereogram of the crystal lattice projected about the optic axis, provided that
the angular width of the pattern is less than 10 or 15°. For larger angles the
pattern is more correctly described as a gnomic projection, but because of the
added complexity this involves it will be assumed here that the small angle
approximation to a stereogram is valid. A m a p can therefore be constructed by
drawing the stereogram and then converting this into the required map.
For cubic crystals a stereogram of any desired size can be drawn using the
procedure discussed by Christian (1956). A pole (hkl) on a stereogram of radius
R has cartesian coordinates (X, Y), relative to the origin (0,0) representing the
pole (001), given by
X = RH/{\ + L)
Y=RK/(\
+L)
(3.15)
and HKL are the normalized Miller indices
if =fc/V(fc + fc -h/ ) etc.
2
2
2
(3.16)
As an example let us construct a m a p for silicon. For a 100 cm radius
stereogram, the (001), (011), (111) unit triangle has its vertices at the
coordinates
{hkl)
(001)
(011)
(111)
(X, Y) cm
(0,0)
(0,41.42)
(36.6,36.6)
For silicon the reflection rules discussed above predict that the low-order
reflections will be (220), (222), (311), (400), (420) etc. F r o m eqn (3.13) the (011)
and the (001) poles both lie on the (400) band, while the (001), (011) and (111)
poles can all lie on 220-type bands, (001) and (111) on a (220) band, and (111)
89
Electron channeling patterns
and (011) on a (022) band. Other possible poles in the m a p can be found simply
by noting that if poles (hkl) and (pqr) both lie on a band then the pole (abc\
where
a = h + np
b = k + nq
(3.17)
c = l + nr
and n is an integer (0,1,2,...), also lies on the same band. Thus (112) lies
between (001) and (111), (122) lies between (011) and (111), (012) between (001)
and (011) and so on. Using eqns (3.15) and (3.16) the position of these poles can
also be drawn in, and the other bands passing through them identified from
eqn (3.13), to give a labeled stereogram such as that shown in Fig. 3.11a.
To give an impression of the E C P m a p each reflection must be converted
into the corresponding band of width 20 by drawing lines at ± 9 about the
reflection. If this m a p is to be for 20keV operation, then the electron
wavelength X is given as
B
B
X = 1 2 . 2 6 / [ £ ( 1 + 0.98 x 1 ( T £ )
1/2
6
1 / 2
] A
(3.18)
where the electron energy E is in eV. So at 20 keV k is 0.086 A giving 2 0 as
2.56° for (220)-type bands, 3.63° for (400)-type bands and so on. The linear
scaling in degrees per centimeter is not constant for a stereogram, but a local
value can be used. Thus for the (220) band between (001) and (111), the angle
between the poles is 54.7° (from eqn (3.12)) while the linear distance between
them is 51.74 cm. Hence the approximate scale factor is 1.05 degrees/cm and so
the (220) band should be drawn 2.6 cm wide. An identical procedure is followed
for each of the other reflections to give the final m a p shown in Fig. 3.11b.
When an experimental channeling pattern, and either an E C P m a p or a
constructed m a p appropriate to the crystal is available, then the orientation
represented by the pattern can rapidly be found by matching the pattern with
the m a p until an identical configuration, or its mirror image, is found. The
center of the u n k n o w n pattern, which represents the direction of the surface
normal, can then be marked on the map. Since in general this will not be a pole,
the orientation can be specified by measuring the angle between the surface
normal and the nearest major poles. Provided that reasonable care is taken it
has been found possible to establish orientations to an accuracy of better than
1° (Joy etaU 1971).
For crystals known to be outside of the cubic system a technique similar in
principle to that described above can be employed. However, the difficulties
become very much greater as the symmetry of the crystal is reduced because
the size of the unit triangle increases. For example for a tetragonal material it
will be necessary to generate or construct a m a p covering the quadrant
bounded by (001), (010), (100), which is a spherical triangle of 90° on each side.
Any m a p of this size constructed by assembling a large number of E C P s will be
seriously distorted and in practice it is therefore better to make several smaller
B
90
D.C. Joy
(011)
(012) (013)
(001)
(a)
Fig .3.11 (a) A labeled portion of the stereographic projection of silicon, and (b) the
corresponding map constructed from the stereogram.
maps centered about major poles. The difficulty of this procedure increases
greatly as the symmetry decreases and for non-orthogonal lattice systems the
work involved may be too great. Even the option of constructing the m a p by
computation is made more difficult because the large angular range required
makes the simple stereographic projection approximation invalid. However,
Electron channeling patterns
91
computer programs for the generation of a general channeling m a p have been
described (Vale, 1985), and an analytical approach has been given by Newbury
and Joy (1971). Fortunately in the context of semiconductor studies these
problems are only of limited concern since most materials of interest are cubic.
Orientation determinations using E C P s are both rapid and accurate. Since
the pattern appears directly on the viewing screen of the SEM it is often
possible, in fact, to identify the orientation visually without the need for any
more detailed analysis. In addition this technique has two very special
advantages not possessed by other comparable methods. Firstly, because the
E C P is generated by scanning the beam over the crystal the pattern contains
both crystallographic and spatial information. Since there is a one-to-one
correspondence between the beam position on the specimen, the spot on the
display screen and the angle of incidence, local changes in the crystallographic
orientation will show up as regions of discontinuity in the pattern on the
screen. The size and position of these regions can be directly inferred from the
known magnification of the SEM. A high-angle boundary, such as a grain
boundary, will be obvious and the relative orientations on either side of it can
be measured using the techniques described above. The misorientation across
a low-angle boundary, can be very accurately measured by noting the offset of
lines and bands as they pass across the boundary. The accuracy of this
procedure is limited only by the beam convergence angle and the general
F i g . 3.12 Channeling patterns from polycrystalline silicon showing both topographic and crystallographic contrast.
92
D.C. Joy
k
200M
F i g . 3.13 Channeling pattern recorded across a mesa-type transistor on a silicon
substrate.
quality of the lattice, and offsets as small as 0.1° have been measured.
Figure 3.12 shows an example of this type of application to a sample of
commercial polycrystalline silicon. Several large grains fall within the field of
view, each of which is delineated both by the topographic contrast at the grain
boundaries and by the individual E C P that it produces. Conversely, the
absence of such effects can be taken as proof that the whole area scanned is of
uniform orientation. E C P s therefore provide an excellent and rapid way of
evaluating the success of crystal growth techniques. An example of this type of
operation from a silicon wafer on top of which have been grown silicide mesastructure diodes is shown in Fig. 3.13. The image shows both the channeling
pattern and the normal topographic contrast from the mesa-diode. It can be
seen that the channeling band runs across the mesa with no bending or offset,
so proving that the silicide orientation is identical to that of the substrate.
A second notable advantage is that, as seen above, E C P contrast comes only
from a shallow region at the surface of the specimen. Unlike the X-ray case it is
therefore possible to determine the orientation of even a very thin epitaxial
film without any interference from its substrate (e.g. Vicario et al, 1971;
Brunner et al., 1978).
93
Electron channeling patterns
3.3.2
Lattice parameter determinations
It should clearly be possible to use an E C P to deduce the lattice spacings of a
crystal. Since the angular width of the bands is 2# , a knowledge of the incident
beam energy will enable the lattice spacing d to be found from eqn (3.1), and
if the bands are self-consistently indexed (that is to say assigned indices
consistent with the choice of poles in the unit triangle), the lattice parameter
can then be deduced. T h e absolute accuracy with which this can be done is
limited by two principal factors:
B
hkl
(a) the width of the bands displayed on the screen has to be coverted to an
angular value by a suitable calibration; a n d
(b) the electron wavelength (i.e. the true incident beam energy) must be known
accurately.
In practice, distortions a n d non-linearities in the scanning display circuits
set a limit of a few per cent to the accuracy of any calibration, while the
indicated accelerating voltage can be systematically in error by 3 - 5 % since on
many SEMs the value shown is for the grid rather than the filament of the
electron gun. Although these errors can be reduced by taking care to calibrate
the system before use on a well-charaterized crystal, the residual errors are still
of the order of 1 or 2% which is at least 100 x worse than can be achieved by
conventional X-ray methods, or by the Kossel pattern technique discussed
below.
While the accuracy with which the absolute value of a lattice parameter can
be determined is poor, the precision with which relative changes in parameter
can be found is higher. This is important in many semiconductor applications
where actions, such as ion implantation or doping, may cause a small change
in the lattice parameter which may need to be determined. The procedure is to
compare under identical conditions the patterns from crystals differing only in
their lattice spacings, for example by examining the position of given lines in a
pattern on either side of a boundary. If the lattice parameter on the two sides of
the boundary is different then all the lines in the pattern will have shifted. The
angular amount, d#, of the shift will depend on the change in lattice parameter,
da, a n d the Miller indices of the line. F r o m eqn (3.1)
sin (0 ) = A/2d
B
where d
result
hkl
= (A/2a)V(/i + k + I )
2
hkl
2
2
(3.19)
is the spacing of the hkl planes. Differentiation of eqn (3.19) gives the
S0 =
tan(0 )(8a/a)
B
(3.20)
so the angular shift is proportional to the fractional change in lattice
parameter, a n d the tan of the Bragg angle for the line followed. Clearly the
94
D.C. Joy
B
F i g . 3.14 Fine structures in the (111) pole of diamond at (a) 25 keV and (b) 30keV.
sensitivity of this method depends very much on 9 . F o r low-index lines, where
9 is of the order of 1°, a lattice parameter change of 1% would only cause a
shift of about 5 x 10 ~ rad, which is about the width of the line itself. However,
if a high Miller index line can be found then the sensitivity will be enhanced
because of the tan (9) factor.
B
B
3
Electron channeling patterns
95
Lines of high index may be found in the centers of major poles. Figure 3.14a
shows an enlarged view of the (111) pole of diamond. The bright center of the
pole is crossed by a fine structure of dark lines. Even a small change in
accelerating potential, as in Fig. 3.14b, is sufficient to significantly change the
pattern. A method for the indexing of these lines, which come from high-index
poles lying close to the major pole, has been given by M a d d e n and Hren (1985).
F o r the (111) pole at around 25keV, for example, indices such as (751), (771)
and (375) are visible. Since these have Bragg angles which are four or five times
that of the (220) bands forming the (111) pole, these fine structure lines are ideal
for examining small ( < 1%) changes in lattice parameters.
3.3.3
Microanalysis
It was shown earlier that reflection rules, resulting from the crystal structure,
govern which lines in a pattern are actually visible, although this result may
also be modified by dynamical diffraction effects. This may sometimes be used
beneficially as a simple type of microanalysis. A c o m m o n situation in
semiconductor technology is to work with materials which are "lattice
matched", that is they have the same lattice spacings and orientations. An
example would be a heterostructure laser where lattice-matched I n P and
G a A s I n P are used. Since these materials have identical lattice parameters and
orientations their channeling patterns will be very similar, but not necessarily
identical. Figure 3.15 shows patterns lattice matched from I n P and G a A s I n P
at the same beam energy. While most of the features are replicated it is clear
that in one case (400) is the lowest reflection while in the other both (200) and
(400) lines can be seen. The two otherwise identical materials can therefore be
distinguished from their channeling patterns.
3.3.4
Crystal perfection
The quality of the channeling pattern, defined by its angular resolution and its
contrast, is a sensitive function of the state of the crystal. Although this
technique is of most use when applied to small selected areas of crystals, and
will be considered more fully later on, it has been used for large single crystals.
F o r example, ion irradiation of crystals such as silicon wafers produces a
marked change in the quality of the pattern (Davidson, 1970: Wolf and
Hunsperger, 1970; Schulson and Marsden, 1975; Yoshida et al, 1978). This is
illustrated in Fig. 3.16 which shows the appearance of the E C P from an area
the right-hand side of which has been irradiated with a dose of 7 x 1 0 Ne
ions at 80 keV. The pattern rapidly deteriorates as it moves into the region
which has been damaged by the ions. The observed pattern quality can be
1 4
+
96
D.C. Joy
InPGaAs
F i g . 3.15 A comparison of the channeling patterns at 30 keV from lattice-matched
InP and InPGaAs.
calibrated in terms of the radiation dose received, and this calibration can then
be used to study the variation of dose with depth or position in other crystals.
In this respect it is useful that E C P contrast information comes from only a
thin layer of the specimen surface since by sectioning, or repeated chemical
removal of the surface the depth distribution of damage can be unambiguously
determined. This is illustrated in Fig. 3.17 which plots the depth distribution of
damage caused by different fluxes of N e ions at 80keV. Each experimental
point on the figure was obtained by obtaining an E C P from the irradiated area
after a known a m o u n t of material had been etched from the surface. The
pattern quality was rated on a scale of 0 - 5 , with 5 being a perfect (undamaged
+
F i g . 3.16 ECP from an area containing an interface between normal silicon and
silicon irradiated with 80keV Ne ions at a flux of 7 x 1 0 per cm . The bright circles
are from the Schottky barriers.
14
2
s i , 80kev Ne
+
PERFECT CRYSTAL
>- 5
H
< 4
CL
3 x10
\
\
o
14
2
500
2000
2500
1500
1000
DEPTH (A)
F i g . 3.17 Depth dependence of radiation damage caused by ion bombardment as
deduced from observation of ECPs from irradiated areas.
98
D.C. Joy
crystal) pattern, and 0 being no pattern at all. Although this approach is
subjective, it is rapid and produces surprisingly detailed information. M o r e
quantitative approaches for the determination of crystal perfection are
described in a later section of this chapter. It should finally be noted that
because the pattern comes from the near-surface region, its quality is very
dependent on the surface preparation of the specimen. Hence the E C P quality
is a sensitive test for surface cleanliness and freedom from damage.
3.4
Channeling
micrographs
When a large single crystal is viewed at low magnification we have seen that an
E C P is produced because of the large included angle of scan. As the
magnification setting of the microscope is increased the angle of scan falls
proportionally and the pattern will spread out a r o u n d the center of the screen.
At a high magnification, therefore, the screen will appear to be uniformly
illuminated with a brightness level equal to that found at the center of the
original pattern. If the crystal were now tilted so as to change the pattern then,
at high magnification, the contrast level on the screen would also change to a
value appropriate to the new level at the center of the new pattern.
Alternatively, if the beam is allowed to scan across not a single crystal but a
material containing grains of different orientation, then each grain in the
micrograph image will show a uniform grey contrast with a level appropriate
to the value that would be found at the center of a channeling pattern taken
from that grain. In general, therefore, each grain will have a different grey level
relative to that of its neighbors. Similarly any change in crystallography within
a grain, such as a twin or a subboundary, will show up as a difference in
brightness in the image.
Figure 3.18 shows a micrograph taken in this mode of operation. The
sample is a thin film of silicon on top of a thick layer of silicon dioxide. The
silicon film was recrystallized from polysilicon by the action of a high-power
strip heater moved over the surface (Pfeiffer et a/., 1985). The channeling
micrograph clearly reveals the complexity of the resultant crystal structure.
Large grains, stretching parallel to the track of the heater motion are evident,
but each large grain also contains a complex array of smaller grains, probably
due to polygonization of defect arrays during recrystallization. The fact that
such crystallographic effects can be made visible without etching the sample
makes this technique very suitable for studies of crystal growth and annealing
since changes can be followed in situ in the SEM.
The conditions are the same as those for the production of a normal
channeling pattern, that is a collimated beam and adequate beam current, but
in addition a small probe size is required to achieve an acceptable micrograph
Electron channeling patterns
99
F i g . 3.18 Channeling micrograph from a thin film of silicon, regrown from
amorphous silicon by a strip heater, on a substrate of silicon oxide.
resolution. Since the pattern itself is not being observed the beam collimation
need not be as high as for E C P observation, and a larger value of a will permit a
smaller probe size while still maintaining the same probe current. Typically the
necessary conditions can be obtained by selecting the final beam-defining
aperture so as to produce a beam convergence angle of a few milliradians, and
selecting a spot size which then produces the necessary level of current. The
channeling contrast produced will still only be of the usual 5% level, so black
level contrast expansion will be required. Since this will also have the effect of
increasing the visibility of other contrast effects, such as topography, it is
desirable to chemically, or electrochemically, polish the sample to give a
macroscopically smooth, flat and clean surface. However, in almost all
circumstances some residual contrast will remain which could be confused
with the channeling effects. The channeling contrast component can readily be
distinguished from other mechanisms by tilting the sample through a small
angle (1 or 2°), or by translating the area of interest from one corner of the
screen to the diametrically opposite one, and observing the result. Effects such
as topographic or atomic number contrast will remain unchanged by such
minor perturbations, but any channeling contrast will change as the beam
incidence angle is varied by the tilt or translation and the relative brightness of
adjacent grains will alter.
Channeling micrographs add a new dimension to the information supplied
D.C. Joy
100
by the SEM, and the technique is readily available on any instrument on which
the beam collimation can be controlled. With a convergence angle of a few
milliradians changes in crystal orientation as little as 0.1° can be detected. The
technique therefore has many obvious and valuable applications in studies of
crystal growth and perfection. The limitation of the method is that it cannot
provide any direct information about the magnitude of the angular offsets
made visible. F o r this a method of obtaining channeling pattern information
from small selected areas is required.
3.5
Selected area channeling patterns ( S A C P )
Although the channeling micrograph m o d e of operation is a valuable one in
the information it supplies about local changes in crystallography, the results
are not capable of quantitative analysis. This is only possible where an actual
channeling pattern is produced since the detailed data about crystalline
orientation and state is deduced from the geometry and quality of the pattern.
With the E C P technique described above, however, patterns can only be
produced from large single crystals because the beam must scan through a
large angle to produce the pattern. Since the channeling contrast arises solely
from changes in the angle of incidence of the beam it is clear that the same
pattern would be produced if no scanning action occurred but instead the
beam "rocked" about a point on the specimen surface. In this case the full
range of incident angles would still be scanned but because there is no lateral
displacement of the beam the pattern would come from an area of the
specimen ideally equal to the diameter of the incident beam. This is the desired
selected area channeling pattern (SACP) technique.
There are several ways of achieving the rocking condition, although in every
case the beam conditions will, of course, be the same as those described above
for generating E C P s and channeling micrographs. That is to say we require a
beam with a collimation of a few milliradians, a probe current of at least
10" A, and a spot diameter of 1 /mn or less.
A direct way of achieving a rocking beam condition would be to hold the
beam fixed and mechanically rock the sample, about the two axes perpendicular to the beam, in such a way that the point on the specimen surface
under the beam remained stationary. If the display CRTs were scanned
synchronously with the mechanical motions then an S A C P would be
produced. This type of device offers electron-optical simplicity and the ability
to tilt the sample through very large angles (up to 90°). The disadvantage is
that precise mechanical design and construction is needed to hold the sample
exactly at rest during the rocking motions. While stages of this type have been
constructed and used (Coates, 1967; Brunner et a/., 1975; Brunner, 1981) it has
9
Electron channeling patterns
101
generally been considered that mechanical problems are less easy to solve than
electron-optical ones, and so most SACP systems use an alternative approach.
The most usual form of scan system in the S E M is the double deflection
method. In this we have two sets of scan coils, the first of which deflects the
beam off-axis by some angle 0, and the second which deflects the beam in the
opposite sense so that it once again crosses the optic axis. Clearly all the
scanned rays pass through one point on the axis. U n d e r normal scan
conditions this point is well above the specimen surface (in fact at the level of
the final aperture) so as to produce a large raster square for any given scan
angle. However, it is clear that by appropriately adjusting the strength of the
second set of coils the scan crossover point could be brought down to the
specimen surface. The incident beam would then rock about that point and
produce an SACP. This approach has been used on several types of instrument
(van Essen and Schulson, 1969; Schulson et al, 1969), and used commercially
on instruments by E T E C and J E O L . While it is easy to apply the minimum
area attainable it is not very small, a value of 50 pm diameter for a rock angle of
10° being typical. The reason is that scan coils are not, in general, precision
components and consequently the scan crossover is not the idealized point,
but a rather larger disc.
The defects of the double deflection system are overcome by the method due
to van Essen et al (1970). The operation of this can be understood from
Fig. 3.19. Figure 3.19a shows the ray diagram of a simple lens. All the rays
leaving the object point O are collected by the lens, deflected, and pass through
the image point I. The object and image points are said to be "conjugate" in
this condition. While we normally understand this type of diagram as implying
that all of the rays are present at one time, this is not necessary. The conditions
shown in Fig. 3.19b would be just as valid. In this any particular pencil of rays
passing through the object point, at some angle to the axis, is deflected by the
lens, just as above, so that it too passes through the image point. If the ray
pencil is kept on the axis of the lens, but a set of scan coils is placed at the object
point, as in Fig. 3.19c, then as the coils deflect the beam about the axis at the
object point, the ray pencil will rock about the conjugate image point. This is
the desired S A C P condition. While the end result is the same as that achieved
by the double deflection condition, a lens is a much better optical component
than a scan coil and consequently the precision with which the rocking beam
can be held at a fixed point is higher. This configuration is now available on
almost all commercial SEMs, and many T E M / S T E M instruments.
In the S E M the normal scan coils and objective lenses are used. F o r normal
imaging the ray paths are as shown in Fig. 3.20a. The crossover from the
preceding condensor lens occurs at point a before the upper scan coil, which
deflects the ray pencil off-axis at point b. The lower scan coil deflects the rays
back across the axis at the final aperture position c, while the objective lens is
(a)
(b)
(c)
Fig . 3 . 1 9 Generating a rocking beam pattern for selected area channeling patterns,
(a) Ray paths in a simple lens, (b) ray pencils passing through the lens, (c) rocking action.
(A)
©
©
F i g . 3.20 Ray diagrams for micrograph and SACP operation in an SEM. (a)
Normal micrograph operation, (b) SACP operation before final focusing, (c) optimized
SACP settings.
Electron channeling patterns
103
set so that the specimen surface S is conjugate with point a, so as to produce a
focused probe. If now the lower scan coil is turned off (Fig. 3.20b), then the
probe will still be in focus on the surface, but the rays deflected by the upper
scan coil will be brought back on to the axis by the lens as described above.
(Note that the aperture at c must now be removed, since it will prevent the
wide-angle rays from passing through, and be replaced by a suitable aperture
below the condensor lens.) Because points a and S are conjugate the "rocking"
point will be below the surface of the specimen. If now (Fig. 3.20c) the lens
excitation is adjusted so that b and S are conjugate then the rocking point will
fall on the surface. At the same time, in order to maintain a focused probe, the
condensor lens excitation must be weakened so that its crossover occurs at the
scan point b. N o w with the lower scan coil off an S A C P rocking beam
condition is achieved, while with the lower scan coil on a normal focused
image will be obtained.
Setting the S E M u p in this m o d e experimentally is straightforward, as
shown in Fig. 3.21. With both scan coils in operation a normal image, as
shown in Fig. 3.21a is obtained and focused at medium magnification, say
x 500. The normal final beam-limiting aperture is removed and replaced by
a suitable aperture above the scan coils. When the lower scan coil is turned
off and the magnification is set to the lowest value available, typically x 20,
the image becomes as shown in Fig. 3.21b. Because the beam is rocking
about a point that is not on the sample surface, some scanning still occurs
and so a somewhat distorted image, usually framed by the shadow of the
limiting aperture, is obtained. As the excitation of the objective lens is
increased the rocking point of the scanned rays moves towards the specimen
surface. The closer this point is to the surface the smaller the area scanned
on the specimen. Since the image magnification in an S E M is defined as the
ratio of the area scanned on the display screen to the area scanned on the
specimen, changing the lens current will cause the apparent magnification
of the image to increase (Fig. 3.21c and d). When the scan rocking point is
exactly on the sample surface then the scanned area should be zero and the
magnification would be infinite. The nearest approach to this condition is
seen in Fig. 3.21e, the magnification is now so high that the grid square has
expanded to the edge of the field of view and the selected area channeling
point from the silicon wafer under the grid is visible. If the lens current is
increased still further (Fig. 3.21f), the rocking point will move above the
surface, the magnification will again start to fall, and the image will invert
through 180°. With a suitable guide, such as a fine mesh grid or a particle
of dust, on the surface of the specimen the correct setting for the objective
lens can rapidly be found by adjusting the lens excitation for maximum
apparent magnification. When the S E M is in S A C P mode the appearance
of the image is very sensitive to the alignment of the column. Thus, if the
104
D.C. Joy
i
I
t
i
B
*
I.
t
f
d
**
\
F
F i g . 3.21 Experimental set-up for SACP operation, (a) Normal micrograph showing target area, (b)-(f) through focus series in single deflection mode. Optimum SACP
condition is at (e).
image does not expand about the center of the screen, or if there is obvious
asymmetry in the image, the mechanical and electron-optical alignment of
the lenses and cleanliness of the column liner and apertures should be
checked. Switching from one mode to the other will generally require some
small adjustments to optimize performance in both the S A C P and image
condition. In the SACP mode varying the condensor lens will affect the
sharpness of the pattern, i.e. the beam collimation, while in the normal image
mode adjustment of the condensor will change the probe focus. Note, however,
that once the rocking point has been set up on the specimen surface all such
focusing adjustments should be carried out using the condensor lens only.
The minimum area from which the SACP can be obtained is invariably
larger than the probe size, because the spherical aberration of the lens causes
the rocking point to move a r o u n d on the surface. The diameter of the
Electron channeling patterns
minimum selected area, d
m i n
105
, is given as
4nn = 0 . 5 C a m m
(3.21)
3
s
where C is the spherical aberration coefficient of the lens (in mm), a n d a is
the rocking angle (in rad). F o r a rock angle of 0.1 rad (about 5°), a n d C of
10 m m which is typical for an S E M lens operating at a working distance of
a few millimeters, then d
would be 5 x 1 0 " m m or 5 / a n . Clearly d
depends on both the rocking angle a n d C . T o achieve the smallest possible
areas C m u t be minimized. This is done by running the lens at the highest
possible excitation, which in turn requires placing the specimen as close to
the lens as possible. Since d
varies as a the area can also rapidly be
reduced by lowering the rocking angle, which can be done by increasing the
indicated magnification of the SEM. A 20% increase in magnification using
the "zoom" control will reduce the selected area by nearly 60%. O n current
state-of-the-art instruments where C values of a few millimeters are possible,
areas as small as 1 /mi are attainable, a n d still smaller selected areas can be
achieved by dynamically correcting the focus of the lens to compensate for
the spherical aberration (Joy a n d Newbury, 1972; Nakagawa, 1985).
s
s
3
min
min
s
s
3
min
s
3.6
Using selected area channeling pattern
3.6.1
A p p l i c a t i o n to microcrystalline orientation
In an earlier section the way in which an E C P could be used to determine
the orientation of a crystal was discussed. T h e procedures for finding t h e
orientation of a n area using SACPs are essentially identical, although n o w
the information is coming from a n area which may be only a few micrometers
in diameter. An example of the power of this approach is shown in Fig. 3.22a
which shows a laser track about 10 fim wide drawn across a poly silicon layer
about 1 fim thick deposited on a silicon substrate. The question as to whether,
or not, the melting induced by the laser beam has resulted in the recrystallization of the polysilicon is rapidly answered by taking an S A C P from some
point along the track region (Fig. 3.22b). A clear channeling pattern is seen
showing that the polysilicon has indeed recrystallized. Patterns taken at other
points along the track indicate that the entire irradiated line has a n almost
constant uniform orientation, so forming a long, thin crystal. A second
example of the value of the S A C P technique is shown in Fig. 3.23a a n d b,
which are selected area patterns from the thermally regrown silicon on oxide
layer shown in Fig. 3.18. In the channeling micrograph mode of operation
it could only be determined that there were angular offsets between adjacent
grains in the regrown film. Using the S A C P technique this information can
106
D.C.Joy
Si
F i g . 3.22 (a) Image of laser track in amorphous silicon and (b) SACP from track
region.
now be made quantitative. In Fig. 3.23a the pattern has been taken from a
region straddling a boundary. Consequently two similar, but displaced, (100)
patterns are seen. The angular separation between similar features can be
measured to give the mismatch across the boundary as being 1.5°, with the
tilt along the (220) direction. A similar analysis can rapidly be made for any
other boundary. Figure 3.23b shows a slightly different situation in which the
selected area has been deliberately increased, by defocusing the objective
lens, so that patterns are obtained across many grains. A well-defined (110)
Electron channeling patterns
107
F i g . 3.23 SACPs across boundary regions in thermally regrown silicon on oxide,
material of Fig. 3.16.
pole pattern is still obtained on this particular sample, but the edges of the
bands are serrated. Each time the beam crosses a boundary the orientation
tilts back by about 0.5°, thus the surface normals of the grains are distributed
in orientation about a common (110) axis.
In many cases it is necessary to be able to specify both the orientation of
the surface normal, and some direction in the plane of the crystal. In an E C P
this is readily done because the channeling contrast is superimposed over
the normal topographic contrast images, and so the direction of edges or
other features can readily be found by comparison with the pattern. In an
SACP no clear image information is present because of the high distortion
associated with the spherical aberration of the lens at the rocking condition.
There is also no simple relation between the direction of a band, relative to
the XY axes of the display screen, in the S A C P and the position of a feature
such as a boundary, relative to the same XY axes, in the image mode. This
is because there is a rotation of the image between the two modes of operation
due to changes in the lens excitations, and switching off the lower scan coils.
It is therefore necessary to know how much rotation has occurred, and in
what sense, before the SACP pattern can be correctly associated with the
image (van Essen and Verhoeven, 1974; Joy and Maruszewski, 1975;
Davidson, 1976). This is done by using a large single crystal, and mechanically
tilting and rotating it so as to produce an E C P with just one major band lying
along either the X or the Y axis of the display. O n switching to S A C P mode the
same pattern will be seen, but rotated through some angle. The magnitude and
sense (clockwise or anti-clockwise) of this rotation must then be measured as a
function of the working distance of the objective lens for the whole range of
D.C. Joy
108
interest, and for all the accelerating voltages normally used. Rotations of the
order of 30-50° are commonly found.
3.6.2
S t u d i e s of crystalline perfection
The applications so far discussed depend on the geometry of the pattern
only, and give information on the lattice type, parameter and orientation.
The other main class of information provided by a channeling pattern relates
to the degree of perfection of the crystal lattice. As shown schematically in
Fig. 3.24 the "quality" of a channeling pattern can be quantified in terms of
two parameters, the resolution (angular width) of a given line, and the contrast
C [ C = ( 7 - / ) / / ] of some feature in the pattern. Which of these
parameters varies depends on the nature of the disturbance to the lattice.
If the crystal is under elastic strain, or contains line defects, such as
dislocations or stacking faults, then the lattice planes will be bent. F o r
example, within a few lattice spacings of the center of a dislocation this
bending is quite high, as much as 1 0 " rad, but even at many hundreds of
lattice spacings away the distortion relative to a perfect lattice may still be
1 0 " rad. Therefore, when an SACP is recorded from an area containing
many such defects the lattice orientation varies from one region to another
by the amount of the local bending. The result of this is that the width of
lines in the pattern will also be broadened as the pattern is averaged across
m a x
m i n
m a x
2
3
BS SIGNAL
!
RESOLUTION = 80
ANGLE
F i g . 3.24 Definition of quality parameters for studies of lattice deformation in
SACP technique.
Electron channeling patterns
109
F i g . 3.25 Effect of strain, from junction region of heterostructure laser, on lines in
SACP from InPGaAs.
the range of orientations. The higher the defect density in the area examined,
the greater the magnitude of the broadening will be. If all of the defects are
aligned, or if the strain is uni-axial, then broadening will only be observed
in one direction, that is for lines from lattice planes with normals perpendicular to the defect or strain direction. Figure 3.25 shows an example of this
in the (440) line in I n P G a A s . In Fig. 3.25a the line in normal, unstrained
material is shown, while in Fig. 3.25b the corresponding line recorded under
identical conditions but from a region of strained material surrounding a
laser device is shown. The marked increase in width is obvious. However,
after plastic deformation when many different slip systems may have been
activated, broadening will be observable on all lines. Figure 3.26 shows an
example of this for the epitaxial growth of C a F on silicon. The pattern
shown has been taken from the angle-lapped interface region between the
two materials. The continuity of the pattern across the interface shows the
materials to be epitaxial, but the distorted and broadened lines on the calcium
fluoride side of the interface show that material to be in a state of strain as
a result of the interface formation.
F o r many purposes only a qualitative feel for the magnitude of the strain
is required. In a typical experiment (Davidson, 1977), a tapered tensile
2
D.C. Joy
110
Interface
Si
CaF,
Epi
|
Substrate
F i g . 3.26 Pattern across an angle-lapped interface between epitaxial C a F and
silicon.
2
specimen of an annealed polycrystal was deformed. The taper provided a
range of final deformations for a uniform starting condition. Patterns were
then obtained from regions of the sample with a common strain value, 0.5%,
1%, etc. These were then used as a calibration series for the study of the
strain present around the tip of a crack. By comparing the SACP from the
crack region with the calibration sequence the approximate local strain could
be deduced. While the accuracy of such a procedure is limited because of its
subjective nature, it is rapidly performed, and provides data that are very
difficult to obtain by any other approach.
Quantification of this effect requires an accurate measurement of the line
profile. This cannot easily be done visually from a photographic image because
the determination of the edge of a line is a difficult process that depends on
many extraneous factors such as the contrast of surrounding features. Instead
Electron channeling patterns
111
the data should be digitized, either off-line from the photograph, or on-line
using analog-to-digital signal conversion, and subsequent computer analysis.
Measurements of this type show that there is a general relationship of the
form
pattern resolution = constant x (dislocation d e n s i t y )
exponent
(3.22)
where the pattern resolution is in radians, the dislocation density is in
threading number per square centimeter, the exponent is typically of order
0.5, and the constant is of order 10 ~ . This implies that defect densities in
the range from about 1 0 to 1 0 should provide useful data. In principle,
therefore, the S A C P technique provides a way of measuring defect densities
without the need to thin the sample for T E M observation. Some caution
must be applied in interpreting such data, however, because the channeling
contrast comes from a relatively shallow surface region and the defect density
here may not be representative of that in the bulk of the sample. However,
in many applications such as the study of wear (Ruff, 1976) this surface
sensitivity is an advantage.
8
1 0
1 3
If the distortion of the lattice planes is comparable with, or exceeds, the
Bragg angle then the electrons can no longer channel but instead are scattered
and form part of the background to the signal (Davidson and Booker, 1970).
As a result the contrast of the signal will fall, although the resolution of the
pattern may be unaffected. Such a situation occurs when a region of the
sample is, or is made, amorphous. Figure 3.27 shows the SACP from a region
of a GaAs wafer covered with a 30nm-thick gold Schottky barrier. In the
SACP signal, collected here in EBIC mode, the channeling pattern from the
underlying silicon is still evident, but at a much reduced contrast to that
from the region outside the gold layer. Note, however, that the line widths
are essentially unchanged. Channeling patterns therefore allow regions which
are deformed or strained, to be distinguished from those which are a m o r p h o u s
in a straightforward manner. Because the contrast of a pattern is low to start
with, a m o r p h o u s regions which are too thick will obliterate all traces of the
lines, typically layers up to about 500 A at 4 0 k e V will allow contrast to
be observed. O n the other hand surface films as thin as a few tens of angstroms
will give a detectable fall in contrast.
In some instances, as, for example, in ion implantation, both line broadening
and a fall in contrast may be observed. At the surface the implantation may
give rise to thin a m o r p h o u s layer and a loss of contrast, while at greater
depths static disorder will produce line broadening. It is typical of damage
of this type that it varies rapidly with depth beneath the surface. Some
information about the depth distribution can be obtained by comparing
patterns recorded at different beam energies, since the contrast information
depth is about linearly dependent on beam energy. Thus a pattern recorded
112
D.C. Joy
F i g . 3.27 SACP from silicon including the Schottky barrier region which is covered
with a 30 nm layer of gold.
from silicon at 5keV is carrying information mostly from the top 15nm,
while at 30keV the contrast will come from about 100 nm.
Finally individual defects, such as dislocations can be imaged in the SEM
using channeling contrast, because as seen above each defect is surrounded
by lattice planes which are bent. In channeling micrograph a single dislocation
in an otherwise perfect crystal should show up as a line of contrast. However
the electron optical conditions needed to achieve this are very stringent
because the extent of the lattice distortion around each defect is limited.
Typically a probe diameter of 2 0 - 3 0 nm is required with a beam convergence
of a few milliradians, together with the normal incident beam requirement of
a few n a n o a m p s (Spencer et al, 1972). As can be seen from an application
of eqn (3.11) this requires an electron source much brighter than conventional
tungsten or L a B thermionic emitters. Cold field emission sources do have
sufficient brightness, and individual defects have been directly imaged in an
S E M using such a source by Morin et al (1979). While it would be true to
say that such experiments are technically very difficult, with the advent of
6
Electron channeling patterns
113
commercial, high-performance, field emission S E M s this technique may prove
to be of significant value.
3.7
Other techniques for S E M crystallography
While the electron channeling technique provides the most convenient and
widely used way of obtaining crystallographic information in the SEM, two
other techniques should be mentioned.
3.7.1
Electron backscattering patterns
If an electron beam is allowed to strike an a m o r p h o u s sample at normal
incidence, then the angular distribution of backscattered electrons is a cosine
function a b o u t the surface normal (Fig. 3.28a). If the a m o r p h o u s sample is
now replaced with a crystal then (Fig. 3.28b) the general form of the
distribution remains the same, but it is modulated in magnitude at certain
angles (Laponsky and Whetten, 1959). These correspond to the Bragg angles
of backscattered electrons diffracted by the lattice as they exit from the lattice
(Alam et al, 1954). The backscattered emission pattern therefore contains
contrast features which reflect the symmetry and orientation of the crystal
lattice. A photographic plate, or a fluorescent screen, placed above the sample
would be able to display this pattern directly. However, at normal incidence
the contrast and visibility of the pattern is poor because the backscattered
electrons have a wide range of energies as they leave, and consequently each
lattice plane produces a spread of Bragg angles. If, however, the specimen
is tilted so that the beam strikes the specimen at nearly glancing incidence
(Fig. 3.28c) then in the specular reflection direction the backscattered electrons
all have energies close to that of the incidence beam (Wells, 1976; Newbury
et a/., 1976). The Bragg angles for each set of lattice planes will therefore be
well defined, and the pattern is readily visible on a suitably positioned viewing
screen.
Backscattered patterns are thus a useful tool for the study of microcrystals.
The pattern information will come from the beam interaction volume, which
for backscattered electrons in a material such as silicon will be of the order
of 1
in diameter, so obtaining a small selected area is simple. Unlike the
E C P technique the beam convergence is not important, so standard optimized
imaging conditions can be used, the only requirement being that the
backscattered signal be strong enough to produce a visible, or photographically recordable, image. A final benefit is that the pattern covers a wide
angular range, permitting a significant fraction of the stereographic projection
114
D.C. Joy
J INCIDENT
t BEAM
F i g . 3.28 Electron emission profiles from (a) amorphous and (b) crystalline
materials, and (c) the geometry for the production of electron backscattering (EBSP)
patterns.
to be viewed at any time. With the use of a sensitive TV camera and a
fluorescent screen these pattern can be displayed in real time as the beam is
scanned giving the operator instant access to the crystallography of the
sample (Venables and Harland, 1973; Dingley, 1981).
In comparison with SACP techniques, the backscatter patterns have both
advantages and drawbacks. The minimum selected area is as small or smaller,
and no modifications are required to the electron optics of the instrument.
The wide angular range of the pattern makes orientation determination
simple since there is a high probability of one or more major poles falling
in the field of view. O n the other hand, using these patterns requires some
modifications to the vacuum system and specimen chamber of the microscope,
and the wide angle displayed, the requirement that the sample be tilted, and
the p o o r angular resolution of the pattern recorded limits the accuracy with
which any orientation measurements can be made.
Electron channeling patterns
3.7.2
115
Kossel patterns
When the electron beam enters the specimen fluorescent X-rays are produced
within the beam interaction volume. F o r some elements, those lying between
silicon and copper in the periodic table, the X-rays produced can be diffracted
by the crystal lattice as they leave (Kossel, 1935; Castaing, 1951). A
photographic plate placed above the sample (Fig. 3.29) will detect these
diffracted X-rays as a series of conic sections whose configuration reflects
the orientation of the crystal. The ellipses traced on the photographic film
represent a gnomic projection of the crystal, and computer programs are
available which rapidly and accurately provide the orientation (Bevis and
Swindells, 1967). Unlike the electron backscattered, or channeling, patterns
these Kossel line patterns are also extremely narrow, having an angular width
of 1 0 " r a d or less. Since the wavelength of the X-rays producing the pattern
is that of the element itself, its value is known precisely, and consequently
by an analysis of the pattern the lattice parameter can be measured with a
precision of the order of 0.01% (Dingley, 1981; Dingley and Razavizadeh,
1981).
4
While the Kossel pattern technique provides good orientation data and
very high accuracy for the determination of lattice parameters, it has several
clear drawbacks. Firstly a special purpose film camera must be built to allow
the patterns to be recorded, either above the sample or on a suitable side port
of the specimen chamber. Secondly, exposure times of typically several
I
INCIDENT
PHOTOGRAPHIC
FILM
FLUORESCENT
X - R A Y SOURCE
F i g . 3.29 The geometry for the production of Kossel patterns using an electron
beam.
116
D.C. J o y
minutes are required to make the very fine lines visible, even using
high-sensitivity X-ray emulsions. Finally, only a very limited number of
materials efficiently diffract their own characteristic X-rays. This can be
overcome by placing a needle target, of iron or copper, just above the surface
of the specimen and using the X-rays produced by this to generate the Kossel
pattern; however, this requires careful mechanical manipulation and significantly degrades the achievable spatial resolution. Although important studies
have been performed using the Kossel technique (Dingley and Biggin, 1973;
Dingley and Steeds, 1974; Dingley, 1975) the practical problems associated
with its use have limited its appeal.
References
Alam, M.N., Blackman, M. and Pashley, D.W. (1954). Proc. Roy. Soc, 221, 224-242.
Bevis, M. and Swindells, N. (1967). Phys. Stat. Sol., 20, 197-212.
Booker, G.R., Shaw, A.M.B., Whelan, M.J. and Hirsch, P.B. (1967). Phil. Mag., 16,
1185-1191.
Brunner, M. (1981). In Scanning Electron Microscopy 1981. Vol. 1, SEM Inc., Chicago,
pp. 385-396.
Brunner, M., Kohl, H.J. and Niedrig, H. (1975). Beitr. Elektronen Mikroskop. Direktabb.
Oberfl., 8, 230-231.
Brunner, M., Kohl, H.J. and Niedrig, H. (1978). Optik, 49, 477-485.
Castaing, R. (1951). PhD thesis, University of Paris.
Christian, J.W. (1956). J. Inst. Metals, 84, 349-350.
Coates, D.G. (1967). Phil. Mag., 16, 1179-1184.
Davidson, D.L. (1976). J. Phys. E, 9, 341-343.
Davidson, D.L. (1977). In Proc. 10th Ann. SEM Symposium, ed. Johari, O., IITRI,
Chicago, pp. 431-438
Davidson, S.M. (1970). Nature, 227, 487-488.
Davidson, S.M. and Booker, G.R. (1970). In Proc. 7th Int. Cong, on EM, Vol. 1, IFSEM,
Grenoble, pp. 235-236.
Dingley, D.J. (1975). In Proc. 8th Ann. SEM Symposium, ed. Johari, O., IITRI, Chicago,
pp. 173-180.
Dingley, D.J. (1981). In Scanning Electron Microscopy 1981, Vol. IV, ed. Johari, O.,
SEM Inc., Chicago, pp. 273-286.
Dingley, D.J. and Biggin, S. (1973). In Scanning Electron Microscopy - Systems and
Applications, Conf. Ser. 18, Institute of Physics, London, pp. 308-313.
Dingley, D.J. and Razavizadeh, N. (1981). In Scanning Electron Microscopy, Vol. IV, ed.
Johari, O., SEM, Inc., Chicago, pp. 287-294.
Dingley, D.J. and Steeds, J.W. (1974). In Quantitative Scanning Electron Microscopy, ed.
Holt, D.B. et al, Academic Press, London, pp. 487-516.
Goldstein, J.I., Newbury, D.E., Echlin, P., Joy, D.C, Fiori, C.E. and Lifshin, E. (1981).
Scanning Electron Microscopy and X-ray Microanalysis, Plenum Press, New York.
Goodhew, P.J. (1984). Specimen Preparation for Transmission Electron Microscopy of
Materials, Oxford University Press, London.
Hall, CR. and Hirsch, P.B. (1965). Proc. Roy. Soc, A286, 158.
Electron channeling patterns
117
Hirsch, P.B. and Humphreys, C.J. (1970). In Proc. 3rd Ann. SEM Symposium, pp. 449455.
Hirsch, P.B, Howie, A., Nicholson, R.B, Pashley, D.W. and Whelan, M.J. (1978).
Electron Microscopy
of Thin Crystals (2nd edn), Krieger, New York.
Joy, D.C. and Maruszewski, C M . (1975). J. Mater. Sci., 10, 178-179.
Joy, D.C. and Newbury, D.E. (1972). J. Mater. ScL, 7, 714-716.
Joy, D.C, Booker, G.R, Fearon, E.O. and Bevis, M. (1971). In Proc. 4th Ann. SEM
Symposium, ed. Johari, O , IITRI, Chicago, pp. 497-504.
Joy, D.C, Newbury, D.E. and Hazzledine, P.M. (1972). In Proc. 5th Ann. SEM
Symposium, ed. Johari, O , IITRI, Chicago, pp. 97-104.
Joy, D.C, Newbury, D.E. and Davidson, D.L. (1982). J. Appl. Phys., 53, R81-R122.
Kossel, W. (1935). Gott. Nachr. Math. Naturw., 1, 229-234.
Laponsky, A.B. and Whetten, N.R. (1959). Phys. Rev. Lett., 3, 510-515.
Madden, M.C. and Hren, J.J. (1985). J. Microscopy, 139, 1-6.
Morin, P , Pitaval, M , Besnard, D. and Fontaine, G. (1979). Phil. Mag., 40, 511-518.
Nakagawa, S. (1985). JEOL News, 24E-1, 7-14.
Newbury, D.E. and Joy, D.C. (1971). In Electron Microscopy and Microanalysis, Proc.
25th Ann. Meeting EMAG, Conf. Ser. 10, Institute of Physics, London, pp. 216-219.
Newbury, D.E, Yakowitz, H. and Myklebust, R.L. (1976). In Use of Monte Carlo
Calculations in Electron Probe Microanalysis
and Scanning Electron Microscopy,
ed.
Heinrich, K.F.J, NBS Special Publication #460, pp. 151-159.
Newbury, D.E, Joy, D.C, Echlin, P , Fiori, C E . and Goldstein, J.I. (1986). Advanced
Scanning Electron Microscopy
and X-ray Microanalysis,
Plenum Press, New York.
Pfeiffer, L , West, K.W, Paine, S. and Joy, D.C. (1985). Mater. Res. Soc. Symp. Proc, 35,
583-592.
Ruff, A.W. (1976). Wear, 40, 59-74.
Sandstrom, R, Spencer, J.P. and Humphreys, C.J. (1974). J. Phys. D, 7, 1030-1046.
Schulson, E.M. (1977). J. Mater. Sci., 12, 1071-1087.
Schulson, E.M. and Marsden, D.A. (1975). Radiation Effects, 24, 195-198.
Schulson, E.M. and van Essen, C.G. (1969). J. Phys. E, 2, 247-251.
Schulson, E.M, van Essen, C.G. and Joy, D.C. (1969). In Proc. 2nd Ann. SEM
Symposium, ed. Johari O , IITRI, Chicago, pp. 45-55.
Spencer, J.P, Humphreys, C.J. and Hirsch, P.B. (1972). Phil. Mag., 26, 193-213.
Vale, S.H. (1985). In Microbeam Analysis - 1985, ed. Armstrong, J.T, San Francisco
Press, San Francisco, pp. 148-150.
van Essen, C.G. and Schulson, E.M. (1969). J. Mater. Sci., 4, 336-339.
van Essen, C.G. and Verhoeven, J.D. (1974). J. Phys. E, 1, 768-769.
van Essen, C.G, Schulson, E.M. and Donaghay, R.H. (1970). Nature, 225, 847-848.
Venables, J.A. and Harland, C.J. (1973). In Scanning Electron Microscopy
- Systems
and Applications, Conf. Ser. 18, Institute of Physics, London, pp. 294-296.
Vicaro, E , Pitaval, M. and Fontaine, G. (1971). Acta Cry St., Ml, 1-6.
Wells, O.C. (1971). Appl Phys. Lett., 19, 232-325.
Wells, O.C. (1974). Scanning Electron Microscopy, McGraw Hill, New York, pp. 172—
179.
Wells, O.C. (1976). In Use of Monte Carlo Calculations in Electron Probe
Microanalysis
and Scanning Electron Microscopy, ed. Heinrich, K.F.J, NBS Special Publication
460, pp. 139-150.
Wolf, E.D. and Hunsperger, R.D. (1970). Proc. 3rd Ann. SEM Symposium, ed. Johari, O ,
IITRI, Chicago, pp. 457-463.
Yoshida, H , Sakuramoto, N. and Kawai, K. (1978). In Proc 9th Int. Cong, on EM, Vol.
1, Imperial Press, Toronto, pp. 566-567.
D.C. Joy
118
Appendix
211
220
111
200
15
20
30
1.21
1.06
0.85
1.40
1.22
1.00
1.99
1.71
1.40
Dia
15
20
30
(0.91)
(0.80)
(0.64)
Fe
BCC
15
20
30
2.00
1.71
1.40
2.43
2.10
1.71
1.49
1.29
1.05
2.80
2.43
1.99
Nb
BCC
15
20
30
1.72
1.50
1.22
2.11
1.87
1.50
Cu
FCC
15
20
30
Ge
Dia
15
20
30
Element
Type
keV
Al
FCC
Si
110
1.40
1.23
0.99
1.24
1.06
0.86
1.37
1.19
0.96
0.87
0.75
0.63
1.58
1.36
1.10
6 is given in degrees for the indicated reflection.
B
2.44
2.20
1.76
2.21
1.94
1.57
1.43
1.25
1.03
301
311
222
2.32
2.02
1.65
1.74
1.52
1.23
2.43
2.10
1.71
1.82
1.60
1.28
3.45
2.99
2.43
3.13
2.71
2.21
2.73
2.37
1.97
2.60
2.26
1.85
1.68
1.45
1.20
3.00
2.60
2.11
2.71
2.36
1.92
1.74
1.51
1.25
4 The Emissive Mode and X-ray
Microanalysis
D.C. JOY
Electron Microscope
Facility, The University of Tennessee, F239 Walters
Life Science Building, Knoxvil/e, TN 37996-0810,
USA and Metals and
Ceramics Division, ORNL, Oak Ridge TN
37831-6376
List of symbols
4.1 Signals in the emissive mode
4.2 Detectors for imaging
4.3 Secondary electron imaging modes
4.3.1 Topographic contrast
4.3.2 Voltage contrast
4.3.3 Magnetic contrast
4.4 Backscattered imaging modes
4.4.1 Backscattered modes
4.4.2 Z-Contrast and topography
4.4.3 Magnetic contrast
4.4.4 Channeling
4.5 X-ray microanalysis
4.6 Quantitative microanalysis
4.6.1 Energy dispersive detectors
4.6.2 Wavelength dispersive detectors
4.7 Qualitative X-ray analysis of an unknown
4.8 Quantitative X-ray analysis
References
H9
120
123
128
128
13°
132
134
134
134
135
138
138
140
140
142
144
146
149
List of s y m b o l s
A
B, C
C
C
d
e
e
p
A
e h
absorption correction
Moseley coefficients
capacitance
weight fraction of element A
lattice plane spacing
electron charge
energy to produce one electron-hole pair
SEM Microcharacterization of Semiconductors
ISBN 0-12-353855-6
Copyright © 1989 Academic Press Limited
All rights of reproduction in any form reserved
D.C. Joy
120
E
Eo
Ec
E2
E<j)
F
I
b
1(E)
K
L
M
A
A
'•x
R
V
z
z
m
X
3
1
P
e
B
electron energy
incident beam energy
critical energy for X-ray line excitation
incident energy for unity yield
value of El at tilt angle cf)
fluorescence correction
incident beam current
specimen current
Bremsstrahlung intensity at energy E
corrected intensity ratio for element A in Ziebold Ogilvie equations
sample to spectrometer distance
Ziebold Ogilvie constant for element A
N u m b e r of electron hole pairs
radius of interaction volume for X-ray production
radius of Rowland circle
voltage
atomic number of target
mean atomic number of mixture Z
Z
X-ray wavelength
tilt angle
secondary electron coefficient
backscattering coefficient
density
Bragg angle
l 5
2
In Chapter 2 the theoretical basis of the interaction between electron beams
and solids was examined. In this chapter the practical aspects of these
interactions will be discussed in the context of producing images and
microanalytical data from an SEM.
4.1
S i g n a l s in t h e e m i s s i v e m o d e
Figure 4.1 shows the energy spectrum of electrons emitted from a solid
specimen b o m b a r d e d at normal incidence by an electron beam. Conventionally, the high-energy part of the distribution, which extends up to the incident
beam energy E and has an average value of about 0.55 E is called the
backscattered, or reflected, electrons. The average number of backscattered
electrons produced by each incident electron is t], the backscatter yield. As
shown in the previous chapter rj is nearly independent of beam energy, but
varies monotonically with the atomic number Z of the target. Typically rj is of
the order of 0.25.
0
0
121
N(E)
The emissive mode and X-ray microanalysis
10eV
lOOeV
IkeV
lOkeV
lOOkeV
Energy (E)
F i g . 4.1
Energy spectrum of electrons from a solid specimen.
The low-energy portion of the distribution, with an energy up to about
50 eV, contains the secondary electrons. F o r most materials the peak in the
secondary electron distribution occurs at about 4 e V (Seiler, 1983). The
average number of secondary electrons d produced by each incident electron is
only weakly dependent on the atomic number of the target. However, S does
vary rapidly with the beam energy, typically being 0.1 at around 20 keV but 1
at 1 keV.
This separation into two classes is obviously an oversimplification. F o r
example, as shown earlier (Chapter 2) there are a few secondary electrons with
energies of u p to half of the incident energy, while some backscattered
electrons may emerge with only a few tens of electronvolts of energy. In
addition, there are characteristic Auger electrons produced. These have
energies in the range 50 eV to 1 keV depending on the chemical composition of
the target. However, except for specially constructed ultrahigh vacuum
instruments the Auger signal is not usable for chemical analysis and can
therefore be considered as an addition to the secondary yield.
The total current flow at the sample must be zero, so
-J
b
+ SJ + i// + J
b
b
8C
= 0
(4.1)
where I is the incident beam current and 7 is the current flowing in the
ground connection to the sample. This "specimen current" contains information about both the secondary and backscatter signals. By collecting and
amplifying this current an important new imaging mode is generated.
It can be seen from eqn (4.1) that if (S + rj) is equal to unity then n o current
flows to earth. At this condition the incident electron beam is neither injecting
charge into the specimen, nor extracting charge from it. If the SEM is being
h
SC
122
D.C. Joy
Total Yield
Electron Yield from Copper
1
10
100
Beam Energy (keV)
Fig. 4.2
Variation of total electron yield (S + rj) with beam energy.
used, for example, to measure a voltage on a device as described in a later
chapter then the beam energy at which this condition occurs is clearly a
desirable one since the device is not "loaded" during the observation. This
condition is also important when dealing with specimens that are not electrical
conductors. When (S + rj) is less than unity, then charge is injected by the beam
into the specimen. Unless the sample can conduct this charge away to earth as
specimen current then the specimen will start to charge negatively-that is the
potential difference between the surface and the incident beam will decrease.
As shown in Fig. 4.2 (<5 + rj) for a typical material rises at the incident beam
energy is reduced because of the rise in S. Thus, as the effective value of E falls
due to the charge-up of the specimen, (d + rj) rises, until eventually at some
energy E the total yield (<5 + rj) becomes unity. Since each incident electron
now produces, on average, one exiting electron no further charge is deposited
and the specimen potential stabilizes. At this E energy it is, therefore, possible
to form an image from an insulating, or poorly conducting, sample.
Table 4.1 gives some E values for some materials of interest (Joy, 1987a).
For many material E is of the order of a few kiloelectronvolts, and this
condition can readily be obtained on a modern SEM, but for other cases E
lies in the region below 1 keV where few instruments operate efficiently.
However, E may be adjusted to a more convenient value by tilting the sample.
It can be shown (Joy, 1987a) that at an angle of incidence (/>, E^, the effective
value of E is approximately
0
2
2
2
2
2
2
2
i ^ = £ /cos </>
2
2
Hence E can be doubled by tilting the specimen to 45°.
2
(4.2)
The emissive mode and X-ray microanalysis
123
T a b l e 4.1 Incident energies for unity yield
of secondary electrons
Material
E
2
Photoresist
Amorphous carbon
Aluminum
Silicon
Teflon
GaAs
Quartz
(eV)
0.6
0.8
1.05
1.15
1.9
2.6
3.0
If (5 + tj) is greater than unity (E < E ) then more electrons leave the sample
than enter it. In principle, this should produce positive charging. In practice,
however, any tendency of a surface to go positive results in the recollection of
secondary electrons, so that the sample remains neutral (Cazaux, 1986).
0
4.2
2
Detectors for imaging
Under typical operating conditions a semiconductor sample produces more
backscattered than secondary electrons. Despite this, probably nine out of
every ten images are recorded in secondary electron mode. O n e of the major
reasons for this is the difference in the efficiency with which the two
components can be collected. Since the incident beam current in small, 1 0 " A
or less, we require an efficient and sensitive collector. At the same time,
however, we also need a detector which can cope with a wide variation in
signal strength ("dynamic range") and which can respond accurately to rapid
changes in the signal as the beam scans the sample ("high bandwidth").
Both secondary and backscattered electrons are emitted from the surface, at
normal beam incidence, with a cos (j) distribution (Fig. 4.3). However, since the
secondaries are low in energy efficient collection may be obtained, even with a
small or distant detector, by applying an electric or magnetic field to
appropriately deflect the electrons. Backscattered electrons, on the other hand,
are high in energy and not easily deflected. Efficient backscatter detectors,
therefore, must be large enough in size, and positioned correctly, so as to
intercept a high fraction of the emitted signal. Since physically large detectors
are often inconvenient, or impossible, to accommodate S E M users have thus
tended to prefer secondary electron imaging.
The basic secondary detector, shown in Fig. 4.4, was described in its current
form by Everhart and Thornley (1960). A variety of interactions are employed
to give a detector which combines high sensitivity and good bandwidth, and
9
124
D.C. Joy
Incident Beam
/l(0)~cos(0)
r
0/]
Surface
F i g . 4.3 Angular distribution of secondary and backscattered electrons.
Chamber wall
Scintillator
Photomultiplier
Light pipe
I
| +10kV bias
F i g . 4.4
Quartz window
Everhart-Thornley secondary electron detector.
yet which is also cheap to produce, and is small and rugged. The secondary
electrons strike the scintillator producing a pulse of light. Since the intensity of
this pulse is linearly proportional to the energy of the electron which caused it,
the low energy (a few electronvolts) of the secondaries would only produce a
small signal. A + 10 kV potential is, therefore, placed on the front face of the
scintillator (the voltage being applied to a thin metal coating) to accelerate all
incoming electrons to a sufficient energy to produce a strong light pulse. The
pulse travels down the light pipe and leaves the SEM vacuum through a quartz
window. A photomultiplier tube, outside of the vacuum, collects the light and
converts it back into an electrical signal. This procedure gives an overall
amplification of the incident electron signal of a factor of from 1000 x to
1,000,000 x . Because of the logarithmic characteristic of the photomultiplier,
The emissive mode and X-ray microanalysis
125
a wide dynamic range is readily obtained, and the bandwidth is limited only by
the decay time of the scintillator. Typically, a bandwidth of many megahertz is
possible. The only problem usually encountered with these detectors is with
the limited lifetime of the scintillator material. The efficiency of light
production falls with the total charge hitting the scintillator, so periodic
replacement is necessary to maintain peak performance (Pawley, 1974).
The E v e r h a r t - T h o r n l e y detector can be configured in several different
ways. Most commonly (Fig. 4.5a) it is placed in the specimen chamber of the
SEM, somewhere below the lens and 1 or 2 cm from the sample. In this
position the field from the + 1 0 kV would deflect or distort the incident beam,
particularly at low beam energies. T o avoid this the scintillator is surrounded
by a F a r a d a y cage of metal mesh which is held at about 200 V positive with
reference to the specimen. This produces a field of about lOOV/cm at the
specimen which is sufficient to attract about 60% of the secondaries towards
the detector but not high enough to interfere with the incident beam. This
arrangement is popular because it allows the detector to be placed in any
convenient location while still maintaining high collection efficiency. N o t e
that 100% collection efficiency is neither necessary nor, always, desirable since
some important contrast effects (voltage contrast, magnetic contrast) rely on
the detector collecting only some fraction of the secondaries. The disadvantage
is that the asymmetric position of the detector can result in variations of
collection efficiency across the field of view which can lead to problems of
interpretation, for example, line-width measurements. The detector is also
liable to collect secondaries produced by the r a n d o m impact of backscattered
electrons on the specimen chamber walls and on the lens pole-piece. These
carry no useful signal information and so reduce the quality of the image
produced.
An alternative arrangement (Fig. 4.5b) uses the magnetic field of the lens to
collect the signal. The secondaries spiral back through the base of the lens and
are then captured by the + 10 kV bias of the scintillator. This configuration
also gives high efficiency, with the additional advantage of having symmetric
collection properties a b o u t the beam axis. Removal of the detector from the
specimen chamber also permits the sample to be placed closer to the lens,
facilitating the production of high-resolution images. This arrangement also
eliminates the collection of the stray secondaries produced by backscattered
electrons.
Finally, electron channel-plates have been used (Fig. 4.5c). These devices
consist of a thin plate containing many thousands of micrometer-sized tubes,
each of which acts as an electron-multiplier (English et al, 1973). Because of its
configuration this type of detector can be mounted beneath the pole-piece to
give efficient and symmetrical detection without pre-empting large amounts of
space in the specimen chamber. The major disadvantage of the channel-plate is
126
D.C. Joy
Specimen
+200V
(a)
Sample
Pole Piece
Channel^^m,,,,,,,,,,,,,,,,,,,,
Plate
Beam
Pole Piece
• IIIIIIIIIIIHIIIIIHIIIHHI.
Collector
Electrode
"""7*
To ground
Screen
Grid
Signal
+lkVbias
(c)
Sample
Fig. 4.5 (a) Standard E - T detector configuration; (b) through the lens position; (c)
channel plate detector.
its limited dynamic range, which necessitates careful adjustment to give
acceptable images.
Backscattered electrons can be detected in several ways. The simplest, but
least desirable, approach is to use the arrangement of Fig. 4.5a but place a bias
of about — 50 V on the F a r a d a y cage. This is sufficient to reject secondary
electrons but allows those backscattered electrons moving towards the
127
The emissive mode and X-ray microanalysis
beam
Light guide
T
to P M T
• • H H H
Sample
(a)
iBeam
Annular Schottky
Barrier detector
To S E M Video
(b)
F i g . 4.6 (a) Backscattered concentric scintillator; (b) solid-state detector.
detector to be collected. However, the solid angle presented by the detector is
small, so the collection efficiency is small (typically less than 5%) and the
asymmetrical arrangement produces heavy shadowing. A better configuration
(Fig. 4.6a) again uses the Everhart-Thornley system but places the scintillator
concentrically around the beam. N o bias is applied, so only high-energy
backscattered electrons will produce an output. At beam energies above a few
kiloelectronvolts such an arrangement is highly efficient ( > 5 0 % ) and has
sufficient bandwidth to permit TV-rate imaging.
A popular alternative (Fig. 4.6b) is to use a solid-state detector. As described
in Chapter 6, a high-energy electron passing through a p - n , or a Schottky,
diode produces an avalanche of electrons, to give a substantial current gain.
The efficiency of this process rises linearly with the energy of the incident
electron, and there is typically a cut-off energy of a few kiloelectronvolts below
which no output is produced. Thus, the detector produces a signal which
favors the contribution of high-energy electrons. These solid-state detectors
are compact, and readily and cheaply available commercially as "solar cells".
However, a detector large enough to be usefully efficient has a high inherent
128
D.C.Joy
capacitance which limits the available bandwidth, and restricts operation to
slow scan modes.
4.3
Secondary electron imaging modes
Any factor which causes the secondary electron signal to vary as the beam
scans from point to point is said to be generating contrast, and so is capable of
being imaged. Contrast can be caused either by a change in the number of
secondary electrons produced, or by a change in the efficiency with which they
are collected.
4.3.1
T o p o g r a p h i c contrast
The most widespread mode of use for the S E M is the secondary electron
topographic image. This form of contrast occurs because secondary electrons
have a limited depth of escape, typically less than 100 A, from beneath a
surface. When the beam enters the surface perpendicularly (Fig. 4.7a) only a
limited fraction of the secondaries are produced within the escape region. If the
sample is tilted to some angle <j> with respect to the beam (Fig. 4.7b) then a
greater fraction of the secondaries are produced within the escape region and
so the secondary yield rises. T o a fair approximation the yield S(4>) at tilt cj) is
given by the equation
S((j)) = 3(0) sec 0
(4.3)
so that tilting the sample from zero to 45° will increase the secondary signal by
Incident B e a m
Incident B e a m
Surface
Escape depth
(a) N o r m a l Incidence
F i g . 4.7
tilt (j).
(b) Tilted Incidence angle 0
(a) Secondary production at normal incidence; (b) secondary production at
129
The emissive mode and X-ray microanalysis
about 30%. Thus, if the beam scans over a surface with topography then the
local angle of incidence, and hence the secondary signal, will vary with position
and a topographic image will be produced. We note from eqn (4.3) that the
change in signal dd for a given change in angle 5$ varies as sec 0, so the
a m o u n t of contrast as well as the average signal can be enhanced by holding
the sample at some non-zero angle of incidence with respect to the beam.
W h a t is, perhaps, surprising is that an image formed in this way should have
any resemblance to the view of things produced by our own eyes. Much of the
popularity of S E M imaging is due to the unlikely fact that the correspondence
is, in many cases, very close. This is because the sec (/> variation is of the same
form as Lambert's Law in optics which describes the reflection of light from a
surface. The S E M operator's viewpoint is from the gun looking down onto the
sample which is "illuminated" from the detector. The eye then interprets the
brightness changes as if the SEM image were an optical image, and because of
the correspondence with Lambert's law this analogy produces easily interpretable data (Fig. 4.8). Because the secondaries are low in energy, and easily
deflected it is possible to image any surface scanned by the incident beam even
2
100 nm
Fig. 4.8
Secondary electron image of gold coating on magnetic recording tape.
130
D.C. Joy
if the surface faces away from the detector, or is a hole. In such cases, however,
the collection efficiency may be reduced. Secondary imaging is, therefore,
analogous to viewing a specimen in diffused light, since strong shadows will be
absent.
This type of image interpretation only breaks down when the beam
interaction volume becomes comparable with the size of the feature that is
being viewed. F o r example, at high magnification it is seen that all the edges in
the image are marked by a bright line. This occurs because, at an edge,
secondaries can escape from two, rather than just one, surface. As feature sizes
fall into the micrometer range such effects become more significant and image
interpretation becomes more difficult. Nevertheless, for the great majority of
operating conditions, the secondary electron topographic image can be
understood in a simple way. Only when detailed quantitative data are
required, as, for example, in line-width measurements (the so-called "critical
dimension metrology"), is it essential to account for the details of the electron
beam interaction.
Topographic imaging has been demonstrated for details as small as 10 A in
size (Kuroda et al, 1985), even though the electron beam travels several
micrometers into the specimen. Because of the limited escape depth of the
secondaries, there are only two occasions when a secondary that is generated
can escape from the specimen - when an electron enters, or is backscattered.
Secondaries produced by incident electrons are called SE1, and carry highresolution information about the specimen surface because they are generated
within a few angstroms of the beam impact. Secondaries produced by
backscattered electrons are called SE2, and emerge from an area that may be
micrometers in diameter. Thus, they only carry low-resolution detail about the
sample. At high magnifications the SE2 signal is effectively constant and so
contrast is visible from the variations in the SE1 signal, even though this is
typically only 15-20% of the total secondary signal (Joy, 1987b). At low
magnifications the image detail is produced by the variation in the SE2 signal.
4.3.2
V o l t a g e contrast
It was in the very early days of scanning microscopy that Knoll (1941) first
observed that surfaces at different potentials gave images of different
brightness. The origin of this effect is explained in Fig. 4.9 which shows
schematically the typical layout of the SEM specimen chamber. For a
specimen at ground potential (Fig. 4.9a) the field from the Everhart-Thornley
detector is of the order of 100 V/cm, and about 60% of the secondaries emitted
will be collected. If, as in Fig. 4.9b, the potentials of points on the surface are
changed to, say + 5 V and — 5 V with respect to earth then the field to the
The emissive mode and X-ray microanalysis
131
Everhart Thornley SE detector
Surface at ground potential
(a)
- 5volts
Ground
+ 5volts
F i g . 4.9 Origin of voltage contrast, (a) Fields in specimen chamber with sample at
ground potential; (b) fields when sample has potentials applied.
detector from the negatively biased strip is increased, while the field from the
positively biased region is decreased. Thus, more secondaries will be collected
from the negatively biased area than from the positively biased area, and the
negative region will show bright "voltage contrast". Figure 4.10 shows a
practical example of such contrast from an integrated circuit powered-up in
the SEM. Clearly, the ability to visualize potentials on an operating circuit is a
powerful diagnostic tool, permitting voltage measurement on a spatial scale
set by the resolution of the SEM.
However, considerable care must be used in interpreting such results. The
observed contrast arises from changes in the electrical field distribution in the
specimen chamber, and so only indirectly the potentials themselves. In
addition to the fields to the detector there are also fields between regions at
different voltages. F o r example, areas A and B in Fig 4.9b are separated by
10 /mi and differ in potential by 10 V, so the field between them is of the order of
1 0 V/cm, which is 100 x greater than the detector field. This "local field" will
modify the collection efficiency point to point, so that regions of constant
potential will not display constant brightness. As a result, the image can only
be used as a qualitative guide to local potentials. Chapter 5 of this book
4
D.C. Joy
132
500
u
F i g . 4.10 Voltage contrast observed from integrated circuit with operating potentials applied.
discusses this topic in more detail and shows how these problems can be
overcome.
Voltage contrast is best observed at low beam energies. Firstly, because this
maximizes the secondary electron yield, and secondly, because by correctly
choosing the beam energy (as described above) the injection of charge into the
specimen can be controlled so as to minimize charge-up, or loading, of the
device under examination. Special purpose instruments designed for this type
of work usually function in the range 0.5-5 keV.
4.3.3
M a g n e t i c contrast
Many materials, such as magnetic recording tape or floppy discs, recording
heads, or naturally occurring substances such as cobalt, have magnetic fields
above their surfaces. A secondary electron leaving the surface will be deflected
by the Lorentz force it experiences as it travels through the field. Since this
deflection will be normal to both the direction of travel of the electron, and to
The emissive mode and X-ray microanalysis
|
F i g . 4.11
Ijnnrn
133
|
Magnetic contrast from a cobalt single crystal.
the magnetic field, a leakage field into (or out of) the plane containing the
specimen and the secondary electron detector will produce a deflection such
that either a few more, or a few less, secondaries will be collected. Thus, the
fields produce a "magnetic" contrast image (Joy and Jakubovics, 1968).
Figure 4.11 shows an example of this type of contrast from a cobalt single
crystal. The pattern that is visible comes from the magnetic field above the
surface, which in turn correlates with the domain structure of the cobalt. If the
sample were rotated in its own plane by 180° then the field directions, and
hence the contrast, would reverse. This way of observing magnetic structures is
a great advance over techniques such as the use of iron powders or colloids,
since it combines high spatial resolution with sensitivity and ease of sample
preparation. O n e useful application of this mode is to record a square wave, at
say 10 kHz, onto conventional cassette tape. The image will now show
contrast bars at a spacing of 4.5 cm/s per 10,000 cycles/s, i.e. 4.5 /im, producing
a handy magnification standard.
In this mode the spatial resolution of the contrast will be limited by the scale
of the structure that produced it. O n bulk materials this may be a micrometer
or so. O n a thin foil the corresponding value may be 0.1 /mi. As for other
secondary electron modes, the performance is best at low voltage, although on
strongly magnetic materials severe astigmatism may result if the beam energy
is chosen too low. Other classes of magnetic material (e.g. "cubic" materials
such as iron) do not have leakage fields above their surfaces and their structure
must be imaged using alternative techniques described later.
134
D.C. Joy
4.4
Backscattered imaging modes
Backscattered (BS) imaging provides information that is complementary to
that from secondary electrons. It also provides some important new data
about the crystallography and chemistry of a specimen.
4.4.1
Backscattered modes
BS imaging modes provide information that is complementary to that from
secondary electron (SE) modes. In general the spatial resolution will be lower,
of the order of the diameter of the beam interaction volume, but for many of
the modes this is not a drawback since they are inherently low magnification
modes.
4.4.2
Z-Contrast and topography
As shown earlier, the BS yield from a specimen varies with the atomic number
of the target. Thus, a heavier material (gold, Z = 79) backscatters more than a
light material (carbon, Z = 6). If the material within the interaction volume is
•
loo H
I
F i g . 4.12 Atomic number contrast from a Al-Zn alloy.
The emissive mode and X-ray microanalysis
135
composed of an atomic mixture of Z and Z then the effective backscattering
coefficient will be that of a c o m p o u n d whose effective atomic number is Z .
x
2
m
Z
m
= xZ +{l-x)Z
1
2
(4.4)
where x is the atomic fraction of Z The variation in signal level of a BS image
can, therefore, reflect, sometimes even at a quantitative level, the changes in
chemistry of the specimen. Figure 4.12 shows an example of image of this type
from a two-phase alloy of Al (Z = 13) and Zn (Z = 26). The low and high Z
phases are readily distinguished in the image as dark and bright regions
respectively.
While this technique is of value and interest, a difficulty arises if the sample is
not completely flat. This is because the BS image also contains topographic
information. Just as for SE the yield of BS electrons increases with the angle of
tilt of the sample surface to the beam. In addition, however, there is another
factor: because BS electrons have high energy they travel in straight lines from
the specimen surface to the detector. Depending on the size and position of the
detector surfaces of the specimen at different angles may be shadowed from the
detector. In either event, the simple correlation between signal level and
atomic number will be destroyed.
These problems can be minimized by using the arrangement of Fig. 4.13 in
which the BS detector is divided into two halves. The signal profiles to be
expected from the detector are shown. If the signals from A and B are added
then, because the shadowing effects are opposite, the topographic components
cancel leaving only the atomic number variation. If, on the other hand, the
signals are subtracted then the atomic number variations, which are the same
for both detectors, disappear leaving just the topography. This scheme can be
further extended by using four q u a d r a n t s instead of two halves to give even
more flexibility. While the compensation for the different contrast effects is
never perfect, the ability to selectively enhance one or the other does make it
possible to interpret the images with confidence.
v
4.4.3
M a g n e t i c contrast
C o m m o n magnetic materials such as iron do not have significant leakage
fields above their surfaces. This is because they can be magnetized along any of
three cubic axes and can therefore always arrange to close their flux internally.
They, therefore, do not produce magnetic contrast in the SE mode described
earlier. However, their magnetic domain structure can still be viewed in the BS
mode as shown in Fig. 4.14. When the beam enters the tilted sample the
Lorentz deflection from the internal flux will, depending on its direction, move
the electron interaction volume either slightly closer to, or slightly further
136
D.C. Joy
Difference Profile
Beam position
A-B
F i g . 4.13 Split detector arrangement for distinguishing atomic number and topographic contrast.
from, the surface, so varying the BS coefficient. N o t e that this will only occur
when the flux has a component parallel to the tilt axis, so rotation of the
sample about its surface normal will cause different magnetization directions
to come into contrast (Fig. 4.15). This effect is very weak, giving only 1 or 2%
contrast changes with most materials. However, its magnitude can be
enhanced by operating the microscope at the highest possible beam energy
(Fathers et a/., 1973, 1974).
since the contrast varies as E
This technique has been successfully applied to the study of magnetic
3/2
The emissive mode and X-ray microanalysis
Incident Beam
Fig. 4.14 Origin of magnetic contrast for cubic materials.
Fig. 4.15 Type II magnetic contrast from an Fe-Si crystal.
137
138
D.C. Joy
recording heads for discs and tape, and for studies of transformer core
materials.
4.4.4
Channeling
The BS yield from a material increases monotonically with the angle of
incidence of the beam. If, however, the sample is crystalline and the electronoptical conditions are correctly chosen then the BS coefficient shows maxima
and minima when the beam is aligned along symmetry directions of the lattice.
This effect provides a way of obtaining information about the crystallography
of a specimen. The technique is discussed in detail in Chapter 3.
4.5
X-ray
microanalysis
As discussed in Chapter 2, many interactions occur when the incident electron
enters the specimen. Some of these have been discussed above, but one of the
most significant is the formation of X-rays. Two kinds of X-ray signals can be
distinguished. The first is the continuum or bremsstrahlung (from the German
"braking radiation"). This arises because the incident electrons are decelerated
by the field from the positive charges on the cores of the atoms. This intensity
extends from zero energy up to the incident beam energy and at some energy £,
the intensity 1(E) has the form
I{E) =
iZ -(E -E)/E
M
0
(4.5)
where i is the electron current, Z is the mean atomic number of the target and
E is the incident energy. The generated continuum intensity therefore rises
rapidly as the energy falls (although as we shall see later, because the lowenergy X-rays will be more strongly absorbed in the specimen as they leave the
actual measured continuum spectrum will peak at some low energy). We note
that the intensity is proportional to the mean atomic number of the sample so
the continuum signal does not contain any specific chemical information.
Secondly, the interaction of an incident electron with an inner-shell electron
can result in an ionization event in which the b o u n d electron is ejected leaving
a vacancy. Subsequently, the a t o m de-excites by an electron dropping from
and outer shell and emits its excess energy either as an Auger electron or as an
X-ray. The energy of the X-ray is equal to that difference in energy between the
inner and outer shells involved in the transition. X-rays as q u a n t a of
electromagnetic radiation, have a wavelength X which is related to the energy
E by the relation
M
0
k= 12.4/£A
(4.6)
The emissive mode and X-ray microanalysis
139
where E is in keV. We can thus also describe an X-ray by its wavelength.
These X-rays emitted are called "characteristic" X-rays because their
energies (or wavelengths) are unique to the particular element that was ionized
to produce them. The energies of the shells vary with atomic number and the
energy difference between shells changes significantly even for atoms with
adjacent atomic numbers. This fact was first discovered by Moseley (1913,
1914) who showed that
(4.7)
X = B/{Z - C)
2
where B and C are constants for each family of X-ray lines, i.e. L , K , etc.
If the energy, or wavelength, of the emitted X-rays can be measured then the
elemental composition of the sample region irradiated by the beam can be
determined. This electron-beam microanalysis was first discussed by Castaing
(1951). Compared to classical "wet chemical" analysis techniques electronbeam microanalysis offers significant advantages. Firstly, it offers spatial
resolution, allowing variations in the composition of inhomogeneous samples
to be studied. The resolution obtained will depend on the size and shape of the
electron interaction volume with the sample, which in turn depends on the
beam energy and the nature of the material (atomic number, density, etc.). As
shown by the M o n t e Carlo simulation of Fig 4.16, this dimension varies
greatly but is typically of the order of a few micrometers in low Z materials. In
practice, the resolution will be slightly better than this because X-rays are only
a
F i g . 4.16
15keV.
p
Monte Carlo simulations of beam interactions with C, Al, Cu and Au at
D.C. Joy
140
generated as long as the electron energy exceeds the critical energy E for the
X-ray line (i.e. a 5 keV electron cannot excite the 6.4 keV X -line from Fe). So
depending on the energy of the line and the incident energy the X-ray
production volume will be less than the total interaction volume. As the beam
energy is reduced towards the critical energy the volume falls rapidly, e.g. r
the approximate radius of interaction is
c
a
x
r =
x
0.0064(£j- -£^ )/p(^)
6 8
(4.8)
8
in the form given by Andersen and Hasler (1966). Since the volume varies as r^,
the sampled size can be as small as 1 0 ~ c m . Secondly, the X-ray method is
non-destructive and rapid, and is readily combined with the sort of image
information provided by the SEM.
1 2
4.6
3
Quantitative microanalysis
In order to make use of the fluorescent X-rays for microanalysis, their
wavelength, or energy, must be measured. Two types of spectrometer are
available to perform this job.
4.6.1
Energy dispersive detectors
An energy dispersive spectrometer (EDS) detector identifies X-ray photons by
their energy. The X-ray is allowed to pass into a p - n junction device (Fig. 4.17).
The p h o t o n of energy E deposits all of its energy in a single scattering event to
Outer shield
Au front contact
X-rays
Li doped Si region
(intrinsic)
Au back contact
Bias Voltage
(-500 to-lOOOV)
F i g . 4.17
Schematic view of solid-state X-ray detector.
The emissive mode and X-ray microanalysis
produce N
e h
141
electron-hole pairs, where
N
eh
(4.9)
= E/e e h
t
and e is the energy required to produce a single electron-hole pair (e.g. 3.6 eV
in silicon). These charges are swept out of the depletion region by the bias field
and if the capacitance of the device is C then a voltage pulse
eh
p
(4.10)
is produced. Thus, the pulse is linearly proportional in energy to the energy of
the photon. This pulse is sensed by a cooled field effect transistor (FET) and is
then shaped, passed into a discriminator, and finally into an analog-to-digital
converter (ADC) which measures the height ("energy") of the pulse. This
energy value (measured to a typical precision of 10 or 20 eV) is used as the
address in the memory of the computer (multichannel analyser, MCA) where
the pulse is stored. The entire process of detecting, measuring and storing the
pulse requires only 100/is or so, thus many pulses per sec can be detected.
Typically, 1000-4000 counts/s can be processed by the spectrometer without
any loss of performance. Hence, the entire spectrum of incoming X-ray
energies appears to be measured simultaneously.
An ideal detector would respond with equal efficiency to all X-ray photons
in the energy range of interest (typically from CK at 0.28 keV to about 20 keV).
At the high-energy end of the spectrum, the efficiency is limited by the depth of
the depletion region. The mean free path ( M F P ) of photons with energies of
> lOkeV in Si is of the order of > 100 /mi. A depletion depth of about 1 m m is
thus required. This requires both high-resistivity material ( > 10 Q cm) usually
achieved by Li compensation of the Si, and a high bias (— 500 Y). At low
energies ( < 2 keV) the efficiency is again reduced. Firstly, photons may deposit
this energy in the gold face or in the low-resistivity region ahead of the
junction. This leads to a low energy "tail" on peaks called incomplete charge
collections. Secondly, photons may be absorbed by the window placed
between the detector and the chamber vacuum to protect the L N - c o o l e d
silicon from contaminants. In older systems, this window is typically about
8 /mi of Be foil, and this restricts the use of the detector to X-ray energies above
1 keV. With improved vacuums in microscopes many newer detectors are now
equipped with thin (1000 A) polymeric windows which allow efficient transmission to energies as low as 0.2 keV.
The major advantages of the E D S are its ease of use, resulting from its close
coupling to the MCA, and the ability to analyse an entire spectrum in parallel.
The detector requires no specified geometry other than an unobstructed view
of the sample, and collects a relatively high fraction (few per cent) of all the Xrays leaving the sample. The major disadvantage is the energy resolution of the
3
2
142
Number of Counts
D.C. Joy
Energy (Channel Number)
F i g . 4.18 Definition of resolution (FWHM) of energy dispersive detector.
detector. This is typically 150eV F W H M (full width at half maximum)
(Fig. 4.18). While this is enough to permit most X-ray peaks of interest to be
unambiguously separated and identified, this resolution broadens the natural
width (20 eV) of the line and so reduces the peak-to-background ratio and
hence the sensitivity of analysis. Careful procedures are thus required to
exhaust peak intensity above backgrounds, as well as to separate overlapped
peaks (see Goldstein et al, 1981).
4.6.2
W a v e l e n g t h dispersive detectors
An alternative approach is shown in Fig. 4.19 in which the X-rays are
diffracted from a suitable crystal when Bragg's Law
n^ = 2dsm6
B
F i g . 4.19 Bragg diffraction from a crystal.
(4.11)
143
The emissive mode and X-ray microanalysis
Incident electron beam
Proporti<
Counter
Analyzing Crysu
Radius 2R
Radius R*
^1
Sample
F i g . 4.20 Focusing X-ray optics for wavelength dispersive spectrometer.
is satisfied. Here n is an integer 1,2,3,... and X is the X-ray wavelength. An Xray of different X is not diffracted but absorbed and scattered and its intensity is
extremely low. The effective energy resolution of a crystal is 10 eV. The X-rays
are detected by a gas-flow proportional counter placed at the exit focus of the
crystal.
Because the X-ray source represented by the specimen is weak, curved
crystals are used to give what is called fully focusing optics. In this case the Xray source, the crystal and the detector all lie on a circle (the "Rowland" circle)
of radius
(Fig. 4.20). If the crystal planes are bent to a radius of curvature of
2K*, and the crystal surface is ground to a radius of curvature of K*, then all Xrays from the point source will have the same incident angle on the crystal and
will be brought in the same focus at the detector. This maximizes the collection
efficiency of the system.
F o r practical reasons, this crystal/detector arrangement is located outside
of the S E M specimen chamber. X-rays must emerge from the sample through
some exit orifice at a fixed angle ij/. The necessary focusing condition is
obtained by moving the crystal away along the take-off direction while
rotating the crystal and detector so as to make the focusing circle rotate about
the point source. Since
L/2 =
R*sm9B
]
(4.12)
B
(4.13)
X = (d/R*)L
(4.14)
and
nk = 2d sin
for first-order reflection
144
D.C.Joy
So the wavelength can be measured by knowing L. Since the complex
mechanical arrangement driving the crystal/detector is fixed to the column
the sample must always be located to a high degree of accuracy (better than
a few micrometers) at the same vertical position. This is usually achieved by
using a light-optical microscope to set the position.
The major advantage of the wavelength dispersive spectrometer (WDS)
is its high energy resolution. This confers several important advantages on the
system. Firstly, the peak-to-background (P/B) ratio of lines in the spectrum is
at least a factor of ten times higher than in the corresponding E D S spectrum,
because all of the X-ray count is concentrated in a narrow energy range. This,
and the fact that the W D S unit can process as many as 50,000 counts/s mean
that the detection limit of the system, which is inversely proportional to the
quantity
peak count x (peak/background)
(4.15)
is much lower than for the E D S case. A W D S system can often detect elements
at a trace level of 0.1% or less, compared with 1-2% for an E D S unit. The
high resolution also makes it possible to resolve lines which are overlapped
on the E D S system. Although this is useful at all regions of the spectrum it
is particularly important in the low energy ("soft") portion of the X-ray
spectrum where M, N and O families of lines from heavy elements often
overlap with K and L lines from lighter elements.
The major disadvantage of the W D S is that it can only examine one
element at a time, and so measurements on several different elements can be
time consuming. However, in many modern instruments this difficulty is
reduced by using the E D S and W D S systems simultaneously. In this way,
the E D S unit can measure major constituents and the W D S can be applied
to elements at trace concentrations, or to unravel overlapped peaks.
4.7
Qualitative X-ray analysis of an u n k n o w n
When attempting to identify the elemental constituents of a sample of
unknown composition it is necessary to approach the task systematically.
Failure to do this can result in a wrong identification, or at least a considerable
waste of effort and time.
The first step is to acquire a suitable spectrum or set of spectra. If the
sample is homogenous then a single spectrum may suffice, but if the specimen
is believed to have variations in composition in either the lateral or vertical
sense then several spectra recorded for different beam positions or beam
energies will be necessary. In any case, at least one of the spectra should be
taken at the highest energy available on the SEM, and with the spectrometer
set so as to be able to record the spectrum up to this energy. Thus, on an
145
The emissive mode and X-ray microanalysis
SEM capable of 30 keV operation, a spectrum should be recorded at 30 keV,
with the spectrometer set for the 0 - 3 0 or 0 - 4 0 keV range. This spectrum will
form the basis of all subsequent identifications because it will contain all the
possible X-ray lines that can be excited by the electron beam available.
Step two is to identify the peaks in this spectrum. The fundamental rule
for doing this (Goldstein et a/., 1981) is to start from the high-energy end of
the spectrum since this is where the K-series of lines will be located. Using
either the built-in markers of the multichannel analyser, or reading the peak
energy from the cursor and applying X-ray tables, the highest energy peak
(or peaks) are tentatively identified. If the peak is believed to be a K-line
then both K and K components must be visible unless the K and K
peaks overlap or the K peak is beyond the end of the energy scale. The
KJKp ratio for the lines should be about 3:1. If the ratio is significantly
different from this then an overlap with another peak, or a wrong identification of the lines in question, should be suspected.
Step three is to identify all of the other lines in the spectrum belonging to
the same element. So, for example, if in a spectrum recorded at 30 keV a pair
of peaks, in about a 3:1 ratio are seen at 22.1 and 24.9 keV then this would
be identified as silver (Ag, Z = 47). If this identification is correct, then a
family of L-lines, at 2.98, 3.15, 3.35 keV must also be present. These
lines should be found on the spectrum and identified as coming from silver.
In addition to identifying other characteristic lines from the same element
it is also necessary to identify and mark two other types of peaks in a
spectrum that may be associated with an element. Firstly, X-rays hitting the
Si(Li) detector may fluoresce a Si K-photon of energy 1.74 keV as they enter.
If their original energy was £ k e V then after this has occurred their energy
will be (£— 1.74) keV. Each line in the spectrum is therefore, potentially,
accompanied by an "escape" line lying 1.74 keV below it. O n most modern
M C A systems these lines are identified automatically. Since, however, they
are usually only 1 or 2% of the strength of line that produced them, escape
peaks are only a problem for the strongest lines in the spectrum. Secondly,
if two X-ray photons E and E arrive at the detector at about the same
time then they will be recorded as a single pulse of energy E + E . If the
spectrum contains one or more dominant peaks then there is a chance of
finding "sum" peaks at such energies, as well as self-sum peaks at
2E 2E ,
etc. Provided that the spectra were recorded under reasonable conditions
such that the count rate was within the system's capability, these peaks should
be small. If major sum peaks are found then a new spectrum at a lower
count rate should be recorded.
Step four is then to repeat the above procedures starting with the next
highest energy unknown line until all lines in the spectrum have been
identified. In some cases, some ambiguity may still remain for some lines,
a
p
a
p
p
x
2
l
2
l9
2
D.C. Joy
146
because of overlaps or the unavailability of a suitable X-line to use as a
cross-check. In such cases, it may be necessary to vary experimental conditions
so as to produce a related but different spectrum for comparison.
4.8
Quantitative X-ray analysis
Once the elemental constituents of the sample have been identified then the
composition can be determined. The basic information required to accomplish
this is the intensity of one (or more) of the X-ray peaks from each element
present. The determination of this intensity depends on the type of X-ray
spectrometer used. F o r a W D S system the peak is so narrow that the intensity
may be taken as the peak count minus the background, which is estimated
by averaging the background count measured on the high and low energy
sides of the peak. With an E D S the peak is broader, because of the poorer
resolution and the bremsstrahlung background, and therefore appears as
relatively more significant. It is therefore necessary to accurately model the
background, strip this from beneath the peak, and then integrate the intensity
in the peak. The background can be modeled using the formula of eqn (4.5),
suitably corrected for absorption of X-rays by the specimen (e.g. Statham,
1976). Alternatively, the background can be stripped from the spectrum by
a digital filtering method which relies on the different shape of the characteristic peaks and the bremsstrahlung (e.g. McCarthy and Schamber, 1981). A
detailed discussion of these methods can be found in Heinrich (1981). Usually
commercial X-ray systems supply software to execute either approach.
The software required to perform the quantitative analysis is also invariably
supplied by the manufacturer of the system. Thus, few users will ever have
to write their own programs to carry out an analysis. An understanding of
the steps involved is, however, vital to a proper application of the technique.
The starting point for most methods is the corrected relative intensity K
for each of the elements, where X is defined as the intensity from element
A measured from the u n k n o w n divided by the intensity measured under
identical conditions from a pure element standard of the element. The taking
of the ratio between the u n k n o w n and the standard is important because it
eliminates the necessity of accurately knowing the efficiency of the X-ray
detector and other relevant parameters.
In the simplest case of a binary mixture of A and B, then the relationships
between the weight fraction C and C of A and B and the corrected relative
intensities K ,K
is sown in Fig. 4.21. The curves obtained experimentally
can be fitted to equations of the type (Ziebold and Ogilvie, 1964)
A
A
A
A
B
B
*a = C / [ M
A
A
+
(1-M )C ]
A
A
(4.16)
The emissive mode and X-ray microanalysis
Corrected Relative Intensity
147
Weight % of A in B
F i g . 4.21
Calibration curve for binary mixture between A and B.
K
B
= C /[M
B
B
+ (1-M
B
)C
B
]
(4.17)
where M and M are constants for elements A and B in the system
AB for fixed beam energy etc.
Given a suitable set of binary standards an experimental calibration curve
can be determined between C and K , and C and K (although since
C + C = 1 this would only be for the purposes of testing). M and M can
then be found by a fitting procedure, and the analysis of any subsequent
unknown can then be carried out by an application of eqn (4.16).
While this procedure is straightforward and accurate it is also lengthy
because several high-quality, homogenous, binary standards are required.
The complexity of the method also increases rapidly when we move from a
binary system to one containing three or more elements. An alternative
approach is therefore required.
The " Z A F " method is the most widely used technique for this purpose. It
is a theoretical method which attempts to correct the data for Z - atomic
number, A - absorption, and F - fluorescence, effects.
The zero-order approximation assumes that the k ratio reflects the
composition, i.e.
A
B
A
A
A
B
B
B
A
fe = C
A
B
(4.18)
A
The Z connection is needed because the fraction of energy backscattered
in the u n k n o w n and in the standard will not be the same. Secondly, the
energy deposited will be divided between the elements in the unknown in a
way which may not be the same as the weight fractions. Thus, to a first
approximation
k — ZC
A
A
(4.19)
148
D.C. Joy
where Z = f(R, N\ R is the backscatter correction and N is the correction
for different number of X-rays produced in the unknown and the standard.
Models for computing the values of R and N require a detailed knowledge
of the electron-solid interaction, such as provided by the Monte Carlo
methods discussed in a previous chapter.
The absorption correction is necessary because between the point at which
they are generated and the point at which they are counted, the X-rays must
pass through the specimen and some fraction of them will be absorbed. The
rate of absorption depends on all the elements that are present so the
absorption will be different in the unknown and in the standard. Thus, the
next approximation has
(4.20)
k = ZAC
A
A
where A = f(E , £ , 9) with E being the beam energy, E the energy of the Xray line and 9 is the angle between the line joining the detector to the sample
and the incident beam direction.
The fluorescence correction arises because not all of the X-rays generated
are produced by the incident beam. For example, if one of the X-ray lines
which is excited is of sufficient energy then it can fluoresce that line and
produce an additional contribution to the spectrum. Thus, the final approximation is
c
Q
Q
c
(4.21)
k = ZAFC
A
A
where F is a complex empirical expression depending on the parameters such
as the energy, fluorescent yield and nature of the X-ray lines as well as on the
beam energy and materials constants.
The software provided evaluates the Z, A and F terms and then calculates
corresponding C value from the measured k data. Clearly, the values of Z, A
and F themselves depend on the composition of the unknown. An iterative
procedure is therefore required. The starting guess for the composition is that
C = k etc. Using this estimate the correction factors are evaluated and new
values for C , C , etc. found, and these are in turn used to find new corrections.
This process is continued until a self-consistent set of data is obtained. Ideally,
at the end, the values of Z, A, F for each element should be close to unity. Any
significant deviation indicates that a large correction has been necessary,
which obviously reduces the accuracy of the result. In such a case the best
procedure is to try and adjust the experimental conditions such as to reduce
the value of the correction required. Detailed discussions of the Z A F
procedure can be found in Goldstein et al. (1981) and Heinrich (1981).
M a n y X-ray systems now offer a "standardless" analysis in which the data
for normalization are supplied either from stored spectra or are computed
from a model. Such procedures can be both fast and accurate in many
A
A
A
A
B
A
The emissive mode and X-ray microanalysis
149
situations, but they d o require special care in setting u p the measurement a n d
in knowing a n d recording all the experimental parameters, as unintentional
misalignments may produce erroneous results. Wherever possible, therefore,
standards should be used since they eliminate completely many of the most
likely uncertainties about the experiment.
It can finally be noted that the Z A F technique, or its variants, are not
suitable for some classes of samples encountered in semiconductor studies,
such as layered compounds. In such cases, approaches based on a detailed
model of the sample geometry a n d composition, a n d the application of a
M o n t e Carlo or transport equation model of the electron beam-solid
interaction are required.
References
Andersen, CA. and Hasler, M.F. (1966). In X-ray Optics and Microanalysis, Proc. 4th
Int. Cong, on X-ray Optics and Microanalysis, eds Castaing, R., Deschamps, P. and
Philibert, J., Hermann, Paris, p. 310.
Castaing, R. (1951). PhD thesis, University of Paris.
Cazaux, J. (1986). J. Appl. Phys., 59, 1418.
English, C.A., Griffiths, B.W. and Venables, J.A. (1973). Acta Electronica, 16, 43.
Everhart, T.E. and Thornley, R.F.M. (I960). J. Sci. Instr., 37, 246.
Fathers, D.J, Jakubovics, J . P , Joy, D.C, Newbury, D.E. and Yakowitz, H. (1973).
Phys. Stat. Sol. A, 20, 535.
Fathers, D.J, Jakubovics, J.P, Joy, D.C, Newbury, D.E. and Yakowitz, H. (1974).
Phys. Stat. Sol. A, 22, 609.
Goldstein, J.I, Newbury, D.E, Echlin, P , Joy, D.C, Fiori, C. and Lifshin, E. (1981).
Scanning Electron Microscopy
and X-ray Microanalysis,
Plenum, New York.
Heinrich, K.F.J. (1981). Electron Beam X-ray Microanalysis, Van Nostrand-Reinhold,
Princeton, NJ.
Joy, D.C (1987a). In Microbeam Analysis - 1987, ed. Geiss, R.H, San Francisco Press,
San Francisco, p. 117.
Joy, D.C. (1987b). J. Microscopy, 147, 51.
Joy, D.C. and Jakubovics, J.P. (1968). Phil. Mag., 17, 61.
Knoll, M. (1941). Naturwissenschaften, 29, 335.
Kuroda, K , Mosoki, S. and Komoda, T. (1985). J. Electr. Microsc, 34, 179.
McCarthy, J.J. and Schamber, F.H. (1981). In Energy Dispersive X-ray
Spectrometry,
eds Heinrich, K.F.J, Newbury, D.E, Myklebust, R.L. and Fiori, C.E, National
Bureau of Standards Publication 604, p. 273.
Moseley, H.G.J. (1913). Phil. Mag., 26, 1024.
Moseley, H.GJ. (1914). Phil. Mag., 27, 703.
Pawley, J.B. (1974). In Scanning Electron Microscopy, 1976, eds Johari, O. and Corum,
I , IITRI, Chicago, p. 27.
Seiler, H. (1983). J. Appl. Phys., 54, Rl.
Statham, P.J. (1976). X-ray Spectrometry, 5, 154.
Ziebold, T.O. and Ogilvie, R.E. (1964). Analyt. Chem., 36, 322.
5 Voltage Contrast and Stroboscopy
S.M. DAVIDSON
Deben
Research,
5 Friars
Courtyard,
Princes
Street, Ipswich,
IP1
1RJ,
UK
List of symbols
5.1 Introduction
5.2 Principles
5.2.1 Voltage measurement
5.2.2 Stroboscopy
5.2.3 Boxcar averaging
5.3 Instrumentation
5.3.1 General resolution considerations
5.3.2 Electron probe
5.3.3 Electron energy
filters
5.3.4 Beam blanking systems
5.3.5 Other equipment
5.4 Applications
5.4.1 Operating conditions
5.4.2 Passivated devices
5.4.3 Passivation removal
5.4.4 Microprocessors and memories
5.4.5 Application-specific integrated circuits (ASICs)
5.4.6 CMOS latch-up
5.4.7 Junction location and leakage
5.4.8 Surface acoustic wave devices
5.5 Recent developments
References
|.
.
.
153
154
156
156
167
175
177
177
178
182
193
200
206
206
213
216
218
223
226
230
234
235
238
List of s y m b o l s
a
electron beam semi-angle
b(t) electron beam time profile
B
electron gun brightness
C
spectrometer constant
C
spherical aberration coefficient
C
chromatic aberration coefficient
d
electron beam spot size
S
e
£, E
E
AE
A/
y
SEM Microcharacterization of Semiconductors
ISBN 0-12-353855-6
Copyright © 1989 Academic Press Limited
All rights of reproduction in any form reserved
s
c
b
s
secondary electron coefficient
electron charge
electron beam energy
secondary electron energy
electron energy spread
signal bandwidth
fraction of collected signal
S.M. Davidson
154
^se
/
X
N(E)
t
m
m
T
5.1
electron beam current
secondary electron current
blanking plate length
electron wavelength
electron energy distribution
beam pulse width (duration)
measurement time/point
time constant
filter grid transmission
v
Vs, V(t)
AV
AV
G
Vf
w
Ax
Z
electron velocity
sample voltage
slope of S-curve
voltage resolution
filter voltage
blanking plate separation
beam deflection
beam path length
Introduction
The origins of voltage contrast can be traced back to the early days of the
development of the scanning electron microscope in Cambridge. Everhart and
Oatley (Oatley and Everhart, 1957; Everhart et al, 1959) noted that the
brightness of the S E M image varied if the potential of the sample was made
positive or negative with respect to ground. In general, the picture became
brighter with a negative voltage and darker with a positive voltage.
This variation in contrast with sample voltage, or voltage contrast as it
became known, was observed to alter both with the beam voltage and the
nature of the sample, being most pronounced under conditions where the
secondary electron yield was highest, i.e. at low beam voltages. It was clear that
two effects were occurring. Both the secondary electron yield and the electron
trajectories were being altered by the specimen voltage. Qualitatively, it is not
difficult to understand why either of these effects should occur. The majority of
secondary electrons have energies of a few electronvolts only. It is reasonable
to expect that these will be influenced in some way by similar potentials
between the sample and ground. A positive sample voltage will decrease the
secondary electron signal by producing an electric field which attracts lowenergy electrons back to the sample. Conversely, a negative potential will
increase the escape probability. The influence of sample voltage on trajectories
is more complicated, with the result that this primitive voltage contrast is
highly dependent on the S E M operating conditions, the nature of the sample,
and in particular on its position and orientation with respect to the SEM
chamber, final lens and secondary electron collector.
Despite this somewhat unpredictable behaviour, basic voltage contrast has
provided a valuable tool for investigating a wide range of simple faults in
microelectronic devices over the last 20 years. In many instances the failure
analyst needs only to know whether the voltage is high or low (typically + 5 V
or 0 V). However, it soon became clear that the technique would be much more
useful if the sample voltage could be measured. In particular, the emerging
electronics industry viewed it as a method for measuring voltages on
Voltage contrast and stroboscopy
155
semiconductor devices without having to make direct physical contact to tiny
regions on the device. Apart from the obvious risk of causing physical damage,
mechanical probing also electrically loads the internal circuitry, and can cause
it to malfunction. With device geometries shrinking, there was a clear need for
some form of non-destructive testing.
An additional requirement was the ability to measure varying, as opposed
to static, voltages. Ten years ago the first microprocessors had made their
appearance, with clock speeds of a few megahertz. A method for examining or
measuring the voltage distribution on an integrated circuit at any point in its
operating cycle with nanosecond time resolution was considered highly
desirable.
It was soon established (Wells and Bremer, 1968; Fleming and Ward, 1970)
that the principal cause of voltage contrast was a variation in the secondary
electron energy distribution with sample voltage. This led to the development
of a wide range of electron spectrometers, analysers and filters to "quantify"
the voltage contrast. Plows and Nixon (1968) showed that voltage contrast
measurements could be performed dynamically on operating devices by
pulsing the electron beam in synchronism with the device signal, effectively
converting the SEM into an electron stroboscope. This in turn led to the
development of electron beam blanking or pulsing systems. Combining
quantitative voltage contrast detection with electron stroboscopy led to the
commercial availability of equipment for making voltage contrast measurements on semiconductor devices - what is now known as electron beam (or Ebeam) testing.
During the 1970s and early 1980s the techniques were developed and refined
in a number of laboratories around the world. Prominent amongst these are
the Universities of N o r t h Wales (Gopinath), Duisburg (Kubalek and Menzel),
Osaka (Fujioka), Edinburgh (Dinnis), and the research laboratories of
Siemens (Wolfgang and Feuerbaum) and IBM (Wells). Reviews of the early
days of voltage contrast and stroboscopy have been published by Gopinath et
al (1978) and Lukianoff (1987).
Electron beam testing has now been widely adopted by the electronics
industry for design validation, debugging and failure analysis. With current
generations of integrated circuits incorporating tracks less than 1
wide,
voltage contrast clearly has a major role to play in the development of future
semiconductor devices. This chapter presents a comprehensive account of
voltage contrast and stroboscopy - principles, practice and applications.
Section 5.2 covers the principles of voltage measurement and stroboscopic
operation, while Section 5.3 discusses the instrumentation which has been
developed for quantitative voltage measurements (E-beam testing). Section 5.4 lists the range of devices which can be examined using voltage contrast
techniques, and illustrates voltage contrast imaging, voltage coding, stroboscopic imaging, logic state mapping, waveform measurement and timing
156
N(E)
S . M . Davidson
J
1
10
100
Energy
1000
10000
(eV)
F i g . 5.1 Energy spectrum of electrons baekscattered/emitted from sample (10kV
primary beam energy).
diagrams with examples from the whole spectrum of semiconductor technology. The final section examines recent developments, and looks into the
future to assess how the technique and equipment must develop to keep pace
with the needs of the electronics into the 21st century.
5.2
5.2.1
Principles
Voltage m e a s u r e m e n t
Voltage measurement using the S E M is based on the principle that the energy
spectrum of the emitted secondary electrons changes in a predictable manner
with specimen voltage. While all emitted electrons are influenced to some
extent by the potential between the sample and its surroundings, only the
secondary and Auger electrons can, in practice, be used for voltage measurement.
Macdonald (1970) showed that the position of the carbon 270 eV peak in the
Auger spectrum shifted linearly with applied voltage over the range — 5 V to
+ 5 V. However, two factors prevented this approach forming the basis of a
voltage measurement system. First, the very low yields of Auger electrons lead
to very long measurement times; we will see later that signal levels are crucial
in determining the voltage resolution of an electron beam testing system.
Second, the ultrahigh vacuum requirements of Auger analysis are somewhat
unrealistic for conventionally packaged semiconductor devices.
In practice, secondary electron energy analysis forms the basis of quantitative voltage contrast. Figure 5.1 shows the complete energy distribution of
electrons emitted or scattered from any material. Two main peaks are
observed, one at high energy corresponding to the backscattered primary
electrons, and one at low energy corresponding to the secondary electrons.
c
CD
"u
4—
M—
CD
O
U
L_
•H 0 D E
-M
(D
U
0)
A:
U
(D
CD
Backscatter coefficient
Beam E n e r g y ( k V )
F i g . 5.2
number.
20
40
B0
Atomic number ( Z )
80
Backscatter coefficient as a function of primary beam energy and atomic
CD
x
c
o
k_
-M
U
_a>
CD
x[
(D
T3
C
o
u
CD
Electron energy (eV)
F i g . 5.3
Secondary electron yield versus primary beam energy.
158
S.M. Davidson
LjU
z
I
I
Fig. 5.4
I
I
I
5
Electron
10
energy (eV)
15
I
Secondary electron energy spectrum.
Small bumps in the intermediate region arise from plasmon losses and Auger
electrons. The numbers of backscattered and secondary electrons are approximately equal. The variation of backscatter coefficient with electron beam
energy and atomic number is shown in Fig. 5.2. In general, the numbers of
backscattered and secondary electrons increase with increasing atomic
number and decreasing beam voltage.
Voltage contrast examination is normally performed at low beam voltages
(0.5-3 kV) on low atomic number materials (silicon, aluminium, or silicon
dioxide). The secondary electron yield from Al under these conditions is shown
in Fig. 5.3; over much of the range it is greater than unity. The electron energies
where the yield is unity are known as the first and second crossovers, and vary
with material. Typically, the first crossover occurs at a few hundred
electronvolts, and the second at energies between 700 eV (Al) and 2.5 kV
( S i 0 ) . It will be seen later that there are certain advantages when operating at
beam voltages close to one of these crossover points.
N(E)
2
Fig. 5.5
5
10
Electron
energy
15
(eV)
Secondary electron energy spectrum versus specimen voltage.
Voltage contrast and stroboscopy
159
The secondary electron signal from a sample under typical voltage contrast
examination conditions is thus comparable with the electron beam current.
The energy distribution of these secondary electrons is shown in Fig. 5.4 for a
sample at ground potential. The peak occurs at typically 3 eV, tailing off as
approximately l/E at high energies. The majority of secondary electrons, with
energies of a few electron volts, will thus be capable of being influenced by small
sample voltages.
The variation of energy distribution with specimen voltage is shown in
Fig. 5.5. With negative specimen voltage, the distribution moves along the
horizontal axis in the direction of higher energy. In other words, all secondary
electrons have their energies increased by an a m o u n t equal to the sample
voltage. Expressed another way, the secondary electrons always have the same
energy distribution with respect to the sample. The specimen voltage then
adds to or subtracts from the electron energy with respect to ground.
When the sample voltage is positive with respect to ground, the situation is
slightly more complex. Electrons with energies higher than the sample voltage
will still escape, but with their energy reduced by the sample voltage. Electrons
with energies lower than the positive sample voltage will not escape. The
resulting energy distribution will thus appear truncated.
Plotting the total number of secondary electrons emitted as a function of
sample voltage gives the solid curve in Fig. 5.6. The origin of voltage contrast
with positive sample voltages is now clear, but this would also suggest that
little change will occur with negative voltages. In practice, this idealized curve
will only result if all the emitted secondary electrons reach the electron
collector. Normally a certain a m o u n t of energy filtering will occur by virtue of
the relative positions of the sample, specimen chamber walls (electrical
ground) and collector. The probability of electrons reaching the collector will
vary with energy (effectively the trajectory effect), with the result that the solid
curve in Fig. 5.6 will be modified by the "filter" characteristic of the collector.
JN(E)dE
-10
-5
0
Specimen v o l t a g e
F i g . 5.6
±
10
(V)
Secondary electron detector signal versus specimen voltage.
160
S.M. Davidson
N(E)
-5
0
5
E l e c t r o n energy
Fig.5.7
10
15
(eV)
Secondary electron spectrum versus specimen voltage with extraction field.
The variation of collected signal with specimen voltage will thus more closely
resemble the dashed line. The origin of the contrast increase with negative
specimen voltage, and its somewhat unpredictable nature, is now apparent.
These qualitative arguments are borne out by computer simulations of
electron trajectories from sample to detector (Nakamae et al, 1981; Menzel,
1981; Menzel and Kubalek, 1983a).
To record the complete secondary electron energy distribution from
samples held at positive and negative potentials, we need to make measurements with respect to a reference voltage more positive than the maximum
positive voltage. In practice this means accelerating all the secondary electrons
away from the sample prior to analysis. The resulting distributions are shown
in Fig. 5.7. Under these conditions it is now clear that the distribution simply
translates along the voltage axis by an a m o u n t equal to the sample voltage. A
measurement system monitoring this peak shift could then form the basis of a
quantitative voltage contrast system.
Voltage measuring systems using this approach have been developed;
however, both practical and theoretical difficulties exist with its implementation. The practical limitations relate to the type of instrument necessary to
record the energy distribution, i.e. an electron spectrometer (a term now
applied indiscriminately to most voltage contrast analysers). A spectrometer,
by definition, only accepts electrons within a narrow band of energies, the
width of this band or window determining the spectrometer resolution. This
window is then swept over the complete energy range to record the spectrum
(Fig. 5.8). The signal level recorded at any point on the spectrum will only be a
small fraction of the total secondary electron signal, giving a poor signal-tonoise ratio. We will see later that a good signal-to-noise ratio is vital to the
performance of any quantitative voltage contrast system.
Another problem arises when attempting to use the secondary electron
Voltage contrast and stroboscopy
Electron energy
F i g . 5.8
161
(eV)
Spectrometer bandwidth definition.
peak position as a measure of sample voltage. As indicated earlier, the peak
occurs at an energy of typically 2 - 3 eV with respect to the sample. Electrons
emitted with such low energies are adversely influenced by transverse or
"fringing" fields which occur near closely spaced conductors at different
voltages. With real samples, a more accurate indication of voltage can often be
obtained by recording the shift in the higher energy part of the distribution,
rather than the peak.
These difficulties have led to the universal adoption of energy filtering
techniques for voltage contrast measurement. If instead of plotting N(E)
against £, we plot the integral of N(E) from E to infinity against £, we get the
curves in Fig. 5.9. Each curve represents the number of secondary electrons
emitted with energies greater than £, as a function of E. The characteristic " S "
shape of these curves has led to the widespread use of the term "S-curve" to
indicate this type of distribution. The position of maximum slope on the Scurve corresponds to the peak of the energy distribution (Fig. 5.7). If the energy
(N (E )dE
1
F i g . 5.9
voltage.
I
I
-15
-10
I
A
I
-5
0
Electron energy
I
I
I
5
(eV)
10
15
Integrated secondary electron energy spectra (S-curves) versus specimen
S.M.Davidson
162
Electron energy (eV)
F i g . 5.10
Energy filter collection efficiency.
distribution does not change shape with sample voltage, an assumption we
will examine later, the corresponding S-curves will simply translate linearly
along the voltage axis. This principle forms the basis of all voltage contrast
measurement systems available today.
Deriving the sample voltage from the S-curve has many advantages over
monitoring the peak position. First, only an energy filter is required, as
opposed to a spectrometer (most so-called voltage contrast spectrometers are,
in fact, filters). An ideal high-pass energy filter will pass all electrons with
energies above a certain value, and block all those with lower energies
(Fig. 5.10). The transfer efficiency of an energy filter is much higher than that of
a genuine spectrometer, improving the signal-to-noise ratio. Second, energy
filters are much simpler to construct than spectrometers. In principle, a single
grid is all that is required.
A third advantage concerns the extraction of the sample voltage from the Scurve behaviour. Voltage measuring systems based on S-curve shift are simple
to implement because of the monotonic nature of the characteristic; one value
of the signal corresponds to one value of voltage. The most popular method for
deriving the sample voltage from the S-curve shift is known as "closed-loop
operation", pioneered by Fleming and W a r d (1970) and G o p i n a t h and Sanger
(1971). Figure 5.9 shows that every point on the S-curve shifts along the
horizontal axis by the same a m o u n t with applied voltage. T o measure the
voltage change, we simply have to define a signal level and arrange a feedback
loop to maintain this level by controlling the filter voltage.
This can be seen more clearly with reference to Fig. 5.11, which shows Scurves recorded from a sample at 0 V and 5 V. We should remember that these
curves are derived by varying the voltage on a filter electrode and recording
the transmitted signal. Assume that the filter is set to — 3 V (the dashed line in
Fig. 5.11). If the sample is at 0 V, the signal level will correspond to point A on
the 0 V S-curve. Let the sample voltage change to 5 V. With the filter still set to
— 3 V, the signal will d r o p to point B on the + 5 V S-curve. The corresponding
voltage contrast image would go dark. The filter voltage is now driven positive
163
Voltage contrast and stroboscopy
0
5
Filter
F i g . 5.11
-5
voltage
-10
(V)
Measurement of specimen voltage using closed-loop method.
to bring the signal back to its original level (point C). If the S-curve has
translated linearly, we can see that the filter voltage will have altered by 5 V to
+ 2 V, the difference between the new and old sample voltage.
This is the basis of closed-loop operation (Fig. 5.12). The signal transmitted
through the filter is compared with a reference, and the difference used to
increase or decrease the filter voltage. If the gain of the feedback loop is
sufficiently high, the filter voltage will always change by the same a m o u n t as
the specimen voltage. In effect, the filter electrode has been AC coupled to the
sample.
Closed-loop voltage contrast will give an accurate measure of the specimen
voltage if the shape of the secondary electron energy distribution, and hence
REFERENCE
ELECTRON
BEAM
COMPARATOR
DETECTOR
F I L T E R GRID
- <
SAMPLE
F i g . 5.12 Closed-loop voltage contrast.
164
S . M . Davidson
DEVICE
F i g . 5.13 Typical device geometry.
the S-curve, is invariant with sample voltage. This does not always happen,
and we now have to consider the factors which control voltage measurement
accuracy and resolution in real situations.
Voltage measurement accuracy, i.e. how closely the measured voltage
follows the sample voltage, is principally influenced by the geometry of the
sample being examined. Voltages on tracks or regions adjacent to the point
being examined produce what are known as fringing fields, and can exert a
large influence on the accuracy of the measurement. The effect is analagous to
cross-talk on electrical circuits, where signals from one track appear on
neighbouring regions.
Consider the device structure depicted in Fig. 5.13, with three adjacent
tracks. If all tracks are at the same potential, then there are no problems. If,
however, the tracks are at different potentials, the trajectories of the emitted
secondary electrons will differ radically from the simple model outlined above.
Figure 5.14, taken from Menzel and Kubalek (1983b), shows equipotentials
for the case where the centre track is positive with respect to its two
neighbours.
Local fields around integrated circuit (IC) tracks can be very high. If the gap
between the tracks is 2/mi, and the difference in potential 5 V, then the
maximum field is 2.5 kV/mm. Typical electric fields used to draw off, or extract
6
F i g . 5.14
Equipotentials: central track 5 V, outer tracks OV.
Voltage contrast and
stroboscopy
165
F i g . 5.15 Equipotentials: extraction field 1000 V/mm.
the secondary electrons, do not normally exceed 1 kV/mm. These transverse
fringing fields can have a dramatic influence on the yield and trajectory of
secondary electrons. In Fig. 5.14, electrons must overcome a potential barrier
of approximately 1 V before they can escape (an extraction field of 400 V/mm
is assumed). Electrons with lower energies will be returned to the track. The
potential barrier increases with voltage on the middle track; as a consequence
the secondary electron spectrum appears increasingly truncated. The S-curves
(Fig. 5.16) corresponding to these distributions no longer simply translate
along the horizontal axis as the simple theory would suggest. If the closed-loop
linearization scheme described above is used, large errors in the measured
voltage could arise because the spectrum shift is not proportional to the
applied voltage.
Increasing the extraction field to 1000 V/mm changes the equipotentials to
those illustrated in Fig. 5.15. The potential barrier has all but disappeared, and
the corresponding S-curves (Fig. 5.16) translate as expected, with only small
errors. An extraction field comparable to the maximum electric field between
conductors is needed to prevent the occurrence of a potential barrier above the
track of interest. In this case the track spacing is 4 /zm, and the corresponding
maximum field 1.25 k V / m m at 5 V.
The situation is more complicated in the asymmetrical case. N o t only will
the local field influence the number of secondary electrons emitted, but also
their angular distribution. Even in the symmetrical case, the fringing fields will
alter the angular distribution of the secondary electrons. This will influence the
resulting voltage measurement if the spectrometer does not analyse or filter all
electrons equally, irrespective of their angle of emission. F o r example, the
planar filters commonly used for voltage contrast linearization (see Section 5.3.1) have a finite acceptance angle, and only act on the component of
velocity (energy) normal to the sample surface. Changes in the angular
emission pattern will influence the numbers of electrons transmitted through
166
S . M . Davidson
Filter voltage (V)
F i g . 5.16 S-curve 0 V and 5 V, extraction field 400 V/mm and 1000 V/mm.
cn
s
Ln
Measurement error (V)
the filter, even if n o change in sample voltage occurs. Typical errors resulting
from both factors have been calculated by Menzel and Kubalek (1983b), and
are shown in Fig. 5.17. These graphs refer to devices with 4 /mi geometry. If the
errors scale inversely with device geometry, then the 400 V/mm curve could
apply to 1 fim devices, but only if the extraction field were 1600 V/mm. O n e of
the prime objectives of many spectrometer development programmes is to
create designs which are not sensitive to the secondary electron angular
distribution.
-
-
400V/min
y
—
1000V/mm
2
4
1
i
1
6
a
10
Line v o l t a g e ( V )
F i g . 5.17 Measurement error on 5 V track: 400 V/mm and 1000V/mm.
Voltage contrast and stroboscopy
167
Voltage resolution, defined as the smallest change in voltage which can be
detected, is principally determined by the strength of the collected secondary
electron signal. This in turn is derived from the transfer efficiency of the energy
filter, and the effective electron beam current. Since the latter is dominated by
beam duty cycle considerations, we will leave further discussion of this point
until after the next section.
5.2.2
Stroboscopy
As stated earlier, voltage contrast techniques are of most value to the
electronics industry if they are capable of measuring high-frequency signals
and recording images from semiconductor devices operating under normal
conditions. The bandwidth of most S E M electron detectors and amplifiers is
limited to a few megahertz. While adequate for some applications, the
requirements of semiconductor device testing now demand the ability to
measure timing to sub-nanosecond accuracy.
Stroboscopic sampling techniques are normally employed to circumvent
the intrinsic bandwidth limitations of the detection chain. Electron stroboscopy is exactly analagous to optical stroboscopy. An optical stroboscope
works by illuminating a rotating (or vibrating) object with short pulses of light
at the rotation frequency. The moving object is then always being viewed in the
same orientation, and appears stationary. If the phase difference or delay
between the light pulse and a reference on the moving object is altered, the
object can be viewed at any instant in its operating cycle.
The essential features of stroboscopy are (a) the movement of the object
must be periodic and (b) a signal must be provided to synchronize the light
source. In electron stroboscopy, the electron beam is pulsed in synchronism
with the voltage on the sample, a n d the same considerations apply. The sample
voltage must be periodic, and be associated with a suitable reference or trigger
pulse.
Stroboscopic techniques have two principal uses in quantitative voltage
contrast - stroboscopic imaging and voltage waveform measurement. Consider first imaging. Figure 5.18 shows input and output waveforms from a
simple device, together with a synchronous electron beam pulse. With the
beam pulse in position A, the input will be low (0 V) and the output high (5 V).
Even though the device is operating at 10 M H z , the corresponding stroboscopic image will be static with the input bright (low) and the output dark (high)
because the device is always being viewed (illuminated) at the same point in its
operating cycle. The image is exactly the same as if the input and output signals
were at D C voltages. Figure 5.19 shows a set of stroboscopic images recorded
at 1 ns intervals (Ura and Fujioka, 1978).
168
S . M . Davidson
>
"D
>
CN
100ns/div
F i g . 5.18 Stroboscopic voltage waveform.
If the electron beam pulse is delayed with respect to the device trigger or
reference point to B, the contrast is reversed. The electron beam now sees the
input dark (high) and the output bright (low). Setting the delay to intermediates values will show the voltages on the device throughout the switching
transition. Stroboscopic imaging thus gives a "frozen phase" picture of the
voltage pattern on the device at one particular point in its operating cycle.
The information which can be derived from such an image, i.e. approximate
voltage levels on all the conductors, is the same as that from a real time image.
However, the values will be less precise because the electron beam pulsing
greatly reduces the effective beam current, and hence the secondary electron
signal. F o r example, if the beam is being pulsed at 10 M H z with a pulse width
of 1 ns, the duty cycle, i.e. the ratio of the beam on time to the pulse period, will
be 1 ns/100 ns or 1%. The primary beam current will be reduced by this
fraction. If the electron beam current were 1 nA continuous, the "effective
beam current" will be 10 pA. This effective beam current, by controlling the
signal-to-noise ratio, plays an important role in determining one of the major
parameters of a quantitative voltage contrast system, the voltage resolution.
The second major application of stroboscopy to quantitative voltage
contrast is waveform measurement. Stroboscopic imaging is performed by
keeping the sampling phase fixed and sweeping the electron beam over the
sample. Waveform recording, on the other hand, keeps the electron beam fixed
at one point on a device and varies the sampling phase. Consider Fig. 5.20.
This shows a simple waveform and a sampling electron beam pulse. Assume
first that the secondary electron signal is being recorded directly. An energy
filter in closed-loop mode is not being used. The signal level at phase 0 is high
(5 V), so the secondary electron signal will be low. This gives point A on
Ons
5 ns
4 ns
F i g . 5.19 Stroboscopic voltage images from integrated circuit (Ura and Fujioka,
1978).
170
S.M.
-
Davidson
WAVEFORM
SIGNAL
BEAM PULSE
A
I
I
I
I
I
B
C
I
I
l
i
100ns/div
F i g . 5.20
Open-loop and closed-loop waveforms.
Fig. 5.20. As the phase is swept from zero through the complete cycle (360°), it
can be seen that the corresponding electron signal will trace out an inverted
version of the waveform. F o r example, at point B on the original waveform, the
voltage is half its maximum value. The corresponding signal level will then
reflect this value. At point C, the waveform voltage is low (0 V); the secondary
electron signal will then be high.
The resulting trace is sometimes referred to as an "open-loop" waveform (by
comparison with the more usual closed-loop operation). N o energy filter or
spectrometer is needed. While sharp transitions in the measured signal occur
at the correct position, it can be seen that the waveform is inverted and nonlinear, reflecting the non-linear dependence of secondary electron signal on
specimen voltage (Fig. 5.6). Inverting the signal electronically is simple
enough, but correcting for the non-linearity is more difficult.
It is more usual now to record waveforms using the closed-loop voltage
linearization method described earlier, i.e. combining quantitative voltage
contrast and stroboscopy. The result is also shown in Fig. 5.20. This corrects
the inversion and non-linearity, assuming of course an ideal specimen and
spectrometer (filter). The only proviso is that the time constant of the
feedback loop which controls the filter electrode voltage should be short
enough to follow the phase sweep. In practice, time constants of 1 ms or less are
Voltage contrast and stroboscopy
171
easily achievable; a 1000 point waveform could be recorded in one second,
although further signal averaging may be needed to reach an acceptable
signal-to-noise ratio.
Both closed-loop and open-loop stroboscopic waveform measurements
have been widely used for device assessment (see references in Sections 5.3 and
5.4). The advantage of the open-loop approach is that no energy filter or
spectrometer is needed. Where only logic levels and timing are required, the
method is often perfectly adequate. In some instances a simple filter is
employed to improve the linearity. The results are best regarded as timing
diagrams, and the method is suited to integrated circuits with well-defined
internal voltage levels, such as C M O S devices. M a n y of the published voltage
contrast waveforms were recorded using this method. O n the other hand, if
accurate voltage levels are required, or the transitions need to be measured
accurately, an energy filter operated in the closed-loop mode must be
employed.
Stroboscopic methods have a further advantage which is particularly
relevant to voltage contrast. Signal levels are generally very low. Because the
voltage being investigated appears static, signal or image averaging can be
employed to improve the signal-to-noise ratio, without compromising the
time resolution. If the phase (time delay) is fixed, the output is a D C voltage.
Long time constant filtering can give very good voltage resolutions, at the
expense of extended measurement times.
The bandwidth of the electron stroboscope is determined solely by the beam
pulse duration, and is not influenced by the time response of the detector or
signal processing electronics. Bandwidth is related to beam pulse width by:
0.4
BW = —
K
(5.1)
Strictly speaking, this applies only to a "square" beam profile. When the beam
on time is very short, the time profile becomes more triangular or Gaussian,
slightly altering the multiplying factor in eqn (5.1).
A word of caution regarding the terminology. Often bandwidth, beam pulse
width and time resolution are used interchangably to indicate the timing
performance of a stroboscopic electron beam system. However, recently time
resolution has been used, perfectly correctly, to indicate the accuracy with
which timing differences can be measured. Defined thus, time resolution is
more a measure of the stability of the delay circuitry than an indication of the
minimum beam pulse width.
Figure 5.21 compares true and measured waveforms for different sampling
beam pulse widths, recorded using the closed-loop method. It can be seen that
the position and shape of waveform transitions is represented most accurately
when the beam pulse is comparable in with the transition time being measured.
172
S . M . Davidson
2V/dlv
i—i—i—i—i—i—i—i—r
I
F i g . 5.21
I
I
I I
I
100ns/div
I
i
»
Stroboscopic voltage contrast waveforms versus beam pulse width.
If the beam pulse is too long, the transition time measured is determined
almost wholly by the beam pulse width. The signal corresponding to any point
on the measured waveform is an average of the secondary electron signal over
the duration of the beam pulse. In fact, the relation between the measured
signal, the beam pulse width and the sample voltage is:
V(t)-
V(t-t')b(t')dt'
(5.2)
where b(t') is the beam profile. The waveform is effectively convolved with the
beam pulse. This convolution will only cause errors where the waveform is
changing rapidly, i.e. at transition points. F o r example, at point B on the
waveform in Fig. 5.20, the electron pulse spends half its time sampling the high
level, and half sampling the low level. Because of the non-linear dependence of
secondary electron signal on voltage, the halfway point on the recorded
waveform, often used as a reference point for timing specifications, will not
necessarily correspond to the halfway point on the original waveform. Where
the beam pulse width is comparable with the transition time (Fig. 5.21), the
errors are least marked.
At the other extreme, when the beam pulse is much shorter than the
transition time, the timing error with respect to the transition time is small.
However, we should note that the signal level is in direct proportion to the
173
Voltage contrast and stroboscopy
i—i—i—i—i—i—i—i—r
I
i
i
i
i
i
i
i
i
i
l
100ns/div
F i g . 5.22 Open-loop and closed-loop voltage contrast waveforms at high (A) and
low (B) beam currents.
beam pulse width. If the open-loop method is used, the resulting signal will
simply decrease in amplitude (Fig. 5.22). However, this cannot happen if the
closed-loop method is employed, because the feedback loop gain will increase
to maintain the same signal level. As a consequence the noise level in the signal
will increase (Fig. 5.22), reducing the voltage resolution. We can see that, while
shorter electron beam pulses give better time resolution, longer beam pulses
give better voltage resolution. A compromise is always necessary. If the
principal objective is to record the position of the transitions, then set the beam
pulse width equal to the transition time. If the shape of the transition is to be
measured, narrower pulses must be employed, with a consequent degradation
of the signal-to-noise ratio.
All forms of stroboscopic operation usually imply low effective beam
currents, the continuous electron probe current being reduced by the beam
duty cycle. Signal processing must be optimized to obtain the maximum
a m o u n t of information. T h e principal parameter used to measure the
performance of a voltage contrast system, particularly in waveform operation,
is voltage resolution. This is defined as the smallest change in voltage
detectable, a n d is determined by the signal-to-noise ratio, a n d the a m o u n t of
further processing. G o p i n a t h (1977) showed that the voltage resolution could
be calculated from the primary beam current, duty cycle, secondary emission
174
S.M. Davidson
coefficient, measurement time and efficiency of the energy filter. His formula is:
AV= 3 A K / [ 2 ^ ( 1 + <5)]-^vW// b )
(5.3)
GV
where AV is the slope of the S-curve, 5 the SE emission coefficient, T the
transmission of the grids, / the bandwidth of the detection system and I the
beam current. This is commonly rewritten:
G
0
h
AF=CV(A/// )
b
or
C/V(U )
(5.4)
b
where C, known as the spectrometer constant, is a measure of the efficiency of
the energy filter or spectrometer. A typical value is 1 0 " VA
S . This
parameter can be determined by measuring the signal-to-noise ratio on a
waveform with a known electron beam current and signal processing
bandwidth. Figure 5.6 shows that the variation of secondary electron signal
with filter voltage is greatest at the point of maximum slope, which
corresponds to the peak of the energy distribution (Fig. 5.5). However, it is
sometimes found necessary to operate at lower signal levels, using the higher
energy secondary electrons, to minimize fringing fields. The slope here is lower,
i.e. larger changes in specimen voltage are needed to give the same change in
signal. Plotting voltage resolution against effective beam current for various
values of filter efficiency gives the curves in Fig. 5.23. F o r a beam current of
1/2
1/2
Voltage
resolution
(mV)
_^
7
Mean beam c u r r e n t
(pA)
F i g . 5.23 Voltage resolution versus mean beam current: measurement time per
point 10ms and Is.
Voltage contrast and
stroboscopy
175
BEAM PULSE
INPUT SIGNAL
BOXCAR AVERAGER
_y
—
SIMPLE FILTER
GROUND
F i g . 5.24 Boxcar averaging versus simple filtering.
100 pA, typical voltage resolutions are 10 mV for l s / p o i n t , or 100 mV for
lOms/point.
5.2.3
Boxcar averaging
The voltage resolution figures presented in Section 5.2.2 are maxima, determined primarily by the statistics of the electron beam, and may be degraded by
the subsequent electronic signal processing. O n e technique widely used to
minimize signal-to-noise degradation by the recording system is boxcar
averaging. The problem is illustrated in Fig. 5.24. Assume that (a) the sampling
phase is fixed, (b) the duty cycle is 1% and (c) the signal coming from the
detector or filter is 1 V (this argument applies equally to open- and closed-loop
waveform recording). It is usual to low-pass filter this signal, optimizing the
filter time constant with reference to the measurement time per point. If a
conventional filter is used, the output will follow the lower line in Fig. 5.26. The
average output level is equal to the input signal times the beam duty cycle, in
this case 10 mV. D u t y cycles less than 0.1% are not infrequently used, giving
output levels less than 1 mV. Subsequent amplification of these low-level
signals can add significantly to the noise.
Another problem with direct filtering is that there may be an input signal
even when the beam is off. This can arise from photomultiplier dark current,
spurious scintillation, or imperfect beam blanking. Such signals can cause
errors in the output and degrade the signal-to-noise ratio. F o r example, a
20 mV input signal during the beam-off period (2% of the beam-on signal) will
alter the output signal to 30 mV, a factor of three. Noise in this offset will also
degrade the system performance.
Boxcar averaging, or signal gating, circumvents these difficulties. To the
176
S.M.
Davidson
>—(Ze=3—?
SIMPLE FILTER
;
;c
c
BOXCAR AVERAGER
F i g . 5.25 Electrical configuration of boxcar filter.
simple filter is added a switch, which is opened and closed synchronously with
the beam pulsing (Fig. 5.25). When the beam is on, the switch is closed,
allowing the signal into the filter. When the beam is off, the switch is open. This
has two important effects. First, it eliminates noise and offsets from the output
signal when the beam is off. Second, the average output signal will equal the
input signal when the beam is on, in this case 1 V, rather than the 10 mV or less
if a simple filter is used. The filter capacitor cannot discharge during the beamoff time; the voltage will thus build up to the input level.
This arrangement, variously known as a boxcar averager, signal gate or
switched filter, while ensuring that the input signal-to-noise ratio is not
degraded by the subsequent electronic processing, does have one drawback.
The boxcar averager is still a low-pass filter; however, the effective time
constant is determined by the duty cycle as well as the filter time constant. The
relationship is:
T =
RC/d
(5.5)
where d is the duty cycle, i.e. the effective time constant is lengthened by the
presence of the switch. O p t i m u m performance is obtained when the effective
time constant matches the recording time, and the filter parameters must
therefore be capable of being adjusted with the duty cycle to achieve this.
Boxcar averaging can be applied to all forms of stroboscopic voltage
contrast - imaging, open-loop waveforms and closed-loop waveforms, timing
diagrams and logic state mapping. A short time constant appropriate to the
video bandwidth will be needed for the imaging applications, otherwise the
principle is the same. It should be remembered that the signal is likely to be
delayed from the beam pulse; it will also be broadened by the time response of
Voltage contrast and stroboscopy
177
BEAM PULSE
SIGNAL
BOXCAR PUL5E
F i g . 5.26
Boxcar pulse requirements.
the detector and any electronics which precedes the boxcar switch (Fig. 5.26).
The pulse which operates the boxcar gate, while synchronized with the
electron beam pulse, must therefore also be delayed and widened. The width
for optimum noise performance is typically the F W H M (full width at half
maximum) of the signal coming into the boxcar averager.
5.3
5.3.1
Instrumentation
General resolution considerations
The performance of a quantitative voltage contrast system or electron beam
tester is principally characterized by three resolution parameters - spatial
resolution, voltage resolution and time resolution. Section 5.2 showed that
voltage resolution was ultimately determined by shot noise in the electron
beam, provided that no further degradation occurred in the energy filter
(spectrometer) or signal processing. The effective beam current is simply the
steady-state electron probe current multiplied by the duty cycle. Using shorter
electron beam pulses to improve the time resolution, while keeping the
frequency fixed, will reduce the duty cycle, the effective beam current and
hence the voltage resolution. If we try to compensate for this by increasing the
steady-state beam current, the electron probe size will increase, degrading the
spatial resolution.
In practical terms, the system parameters are determined by a combination
of electron optical performance, energy filter efficiency (spectrometer constant)
and beam blanking speed. In addition, the design of energy filters and beam
blankers must be such as not to degrade the spatial resolution of the electron
optics by distorting, defocusing or shifting the electron beam. This section will
look at the factors controlling practical voltage contrast performance by
S . M . Davidson
178
T a b l e 5.1 Principal units of an electron beam testing system
Primary
facilities
Electron probe system (SEM)
Electron energy filter
Beam blanking system
Secondary
facilities
IC/wafer stage
Image processor
Beam position generator
Computer interface
considering the design of the building blocks which make up an electron beam
testing system.
The principal units, listed in Table 5.1, can be divided into two categories,
primary and secondary. Primary building blocks include the electron beam
system (usually a scanning electron microscope), the energy filter and control
electronics, and the beam blanking system and phase (delay) sweep generator.
These units are essential for any stroboscopic voltage contrast system.
Secondary building blocks add facilities which are being increasingly
regarded as essential features of any voltage contrast system. Indeed, many of
these secondary facilities are built into stand-alone electron beam testers. The
most common additional requirement is some form of specialized device or
wafer handling stage, while other important add-ons include an image
processor to improve the often very noisy stroboscopic images, some form of
automatic beam positioning to rapidly select different points on the device,
and computer control which can be interfaced to the wide range of design and
test instrumentation in everyday use throughout the microelectronics
industry.
5.3.2
Electron probe
Voltage contrast information is derived from the secondary electron signal. By
contrast with other electron beam analytical methods, such as EBIC or X-ray
analysis, it is therefore the probe diameter, and not the generation volume,
which ultimately sets the resolution limit.
In most instances the specimens being investigated are integrated circuits,
fabricated using a wide range of semiconductor technologies. IC technologies
are usually classified according to the dimension of the smallest feature
present, for example a 2.5 fim C M O S process. This means that the narrowest
tracks on the device will be 2.5 /mi wide. Devices being developed today (1988)
have minimum dimensions in the range 0.5-1 /on, and we can expect this figure
to shrink to 0.1-0.2/im within ten years.
The principal yardstick which determines the spatial resolution needed for a
Voltage contrast and stroboscopy
179
voltage contrast system is therefore the feature size of the IC technology being
investigated - say 0.5 fim for 1988 technology. The electron probe diameter
must be smaller than this dimension for accurate measurements. In practice, it
appears that the optimum probe size should lie in the range f/3 to / / 5 , where /
is the IC feature size.
The reasons for using a much smaller probe than might otherwise appear
necessary are three-fold. First, the energy filter and beam blanking system may
degrade the spatial resolution, and some allowance must be made for this.
Second, the electron probe must not be positioned too close to the edge of a
track; secondary electrons emitted from the edge will not necessarily have the
same energy and angular distribution as those emitted from the centre of a
plane region, where the analysis presented in Section 5.2.1 is valid. Third, it is
generally found that a probe much smaller than the feature size is needed to
identify the region or track where the measurement is to be performed. The
SEM image of a device with 0.5 /xm features taken using a spot size of 0.5 /mi
would appear very blurred and indistinct.
Today, stroboscopic voltage contrast techniques are being applied mostly
to devices with minimum feature sizes in the range 0.5-3 //m. The electron
probe diameter should therefore lie between 0.1 and 0.5 jum. The probe current
under these conditions is given by
(5.6)
where B is the gun brightness, a the semi-angle of the illumination at the
specimen, C and C the chromatic and spherical aberration coefficients of the
final lens, A E the energy spread and X the electron wavelength (Wells, 1974).
Voltage contrast investigation is mostly performed at low electron beam
energies to avoid damaging the device; typical accelerating voltages lie
between 0.5 and 2.5 kV. U n d e r these low voltage conditions, the most
important factors determining the probe current for a given probe size are gun
brightness and chromatic aberration. F o r this simple case, i.e. ignoring
spherical aberration and diffraction, we can simplify eqn (5.6). Assuming that
the aperture size, which determines a, is optimized for any spot size gives:
c
s
b
(5.7)
Probe current is plotted against spot size in Fig. 5.27 for an accelerating
voltage of 1 kV. Brightness values for tungsten, L a B and field emission guns
are taken from Orloff (1984), who has published a comparison of electron guns
used for E-beam inspection. Typically, into a 0.2 /mi probe a tungsten filament
gun will give 20 pA, a L a B gun 80 pA and a field emission gun several
6
6
180
S . M . Davidson
L
0.01
h
1kV
Probe diameter
(urn)
1-0
100
10
Probe
current
1000
(pA)
F i g . 5.27 Electron probe diameter versus probe current for tungsten (W), LaB and
field emission (FE) electron guns.
6
nanoamperes. The reasons for the greatly superior performance of the field
emission system are two-fold. First, the fundamental gun brightness is much
higher because of the very small emitting area of the source. Second, field
emission guns, in particular those operating at low temperature, have a much
lower energy spread. The influence of chromatic aberration is significantly
lower. At larger spot sizes the advantage of the field emission gun is less
marked; into a 1 fim probe field emission and L a B electron guns have similar
performance.
There are two additional factors which affect the performance of low beam
voltage electron optical systems which can often be neglected at higher beam
voltages. The first is the interaction between the electrons near crossover
points in the column, where the electron density is greatest. This, the Boersch
effect, can cause a broadening of the electron beam and increase in the energy
spread, making the effect of chromatic aberration larger. This effect appears
most pronounced for L a B guns, where the electron emission currents are
high. The second factor is the influence of stray AC magnetic fields,
particularly between the final lens and the specimen. The relationship between
the beam deflection, magnetic field and distance for a 1 kV electron beam is:
6
6
Ax =
(e/8mE y/ (Z B/f)
2
B
2
(5.8)
181
Displacement (nm)
Voltage contrast and stroboscopy
I
I
I
1
10
I
Magnetic f i e l d (mG)
F i g . 5.28 Electron probe displacement (lkV) versus magnetic field at 25mm
working distance.
where / is a screening factor determined by the specimen chamber material
and wall thickness. F o r typical mild steel construction / may be 10. This is
plotted in Fig. 5.28. If the influence of stray fields is t o be less than 0.1 fim at a
working distance of 25 mm, the field strength must be less than 3 m G (peak-topeak).
Combining the results from Fig. 5.23 with those of Fig. 5.27, we can plot
voltage resolution against p r o b e size, or spatial resolution. Figure 5.29 shows
the result, assuming a beam duty cycle of 1%, a spectrometer constant of
2 x 1 0 " , and a measurement time per point of 100 ms. Again, the influence of
the different type of electron gun is clear. O n the assumption that 100 mV is an
acceptable voltage resolution, we can see that tungsten guns will be
satisfactory for probe sizes down to 0.3 /mi, L a B to 0.15 /mi and field emission
to 0.03 /mi. Using the yardstick that the probe size should be the feature size
divided by four implies minimum device geometries for the three types of
electron gun to be approximately 1 /mi, 0.5 /mi and 0.1 /mi. Voltage or spatial
resolution can be improved, but only at the expense of increasing the
measurement time or the beam duty cycle.
The interdependence of the resolution parameters is clear. Electron optical
systems using thermionic (tungsten or L a B ) emitters are just capable of
7
6
6
182
S.M. Davidson
* m = 100ms
1000
W
—->
E
100
\
resol
|
LaB6\
\ F E
CD
U)
JS 10
o
>
1
1
1
10
100
1000
Spatial
r e s o l u t i o n (nm)
F i g . 5.29 Voltage resolution versus spatial resolution: measurement time per point
100 ms.
m e e t i n g the electron b e a m testing requirements of today's integrated circuits.
H o w e v e r it is likely that field e m i s s i o n sources will b e found in t h e next
g e n e r a t i o n o f electron b e a m testing e q u i p m e n t .
5.3.3
Electron energy filters
Q u a n t i t a t i v e v o l t a g e contrast requires t h e u s e o f a n energy filter o r spectrometer, o p e r a t e d in the c l o s e d - l o o p m o d e a s described in S e c t i o n 5.2. It is
fair t o say that m o r e w o r k has b e e n p u b l i s h e d o n s p e c t r o m e t e r d e s i g n t h a n o n
a n y other aspect of v o l t a g e contrast a n d s t r o b o s c o p y . T h e s e p u b l i c a t i o n s are
tabulated later in the section. M a n y different designs o f filter a n d spectrometer
h a v e b e e n d e v e l o p e d for v o l t a g e linearization, but o n l y a few are in current use.
All energy filters in use t o d a y are b a s e d o n the retarding electrostatic field
principle. V o l t a g e s o n o n e o r m o r e electrodes s l o w d o w n a n d s t o p electrons
with energy less t h a n a certain value. T h e principal difference b e t w e e n t h e
v a r i o u s designs c o n c e r n s the g e o m e t r i c a l form of the retarding field, w h i c h c a n
be planar o r hemispherical (Fig. 5.30). H e m i s p h e r i c a l analysers were a m o n g
the first t o be d e v e l o p e d , a n d h a v e the theoretical a d v a n t a g e o f filtering equally
Voltage contrast and stroboscopy
ELECTRON BEAM
183
ELECTRON BEAM
PLANAR FILTER
HEMISPHERICAL FILTER
Fig. 5.30 Configuration of planar and hemispherical electron energy filter.
all the secondary electrons emitted from the sample, irrespective of their initial
direction. The main problem with the hemispherical filter is the difficulty of
designing an electron collector which can detect all the electrons passing
through the filter, while keeping the whole assembly to a reasonable size. The
height in particular should be kept as small as possible to minimize the
working distance, as discussed in the previous section.
Most spectrometers designed to be fitted below the SEM objective lens are
planar filters, i.e. they effectively act on the normal component of the
secondary electron velocity. As we have seen in Section 5.2, this can cause
measurement inaccuracies. For this reason hemispherical energy filters have
been making a comeback recently, as they can be relatively easily incorporated
into the newer integrated lens/spectrometer designs.
The principle of the retarding field analyser or filter is illustrated in Fig. 5.31.
The simplest construction is three electrodes, here grids, positioned above the
sample, with a central hole to allow the primary beam to pass through. The
two outer electrodes are connected to ground, and the inner electrode to the
filter voltage. Electrons emitted from the sample with a normal component of
energy greater than the filter voltage will pass through. Those with energies
less than the filter voltage will be reflected. According to Menzel and Kubalek
(1983b), this can be written:
(5.9)
E cos a-eV >eV
2
s
s
f
where V is the sample voltage, E the secondary electron energy, V the filter
grid voltage and a the angle of emission of the electrons. The angular
distribution of electrons emitted from a sample roughly follows a cosine law:
s
s
T~T
{
0
cos a
(5.10)
where T is the transmission factor of the filter grids. The collected current for a
0
184
S.M.Davidson
F i g . 5.31
Typical electron trajectories through planar filter.
retarding field analyser is then given by:
^s = / E «
E
S
2JV(£ + F ) c o s a d £ d a
2
e
M
JO
s
(5.11)
JeV/cos a
2
where N(E) is the secondary electron energy distribution (Fig. 5.4). The result
is plotted in Fig. 5.32, and is the S-curve or integral distribution discussed in
Section 5.2.1. The maximum collected current is approximately 80% of the
total number of secondary electrons.
The simple analyser depicted in Fig. 5.31 has two drawbacks. It can not be
used for positive specimen voltages because the retarding field between the
specimen and bottom electrode will prevent any electrons getting into the
filter. It is also very sensitive to transverse electric fields on the specimen
surface. Such fields occur on integrated circuits because of the presence of
closely spaced tracks at different voltage levels.
These difficulties are circumvented by using an electrode at a high positive
potential above the sample, usually called an extraction electrode, extraction
grid or simply extractor. In the simplest case, the extractor replaces the bottom
earthed electrode (Fig. 5.33). The extractor is typically operated at a voltage
which produces a field above the sample between 100 V/mm and 1 kV/mm.
For example, a 1 kV extraction voltage 2 m m above the device will produce a
field equal to 500 V/mm. This high surface field ensures that all secondaries
from the sample will enter the filter, irrespective of sample voltage. It will also
greatly reduce fringing field problems by at least partially compensating for
the transverse field as discussed in Section 5.2.
k
Detector signal
(normalised)
1
I
I
I
I—
I
-4
-8
-12
-16
Filter
grid voltage ( V )
F i g . 5.32 Detector signal versus filter grid voltage.
DETECTOR
SAMPLE
F i g . 5.33 Typical electron trajectories with extraction field.
186
S . M . Davidson
So far we have assumed that an electrode connected to a suitable amplifier
collects the transmitted signal. While satisfactory for D C measurements, the
frequency response of this arrangement is generally inadequate for imaging.
An Everhart-Thornley ( E - T ) collector, i.e. a Faraday cage (optional),
scintillator, light guide and photomultiplier, is normally used. This in turn can
cause problems because the high fields associated with the Faraday cage
and/or scintillator can influence the filter characteristics and deflect or distort
the primary beam.
Menzel and Kubalek (1983b) have published a comprehensive review of
secondary electron detection systems for quantitative voltage measurements.
Table 5.2, taken from this paper, summarizes the nature and performance of
these detectors. The improvement in voltage resolution over the years is
evident. Performance simulations of some of these detectors has been
published by Khursheed and Dinnis (1983, 1985). While each design has its
own merits, it is fair to say that only two basic types have been developed
commercially - the Feuerbaum (1979) spectrometer used by I C T and Cambridge Instruments, and the energy filter designed by Plows (1981) and used by
Lintech Instruments in their voltage contrast and electron beam testing
systems (Lintech, 1984). M o r e recently, the energy filter has been combined
with the final lens of the SEM, permitting operation at short working
distances. These are commonly referred to as through-the-lens (TTL) analysers or filters, and are incorporated in electron beam testing equipment
manufactured by Lintech, ICT, Sentry, ABT and Hitachi. We will come to
these later in this section.
Stand-alone
energy
filters
Figures 5.34 and 5.35 illustrate the two post-lens energy filters in most
common use today - the Feuerbaum and Lintech designs. Both are essentially
planar field filters, with Everhart-Thornley collectors, but their implementation is radically different.
The Feuerbaum design (Fig. 5.34) uses a planar extraction grid mounted at
the bottom of an insulating tube. This is normally positioned 1-2 m m above
the device. The upper half of the tube is conducting, with filter grid mounted at
approximately the halfway point. T o the side of the upper part of the tube is a
collector grid, which is biased to 120 V. Secondary electrons are accelerated by
the extraction grid into the lower half of the tube. There they are decelerated,
only those with energies greater than the filter grid voltage passing into the
collector region. They are then accelerated through the collector grid into a
conventional SEM detector. An analysis of this design appears in Menzel and
Brunner (1983).
The Lintech energy filter (Fig. 5.35) uses apertures, rather than grids. The
T a b l e 5.2 Nature and performance of electron spectrometers
Authors
Wells and Bremer
(1968)
Driver
(1969)
Wells and Bremer
(1969)
Plows
(1969)
Fleming and Ward
(1970)
Gopinath and
Sanger (1971)
Beaulieu
et al (1972)
Hannah
(1974)
Fentem and
Gopinath (1974)
Hardy
et al. (1975)
Balk
et al. (1976)
Gopinath and
Tee (1976)
Duykov et al.
(1978)
Extraction
field
Spectrometer
type
Voltage
resolution
Working
distance
(mm)
—
Cyl. mirror
analyser
Hemi. retarding
field
63 Deflector
+ collimator
Planar retarding
field
Planar retarding
field
Planar retarding
field
Planar retarding
field
63 Deflector
retarding field
Hemi. retarding
field
Hemi. retarding
field
127 Deflector
+ ret. field
Hemi. retarding
field
V
20
V
—
±iv
20
IV
30
250 mV
—
—
30
10 mV
30
100 mV
65
80 mV
15
0.5 V
22
25 mV
22
10 mV
15
Retarding field
lens
Planar retarding
field
Planar retarding
field
127 Deflector
planar retarding
field
Retarding field
lens
Hemi. retarding
field
50 mV
37
20 mV
40
lmV
10
0.5 mV
15
lmV
19
—
—
400 V/mm
grid
300 V/mm
grid
—
—
1000 V/mm
lens
—
10-100 V/mm
300 V/mm
imm. lens
—
Rau and Spivak
(1979)
Feuerbaum
(1979)
Menzel
(1981)
Sev
100 V/mm
imm. lens
500 V/mm
planar grid
600 V/mm
planar grid
1000 V/mm
imm. lens
Plows
(1981)
Goto et al.
(1981)
1200 V/mm
field lens
1000 V/mm
hemi. grid
—
30
188
S.M.
Davidson
ELECTRON BEAM
^|
V
FILTER
DEFLECTOR
(H20V)
EXTRACTOR
(+B00V)
F i g . 5.34
DETECTOR
Feuerbaum electron spectrometer (schematic).
ELECTRON BEAM
SUPPRESSOR
SCINTILLATOR
(12kV)
FILTER
(+/-15V)
EXTRACTOR
7^
V
L
~
<5kv)
I D E V I C E I
F i g . 5.35
Lintech electron detector (schematic).
extraction structure behaves as an electron lens, accelerating and focusing the
secondary electrons into the filter region. The extraction voltage is typically
2 - 5 kV, giving field strengths at the sample up to 500 V/mm. The filter takes
the form of a tube at a constant potential.
Simulations have shown that this arrangement will give a planar filtering
field if the tube has the correct geometry. Above the filter tube is a suppressor
electrode, with a smaller aperture than the extractor. This serves to stop
tertiary electrons, i.e. secondaries generated by backscattered primaries,
reaching the collector. An annular scintillator, linked to a photomultiplier by
fibre optics, surrounds the filter. Electrons which pass through the filter are
accelerated towards the scintillator through the gap between filter and
189
Voltage contrast and stroboscopy
Table 5.3
Performance parameters of Feuerbaum and Lintech filters
Feature
Feuerbaum
Lintech
Diameter
Height
Working distance
Overall working distance
Extraction voltage
Extraction field (max)
Extraction electrode
Filter electrode
Filter voltage range
Field of view (total)
Field of view (unobstructed)
Collector
Spatial resolution
Image shift
Voltage resolution
S-curve monotonicity
Fringing field performance
10 mm
10 mm
1-3 mm
ll-14mm
0-600V
600 V/mm
Grid
Grid
±25V
7 mm
0.5 mm
External E-T
0.5 fim
70 mm
22 mm
2-8 mm
24-30 mm
0.5-5 kV
- 4 0 0 V/mm
Aperture
Tube
±25V
7 mm
7 mm
Integral E-T
0.2 fim
<0.1/mi/V
10 mV
Very good
<5%@2jim
< 0.2 fim/V
5mV
Good
<2% @ 5 m
M
suppressor. Unlike the Feuerbaum analyser, the Lintech design is completely
cylindrically symmetric.
Table 5.3 compares the characteristics of the two filters. The larger size of
the Lintech filter is primarily to accommodate the integral Everhart-Thornley
(E-T) secondary electron collector. The Feuerbaum filter uses a separate
electron collector, often the standard E - T collector supplied with the SEM.
The merits and demerits of each design revolve around such parameters as
field of view, voltage resolution, and probe degradation (beam shift, defocusing, astigmatism). Both filters give a field of view up to 7 mm, but in neither case
is this clear from distortion. Most of the distortion results from the extraction
electrode field. In the Lintech design, the extractor acts as a lens for both the
primary beam and the secondaries. Because the scanning point of the S E M is
well above the extractor, this lens will alter and somewhat distort the scan field.
Typically, at high extraction voltages, the normal scan field is halved, with
some distortion a r o u n d the edges of the extractor. The extraction grid used by
Feuerbaum also causes degradation by not only obstructing part of the image,
but also deflecting the primary beam close to the grid bars. This can cause
double imaging. Measurements must be performed through the central hole in
the grid, which limits the field of view to a few hundred micrometres.
Voltage resolution and collection efficiency are similar for the two detectors.
The more planar filtering field generated with the Feuerbaum design will give a
sharper, or steeper S-curve. As seen earlier, this should improve the voltage
190
S.M.
Davidson
resolution for a given signal-to-noise ratio. Fringing field performance is
similar - since both are essentially planar filters this is mainly determined by
the extraction field.
The other main comparison is related to the imaging performance. While
voltage resolution for a given beam duty cycle is principally determined by
probe current, and hence probe size, this will only be true if the probe is not
degraded by the filter. In general, the cylindrically symmetric nature of the
Lintech filter will perform better than the Feuerbaum design, with its grids and
off-axis collector. Defocusing can be easily corrected, but astigmatism
resulting from non-symmetric electrodes is less easy to compensate for. The
problem is exacerbated by the low beam voltages ( ~ 1 kV). Transverse electric
fields will cause astigmatism (as well as deflection) because of the chromatic
energy spread in the primary beam, i.e. different energy electrons will be
deflected by different amounts. If the energy spread was 1 eV, the chromatic
astigmatism will be 0.1% of the deflection.
Beam shift can be a problem with all energy filters. When ICs are imaged
using a filter or analyser, the filter voltage is fixed. However, when closed-loop
waveform measurements are being performed, the filter voltage varies with the
sampled device voltage. If this varying voltage is allowed to deflect the primary
beam, the electron probe will move over the IC track during the measurement
(Fig. 5.36). In extreme cases the probe could move off the track, causing gross
errors. Beam shift can be minimized by accurately centering the filter with
respect to the electron probe axis, and by using a symmetrical design. Both the
Feuerbaum and Lintech filters can be aligned to limit the beam shift to a
fraction of a micrometre; however, it remains to be seen whether this will be
adequate for sub-micrometre device characterization.
ELECTRON BEAM
Vs=0V
Vs=5V
DEVICE
F i g . 5.36
Effect of beam shift through energy filter on voltage measurement.
Voltage contrast and stroboscopy
191
New developments in stand-alone energy filters/spectrometers revolve
a r o u n d improving the efficiency. One approach to this is to use a dispersive
(energy or time) analyser, thereby collecting more of the signal simultaneously.
Progress in this area has been reported by D u b b l e d a m and Kruit (1987) and
Dinnis (1987).
Combined lens/energy
filters
One major limitation of all energy filters is the fact that their location imposes
a minimum working distance between the S E M final lens and the specimen.
Table 5.3 shows that this is typically 13 m m for the Feuerbaum analyser and
25 m m for the Lintech filter. In general, S E M performance improves at smaller
working distances because (a) the lens aberration coefficients (C and C )
reduce with focal length and (b) environmental factors such as stray magnetic
fields become less significant. Combining the final lens and energy filter allows
us to escape from this limitation. First to develop this concept were Menzel
and Buchanan (1984) in the ABT E-beam tester.
s
c
It has been known for many years that it is possible to collect secondary
electrons by placing a detector above the SEM final lens. This is c o m m o n
practice in S T E M instruments, and is also employed by some S E M
manufacturers (ISI and Hitachi). The sample can then be brought very close
to, or even inside, the final lens, producing a very small working distance
(Fig. 5.37). The emitted secondary electrons are forced into a spiral path by the
lens magnetic field. Where the field is highest, in the centre of the lens, the spiral
radius is smallest. The spiral becomes larger as the electrons emerge from the
lens field, allowing them to be collected by a conventional secondary electron
detector.
Incorporating extraction and filter electrodes into this arrangement is
relatively straightforward. While manufacturers differ slightly in their approaches, the general principle is the same (Fig. 5.37). The energy filter is
effectively split; the extractor is mounted under the lens, and the filter and
collector positioned above the lens. Electrons emitted from the sample are
accelerated by the extractor back through the final lens into the filter. Those
with energies higher than the filter potential will be collected. The working
distance can be reduced to a few millimetres, giving an improvement in spatial
resolution, or more important, an increase in the probe current for a given
probe size. Another important benefit is the increase in space available for the
filter and collector. Freed from the restriction of keeping the working distance
low, hemispherical filters and collectors can be used, giving an improvement in
fringing field performance.
Through-the-lens energy filters suffer from many of the same defects as
below-the-lens designs. The field of view is limited by the working distance and
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S . M . Davidson
ELECTRON BEAM
F i g . 5.37 Through-the-lens electron filter (schematic).
the scan angle to a few millimetres. Extraction grids, if used, will still cause
local distortions. Likewise, the electron collector must not unduly deflect or
distort the primary beam. Centering the filter with respect to the optical axis
remains vital to minimizing beam shift during waveform measurements. Few
figures are currently available for the collection efficiency or spectrometer
constant of through-the-lens filters. Likewise there have been few published
simulations of their behaviour. The influence of the lens magnetic field on
performance is therefore not clear, but experience appears to suggest that such
analysers have better fringing field performance than below-the-lens designs.
The magnetic field produced by the lens appears to assist in the extraction
process (see below).
An alternative approach to combining the energy filter and SEM lens has
been investigated by G a r t h et al. (1985, 1986). A monopole final lens is used,
positioned under the specimen (Fig. 5.38). A small extraction field draws the
secondary electrons into a conventional planar field energy filter and collector.
The lens focal length can be as small as the specimen thickness, giving a very
low working distance. The advantages of this arrangement lie not only in the
low working distance. The magnetic field is very high close to the specimen,
causing any secondary electrons to travel in a very tight spiral. As the magnetic
field decreases above the sample, the spiral unwinds. Electrons initially
emitted at large angles to the specimen normal will end up travelling more
parallel to the beam direction. As a result, the electrons can be "collimated"
Voltage contrast and stroboscopy
193
ELECTRON BEAM
DETECTOR
FILTER
EXTRACTOR
(+50 V)
SAMPLE
/
\
OBJECTIVE LENS
F i g . 5.38 Electron energy filter proposed by Garth et al. (1986).
into the filter without using high extraction fields. The tight spiral close to the
sample also improves fringing field performance, again without the use of high
extraction fields. Both features are of importance when examining the next
generation of small geometry devices, particularly where sub-surface layers are
concerned. However, it remains to be seen whether the G a r t h design is a
practical solution to the problem.
5.3.4
Beam blanking systems
Stroboscopic operation depends on the ability to switch the electron beam on
and off at high speed. We should note that the requirements here are somewhat
different than for cathodoluminescence or EBIC work. In those circumstances
the electron beam, normally on, is switched off rapidly to permit measurement
of luminescence decay or minority carrier lifetime. The beam duty cycle is
typically 50%. The principal performance criterion is the fall time of the beam
pulse.
Stroboscopic voltage contrast operation, on the other hand, relies on the
S . M . Davidson
194
T a b l e 5.4
Relative performance of four methods of beam switching
Wehnelt modulation
Electromagnetic deflection
Electrostatic deflection
Conjugate electrostatic
Speed
Resolution
Medium
Low
High
High
Good
Poor
Fair
Good
generation of very short electron beam pulses, often at high frequencies. The
electron beam is normally off, and is pulsed on for a short period to sample the
voltage contrast. Duty cycles are typically 0.01-1%. The width of the beam
pulse determines the time resolution or bandwidth of the stroboscopic system.
The time resolution needed is set by the IC technology under investigation ECL devices currently have transition times of a few hundred picoseconds,
while for 2/mi C M O S ICs, the corresponding figure is 1-3 ns. Smaller
geometry devices are intrinsically faster; we can expect 0.5 /mi C M O S devices to
have propagation times of the same order as E C L components. An electron
beam testing system needs sub-nanosecond time resolution.
Beam switching, or beam blanking as it is commonly known, can be
performed in a number of ways, and Table 5.4 compares the performance of
the most common methods. These are illustrated in Fig. 5.39.
With Wehnelt modulation the beam is switched off by driving the gun bias
negative, and switched on by driving it positive. This approach has not been
WEHNELT
ELECTROMAGNETIC
ELECTROSTATIC
F i g . 5.39 Electron beam blanking methods: Wehnelt modulation, electromagnetic
and electrostatic deflection.
195
Voltage contrast and stroboscopy
widely used for stroboscopic work, suffering from two disadvantages. The
beam blanking voltage varies considerably with gun operating conditions and
kilovolts - typical values are 20 V for 2 kV and 100 V for 20 kV - and the beam
pulse generator must be coupled to the gun at high voltage. While capacitor or
optical coupling can be used, the relatively high blanking voltages limit
Wehnelt modulation to moderate frequencies.
All other methods of beam blanking operate by deflecting the electron beam
from its normal path down the axis of the lens column (Gopinath and Hill,
1977). Either electromagnetic or electrostatic deflection can be used. Some
early beam blanking systems used electromagnetic deflection, but this has
proved too slow for stroboscopic voltage contrast. In practice, all beam
blanking systems for stroboscopic electron beam testing use electrostatic
deflection. The principle is illustrated in Fig. 5.40. A set of blanking plates is
located in the column. The most c o m m o n position for the plates is between the
electron gun and the first lens (as shown in the figure), but we will see that other
locations have benefits. When an electron beam of energy E passes between a
pair of plates (length /, separation w), the deflection is:
h
V I
E 2w
b
where V is the voltage between the plates. In general, only the electrons passing
down the centre of the column, precisely on axis, will contribute to the beam
going through the final aperture. All others will strike the aperture or the
column liner walls. To switch the beam off, it is therefore necessary to deflect
F i g . 5.40 Electrostatic beam blanking.
196
S . M . Davidson
the beam by an a m o u n t greater than the semi-angle of the beam divergence
entering the plates. The beam blanking sensitivity is determined by the size of
any defining aperture above the plates, and its position with respect to the
previous crossover point, in this case the source crossover. By selecting a
suitable size aperture, it is then possible to determine the blanking voltage for a
particular plate geometry, or the plate size and separation for any required
voltage.
There is another factor to be taken into account. Normally a voltage is
applied to the plates, holding the beam off. T o generate a beam pulse, the
voltage on the plates must be reduced to zero and held there while the electron
passes through. Electrons take a finite a m o u n t of time to travel through the
blanking plates. F o r the blanking or pulsing to be totally effective, the transit
time must be shorter than the required pulse width. Electrons of energy E
have velocity given by:
h
(5.13)
The maximum plate length for generating beam pulses of width t is therefore:
(5.14)
This is plotted in Fig. 5.41 for various beam energies. At 1 kV, generating
200 ps beam pulses requires plates no longer than 3 mm. The other parameter
we need to define is the plate separation. This cannot be smaller than the
diameter of any defining aperture above it. In practice, it is often at least a
factor of two larger to minimize contamination. Substituting eqn (5.14) into
eqn (5.12), and assuming a plate separation of 1 mm, gives:
V = 100
(5.15)
relating the beam blanking voltage, deflection angle, beam voltage (kV) and
pulse length. Assuming 1 kV operation and a deflection angle of 1 0 " rad,
corresponding to a 200//m aperture 10 mm below the gun crossover,
generating a 200 ps beam pulse will require a minimum pulse amplitude of 5 V.
Faster pulses need higher voltages because the plates must be shorter. A
smaller aperture will improve the sensitivity but will need more accurate
alignment and will be prone to contamination. Beam blanking systems for Ebeam testing have been reviewed by Fujioka (1983), while more detailed
analyses of high-speed blanking systems have been published by Lischke et al.
(1983, 1987).
The foregoing analysis can be used to determine the blanking sensitivity for
2
197
Blanking plate length (mm)
Voltage contrast and stroboscopy
Beam pulse
F i g . 5.41
width ( n s )
Maximum beam blanking plate length versus beam pulse width.
most positions of blanking plates in the column, including conjugate positions.
There is a n assumption that any deflection of the electron beam by the
blanking plates will be magnified by the subsequent electron lenses, in much
the same way as the angular distribution of the beam from the gun. This is not
always true. F o r example, if the plates are located a t the back focus of a
subsequent lens the lens will bring any deflected rays back on axis. The beam
blanking sensitivity will be effectively zero, i.e. the beam cannot be blanked.
While an extreme case, this situation can arise in practice because the first lens
is often used to control the probe size, or current. In these circumstances the
blanking sensitivity will be a function of spot size, decreasing as the probe
becomes larger, going through zero and possibly increasing in the opposite
direction.
Beam blanking can degrade the resolution of the electron probe by causing
a smearing of the image. Figure 5.42 shows what happens during the blanking
transition. As the beam is deflected, the effective position of the source also
moves by a n a m o u n t determined by the deflection angle and the distance
between the plates and the crossover. In fact, if we assume that the beam is
blanked when deflected by 8, the a m o u n t of source movement is approximately equal t o the aperture radius. With a 300 fim beam-defining aperture,
the source could move 150 /mi, or three times a typical source diameter. This
S . M . Davidson
198
SOURCE SHIFT
— ^
F i g . 5.42 Apparent source movement produced by non-conjugate deflection beam
blanking.
source shift will cause probe movement during waveform measurements, and a
smearing of any stroboscopic image in one direction. The effect will appear
similar to uncorrectable astigmatism.
The apparent source movement will only affect measurements if the beam
transition times (rise and fall times) are a significant fraction of the total beam
on time. If, for example, the nominal beam pulse length is 1 ns (Fig. 5.43), and
the transition times 300 ps, then the ratio of the beam fully on to the transition
time will be 7/6. Substantial image smearing or probe shift will occur. F o r a
pulse length of 10 ns however, the ratio will be 97/6 and the effect much less
noticeable.
-0.3ns
1ns
10ns
F i g . 5.43 Possible error caused by beam rise and fall times.
Voltage contrast and stroboscopy
199
LENS
F i g . 5.44 Conjugate beam blanking.
As might be expected, the problem becomes more severe with shorter beam
pulses. Transition times shorter than 100 ps are difficult to generate, with the
result that pulses shorter than 300 ps are dominated by the edge behaviour.
The solution to the problem is to position the blanking plates at a conjugate
point in the electron optical column, the image plane of either lens 1 or lens 2.
Figure 5.44 shows the principle. When rays are deflected by an electrostatic
field, the back projection of the trajectories will pass through the centre of the
plates. In other words, the deflection will effectively rotate the beam about
the centre of the plates. If the beam is focused to this position, then no
probe shift will occur during the blanking transition. This is k n o w n as
conjugate blanking, and is adopted by most of the suppliers of commercial
instrumentation.
The problems with conjugate blanking are two-fold: it is not easy to fit to
existing electron optical columns, and the lens or lenses prior to the blanking
plates must be operated in such a way as to maintain a fixed image position,
at the centre of the plates. If, for example, the plates are between lens 1 and lens
2, then the demagnification of lens 1 must be fixed, and cannot be used as part
of the spot size control. Some flexibility in the operation of the electron optics
is lost.
Where conjugate blanking cannot be employed, there are two approaches
to reducing the effect of image shift. The first is to position the blanking plates
as close to a conjugate plane as possible, the most convenient conjugate plane
200
S . M . Davidson
being the source position or gun crossover. Plates located underneath the
anode will then blank the beam with a small a m o u n t of degradation. The
difficulties with this approach mainly relate to blanking sensitivity. The close
proximity of any defining aperture to the crossover will increase the angular
spread of the beam entering the plates. The blanking drive voltage must
therefore also increase unless the aperture is made very small. At the low beam
voltages ( < 2 kV) used for stroboscopic voltage contrast this technique works
reasonably well, having been adopted by I C T for most of its electron beam
testing accessory systems. Its general application to higher beam voltages is
more uncertain.
The second way to reduce smear with non-conjugate blanking is to
incorporate an adjustable aperture above the plates. Since the blanking
deflection is only in one direction, the aperture need only be a plate with a
sharp edge. The plate, or knife edge can be positioned to an accuracy of a few
micrometres; the effective aperture is thus very small, improving the blanking
sensitivity and reducing the degradation. The Lintech non-conjugate blanking
system fitted to many SEMs uses this method.
F o r very high-speed devices, for example microwave components, special
beam blanking techniques must be employed. At frequencies in excess of
1 G H z , the simple blanking plates are replaced with a microwave structure, for
example meander lines or tuned cavities. Gopinath and Hill (1973) and
Fujioka and U r a (1981) have both used this type of approach to examine G u n n
diodes. M o r e recently, Brunner et al (1987) have described an E-beam test
system for GaAs logic operating at 5 G H z .
5.3.5
Other e q u i p m e n t
An electron probe, energy filter and beam blanking system are essential for
quantitative stroboscopic voltage contrast. There are, however, other requirements which form an integral part of most fully fledged electron beam testing
systems. Principal amongst these are special device handling specimen stages,
image processing equipment and computer interfacing and control.
Specimen
stages
Stroboscopic voltage contrast techniques are used primarily for design
validation and fault diagnosis in integrated circuits. F o r correct operation,
integrated circuits normally need to be connected to sophisticated drive
electronics, often by more than 100 cables. A prime requirement of an
integrated circuit specimen stage is thus the capability of making highintegrity connections from the drive electronics in atmosphere to the device in
Voltage contrast and stroboscopy
201
the vacuum environment of the S E M specimen chamber. In addition, the
device under test (DUT) may be mounted in an IC package, or could be part of
a 6-inch silicon wafer. In the first case, the device is normally plugged into a
suitable socket, to which the electrical connections are made; in the second
instance the connections are made by means of a probe card, with fine probes
making contact with bond pads on the device.
If testing at high speed is anticipated, the drive electronics must either be
positioned close to the device under test, or must be capable of being linked to
the device using high-frequency transmission lines, for example 50 Q coaxial
cables. The speed requirements for wafer and package device testing are
sometimes different, in that the probe card itself may well impose limitations
on the maximum frequency at which testing may be performed. G o o d highfrequency connections tend to be more important for packaged device testing
than for wafer testing.
Various approaches have been adopted by the different manufacturers to
the problem of making high-integrity connections to both packaged devices
and probe card stages. With packaged devices, good high-frequency connections are more important. There are two alternatives. The first is to put the
speed-sensitive drive electronics inside the vacuum chamber (Fig. 5.45). Drive
circuitry usually takes the form of one or more printed circuit boards on which
the device under test is mounted. While ensuring that the speed and timing of
F i g . 5.45 Typical device arrangement with drive electronics in chamber.
202
S . M . Davidson
DUT
minium
ATE
EQUIPMENT
F i g . 5.46 Typical device mounting arrangement with drive electronics outside
chamber.
the device drive signals are not compromized by any cabling, there are some
drawbacks. The size of the S E M specimen chamber often limits how much
drive circuitry can be installed; the quality of the vacuum may be affected by
outgassing from the printed circuit board and components; heat dissipation
from the drivers may be a problem; and finally a new drive board must be
designed and manufactured for each device, possibly even for different tests on
the same device. Nevertheless, this is often a valid approach if the device is not
too complex.
The alternative is to m o u n t the drive electronics outside the vacuum
chamber, but very close to the device under test. This can be achieved by
making the device holder the vacuum feedthrough. The IC is thus on one side
of the vacuum wall, and the drive electronics on the other (Fig. 5.46). The
distance from driver to IC can be as short as 10 mm. This approach has been
adopted by Siemens, Lintech and Sentry Schlumberger. One difficulty with
close coupling of IC and drive electronics is that both must move together if
different parts of the device are to be viewed. This can limit the speed at which
the device can be repositioned.
Specimen stages for electron beam testing are usually automated, using
either stepping motors or D C servo motors, with or without position
encoders. The ability to remotely control the position of the device with
respect to the electron beam is vital for efficient testing. In most instances
electron beam testing involves making measurements or recording strobos-
Voltage contrast and stroboscopy
203
copic images at many different points on a complex circuit. M a n u a l
repositioning would be extremely tedious. In many ways the specimen stage
requirements are similar to those of other analytical techniques, e.g. X-ray
analysis.
The same criteria which determine the maximum electron probe size for a
particular device geometry (Section 5.3.1) can be used to define the necessary
repositioning accuracy. The repositioning accuracy or repeatibility should be
typically one-third the feature size. Mechanical repeatibility depends on the
precision of the stage mechanics, but with good quality lead screws and
precision slides, 0.5 fim should be achievable. Thermal effects on the stage
mechanisms start becoming important at a r o u n d this level. The implication is
that pure mechanical repositioning can only be relied on when the device
geometry is greater than 1 /mi.
When repositioning to a greater accuracy is needed, an alternative approach
must be used. One possibility is to fit a laser interferometer measuring system
to the stage. These are used extensively on electron beam microfabrication
equipment, and are capable of a resolution of tens of nanometres. Strictly
speaking, it is the block or holder on which the device or wafer is mounted
which can be positioned to this precision; differential movement between
device and holder cannot be allowed for.
A completely different approach is to use geometrical information about the
device being investigated to aid repositioning. F o r example, we normally want
to position the electron beam at the centre of a track or pad. If the stage is
capable of moving the device to within the width of a track of the correct
location, the electron beam can then be used for automatic fine adjustment of
position. The beam scans a small area a r o u n d the point of interest, detects the
edges of the track or pad, and positions itself centrally with respect to these
edges. Siemens have used this technique in one of their laboratory E-beam
testers, but it has yet to be adopted on commercial equipment. A similar
approach relies on the availability of an image store. An image of the area
immediately around the point of interest is stored. Final repositioning is then
performed by shifting the beam so that the stored image exactly matches the
live image. While these automatic repositioning procedures relying on image
information are conceptually straightforward, there are difficulties because the
contrast in the image will vary not only with the voltage on the track of
interest, but also with signals on adjacent areas. Repositioning using pattern
matching techniques is thus not as simple as might first appear. However, with
image stores now integrated into virtually all commercial electron beam
testing equipment, this approach may be pursued in the future.
Repositioning solely using electron beam movement should also be
mentioned. This is very much faster than mechanical repositioning, with or
without E-beam correction. The technique, while superficially attractive, does,
204
S . M . Davidson
however, have several drawbacks. First, the area which can be covered is small,
and dependent on the electron beam deflection system. Second it varies with
working distance. Third, because the beam will be travelling through the
spectrometer off axis, the beam will both be deflected and distorted by the
voltages on the spectrometer electrodes. While these can be corrected for to
some extent, they d o limit the performance. Fourth, the deflection is very
difficult to calibrate accurately. Finally, if the spectrometer uses grids (filter
and/or extractor) which are in a fixed position with respect to the sample, some
parts of the device will be permanently obscured. The technique is practical
with the Lintech type of spectrometer, and with some of the newer throughthe-lens designs. However, current IC die sizes are now such (10 m m or more)
that vector beam methods using conventional E-beam deflection systems are
not practical for repositioning over large areas. The use of precision large-area
beam deflection systems such as those employed in electron beam writing
equipment may be considered, but even here there could be problems because
of the requirement of uniform secondary electron collection efficiency. Vector
beam techniques are best reserved for rapid beam positioning over small local
areas, e.g. logic cells or data buses.
Image
processing
Another important feature of most electron beam testing systems is some
image processing capability. This is particularly important because of the poor
signal-to-noise ratio of many images. In general, low beam voltage ( ~ 1 kV)
images will be noisy, particularly if acquired at TV rates. Stroboscopic images
will, of course, be even more noisy because the effective beam current is
reduced by the beam duty factor. In many instances slow scan imaging must be
used to obtain an acceptable signal.
Image processors serve several functions. First, they can store and noisereduce successive TV frames, usually by recursive filtering. Second, they can
convert SEM slow scans into TV for convenient viewing, with recursive
filtering if necessary. Third, many offer the capability of storing more than one
image, thereby allowing instant comparison between voltage maps of the same
area but under different conditions. Finally, once the image is stored in digital
format, it is then capable of further analysis (manual or automatic), or
comparison with simulated data from computer-aided design (CAD) databases. Currently, the imaging mode of operation (real time or stroboscopic)
is mainly used for locating the area or feature of interest. Detailed measurements are then performed in waveform mode. However, the development
of more sophisticated image processing equipment may enable quantitative information concerning voltages and timing to be derived from
images more efficiently than from the present point-by-point analytical
methods.
Voltage contrast and stroboscopy
205
Image comparison techniques for IC failure investigation have been
developed by M a y et al (1984), who have called the method dynamic fault
imaging. First, a known good device is examined in the electron beam tester. A
series of stroboscopic images (often several hundred) is acquired at various
intervals through the test pattern. These are stored on hard disc. The suspect
device is then subjected to the same test pattern, stroboscopic images acquired
and compared on a frame-by-frame basis with the stored good images. Faults
are quickly located. Drawbacks of the method are the long times needed to
record and compare the stroboscopic images, the large a m o u n t of storage
required ( > 100 Mb), and the necessity of having a good device for
comparison.
Computer
control
In recent years, electron beam testing has developed from a research
laboratory curiosity into an essential technique for IC design validation and
failure analysis. To complete the transition from laboratory to production test
equipment, the E-beam tester must be interfaced to and integrated with the
wide range of equipment currently in use within the semiconductor industry.
All of this is computer controlled; the electron beam tester must also be
capable of remote operation. This implies not only automatic positioning and
waveform acquisition, as detailed earlier, but also all the normal S E M
functions such as contrast and brightness, focusing and astigmatism correction, beam control and alignment, and magnification. Ideally, the E-beam
tester should be controlled from the same C A D workstation which the
semiconductor engineer uses for design, simulation and testing. Device
coordinates from the design data could then be used to define the regions of
interest where detailed analytical data is required. Test data could be
downloaded into the pattern generator which drives the device; waveforms
and/or images could be transmitted back to the workstation for instant
comparison with simulation. The only operator involvement with the
equipment would be to load or change the device.
Most of the commercially available E-beam test equipment is interfacable to
IC test and design equipment (Concina et al, 1986; Henning et al, 1987;
Frosien and Plies, 1987). Three computer interface standards are used in
connection with E-beam testing: RS232 (or similar), IEEE-488 and Ethernet.
RS232 is the simplest, cheapest and slowest ( ~ 1 kHz), and is suitable for
sending and receiving commands, coordinates and waveform data over long
distances (several hundred metres). IEEE-488 data transfer is much faster
(over 100 kHz), but is limited to short runs ( - 5 m ) . Ethernet and similar local
area networks, based on high-speed coaxial cable, offer data transfer rates in
excess of 1 M H z , but are considerably more complex in terms of both
hardware and software.
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S . M . Davidson
5.4
Applications
5.4.1
Operating c o n d i t i o n s
Voltage contrast investigation or electron beam testing can be applied to any
semiconductor device. Before describing applications, it is useful first to
consider the operating conditions and any necessary specimen preparation.
Current semiconductor devices are manufactured using a wide range of
T a b l e 5.5
Silicon technologies and examples of their device applications
Technology
Bipolar
NMOS
CMOS
DMOS/VMOS
JFET
GaAs
Device
Diode (p-n junction and Schottky)
Transistor (low and high power)
Photodetector
Thyristor and triac
TTL logic (H, L, LS, S, ALS, F series)
ECL logic (10 K, 100 K series)
Memory (PROM, ROM, high-speed RAM)
Operational amplifiers/comparators
Data conversion (ADC, DAC)
Programmable array logic (PALs)
Gate arrays
Dynamic RAM (DRAM)
EPROM and EEPROM
Microprocessors
MPU interface devices
DRAM
Static RAM (SRAM)
EPROM and EEPROM
TTL logic (4000, HC, HCT, AC series)
Operational amplifiers/comparators
Analogue switches
Data conversion (ADC, DAC)
Programmable array logic (PALs)
Microprocessors and interface devices
Digital signal processors (DSPs)
Gate arrays
Application-specific IC (ASIC)
Power transistors
Analogue switches
Small signal transistors
Operational amplifiers
High-speed FETs
High-speed logic
Optoelectronics (LEDs, lasers)
Microwave oscillators/amplifiers
207
Voltage contrast and stroboscopy
technologies: bipolar, metal-oxide-semiconductor (MOS) in its many variants
( C M O S , N M O S , P M O S , V M O S ) and GaAs. Some of these are listed in
Table 5.5. N o t all these devices can derive the same benefit from voltage
contrast investigation. F o r example discrete components (transistors, diodes,
etc.) are relatively large scale devices manufactured using mature technology.
Occasionally voltage contrast can be used as an aid to failure analysis.
However, the problem is usually obvious and catastrophic. Electron beam
testing, as might be expected, is principally of value on devices where we need
to know the voltage distribution on a micro-scale, say less than 10 /mi. While
E-beam testing is not restricted to large-scale and very large-scale integrated
(LSI and VLSI) circuits, such as microprocessors, memories, applicationspecific integrated circuits (ASICs) and gate arrays, and digital signal
processors, most of the published applications fall into these categories.
As shown in Table 5.5, VLSI devices are currently being manufactured using
both bipolar and M O S technology, with C M O S the dominant technology for
new devices. Estimates suggest that within five years more than half of all
devices manufactured, and approaching 80% of new designs, will be C M O S .
Table 5.6 shows the different characteristics of the device technologies and
how they affect electron beam testing conditions.
Voltage contrast has been principally used for investigating logic devices, in
particular microprocessors, memories and ASICs. Signal-to-noise ratio
considerations imply that devices with large logic swings will, in general, be
easier to electron beam test. In this context, the trend towards C M O S
technology, with its well-defined internal voltage levels (5 V or 0 V), is
encouraging. O n the other hand, bipolar devices, in particular those employing E C L or IIL (integrated injection logic) have very low internal voltage
swings, and present much greater problems. N M O S devices, mainly microprocessors and memories, have internal voltage swings which are a significant
fraction of the supply voltage (5 V).
Also noted in Table 5.6 is the sensitivity of the oxide insulator to electron
bombardment. With bipolar devices, the oxide layers do not,form part of the
active device. Charge generated by the electron beam in these layers should
T a b l e 5.6
Some characteristics of silicon technologies
Technology
Logic swing
(V)
Oxide
sensitivity
Electron beam
voltage(kV)
Bipolar (TTL)
Bipolar (ECL)
PMOS
NMOS/CMOS
5
0.8
10
5
Very low
Low
High
Very high
Up to 20
Up to 20
<5
<1.5
208
S . M . Davidson
electron
beam
charge generation
s
In oxide
BSSSSSSSS
n
F i g . 5.47 Charge generation by electron beam in bipolar transistor structure.
not, to a first approximation, influence the device operation. There may,
however, be secondary effects. If charge is generated in an oxide layer
immediately over a junction edge (Fig. 5.47), then the carrier concentration
near to the surface may be enhanced or depleted. This may in turn affect the
junction leakage or breakdown voltage. In general, bipolar transistor circuits
can be examined using high-energy electron beams, where the electrons
penetrate the surface oxide layers, without seriously affecting device operation.
O n e factor which should be borne in mind under these conditions is the
possibility of generating electron beam-induced current effects, discussed in
another chapter. If the electron beam current is sufficiently high, this induced
current may alter the characteristics of the device or circuit.
The situation is quite different with M O S devices. Figure 5.48 shows cross
sections of typical p- and n-channel M O S transistors found in a C M O S IC.
The critical region is the thin layer of gate oxide, less than 100 nm thick,
between the gate (usually polysilicon) and the silicon. In operation, the voltage
on the gate electrode controls the flow of current from the source to the drain
by enhancing or depleting the majority carrier concentration at the o x i d e silicon interface.
Consider the n-channel transistor (enhancement type). Source and drain are
heavily doped n-type silicon, while the gate region is lightly doped p-type (the
n-channel
p-channel
F i g . 5.48 Typical n-channel and p-channel MOS transistor geometries.
(UA)
D5
I
0.5
V
T
1.0
1.5
VL-
(volts)
DS
2.0
F i g . 5.49 Typical n-channel transistor characteristic showing threshold voltage (V ).
I
D5
(uA)
t
0.5
1.0
"v*
1.5
2.0
(volts)
F i g . 5.50 Variation of n-channel MOS transistor threshold with irradiation.
210
S . M . Davidson
converse is true for the p-channel transistor). With zero bias on the gate, no
current will flow from source to drain. When the gate voltage is made positive
with respect to the source, bending on the conduction and valence bands will
invert the surface of the p-type gate region, i.e. effectively convert it to p-type.
Conduction between source and drain can then occur. Larger gate voltages
will increase the enhancement effect, reducing the channel resistance.
Figure 5.49 shows a typical transistor characteristic. The behaviour of pchannel transistors is similar. In this case a negative voltage on the gate with
respect to source will invert the silicon surface to create the conducting
channel.
An important parameter which specifies the transistor behaviour is the
threshold voltage, defined as V in Fig. 5.49. This is effectively the voltage at
which conduction starts, and is typically 0.5-1 V. The threshold voltages are
largely determined by the quality of the gate oxide, and in particular by the
a m o u n t of the charge stored there. Stored charge normally takes the form of
positive ions, which drift to the oxide-silicon interface. Clearly, an additional
positive potential will turn an n-channel transistor on, and a p-channel
transistor off. In other words, stored charge will decrease the threshold voltage
of an n-channel transistor, and may make it negative (Fig. 5.50). Under these
circumstances, the transistor will be turned on continuously, and cannot be
switched off. With a p-channel transistor oxide charge increases the threshold
voltage (Fig. 5.51). Figure 5.52 shows the effect of oxide charge on the
I
DS
<uA)
t
-0-5
-1.0
U
-1-5
-2.0
(volts)
F i g . 5.51 Variation of p-channel MOS transistor threshold with electron
irradiation.
211
Voltage contrast and stroboscopy
increased
irradiation
1
OUTPUT
—i
Amplitude (V)
i
INPUT
±
±
±
100ns/div
F i g . 5.52 Behaviour of CMOS inverter following electron irradiation.
operation of the C M O S inverter, depicted in Fig. 5.53. Above a particular
charge level, the output of the inverter will not change from low to high, i.e. the
device will fail.
Electron b o m b a r d m e n t of the gate region of a M O S device will always
increase the level of charge in the gate, altering the transistor characteristics.
The measuring electron beam must, therefore, N O T be allowed to penetrate to
the gate oxide. Miyoshi (1982) has measured the change in transistor
characteristics with electron beam dose over a wide range of beam energies
and transistor geometries. His results, illustrated in Fig. 5.54, show that the
allowable electron beam doses for a change in threshold voltage less than 0.1 V
vary dramatically with beam energy and transistor channel length. At high
kilovolts, the allowable dose is extremely small, corresponding to milliseconds or microseconds of operation at normal beam currents. However, at
low beam voltages, hours of examination are possible without seriously affecting device performance. Miyoshi's work has been extended by Ranasinghe
et al (1987) to lower beam voltage investigation. Somewhat surprisingly,
they found that device degradation occurred, albeit very slowly, at low beam
voltages where the incident electron beam could not possibly penetrate to the
gate oxide. X-rays generated by the primary electron beam in the surface layer
were thought to be responsible for these small threshold shifts.
Small changes in the characteristics of M O S transistors may therefore occur
during electron beam testing. However, these changes can be ignored provided
5V
p-channel
output
input
\—^
n-channel
0V
F i g . 5.53
Typical CMOS inverter.
(5um)
Threshold shift
(V)
n-channel
electron
F i g . 5.54
dose
(e/cm )
2
Variation of threshold shift with electron dose.
Voltage contrast and stroboscopy
213
that the beam voltage is kept below 1.5 kV, and the (mean) beam current below
I n A . Most electron beam testing and voltage contrast investigations of
integrated circuits are performed under these conditions. In any case, as we
have seen earlier, the beam current is often set by the spatial resolution
required, i.e. the device feature size. Beam currents significantly in excess of
I n A would correspond to electron probes too large to distinguish submicrometre features.
5.4.2
Passivated d e v i c e s
The operating conditions outlined above specifically relate to unpassivated
devices. If it is not possible either to obtain devices prior to passivation, or to
remove the passivation (Section 5.4.3), then some restrictions exist as to the
types of voltage contrast measurement possible, and their accuracy.
The most important point is that measurements are not being made on a
conducting surface. Voltages on the metal interconnects will be coupled to the
surface of the passivation by the capacitance of the insulator; we have to
observe or measure this impressed voltage with the electron beam without
significantly disturbing it.
A typical situation is depicted in Fig. 5.55. Equilibrium operating conditions
must first be established. Assuming that the voltage on the track or pad does
not change, then equilibrium will only be established if the secondary electron
signal equals the incident beam current. F o r silicon dioxide the secondary
emission coefficient exceeds unity roughly over an incident beam energy range
500 V to 2 kV. Electron b o m b a r d m e n t in this energy range will thus cause the
electron
beam
passivation
silicon
F i g . 5.55 Passivated track (schematic).
214
S . M . Davidson
surface to charge positively, reducing the secondary yield to unity. The closer
to the first crossover, the smaller the positive surface potential. Although the
same effect could, in theory, be obtained operating near the second crossover,
the deeper penetration of the higher energy primary electrons seems to
influence the establishment of the equilibrium.
Assume that the voltage on the track changes, say from 0 to 5 V. This step
change will appear immediately on the surface of the passivation (Fig. 5.55),
increasing the voltage by 5 V, and charging the passivation "capacitor". This
increase in surface voltage will unbalance the equilibrium between primary
and secondary electrons, in this case by reducing the secondary electron yield
(compare normal voltage contrast). Electrons will be accumulated at the
surface, driving the potential less positive until equilibrium is again restored.
Similar behaviour occurs if the track voltage changes in the opposite direction.
The resulting signal on the passivation thus appears as if AC coupled through
a high-pass filter (Fig. 5.56), the time constant of which is determined by the
beam current and the capacitance of the passivation layer.
Assuming a thickness of 0.5 /mi for the passivation, the capacitance of a
region 2 /mi square is ~ 1 0 ~ p F . With a beam current of 100 pA, the rate of
change of voltage is given by:
4
d
V
dt
L
C
(5.15)
or about 1 V//zs. With continuous bombardment, the voltage contrast would
disappear in a few microseconds. Another way of thinking of this is to calculate
5us/division
F i g . 5.56 Voltage contrast signal recorded from passivation.
Voltage contrast and stroboscopy
215
the number of electrons needed to re-establish equilibrium. This is given by:
n = CV/e
(5.16)
or approximately 3000 in this case. This then sets an upper limit on the voltage
resolution which can be measured from a passivated device. If the spectrometer anddetection system are 100% efficient, the best that can be expected
is 5 V / ^ 3 0 0 0 or ~ 1 0 0 m V . In practice, the situation may be much worse.
M o r e detailed analyses of capacitance-coupled voltage contrast, as the
technique is known, have been presented by Fujioka et al (1983) and Gorlich
et al (1986).
The fact that voltage contrast images can be observed on passivated devices
for more than a few microseconds is simply because the electron beam is
scanning across the sample. At TV scanning rates, the beam will only dwell on
any particular point for a fraction of a microsecond. Typically 10-100 frames
can be scanned before the voltage contrast image fades away; this takes a few
seconds. Slow scanning is much less satisfactory. If the dwell time is more than
a few microseconds per point, i.e. if the line time exceeds 1 ms, then any voltage
contrast will be eliminated in a single frame. These times will, of course, be
extended by the beam duty cycle if stroboscopic imaging is employed, but the
ultimate limit on signal-to-noise ratio, or voltage resolution, will remain.
Other problems exist with passivated devices. The foregoing analysis
assumes that the passivation surface is always allowed to reach equilibrium, by
balancing the secondary electron emission coefficient with the primary beam
current. This can only happen if there is no extraction field. When such a field is
present, then all electrons emitted from the sample will be pulled off,
irrespective of the surface voltage. The surface will, in fact, charge u p to a high
positive potential, only limited by breakdown or leakage. Little voltage
contrast is observable under these conditions.
Very low electrostatic extraction fields must therefore be used, implying that
fringing field effects will be more pronounced. Nye and Dinnis (1985) have
developed special detectors which operate well under these conditions. The
magnetic extraction approach of G a r t h and Nixon (1986) may be a more
sensible approach, and there is some evidence that through-the-lens spectrometers, which combine electrostatic and magnetic extraction, are more
successful on passivated devices than the older electrostatic filters.
Even if we can collect the small number of secondary electrons using low
extraction fields, another problem arises, particularly with multilevel interconnects. Equipotential calculations by O o k u b o et al (1987) show that the
potential on the surface is only one-third of the lower track voltage for the
geometry shown. Figure 5.57 plots the capacitance coupling error as a
function of line width for measurement on the first- and second-level metal.
Large errors such as these call into question the wisdom of attempting to
216
S . M . Davidson
100
o
50
1
2
L i n e width
3
4
(urn)
F i g . 5.57 Voltage measurement error through passivation to 1st- and 2nd-level
metal tracks.
derive quantitative voltage information from passivated device structures,
particularly because there is no obvious method for correcting the error.
By contrast, timing measurements are not seriously affected by the
passivation. M a n y waveform measurements described in the next sections
have been taken from passivated devices. Under these circumstances the use of
a conventional Everhart-Thornley electron collector may be preferable to the
more usual spectrometer, with its high extraction field. The measurements will
be sensitive to fringing fields, and care must be taken that these do not
influence the result.
5.4.3
Passivation removal
Under some circumstances, it is possible to remove the insulating layer or
layers which cover the region of interest. All semiconductor devices comprise
layers of variously doped silicon, silicon dioxide and/or silicon nitride,
polycrystalline silicon (polysilicon), and metal. The polysilicon is used for the
gates of M O S transistors and often for the first layer interconnect. Upper level
interconnectors are usually metal (aluminium), insulated from each other with
oxide. The complete device structure is then protected with an overall
passivation layer. Again, this is commonly oxide, although nitride and
Voltage contrast and stroboscopy
217
polyimide are also in use. In a production device, all the active regions and
interconnects of a complete integrated circuit are covered with one or more
insulating layers. The only regions of metal exposed will be the bond pads.
When ICs are being developed, it is often possible to obtain devices prior to the
deposition of the final surface passivation.
M o r e recently, multi-level metal has become common; and it is sometimes
necessary to measure voltages on these lower level metal layers. While the
complete surface passivation can be removed, this is not possible for the intermetal insulation while maintaining the integrity of the device. Methods for
localized removal are thus also needed.
Removal of passivation or insulating layers can be achieved chemically or
using plasma methods. Chemical techniques are suitable for the removal of
oxide or phospho-silicate glass, which are c o m m o n passivating materials.
Buffered hydrofluoric acid (a mixture of H F and a m m o n i u m fluoride) is the
usual agent. Careful attention to the strength of the buffered H F (the ratio of
H F to a m m o n i u m fluoride) and the etching time are needed if the passivation
is to be cleanly removed without significantly attacking the underlying
aluminium metallization. Typical strengths used are 10-20% H F by volume in
saturated a m m o n i u m fluoride. Residues of hydrofluoric acid will attack
aluminium; it is important that the device is washed thoroughly following depassivation.
Plasma methods, where the device is subjected to b o m b a r d m e n t with an
ionized gas plasma at low pressure (0.1-1 torr) can also be used for the removal
of oxide passivation. However, this approach is used much more for the
removal of nitride and polyimide layers. F o r oxide and nitride removal C F
and C H F are commonly used, sometimes in a mixture with oxygen. Pure
oxygen plasmas are mostly employed to remove organic matter, for example
photoresist, and are partly successful in removing polyimide passivation. Most
plasma methods are passive, i.e. the ions are not accelerated onto the device. It
is possible that the newer reactive ion etching techniques, a combination of
sputtering and plasma attack, may prove more effective.
The methods outlined above will remove a complete layer of oxide or other
passivation. If local removal is needed, some method must be found for
masking the regions which are not to be attacked. Photoresist can be used,
with the required windows exposed using a mask or scanned light spot or laser
probe. O n e possible alternative is laser ablation. The device is in a reactive gas
environment, and a powerful focused laser excites the gas at the region of
interest, causing local plasma etching. The development of this and similar
local removal methods may be vital if electron beam testing is to be
successfully applied to future generations of devices with multiple levels of
interconnect.
4
3
218
5.4.4
S . M . Davidson
Microprocessors a n d memories
Voltage contrast methods have been applied to integrated circuits in many
laboratories (Crosthwait and Ivy, 1974; Gonzales and Powell, 1975; Rau and
Spivak, 1979; Fujioka et a/., 1980). However, the lion's share of the applications
have been published by Wolfgang and his colleagues, working at the Siemens
Research Laboratories in Munich, for example Wolfgang et al (1976, 1979),
Feuerbaum et al (1978), Crichton et al (1980), Wolfgang (1981), Kollensperger et al (1984). M u c h of this early work was concerned with
developing the techniques of electron beam testing, and applying them to the
device development which was taking place in the laboratory in the 1970s and
early 1980s. At that time one of the main emphases was the development of
faster versions of some of the standard microprocessor families, such as the
8085. As our first illustration of electron beam testing in action, we will
describe the work of Crichton et al (1980) on microprocessors.
Stroboscopic electron beam testing implies that any test pattern applied to
the device must be cyclic. F o r a good signal-to-noise ratio, it must repeat over
a short period to enable the beam duty cycle to be as high as possible.
Microprocessors pose particular problems in this respect because of their large
instruction set. To exercise all possible modes of operation, long instruction
cycles may be needed. If good time resolution is also required, for example 1 ns,
the beam duty cycle may be so low as to limit the ultimate voltage resolution.
In the particular example described by Crichton, it was possible to use the
following short program loop to exercise the device:
Address
02
03
04
Instruction
INRA
DCRA
JMP02
Code
3C
3D
C3
Machine
4
4
10
states
Before the loop is entered, data 03 are written into the accumulator. The value
in the accumulator (register A) should toggle between three and four. As the
clock frequency was raised, it was noted that at 5.9 M H z incorrect data were
present in the accumulator.
A range of electron beam testing techniques were used to investigate the
problem. In particular, it was necessary to discover whether the fault lay in the
instruction fetch, the instruction decode or the arithmetic logic unit. The
observed error could arise from any of these faults. First, voltage contrast
imaging was used to examine the instruction register and instruction decoder.
Figure 5.58 suggests that at 5.9 M H z , a different instruction is being fetched
from the register than at 5 M H z .
To examine this in more detail, logic state mapping was used to reveal the
Voltage contrast and stroboscopy
( a ) 5.0MHz
219
(b)5.9MHz
F i g . 5.58 Voltage contrast images of operating microprocessor (Crichton et al,
1980).
logic levels on the interconnects from the instruction register to the decoder.
Logic state mapping is an extension of stroboscopic imaging, where the
sampling phase is swept in synchronism with the X or Y electron beam scan. It
is principally of value for reading logic levels from data and address buses, or
other arrays of parallel conductors. The major advantage over waveform
recording is that the signals on many parallel tracks can be recorded
simultaneously, yielding a display similar to a logic analyser. Figure 5.59
shows the resulting logic state maps at 5.0 M H z and 5.9 M H z . It is clear that
one of the bit lines (bit 1) has changed from zero to one, altering the first two
instructions - I N R A and D C R A — t o M V I A (move immediate to the
accumulator). The J M P instruction is unchanged. A more detailed examination of the logic state maps at the higher frequency showed that spikes
appeared on the interconnection, corresponding to glitches in the signal.
To investigate the situation further, stroboscopic waveforms were recorded
from internal nodes in the instruction register. These are shown in Fig. 5.60. At
the faster speed the internal data bus does not have enough time to settle to the
correct value; the wrong value is then sent to the instruction register. In this
case, the problem was traced to delays in acquiring the correct instruction, due
in part to the access time of the program memory.
The value of this particular example lies in the way it uses a range of voltage
contrast techniques to track down the source of a device problem. This is
typical of the way in which electron beam testing can be applied to what is
known as "design validation", i.e. checking that a device operates over its
220
S . M . Davidson
Bit INR DCPJ JMP
U
1
1
0
7
0
0
1
1
0
0
1
2
1
1
0
CLK= 5.0 MHz
o
Instr. I
V
T
3'
TIME Cps]
a)
JMP
MVIA
I Bit I
100
1 7
E
•3*50
J
x
l l l l l l l l l l
T
2"
TIME Cms]
F i g . 5.59
|MVIA|JMP
1
0
0
1
1 0
2
CLK = 5.9 MHz
b)
Logic state maps of microprocessor (Crichton et al, 1980).
complete frequency range, and investigating in detail any failure mechanism.
Any design weaknesses can then be corrected before the chip goes into full
production.
Voltage contrast techniques have also been used during the development of
semiconductor memories, in particular D R A M s . Information is stored in
D R A M s as a charge on a capacitor, which must be refreshed at regular
Voltage contrast and stroboscopy
time
(ns)
221
time ( n s )
F i g . 5.60 Stroboscopic voltage contrast waveforms recorded from 8085 microprocessor at 5.5 MHz and 5.9 MHz.
intervals. The value of the capacitor is tiny, a small fraction of a picofarad. O n e
of the important components of a D R A M is the sense amplifier, which detects
this charge and converts it into a logic level. At the input of the sense amplifier,
the difference in charge corresponding to logic " 1 " and logic " 0 " may only be a
few hundred millivolts. The sensitivity of this amplifier can influence the
memory access time, an important yield-determining parameter.
Figure 5.61 shows the circuit configuration around the sense amplifier, and
Fig. 5.62 shows some of the waveforms recorded, taken from the work of
Wolfgang (1981). The steps on the waveform correspond to the data in the
memory cell being switched from logic " 1 " to logic "0". It can be seen that the
difference between high and low is only 270 mV, somewhat smaller than the
calculated value of 450 ns. While this did not matter for the 16 K D R A M
investigated here, it could be important for more sophisticated devices. An
important point concerning this particular measurement is that it is not
possible using a mechanical probe. The probe would add so much capacitance
12V
H
12V
J
Sense
I - PRE
amp.
ws
DC
I
(a)
(b)
F i g . 5.61
Voltage measurements from sense amplifier in MOS memory.
9 MHz
7 MHz
x 60
ARROWED CELL CLOCKING
ARROWED CELL STOPPED
F i g . 5.62 Voltage contrast images of CMOS ASIC at 7 MHz and 9 MHz.
Voltage contrast and stroboscopy
223
to the sense amplifier input that it would no longer function correctly. Similar
investigations have been performed for 64 K D R A M s .
Static R A M s are now mostly C M O S , although some N M O S and E C L
bipolar devices are also available. Sense amplifiers as such do not exist in these
devices, which can be treated in the same way as other C M O S or bipolar ICs.
5.4.5
A p p l i c a t i o n - s p e c i f i c integrated circuits ( A S I C s )
One of the biggest growth areas in semiconductor technology is the
application-specific market. Devices are designed for specific customers'
applications. In the main, such devices split into gate arrays, standard cell
designs and full custom.
In gate arrays the cells are identical, typically an A N D - N O R configuration.
These are configured to the customer application in two stages. The cells are
interconnected to form the required logic gates, flip-flops, counters and
registers; these "macro-cells" are then linked to create the complete circuit.
With standard cell designs the manufacturer has a complete library of
optimized logic elements; these are then positioned on the die and linked
together appropriately as before. A complete set of masks for photolithography must be produced, as opposed to just one for the gate array, and the
complete processing cycle must be performed. Where high-performance
devices are needed, e.g. for digital signal processing, the only solution is for the
device to be designed from the ground up, i.e. full custom.
Electron beam testing can play an important role in evaluating and
debugging all forms of ASIC. This applies particularly to timing problems,
where the simulation may not be sufficiently accurate to predict the influence
of interconnections and loading. Another value of E-beam testing is that it can
help to resolve arguments or disputes between designer and manufacturer if
the device does not meet its specification. The designer may be working too
close to the limits of the processing, the simulation may not be sufficiently
accurate, or the processing itself may not be under complete control.
As an example of the application of voltage contrast techniques to a
standard cell device, consider the circuit in Fig. 5.63. The device, designed for
use in communications equipment, had a problem similar to that of the
microprocessor. In this case the device, specified to operate up to 9 M H z , failed
at ~ 7.5 M H z . Figure 5.62 shows voltage contrast images of the device below
and above the cut-off frequency. M a n y changes in the voltage distribution are
apparent; parts of the circuit simply stop operating above the critical
frequency. A block diagram of the circuit is shown in Fig. 5.63. It comprises
two programmable counters (dividers), with the terminal count being used to
reload the divide ratio. Figure 5.64 shows stroboscopic waveforms recorded at
224
S.M. Davidson
BINARY
<
COUNTER
Q
PARALLEL
CD
in
n
LOAD
TIMING
CLOCKTC
DECADE
<-
COUNTER
CD.
in
PARALLEL
LOAD
F i g . 5.63 Block diagram of divider section of ASIC.
i — i — i — i — i — i
1
l
I
i
I
I
I
i
i
r
I
I
I
1
100ns/div
F i g . 5.64 Stroboscopic waveforms recorded from CMOS ASIC showing critical
delay.
various points in the circuit. The countdown sequence can be clearly seen, with
the terminal count appearing when the count is zero. Although the counter is
synchronous, i.e. the outputs all change state at the same time in synchronism
with the main clock, the terminal count is generated by a signal which "ripples"
through a long chain of gates. The total propagation delay was ~ 130 ns,
corresponding to a frequency of 7.6 M H z . Above this frequency, the divider is
Voltage contrast and stroboscopy
225
not reset correctly. The simulated delay was — 110 ns, and it is interesting to
consider where the discrepancy arose. The individual cell propagation delays,
at 10 ns, were close to the simulation values. However, no account was taken of
the delays caused by the interconnects, particularly those in polysilicon. One
of the significant tracks is arrowed in Fig. 5.62. Tracks like this can have a
resistance of several kilo-ohms. Combining this with the capacitance of the
subsequent metal interconnect and the next stage can produce a time constant
of 2 0 - 3 0 ns, generating a significant signal delay. Most of the additional
propagation delay could be accounted for in this way. Even if this were not a
limiting factor, the original design was clearly operating too close to the limits
of the process for 9 M H z operation; a substantial re-design was needed. As
with the previous examples, mechanical probing would have loaded the circuit
so much that the real design defect would have been masked.
A second example concerned a gate array ASIC, again designed for
communications purposes. The problem was again timing, in this case devices
were being produced with a wide timing spread. Input to output delay should
have been of the order of 150 ns; in practice values ranging from 150 ns to
230 ns were being seen on nominally identical devices. Electron beam testing
techniques were used to examine the signal path in an attempt to ascertain
whether any specific part of the circuit could be responsible. Waveforms
recorded from two devices shown are in Fig. 5.65. While there are small timing
50ns/div
F i g . 5.65 Voltage contrast waveforms recorded from CMOS ULA showing delay
spread.
226
S . M . Davidson
]
3
o-
p-channel
O-
INPUT5
OUTPUT
o•pi
'n
r
n-channel
F i g . 5.66 Schematic of 3-input CMOS NOR gate.
spreads from the input up to node D, we see that there is a very slow rising edge
to the signal at node E. The 10-90% risetime is as long as 80 ns in some cases.
As a result, the signal at the next node is significantly delayed, and what is
more, the delay varies from device to device. Small variations in transistor
characteristics caused by the processing can cause large changes in delay for
slow edges.
The reasons for the slow edge are two-fold and are related to the basic gate
array design, and the layout. The gate driving node E is a 3-input N O R gate,
depicted in Fig. 5.66. Three n-channel transistors in parallel form the pulldown, while three p-channel transistors in series form the pull-up. P-Channel
transistors in general have a higher series resistance than n-channel devices;
this is normally compensated for by making them much wider. This is possible
in standard cell designs, but not in gate arrays where all the transistors are
effectively the same size, irrespective of the type of logic gate they are used in.
As a consequence, the output drives of multi-input logic gates manufactured
using gate arrays will be asymmetrical. In this case the gate was driving a large
capacitative load, approximately 3 m m of track, compounding the problem.
The reasons for the timing spread were thus a combination of possibly
unsuitable technology, unsatisfactory layout and inadequate process quality
control. Again, only voltage contrast techniques could give a definitive answer.
5.4.6
CMOS latch-up
Another area where voltage contrast techniques have been used to aid IC
development and failure analysis concerns the characterization of latch-up
paths in C M O S ICs. Latch-up occurs because closely spaced n-channel and p-
Voltage contrast and stroboscopy
227
parasitic S C R
n-channel
p-channel
n
F i g . 5.67 CMOS transistor pair showing parasitic SCR (p-n-p-n) structure.
channel transistors can interact, forming a coupled pair of parasitic bipolar
transistors (Fig. 5.67). These bipolar transistors effectively form a silicon
controlled rectifier (SCR) structure, which can be triggered on with a current
spike. Once the parasitic SCR is triggered, a destructively high current flows
through the device, frequently causing permanent damage.
M a n y techniques have applied to the study of latch-up in C M O S devices electron beam-induced current, laser probe, thermal mapping, and the
detection of recombination radiation (see references in Canali et al, 1986).
While these methods often reveal the region of the device where the latch-up is
occurring, they cannot provide specific information about the latch-up path,
i.e. the route taken by the current. This is a vital piece of information if the IC
design is to be improved to reduce latch-up senstitivity. Basically, we need to
know the voltage distribution on the diffusion and the silicon substrate.
Voltage contrast techniques can be used to provide this information, but
special variants are needed because the voltages in question lie underneath one
or more layers of oxide. In this case there is no question of removing the oxide;
the device would be destroyed by such action. Davidson (1983) and Canali
et al (1986) developed voltage contrast methods which allowed the potential
on the diffusions and substrate to be viewed or recorded. The basic principle is
capacitatively coupled voltage contrast (CCVC), whereby voltage changes on
subsurface layers are coupled by the oxide capacitance to the surface. Only
varying voltages can be recorded in this manner; it is therefore necessary to
synchronize the device signals with the SEM scan. Figure 5.68 shows a result
obtained with this approach. The device is a C M O S ASIC, and the region
under investigation is the input protection diode structure. EBIC imaging
(Fig. 5.69) showed a dramatic contrast increase in this area when latch-up
occurred, indicating that some change in the current flow was taking place.
The voltage contrast image prior to latch-up (Fig. 5.68) clearly shows the pwell as bright (0 V) and the substrate as dark (10 V). When latch-up is initiated,
228
S . M . Davidson
UNLATCHED ( V
D D
= 10V)
LATCHED ( V
D D
= 3V)
F i g . 5.68 Voltage contrast images of CMOS protection diode structure showing
latch-up.
the upper part of the p-well stays bright (0 V), but the lower region goes dark,
indicating that it is being pulled towards the substrate potential. This can only
happen if a substantial current is flowing from the substrate into the bottom of
the p-well, along the well and out through the guardband at the top. The latchup path can thus be identified. In this case the guardbands (heavily doped nand p-regions) which are supposed to prevent this behaviour are too close
together. In fact they serve to sustain the latch-up once it has been initiated.
Re-design of the input protection diode structure eliminated the problem.
The C C V C technique was taken a stage further by Canali et al. (1986) by
combining voltage contrast, topography subtraction and digital beam control
to produce much clearer images of potentials on p-wells and substrate. They
also investigated latch-up time evolution, i.e. the way the latch-up was
initiated and propagated. Stroboscopic imaging enabled voltage maps to be
recorded from the substrate and p-wells at different times through the latch-up
Voltage contrast and stroboscopy
229
Ml
EMISSIVE + EBIC
UNLATCHED
EMISSIVE + EBIC
LATCHED
P-WELLS BRIGHT
LATCHED I/P - STRONG EBIC
OTHER I/Ps - NO EBIC
F i g . 5.69 EBIC image of structure depicted in Fig. 5.68 showing latched diode.
process. Some of these are shown in Fig. 5.70. Figure 5.70a shows the device in
the unlatched state. In Fig. 5.70b the input pulse has just been turned off. A
large potential increase is visible in the p-well adjacent to the input protection
diode, while the p-well above has not yet latched. With increasing time
(Fig. 5.70c and d) a large potential d r o p appears in the upper p-well. Steadystate occurred after 8 jus. These results were confirmed by recording stroboscopic waveforms (Fig. 5.71), which show the manner in which the voltages on
the p-well and substrate change with time. Measurements such as these can
provide useful insight into latch-up triggering mechanisms.
Electron beam techniques can also aid latch-up investigation by indicating
the regions of the device which are most sensitive to triggering. In this case a
high electron beam potential must be used, injecting excess carriers into the
suspect region. High beam voltages would ordinarily affect device operation.
However, the system described by Canali allows particular scan patterns to be
programmed which avoid sensitive regions of the IC. Laser probe methods can
also be used here; however, the control of depth penetration which the electron
beam provides is a positive advantage, as is the ability to excite regions under
metallization.
230
S . M . Davidson
F i g . 5.70 Time-resolved voltage contrast images showing latch-up propagation
through CMOS input structure (Canali et al, 1986).
5.4.7
J u n c t i o n location a n d leakage
Voltage contrast techniques are normally used to examine voltage distributions on the surface of a semiconductor. Depth information can, however,
also be acquired if the device is sectioned prior to examination. While this
would not normally form part of a design validation or failure analysis
strategy, there may be occasions where confirmation of the junction location
or depletion region width is needed. Metallurgical junction depth can be
measured by a wide range of methods, bevelling and staining, and spreading
resistance being just two. However, these methods normally give no indication
of the lateral spread of the junction, nor the depletion region width and its
variation with reverse bias.
Figure 5.72 shows EBIC images of a cross section through a C M O S output
Supply
voltage
Input
Supply
pulse
current
n-substrate
p-well
2us/div
F i g . 5.71
1986).
Voltage contrast waveforms showing latch-up propagation (Canali et al,
EMISSIVE + EBIC - ZERO BIAS
EMISSIVE + EBIC:
VQD - 10V
V
0 P
= OV
P-WELL/SUBSTRATE JUNCTION ARROWED
EMISSIVE + EBIC:
V
D D
, V
0 P
= OV
EMISSIVE + EBIC:
V
D D
, V
0 P
= 6V
F i g . 5.72 EBIC image showing cross section of n-channel output transistor and pwell.
232
S . M . Davidson
VOLTAGE
CONTRAST
V
v
DD
o p
= 10V
= 0V
P-WELL ARROWED
d
VOLTAGE
CONTRAST
V
DD
= 10V
V
0 P
= 10V
SOURCE/DRAIN
DIFFUSIONS
ARROWED
F i g . 5.73 Voltage contrast image of device depicted in Fig. 5.72.
driver. Very low beam voltages (2-3 kV) were used to obtain good spatial
resolution. The p-well and n-type source and drain regions can be clearly seen.
With increasing reverse bias, the depletion regions widen as expected. In
particular, the effective channel length becomes much shorter than the actual
channel length. Also shown (Fig. 5.73) are voltage contrast maps. The
boundary between n-type and p-type regions is clearly visible, as is the effective
channel length. This information can be of considerable value when modelling
the behaviour of the device.
Voltage contrast methods can sometimes help with the detection of leakage
sites in devices. C M O S ICs in particular should take no current under D C
conditions, because either the p-channel or the n-channel transistor in every
gate will be turned off. Should either transistor not be totally turned off,
because of a manufacturing defect, then current will flow through the device.
Voltage contrast and stroboscopy
233
F i g . 5.74 Voltage contrast image showing CMOS device in low and high leakage
states.
Electron beam testing, of course, measures or detects the voltage on a device; it
can only detect current flow if this causes a significant d r o p in the voltage at an
internal node.
Figure 5.74 shows images of a C M O S ASIC at two logic states. In this case
one logic state exhibited high leakage, the other low leakage. In Fig. 5.74a all
the lines appear uniformly bright or dark, while in Fig. 5.74b one region shows
an intermediate degree of contrast, indicating that the voltage here lies
between K and V (the power supply voltage). While D C voltages are difficult
to measure accurately using voltage contrast (the technique is fundamentally
AC), we can nevertheless tell that the n-channel transistor driving this node is
not switching off totally. This is confirmed by noting that the intermediate
voltage contrast, as well as the leakage current, increased with supply voltage.
In many ways this particular example is exceptional; the leakage current
was sufficiently high ( ~ 10 mA) and sufficiently localized to cause an easily
observable change in contrast. M o r e typically, leakage in C M O S devices is
much lower and often spread over a large number of nodes. U n d e r these
circumstances, the use of voltage contrast methods is of limited value. One
ss
dd
234
S . M . Davidson
F i g . 5.75 Voltage contrast image showing propagation (a) and reflection (b) of
waves in SAW filter (Eberharter and Feuerbaum, 1980).
possible approach might be to note any change in the device leakage with logic
state. Voltage contrast mapping could then be used to correlate the nodes
which changed state with possible leakage paths.
5.4.8
Surface acoustic wave devices
Voltage contrast methods are not limited to semiconductor devices, although
they do provide the bulk of the applications. The voltage pattern on any
Voltage contrast and stroboscopy
235
sample can be visualized in this way. Surface acoustic wave (SAW) devices are
normally used as transducers or filters in high frequency circuits ( > 10 MHz);
the 35 M H z bandpass intermediate frequency filter in television sets is perhaps
the most c o m m o n example.
SAWs are fabricated from piezo-electric material, commonly lithium
niobate, with complex electrode patterns formed by photolithography. In
operation, various standing and travelling wave patterns are set up in the
substrate by suitable signals applied to the electrodes. The piezo-electric
nature of the material means that these patterns appear as voltages on the
surface of the transducer. Stroboscopic imaging will reveal these voltage
patterns in exactly the same way as on an integrated circuit. The only difference
is the insulating nature of the sample; low beam voltages and currents must be
used to avoid disturbing the surface potential pattern.
Figure 5.75a, taken from the work of Eberharter and F e u e r b a u m (1980),
shows an interdigital transducer radiating at 36 M H z . Strong excitation of the
z-propagating and x-propagating waves can be seen. While these images are
often difficult to interpret in a truly quantitative manner, for example, to
determine the power in each m o d e of excitation, they can reveal very quickly if
any unwanted modes or reflections are present. Figure 5.75b shows waves
from a transducer being reflected from the edge of a crystal. It is also possible
to discover if the wave pattern changes with frequency over the bandwidth of
the device, producing unwanted features in the transmission characteristic.
The foregoing represent a small sample of the potential applications of
voltage contrast and stroboscopy, selected to illustrate the wide range of
measurements possible. In practice, the voltage distribution on any conducting or insulating sample can be investigated.
5.5
Recent developments
Since the availability of the first commercial voltage contrast systems in 1980,
electron beam testing has been widely adopted for design debugging and
failure analysis in the semiconductor industry. This period has seen much
development of the instrumentation, with the result that the electron beam
testing system of 1988 bears little resemblence to its 1980 counterpart. In 1987,
the first conference solely devoted to electron beam testing was held, signifying
the emergence of the subject as a field of study in its own right (Electron and
Optical Beam Testing of Integrated Circuits, Grenoble). The proceedings have
been published in Microelectronic Engineering (Vol. 7).
Most of the recent developments concern advances in the equipment,
notably electron optical columns, spectrometers, blanking systems, computer
control and interfacing to C A D systems and automatic test equipment (ATE).
236
S.M. Davidson
A lot of effort h a s a l s o g o n e i n t o the d e v e l o p m e n t of the m e t h o d o l o g y of
electron b e a m testing, i.e. the routines w h i c h e n a b l e rapid identification of the
faulty region of the device. Earlier sections of this chapter h a v e described m a n y
n e w d e v e l o p m e n t s in the c o m p o n e n t s of the instrument. P e r h a p s the m o s t
significant t h e m e of this d e v e l o p m e n t p r o g r a m m e c a n be described b y o n e
w o r d - integration.
In the past, the electron b e a m tester h a s b e e n seen as a s t a n d - a l o n e
instrument w h i c h performs s o m e specific functions - i m a g i n g v o l t a g e patterns
a n d m e a s u r i n g v o l t a g e w a v e f o r m s . T h e a s s u m p t i o n is that the user will bring
his device a l o n g t o the S E M or E - b e a m tester together with all the necessary
d o c u m e n t a t i o n - circuit d i a g r a m s , n o d e lists, l a y o u t s , test pattern data,
c o m p u t e r s i m u l a t i o n s a n d A T E results. T h e user m u s t a l s o supply test
e q u i p m e n t t o drive the device, a n d often s o m e form of h o l d e r a n d / o r
i n t e r c o n n e c t i o n arrangement.
Before testing starts, the user m u s t l o c a t e the region or n o d e s of interest with
reference t o the circuit d i a g r a m a n d layout. H e m u s t then set u p the correct test
c o n d i t i o n s a n d d e c i d e w h i c h m o d e of v o l t a g e contrast o p e r a t i o n will m o s t
efficiently p r o v i d e the necessary i n f o r m a t i o n or fault d i a g n o s i s , for e x a m p l e
v o l t a g e m a p p i n g , s t r o b o s c o p i c i m a g i n g , l o g i c state m a p p i n g , w a v e f o r m
m e a s u r e m e n t or t i m i n g d i a g r a m recording. T h e S E M or electron b e a m
c o n d i t i o n s m u s t then be o p t i m i z e d for the device in q u e s t i o n , for e x a m p l e
accelerating v o l t a g e a n d b e a m current, spatial a n d t i m i n g resolution. Likewise, the v o l t a g e s o n the spectrometer (extraction, filter a n d suppressor if
fitted) m u s t b e e s t a b l i s h e d a n d o p t i m i z e d . F o c u s i n g , a s t i g m a t i s m a n d b e a m
a l i g n m e n t h a v e t o be c h e c k e d at regular intervals. T h e correct d u t y cycle a n d
s a m p l i n g t i m e b a s e m u s t be c h o s e n .
Clearly, m u c h m a n u a l setting u p n e e d s t o be performed. This, h o w e v e r , is
o n l y the beginning. A suitable test strategy m u s t be a d o p t e d . T h e A T E results
m a y give s o m e g u i d a n c e as t o the l o c a t i o n of the suspect region of the chip. If
this is n o t o b v i o u s , the best a p p r o a c h m a y be t o c o m p a r e the suspect device
with a k n o w n g o o d I C , p o s s i b l y using d y n a m i c fault i m a g i n g . O n c e the correct
regions of the I C h a v e b e e n l o c a t e d , suitable n o d e p o s i t i o n s (for w a v e f o r m
m e a s u r e m e n t ) m u s t b e defined. It s h o u l d be n o t e d that a single n o d e o n the
circuit c a n c o r r e s p o n d t o a multiplicity of physical l o c a t i o n s o n the chip, e.g. a
l o n g track or tracks. A d e c i s i o n as t o the best p o i n t a l o n g this track t o m a k e the
m e a s u r e m e n t m u s t be m a d e .
T h e final stage in m a n y analyses often consists in recording sets of
w a v e f o r m s at a series of n o d e s o n the device, usually with a range of input test
patterns. If the s p e c i m e n m u s t be r e p o s i t i o n e d m a n u a l l y b e t w e e n e a c h
m e a s u r e m e n t , the w h o l e o p e r a t i o n b e c o m e s very t e d i o u s a n d p r o n e t o
o p e r a t o r error. E v e n after the results h a v e b e e n acquired, c o n s i d e r a b l e
analysis m a y be n e e d e d t o d e t e r m i n e the cause of the p r o b l e m .
Voltage contrast and
stroboscopy
237
We can thus see that current electron beam testing equipment requires a
great deal of highly skilled operator involvement if meaningful results are to be
obtained. The whole operation is time-consuming and inefficient. M a n y
laboratories and instrument manufacturers are now carrying out research and
development into methods for streamlining the whole testing process.
One of the more significant milestones is the A D V I C E project, funded by
the E E C under the Esprit programme. Five laboratories in four countries (BT,
CSELT, C N E T , I M A G and Trinity College, Dublin) are collaborating in the
development of techniques for the Automatic Design Validation of Integrated
Circuits using E-beam (ADVICE). Some preliminary results from this
programme have been published by Cocito and Melgara (1987) and Melgara
et al (1987). This project addresses the problems associated with E-beam
testing outlined above, in particular attempting to (a) reduce the time required
to position the beam and make the measurements, (b) generate a debugging
strategy which minimizes the number of test patterns, and (c) provide
techniques to isolate design problems. The A D V I C E project aims to provide
the design or test engineer with an interactive test environment, fully
integrated with the design environment, so that all design validation and fault
location can be performed using modern computer-aided technology. A key
point in the project is seen to be the integration of the design and test
environment. The full use of all available design data - physical coordinates,
node identifiers, layout geometry, simulation results - is seen as essential to
make the debugging process as efficient as possible. The idea is that all E-beam
testing will be controlled from the engineer's C A D workstation; the A D V I C E
system will thus comprise a hardware package - fully automatic E-beam
tester with computer control - linked to a sophisticated software package
which will run on any of the commonly used workstations.
Equipment manufacturers, e.g. Lintech, Schlumberger and I C T are working
along similar lines, while comparable research is being carried out in the
laboratories of some of the Japanese electronics companies. The general
feeling is that voltage contrast examination, or electron beam testing, must be
simplified if wide acceptance is to be achieved - hence the adoption of
computer control to reduce operator involvement.
Another significant factor is the measurement time per point. With current
electron beam testing technology, this is likely to rise as device geometries
shrink. Figure 5.76, taken from H e r r m a n n and Kubalek (1987), shows that
device geometry considerations could cause the measurement time to increase
by a factor of 30 by the year 2000 if significant improvements in electron optics,
spectrometers and measurement procedures do not occur. Kubalek speculates
that the performance of the instrumentation could be improved by a similar
factor over the same period, but it would appear that radically new approaches
may be needed if E-beam measurements are to be significantly speeded up.
S . M . Davidson
Increase in measurement time
238
F i g . 5.76
Projected increase in E-beam measurement time to the year 2000.
T o conclude, voltage contrast a n d stroboscopy have come a very long
way from the initial observations of Everhart. C a n the techniques be further
improved to keep pace with corresponding developments in semiconductor
technology? T h e prospects are encouraging, but new ideas will be needed.
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6 The Conductive Mode
D.B. HOLT
Department
Prince
of Materials,
Consort
Road,
Imperial
London
College
of Science
and
Technology,
SW7 28 P, UK
List of symbols
6.1 Basic physical principles
6.1.1 The barrier electron voltaic effect: EBIC and EBIV signals from
p - n junctions
6.1.2 Other types of elecrical barrier
6.1.3 The bulk electron voltaic effect
6.1.4 ^-Conductivity signals
6.1.5 Hole-electron pair generation
6.1.6 Plasma regime effects
6.1.7 Time resolution
6.2 Detection systems and contacts
6.3 EBIC and EBIV measurements
6.3.1 Modelling EBIC charge collection in defect-free material . . .
6.3.2 Charge collection by a Schottky barrier normal to the beam . .
6.3.3 The EBIC current collected by a p - n junction or Schottky barrier
parallel to the beam
6.3.4 Time-resolved EBIC
6.3.5 The EBIC current collected by p - n junctions and Schottky barriers
normal to the beam
6.3.6 Schottky barrier height determinations and microcharacterization:
EBIV versus EBIC
6.3.7 Heterojunctions and barriers in striated ZnS platelets . . . .
6.3.8 Plasma effect contrast
6.4 Theory of EBIC and CL defect contrast
6.4.1 The phenomenological theory of EBIC defect contrast . . . .
6.4.2 Linear dislocation EBIC contrast theory
6.4.3 Second-order dislocation contrast theory
6.4.4 Plasma effects on dislocation EBIC contrast
6.4.5 Grain boundary EBIC contrast
6.4.6 EBIC contrast of precipitates and stacking faults
6.4.7 Dislocation CL contrast
6.4.8 Phenomenological theory of dislocation dark CL contrast . . .
6.4.9 Bright dislocation CL contrast
SEM Microcharacterization of Semiconductors
ISBN 0-12-353855-6
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Copyright © 1989 Academic Press Limited
All rights of reproduction in any form reserved
D.B. Holt
242
6.4.10 The temperature dependence of dislocation EBIC contrast: the
limits of the phenomenological model
6.4.11 Physical dislocation contrast theory
6.5 ^-Conductivity
6.5.1 Constant voltage bias ^-conductivity
6.5.2 Experimental verification
References
317
319
327
328
330
333
List of symbols
a
A
A,
A*
a constant
area of the EBIC contrast profile of a defect
area of a diode
the
Richardson
constant
for
thermionic
( = 1 2 0 A / c m / K for free electrons)
2
b
B
C
C
e
D
*i
E
E
b
f
f
F
Go
G
G(r)
h
H
i*
emission
2
ratio of the electron to the hole mobility
a constant
defect EBIC or C L (maximum) contrast
probability of an electron transition between the dislocation energy
level and the conduction band
junction depth
electron diffusion constant
"ionization" energy, i.e. the effective average energy required to
generate a hole-electron pair
field in the charge collection region
energy of the electrons in the beam in keV
b a n d g a p energy
average fraction of the energy of the incident electrons lost by
backscattering
fraction of dangling bonds along a dislocation that are occupied by
a second electron
geometrical and beam parameter function relating dislocation
strength to EBIC contrast, i.e. the contrast correction factor
strength of a point source of carriers
generation function, the number of hole-electron pairs generated
per second at the point or depth
Everhart-Hoff universal depth-dose function
generation factor, the number of hole-electron pairs generated per
incident beam electron
net carrier generation rate
thickness of the layer of reduced lifetime at a grain boundary
one- or two-dimensional analytical generation function
EBIC contrast profile
The conductive mode
•* e
i
j
-*m
^0
*S
* SC
p
I*
J.
A
k
k
L
L
L
B
D
"o
n(r)
AN
N
A
N
B
N
c
N
d
P (r)
P
Ap
<i
Q
Ar
243
externally observed (EBIC) current: I(t) and 1(0) are the values at
times t and 0 respectively
actual m a x i m u m value of E B I C current as the beam scans across
the barrier
electron beam current
emitted electron current
generation current of electron-hole pairs
current through a p - n junction under b o m b a r d m e n t
theoretical maximum value of EBIC current for the beam incident
edge-on at the barrier
saturation reverse current through a p - n junction
specimen (absorbed electron) current to earth
short-circuit (EVE) current (EBIC signal)
EBIC current collected in defect-free ("perfect") material
EBIC current reduction at a defect
net rate of electron capture by a dislocation per unit length
rate of hole capture per unit length of dislocation
Boltzmann's constant
parameter appearing in eqns 6 . 3 3 and 6 . 3 4
minority carrier diffusion length
light (CL) intensity with the beam incident on good "bulk" material
light (CL) intensity with the beam incident on a defect
equilibrium electron density in the absence of a dislocation
minority carrier density
number of recombination centres per unit length of dislocation
total number of hole-electron pairs generated per second
acceptor density
doping concentration under a Schottky barrier
density of states in the conduction band
number of energy states per unit length of a dislocation
minority carrier density in defect-free ("perfect") material
excess density of the beam-induced minority carriers
charge on the electron
charge per unit length on a dislocation
electron beam-induced reduction in specimen resistance
radius of the cylinder round a dislocation in which the lifetime is
reduced
Griin range (R, the "electron range", is usually taken to be R )
resistance of a specimen in the absence of the electron beam
reduced surface recombination parameter
cross section of a rod including the generation volume and running
from one rectangular contact to a second parallel one
temperature in degrees Kelvin
G
RG
S
So
T
244
V
v
v
h
c
v
d
v
D
v
oc
7
v
t
w
P
S
</>B
y
(7,Z
G
°d
°
T
da
i(r)
T'
T
P
D.B. Holt
surface recombination velocity of the free surface. By analogy, also
the grain boundary recombination strength
externally observable voltage (EBIV signal) across a b o m b a r d e d
barrier
beam accelerating voltage
chemical (bulk electron voltaic effect) contribution to the opencircuit voltage
Dember potential contribution to a bulk electron voltaic effect
open-circuit voltage
built-in (equilibrium) diffusion potential d r o p across a p - n
junction
open-circuit voltage of an EVE (EBIV signal)
reverse bias voltage
width of the depletion region at a barrier
quality factor for p - n junctions: jS = 1 for zero recombination,
P = 2 for linear recombination and jS > 2 for less-developed
materials
the Dirac delta function
charge collection probability (fraction of carriers generated at the
point that are collected)
Schottky barrier height
strength or line recombination velocity of a dislocation
the charge collection efficiency (fraction of N collected)
potential barriers against electrons entering and leaving dislocation energy states, respectively
conductivity (in ^-conductivity section)
variance of a grain boundary EBIC profile (eqn 6.65)
cross section of the cylinder round a dislocation in which the
lifetime is reduced
capture cross section of recombination centres along a dislocation
element of area of a grain boundary
minority carrier lifetime far from any defect
(local) minority carrier lifetime
reduced lifetime near a defect
non-radiative recombination time
the plasma time (time required by the field to extract the average
carrier from the plasma region)
radiative recombination time
Each of the six modes of operation of the SEM is defined by the type of signal
detected (Chapter 1). The conductive mode signals are the currents or voltages
induced in the specimen by electron beam bombardment. The three types of
245
The conductive mode
( a )
(b)
(c)
F i g . 6.1 The three essentially distinct types of conductive mode signal: (a) specimen
(absorbed electron) current from the beam to earth; (b) charge collection signals, due to
electron collection by one contact and hole collection by the other; and (c)
conductivity signals detectable in the presence of an external bias.
conductive mode signals can be distinguished in the situations in Fig. 6.1. The
specimen (absorbed electron) current flows to earth (Fig. 6.1a). The charge
collection (CC) signals are detected between two contacts, one of which
"collects" electrons and the other, holes. In the absence of any externally
applied bias (Fig. 6.1b), C C signals arise only if electromotive forces are
generated in the specimen. The phenomena that do this are called electron
voltaic effects (EVEs) and are analogous to the photovoltaic effects. Even if no
electron voltaic effects occur, the beam injects excess local "jS-conductivity"
(conductivity due to /?-ray bombardment). This is the analogue of p h o t o conductivity. T o obtain a C C signal from this effect, an external bias is
necessary (Fig. 6.1c). An historical account of the electron voltaic and /?conductive effects and their discovery will be found in Holt (1974) and much
additional information in Ehrenberg and G i b b o n s (1981). A brief account of
the basic physical mechanisms involved in C C signal generation will be given
in the next section.
The most important type of signal in the C C m o d e is E B I C (electron beaminduced current) and an important phenomenological (Donolato) theory of
EBIC contrast is now available. Most of this chapter is devoted to this, with n o
attempt to present a complete C C literature review.
6.1
Basic physical principles
The incident electron beam I generates a number of hole-electron pairs per
second given by
b
(6.1)
&N = GI /q
b
where
G = (l-/)E /*
b
i
(6.2)
/ is the average fraction of the energy of the incident beam electrons lost by
D.B. Holt
246
backscattering, q is the charge on the electron, E is the energy of the incident
beam electrons (in eV), and e is the "ionization" energy, i.e. the effective
average energy required to generate a hole-electron pair. e is about 3 times £ ,
the b a n d g a p energy, due to other forms of energy loss and losses of carriers by
immediate recombination. When E is tens of kiloelectronvolts, G is of the
order 1 0 - 1 0 so C C currents are often much larger than the specimen or
beam current. The hole-electron pairs are produced in a generation or energydissipation volume. This volume acts as a probe, determining the spatial
resolution of the C C mode.
The specimen current (Fig. 6.1) is simply the incident beam current minus
the total emitted current (primary or backscattered, secondary and tertiary),
i.e.
h
{
g
{
b
3
4
Wb-/«
(6.3)
Consequently, the contrast in I micrographs will be the inverse of that in the
(total) emitted current. Some information can be obtained by intercomparing
the secondary and primary emitted electron micrographs with the specimen
current micrograph, but this has not been found very useful.
By far the most widely used form of C C signal is the barrier electron voltaic
effect (barrier EVE) electron beam-induced current (EBIC).
s
6.1.1
T h e barrier electron voltaic effect: E B I C a n d E B I V s i g n a l s from
p - n junctions
The principle of the barrier EVE is shown in Fig. 6.2 for the specific case of a
p - n junction. It is analogous to the barrier photovoltaic effect exploited in p - n
junction photodetectors and solar photovoltaic cells. Hole-electron pairs
generated in the depletion region (Fig. 6.3b) are separated by the built-in field.
(a)
(b)
(c)
F i g . 6.2 The barrier electron voltaic effect in a p-n junction: (a) detection
configuration; (b) diode characteristics in the dark and under illumination (photovoltaic effect) or electron bombardment (EVE); (c) barrier EVE characteristic showing the
short-circuit current, J , and open-circuit voltage, V .
sc
oc
The conductive mode
247
Carriers generated near this region can also diffuse to it and be "collected" by
the built-in diffusion potential. If the junction is short-circuited a current of
this (total) number of carriers per second will flow externally. This is the shortcircuit current, 7 of the barrier EVE characteristic (Fig. 6.2). If the diode is
open-circuited, the electrons collected to the n-side and holes to the p-side
produce a non-equilibrium, forward-bias K , the open-circuit voltage
(Fig. 6.2). This rises with beam power to a limiting value in the flat-band
condition (Fig. 6.3f). This is only reached for sufficiently intense b o m b a r d ment so the high-injection, saturation value is:
SC
oc
K>c
( m
ax)=^D
(6.4)
where V is the built-in diffusion potential d r o p across the junction.
Pfann and van Roosbroeck (1954) treated the EVE using the equivalent
circuit for a diode under electron b o m b a r d m e n t of Fig. 6.4, neglecting both
surface leakage and bulk resistance. The E V E charge collection is represented
by a generator producing a current 7 . The resultant forward biasing of the
junction results in a junction (forward) current I The difference is the current
/ flowing through the (detector) resistance r, i.e.
D
g
y
/ , = /j + /
(6.5)
The junction current is given by the diode characteristic:
/ . = J [exp(< F//Wc7)-l]
J
0
Z
(6.6)
where I is the saturation reverse current, q the charge on the electron, V the
externally observable voltage d r o p across the barrier under b o m b a r d m e n t , /?
the "ideality factor" is > 1 if recombination occurs at the junction but = 1
otherwise and the other symbols have their usual meanings. The externally
observable voltage is:
0
(6.7)
V = Ir
Substituting eqn (6.6) into (6.5) yields:
I = I - I [exp(qV/pkT)
g
0
- 1]
(6.8)
which is the barrier EVE characteristic shown in Fig. 6.2b and c. The shortcircuit current is obtained by setting V = 0, i.e.
'sc = /
g
(6.9)
The generated current is the fraction of the injected carriers that are collected,
i.e.
(6.10)
where rj
cc
is the charge collection efficiency of the barrier.
Diffusion
^ * Repulsion
!9n
r
<^ ( vacuum
level)
n
V
Ep
p-type
Diffusion
0
9D
Energy
bond
Diffusion
Repulsion
! n-type
•_-; + + ! Space charge
• - 1 + +! layers
'on
Diffusion
n-type
p-type
(b)
Depletion
region
(a)
Bombardmentgenerated
. «•—Current
_
_ J__ l_ l 5
f
r l
t
Electrons
E f
v
P-type
Vondl
mtermediote
Voiues
Bond diagram
r(O<r<00)
Circuit
n-type
(c)
Electrons
S^Ort Circuit
I •-max
V=0
E f
$ c
p-type
O
Bond diogrom
JL.
Circuit
n -type
(d )
Bombardment
Current ^
Diffusion
j
Current
Electrons
Open circuit
I net --0
V
nf
= man
Bond diogrom
Diffusion
Bombordment
(•)
t
-
I
(f)
l
f 0
:
249
The conductive mode
Generator
r
V
1
Fig. 6.4
r
I
s/WWvV
V
Equivalent of an ideal diode under electron bombardment.
The open-circuit current is obtained by setting / = 0 in eqn (6.8):
K = 0 8 k T / « ) ] l n [ ( / / / ) + .l]
oc
M
(6.11)
o
EBIC is the widely used terminology for observations employing the shortcircuit current as signal. Similarly, EBIV is used when V is employed.
oc
6.1.2
Other types of electrical barrier
EBIC and EBIV signals can be obtained from any other form of rectifying
electrical barrier, i.e. any interface at which there is a depletion region across
which a diffusion potential difference occurs. Examples are Schottky barriers
(Fig. 6.5) and heterojunctions. The physics and technology of Schottky
barriers is now relatively well understood. That of heterojunctions is less so.
Other types of barrier are even less understood. However, so long as the
barrier exhibits a rectifying characteristic of the form of eqn (6.6), the above
treatment can be applied.
Some grain boundaries in semiconducting compounds act as electrically
active barriers and can be treated as two Schottky barriers back-to-back, with
Fig. 6.3 Junction energy band diagrams for the barrier EVE in a p - n junction, (a) A
junction in equilibrium without bombardment, (b) "Charge collection" under bombardment is the separation of electrons and holes generated in the depletion region by the
built-in field plus the acceleration across the junction of minority carriers generated at a
distance that diffuse to the junction. The result produced depends on the value of the
external load resistance r. (c) For an intermediate value, both a voltage and a current
will appear externally, (d) Under short-circuit conditions a maximum short-circuit
current will be detected, but no voltage, (e) Under open-circuit conditions a maximum,
open-circuit voltage will appear, (f) As the beam power is increased, the open-circuit
voltage rises to saturate at the flat band condition, when the externally detected voltage
equals the built-in diffusion potential drop.
250
D.B. Holt
I
Metal
metal
/ / / / / / / ,
+
+
semiconductor
r
+
+
+ ,
i
+i
i
Depletion
region
(a)
(b)
F i g . 6.5 The Barrier EVE for a Schottky barrier: (a) detection configuration and (b)
energy band diagram.
different barrier heights (Ziegler et al, 1982). Grain boundaries in the
elemental semiconductors, however, exhibit only EBIC dark contrast. These
boundaries can be modelled, like dislocations, by locally faster recombination
represented by a surface (interface) recombination velocity (e.g. Donolato,
1985a). Phase interfaces such as polytype interfaces in striated platelets of ZnS,
can also give rise to C C signals showing that some form of barrier is involved
(Holt and Culpan, 1970).
The usual geometries used in observations on electrical barriers are shown
in Fig. 6.6. The edge-on scan geometry is useful for determining materials and
barrier parameter values. Plan-view scanning occurs when planar technology
devices and epitaxial layers or multilayer (hetero) structures are examined.
Spatial uniformity and the contrast properties of any electrically active defects
present can readily be determined.
6.1.3
T h e bulk electron voltaic effect
Whenever the doping concentration changes markedly as in p / p or n / n
interface regions, the position of the Fermi level in the b a n d g a p changes (at
temperatures in the extrinsic conduction range). In equilibrium, the Fermi
energy (the electrochemical potential of the carriers) must be everywhere the
+
+
la)
(b)
F i g . 6.6 Basic geometries of observation of electrical barriers in semiconductors: (a)
p - n junction edge-on (the plan-view case is in Fig. 6.2) and (b) Schottky surface barrier
edge on (the plan-view geometry is shown in Fig. 6.5).
P-type
N - 1 ype
built-In
electrical field
region
P* (degenerate)
highly- doped
material
P - t y p e less
highly doped
material
built - In
electrical field
region
F i g . 6.7 Energy band diagram for a p / p doping transition region showing that
band bending, a diffusion potential difference V and a built-in field results. The field
collects (separates) charge carriers produced during bombardment of such a region and
this gives rise to a bulk electron voltaic effect.
+
p
Q.
9
The conductive mode
Fig. 6.9
253
^-Conductivity arises from carrier injection.
same. Therefore b a n d bending must occur as is shown for the case of an p / p
concentration change in Fig. 6.7. In just the same way as shown for the p - n
junction in Fig. 6.3, the built-in field in the interface region will "collect"
carriers generated locally and give rise to a "bulk electron voltaic effect" (bulk
EVE) analogous to the bulk photovoltaic effect.
Examples are exhibited by the line scans across a simple Si rectifier
(Fig. 6.8a). The doping profile of this device (Fig. 6.8b) exhibits a p - n junction
and both p / p and n / n bulk band bending regions. (The heavy doping is to
reduce the series resistance Joule heating and to allow ohmic contacts to the
ends of the diode.) Figure 6.8c shows a number of EBIC line scans recorded at
increasing beam currents for a constant beam voltage. The lowest exhibits
principally the barrier E V E peak generated at the p - n junction but there is
also a marked shoulder due to the n / n bulk EVE. As the beam current is
increased this and the p / p bulk EVE peak rise. The bulk E V E makes it
possible to confirm the existence and position of concentration profiles. The
theory and simulations of M a r t e n and Hildebrand (1983) incorporated both
bulk and barrier (junction) EVEs.
+
+
+
+
+
6.1.4
^-Conductivity signals
In the generation volume there is an excess local carrier density and hence an
increase in conductivity (Fig. 6.9). U n d e r an applied bias this will result in an
additional contribution to the signal. T w o simple extreme cases can be
distinguished. U n d e r constant current bias, a change in voltage is detected and
under constant voltage bias, a change in current will be observed on beam
Fig. 6.8 (a) Geometry and (b) doping profile of a simple Si rectifying diode and (c)
experimental EBIC line scans across such a specimen exhibiting two bulk EVE peaks in
addition to the p - n junction barrier EVE peak and (d) experimental EBIV line scans.
Successively higher line scan profiles are for higher beam currents of 37, 62, 76 nA and,
in the EBIV case, 86 nA at 30keV.
D.B. Holt
254
bombardment. These two cases, analogous to EBIC and EBIV, can be referred
to as /J-current and /J-voltage signals.
Instrumental discrimination between EBIC and EBIV, /J-current and /?voltage is C C m o d e signal (spectral) resolution.
6.1.5
Hole-electron pair generation
The energies required to generate electron-hole pairs in a number of materials
are listed in Table 6.1. Klein (1968) noted the linear relation between this
formation ("ionization") energy e and the b a n d g a p energy £ (Fig. 6.10) which
he wrote as the sum of the minimum energy separation of a pair (£ ), an
average pair kinetic energy and a number of optical phonons. Ehrenberg and
Gibbons (1981) extended the plot by including solid inert gas (large E ) data
g
x
g
g
T a b l e 6.1
Electron-hole pair formation energies
Material
e,(eV)
Reference
C (diamond)
CdS
13.07
7.3
7.8
5.0
4.65
4.6
6.8
4.4*
7.8
2.84
4.4
3.95*
0.42
1.1
Kozlov et al (1975)
van Heerden (1957)
Munakata (1966)
Vavilov et al (1964)
Mayer (1967)
Wittry and Kyser (1965)
Kalibjian and Maeda (1971)
CdTe
GaAs
GaP
Ge
InSb
InP
PbS
PbO
Si
2.2*
2.0
8
3.6
SiC
SiC (6H)
9.0
11.3
Goldstein (1965)
McKenzie and Bromley (1959)
Rappaport et al. (1956)
Ivakhno and Nasledov (1965)
Klein (1968) from data of Tauc and Abraham
(1959)
Smith and Dutton (1958)
Lappe (1961)
Wu and Wittry (1978) and references therein
i
Golubev et al (1966)
Koninger (1971)
•Values obtained by D.C. Joy and D.B. Holt (unpublished work) by scanning over the edge of a
Schottky barrier and using Monte Carlo electron trajectory simulations to calculate the
backscattered energy loss correction.
255
RADIATION IONIZATION ENERGY
(tV)
The conductive mode
BAND GAP ENERGY (tV)
F i g . 6.10 Hole-electron pair formation energy versus bandgap energy after Klein
(1968).
and found
^ = 2.1£ +1.3
g
(6.12)
where all terms are in eV.
The values of e enable one to calculate the total number of carriers
generated using eqn (6.2). F o r many purposes the distribution of the carriers is
also important. T o discuss this, a few terms must first be defined.
{
Ranges and dose
functions
The depth of penetration, in the incident beam direction, at which the primary
electrons have been slowed to thermal equilibrium with the lattice is the range
R. This is less than the Bethe range which is the total, multiply deflected,
drunkards-walk-type primary electron path length calculated using a theoretical expression due to Bethe (see Chapter 2). It is also slightly greater than the
usual empirical measure used, the G r u n range which will be defined below.
Two types of analytical function are often used. One represents the depthdose which is the energy loss per unit depth in the beam direction. This
D.B. Holt
256
determines the depth resolution. The lateral-dose function represents the
energy deposited per unit distance at right-angles to the beam direction. This is
important for the (lateral, "spatial") resolution of the CC, C L and X-ray
modes.
The work of Griin
Griin (1957) photographed the volumes of air that luminesced under
b o m b a r d m e n t by electron beams of different energies to determine the energy
dissipation volumes and depth-dose relation. He found that the penetration
range increased with the accelerating voltage V but the shape of the curve of
energy loss per unit length, when normalized to the range for a particular
acceleration, was constant as shown in Fig. 6.11. Griin suggested using the
value obtained by extrapolating the linear region of negative slope to zero
energy. This is now known as the Griin range and is given for any material by
his empirical expression:
b
K = [(3.98xl0- )/p]£
2
G
(6.13)
7 5
o
where p is the density in g/cm . This equation gives the range in /mi if E is in
kV.
3
0
The Everhart-Hoff
depth-dose
function
M o n t e Carlo simulations (Chapter 2) are generally the best means for
computing results for curve fitting to extract quantitative data from observations. Depth-dose, lateral-dose and other dose distributions can be readily
extracted from the data so generated. However, for many purposes it is
important also to have available analytical approximations. These are used in
mathematical treatments and can give a useful idea of the way energy is
deposited in the solid under the beam and the volumes throughout which
various types of signals are generated. Some knowledge of the commonly used
analytical expression is necessary to critically appreciate much of the EBIC
literature.
The most widely used semi-empirical, analytical expression for the energy
deposited per unit depth is that of Everhart and Hoff (1971). They determined
the depth-dose curve from measurements of damage in polymers and found it
to be of the same form as that of Griin for air. They found they could
approximate this "universal" depth-dose curve by a polynomial:
h(Q = 0.60 + 6.21£ - 12.4£ + 5.69£
2
3
(6.14)
where £ is the depth divided by R . This expression has been found to give
reasonably accurate results. F o r greater accuracy variants of the Griin range
G
257
The conductive mode
t
UJ
x
X/R *y a
(a)
r
(»Ok«V)
Ot
3h
IN)
(30ktV)
(35ktV)
~
O
—
(40 ktV)
Fig. 6.11 (a) The reduced depth-dose distribution and the definition of the Grun
range R (after Grun, 1957). (b) The Everhart-Hoff expression for the electron-hole
pair density versus depth in silicon (after Leamy 1982).
G
expression for different regions of beam energy (accelerating voltage) can be
used (see Everhart and Hoff for details).
Other depth-dose
functions
A distribution function of combined Gaussian and exponential form was used
by W u and Wittry (1978) and is fairly popular and a simpler Gaussian form
258
D.B. Holt
was used by Davidson and Dimitriadis (1980). Reviews of a number of such
analytical models will be found in Bishop (1974), H a n o k a and Bell (1981) and
Leamy (1982).
Lateral-dose
function
The spread of energy sideways from the beam impact point is also needed for
some calculations. An empirical expression for this was proposed by Shea
et al. (1978) based on the data of Griin.
Carrier distribution
models
A widely used model is the uniform generation sphere. This is of diameter R
tangential to the surface. Equations (6.1) and (6.2) give the number of carriers
distributed uniformly through the sphere. This not a bad approximation for Si
and beam energies of tens of kiloelectronvolts. The simplest of all models, but
adequate for some purposes, assumes this number of carriers to be generated
at a point at a depth of, say, 0.41 R . This is the centre of gravity of the carrier
distribution as given by the Everhart and Hoff depth-dose function. Other
geometrical models of the distribution have been used and will be found in the
reviews of Bishop (1974), H a n o k a and Bell (1981) and Leamy (1982).
G
G
Monte Carlo electron trajectory
simulations
N o w that inexpensive and powerful microcomputers are available, M o n t e
Carlo simulations (Chapter 2) provide a practical general method for treating
beam-specimen interactions. Among the advantages of the M o n t e Carlo
method are that: (i) it automatically computes the appropriate value for the
backscattering loss factor / in eqn (6.2) (for which reliable experimental values
are often not available); (ii) it is applicable to multilayer samples for which
analytical expressions are not available (Napchan and Holt, 1987); (hi) it
readily yields not only depth- but also, for example, lateral- and radial-dose
distributions that are convenient for treating particular detecting barrier and
defect geometries.
It is important to know the carrier densities produced by electron
bombardment. Additional phenomena can affect charge collection when the
generated carrier density becomes larger than that of the equilibrium carriers,
i.e. at high injection levels. Recombination centre saturation can occur. Each
centre takes a finite time to capture and recombine a pair. There is, therefore,
an upper limit to the density of carriers per unit time that can recombine via a
given concentration of centres and when this is exceeded the centres are said to
be saturated. At higher densities the minority carrier lifetime increases. Other
259
The conductive mode
effects arise from the shielding of the interior of the energy dissipation volume
at high carrier densities, as will be discussed next and in Section 6.4.2.
6.1.6
P l a s m a regime effects
Leamy et al. (1976) first pointed out that the plasma regime effects previously
found in semiconductor charged particle detectors (Tove and Seibt, 1967) also
affect EBIC observations. At sufficiently high injected hole-electron pair
densities, the carriers constitute a plasma which polarizes at the edges. This
shields the carriers in the interior of the excited volume from the charge
collecting field of the barrier so the EBIC current decreases in this plasma effect
regime. This results in a minimum in the observed EBIC current when the
objective lens is exactly focused (Fig. 6:12). The energy dissipation volume is
then minimized and the injected carrier density maximized for a constant
Js"l
it
CflA)
lt.O..
r r r
r—
A* OAJtftlCft
r
T.Ov
t
t
9.0*
t
•••••
TO
I»—
•O
SO
40
90
tO
OSJKTIVC LCNS CUfWCNT I f f * )
F i g . 6.12 The variation in the charge collection current as the SEM beam passes
through focus at an objective lens current of 40 mA. At high specimen currents I (i.e. at
high beam currents) plasma formation occurs and a large decrease in I occurs at focus.
(After Leamy, 1982.)
s
cc
D.B. Holt
260
o
(a)
t
(b)
F i g . 6.13 Time-resolved EBIC: (a) a typical experimental arrangement and (b) the
form of result obtained when the beam is chopped at a time t ±= 0.
beam power as indicated schematically in the inset sketches in the figure. The
recombination rate under plasma regime conditions is controlled by the
plasma time, T , the time required by the field to extract the average carrier
from the plasma region (Tove and Seibt, 1967). Plasma formation is therefore
favoured (Leamy et al, 1976) by high generation densities, i.e. by low E and
high J and, since T is proportional to the field E in the charge collection
region, by a low value of E.
p
h
b
6.1.7
p
T i m e resolution
Time resolution is an important form of signal resolution in the C C mode. If a
stationary beam, incident near a detecting barrier (Fig. 6.13) is chopped, the
decay characteristic of the EBIC current is often of the simple form:
7(r) = / ( 0 ) e x p ( - r / T )
(6.15)
F r o m such an observation the minority carrier lifetime, T , can be obtained at
the beam impact point.
6.2
Detection systems and contacts
EBIC is usually observed simply by connecting a high-gain, large-bandwidth
amplifier across the specimen. As charge collection currents in Si are
thousands of times greater than beam currents (eqns (6.1) and (6.2)) microscopy
is easy. Interpretation, however, is not, as the short-circuit current or the opencircuit voltage must be obtained for quantitative evaluation of the data. Thus
the input impedance of the detection amplifier must be very low relative to that
of the specimen for true EBIC but very high for true EBIV.
The conductive mode
261
If materials other than Si or devices other than transistors and integrated
circuits are encountered, additional requirements arise. F o r example, large
devices such as solar cells and photodetectors produce large currents under
bias and capacitative noise may be a problem. Power devices and reachthrough avalanche photodiodes require high voltage biasing.
F o r general use, besides low-noise, high-bandwidth and high-gain, and the
ability to detect b o t h EBIV and EBIC, a detection system thus should have: (i)
facilities for biasing the specimen and backing off the resultant D C current for
observing devices under operating conditions; (ii) simple electronic signal
processing such as filtering to minimize noise for microscopy; (iii) digital
monitoring of the signal from the specimen, the bias voltage and the back-off
current; (iv) an analogue-to-digital interface for connection to microcomputers or image processing systems. Such a system was reported by
Lesniak et al (1984a) and a commercial model is available.*
Image processors provide frame storage and signal as well as picture
("image") processing software and a variety of peripherals: interactive
processing devices like digitizing pads and light pens and hard-copy facilities.
F r a m e storage and image processing facilities are also provided in some
energy dispersive X-ray microanalysis systems. At least one current model of
digital S E M has such systems incorporated in the basic instrument. The
increasing availability of such equipment makes both quantitative C C m o d e
microcharacterization and improved EBIC microscopic examination of
structure more convenient.
1
Serious difficulties in quantitation can arise from the signal processing effect
of the specimen itself. The simplest case, a single diode, has an R C (resistance
capacitance) time constant which can affect the observed signal. In a bipolar
transistor, a charge collection voltage generated at one junction can affect the
charge collection current from the other (Hungerford, 1987). Varying signal
processing effects can occur in VLSI (very large-scale integrated) circuits.
Contacts
To avoid unexpected internal (specimen) signal processing reliable Schottky
and ohmic contacts are necessary. Schottky barrier contacts have simple
rectifying characteristics (Rhoderick and Williams, 1988). EBIC and EBIV
methods for their study are dealt with in Section 6.3.4. Ohmic contacts are,
strictly, those with a linear I - V characteristic. The properties of contacts on
H I - V compounds are now known to depend on complex interfacial chemistry
•ICVM-5 from Matelect Ltd, 33 Bedford Gardens, London W8 7EF, UK.
tStereoscan 360 from Cambridge Instruments, Viking Way, Bar Hill, Cambridge CB3 8EL,
D.B. Holt
262
and metallurgical microstructure and contacts are called ohmic if their
impedance is low. This is often achieved by making the Schottky barriers
present thin, by heavily doping the semiconductor surface layers, to allow
tunnelling currents to flow at small biases. Thus the distinction is a practical
rather than a fundamental one. Reviews of the literature on contacts will be
found in Rhoderick and Williams (1988), Sharma (1981), Brillson (1983),
Brillson et al (1983), Henisch (1984), Cohen and Gildenblat (1986) and
Woodall et al (1987).
SEM CC microscope
optimization
It is not our purpose to describe the practical operation of SEMs but some
special features of the C C mode require mention. It is important to minimize
the electron b o m b a r d m e n t of the specimen. Beam blanking plus frame
grabbing facilities enable one to scan a frame once, or a few times for signal
averaging, and study the image at leisure on the monitor without continuing to
beam scan the specimen. This is essential in the inspection of M O S devices and
ICs. Computerized detection systems that make possible rapid recording of
data were also found essential for quantitative studies of defects of low EBIC
contrast (Wilshaw et al, 1983).
O p t i m u m focus is not easy to define. It is a c o m m o n experience that the
sharpest focus for EBIC observations of defects at a depth of a few micrometres
is significantly different from that for the secondary electron emissive mode
(surface) picture. It is as though one had to focus down into the interior. If
plasma regime (very high injection level) conditions occur, the C C signal and
EBIC dislocation contrast both pass through a minimum at focus, defined as
the condition giving the smallest energy dissipation volume (see Sections 6.1.6
and 6.4.2).
6.3
EBIC and EBIV measurements
EBIC measurements and defect contrast studies led to detailed theoretical
treatments. EBIV has received much less attention and /^-conductivity has
been almost totally neglected since the early 1970s.
Most EBIC measurements of materials and device parameters have been
made using line profiles recorded scanning edge-on (Fig. 6.6). Planar technology device structures are naturally scanned in plan as the charge collection
barriers are parallel to the surface (Figs 6.2 and 6.5). Methods for evaluating
the essential parameters in this geometry have also been developed. Scanning
over angle lapped surfaces, i.e. at a small angle to a p - n junction, has been
found unnecessary. Almost all publications concern well-developed p - n
junctions and Schottky barriers.
The conductive mode
(a)
263
(b)
m
F i g . 6.14 Charge collection by a Schottky barrier in plan-view: (a) generation and
diffusion and (b) boundary conditions and image for a point source of carriers.
6.3.1
M o d e l l i n g E B I C c h a r g e collection in defect-free material
T o interpret E B I C results it is first necessary to calculate the current collected.
The account here is due to Donolato. The carriers produced by electron
b o m b a r d m e n t in the generation volume diffuse away, recombining as they go
(Fig. 6.14a). This behaviour is described by the continuity equation which in p type material, in which the excess minority carrier density is n(r), takes the
form:
DV n(r) - n(r)/T(r) + g(r) = dn{r)/dt
(6.16)
2
where g(r) is the generation function, D the electron diffusion constant and t(r)
the local minority carrier lifetime. F o r steady-state conditions the right-hand
side of this equation is = 0.
6.3.2
C h a r g e collection by a S c h o t t k y barrier normal to the beam
We start by treating a point source of carriers of strength g
beneath a surface Schottky barrier. Then:
0
DV n(r)-n(r)/i = ^ ( r - r )
2
0
at a point r
(6.17)
where <5(r — r ) is the Dirac delta function and the solution at a point at a
distance r from the source is:
0
x
The exponential carrier density decrease is due to recombination during
diffusion and r in the denominator represents the decrease with distance due
to geometry that would occur even if the diffusion length L were infinite. The
x
264
D.B. Holt
value of L does not have as great an influence on resolution as was
pessimistically expected in early work, partly due to this geometrical factor.
The charge collection, EBIC current is found by applying boundary
conditions that determine the solution to the continuity equation for the
particular experimental situation. The boundary conditions must represent
the collection barrier appropriately. In principle, the continuity equation also
contains a field-dependent current term (see, for example, Reimer, 1984) but
the effects of local fields are not calculated directly. The charge collecting effect
of the field in the depletion region of the barrier is represented by assuming
that all the minority carriers reaching the boundary of this region are collected,
i.e. assuming an infinite surface recombination velocity i; so n(r) = 0 at z = 0 in
Fig. 6.14. The EBIC current is then obtained by integrating the flux of
minority carriers diffusing to the surface, over the barrier area.
Such problems are treated by the method of images, borrowed from
electrostatics (Fig. 6.14). The result in the Schottky case is that the minority
carrier density is given by the Green's function (Donolato, 1978/79):
s
n(r) = ( l / 4 r Z ) ) [ ( l / r ) e x p ( - r / L ) - ( l / r ) e x p ( - r / L ) ]
7
1
1
2
(6.19)
2
The number of carriers collected per unit time is obtained by integrating the
vertical carrier flux over the surface to obtain
(6.20)
which Donolato calls the charge collection probability, i.e. the current due to a
unit source at the point r at a depth z . The macroscopic C C efficiency of a
device (eqn (6.10)) is the fraction of the injected charge that is collected and so
is given, using the Everhart-Hoff function h(£) (eqn (6.14)) = h(z/R ) by the
integral:
0
G
(6.21)
That is, the C C efficiency is an average of the C C probability weighted with the
depth-dose function.
Multiplying the source strength g (number of carriers generated per second)
at each point by the collection probability and integrating over the generation
volume gives the EBIC current in "perfect", defect-free material:
g(x y, z) exp (— z/L) dx dy dz
9
dz exp (— z/L)g(x, y z) dx dy
9
265
The conductive mode
where g(x, y, z) can be obtained directly from a M o n t e Carlo simulation or, for
example, by scaling the Everhart-Hoff depth distribution function by
multiplication by G / (see eqn (6.10)). By symmetry this is essentially a onedimensional problem so:
b
(6.22)
I = ^dztxp(-z/L)g(z)
p
is the EBIC current collected by a Schottky barrier in defect-free material.
The inverse transform in charge-collection
microscopy
D o n o l a t o (1986a) addressed the problem of inverting the transform of
eqn (6.22) in its general form, i.e.
(6.23)
<t>(z)g(z)dz
to obtain 0(z), the C C probability function characterizing the charge
collection properties, from the experimentally observable EBIC current J, or
C C efficiency, rj without any specification of the device structure. Using the
Everhart-Hoff depth-dose function h in eqn (6.21) he obtained an explicit
solution for </>(x). However, D o n o l a t o pointed out that, in practice, rj(E)
(eqn. (6.21)) is available only for a limited number of values of E which are
subject to errors, and the function rj(E) will have to be obtained by curve-fitting
and must satisfy a number of mathematical conditions.
9
Experimental
verification
The penetration range of the beam and the total number of generated carriers
distributed over the depth-dose function and therefore the measured C C
efficiency of Schottky barriers depends on the beam energy, E in keV:
h
n(E ) = I (E )/GI
h
p
h
h
(6.24)
where G is given by eqn (6.2) and rj is given by eqn (6.21). The treatment of the
barrier as having n o thickness above was a first approximation. Real Schottky
barriers have a metal thickness t and a depletion layer depth W(Fig. 6.15) so <\>
and rj are functions of these parameters as well. It is generally assumed that all
the carriers generated in the depletion region of any barrier are collected so the
C C probability there is unity. The plane bounding the depletion region as
before is assumed to have an infinite recombination velocity, to represent the
combined effect of diffusion to the depletion region and collection. The result
can be computed and compared with experimental measurements. This was
D.B. Holt
266
(a)
fbj
F i g . 6.15 Schottky surface barrier: (a) structure and (b) charge collection probability, 0, and efficiency n. In the metal layer of thickness t the charge collection
probability is zero, in the depletion layer of depth W it is assumed to be unity and in the
bulk it falls exponentially. (After Donolato, private communication.)
done by W u and Wittry (1978), who carried out the calculations using their
own depth-dose function, with the results in Fig. 6.16. By curve-fitting, values
of the device parameter t and the materials parameters W (which depends on
the Si doping) and L are obtained.
Pietsch and Rodemeier (1981)'used a simple approximation to the W u and
Wittry depth-dose function in their calculation and made measurements on
BEAM VOLTAGE ( K V )
F i g . 6.16 Experimental points and calculated curves of charge collection efficiency
versus beam voltage for Au-GaAs(n) Schottky barrier diodes. Data for three specimens
of different minority carrier diffusion lengths are shown. (After Wu and Wittry, 1978.)
267
_« I
.
.
.
.
.
.
00
01
it 2 4 12 4 0
4t
SJ
The conductive mode
F i g . 6.17 Two-dimensional diffusion length maps for scanned areas on Schottky
barriers to (a) GaAs and (b) GaAs P
(After Pietzsch and Rodemeier, 1981.)
0 6
0 A
Schottky barriers on GaAs and G a A s P . Their equipment was computerized and the beam was sinusoidally modulated. This enabled them to
obtain both diffusion length and lifetime values for each point of the area
scanned. They represented their lifetime results graphically as in Fig. 6.17.
Joy (1986) showed that the problem can be readily solved by using M o n t e
Carlo simulations for the carrier generation distribution with all the attendant
advantages of speed and the ability to put in the actual values of the
parameters for the specimens used. As a test, he showed that fitting
experimental results for an I n P Schottky barrier to computed curves gave the
metal thickness as 30 nm (Fig. 6.18).
Tabet and Tarento (1988) calculated the charge collection efficiency of
Schottky contacts assuming a linear variation of the electric field in the
depletion zone, and taking into account recombination at the m e t a l semiconductor interface. They found that majority carrier injection from the
0 6
0 4
268
D.B. Holt
5000
r
4000
z
<
3000
2000
lOOOl
BEAM ENERGY(keV)
F i g . 6,18 Current gain (I /I ) versus beam energy in keV for a Schottky barrier on
InP. The solid points are measured values and the curves were obtained using Monte
Carlo simulation and assuming a hole-electron pair formation energy of 2.2 eV, a
depletion depth of 1 jrni and the gold Schottky film thicknesses marked on the three
curves. (After Joy, 1986.)
sc
h
semiconductor into the metal was non-negligible for low doping levels and low
beam energies. Their experimental results for Au/nGe Schottky barriers
showed that the assumption of 100% collection efficiency for minority
carriers generated in the depletion region leads to an overestimate of the EBIC
current, particularly for low minority carrier diffusion lengths.
6.3.3 The E B I C current collected by a p - n junction or Schottky
barrier parallel to t h e b e a m
The case of a beam scanned along a line normal to a p - n junction (Fig. 6.6a)
was first treated by Wittry and Kyser (1965) as follows. Assuming a point
source of carriers and spherical symmetry, the continuity equation has the
solution:
p = ,4exp(-r/L)/r
where A is a constant with dimensions c m '" ( c(cf . eqn (6.18)).
22
(6.25)
The conductive mode
9
269
9
\
0-
- 9
n
P
(b)
(a)
F i g . 6.19 Scanning across a p - n junction edge-on. (a) The use of a single image
source to treat the problem ignoring surface recombination and (b) the three image
sources needed to take into account surface recombination also.
Wittry and Kyser assumed that (1) all the minority carriers diffusing to the
boundary of the junction depletion region are collected so the carrier density is
zero there and (2) surface recombination can be neglected. Assumption (1) is
equivalent to the infinite barrier recombination velocity, zero density assumption used for the Schottky barrier above. The problem can then be solved by
the method of images borrowed from electrostatics for this diffusion problem.
That is, the effect of the junction can be modelled by including an image source
of opposite sign (Fig. 6.19a). Then, as before, the current of minority carriers
collected is found by calculating — Ddp/dx at the junction (x = 0) and
integrating over the junction area (cf. eqn (6.20)). The result is 2nADexp
(— x/L). The source strength, found by calculating the limiting flux through a
hemisphere of radius r as r approaches 0, is In AD. Thus the solution for the C C
(EBIC) short-circuit current in the absence of electrically active defects and
neglecting surface recombination is
(6.26)
J = J exp(-x/L)
P
m
where the source strength is
/
m
= G/
(6.27)
b
(see eqns (6.1) and (6.2)). This is the theoretical maximum current and is
obtainable by extrapolating experimental EBIC plots of log I versus x back to
the junction (Fig. 6.20).
F o r small values of x and w, the depletion region width, relative to the
diameter of the generation volume, the EBIC current will be reduced
(Fig. 6.21). This is because, as shown for x = 0, the carriers generated will be
collected with maximum efficiency ( ~ 100%) only in the depletion region.
Thus in practice the EBIC current versus x (and log I versus x) plots usually
are concave downwards near the junction position. In such cases the
0
270
D.B. Holt
X
(a)
(b)
F i g . 6.20 The form of (a) EBIC current variation with x and (b) log / versus x in the
absence of significant surface recombination.
'lb
R
w
F i g . 6.21 The effect of overlap of the beam energy dissipation (generation) volume
with the junction depletion region for small x (e.g. for x = 0 as shown) and R » w is that
the peak value of the EBIC current is reduced compared to the theoretical maximum
I due to the carriers being collected with maximum efficiency ( ~ 100%) only in the
depletion region.
m
plot takes the form shown and the actual maximum current observed is
h = rj GI
cc
h
(6.28)
where rj is the C C efficiency of the junction. It is given by expressions
analogous to that of eqn (6.21) for the portions of the generation volume (i) in
cc
The conductive mode
271
the p-material, (ii) in the depletion region, and (iii) in n-material:
fee
-J.
I*
-w/2
'w/2
'Jt/2
Ch(x) dx +
(j)(x)h(x) dx +
'w/2
-w/2
h(x) exp ( - x/L ) dx +
Ch(x) dx
e
- J R/2
+
(f)(x)h(x) dx
w/2
-w/2
R/2
-w/2
[R/2
J w/2
x) exp( —x/L ) dx
(6.29)
h
where C is the constant fraction of the carriers generated in the depletion
region that are collected. It is usually assumed that C = 1. This will not be the
case if there is significant recombination in the depletion region.
F r o m plots like that of Fig. 6.20 the C C efficiency can be obtained since
fee =
Experimental
(6.30)
hlh
verification
The simple exponential variation with distance of eqn (6.26) is often seen in
semiconducting compounds, presumably because the surface recombination
I (nA)
ICOO^
5
15
X(/t*m)
20
F i g . 6.22 EBIC line scan profile across a grain boundary in CdS. (After Munakata,
1966.)
D.B. Holt
272
6
Current ( A )
i c r
i
12
i
» i i i i i i
18
14
10
6
i
i
i i i i
2 0 2 4 6
N
i
8
Distance /im
F i g . 6.23 EBIC line scan profile of a GaAs p - n junction laser diode. (After Chase
and Holt, 1973.)
velocity in these materials can be negligible in the present context. Perhaps the
earliest example was reported by M u n a k a t a (1966) for a grain boundary in
CdS. Figure 6.22 is his EBIC log I versus x plot exhibiting the simple
exponential form (and concave downwards showing that rj < 1 at the peak).
Sometimes two exponentials of very different apparent minority carrier
diffusion lengths are observed in different ranges of distance x from the
junction. Wittry and Kyser (1965) observed the first such case in G a A s diodes
(Fig. 6.23). They suggested that while the steeper exponential was, in fact, due
to minority carrier diffusion leading to collection as treated in the theory
above, the second, less-steep exponential, visible at greater distances, was due
to the self-detection of infrared photons. Holt and Chase (1973) showed
quantitatively that this was, in fact, the case.
A similar observation with a different explanation was reported for Si
avalanche photodiodes by Lesniak et al (1984a). In this case the two
exponentials correspond to minority carrier diffusion with different values of
minority carrier (electron) diffusion length in a (relatively) narrow p-layer and
a wide n (lightly doped p) region.
O n e important application of such line scan observations is the measurement of minority carrier diffusion lengths by determining the slopes of EBIC
l o g / versus x plots. To d o this reliably, the possible effect of surface
recombination must be taken into account, however.
cc
The effect of surface
recombination
Surface recombination was neglected in the treatment leading to eqn (6.26) but
it can have a marked effect. The effect of surface recombination was treated
The conductive
273
mode
10"r 7
1 normalized
experimental
J 5kV scans
theoretical
curve for
S =20
fc
• EBIC(A)
10"
10"•12
0.0
2.0
1.0
3.0
- • X
s
= x /L
5.0
s
F i g . 6.24 The effect of surface recombination on the form of the EBIC line scan
profile on one side of a p - n junction in GaP is to produce a small upward concavity at
small distances, x as predicted by the dotted curve. The solid and dashed lines are
experimental data normalized to the correct diffusion length L = 0.76/mi and values
10% higher and lower. (After van Opdorp, 1977.)
s
first for a light spot scanned across a p - n junction by van Roosbroeck (1955).
It was treated for EBIC line scans by Bresse and Lafeuille (1971), Hackett
(1972), Berz and Kuiken (1976), van O p d o r p (1977), H u and Drowley (1978)
and Oelgart et al. (1981). The effect is that Whereas the simple expression of
eqn. (6.26) yields a straight line on a semi-log plot, the complicated Bessel
function expressions yielded by the theories for s > 0 appear concave upward
near the junction on such plots (Fig. 6,24). sf is the reduced surface recombination parameter
s = V T/L
(6.31)
S
where v is the surface recombination velocity.
D o n o l a t o (1982) used a Fourier transform treatment and took account of
the translational invariance parallel to the junction (along y) to obtain a
simpler expression for the current profile as follows. The current can be written
in terms of an effectively two-dimensional C C probability (f>(x,z) and
generation function g(x,z) (cf. eqn (6.21)) as
s
7 =
dx
P
o
g(x,z)(j){x z)Az
i
Jo
(6.32)
D.B. Holt
274
He showed that the C C probability was given by
sin (kx) dk
*00
where n = (k + 1 / L )
2
2
1/2
(6.33)
\j/(k, z) sin (kx) dk
o
• (/>(*, z) is thus the Fourier sine transform of a function
(6.34)
containing only elementary functions
Equation (6.32) can be put in the form of a convolution and the Faltung
theorem for Fourier transforms applied, yielding finally the expression:
r oo
r oo
(6.35)
^(k, z)g{k, z) dz
Jo
Jo
where g(k z) is the Fourier transform of g the two-dimensional carrier
generation distribution. This expression is equivalent to that previously
generally used and applies equally to profiles scanned away from a vertical
Schottky barrier instead of the p - n junction assumed above.
The "back" contact, at the right-hand edge of the material (Fig. 6.25), begins
to allow carriers to flow to earth as the beam approaches it. This reduces the
EBIC signal due to charge collection by the distant junction and produces a
steep final fall in the I (x) profile. This was treated by von Roos (1978) and by
Fuyuki et al. (1980a, b). D o n o l a t o (1982) remarked that the analysis outlined
above could readily be extended to treat this case of a sample with finite
thickness and that it is convenient for discussing the case of an extended
generation volume. While the expression for I (x) appears formidable, it is in a
form suited to microcomputer EBIC simulations.
I (x) = 2 ( 2 / 7 t )
0
1/2
dfe sin (kx)
9
9
0
0
F i g . 6.25 Real diodes are finite and the "back" contact acts to reduce charge
collection by the junction when the beam is incident nearby.
The conductive mode
1 r—
-i
r
1—-t——r
«
1
1
1
275
1
r
electron
beam
Z
X
01
E = 30keV
•••..20'
, ^ £ = 30keV
- £
0.01
2 x
—J
0
I
I
1
20
I
40 x 60
80
(urn)
100 120
F i g . 6.26 Normalized EBIC profiles I (x)/I (0) for the n-side of a p - n junction in Si
from data of Oelgart et al (1981) with plots of xl (x) for evaluation by the moment
method. (After Donolato 1983d.)
sc
sc
sc
The method of moments
D o n o l a t o (1983) developed the method of moments for evaluating L from the
E B I C profile. " M o m e n t " is used as in statistics (Donolato, 1985b), i.e. the first
m o m e n t a b o u t the origin of a distribution function Q(x, z) is
()
m x
—
Jo
(6.36)
Q(x,z)xdx
Using for Q the expression for il/(k, z) of eqn (6.34), ij/ is dimensionless so m(x)
has the dimensions of length squared and is given by the area under the lower
curves in Fig. 6.26. Applying to eqn (6.35) the m o m e n t theorem for Fourier
transforms, D o n o l a t o obtained the expression
m(z) =
*=o
= lim^ (fc,z)
*-o
(6.37)
fc
Substituting eqn (6.34) into (6.37) led to
m(z ) = L {1 - [sL/(l + 5 L ) e x p ( - z / L ) ] }
2
0
0
(6.38)
D.B Holt
276
assuming carrier generation by the beam can be represented by a point source
at a depth z . This depends on the beam energy through the dependence of
z = 0A\R
on E . Determination of m(z ) at two beam energies makes it
possible to obtain values for L and s. As a test, D o n a l a t o applied this method of
analysis to the results of Oelgart et al (1981). In Fig. 6.26, the curves of x/ (x)
were plotted as well as I (x) for 20 and 30 keV. The value of L obtained was
much larger than that from the slope of I (x) or that obtained by Oelgart et al
using a generation function different from that of Everhart and Hoff. Use of the
results of a M o n t e Carlo simulation for the generation function would avoid
this problem.
Experimentally, the result depends strongly on the point chosen as origin of
the I (x) profile. This should be the edge of the depletion region. It is assumed
to be the point of inflection where the semi-log EBIC profile changes from
concave downward as the junction is crossed, to concave upward due to the
effect of surface recombination (Oelgart et al, 1981; Donolato, 1983d).
0
0
G
h
0
p
p
0
0
Experimental
verification
Experimental tests of the theory were made by Bresse (1972) and van O p d o r p
(1977) as shown in Fig. 6.24. Bresse used a variable electric field in, and parallel
to, the surface to represent the effect of varying the surface recombination
velocity. The paucity of measurements of L and S reflects the laboriousness of
the calculations involved in theoretical curve-fitting prior to the introduction
of the simpler D o n o l a t o expression.
Hungerford (1987) carried out a series of EBIC line scan profile measurements on Si p - n junctions specially grown for the purpose. (The values of L in
Si range up to hundreds of micrometres and the width of the p or n layer to be
profiled must be at least 3 or 4L). Hungerford wrote a microcomputer EBIC
program based on the D o n o l a t o expression, outlined above. He also
incorporated the effect of the back contact to simulate EBIC I (x) profiles for a
finite specimen. He obtained his carrier distribution from M o n t e Carlo
simulations using the program of N a p c h a n and Holt (1987), based on those of
Myklebust et al (1976) and Joy (1986).
The success with which Hungerford's experimental results could be fitted to
the curves computed using the D o n o l a t o expression, can be seen in Fig. 6.27.
Hungerford found that such curve-fitting gave the values of L to within a few
per cent and those of s to within a few tens of per cent. This was in agreement
with the experience of Bresse (1972) for data fitted to an earlier expression for
I (x). The use of microcomputer simulations of the simple D o n o l a t o
expression makes determination of L and S values by this method sufficiently
rapid to be practical.
The values of s found by Hungerford were strongly dependent on the
electron beam current, voltage and scan speed. Careful selection of S E M
p
0
The conductive mode
1
277
r-*
distance from junction, microns
F i g . 6.27 Agreement between experimental points and a curve computed using the
Donolato expression for a p - n junction profile in a finite Si specimen. (After
Hungerford, 1987.)
operating parameters is, therefore, necessary to obtain the intrinsic surface
recombination velocity.
Fuyuki et al. (1980a) carried out EBIC line scan profile measurements on a
Si Schottky barrier and found good agreement with theoretical curves. These
they calculated using an analytical approximation for the carrier generation
distribution. They also took into account the effect of the ohmic contact at the
other side of the Si slab.
The effects of surface oxide charging by the beam
The most striking of the effects of the beam on the surface recombination
velocity found by Hungerford was the production of very effective charge
collecting inversion layers due to strong surface charging (Hungerford and
Holt, 1987). This not only reduced the carrier losses due to surface
recombination but produced charge collection of unity efficiency u p to
hundreds of micrometres from the junction. This is illustrated microscopically
in Fig. 6.28 and graphically in Fig. 6.29. This effect had been "written" by the
beam under one set of magnification, beam voltage and current, and scan
278
D.B. Holt
b
F i g . 6.28 EBIC micrographs showing the same area of a Si diode (a) in the initial
condition with only the EBIC peak at the p - n junction appearing bright and (b) after a
smaller area had been scanned for a time at a higher magnification so it developed a
high charge collection efficiency and consequently appears as bright as the junction.
(After Hungerford and Holt, 1987.)
speed conditions to create the bright area in Fig. 6.28. It could then be
gradually "erased" by a series of successive line scans, as numbered in Fig. 6.29,
at a different scan speed etc. due, apparently, to the beam emptying traps in the
oxide and/or interface.
The effect of reverse bias and its
verification
The effect of the overlap of the carrier generation volume and the depletion
region of the barrier such as that of the p - n junction shown in Fig. 6.30
1
The conductive mode
short c i r c u i t current
r~
-
'11|
1
|
1
279
! '
1»
junction
scan 1
-A—-
-
-
\ 7
-
"
/
12
rr
1 1 1 efapcie
20
L.
I 1i
back
contact
A
m
394 urni
i1
F i g . 6.29 EBIC line scans across a line through a bright area such as that in
Fig. 6.28. The first scan shows the charge collection current to be uniformly high over
the entire width of the Si to the back contact. After successive scans (the number of the
scan is marked) the charge collection efficiency at large distances from the junction is
progressively reduced. Finally, normal behaviour is re-established. (After Hungerford
and Holt, 1987.)
(a)
(b)
F i g . 6.30 The effect of overlap of the beam energy dissipation (generation) volume
with the junction depletion region for R » w was shown in Fig. 6.21. For w » R, (a)
there will be a range of x values for which the carriers are collected with the
approximately constant maximum efficiency characteristic of the depletion region to
give (b) a flat-topped EBIC line scan profile.
depends o n the relative values of the depletion region width w a n d the
generation volume dimension K, which is approximately the Griin range. If
w < R, when the beam t o barrier distance x is small, overlap results in a
reduction of the EBIC current as described by eqn (6.29). When w > R, a flat
maximum will be observed in the EBIC profile since the charge collection can
be expected to be uniformly high across the depletion region. It is customary in
elementary accounts t o assume the collection efficiency there t o be unity.
D.B. Holt
280
The depletion region can be widened by reverse biasing. In the case of a
"one-sided" junction, i.e. one heavily doped on one side and lightly doped on
the other, the widening effectively occurs only on the lightly doped side and the
width is given by
(6.39)
(V +V )J'
2
D
r
where V is the built-in potential difference (diffusion potential) across the
junction, V is the reverse bias, e is the static dielectric constant and N is the
impurity concentration o n the lightly doped side (assumed p-type so N is the
acceptor density). The only published measurements of this kind are those of
M a c D o n a l d and Everhart (1965) shown in Fig. 6.31. The experimental points
fall well on the curve representing eqn (6.39) and the value of N was defined
rather closely.
Hungerford (1987) also carried out observations of widening of the
depletion region under reverse bias. H e used an EBIC simulation program
written to include the effect of overlap in accordance with eqn (6.29), the limits
of the three integrals being varied to correspond to the beam positions as the
scan crosses the junction. It is possible t o obtain information in this way, for
example, on the position of the junction. Figure 6.32 shows the result of curveD
r
A
A
Depletion-layer vndth -^m
A
/
\1
4
/
/ / '
curve = 4 7 x I O ~ c m ( v o l t f
6
N
II ' ' '
0
Slope of experimental
1
2
A
=6xl0
1 3
cm'
4
3
5
(Junction v o l t a g e ) « ( V + V )
l/2
r
1 / 2
3
, / 2
0
F i g . 6.31 Measured values of the depletion region width as a function of the reverse
bias voltage V for a Si p - n junction. (After MacDonald and Everhart, 1965.)
r
Aip/sduiv
9
_0I
S
°I
Distance from silicon edge, microns
• J"!
lb =
:
2.38
: fa =
1-1
V
T 7- T t
J I
'. a
V
r
=
20 V
-
O
V
r
=
12 V
;
a
V
r
=
0 V
•
•
t
1
• '
~
T
•
- •"";
(b)
\
\
•
A
•
A
• •
O
O
A
&
o
°OO O O
I
10 ~
6
•
T T .
nA
2 5 kV
v
Amps/div.
r
i
A
^A^A A A A
.
,
Distance
from
i
. . . .
silicon
edge,
1
0
10
20
30
.
microns
F i g . 6.32 Experimental points and Monte Carlo EBIC simulation curves for a
reverse biased Si p-n junction assuming the depth of the junction to be (a) 10^m as given
by the bevel and stain technique and (b) 10.6 jum. Altering the doping density by an
order of magnitude in (a) did not significantly improve the fit. (After Hungerford, 1987.)
282
D.B. Holt
fitting on the information that the depth of the junction was 10 fim from the
growth rates and times used. The fit was poor and not improved by trying
alternative values of the doping density N as can be seen. It was found that the
depth of the junction was, in fact, 10.6 fim as shown by the excellent fit of the
simulated and experimental results in Fig. 6.32. This method can determine
junction depths to within 0.1 jum which accuracy is not readily obtainable
otherwise.
Figure 6.33 shows the results for a junction in which the simulated and
experimental profiles agreed well in shape and position but not in height,
assuming 100% C C efficiency in the depletion region. The results agreed for a
C C efficiency of 88% (Fig. 6.33b) indicating that in this junction there was a
loss of about 12% of the carriers due to recombination.
Such results give confidence in the EBIC Monte Carlo simulation approach
and demonstrate the practical importance of the speed of this method of
analysis. There could be a problem, however, in incorporating computer
programs into the scientific literature. It is necessary that scientific work be
openly published, with sufficient detail given concerning both the theory and
the material and experimental technique so the work can be repeated to check
its reproducibility. Neither descriptions and flow diagrams at one extreme nor
full listings at the other are satisfactory means of publishing the details of
computer methods. Joy introduced the practice of freely giving to all enquirers
copies of his EBIC M o n t e Carlo simulation programs on magnetic floppy
discettes. N a p c h a n and Holt followed the same practice and it is recommended for general adoption. This not only allows critical assessment of
the programs but it eases their adoption, modification and extension for the
benefit of all.
A
An early use of microcomputer simulations of EBIC line scans was that of
Marten and Hildebrand (1983). They obtained a general theoretical expression for the EBIC signal for arbitrary doping profiles and generationrecombination processes. They used a Gaussian generation (depth-dose)
function and produced line scans for linearly graded and more complex
junction doping profiles such as p p n - j u n c t i o n s . Experimental results and
simulations for Cd-diffused I n P p p n - j u n c t i o n s were in agreement. It appears that their simulation covered both a bulk electron voltaic effect (in the
p p region) and a barrier electron voltaic effect in the p - n boundary
region.
Fuyuki et al. (1980b) calculated the form of EBIC line scans up to a GaAs
Schottky barrier using an analytical approximation for the carrier generation
distribution. They showed that a peak would be expected to occur before the
beam reached the metal. Their experimental data were in reasonable
agreement with their theoretical curves.
+
+
+
Amps/div.
7
I 10 ~
sc
from silicon edge,
microns
sc
I 10 ~
7
Amps/div.
Distance
I
I
1I
I
I
30
20
10
0
Distance
from
silicon
edge,
I
microns
F i g . 6.33 Experimental points and theoretical EBIC profiles for a reverse biased Si
p - n junction assuming (a) 100% charge collection efficiency in the depletion region and
(b) 88% efficiency. (After Hungerford, 1987.)
The conductive mode
Micrometre
and sub-micrometre
diffusion
285
lengths
Luke et al. (1985) treated the E B I C profile in cases of small L using a variety of
analytical generation functions and taking surface recombination into
account. F r o m the computed E B I C line scan profiles across p - n junctions
they obtained methods for determining the diffusion length and the surface
recombination velocity. They discussed the conditions under which the
generation source shape becomes insignificant and the lower limit of diffusion
length which can be determined by the EBIC technique.
6.3.4
Time-resolved E B I C
Z i m m e r m a n n (1972) showed that it was possible to measure minority carrier
lifetimes with a high spatial resolution. This is done by chopping (cutting off) a
stationary beam, incident near a charge collecting barrier such as a p - n
junction, and observing the decay of the E B I C current. In simple cases this
takes the form
/(t) = / ( 0 ) e x p ( - t / T )
(6.40)
where 7(0) is the constant E B I C current detected with the beam on a n d T is the
minority carrier lifetime. Z i m m e r m a n n used the method to measure lifetimes
greater than 0.3/xs at distances > ~ 3Lfrom a p - n junction with a high spatial
resolution in Si power diodes and thyristors.
Again the possible complicating effects of surface recombination must be
taken into account. Kuiken (1976) treated the problem and concluded that the
time-dependence of I(t)/I(0) would take the form shown in Fig. 6.34. In general
there is a time delay before the onset of an approximately exponential decay
a n d this depends on the distance of the beam impact point from the junction
relative to the diffusion length, i.e. the value of d/L and u p o n the surface
recombination velocity v .
If both L and x are measured, the diffusion coefficient for the minority
carriers can be obtained since
s
L = (DT)
1 / 2
(6.41)
Fuyuki and M a t s u n a m i (1981) introduced a phase-shift technique for the
determination of lifetime. They treated the case of an intensity modulated
F i g . 6.34 EBIC current decay with time relative to the minority carrier lifetime for
various values of the beam-junction distance d relative to the carrier diffusion length
for the surface recombination velocity V (a) = 0 and (b) = oo. (After Kuiken, 1976.)
s
D.B. Holt
286
beam scanned across a Schottky barrier and showed that the phase of the
EBIC current will be shifted from that of the excitation source due to
recombination. They solved the three-dimensional time-dependent diffusion
equation including the effect of surface recombination and obtained the
relation between the lifetime and the phase shift. The phase shift increases
linearly with the scan distance. With the aid of a curve of the normalized phase
shift versus COT, where co is the angular frequency of the modulation, the lifetime
and diffusion constant can be determined for any modulation frequency. Their
results for Si were in good agreement with this theory.
6.3.5 The EBIC current collected by p - n j u n c t i o n s and S c h o t t k y
barriers normal t o t h e b eam
The p - n junction case involves three boundary surfaces. The beam-entry
surface has a surface recombination velocity. All points in the junction
depletion region were assumed to have unity charge collection probability and
both the upper and lower boundary planes of this region to have infinite
recombination velocity in the treatment of Pasemann (1981a, b) and
Pasemann et al. (1982). If the p - n junction is at a depth greater than the
electron beam range R , using the uniform generation sphere model they
found
G
(6.42)
where S = v z/L d
is the depth of the junction, a = R/2L and G is the
generation factor of eqn (6.2). F o r j R / 2 < 0 . 3 L (usually the case for Si) the
J - R characteristic is approximately linear with slope
s
i
i
p
dI /dR
p
(6.43)
= (S/L)I
p0
where
(6.44)
which is the current for a point source of excitation on the surface.
The parameters L and S of the top (p or n) region of the diode can now be
determined from the dependence of the EBIC current I on the beam voltage
V (which determines R). The experimental points obtained by Pasemann et al.
by varying V but keeping the beam power constant fell on a straight line
(Fig. 6.35). F r o m the experimental values of slope and intercept, using
expressions (6.43) and (6.44), values of L = 1.5 /mi and S = 55 were obtained.
Later work (C. N o r m a n , private communication) confirmed that it was
p
h
b
287
The conductive mode
U (kV) •
5 7 9 11 13 15
b
025-T
0
I
I
I
I 1 I
I
I I
01 0.4 0.6
R(jjm) —-
0.8
F i g . 6.35 Experimental measurements (x) and theoretical EBIC current (eqn. (6.42))
as a function of half the electron range for a constant beam power of 1 //W. (After
Pasemann et al, 1982.)
essential to keep the beam power I V constant to obtain data exhibiting a
linear dependence like that in Fig. 6.34.
The case of a surface Schottky barrier was treated by EBIC M o n t e Carlo
simulation by Joy (1986). He simulated curves for the current gain defined as
h
h
G=
IJI
b
(6.45)
(the quantity of eqn (6.2) allowing for the beam energy absorbed in the metal of
the Schottky contact). The dependence of this current gain on the contact
thickness, beam voltage a n d Schottky barrier height can be simulated and
curve-fitting then gives values of the parameters involved. Figure 6.18 above
showed the agreement between measured gain versus beam energy values and
the simulated curve for a Schottky barrier on I n P , taking into account beam
energy losses by absorption in the metal (Au) layer. The Au thickness was
found to be 30 n m as can be seen by the agreement with the middle curve.
Figure 6.36 shows the situation as the beam range R increases relative to the
depletion region depth w. At first, (R « w), the gain increases linearly with
beam energy by eqn (6.24) as the charge collection efficiency is constant and
approximately = 1. When R>w, however, an increasing fraction of the
carriers are generated at increasing distances below the lower boundary of the
depletion region. These carriers are collected with a decreasing efficiency. This
leads to a falling slope of the gain versus beam energy slope. The value of gain
D.B. Holt
288
G/10
3
(a)
5
10
15
E (kV)
F i g . 6.36 (a) The effect of varying the beam voltage and hence the penetration range
for a fixed depletion region depth under a Schottky barrier, (b) The form of the EBIC
gain versus beam voltage for various values of Schottky barrier height and hence
depletion depth w. (After Gibson et al, 1987.)
at which this begins depends on the value of w and hence of the barrier height
as shown in Fig. 6.36b. By fitting experimental measurements to such
simulated curves values for barrier heights may be obtained. Their determination will be discussed further in Section 6.3.6.
Surface recombination
velocity
W a t a n a b e et al (1977) analysed EBIC employing an effective excitation
strength for the carriers and took into account possible recombination
sources. This made possible three-dimensional evaluation of the minority
carrier lifetime in the bulk and two-dimensional mapping of the surface
recombination velocity of specimens containing a p - n junction below and
parallel to the surface scanned. Their results showed variations by factors of 10
The conductive mode
289
or 15 in recombination velocity where a scratch crossed the area scanned on P diffused Si diodes. By a similar method Jastrzebski et al. (1977) mapped the
surface recombination velocity over a GaAs p - n diode and found variations of
a factor greater than 3.
Other
geometries
I o a n n o u and Davidson (1979) and I o a n n o u and Dimitriadis (1982) showed
that the EBIC current varies with the distance x from the edge of a Schottky
barrier (Fig. 6.37) as
I(x) oc exp ( - x/L)/x
(6.46)
3/2
assuming a semi-infinite sample and an infinite recombination velocity at the
uncovered semiconductor surface. They showed that experimental plots of
In (Ix ) versus x are straight lines. Kuiken and van O p d o r p (1985) treated the
case of a finite surface recombination velocity and gave an expression for
determining L and v from the EBIC profile. D o n o l a t o (1985b) treated the case
v — 0 and showed that the value of L can be obtained by evaluating the
variance of the profile derivative at two beam energies without knowing the
value of v
Hollo way (1984) treated the peripheral EBIC response of a shallow p - n
junction (Fig. 6.38). This was previously considered by Dimitriadis (1984) and
Davidson and Dimitriadis (1980) only for the case of the beam far from the
312
s
s
y
beam
F i g . 6.37 "Planar collector" geometry with a Schottky barrier or very shallow p - n
junction over part of the scanned surface. (After Kuiken and van Opdorp, 1985.)
290
D.B. Holt
n-typt
P-typt
F i g . 6.38 Peripheral (adjacent) scanning across a shallow diffused p - n junction.
(After Holloway, 1984.)
junction. The situation of Fig. 6.38 is the usual one in planar technology
bipolar devices and in integrated circuits, etc. It is not possible to scan far from
such peripheral regions due to the close packing of numbers of devices.
Holloway found that the response of a shallow junction is different from that of
a deep one, that the response is affected by the reduction of the semiconductor
thickness or of the junction dimensions to values less than L and by
competition with adjacent junctions and by surface recombination.
Depth varying minority carrier diffusion
lengths
Donolato and Kittler (1988) analysed the problem of determining the
variation of L with depth in the important case of intrinsically gettered Si
wafers. Intrinsic gettering is the annealing of Czockralski-silicon to form a
defect denuded zone at the surface of the wafer and produce oxygen
precipitates in the interior of the wafer. The depth variation of L can be studied
by applying a Schottky barrier over the edge of an angle-lapped surface on
such wafers as shown in Fig. 6.39 but the problem is to extract the depthvarying values of L from the observed EBIC profile I(z). The depth z is related
to the distance scanned over the angle-lapped surface as z = ^ sin a. F r o m
the EBIC profile, the charge collection efficiency profile can be obtained
since
n
cc
= I(z)/GI
h
where G = E (l — f)/e . In an homogeneous sample, treating the effect of beam
bombardment as equivalent to introducing a point source of GI carriers at a
h
{
h
The conductive mode
291
(a)
zl
zl
(b)
F i g . 6.39 (a) Geometry of EBIC line scans over a Schottky barrier on an anglelapped surface of an intrinsically gettered Si wafer, (b) Schematic point source
generation model for treating the effective depth penetration of the beam. (After
Donolato and Kittler, 1988.)
depth a where a = 0.41 R :
G
rj = exp ( cc
a/L)
D o n o l a t o and Kittler showed that, writing L*(z) for the value obtained by
assuming these relations to apply, i.e.
L * ( z ) = - a/log ?/ (z)
cc
D.B. Holt
292
the minority carrier diffusion length is L(z) = L*(z)C(z\
factor C(z) is given by
where the correction
C(z)=l/[1+L*(z)]
(6.47)
Their experimental data analysed in this manner gave curves for L(z) that
were of physically acceptable forms. The method is applicable to studies of
passivation and other cases in which variations of L with depth are
encountered.
6.3.6
S c h o t t k y barrier height determinations a n d
E B I V versus E B I C
microcharacterization:
The first determination of Schottky barrier heights in the S E M was that of
H u a n g et al (1982). They pointed out that under open-circuit conditions the
carriers generated by the beam cause the potential of the diode to rise until the
forward bias current equals the generation current, i.e.
G / = A A*T
2
b
d
exp (qfiJkT)
exp ( - VJfikT)
(6.48)
which leads to the equivalent of eqn (6.11) for Schottky barriers:
V
= PWB + (kT/q)ln(GI /A A*T )l
(6.49)
2
oc
h
d
where </> is the Schottky barrier height, A is the diode area and A* is the
Richardson constant. Their measurement of V versus log J for PtSi, P d S i
B
d
b
E-BEAM INDUCED VOLTAGE ( V )
oc
i
i
•
1
;
i ;
1
1—r-r-|
1
2
i—R—RR
INCIDENT BEAM CURRENT ( A )
F i g . 6.40 Open-circuit voltage versus the log of the beam current for three types of
silicon/silicide Schottky barriers. (After Huang et al, 1982.)
293
The conductive mode
—i
>
UJ
O
Q
UJ
1
1—r-r-j
Si + Ti(40 n m )
0.2
1
1 — r - ^ —
114 jum d i a m .
• As De
<
_J
o
>
1—rr-|
• 600°
0.1
O
Q
Z
i
UJ
QD
I
o
-J
10
-
10
- 1 0
i
I
1
10"
I
I
L-L_
1CT
9
8
10"
INCIDENT BEAM CURRENT ( A )
F i g . 6.41 The effect of annealing to form TiSi on the open-circuit voltage versus log
of beam current characteristic of a Si/Ti contact. (After Huang et al, 1982.)
2
and TiSi contacts on Si followed the linear form of eqn (6.43) (Fig. 6.40). The
slopes of the lines gave values of the ideality factor /? = 1.02 in all three cases.
By determining G, values were obtained for 0 that were in agreement with
those obtained from current voltage measurements. H u a n g et al pointed out
that the method was particularly good for the study of changes in barriers of
small height. They used it to study the effect of annealing Ti on Si to form T i S i
as shown in Fig. 6.41.
Curve-fitting to M o n t e Carlo simulations of E B I C gain versus beam voltage
(Fig. 6.36) is an alternative method for determining Schottky barrier heights.
The most significant difference between the EBIC and EBIV methods
emerged in considering the spatial resolution of variations in barrier height.
A striking recent discovery was that N i S i contacts can be grown epitaxially
in ultrahigh vacuum with two double-position-twin related orientations (i.e.
differing by a twinning rotation about the (100) Si substrate normal). N i S i
layers of these two orientations appeared to have two distinctly different
Schottky barrier heights (Gibson et al, 1985). G i b s o n et al (private communication) obtained the experimental results for the two forms, A and B, of N i S i
epitaxial contacts on Si in Fig. 6.42. Using the difference in barrier height and
hence in current gain (Fig. 6.42a) for a suitable beam energy, the two forms can
be distinguished by their EBIC contrast (Fig. 6.42b).
Gibson et al point out, following H u a n g et al, that in EBIV the collection of
the generated carriers raises the diode potential until the forward bias current
equals the generation current. Consequently EBIV lacks sensitivity to local
2
B
2
2
2
2
EBIC
2
- 60 A
current gain (g)
NiSi
beam energy
inevj
The conductive mode
295
barrier height variations just as does the classical I-V measurement. This is
because the forward bias current is not constrained to flow locally as the
potential of the whole metal film must be the same. Joy et al. used the EBIV
method of H u a n g et al. and found the value of barrier height did not vary
locally and was the same exponentially weighted average seen in I-V
measurements. They confirmed this by measurements on N i S i barriers
consisting (like the contact in Fig. 6.42b) of areas of both orientations. It is
possible that much of the variation in Schottky barrier height values in the
literature is due to the contacts consisting of variable areas of different barrier
heights, as in this well-characterized, simple case.
2
6.3.7
Heterojunctions a n d barriers in striated Z n S platelets
In addition to the well-understood p - n junction and the fairly wellunderstood Schottky barrier, EBIC and EBIV signals can be collected by a
variety of other barriers which are not well understood.
The most important are heterojunctions between two different semiconducting materials. The basic principles on which the energy band diagrams
of these barriers should be constructed are, to some extent, controversial and
many of the parameters required do not have known or, in some cases, welldefined values. Nevertheless, heterojunctions are increasingly used in devices
such as heterostructure bipolar transistors and double heterostructure lasers.
Clearly heterojunctions can act as electrical barriers with built-in fields
capable of charge collection. Hence it is possible that the application of S E M
C C analyses might help clarify the electrical character and hence the band
structures of these barriers. N a p c h a n extended the EBIC M o n t e Carlo
program of Joy (1986) so it applied to multilayer materials such as
heterostructures of epitaxial films grown on a substrate. It was shown that this
program could successfully simulate the beam voltage dependence of the
EBIC current collected by In/CdTe/Si heterojunction devices (Napchan and
Holt, 1987).
An interesting, ill-understood type of barrier is that responsible for the
anomalous photovoltaic effect in ZnS. This is the generation of u p to hundreds
of volts per cm perpendicular to the layers in striated ZnS platelet crystals.
This is believed to occur by the generation of voltages, each less than the
F i g . 6.42 (a) Measured values versus simulated curves of gain versus beam voltage
for the Schottky barrier heights corresponding to the two forms of epitaxial Ni Si/Si
contacts, (b) EBIC micrograph of such a contact showing contrast due to the two
heights of barrier in areas of the two forms. (After Gibson et al, 1987.)
2
296
D.B. Holt
forbidden gap value at all, or some of the numerous interfaces between the
different polytype regions in striated ZnS. These were early shown to exhibit
C C and C L contrast (Holt and Culpan, 1970). Subsequent studies indicated
that there occur high electric field regions corresponding to heavily faulted
regions of low C L emission intensity (Datta et al, 1977). Recent observations
(Holt et al, 1989) suggest the barriers behave somewhat like the asymmetric
grain boundaries in G a P (Ziegler et al, 1982) which were modelled with some
success as two Schottky barriers of unequal heights back-to-back.
6.3.8
P l a s m a effect contrast
Impurity growth striations and "swirl defects" are important forms of nonuniform distribution of point defects in as-grown crystals. They can be seen
under Schottky contacts in EBIC micrographs. Two forms of contrast were
found in such observations (Leamy, 1982). F o r R>w,
greater collection
(larger EBIC current) will be seen in regions of lower N , where N is the
doping concentration under the barrier. This is because w will be larger there
giving high efficiency collection over a larger fraction of the generation volume
(Leamy et al, 1976). In this case the contrast AI /I ccN .
When
R~w
striation contrast vanishes and for R < w it is reversed. That is, under the latter
condition, the greater charge collection efficiency and higher E B I C current
corresponds to regions of larger N (Leamy et al, 1976). This contrast arises
from the plasma regime effect (Section 6.1.6).
B
cc
cc
B
B
B
6.4
Theory of EBIC and C L defect contrast
This field is currently attracting great interest. These two techniques alone
have the spatial resolution to allow the electronic properties of individual
defects such as dislocations to be measured. Extensive studies of the electrical
effects of the plastic deformation of semiconductors were difficult to interpret
because they were due to large numbers of dislocations of all types (plus
probable point defect debris). T o obtain a fundamental understanding it is
more effective to study the electrical effects of single dislocations of wellcharacterized type, e.g. 60° or edge, dissociated and/or impurity decorated or
not. The results can be interpreted in terms of the atomic core structure, which
can now (just) be seen using atomic resolution transmission electron
microscopy, and electronic states calculated using fairly reliable q u a n t u m
mechanical models. Moreover, new materials, new process technologies and
more defect-sensitive devices continually draw attention to the influence of
defects on device performance.
The conductive mode
6.4.1
297
T h e p h e n o m e n o l o g i c a l theory of E B I C defect contrast
The first paper on EBIC (Lander et al, 1963) noted that dislocations appeared
as dark lines. This is attributed to enhanced recombination at dislocations and
other extended defects. Defects are, therefore, modelled phenomenologically
as reducing the minority carrier lifetime from the bulk value i to a smaller
value T' inside a volume F (Fig. 6.43).
The starting point for the theory is the calculation of the barrier electron
voltaic effect short-circuit current (EBIC) in perfect material, J , for example
under a thin Schottky barrier (Fig. 6.14). The first-order, linear theory of
D o n o l a t o (1978/79 and, for reviews: 1983a, 1985a) assumes that the carrier
density, p , is not significantly reduced in the volume F of reduced lifetime
round the defect. Then the net carrier generation rate can be written:
0
p
p
G(r) =
g(r)(V)-(l/T')p (r)(F)
(6.50)
p
where V is the total volume and the EBIC current can be written:
1=
\G(r)(t>(z)dV
= / -(l/r')
p
Pp
(r)0(z)dK = / - / *
p
(6.51)
where J is the current that would be collected in perfect material (cf.
eqn (6.22)) and J* is the reduction in EBIC current at the defect. The contrast
profile (Fig. 6.44) is defined to be
p
i* = J * / /
P
(6.52)
0
F i g . 6.43 Charge collection by a Schottky barrier in plan-view in a region
containing a defect of volume F. Compare Fig. 6.14. (After Donolato, 1985a.)
298
D.B.
a)
Holt
l(*o)
b)
-i (* )
#
0
c
2L
0
0
*0
F i g . 6.44 (a) EBIC line scan profile across a defect (eqn (6.51) and Fig. 6.43) and (b)
the defect recombination current reduction profile. (After Donolato, 1985a.)
while the (maximum) contrast as usually defined is given by
C = (/ -/ )//p= £
p
where J
D
D
(6.53)
a x
is the minimum EBIC current at the defect and
(6.54)
p (r)dK
J * = (1/T')
p
F
This first-order theory is applicable to defects of any form: point, line or
surface.
The predictions of this theory of EBIC defect contrast have been satisfyingly
confirmed. Donolato's (1978/79) model of recombination at a point defect was
extended by him to line defects (for a review see D o n o l a t o , 1983a) and was used
to generate computer simulations of series of EBIC images for increasing beam
voltages (Donolato and Klann, 1980). These were in good agreement with
experiment for dislocation half loops and tetrahedral stacking faults. Quantitative verification of predictions of the theory concerning resolution (the
width of dislocation images) was provided by T o t h (1981). EBIC contrast
studies are used for the determination of the electronic effects of single
dislocations and the separation of those due to the core structure and those
dominated by impurity decoration. The availability of this theory also
provided the basis for the treatment of C L dislocation contrast and of grain
boundary EBIC contrast. A later recombination physics model due to
Wilshaw and Booker (1985, 1987) can apparently account for the strong
temperature dependence of dislocation E B I C contrast and indicates the way
on beyond the phenomenological theory.
6.4.2
Linear dislocation E B I C contrast theory
Dislocations are represented by cylindrical volumes of cross section a along
the line <r = nr\. Where r is the radius of the cylindrical volume, F , a r o u n d the
d
d
d
299
The conductive mode
dislocation. Hence dV = o dl
and
A
/*
=
p (r) dl = y
(* A')
p
D
i
Pp(r)d/
P
(6.55)
where y — [ojx') (cm /s) is the strength or line recombination velocity of the
dislocation. It is the property of the individual dislocation that determines the
magnitude of contrast produced.
The concept of defect recombination strength was introduced by D o n o l a t o
(1978/79) for a point defect. This was extended by Kittler and Seifert (1981b) to
the point-like defect characterized by a reduced diffusion length L < L, the
value far from any defect in "perfect" material. The point-like defect consists of
an accumulation of statistically distributed, non-interacting recombination
centres. The dimension of the defect, r , was assumed to be small compared
with L or the distance of the defect from the charge collecting barrier. The
strength of such point-like defects is given by
2
d
(6.56)
y = l (l/L' -l/L )
3
2
2
where L ' = Dx'.
The dislocation can then be regarded as a row of point-like defects. U n d e r
the condition that the diameter of this dislocation pipe of reduced diffusion
length material is small compared to both the defect-barrier distance and to
the diffusion length, the dislocation strength can then be expressed in the form:
2
v =
nr (\/L -\/L )
2
f2
2
(6.57)
Kittler and Seifert assumed that (L'/L)
express the reduced lifetime in the form
« 1 and that it was possible to
2
T
' =(N <7 l> )~
R
r
1
th
where the subscript r indicates values for the deep recombination centres
assumed to be responsible for the EBIC contrast, and v is the thermal velocity
of the carriers. Thus they assumed it was possible to express the dislocation
strength in the form
ih
y
=
nrlN a vJD
t
= n a vJD
r
T
r
(6.58)
where n is the line density of recombination centres along the dislocation.
T
Evaluating
dislocation
strength
Kittler and Seifert (1981a, b) also noted that one of the relations obtained for a
D.B. Holt
300
p o i n t defect b y D o n o l a t o ( 1 9 7 8 / 7 9 ) c o u l d b e written
C = yf(R,L,
g e o m e t r y of the s p e c i m e n a n d defect)
(6.59)
w h e r e / is a "correction" factor e n a b l i n g t h e characteristic defect strength t o
be o b t a i n e d from t h e o b s e r v e d E B I C contrast. T h e y c o n c l u d e d that, as a
d i s l o c a t i o n c o u l d b e regarded as a r o w of p o i n t defects ( D o n o l a t o , 1978/79), a n
a n a l o g o u s relation w o u l d h o l d , n a m e l y
C = yF(R
9
L , g e o m e t r y of the s p e c i m e n a n d defect)
(6.60)
H e n c e v a l u e s of d i s l o c a t i o n strength c o u l d b e o b t a i n e d from E B I C m e a s u r e m e n t s u s i n g the g e o m e t r i c a l a n d S E M o p e r a t i n g p a r a m e t e r "correction"
factor F. T h e y o b t a i n e d a n e x p r e s s i o n for F for d i s l o c a t i o n s inclined t o a
surface S c h o t t k y barrier (Kittler a n d Seifert, 1981a) a n d c o m p u t e d curves of F
for d i s l o c a t i o n s p e r p e n d i c u l a r t o t h e barrier a n d at a c o n s t a n t d e p t h (Kittler
a n d Seifert, 1981b) b y integrating D o n o l a t o ' s p o i n t defect c o r r e c t i o n factor /
a l o n g the d i s l o c a t i o n line. P a s e m a n n et al (1982) o b t a i n e d a n e x p r e s s i o n for
the c o r r e c t i o n factor F for a d i s l o c a t i o n at a c o n s t a n t d e p t h , a n d lying a b o v e a
charge collecting p - n j u n c t i o n . D o n o l a t o a n d B i a n c o n i (1987) s h o w e d that y
c a n a l s o be o b t a i n e d from the area A o f the E B I C profile. T h e early studies
simply m e a s u r e d the E B I C contrast, w h i c h suffices for c o m p a r i s o n s of the
electrical effectiveness of defects in similar g e o m e t r i c a l situations.
Dislocation
resolution
Initially, it w a s feared that d u e t o t h e large m i n o r i t y carrier diffusion lengths in
the m o r e d e v e l o p e d s e m i c o n d u c t o r s the r e s o l u t i o n of d i s l o c a t i o n i m a g e s , i.e.
the w i d t h ( F W H M , full w i d t h at half m a x i m u m ) of profiles like that in Fig. 6.44
w o u l d b e large. It w a s t h o u g h t pessimistically it m i g h t b e = R + 2 o r 3 L. It
w a s f o u n d experimentally, h o w e v e r , t o b e =R i n d e p e n d e n t o f L ( D a r b y a n d
B o o k e r , 1977; D a v i d s o n , 1977; I o a n n o u a n d D a v i d s o n , 1978). D o n o l a t o
(1979a, b) c o m p u t e d the r e s o l u t i o n ( F W H M contrast) for d i s l o c a t i o n s n o r m a l
to a charge c o l l e c t i n g S c h o t t k y barrier a n d o b t a i n e d t h e results s h o w n in
Fig. 6.45. It c a n b e seen that t h e value o f w is never very different from R
w h a t e v e r t h e value o f L. T o t h (1981) m e a s u r e d t h e r e s o l u t i o n of a d i s l o c a t i o n
in this configuration a n d verified the predictions of the theory.
T h e physical r e a s o n s for t h e L - i n d e p e n d e n c e of the r e s o l u t i o n c a n be
u n d e r s t o o d a s follows. A s s u m i n g a p o i n t source of carriers a n d spherical
s y m m e t r y , the c o n t i n u i t y e q u a t i o n h a s the solution:
p = a e x p ( - r/L)/r
(6.61)
where a is a c o n s t a n t w i t h d i m e n s i o n s c m . D o n o l a t o (private c o m m u n i c a t i o n ) p o i n t e d o u t that the g e o m e t r i c a l factor 1/r (due t o t h e carriers diffusing
- 2
301
The conductive mode
E(keV)
25
30
35
40
w(Rp,L) (u>m)
5 10 15 20
Rp(lim)
F i g . 6.45 Calculated resolution (half width w) of the EBIC profile of a dislocation
running vertically down into a Schottky diode as a function of the beam range (energy)
for the values of diffusion length marked. (After Donolato, 1979a.)
out radially) largely explains the relative independence of L exhibited by the
E B I C resolution. The other contributing factor is that the generated carrier
density is not uniform throughout the volume but is concentrated toward its
carrier centre of gravity. O u t w a r d diffusion results in a m o r e uniform
distribution throughout the sphere of diameter R .
G
6.4.3
S e c o n d - o r d e r dislocation contrast theory
Pasemann (1981a,b) applied a perturbative approach to include higher-order
effects in the phenomenological theory. W h a t this does is lift the assumption
underlying eqn (6.50) that the minority carrier density in the defect volume
remains unaltered and equal to p (r). Experimental evidence of the predicted
second-order effects was found by Pasemann et al (1982) as will be seen below
and experimental EBIC contrast profiles of dislocations were found to be in
good agreement with the theory (Fig. 6.46).
p
EBIC dislocation
studies
T o relate the electronic properties of dislocations to type or core structure
both S E M EBIC and T E M or S T E M observations have to be made on the
302
D.B. Holt
(pm)
F i g . 6.46 Experimental (solid line) and theoretical (broken line) EBIC line scan
profiles recorded across a dislocation. (After Pasemann et al, 1982.)
same dislocations. Relatively few such studies have been published and none
as yet have used atomic resolution T E M .
O u r m a z d and Booker (1979) observed the recombination efficiency of
dislocations as indicated by EBIC contrast for dislocations at the same
distance from the charge collecting barrier. They found that it increased with
the percentage of the length of edge dislocations that was dissociated.
O u r m a z d et al (1981) used relative recombination efficiencies to compare the
electrical activity of the screw and 60° segments of hexagonal dislocation loops
in Si. Blumtritt et al. (1979) found evidence that the contrast was higher where
dislocations were impurity decorated.
Petroff et al. (1980) made EBIC, C L and S T E M observations on misfit
dislocation networks in epitaxial GaAlAsP. They found all the 60° dislocations to give both EBIC and C L contrast but the one sessile edge dislocation
exhibited neither.
Studies of dislocation EBIC
strength
The linear recombination velocity or strength of dislocations can be obtained
from the contrast (eqn (6.59)). This was first done by Kittler and Seifert (1981b)
who measured values of contrast of tens of per cent for shallow dislocations in
Si under Schottky barriers. This level of EBIC contrast led to strengths that
they suggested could not be explained in terms of recombination at dangling
bonds. The argument was that the expected small recombination cross
sections of such centres times the maximum conceivable density of dangling
303
The conductive mode
bonds (three per atom length along the dislocation) gives a strength
(eqn (6.57)) an order of magnitude lower than such experimental values.
Impurity decoration, however, because of the much larger capture cross
sections, required perhaps only a few hundred atoms per fim along the
dislocation to give such strengths. Moreover, annealing resulted in increases in
contrast and strength which were consistent with decoration. However, it is
now clear from the work of Wilshaw and Booker (Section 6.4.11) that the
minority carriers are attracted to a clean dislocation line by its electrostatic
field and that contrast of the order of 10% can be exhibited by the cleanest
dislocations available at present. However, the conclusion that the dislocations in device silicon are decorated, due to the heat treatment in the presence
of doping, and that this dominates their properties, is in agreement with much
other evidence (Holt, 1979).
Second-order
contrast theory and dislocation
strengths
Pasemann's (1981a, b) higher-order contrast theory was applied by Pasemann
et al. (1982) to experimental observations on dislocations lying parallel to and
above a shallow p - n junction in Si. They applied the second-order correction
5 <
Ol
I
I
I
I
0.5
0.4
0.3
0.2
0.1
h-z
0
I
0
(/im )
F i g . 6.47 Dependence of the line recombination velocity on the height of the
dislocation above the p - n junction. The data are taken from Pasemann et al. (1982)
replotted by Donolato (1983). The filled, black points are the first-order, effective
strength values and the open circles are the values with the second-order corrections on
the theory of Pasemann (1981).
D.B. Holt
304
to the "effective" (Donolato) strength values obtained from the observed
contrast values by applying eqn (6.59). Recombination at the defect reduces
the minority carrier density locally. Hence the first-order (Donolato) theory
which neglects this, leads to a value of y that is too large. The reduction from y
to y*~(effective and "real", i.e. second-order corrected strengths in the
Pasemann et al. notation) is largest for large values of y since then the effect of
the defect is largest. Pasemann's treatment also showed that the correction is
greatest when the defect is closest to the charge collection barrier, i.e. for small
values of h — z . Both these predictions can be seen to be borne out in Fig. 6.47.
When the second-order correction was applied, the line recombination
velocities of the 14 dislocations all fell within a few per cent of one of the values:
0.29 (60° dislocations, assumed to be constricted on the basis of the work of
O u r m a z d et a/., 1981), 0.68 (60° dislocations assumed to be dissociated)
(Fig. 6.47) and 0.02 (a screw dislocation). The dislocation types and depths
were determined by T E M . The results of Pasemann et al. showed the secondorder correction to be significant only for the dissociated 60° dislocations and
then only when less than about 2.5 /mi from the charge collecting junction.
However, without the correction, the effective strength values, y, for 60°
dislocations were scattered from 0.25 to 0.725 so no distinction between the
electrical activity of the two types would have been possible.
0
The second-order theory also predicted values of resolution (image line half
width) and EBIC profiles in good agreement with experiment (Fig. 6.46).
Monte Carlo simulations and studies of dislocation EBIC
contrast
T o determine the recombination strength from the EBIC contrast profile
requires an accurate knowledge of specimen parameters like Schottky barrier
thickness or p - n junction depth, materials properties like the surface
recombination velocity and the minority carrier diffusion length as well as
parameters that vary with the SEM operating conditions like the backscattered electron energy loss. It was seen above that S and L can be obtained
from EBIC measurements in favourable cases quite conveniently using EBIC
Monte Carlo simulations. This is possible in either the case that the beam is
incident normal to the charge collecting barrier (e.g. Pasemann et al.) or
parallel to it (Donolato, 1982). Such determinations were laborious prior to
the use of M o n t e Carlo microcomputer simulations and they have not been
widely made.
Similarly, backscattering loss values were taken from the (elderly and
limited) literature. Again M o n t e Carlo simulation provides a means for
rapidly obtaining values appropriate to the specimen geometry and SEM
beam voltage to be used. The method can also be applied to complex epitaxial
multilayer materials for which no literature values exist and no analytical
The conductive mode
305
depth-dose functions are available for use in E B I C calculations (Napchan and
Holt, 1987).
6.4.4
P l a s m a effects on d i s l o c a t i o n E B I C contrast
Toth (1987) carried out a systematic test of plasma effects on dislocation EBIC
contrast in Si specimens under Al Schottky barriers. The dislocations were
perpendicular to the surface and the bias voltage was varied from — 10 to
+ 1 V to alter the charge collection field and hence the value of T and the
contrast measured with the results shown in Fig. 6.48. The bias voltage for the
peak in the contrast varied with the beam current as
p
F L x = 0.7 + 0 . 1 6 /
(6.62)
b
as shown in Fig. 6.48b. Toth suggested that the contrast maximum might be
due to enhanced recombination inside an electron-hole plasma which was
shielded from the collecting field by polarization at the edges. T o test this he
measured the plasma loss (PLL) defined as
PLL = ( /
D F
-/ )/J
F
(6.63)
D | r
where D F and F designate the values of the charge collection (EBIC) signal for
defocused and focused conditions respectively. The results are shown in
Fig. 6.49a. The plasma loss contribution varied with bias voltage as shown in
Fig. 6.49b, occurring under these conditions only for charge collection field
(a)
(b)
F i g . 6.48 (a) Typical contrast versus bias voltage curve and (b) the beam current
dependence of J£ . (After Toth, 1987.)
ax
D.B. Holt
306
( a )
(c )
( b )
F i g . 6.49 (a) The definition of PLL, (b) the PLL versus bias voltage curve and (c) the
beam current dependence of
(After Toth, 1988.)
values corresponding to bias voltages between V and V . The bias voltages
varied with beam current as shown in Fig. 6.49c, the voltage for maximum
plasma loss varying as
x
F ^ = 0.07 + 0 . 1 6 /
h
(6.64)
b
in remarkable agreement with the form of eqn (6.62). The dependence of the
V mk versus I relation on beam voltage is shown in Fig. 6.49c.
?
h
6.4.5
Grain b o u n d a r y E B I C contrast
Grain boundaries are of practical interest because they reduce the efficiency of
polycrystalline solar cells for possible use in terrestrial power generation.
D o n o l a t o (1983b, 1985a) applied the general approach of eqns (6.51) and
(6.54) to the treatment of EBIC grain boundary contrast as follows. Suppose
that the grain boundary is planar and perpendicular to the surface, and that
there is a p - n junction parallel to the surface at a small depth (Fig. 6.50) as
in polycrystalline Si solar cells. The boundary was modelled by Donolato
as a layer of thickness h within which the lifetime is reduced to a value T'.
Then dV = h da, where da is an element of area on the boundary. Substituting
into eqns (6.51) and (6.52) gives the EBIC image contrast profile as
1
5
p (r )(t)(z )da
7
0
0
(6.65)
0
where
(6.66)
v = h/r'
s
and Z indicates integration over the grain boundary surface. v is the
s
The conductive mode
307
light or
electron beam
p-n junction
grain
boundary
Fig. 6.50 Geometry of EBIC observations of grain boundaries running vertically
through Si solar cells with shallow p - n junctions. (After Donolato, 1985.)
recombination strength of the boundary. It has the dimensions (cm s~ *) and is
referred to as the interface recombination velocity by analogy with the wellknown surface recombination velocity.
F o r a boundary perpendicular to the surface D o n o l a t o also gave an exact
treatment by solving the continuity equation with appropriate boundary
conditions. This can describe the effect of strong, high-contrast defects for
which the first-order theory may be inadequate. Application of the theory to
experimental observations by D o n o l a t o (1983b, 1985a) indicated that the firstorder treatment sufficed for boundaries in silicon.
The grain boundary is characterized by measuring the area, A, and variance,
cr , of the EBIC contrast profile:
2
A=
and
i*(x )dx
0
J - OO
1 f
0
00
xli*(x )dx
0
0
(6.67)
F o r the convenience of experimentalists, D o n o l a t o developed an elegant
method resulting in a rectilinear plot of A/R versus a/R (where R is the
electron range for the beam voltage used) and a superimposed curvilinear
plot of L/R versus sL (Fig. 6.51). By measuring A and a from an experimental
line profile, the point representing the boundary can be found using the
rectilinear coordinates and the values of L/R and sL read off the curvilinear
scales. Since R is known, first L and then s can be obtained. Applying this
treatment to experimental curves for grain boundaries in Si solar cells,
D o n o l a t o showed that even when the profile is asymmetric the same value
F i g . 6.51 Diagram for obtaining values of L and S for grain boundaries from
measurements of A and o. (After Donolato, 1985.)
F i g . 6.52 Grain boundaries in GaP: (a) EBIC micrograph showing complex
contrast and (b) line scan across such a grain bounday. (After Ziegler et al, 1982.)
The conductive mode
309
of s is obtained from both sides of the grain boundary while the values of L
on either side differ - which makes sense physically. H e also found that grain
boundary passivation treatments (to improve solar cell efficiency) reduced
the value of s and hence the contrast until the grain boundaries were finally
EBIC invisible. Other treatments of EBIC grain boundary contrast were
published by Marek (1982) and Romanowski and Buczkowski (1985).
Both bright and dark EBIC grain boundary contrast can be seen in
polycrystalline c o m p o u n d semiconductors, e.g. ZnS (Russell et a/., 1980,1981)
and G a P (Ziegler et al, 1982). Bright contrast shows that the boundaries act
as charge collection barriers. Ziegler et al. particularly noted the asymmetry
of many of the images that were dark one side and bright the other (Fig. 6.52).
They interpreted their results in terms of a model of the boundary as a pair
of Schottky barriers of different heights back-to-back. N o quantitative model
is presently available for the evaluation of the heights of the two barriers,
but the model accounted qualitatively for the changes of contrast with bias
voltage. Thus there is ample scope for the use of EBIC to measure electronic
properties of individual planar defects in a variety of materials.
6.4.6
E B I C contrast of precipitates a n d s t a c k i n g faults
Small precipitates generally give point defect recombination (dark) contrast in
accordance with the original D o n o l a t o (1978/79) treatment. The variation of
the contrast with beam voltage can be used to distinguish such
a small precipitate below a Schottky barrier from a dislocation normal to the
surface (Sieber and Farvacque, 1987).
Jakubowicz and Habermeier (1985), however, observed both dark and
bright EBIC contrast due to oxygen-related defects in Czochralski silicon.
Bright contrast is an increase in the current above the perfect crystal value for
which they considered two possible explanations: (i) a locally enhanced electric
field leading to impact-ionization multiplication of carriers, i.e. a microplasma
effect and (ii) a recombination velocity less than unity due either to a carrier
reflecting interface state charge or to a recombination centre-denuded zone
round the precipitate. Heat treatment of oxygen-rich silicon is known to
produce precipitates, dislocation loops and stacking faults. These, if small,
cannot be resolved by EBIC and the two forms of contrast may arise from
different defects.
Stacking faults threading silicon p - n junctions were studied by Ravi et al.
(1973) who were able to resolve the two ends of the partial dislocation half
loops at the top surface. They showed that the electrical effects of the defects
were essentially due to precipitates decorating the bounding dislocation. The
maximum effect occurred when the bottom of the loop passed along the p - n
310
D.B. Holt
F i g . 6.53 Charge collection micrographs recorded at (a) 278 K and (b) 82 K of a
circular stacking fault bounded by a dislocation loop and surrounding a central
precipitate. (After Kimerling et al, 1977.)
junction depletion region. D o n o l a t o and Klann (1980) successfully simulated
stacking fault EBIC images using the D o n o l a t o theory. The images essentially
showed the bounding partials.
Kimerling et al. (1977) presented charge collection micrographs of a circular
stacking fault centred on a precipitate in heat-treated oxygenated silicon. They
found that at 278 K only the bounding dislocation was in contrast but at 82 K
the entire fault area was in contrast (Fig. 6.53).
6.4.7
D i s l o c a t i o n C L contrast
Esquivel et al. (1973) in GaAs and Davidson et al. (1975) in G a P found that
dislocations, introduced by plastic deformation so as not to be heavily
The conductive mode
311
decorated by impurity atoms, appeared as dark lines in panchromatic and
bandgap C L S E M micrographs. Dislocations can also produce bright
contrast in C L micrographs at longer wavelengths (lower p h o t o n emission
energies). In diamond some dislocations emit yellow-green and others blue C L
(Hanley et al, 1977).
Dislocation C L spectra have been reported for diamond (Yamamoto et al,
1984), ZnSe (Myhajlenko et al, 1984) and GaAs (Bailey, 1988). Dislocation CL
spectra obviously provide information on the radiative recombination
properties of centres associated with the dislocations.
The first dislocation C L phenomenon to be analysed was dot-and-halo
contrast in Te-doped GaAs (Kyser and Wittry, 1964; Casey, 1967). The effect
was shown to be due to Te decoration of the dislocations. The evidence is,
firstly, that the effect is seen in Te-doped GaAs but not in Se- or Si-doped
material. The elastic interaction resulting in Cottrell impurity atmosphere
formation depends on the impurity misfit in the sites occupied. The atomic size
misfit for Te is 12% whereas it is only 3 and 7% for Se and Si respectively (Shaw
and Thornton, 1968). Secondly, the observation of a bright region ("halo")
surrounding a dark dot in the case of a dislocation viewed end-on, is only one
of a number of forms of contrast that can occur. These can all be explained by
impurity segregation to the dislocation line and the formation of an impuritydenuded zone around it, together with the variation of C L intensity with
doping concentration (Shaw and Thornton, 1968; Holt and Chase, 1973).
This is further evidence that dislocation properties are often impurity
decoration-dependent. Whether it is possible to avoid these effects entirely to
study the intrinsic atomic bonding core structure properties is not yet certain.
However, dislocation C L spectroscopy is clearly a powerful method for the
study of the recombination centres in and near the core.
Evidence that C L contrast may not always be (completely) dominated by
impurity decoration is the observation of differences in contrast with
dislocation type. Petroff et al (1980) observed that in misfit dislocation
networks in epitaxial GaAlAsP the 60° dislocations gave C L contrast but a
sessile edge dislocation did not. Yamaguchi et al (1981) used spatially resolved
P L (photoluminescence) microscopy to show that of the two orthogonal sets
of <110>-aligned misfit dislocations in a (100) I n G a A s P interface, one gave
much stronger P L contrast than the other. The dislocations of the two sets
differ in polar symmetry (Holt and Saba, 1985).
6.4.8
P h e n o m e n o l o g i c a l theory of dislocation dark C L contrast
The D o n o l a t o theory was extended to cover dark C L contrast in integral or
bandgap C L micrographs by Lohnert and Kubalek (1984). Pasemann and
312
D.B. Holt
Hergert (1986) and Jakubowicz (1986) independently realized that the CL
contrast depends on the self-absorption of the C L which has no analogue in
EBIC contrast and showed that the ratio of the two types of contrast depends
on the defect depth (see, for example, eqn (8.18) of Chapter 8 on CL).
The result of the theory can be plotted as shown, for example, in Fig. 6.54
and the experimental results are in agreement (Jakubowicz et al, 1987).
<«©>
SUBSTRATE
(a)
6 0 r
?
contrast
[%]
5.4 -
distance
[tim]
F i g . 6.54 (a) Geometry of a comparison of the EBIC and CL contrast of a
dislocation: the distance scanned along the surface corresponds to an increase in the
depth of the dislocation lying along <110>. (b) The predicted (broken curve) and
experimental (solid curve) variations of EBIC and CL contrast for the specimen shown
in (a). (After Jakubowicz et al, 1987.)
The conductive mode
313
The experimental "tails" to the left of the contrast peaks are due to carriers
diffusing to recombine at the point of emergence of the dislocation at the
surface. This gives a reduction of EBIC current, i.e. a rise of contrast, before the
dislocation is reached.
D a r k C L defect (percentage) contrast is defined analogously to EBIC
contrast, i.e. as
C=100[(L -L )/L ]
B
D
B
(6.68)
where L is the C L intensity and the subscripts identify the values in the bulk
(B), i.e. in good crystal, and at the dislocation (D).
The basic assumption of the phenomenological theory is that the minority
carrier lifetime is reduced in the vicinity of the dislocation. This was previously
tested experimentally by Rasul and Davidson (1977). They expressed the
contrast in terms of the radiative and non-radiative recombination times for
minority carriers:
C = 100 [(T - T ' ) / T ]
(6.69)
where T and T' are the lifetimes in the bulk and in the vicinity of the dislocation
and T can be written:
1/T=l/T„+1/T
R
(6.70)
where i and i are the non-radiative and radiative recombination times
respectively.
Rasul and Davidson measured the C L contrast of dislocations in G a P to be
38%. They also measured the lifetimes to be T = 156 ns and i ' = 96ns.
Substitution into eqn (6.69) yielded C = 12%, in reasonable agreement for this
simple approach which neglects, for example, surface recombination. (For
further discussion see Holt and Datta, 1980.) Similar measurements were made
by Chu et al. (1981) and Hastenrath and Kubalek (1982). The latter authors
explicitly determined the surface recombination velocity from measurements
of the C L decay time as function of the beam energy (range).
The determination of C L decay times, i.e. lifetimes, is known as timeresolved CL. It can produce spatially resolved lifetime maps or profiles.
Hastenrath and Kubalek (1982) measured a minority carrier lifetime profile
across a dislocation in Se-doped GaAs and found a decrease in both the
lifetime and C L intensity at the dislocation, as expected. Steckenborn et al.
(1981a, b) carried out similar measurements on Se-doped GaAs and observed
an increase in lifetime at the dislocation but a decrease in C L intensity at a
temperature of 50 K. Balk et al. (1976) had found that the contrast at such a
dislocation inverted from bright to dark with increasing beam current,
suggesting that temperature may be responsible for the discrepancy.
n r
r
314
6.4.9
D.B. Holt
Bright dislocation CL contrast
Bright dislocation contrast can be observed in some materials in micrographs
recorded at longer wavelengths due to radiative recombination at the
dislocation. In natural diamonds some dislocations emit yellow-green luminescence and others blue C L (Fig. 6.55) (Hanley et al, 1971; Y a m o m o t o et al,
1984). Clearly, point defect decoration of two different types is responsible for
these emission bands since the b a n d g a p in diamond is 5.4 eV corresponding to
ultraviolet emission. Berger and Brown (1984) found that almost all the visible
C L from semiconducting type l i b diamonds came from dislocations whereas
none of the visible C L from type Ha diamonds came from dislocations. Blue
The conductive mode
315
F i g . 6.55 CL micrographs (flood electron bombardment and direct photographic
recording) of dislocations in a diamond emitting (a) in the yellow-green, (b) in the blue,
and (c) as in (b) but with a (polarized light) analyser turned to attenuate the horizontal E
vector and hence the contrast of the horizontal dislocation images. (After Hanley et a/.,
1977.)
dislocation C L in diamonds is polarized along the dislocation line (Kiflawi
and Lang, 1974; Y a m a m o t o et al, 1984) (Fig. 6.55).
C L micrographs that showed misfit dislocations in G a A s - A l ^ G a ! _ A s
interfaces in bright contrast were recorded by Bailey (1988). Again the C L
emission bands involved were believed to arise from impurity centres.
C L emission spectra were recorded for ZnSe at and away from dislocation
lines (Fig. 6.56) although bright dislocation contrast micrographs were not
x
F i g . 6.56 (A) TEM micrograph of a typical dislocation tangle in Al-doped ZnSe and
(B) spectra recorded at 30 K with the probe (a) away from the tangle and (b) and (c) on
the tangle. (Batstone and Steeds, 1985.)
317
The conductive mode
recorded. Here, too, at least one of the dislocation C L bands was apparently
impurity related. T o provide the necessary spatial resolution, T E M and
S T E M C L of thinned specimens are the preferred techniques for this field.
The first direct experimental test of the phenomenological model of C L
dislocation contrast is that of Bailey (1988). H e compared calculated
dislocation C L contrast profiles with experimental data for both the dark and
bright contrast of misfit dislocations in G a A s - A ^ G a ^ ^ A s interfaces and
found reasonable agreement.
6.4.10
T h e temperature d e p e n d e n c e of d i s l o c a t i o n E B I C contrast: the
limits of the p h e n o m e n o l o g i c a l m o d e l
EBIC contrast is temperature-dependent. It decreases strongly with temperature for device dislocations, thought to be impurity decorated (Ourmazd and
Booker, 1979; Lesniak and Holt, 1985) but increases with temperature in the
case of clean dislocations (Ourmazd et al, 1983).
The form of the temperature dependence of clean dislocations was analysed
by O u r m a z d et al. (1983) as follows. F r o m eqn (6.60), i.e. C = yF it can be seen
that by measuring the contrast normalized to room temperature, the difficultto-determine factor F can be eliminated:
C (T) = C/C
n
(6.71)
= y/y
RT
RT
Their experimental results, however, showed that this did not eliminate the
differences between individual dislocations (Fig. 6.57), i.e. the dislocations
differed in more than their geometrical situations relative to the charge
collecting barrier. The temperature dependence of the E B I C contrast had the
form
dC/dT
= aC
RT
(6.72)
+p
where a and /? are constants, as shown by the data for eight dislocations plotted
in Fig. 6.58. The broken line marked "Theory" in the figure was obtained from
the phenomenological theory on the implicit assumption that the dislocation
strength has the form
y(N ,T)
(6.73)
= N <t>(T)
d
d
i.e. that the recombination centre line density is temperature-independent, as
D o n o l a t o (1986c) pointed out. However, if it is assumed to have the form
y(N , T) = y(N , T ) [ l + e(N )(T
d
d
0
d
- T )]
R T
(6.74)
the empirical relation (6.72) is in agreement with the phenomenological theory
(Donolato, 1986c). Thus the observations of O u r m a z d et al. can be held to
N o r m a l i s e d EBIC Contrast
Temperature
(°K)
Fig. 6.57 Plots of the EBIC contrast normalized to the room temperature value for
two dislocations (square and cross points) (After Ourmazd et al, 1983.)
Fig . 6 . 5 8 Plot of the rate of change of EBIC contrast with temperature versus room
temperature contrast for eight different dislocations (After Ourmazd et al, 1983.)
The conductive mode
319
imply a particular form of linear variation of dislocation recombination
strength with temperature.
O u r m a z d et al (1983), Pasemann (1984a) and Jakubowicz (1985) gave
alternative interpretations of the implications of the observations of Figs 6.57
and 6.58 for the phenomenological theory.
O n the interpretation of D o n o l a t o (1986c), the fact that the temperature
dependence of the E B I C contrast of clean and impurity decorated dislocations
is of opposite sign (Ourmazd and Booker, 1979 and Lesniak and Holt, 1985
versus Wilshaw and Booker, 1985 and 1987) means that the function s(N ) in
eqn (6.74) is of opposite sign in the two cases.
The fact that an empirical temperature dependence of the dislocation
strength has to be introduced to bring the observations into line with the
theory suggests the necessity to move on to a physical theory of defect EBIC
contrast.
d
6.4.11
P h y s i c a l d i s l o c a t i o n contrast theory
We have seen above that the phenomenological theory of dislocation EBIC
contrast is well developed and in good agreement with experiment. Beyond the
phenomenological theory of dislocation EBIC contrast, the physics of
recombination at dislocations must be treated to deduce the temperature and
injection level dependence of dislocation EBIC contrast. It will be seen below
that the application of such a theory to experimental data can elucidate the
electronic energy states associated with the core.
Wilshaw and Booker (1985,1987) treated EBIC contrast on the basis of the
Read (1954,1955a and b) model and the work on dislocation recombination of
Figielski (1978).
The Read model
Shockley (1953) suggested that there would be "dangling bonds", in the core of
dislocations, thought of as having core structures like the undissociated shuffle
set 60° dislocation of Fig. 6.59. The dangling bond states should be intermediate in energy between the bonding states which correspond to the valence
band and the covalent antibonding states corresponding to the conduction
band (Fig. 6.60a). Such deep states are thought to be responsible for the
electrical effects of clean dislocations.
Early experimental work showed that dislocations had relatively large
effects on the conductivity of n-type G e but relatively small effects in p-type
Ge. Read (1954) therefore assumed that dangling bond states deep in the
forbidden gap act as acceptors, able to take u p a second electron. Thus, in
F i g . 6.59 The unit 60° shuffle set dislocation in the diamond structure, a, the
dislocation line direction and b, the Burgers vector differ by 60°. (After Hornstra, 1958.)
F i g . 6.60 (a) The acceptor action of dislocation deep states of energy E results on
the Read (1954, 1955a, b) model in (b) a negative line charge and screening positive
space charge cylinder which results in (c) local band bending and a potential ij/ that
repels electrons and attracts holes (Figielski, 1978; Wilshaw and Booker, 1985, 1987).
d
321
The conductive mode
Read's model, dislocations in n-type G e have a negative charge, Q, per unit
length which is screened by an equal positive space charge in a surrounding
volume of radius r (Fig. 6.60b). The spacing of dangling bonds along the
dislocation of Fig. 6.59 is the spacing of neighbouring atoms in a <110>
direction which is equal to b, the Burgers vector. The line charge is the number
of dangling bonds per unit length times the occupation function, / ' (fraction
occupied by a second electron). Hence, for unit length of 60° dislocation we can
write:
Q = nr qN
= qf/b = qf'N
(6.75)
d
2
D
d
where N is the d o n o r density and N is the number of acceptor states per unit
length of the dislocation (=l/b
for the original Shockley model). The
occupation fraction, / ' , is given by F e r m i - D i r a c statistics modified by the
electrostatic repulsion between the accepted electrons and configurational
entropy (Read, 1955a).
D
d
Recombination
at
dislocations
The dislocation line charge of the Read theory is a dynamic equilibrium
quantity. The dislocation energy levels act as generation/recombination
centres and both electrons and holes are captured and emitted. The effect of
dislocations on photoconductivity was studied extensively by Polish workers
and treated by an extension of the Read model. (See the review by Figielski,
1978). The additional recombination via dislocation states is the same as that
which produces dark EBIC dislocation contrast.
At dislocations in n-type material there will be a flux of electrons trapped
and another of electrons activated back into the conduction band and a flux of
holes captured to recombine with electrons via the dislocation centres.
The net rate of electron capture per unit volume and time can be written
(Wilshaw and Booker, 1987):
Je = C e JV d [(l - / > 0 e x p ( - # / / c T ) -
/W exp(-# /*r)]
(6.76)
0
c
where C is the probability of an electron transition between the dislocation
energy level and the conduction band, / ' is the dislocation state occupancy
factor, N is the density of states in the conduction band and ij/ and \j/ are the
potential barriers against electrons entering the dislocation states from the
conduction band and vice versa, respectively (Fig. 6.60).
Treating the dislocation as a cylinder of radius r in which the minority
carrier lifetime is reduced from T to T', the rate of hole capture per unit
dislocation length is:
e
c
0
d
J = nr Ap/T
2
h
d
where Ap is the beam-induced excess density of minority carriers.
(6.77)
D.B. Holt
322
In equilibrium, J = J , the electrons recombining with the holes via the
dislocation centres.
e
h
The Wilshaw and Booker
model
This, too, assumes the dislocation to be a charged line subject to recombination fluxes of carriers. The dislocation EBIC strength y can then be written:
(This holds for i ' « T, see eqn (6.57).) Wilshaw a n d Booker also assume for
simplicity that
<A = AQ
(6.79)
where A is a constant.
F r o m eqn (6.76)
— qi/j/kT
(6.80)
= In
where n is the equilibrium electron density in the absence of dislocations.
But in eauilibrium. 7 = J and, substituting from eqn (6.78), vields:
0
u
(6.81)
From eqns (6.75), (6.78) a n d (6.79):
y = M{An qD T')
0
h
(6.82)
Substituting (6.81) into (6.82) gives:
(6.83)
Wilshaw and Booker (1987) assumed that holes which are captured into
bound hole states are not re-emitted so the reduced minority carrier lifetime
depends on the cascade capture of holes into the potential well of the
dislocation. They quote a theoretical treatment by Sokolova (1970) leading to
the conclusion that T' varies as T . They state that experimentally it is found
that D varies as T
so r D should be virtually independent of temperature.
Then eqn (6.83) can be written:
1 5
-
h
1 4
h
(6.84)
323
The conductive mode
where, from eqn (6.78):
j =j
h
= ApyD
h
= the recombination flux
(6.85)
and
(6.86)
R = C N f'N exv(-qils /kT)
e
d
c
0
is the rate of electron (re)emission from the dislocation.
Equations (6.83) and (6.84) express the EBIC contrast strength in terms of
fundamental dislocation parameters, \jj = E — E , N the line density of
recombination states and C the probability of transitions from E to E and
vice versa plus fundamental materials parameters like N the conductionband density of states. As rD is nearly independent of temperature,
eqns (6.75) and (6.78) mean that y is approximately proportional to Q, the
dislocation line charge.
c
d
d
e
c
d
c
h
Temperature
dependence of dislocation EBIC
contrast
Donolato's phenomenological treatment led to the conclusion (eqn (6.60)) that
the measured EBIC contrast is proportional to the dislocation strength. Hence
(6.87)
where F is a constant equal to the value of the correction factor, depending on
microscope operating and specimen geometrical parameters, in eqn (6.60).
(6.88)
Therefore
(6.89)
where G, the generation factor, is the number of hole-electron pairs generated
per incident beam electron and / is the length of the dislocation. It is implicitly
assumed here, for simplicity, that all the carriers are collected. If this is not so,
the expression should be multiplied by the charge collection efficiency, n , the
fraction of the pairs collected by the barrier, e.g. the surface Schottky barrier of
Fig. 6.43.
The behaviour of the EBIC contrast expression (6.87) depends on the
relative magnitudes of J and R. F o r large beam currents (and hence large
excess minority carrier densities Ap), or a small number of states in the gap, JV ,
or for levels deep within the gap (large ^ ) , J » R. Then (6.87) reduces to
cc
d
0
(6.90)
324
D . B . Holt
and the contrast is dependent on the beam current (since Ap oc I ) and the
charge on the dislocation is increased above its equilibrium value (since J, the
capture rate, »R, the re-emission rate). F o r constant beam current, C
is approximately proportional to T while, at constant temperature, C is
approximately proportional to In (7 ). These predictions were found to be in
agreement with experimental results for clean dislocations in Si at low
temperatures and high beam currents by Wilshaw and Booker (1987)
(Figs 6.61 and 6.62).
At relatively high temperatures and small beam currents R > J and
eqn (6.87) takes the form:
h
b
(6.91)
and the contrast is independent of the beam current as confirmed by the low
current region of Fig. 6.62. In this case the charge on the dislocation is near the
equilibrium value and the variation of the contrast with T depends on the line
density of dislocation recombination states. (1) If N is large the defect states
will be pinned at the Fermi level. As T rises, the Fermi level moves toward the
mid-gap position so the charge and hence the contrast (from eqns (6.60), (6.79)
and (6.83) C ocy oc ij/ = AQ) of the dislocation falls. (2) If N is small, all the
states may be occupied without the excess line charge and consequent band
bending being sufficient to raise the states to the Fermi level. Then for small I
and high T, the dislocation line charge and hence contrast (since, as before,
d
d
b
( %llSV«lNO0
4J
100
,
,
200
300
,
400
F i g . 6 . 6 1 EBIC contrast versus temperature for a screw dislocation in silicon. (After
Wilshaw and Booker, 1987.)
EBIC CONTRAST (%)
F i g . 6.62 EBIC contrast versus ln(/ ) for a screw dislocation in silicon. (After
Wilshaw and Booker, 1987.)
b
N large
EBIC CONTRAST
d
(5)-»
TEMPERATURE
F i g . 6.63 Schematic dependence of dislocation EBIC contrast on beam current and
temperature. Regime (1): Q is largely determined by the recombination flux, f < 1.
Regime (2): For large N Q is determined by both the recombination flux and the
Fermi level, f < 1. Regime (3): For small N all the dislocation states are occupied
without producing sufficient band bending to raise these states to E . Q is determined by N alone, f ~ 1. Regime (4): The Fermi level is deep in the gap and Q is
determined largely by it, / < 1. Regime (5). For high T or small \p , E lies below
the dislocation states so 2 ^ 0 . Some residual recombination occurs via the
uncharged recombination states, f ^0. (After Wilshaw and Booker, 1987.)
d
d
F
d
0
F
326
D.B. Holt
C = AQ) are independent of both as shown by the high-temperature portion of
Fig. 6.61. These patterns of the dependence of contrast on beam current and
temperature are represented schematically in Fig. 6.63.
Wilshaw and Booker did not use in their computations the assumption that
ijj = AQ (eqn (6.79)) but Read's expression for the electrostatic potential due to
the dislocation line charge:
<A = (Q/2nee )i{In
0
Fundamental
- 0.616}
LQ/(nn ) ql
ll3
0
dislocation parameters obtained from
(6.92)
EBIC'contrast
Wilshaw and Booker made measurements on high-purity, float-zone-grown
n-type ( 1 0 c m ~ ) Si deformed under clean conditions in two-stage compression at 850 °C (to generate dislocations initially) and 420 °C to multiply
and move dislocations without point defect diffusion. This procedure,
developed by Professor H. Alexander and his co-workers, produces the
cleanest dislocation cores currently attainable. The specimens contain large
loops of crystallographically aligned dislocations of the type reported by
Wessel and Alexander (1977).
The results of some of the measurements of EBIC contrast are shown in
Figs 6.61 and 6.62. In Fitting the theory above to the C versus In (I ) data at a
given T only four parameters are unknown: F, a geometric scaling factor, C ,
N and i ^ . F r o m the straight-line regions of the curve, for which J » R (see
eqn (6.90) and the discussion thereof) values of F and the product C iV are
obtained. In attempting to fit the theory with these values to the curved
portions of the data it became clear that this could be done for all T only by
using a small value for N .
In this way all three parameters can be evaluated separately. The result
Wilshaw and Booker obtained was N (the number of dislocation states per
unit length) = 1.6 x 1 0 c m " for both the screw and 60° dislocations
investigated. They found that the EBIC contrast was not strongly dependent
on i// (the energy depth of the states below the conduction-band edge) which
could not, therefore, be evaluated. However, from the data the charge on the
dislocation per unit length was Q = 2.6 x 1 0 " C c m ~ \ Hence the band
bending can be calculated from eqn (6.85). Since the dislocation has a negative
charge the defect states must lie below the Fermi level, which can be calculated
for 1 0 material at 350 °C. This leads to the conclusion that the defect level for
both screw and 60° dislocations is at a depth ^ 0.55 eV below the conductionband edge. (The bandgap in Si is ~ 1.1 eV so this is the approximate mid-gap
position.) This is in agreement with the D L T S results of various groups on
bulk deformed material. However, the state line density is much lower than
even recent theories suggest.
1 5
3
b
e
0
d
e
d
d
6
1
0
1 3
1 5
d
The conductive mode
6.5
327
^-Conductivity
In regions where the net doping concentration varies, the position of the Fermi
level in the forbidden gap will vary (Fig. 6.7). Electron b o m b a r d m e n t of the
resulting electric field regions will generate a bulk electron voltaic effect opencircuit voltage (Fig. 6.8) by two mechanisms:
V =V
0C
c
+ V
d
(6.93)
where V is the "chemical" contribution due to the charge collection effect and
V is the Dember potential. The latter arises because the electron and hole
mobilities are generally different so charge carriers of one sign diffuse farther
than the other. This does not occur with lateral symmetry a r o u n d the beam
impact point due to the non-uniform doping. The resultant asymmetric
separation of charges of opposite sign produces the Dember potential
difference. This method can be used to observe changes in doping concentrations as M u n a k a t a (1965) showed for n-type Ge. However, he found the
induced voltage was so small that he applied a constant current bias to
improve the signal and termed the modified technique /J-conductivity (betaray induced conductivity). The p h e n o m e n o n involved is analogous to
photoconductivity.
c
d
The constant-current-bias form of ^-conductivity was analysed by M u n a kata (1968a, b, 1972). H e showed that the voltage signal for n-type material in
the experimental arrangement of Fig. 6.64 can be written in the
form:
V= I R,
S
+ AaAxp J
2
+ ArjAx——^— ^
q b + 1 dx
(6.94)
where Rt is the resistance to earth from the point of impact of the beam, ACT is
the change in conductivity due to the extra electrons and holes in the
generation volume assumed to have a length Ax along the scan line, p is the
local resistivity, J is the biasing current density and b is the ratio of electron-tohole mobilities. The first term above is the ohmic d r o p due to the specimen
(absorbed electron) current flowing to earth. The second is the /^-conductive
contribution and the third is that due to the bulk electron voltaic
effect.
The attraction of the method is that the /^-conductivity signal alone is
proportional to the bias current, so it can be linearly increased by biasing.
Moreover, this term is proportional to the square of the local resistivity so
extracting the square root of this component of the signal gives a direct
measure of any variations of resistivity. F o r details of the analysis see the
papers of M u n a k a t a or Holt (1974).
328
6.5.1
D.B. Holt
Constant voltage bias /J-conductivity
Gopinath (1970) and Gopinath and de M o n t s de Savasse (1971) developed the
method using instead a constant voltage bias. In this case the varying current is
used as a /^-conductivity signal. Recent work on semi-insulating GaAs used
this method so it will be reviewed below. Distinguishing between current and
voltage ^-conductivity is a form of signal spectroscopy.
Consider the specimen geometry illustrated in Fig. 6.64. In the absence of
the beam, Ohm's Law states for the scanned rod that
(6.95)
R I=V>
0
where V is the applied voltage. Under beam bombardment this becomes
a
(R -Ar)(I
0
+ AI)=V
a
+ AV
T
F i g . 6.64 (a) Schematic diagram of the (hatched) volume of increased conductivity
ACT under the beam and the scanned line "rod" in which it occurs in a rectangular slab
specimen and (b) the equivalent circuit for the constant voltage bias case. (After
Gopinath, 1970.)
The conductive mode
329
However a constant voltage source is used so A K = 0 and therefore:
(6.96)
ArI~AIR
0
since ArAI can be neglected. Combining (6.95) and (6.96) we have
A / - ^ K
(6.97)
a
In an n-type specimen b o m b a r d m e n t generates Ap minority carriers and
produces a change in local conductivity of
AX(x) = ^Ap(x)(l + %
p
(6.98)
where q is the charge on the electron, b is the ratio of electron-to-hole mobility
and fi is the hole mobility. The u n b o m b a r d e d resistance of the scanned rod is
p
C~
dx
]-
^
L
R
o
=
X0
X0
where 5 is the cross section of the rod. The effect of the beam is to reduce this
to
0
(6.99)
Substituting (6.99) and (6.98) back into (6.97) leads to
(6.100)
The pre-integral term is constant. Thus the integral term gives the variation of
current signal with beam position x along the line scan as a function of 1/Z
(i.e. p~ ) and Ap(x) which should be constant. Hence, just as in the constant
current bias case, the constant voltage bias method gives a signal that varies
essentially with p .
Subsequent to the above mentioned papers of M u n a k a t a and G o p i n a t h
little work was reported using ^-conductivity. Shaw and Booker (1969) used
the method on a disc of material thinned centrally for transmission electron
microscopy and showed the signal was related to specimen thickness and
made defects visible. Kajimura and N a k a m u r a (1973) used DC-biasing and a
pulsed electron beam to observe doping profiles in the active layers of G u n n
diodes. Lohnert and Kubalek (1983) m a d e a brief mention of /^-conductivity
when they had to apply a voltage across two ohmic contacts on a Z n O varistor
to observe an EBIC signal. The technique was limited in their work by the
varistor threshold voltage.
2
2
2
330
6.5.2
D.B. Holt
Experimental verification
Semi-insulating (SI) GaAs has a cellular structure of tangled dislocation walls
surrounding low dislocation density regions. S E M C L studies established that
the cell walls luminesce differently from the cell interiors and they are found to
charge up under the S E M beam to give a form of voltage contrast. The point
defect segregation and non-uniform compensation at the cell walls that this
implies suggests they represent undesirable non-uniformities in resistivity.
Wakefield et al (1984), Warwick and Brown (1985) and Koschek et al (1988)
will provide an introduction to the extensive literature on SI GaAs S E M
characterization.
Pratt (1988) applied the constant voltage /J-conductivity method to
microcharacterize the conductivity of SI GaAs and test the value and
difficulties of the method.
Charge collection current line scans across a sample of SI GaAs were
recorded with the experimental arrangement of Fig. 6.65. All the specimen
current passes through a portion of the sample of resistance R to virtual earth
x
Contact to
voltage
amplifier
Contact to
specimen
currtnt
amplifier
650
oc
1.9x10" A
10
Distance
F i g . 6.65 Experimental arrangement for recording ohmic and ^-conductivity line
scans. (After Pratt, 1988.)
331
The conductive mode
via a high-sensitivity current amplifier. The ohmic voltage d r o p produced was
measured by a voltage amplifier connected to the other contact. When the
electron probe was incident on the contact to the voltage amplifier the
maximum voltage V was registered. F r o m this the resistance of the specimen
can be obtained as
m
R=VJI
F o r a sample in rectangular bar form, the resistivity is then given by
p=
RA/L=(V A)/(IL)
m
The result of such a line scan is shown in Fig. 6.66. F o r the specimen observed
here the resistance value obtained was p = 1.66 x 1 0 Q c m and the corresponding sheet resistance was 3.3 x 10 Q in good agreement with the value of
3 . 4 x l 0 Q provided by the suppliers of the wafer. Since this zero
conductivity profile can be obtained experimentally it is not necessary to
calculate it in this case as M u n a k a t a , G o p i n a t h and Shaw and Booker did. The
slight deviations from a straight line in the profile were due to noise in the pen
chart recorder. The result of biasing is shown in Fig. 6.66 in which the /Jconductivity effect clearly reveals large resistivity variations.
7
8
Current ( x 10" A )
IxlO^A
8
F i g . 6.66 Ohmic (lower) and constant voltage bias ^-conductivity (upper) line scans
across a rectangular slab specimen of semi-insulating GaAs. (After Pratt, 1988.)
A
i
§
5
30,<V
§
300HM
80.,98
B
§
•
3
30KV
•
300HH
»
80. 8 i
•
:
F i g . 6.67 (a) Differentiated CL and (b) differentiated constant voltage bias pconductivity micrographs of a rectangular slab specimen of semi-insulating GaAs.
(After Pratt, 1988.)
The conductive mode
333
An experimental difficulty was that, due to the high resistivity of the
material, large voltages were needed to produce small currents. The resultant
danger of breakdown necessitated use of a protective series resistance.
Moreover, drift of the results with time occurred due to heating. When
sufficiently low fields were used to avoid heating the signals and contrast were
low. However, it proved possible, by using signal differentiation to enhance
contrast to see the cell structure in /^-conductivity as Fig. 6.67 shows.
SI GaAs provided a severe test of the technique. With lower resistivity
materials the direct observation of non-uniformities in resistivity should be
relatively easy.
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7 Scanning Deep Level Transient
Spectroscopy
0 . BREITENSTEIN a n d J . H E Y D E N R E I C H
Institut fur Festkorperphysik
Wissenschaften
der DDR,
Democratic
Republic
und Elektronenmikroskopie,
Postfach
250, DDR-4020
List of symbols
7.1 Introduction
7.2 Fundamentals
7.2.1 Trap population statistics
7.2.2 The SDLTS excitation process
7.2.3 Capacitance versus current SDLTS
7.2.4 Instrumentation
7.3 Special techniques
7.3.1 Optimization of the imaging conditions
7.3.2 Signal identification
7.3.3 SDLTS on semi-insulating materials
7.4 Applications
7.5 Conclusions
Acknowledgements
References
Akademie
der
Halle,
German
*
339
340
345
345
347
350
352
355
355
358
362
365
369
370
370
List of s y m b o l s
A
c
n ; p
sample area
capture coefficient for electrons or holes, respectively
AC
e
e ._
change in capacitance of a space charge layer
charge on the electron
emission rate for electrons or holes, respectively
9
J
degeneracy factor
current density
n
SEM Microcharacterization of Semiconductors
ISBN 0-12-353855-6
Copyright © 1989 Academic Press Limited
All rights of reproduction in any form reserved
O. Breitenstein and J. Heydenreich
340
J(t)
n
current S D L T S signal
free electron concentration
n
JV
iV
iV
p
Q
t
t
(¥}
V
V
W
££
rf
r\%
t]%
T
t
t
total number of traps in the excited area of a space charge region
concentration of a (trap) level
donor or acceptor concentration, respectively
effective density of states in the conduction or valence band,
respectively
free hole concentration
trapped charge
times after switching off the electron beam
trap filling pulse width
electron drift velocity (often assumed to be the thermal velocity)
reverse bias
built-in diffusion voltage
space charge region width
permittivity
electron occupancy factor
electron occupancy factor at time 0
equilibrium electron occupancy
relaxation time constant
emission time constant
trap filling time constant
7.1
Introduction
T
t
l 2
f
D
0
e
f
D;A
c;v
The microscopical investigation of the spatial distribution of point defects in
semiconductors is of great interest because it allows conclusions to be drawn
about interactions between point defects and extended crystal defects and
about the influence of technological processing steps on point defect
behaviour. Since point defects may influence the properties of semiconductors
even at very low concentrations down to 1 0 c m , conventional microanalysis methods such as energy dispersive spectroscopy (EDS) or secondary
ion mass spectromety (SIMS) are seldom applicable to this purpose due to
their lack of sensitivity. Cathodoluminescence only allows spectral investigations on radiative recombination centres. Integral cathodoluminescence and
EBIC (electron beam-induced current) can detect the presence of recombination centres but not their entire nature; point defects acting as trapping
centres are, in principle, not detectable by these methods.
1 2
- 3
The most powerful method available to detect all types of deep point defect
levels is the deep level transient spectroscopy (DLTS) technique introduced by
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
SDLTS
signal
S E M
beam
blanking
sample
cryostat
F i g . 7.1
341
_ J
DLTS
spectrometer
T contol
unit
Basic experimental arrangement for SDLTS.
Lang (1974), which in its standard configuration can be used to investigate the
depth profile of the concentration, but not its lateral distribution. It was
therefore a straightforward idea by Petroff and Lang (1977) to combine the
D L T S detection technique with the electron probe excitation facility of an
S E M to establish the scanning D L T S techniques (SDLTS). Figure 7.1 shows
its fundamental arrangement. The sample, which is a space charge structure
( p - n junction or Schottky diode), is mounted on a temperature control stage
within an S E M and is electrically connected with a D L T S spectrometer. Then,
under appropriately selected experimental conditions the spectrometer output
signal reflects the concentration of a spectroscopically well-defined deep level
in electron beam position.
The first S D L T S system developed by Petroff and Lang used an S T E M and
worked with current detection (see Section 7.2.3) and on-line image recording.
In spite of several promising results of this group (see, for example, Petroff
et al, 1978,1979; Petroff, 1983) it took more than five years for the method to
become further developed to work with capacitance detection (Breitenstein,
1982) and to be controlled by a microprocessor system (Breitenstein and
Heydenreich, 1983, 1985). Meanwhile several groups have been working on
S D L T S (see, for example, Sporon-Fiedler and Weber, 1986; Inoue et al, 1986;
W o o d h a m and Booker, 1987; Dozsa and Toth, 1987; Heiser et al, 1988) and
the interest in this technique is increasing.
The physical process used for S D L T S detection is the thermal ionization of
carriers trapped by point defect levels. Let us consider, for example, a hole trap
within a space charge region (SCR) of an n-type Schottky barrier (Fig. 7.2). At
342
O. Breitenstein and J. Heydenreich
0
0
0
b,
a.
c,
F i g . 7.2 Schematic band diagram of an n-type Schottky barrier with a hole trap
level: (a) thermal equilibrium; (b) electron beam excitation; (c) thermal trap emission
(measure phase).
thermal equilibrium (a) the traps are typically ionized by holes (see next
section). If minority carriers are generated by the action of an electron beam (b)
holes flow through the SCR causing trap filling. After switching off the electron
beam (c) the filled traps thermally ionize and the carriers are swept away by the
electric field. This process is associated with a measurable transient current
and a transient capacitance change, respectively, representing the two
alternative primary measurement signals (see Section 7.2.3).
Depending on the sample temperature the thermal emission time constant,
t , changes and the simplest way of yielding the D L T S signal is to subtract the
primary signal values at two times t and t after the pulse from each other as
outlined in Fig. 7.3. This difference exhibits a peak at that sample temperature
where the emission rate e (being the inverse of T ) of the level amounts to (see
Lang, 1974).
e
x
2
c
p
(7.1)
Hence the selection of t and t opens a so-called "rate window" in which the
emission rate has to fall so that a peak appears. Other possibilities for D L T S
correlation are lock-in rectification or linear exponential correlation (see
Miller et al, 1975). Since the temperature dependence of the thermal emission
rate is governed by the thermal activation energy E and the temperature T
according to the generally accepted relation (see Shockley and Read, 1952)
x
2
t
(7.2)
(where N = effective density of states of the corresponding band;
c = capture coefficient for electrons or holes, respectively; g = degeneracy
factor), the rate window dependence of the D L T S peak temperature allows
c;y
n ; p
343
CAPACITANCE TRANSIENTS AT VARIOUS TEMPERATURES
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
F i g . 7.3 Principle of the DLTS detection technique using a double boxcar
integrator. (After Lang, 1974.)
one to measure E * I F the sample temperature and the rate window are
matched to fit a well-defined D L T S peak, the D L T S signal is proportional to
the concentration of this level.
There are two possibilities for carrying out spatially resolved D L T S
t
* N o t e that the activation energy and the prefactor of the thermal emission rate are good
fingerprints of a level; one has to be careful, however, to associate these values with physically
relevant level parameters (cf. e.g. Bourgoin and Lannoo, 1983). Thus, in the case of a temperaturedependent capture coefficient E actually represents the sum of the capture activation energy and
the actual ionization energy, and the prefactor only contains the high-temperature limit of the
capture coefficient. Generally speaking, the ionization energy measured by D L T S actually
represents a non-equilibrium activation enthalpy for the emission into the corresponding band
that does not necessarily coincide with the equilibrium energy position of the level within the
energy gap. Thus, at least for levels with electron and hole emission rates in a similar order of
magnitude, actually two ionization energies are defined corresponding to the emission into the
two bands.
t
344
Heydenreich
SDLTS SIGNAL (ARBITRARY UNITS)
O. Breitenstein a n d J.
E3
1
1
1
1
I
I
I
1
1
-150-100
-50
0
50
100
150
200
250
300
TEMPERATURE C O
Fig. 7.4 Local current DLTS spectra of a G a _ Al As (DH) laser device showing
the DX deep level centre and the E3 centre produced by the damage after proton
bombardment. The upper spectrum corresponds to the edge of the proton-bombarded
stripe of the device and the lower one to the centre of the laser stripe. (After Petroff
et al, 1978.)
t
x
x
investigations. The first consists of a temperature scan with the electron beam
fixed, thus revealing the deep level spectrum in this very position. The practical
problem of this variant is to ensure that the cryostat moves as little as possible
under the electron beam during the temperature cycle. Figure 7.4 represents a
typical result of such an investigation. We prefer to denominate this technique
"local D L T S " , because the beam is not scanned. O n the other hand, scanning
the electron beam at the D L T S peak temperature leads to a line scan or an
image that can be interpreted as a display of the concentration at a welldefined level. A typical example of such an SDLTS procedure is shown in
Fig. 7.5.
In Section 7.2 some fundamentals are given which are important for the
practical application a n d evaluation of SDLTS measurements. Section 7.3
represents and discusses some special techniques to obtain more quantitative
results, a n d describes the use of S D L T S on semi-insulating materials. Some
typical experimental examples demonstrating the application of the technique
to physically relevant problems are introduced in Section 7.4, a n d the
possibilities and limitations of the techniques are Finally summarized in
Section 7.5.
Scanning deep level transient spectroscopy
345
f l t f H'
F i g . 7.5 Current SDLTS image of a Cu-doped G a A s / A ^ G a ^ ^ s ^ y P y p - n
junction showing a reduced Cu signal (dark contrast) in the regions ol misfit
dislocations. (After Petroff and Lang, 1977.)
7.2
Fundamentals
7.2.1
T r a p population statistics
The generation and recombination statistics of carriers at deep levels in
semiconductors has been reviewed in detail, for example, by Sah et al. (1970).
Here, only the facts important for S D L T S will be discussed. An isolated point
defect level having two possible charge states is characterized by the two
capture coefficients c and c for electrons and holes, respectively, by its
thermal emission rates e and e which, according to eqn (7.2), define the
activation energies for the emission into the two bands, and by its concentration N . In the absence of light the rate equation of a system of levels has
the form
p
n
n
p
t
^
= (1 - rj')(e + c n) - f(e
p
n
n
+ c p)
p
(7.3)
where rj = electron occupancy factor; n = free electron concentration; p = free
hole concentration. If n and p do not vary with time the solution of eqn (7.3)
e
346
O. Breitenstein and J. Heydenreich
with rj as the starting electron occupancy for t = 0 has the general form
e
0
(7.4)
with
being the equilibrium electron occupancy
(7.5)
and T being the relaxation time constant
(7.6)
This means that, as a rule, all level recharging processes originating from a
change of the free carrier offer should have an exponential behaviour with a
time constant governed by the fastest process involved. If, for example, the free
carrier concentration is negligible (which is relevant in a reverse biased SCR
without irradiation) the occupancy is governed only by the two emission
processes, and for levels in the upper half gap electron emission dominates,
hence they are ionized by electrons (rj^ = 0) in thermal equilibrium; levels with
comparable hole and electron emission rates may be partly filled, and levels in
the lower half gap are filled with electrons, hence they are ionized by holes. If,
at t = 0, due to the action of the electron beam carriers are introduced into the
SCR,
may vary according to eqn (7.4) and the levels exponentially relax into
the new filling state with a time constant governed by the free carrier offer and
the corresponding capture coefficient. Note, however, that yf does not have to
change noticeably in all cases due to the introduction of free carriers. The
introduction of electrons, for example, does not change the charge state of a
level in the lower half gap because it is already filled with electrons; the same
holds for holes and levels in the upper half gap. If both electrons and holes are
introduced into the SCR, the two capture coefficients and the electron-to-hole
concentration ratio determine whether a level will become entirely filled,
partly filled or remain ionized.
It should be noted that the above description of the deep level behaviour
represents the idealized behaviour. Depending on the position of the levels
within the SCR the electric field may, for example, influence the properties of
the levels, and also the residual free carrier concentration is positiondependent and not negligible in the edge region, thus often leading to a more
or less non-exponential behaviour of the levels. The result is a somewhat
distorted D L T S peak, but the general behaviour remains as described above.
The trap recharging behaviour essentially changes if instead of isolated
point defects locally interacting levels are considered with the defect density
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
347
being so high that the properties of one level depend on the filling state of the
adjacent levels (see, for example, Ferenczi and Dozsa, 1982). This can hold true
for levels extended defects like dislocation lines or other crystal defects,
point defect clusters or clouds, or for interface states on inner or outer surfaces
including the Schottky barrier under investigation itself. F o r these states the
thermal capture and emission probabilities are n o longer constant but vary
with the varying defect occupancy leading to a non-exponential behaviour.
Hence, S D L T S investigations of extended defects are generally also possible,
the corresponding signals of the latter, however, may n o longer exhibit a welldefined peak but rather a broad band in the temperature spectrum. This
different behaviour of isolated point defects and extended defects has to be
taken into account in the quantitative interpretation of S D L T S results (see
Section 7.3.2).
7.2.2
T h e S D L T S excitation p r o c e s s
Table 7.1 shows the most important sample geometries relevant for S D L T S
investigations with their fundamental excitation properties. F o r each geometry, of course, the complementary type exists if the conductivity type a n d
the carrier sign are changed. Except the first, all geometries can be prepared
also as thin films to carry out parallel T E M or S T E M investigations (see
Petroff and Lang, 1977). It has generally been assumed that t r a p filling occurs
due to the thermalized excess carriers flowing through the space charge region
(SCR) rather than to the hot electrons within the generation volume. As a
function of the sample geometry this electron beam-induced current can either
be an electron or a hole current, or a mixed one. If we classify the levels as traps
whenever their capture coefficient to the neighbouring band is largest, and as
recombination centres whenever the other one dominates, according to the
statements of the previous section, only some types of levels may be filled in a
given structure as listed in Table 7.1. It should be noted, however, that for the
S D L T S excitation process the capture coefficients influenced by the electric
field within the SCR are decisive a n d not those measured by standard D L T S in
neutral material.
Table 7.1, of course, characterizes solely the typical limiting case; there may
be intermediate cases where the traps are only partly filled. Thus the
distinction between a shallow and a deep p - n junction is naturally relative and
depends on the acceleration voltage chosen. The relation of the capture
coefficients may also vary depending on the level species ranging from extreme
values to unity; and in a Schottky diode the electron-to-hole current ratio also
varies with the applied bias and the acceleration voltage. An experimental
example of such a dependence is given in Fig. 7.6, where at 5 kV acceleration
348
O. Breitenstein and J . H e y d e n r e i c h
T a b l e 7.1 Most important SDLTS excitation configurations with their basic
excitation properties.
Geometry
Characteristic
Deep p - n junction
(low acceleration
voltage)
Carriers in
the SCR
Detectable
level types
Only electrons
Electron traps,
electron
recombination
centres
Shallow p - n junction Electrons and holes Electron traps, hole
(high acceleration
traps
voltage)
Surface Schottky
barrier
Electrons and holes Electron traps, hole
traps
p - n junction cross
section
Only electrons or
only holes
Electron traps and
electron
recombination
centres, or hole traps
and hole
recombination
centres
voltage due to the small penetration depth the exciting current mainly consists
of majority carriers (leading to negative peaks). At 25 kV the increasing hole
contribution leads to a reduction of the majority carrier peaks and to the
occurrence of a new positive minority carrier peak at 130K.
Further arguments exist for deviations from the general rules presented in
Table 7.1. Thus, if the electron beam impact generates light (cathodoluminescence) either an unexpected photoexcitation of certain levels may occur, or an
expected trap filling may be quenched by a photoionization process. It is also
widely unknown in which way the hot carriers within the generation volume
affect the trap-filling process if the generation volume crosses the SCR.
Moreover, since the electron beam may also excite minority carrier traps
outside of the SCR (e.g. surface states above a p - n junction), their thermally
emitted carriers may drift to and through the SCR after the pulse. F o r current
S D L T S they may contribute to the signal (see next section), but they might
also suppress regular thermal emission from a level within the SCR. The above
discussion may allow the general conclusion that if a level is characterized by
standard D L T S , unfortunately one cannot be sure that this level is also
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
349
F i g . 7.6 Influence of the SEM acceleration voltage on the electron beam-excited
capacitance DLTS spectrum of a plastically deformed Si crystal.
excitable in an S D L T S experiment. Thus, in all cases it is advisable to prove the
identity of the measured S D L T S signal as outlined in Section 7.3.2.
The so-called double pulse or "clear" pulse technique is a special excitation
technique originally developed to measure depth profiles or majority carrier
capture cross sections of minority carrier traps (see Lang, 1974). Here, the
levels are filled with an excitation pulse, and the trap filling is quenched
afterwards by a second "clear" pulse introducing the other carrier type and
leading to a recombination of the previously captured carriers. Ferenczi's
proposal (personal communication), which was recently systematically accomplished by W o o d h a m and Booker (1987), was to use a bias pulse to fill the
levels over the whole sample area, to quench the trap filling afterwards locally
using an electron beam "clear" pulse, and to display the difference between the
S D L T S signals with and without "clear" pulse as a measure of the local
concentration of the levels. The excitation technique is advantageous if it turns
out that a level can be filled by using only bias pulses, but no electron beam
pulses. Such a behaviour may be due to, for example, the inevitable presence of
the second carrier type during the electron beam impact, or a capture cross
section of a level strongly depending on the electric field. The practical
problem in the application of this excitation technique to S D L T S experiments
is that here the signal of interest is the small difference between two large
D L T S signals. Hence, the presupposition to overcome the noise is that the
dynamic range of the D L T S detection system has to exceed the ratio of the
O. B r e i t e n s t e i n and J . H e y d e n r e i c h
350
sample area to the excited one, which sets a limit to the spatial resolution to be
attained.
7.2.3
C a p a c i t a n c e versus current SDLTS
In the total depletion approximation, neglecting edge effects, the capacitance
of a space charge layer (Schottky barrier or asymmetrical p - n junction) can be
expressed as (see, for example, Miller et a/., 1977):
(7.7)
where ss = permittivity; A = sample area; W = space charge width, with
0
(7.8)
where (]V - N ) = net doping concentration; V = reverse bias; V = built-in
diffusion voltage. Changing the charge condition of a level with the
concentration JV being small against the net doping concentration leads to a
capacitance change of
D
A
D
t
(7.9)
Inserting eqn (7.7) and replacing ee by using eqn (7.8) leads to
0
(7.10)
where n is the total number of recharged levels in the SCR. This expression is
valid also if A is the small excited sample area of an S D L T S experiment with
the rest of the sample area remaining passive. Thus, assuming total trap filling
in this area, the primary transient signal of the capacitance meter ouput after
the end of the filling pulse is expressed by (see Section 7.2.1):
t
(7.11)
where n (t) = n rj (t) with n being the total number of traps within the excited
area of the SCR. The sign of AC depends on the emission of either electrons or
holes; majority carrier emission leads to negative transients and minority
carrier emission to positive ones.
F o r current S D L T S the corresponding signal can be calculated directly
e
t
T
T
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
351
from the contributing trapped charge Q = en to be
t
(7.12)
where the excited volume may no longer be AW, but may extend into the
neutral region as discussed below. Comparing eqns (7.11) and (7.12) reveals an
essential difference between the two S D L T S variants: unlike capacitance
SDLTS, for current S D L T S the signal amplitude is proportional to the
emission rate, so that for current S D L T S the sensitivity is only high for large
rate windows, whereas for capacitance S D L T S the practically usable rate
window range is much larger. Thus, the identification of the S D L T S signal by
performing a rate window scan (see Section 7.3.2) is only practicable for
capacitance D L T S . Moreover, it is only for capacitance S D L T S that the signal
sign depends on the carrier type emitted, yielding the very important
information of whether the detected level lies in the upper half gap or in the
lower one. Current S D L T S , on the other hand, is much easier to realize, and
the current amplifier can be directly used for the EBIC investigation of the
sample which has to be managed separately for capacitance SDLTS. Another
important difference is also the different region where the signal comes from.
Measuring the capacitance yields a signal only if the recharging process occurs
within the SCR, and the resulting signal amplitude also depends on the depth
position within the SCR (see, for example, Pons, 1984). F o r current SDLTS, on
the other hand, the signal is independent of the position within the SCR, and
even if minority carriers are emitted outside the SCR in the neutral material
roughly within the distance of a diffusion length, they may drift to and through
the SCR contributing to the signal. Another argument arises if not single traps
but multiple levels are considered. If an electron and a hole are emitted at
almost the same time (the corresponding centre would be a kind of deeply
b o u n d exciton), this process would be detectable by current S D L T S but not by
capacitance SDLTS.
It is hard to give general information on the detection limits of both S D L T S
variants since several factors are decisive. F o r their current S D L T S arrangement Petroff and Lang (1977) reported a sensitivity of the order of 10,000
atoms per scanning point. Employing a special resonance-tuned capacitance
S D L T S system under favourable conditions the authors measured a noise
level corresponding to % 100 atoms (Breitenstein, 1982). It may, however, be
misleading to compare these values directly. In addition to the quality of the
measurement circuit the sensitivity is influenced also by the signal integration
time chosen and the leakage behaviour of the sample. F o r capacitance S D L T S
the sensitivity is additionally affected by the series resistance limiting the
measurement frequency, by the applied AC voltage and by the total
capacitance of the sample. N o t e also that, since for current S D L T S the signal
352
O. Breitenstein and J . H e y d e n r e i c h
may be generated also outside the SCR, a certain sensitivity given in atoms per
scanning point may be associated with a lower impurity concentration for
current SDLTS than for capacitance SDLTS. Altogether, both SDLTS
variants obviously have their own inherent advantages and disadvantages so
that it is advisable to have both available. This finding, by the way, also holds
for standard D L T S .
7.2.4
Instrumentation
The main components of an S D L T S arrangement were shown in Fig. 7.1. In
principle, any type of S E M or S T E M may be used for SDLTS. General
demands are the following: equipment with a beam blanking unit enabling the
application of short excitation pulses (at least in the microsecond range);
possibility of an external beam deflection control for computer-controlled
data acquisition; equipment with a temperature control stage; and availability
of electrical feed-throughs to connect the sample. In order to keep the critical
electrical connections as short as possible it is advisable to place the
preamplifier circuitry within the microscope near the sample. The temperature
of the temperature-control stage should range between liquid nitrogen
temperature and at least 400 K (for current S D L T S even higher due to the
necessarily higher rate window), otherwise the detectable energy range is
limited. Since a fast temperature adjustment is recommended for S D L T S an
evaporator cryostat, for example, as shown in Fig. 7.7 is better suited than the
F i g . 7.7
Cooling stage (LNT) constructed for the SEM type BS 300 (Tesla).
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
353
more popular SEM cryostats with flexible heat conductor and the liquid
nitrogen (or liquid helium) bath outside the SEM. The use of a microminiature
refrigerator system ( M M R , see Yakushi et al, 1982) should perhaps also be
possible for SDLTS.
If an S E M with an oil pumping system is employed an anticontamination
facility (cryotrap) is strongly recommended for carrying out investigations
below room temperature; an even better solution would be an oil-free vacuum
system. There are very low demands on the spatial resolution of the electron
probe. As will be discussed in the next section, as a rule the resolution attained
is not governed by the beam diameter. The beam current, too, is not a critical
parameter; it should be adjustable over 2 - 3 orders of magnitude, e.g. from
100 pA to 100 nA, in order to allow a simple optimization of the imaging
conditions (see next section). Very critical, however, is the long-time stability of
the beam current. While recording an image, which probably takes 1 hr or
more, the change in the beam current should be well below 10%. The
acceleration voltage applied influences the excitation processes as discussed in
Section 7.2.2. Hence, the larger the acceleration voltage range, the higher the
flexibility with respect to the sample geometries used.
A scanning optical microscope (SOM, see, for example, Wilke, 1985) can just
as well be applied to S D L T S investigations if the above conditions are fulfilled
in a respective sense. The advantages of an S O M would be: the sample can be
kept in dry gas instead of vacuum, the contamination should not be severe, and
the S D L T S apparatus may become more compact. O n the other hand, using
light requires semitransparent metallizations, and the usual restriction to one
wavelength determines the penetration depth for a given semiconductor
material thus reducing the variability with respect to the sample geometries to
be applied (Heiser et al, 1988).
The attained detection sensitivity mainly depends on the primary signal
measurement system, hence on the quality of the current amplifier or the
capacitance meter, respectively. F o r the current amplifier the noise current
should be low, the speed high and the input impedance low, which are partly
contradictory demands. N o t e that the sample and stray capacitance together
with the preamplifier input resistance yield an RC-link that is recharged by the
excitation-induced current and relaxes with its internal time constant. This
relaxation is always superimposed on the signal to be measured; they can be
separated only if the internal RC time constant is much lower than that of the
trap emission. The latter, on the other hand, should be chosen as low as
possible to yield a large relaxation current (cf. Section 7.2.3).
F o r carrying out capacitance S D L T S experiments the sample capacitance
can be measured by using either bridge methods in the deflection mode with an
applied AC voltage of a fixed frequency or by the oscillator method. Very
sensitive resonance-tuned LC bridge circuits have been introduced, e.g. by
354
O. B r e i t e n s t e i n and J . H e y d e n r e i c h
Mirachi et al. (1980), and Breitenstein (1982). The oscillator method, where the
sample capacitance governs the frequency of a radio frequency oscillator
circuit, the output of which is demodulated by an fm demodulator, has been
employed for D L T S , e.g. by Breitenstein and Pickenhain (1985) and for
"capacitance contrast" experiments within the S E M by Chubarenko et al
(1984).
Miller et al (1975) showed that the different ways of producing the D L T S
signal from the primary measurement signal (double boxcar or double sample
and hold, lock-in rectification, analogue exponential correlation) differ at best
by a factor of 2 in their figure of merit. Accordingly, the correlation method
itself is not decisive for sensitivity, but rather the fulfilment of some basic
demands on it in order to avoid the additional introduction of noise by the
correlator. Thus, the excitation pulse period with its probable subsequent
overload period has to be blanked out reliably, and the correlator should
provide a perfect D C rejection. Especially for lock-in systems, any phase jitter
between the excitation pulses and the correlation function should be avoided,
and for the discrete sampling variants the gates should be large enough to gain
information without losing too much measurement time.
There are several reasons why a central microprocessor control system
should be applied to S D L T S experiments. The most important one is the
possibility of adjusting the image contrast and brightness after the measurement once all values are stored. N o t e that S D L T S is a very slow imaging
technique. Depending on the number of image points and on the noise level
(governing the desired integration time) it may take minutes up to hours to
record a two-dimensional image. Hence, it takes at least the same time to look
for the maximum and minimum values in order to optimize the photographic
or plotting conditions. Thus only the use of a computer-controlled data
acquisition system allows time-effective S D L T S investigations to be carried
out. It is also quite clear that once the data are stored they can be displayed
much more extensively than by on-line recording. Other reasons are given in
the following two sections, i.e. that useful procedures such as a filling pulse
width scan or a rate window scan are only manageable in a simple way by
computer control.
The usual way to perform computer-controlled D L T S investigations is to
digitize the primary measurement signal point-by-point at different times after
the excitation pulses and to manage a software-controlled correlation (see, for
example, Okushi and T o k u m u r a , 1980). This method, however, is not
optimum as to attain maximum sensitivity for one rate window, since at least
for low rate windows relative to low digitizing rates a great deal of the
measurement time is spent without yielding any information. Moreover, for
large rate windows, which are desirable for current SDLTS, the demands on
digitizing and computation speeds are very high. Thus, a hybrid system should
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
355
Microprocessor
system
SEM
- 8k R0M/4dk
RAM
- digital • analog I/O
- special DLTS hardware
gray value
, beam deflection
L
T
beam blanking
|
EBIC
biasj
f
correlator
C-meter
preamp
EBIC-amp
T-control
unit
F i g . 7.8
corn
funct.
DLTS
J
/integrator
spectrometer
Functional block diagram of the computer-controlled SDLTS system.
be preferred as shown in Fig. 7.8. Here the D L T S signal is formed conventionally using analogue techniques, and the computer is only employed to control
the image scan and the temperature, to digitize and store the spectrometer
output signal, and (by using special hardware) to control the excitation pulse
width and to deliver the analogue correlation function governing the rate
window over a wide range. After measurement, the result can be displayed
either as a grey-patch image on the S E M C R T screen, or as a Y-modulation or
topological image on the x-y plotter where more quantitative inspection is
possible. A special scanning D L T S spectrometer of the type described above,
containing the actual spectrometer, the D L T S hardware and an IEC-bus
interface to a personal computer, is now commercially available.*
7.3
7.3.1
Special techniques
Optimization of the i m a g i n g c o n d i t i o n s
According to Section 7.2.1 the trap-filling process within an SCR can be
expected to be an exponential one with a filling-time constant (assuming, for
example, electron capture to be the dominant process)
(7.13)
*Raith K G Dortmund (FRG)
O. Breitenstein and J. Heydenreich
356
where j = current density and < V} = electron drift velocity, often assumed to
be the thermal electron velocity. Hence, the degree of trap filling and
consequently also the expected signal have an exponential saturation type
dependence on the product of the filling pulse width t and the exciting current
density. If the electron beam is focused the current density shows a bell-shaped
distribution around the beam position due to carrier spreading, and the local
degree of trap filling depends on the distance from the electron beam.
Denominating the product of the filling pulse width and the beam current as
the excitation intensity, in the low excitation intensity limit the degree of trap
filling is always « 1 and the dependence of the signal on t is linear. In this
linear range the spatial resolution is the best possible one (viz. the EBIC
resolution), but the signal height is small and all factors influencing the
electron beam-induced current also affect the S D L T S signal leading to the socalled "excitation contrast" (see below).
If the excitation intensity is increased in the centre of the excited area the
traps begin to get saturated (rj -> 1) leading to the beginning of a sublinear
dependence of the signal on t . This range can be regarded as best suited for
SDLTS, because the resolution is only slightly degraded, the signal height is
optimum for this resolution, and the initial saturation reduces the excitation
contrast phenomena. If the excitation intensity is further increased the
behaviour in principle remains the same, except that even more distant from
the electron beam the saturation is already reached. Hence, the signal height
increases and the resolution deteriorates. Since the excitation current density
should d r o p more or less exponentially with distance from the electron beam, a
logarithmic dependence of the signal on t can be expected in this range.
Figure 7.9 demonstrates the measured signal dependence on t in a doubleand half-logarithmic representation for the 0.54 eV Au-level in Si showing the
f
f
e
{
f
log DLTS —
f
10JJS
100
1ms
10
1us
10
100
1ms
10
F i g . 7.9 Double logarithmic and half logarithmic dependence of the capacitance
SDLTS signal of the 0.54 eV Au acceptor level in Si on the filling pulse width t .
f
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
357
linear range at the beginning and the logarithmic dependence for t > 100 /is.
Thus, in order to optimize the imaging conditions with respect to the spatial
resolution, one has to perform a "filling pulse width scan" and to look for the
optimum t where the linear range remains. If this optimum turns out to lie
beyond the adjustable pulse width range the beam current has to be corrected
accordingly.
The real extent of the excited area is, of course, still unknown, but it can be
estimated indirectly by, for example, displaying the signal d r o p to zero at the
edge of the investigated diode, which represents a natural sharp step function
of the detectable level concentration, or simply by checking the resolution of
details in the S D L T S image. If reducing the excitation intensity n o longer
improves the spatial resolution, the imaging conditions can be assumed to be
sufficient for the problem under investigation. If, however, the noise dominates
before the desired spatial resolution is reached, one has to find a compromise
between the latter and the signal-to-noise ratio.
One may enlarge the excited area in a defined way, for example, by
defocusing the exciting electron beam. If the defocus dominates over the
carrier spreading the excited area becomes well defined and the exciting radial
current density profile can be regarded as rectangular. An alternative way to
excite a well-defined area, which has recently been proposed by W o o d h a m and
Booker (1987), is to scan the focused electron beam during each excitation
pulse at least once over a certain sample region using the selected area function
of the SEM. Then, an exponential trap filling can be expected inside this area,
but almost none outside, and a quantitative analysis is possible at least for
capacitance S D L T S (see Heydenreich and Breitenstein, 1986). It should be
noted, however, that revealing relative concentration variations as a rule is far
more interesting than estimating an absolute concentration by S D L T S , since
at least the average value of the absolute concentration can be measured more
easily by using standard D L T S .
f
{
Finally, the influence of spatially varying electronic properties of the neutral
crystal material on the S D L T S contrast should be discussed. Considering trap
detection within the SCR the local minority carrier lifetime influences the
horizontal excitation current profile, governing the excited area, and the
magnitude of the exciting current influences the degree of trap filling.
According to the previous discussion these influences can be diminished by
working in the saturation range with a defocused beam. Their residual effect
can be quantitatively estimated using the fact that the trap filling depends on
the product of t and the EBIC signal J. Thus, since the S D L T S signal
dependence on t can be measured by performing a filling pulse width scan, for
the chosen t the signal dependence on J is the same, and the induced S D L T S
contrast can be estimated from the measured EBIC contrast. A different
situation occurs, if for current S D L T S on minority carrier traps the signal
originates mainly from emission outside the SCR. F o r this case Petroff et al
f
{
{
358
O. B r e i t e n s t e i n a n d J . H e y d e n r e i c h
(1979) proposed a deconvolution procedure to correct the SDLTS contrast for
the EBIC contrast. All these procedures, however, may have only approximate
character because they neither take into account the real geometry of the
defects leading to the EBIC contrast, nor the fact that the EBIC current may be
a mixed electron and hole current, only one of which being responsible for the
trap filling. Note, however, that generally any responsibility of a spatially
varying minority carrier lifetime for the measured S D L T S contrast can
be excluded, if the S D L T S contrast exceeds the EBIC contrast or if even
an anticorrelation between the S D L T S and the EBIC contrast is
observed.
Another factor influencing the S D L T S signal, at least if it originates within
the SCR, is a spatially varying net doping concentration (see Section 7.2.3).
This influence can be separated from deep-level inhomogeneities only by
means of independent methods displaying net doping fluctuations. This can be
realized on Schottky barriers by using special EBIC techniques (see, for
example, Chi and Gatos, 1979; Heydenreich and Breitenstein, 1986) on free
surfaces, e.g. by using spreading resistance techniques or optical methods, or
on cross-section geometries by measuring the space charge width directly by
EBIC techniques. O n planar p - n junctions the non-destructive estimation of
net doping fluctuations is still an open problem.
Thus, only if a locally varying net doping concentration and/or minority
carrier lifetime have been excluded as causes of the S D L T S contrast or have
been properly taken into account, is it justified to scale the S D L T S signal in
trap concentration units. Otherwise, only a scaling in units of detected charges
is justified.
7.3.2
S i g n a l identification
In general, thermal transient methods enable only the characterization of
levels with respect to their activation energy and the prefactor (see Section 7.1);
but they do not enable the identification of the chemical or structural nature of
the respective defect. Hence, since several centres may lead to similar
electrically undistinguishable levels, the real identification of a detected level
requires additional information.
The measured S D L T S signal itself may always be a superposition of the
signal of the level of interest with that of energetically adjacent levels and
extended defect levels, which both might account for the detected SDLTS
contrast. Interface state levels of the investigated Schottky barrier, for
example, may always be recharged because the primary electron as well as the
generated minority carrier current penetrate the semiconductor-metal interface. Thus, reliable S D L T S findings require the checking of whether the
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
359
detected signal or at least some details in an S D L T S image are indeed caused
by the interesting levels, or not.
As mentioned above, the simplest and most effective way to prove the nature
of the S D L T S signal is to perform a temperature scan with fixed rate window
and beam position (local D L T S , see Fig. 7.4). If spatial resolution is not desired
this procedure can be performed by using a strongly defocused beam and a
high excitation intensity to yield a high signal as the average over a larger
sample part.
A simple method to prove the identity of certain image structures is to take
the S D L T S image at and beside the D L T S peak temperature. If a structure is
visible only at the peak temperature it can be assumed to be due to the point
defects; if it appears at both temperatures it should be due to extended defects.
This is demonstrated in Fig. 7.10, where only the sharp signal m a x i m u m in the
upper part of the investigated region is due to the point defects.
An alternative procedure to identify the S D L T S signal is to keep the
temperature constant and to prove the exponentiality of the detected signal.
O n e possibility of doing this is to perform a computer-controlled "rate
window scan", hence to measure the electron beam-excited D L T S signal at
different rate windows and to plot it versus the logarithm of the rate window
(see also Ferenczi et al, 1986). If this procedure is applied to an exponential
transient a peak with a well-defined half-width will appear; other point defects
or extended defects will contribute to superimposed peaks or broad bands, just
as with the temperature scan. The advantage of the emission rate scan is that it
can be performed computer-controlled much faster and that there will be no
harm in changing the sample position under the beam, which can hardly be
entirely avoided for a temperature scan. The drawback of the rate window
F i g . 7.10 SDLTS Y-modulation representation of a p - n junction (cross section) in
GaP, taken at (a) 315 K and (b) 275 K (at DLTS peak 500 meV hole trap).
O. Breitenstein and J. Heydenreich
360
a
•si
!§|
/fate window:2000s'
1
I
100 150 200 250
300
Temperature [K]
b
Temperature. 250K
I
t/>'
3
50 no 200500 10002000 500010000
Rate windowfs' ]
1
F i g . 7.11 Capacitance SDLTS signal identification by means of a temperature scan
(a) and a rate window scan (b) for a 400 meV hole trap level in a GaAs Schottky barrier.
s c a n is that as a rule the e x p e r i m e n t a l l y adjustable rate w i n d o w range c a n
hardly be e x t e n d e d o v e r m o r e t h a n 3 - 4 d e c a d e s w h i c h still c o r r e s p o n d s to a
relatively small t e m p e r a t u r e range (cf. e q n (7.2)). F i g u r e 7.11 c o m p a r e s
experimental results from b o t h p r o c e d u r e s a p p l i e d t o the s a m e sample.
A particularly useful t o o l for identifying certain details in a n i m a g e is t o
perform a c o m b i n e d rate w i n d o w - x - s c a n as d e m o n s t r a t e d in Fig. 7.12 (see
W o s i n s k i a n d Breitenstein, 1986). H e r e it s h o u l d be p r o v e n w h e t h e r the
m a x i m u m in the S D L T S line s c a n o v e r a certain s a m p l e r e g i o n t a k e n at the
rate w i n d o w of a certain level is i n d e e d d u e t o this level or not. T h e rate
w i n d o w - x - s c a n p r o v e s this a s s u m p t i o n t o be true, but it a d d i t i o n a l l y reveals,
for e x a m p l e , the t w o local m i n i m a t o the left a n d right of the m a x i m u m n o t t o
originate from this level, since they o c c u r at all rate w i n d o w s .
A p r o c e d u r e w h i c h is simpler b u t n o t s o informative is t o m e a s u r e a n i m a g e
at a n d beside the D L T S p e a k rate w i n d o w , just as w i t h the t w o temperatures,
a n d t o c o m p a r e these i m a g e s . If b o t h i m a g e s are stored it is a l s o p o s s i b l e t o
subtract o n e i m a g e from the o t h e r in order t o display a pure "point defect
i m a g e " (see Breitenstein a n d H e y d e n r e i c h , 1985).
It is a l s o p o s s i b l e t o p r o v e the e x p o n e n t i a l i t y of the S D L T S signal using a
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
361
F i g . 7.12 SDLTS line scan (top) and rate window-line scan (bottom) across a local
maximum of the so-called H level in plastically deformed GaAs.
a
constant trap-filling repetition frequency. The simplest way of doing this is the
so-called "Isothermal D L T S " procedure as introduced by Okushi and
T o k u m u r a (1980). Here the primary signal is digitized at several times t --t„
after the pulse, and D L T S signals of different rate windows are obtained by
respectively subtracting different appropriate pairs of the measured values.
Another more informative procedure though also more complicated has
recently been introduced by M o r i m o t o et al. (1986). In their "Multiexponential D L T S " version they measured the primary transient also point by point,
but they evaluated the result in a deconvolution analysis procedure to yield the
real exponential transient components. Recently, a numerical full transient
analysis method offering improved sensitivity has been applied to S D L T S
by Heiser et al. (1988).
It should be noted that for general reasons all these procedures using one
constant pulse repetition frequency become insentitive to the analysis of high
1
362
O. Breitenstein a n d J.
Heydenreich
emission rates, whenever the emission is to be displayed over a large range.
This is because the pulse repetition frequency chosen has to be very low, of the
order of the lowest emission rate to be detected, so that for high emission rates
only the first few measured values contribute to the information. By the way,
this effect is the converse of the increase in sensitivity for high rate windows in
current SDLTS. It is therefore possible that, at least for current SDLTS, the
direct transient analysis method will increasingly gain importance in future.
7.3.3
S D L T S on s e m i - i n s u l a t i n g materials
All previous considerations were based on the presence of a space charge layer
in a doped crystal that virtually does not exist in semi-insulating (SI) materials.
If, however, an SI crystal is metallized on both faces and a bias is applied to it,
the irradiation of electrons on the top contact may lead to a current flow, in
spite of the near surface excitation. The mechanism of such a carrier drift
process is not yet entirely clear; it can be expected to depend on the contact
properties as well as on the electronic properties of the material itself. Due to
the absence of free carriers all levels within the energy gap of SI materials can
be expected to tend to act as traps rather than as recombination centres so
that, once the traps are filled, the excess carrier lifetime could assume large
values. O n the other hand, if a remarkable a m o u n t of all traps within the
material should be filled with one carrier type the resulting space charge would
screen the accelerating electric field, thus preventing further carrier transport.
It is therefore more realistic to assume that a kind of hopping conduction
(subsequent drift, capture, thermal emission and further drift) plays an
important role in the excess carrier conduction mechanism in SI materials.
If, due to the action of the electric beam, empty traps under the top surface
become filled, the thermally emitted carriers may drift through the crystal also
yielding a measurable current transient after the excitation pulse. Thus,
current SDLTS can also be performed in SI material if a bias is applied to the
structure. It should be noted that the same procedure using light as the
excitation source has become popular under the name photo-induced
current transient spectroscopy (PICTS) and is a successful technique for
investigating deep levels in SI materials (see, for example, Balland et al, 1986).
The main difference between P I C T S and S D L T S on SI materials is that for
P I C T S the excitation can be assumed to be homogeneous between the two
contacts so that - unlike S D L T S - the quantitative evaluation can make use
of the homogeneous photoconductor model. This depth homogeneous
excitation is also the reason why for the spatially resolved P I C T S variant using
focused white light for excitation, the spatial resolution was reported to be
only in the order of the wafer thickness ("Scanning PICTS", Yoshie and
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
363
Kamihara, 1985). Instead, for electron beam excitation similar argument with
respect to the excited volume as outlined in Section 7.3.1 for doped materials
are conclusive except that the excited region here also spreads into the depth.
Hence, there also exists here a compromise between spatial resolution and
signal height; a low excitation intensity yields a good spatial resolution in the
micrometre range at the cost of a reduced signal height.
Figure 7.13 illustrates the physical process underlying the S D L T S investigation of SI materials, which considerably differs from that for doped materials
a)
b)
c)
F i g . 7.13 Schematic representation of the current SDLTS process on SI materials:
(a) beginning of the trap-filling pulse; (b) establishing of a near surface space charge
region due to trapped carriers; (c) thermal detrapping and excess carrier drift through
the crystal (measure phase).
364
O. Breitenstein and J . Heydenreich
(cf. Fig. 7.2). In thermal equilibrium the sample material can be assumed to be
neutral. If a bias is applied to the structure, and electron-hole pairs are
generated, e.g. at the negatively biased contact (a), electrons are swept into the
material where they are captured by traps forming a near surface space charge
region thereby polarizing the structure (b). With the excitation pulse being
stopped (c) the captured electrons are emitted and flow through the crystal
where they may be recaptured and re-emitted as discussed above, or they
recombine with residual holes. Thereby the neutrality of the material reestablishes and the polarization of the structure decays leading to a
measurable relaxation current, which is a measure of the number of initially
trapped carriers.
Figure 7.14 demonstrates an S D L T S image of an SI G a A s : C r crystal
together with the etched surface micrograph. The dominant S D L T S signal
appeared at T = 3 7 0 K and e = 1 0 0 0 s " under negative bias condition. A
correlation to dislocations arranged in a cell wall (see arrows) is visible; the
S D L T S image, however, reveals additional inhomogeneities in the material,
which cannot be concluded from the surface etch pattern.
The interpretation of S D L T S results from SI materials is far more
complicated then for doped materials. The reason is that the measured current
strongly depends on the bulk transport properties, which cannot simply be
described as a path resistance but which are time-dependent due to the action
of trapping centres here. This transport induces a distortion of the transient so
that the peak position of a temperature scan does not necessarily coincide with
that measured by D L T S on space charge structures. Moreover, the bulk
transport properties may be position-dependent yielding a contrast that is
superimposed on the interesting S D L T S contrast. This influence can at least
n
1
F i g . 7.14 Etched surface topograph (a) and current SDLTS image of the framed
region (b) of SI GaAs:Cr crystal.
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
365
approximately be corrected by referring the S D L T S signal to the EBIC signal
of the same sample position (see Breitenstein and Giling, 1987). In spite of these
problems current S D L T S represents a promising technique for investigating
the homogeneity of the incorporation of deep levels in SI materials. F u t u r e
experimental and theoretical studies are, however, necessary to improve
understanding of the underlying physical processes and to enable a more
reliable interpretation of the results.
7.4
Applications
Like any other microanalytical method scanning D L T S should be applied in
conjunction with other techniques in order to gain physically reliable results.
A trivial demand is that the sample should be investigated thoroughly before
by standard D L T S in order to characterize the levels in the material. F o r this
the use of light excitation with hv > E is advantageous because as a rule it
leads to excitation conditions similar to those for electron beam excitation.
The first and most obvious correlation of the S D L T S image is that to the
EBIC image of the same sample. This is necessary not only for a rough
inspection of the sample area before measurement; the comparison of b o t h
images delivers important complementary information: E B I C enables the
localization of extended crystal defects and general estimation of the
recombination efficiency of defects, irrespective of their energetic position in
the gap. S D L T S , on the other hand, reveals the distribution of energetically
well-defined levels, irrespective of whether they are acting as recombination
centres or not. Since for capacitance S D L T S and current S D L T S on majority
carrier traps the information depth is within the SCR, whereas for E B I C and
current S D L T S on minority carrier traps it is mainly outside of it, it is
advisable when working with Schottky barrier samples to use E B I C under
zero bias conditions, but t o apply a reverse bias to the sample at least for
capacitance S D L T S investigations.
G
It has been argued whether or not the exciting electron beam itself is able to
create or quench deep levels to be investigated by means of any kind of
radiation damage (see, for example, Petroff, 1983). Indeed, in a few cases the
authors have observed changes in the S D L T S signal as well as in the E B I C
signal due to the impact of the exciting electrons (see Breitenstein and
Heydenreich, 1983). Hence, though a real a t o m displacement seems to be
unlikely for beam energies below 100 keV, at least certain changes in this
electrical activity of defects may be caused by the electron beam. According to
the previous experience of the authors, however, this has been the exceptional
case; as a rule, the S D L T S images of most samples were found to be
reproducible, i.e. to be unaffected by the exciting electron beam.
O. Breitenstein and J. Heydenreich
366
SDLTS .
25Qu
-30*
EBIC
-30°C
F i g . 7.15 Current SDLTS micrograph (A) and EBIC image (B) of a Ga! .^Al^As
(DH) laser structure. The SDLTS signal corresponds to a map of the DX-centre
distribution. Dark areas in the SDLTS image indicate a lower DX-centre concentration. (After Petroff et al, 1978.)
One of the first published sets of S D L T S and EBIC images is shown in
Fig. 7.15 (taken from Petroff et al, 1978). The current S D L T S image
represents the spatial distribution of the so-called DX-level in a G a .^Al^As
double heterostructure diode. N o t e that in spite of the relatively strong EBIC
contrast the S D L T S image shows very little excitation contrast, pointing to
the fact that the excitation should have been in the saturation region (see
Section 7.3.1). The additional information gained from the DX-centre distribution here, for example, is a hint at the lateral homogeneity of the epitaxy
process that cannot be concluded from the EBIC image.
Figure 7.16 shows a comparison between the topographical representation
of the EBIC image and the capacitance S D L T S image of the dominant peak of
a copper-doped Si sample (see Breitenstein and Heydenreich, 1983). Two local
minima of the EBIC signal point to the existence of dislocations emerging into
the surface at these points. The copper-induced S D L T S signal is enhanced in
the general vicinity of these points, but in the vicinity of the defects the signal is
reduced. This finding suggests a certain copper gettering efficiency of the two
corresponding defects.
Figure 7.17 demonstrates the spectral selectivity of the method (see
Breitenstein and Heydenreich, 1985). The sample is a circular diode of a
G a ! _ A l A s on G a A s heterojunction. In standard D L T S two main peaks
appear corresponding to hole traps at £ -1-400 meV and E -1-580 meV,
respectively, the first one possibly being the so-called "A-level", in GaAs (see
Lang and Logan, 1975). U n d e r electron beam excitation conditions a signal
part of hitherto unknown origin additionally appears at low temperatures.
The circular dark area in the EBIC image at the upper right is the shadow of
the p-contact metallization. The capacitance S D L T S images of the region
2
x
x
v
y
a
,
10jum
b
F i g . 7.16 SEM/EBIC (a) and capacitance SDLTS (b) Y-modulation representation
of a Schottky barrier region on a copper-doped p-Si crystal.
F i g . 7.17 DLTS spectra, EBIC image and different capacitance SDLTS images of
the framed region of a G a ^ A l ^ A s on GaAs heterojunction mesa diode (300™
diameter).
368
O. B r e i t e n s t e i n and J . H e y d e n r e i c h
F i g . 7.18 EBIC image (a) and capacitance SDLTS image (b) of a region of a GaAs
(Au) Schottky barrier. The SDLTS parameters are chosen to display a 400 meV hole
trap.
framed in the EBIC image clearly differ from each other, and the 400 meV level
especially seems to be influenced by the presence of the p-contact layer.
Different gettering activities of different crystal defects in GaAs can be
deduced from Fig. 7.18. In the given material a dominant hole trap level with
an activation energy of 400 meV was present, the nature of which is not yet
entirely clear (see Breitenstein and Diegner, 1986). The comparison of the
EBIC image (a) with the S D L T S image (b) clearly shows that the different
types of crystal defects exhibit strongly different interactions with the levels
detected. While the defects A exhibit a bright S D L T S contrast in their
surrounding, pointing to an increased trap concentration, the defects C seem
to have a strong gettering efficiency with respect to these levels. The elongated
defect B showing the strongest EBIC contrast, on the other hand, seems to
have a very weak interaction with the 400 meV levels. Statements of this kind
are of essential scientific and technological importance in semiconductor
research.
The last example in Fig. 7.19 demonstrates the spectral selectivity of the
S D L T S method when applied to semi-insulating GaAs:Cr, in material (see
Breitenstein and Giling, 1987). Grown-in dislocations in GaAs are often
arranged in a complex structure, e.g. forming a "streamer" (see Weyher and
van de Ven, 1983). Point defects were argued to participate in the formation of
these "streamers", which could be verified by current S D L T S investigations
S c a n n i n g deep level t r a n s i e n t s p e c t r o s c o p y
369
Fig . 7 . 1 9 Etched surface structure (a) showing "streamers" (see arrows) and current
SDLTS images of the framed region of an SI GaAs.Cr, In crystal measured under
different conditions: (b) negative bias, T = 70°C; (c) negative bias, T = 20°C; (d) positive
bias, T = 50°C. The rate window was 100 s ~ the sign was always chosen so that bright
contrast corresponds to a high transient signal level.
under applied bias (see Section 7.3.3). The experimental finding that the
obtained micrographs strongly vary with the bias polarity and the sample
temperature points to the fact that they all belong to different impurity species.
The finding of Section 7.3.3, however, should be kept in mind that here it is
complicated to decide whether or not one of the micrographs reflects, for
example, the E L 2 concentration distribution due to the several factors
influencing the S D L T S peak position.
7.5
Conclusions
Scanning D L T S was shown to provide unique possibilities for displaying
inhomogeneities in the concentration of non-radiative deep-level defects
370
O. Breitenstein and J. Heydenreich
well below the detection limits of other microanalytical tools. T h o u g h the
chemical and structural composition of the detected levels cannot be proved
by the method itself, techniques have been proposed and demonstrated of
identifying the signal reliably at least in terms of levels that are characterized
by standard D L T S methods. Practical experience and theoretical considerations show, however, that the detection of certain level types may be possible
only for certain sample geometries, and that the quantitative interpretation of
the micrographs in terms of real concentrations additionally requires
investigations to be carried out. But, if a level is excitable by the action of the
electron beam, even qualitative S D L T S investigations in connection with
EBIC investigations deliver unique information about its microscopical
incorporation. Thus, in spite of its inherent limitations, scanning D L T S apart from the other microanalytical m e t h o d s - c a n be expected to be
successfully applied to the investigation of defect behaviour of semiconductors
in the future.
Acknowledgements
The authors are indebted to Professor P.M. Petroff (Santa Barbara) for
permission to include S D L T S results of his work in this article, to D r T.
Wosinski (Warsaw) for experimental cooperation and to D r A.F. Jarykin
(Chernogolowka), Professor D r G. Oelgart (Leipzig), D r H. Menniger and B.
Diegner (both Berlin), Professor L.J. Giling (Nijmegen) a n d D r J. N o w a k
(Bratislawa) for submitting samples for these investigations. The assistance of
M. Taege, Th. Nerstheimer, A. Pippel and J.M. Langner (all Halle) in
constructing the computer-controlled S D L T S equipment is gratefully
acknowledged.
References
Balland, J.C., Zielinger, J.P., Nouget, C. and Tapiero, M. (1986). J. Phys. Lond. D, 19,
57-70.
Bourgoin, J. and Lanoo, M. (1983). Point Defects in Semiconductors II, Springer, Berlin,
Heidelberg, New York.
Breitenstein, O. (1982). Phys. Stat. Sol, a71, 159-167.
Breitenstein, O. and Diegner, B. (1986). Phys. Stat. Sol. a94, K21-K24.
Breitenstein, O. and Giling, J. (1987). Phys. Stat. Sol, a99, 215.
Breitenstein, O. and Heydenreich, J. (1983). J. Phys., 44, Colloque C4, 207-215.
Breitenstein, O. and Heydenreich, J. (1985). Scanning, 7, 273-289.
Breitenstein, O. and Pickenhain, R. (1985). Patent No. DD 200267 Bl, 601 N 27/22.
Chi, J.Y. and Gatos, H.C. (1979). J. Appl. Phys., 50, 3433.
Chubarenko, V.A., Rau, E.I. and Spivak, G.V. (1984). In Proc. 8th Europ. Congr. on
Electron Microscopy, Budapest, pp. 983-984.
Scanning deep level transient spectroscopy
371
Dozsa, L. and Toth, A.L. (1987). Proc. Int. Summer Inst. NDSP-2, Szeged, pp. 115-119.
Ferenczi, G. and Dozsa, L. (1982). Cryst. Res. Technoi, 16, 203-208.
Ferenczi, G , Boda, J. and Pavelka, T. (1986). Phys. Stat. Sol, a94, K119-K124.
Heiser, T , Mesli, A, Courcelle, E. and Siffert, P. (1988). J. Appl. Phys., 64, 4031-4040.
Heydenreich, J. and Breitenstein, O. (1986). J. Microsc. (London), 141, 129-142.
Inoue, N., Ikuta, K. and Wada, K. (1986). Proc. Int. Congr. Electron Microsc, Kyoto,
p. 401.
Lang, D.V. (1974). J. Appl. Phys., 45, 3023-3032.
Lang, D.V. and Logan, R.A. (1975). J. Electron Mat., 4, 1053-1066.
Lax, C.T., Forbes, L., Rosier, L.L. and Tasch, A.F. Jr. (1970). Sol. State Electron., 13,
759-788.
Miller, G.L., Ramirez, J.V. and Robinson, D.A.H. (1975). J. Appl. Phys., 46,2639-2644.
Miller, G.L., Lang, D.V. and Kimerling, L.C. (1977). Ann. Rev. Mater. Sci., 8, 377-448.
Mirachi, S., Peaker, A.R. and Hamilton, B. (1980). J. Phys. Lond. E, 13, 1055-1061.
Morimoto, J., Kida, T , Miki, Y. and Miyakawa, T. (1986). Appl. Phys. A , 39, 197-202.
Okushi, H. and Tokumura, Y. (1980). Jap. J. Appl. Phys., 19, L335-L338.
Petroff, P.M. (1983). In Proc. Micr. Electron, en Sci. des Materieux,
Bomhannes 1981,
pp. 311-326.
Petroff, P.M. and Lang, D.V. (1977). Appl. Phys. Lett., 31, 60-62.
Petroff, P.M., Lang, D.V., Strudel, J.L. and Logan, R.A. (1978). Scanning Electron
Microscopy, I, 325-332.
Petroff, P.M., Lang, D.V., Logan, R.A. and Johnston, W.D. (1979). Institute of Physics,
Conf. Ser. No. 46, 427-432.
Pons, D. (1984). J. Appl. Phys., 55, 3644-3657.
Sah, C.T., Forbes, L., Rosier, L.L. and Tasch, A.F. Jr. (1970). Sol. State Electron., 13,
759-788.
Shockley,'W. and Read, T. (1952). Phys. Rev., 87, 835-842.
Sporon-Fiedler, F. and Weber, E.R. (1986). Proc. SPIE Int. Soc. Opt. Eng., 623, 72.
Weyher, J.L. and van de Ven, J. (1983). J. Cryst. Growth, 63, 285.
Wilke, V. (1985). Scanning, 7, 88-96.
Woodham, R. and Booker, B.R. (1987). Microscopy of Semiconducting Materials, 1987;
Conf. Series No. 87, pp. 781-786.
Wosinski, T. and Breitenstein, O. (1986). Phys. Stat. Sol, a96, 311-315.
Yakushi, K., Kuroda, H., Hollmann, R. and Little, W.A. (1982). Rev. Sci. Instrum., 53,
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Yoshie, O. and Kamihara, M. (1985). Jap. J. Appl. Phys., 24, 431-440.
8 Cathodoluminescence Characterization
of Semiconductors
D.B. H O L T
Department
of Materials, Imperial College of Science
Prince Consort Road, London SW7 2BP, UK
and
Technology,
and
B.G. Y A C O B I
Microscience
USA
Research,
P.O. Box 67034,
Newton,
Massachusetts
List of symbols
*
8.1 Introduction
8.2 Luminescence phenomena
8.2.1 Luminescence mechanisms and centers
8.2.2 Recombination processes
8.3 Cathodoluminescence
8.3.1 Introduction
8.3.2 Generation of the CL signal and its dependence on excitation
conditions and materials properties
8.3.3 Interpretation of cathodoluminescence
8.3.4 Spatial resolution and the detection limit
8.3.5 Artifacts
8.4 Cathodoluminescence analysis techniques
8.4.1 Cathodoluminescence scanning electron microscopy . . . .
8.4.2 Cathodoluminescence scanning transmission electron microscopy
8.4.3 Non-scanning cathodoluminescence systems
8.5 Applications
8.5.1 Defect contrast studies
8.5.2 Time-resolved cathodoluminescence
8.5.3 Depth-resolved cathodoluminescence
Bibliography
References
SEM Microcharacterization of Semiconductors
ISBN 0-12-353855-6
02167,
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385
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419
Copyright © 1989 Academic Press Limited
All rights of reproduction in any form reserved
374
D . B . H o l t and B.G. Y a c o b i
List of s y m b o l s
D
E\, e
E ,V
d
b
b
f(A),f(R)
g
G
/b
L
L
An
N
D
K
S
S=
8
n
T
^rr» ^nr
8.1
st/L
diffusion coefficient
binding energies of the acceptor and d o n o r
electron beam energy and voltage
excitonic binding energy
absorption and reflection loss factors
the generation rate of excess carriers per unit volume
number of electron-hole pairs generated per incident beam
electron
electron beam current
carrier diffusion length
luminescence intensity
cathodoluminescence intensity
excess minority carrier density per unit volume
dislocation density
electron penetration range
surface recombination velocity
the reduced surface recombination
absorption coefficient
dielectric constant
radiative recombination efficiency (internal q u a n t u m efficiency)
reduced effective mass
minority carrier lifetime
radiative and non-radiative recombination lifetimes
Introduction
As outlined in this book, scanning electron microscopy (SEM) techniques are
well suited for the microcharacterization of semiconductors, since they
provide high spatial resolution and the simultaneous availability of a variety
of modes and forms of contrast. The cathodoluminescence (CL) and charge
collection modes constitute the optoelectronic microcharacterization capability of the S E M (or STEM). A variety of recent applications demonstrated
the great value of these modes in characterizing the electronic properties of
materials with a spatial resolution of 1 /im and less. CL, i.e. the emission of light
as the result of electron ("cathode ray") bombardment, offers a contactless and
relatively "non-destructive" method with high spatial resolution for microcharacterization of luminescent materials. Often an analysis is considered to
be non-destructive if the physical integrity of the material remains intact.
C a t h o d o l u m i n e s c e n c e c h a r a c t e r i z a t i o n of s e m i c o n d u c t o r s
375
However, electron irradiation may ionize or create defects and so alter
electronic properties of the material temporarily or permanently.
Cathodoluminscence analysis can be performed also in a relatively simple
high-vacuum chamber equipped with an electron gun and optical windows.
Although the absence of scanning capability will limit its applications, it will
still be very useful in depth-resolved studies of ion-implanted samples and
characterization of semiconductor interfaces. Non-destructive depth-resolved
cathodoluminescence studies are performed by varying the range of the
electron penetration, which is dependent on the electron beam energy, in order
to excite C L from different depths in the material. Moreover, simple "flood
illumination" electron b o m b a r d m e n t can produce large total C L intensities
enabling higher spectral resolution to be attained. F o r this reason, an S E M
intended for C L use should provide the largest possible maximum beam
current (1 juA at least) with a widely defocused spot size.
The mechanisms leading to the emission of light in a solid are similar for
different forms of the excitation energy. Cathodoluminescence and other
luminescence phenomena, such as photoluminescence (PL), for example, yield
similar results with some possible differences associated with the details of the
excitation of electron-hole pairs, for example in the generation rate and
volume excited. Electron beam excitation in general leads to the emission by
all the luminescence mechanisms present in the semiconductor. P L emission,
on the other hand, may strongly depend on the excitation photon energy,
which can provide additional important information. An advantage of CL, in
addition to the high spatial resolution, is its ability to obtain more detailed
depth-resolved information by varying the electron beam energy. An additional advantage of C L S E M analysis is the availability of complementary
information obtained from such S E M modes as, for example, electron beaminduced current (EBIC) and electron probe microanalysis (EPMA).
In recent years, the need for microelectronic characterization of inorganic
solids, and especially of semiconductors, has led to the development of the
quantitative capabilities of the electron microscopy techniques. Quantitative
interpretation of CL, however, is more difficult than in the case of the X-ray
microanalysis method, as it cannot be unified under a simple law. Characteristic X-rays are emitted due to electronic transitions between sharp, inner-core
levels. The lines, therefore, are narrow, characteristic of the particular chemical
element and are unaffected by the environment of the atom in the lattice. The
C L signal is formed by detecting photons of the ultraviolet, visible and near
infrared regions of the spectrum. These photons are emitted as the result of
electronic transitions between the conduction and valence bands and levels
lying in the b a n d g a p of the material. M a n y useful signals in these cases are due
to transitions which involve impurities and a variety of defects. Therefore,
there is no general rule which would serve to identify bands or lines in the C L
376
D . B . H o l t and B . G . Y a c o b i
spectrum. The intensity of emission depends on the concentrations not only of
the particular luminescence (radiative recombination) center but also of all the
competing recombination centers. The influence of defects, of the surface and
of various external perturbations, such as, for example, temperature, electric
field and stress, have to be taken into consideration in the analysis of the C L
signal. Thus, quantitative C L analysis is still limited due to of the lack of any
generally applicable theory for the wide variety of possible types of luminescence centers and radiative recombination mechanisms. It should also be
emphasized that, in addition to these problems, quantitative information on
defect-induced non-radiative processes is unavailable in spectroscopic C L
analysis. The nature of an impurity can best be determined by comparison
with luminescence data in the literature, and its concentration can best be
found by comparison with intentionally doped standards (provided no
additional factors, such as, for example, presence of non-radiative defects,
affect the luminescence signal). If no published data are available about the
observed emission band, an ab initio study must be carried out. The absence of
any general method of identification and the lack of any universally applicable
quantitative theory impose general limitations on developments of C L as an
analytical technique.
Effort spent on the development of the C L mode is motivated by its two
advantages. Firstly, in favorable cases, i.e. when an impurity is an efficient
recombination center and competing centers and self-absorption are absent,
the detection limit can be as low as 1 0 a t o m s / c m , which is about six orders
of magnitude lower than that of the X-ray mode. Secondly, in light-emitting
optoelectronic materials and devices, it is the emission properties that are of
practical importance.
The purpose of this chapter is to outline the basic principles and recent
applications of cathodoluminescence in the microcharacterization of semiconductors. These mainly include analyses of defects, interfaces and various
electronic properties of semiconductors.
1 5
8.2
8.2.1
3
Luminescence phenomena
L u m i n e s c e n c e m e c h a n i s m s a n d centers
In semiconductors light is emitted as the result of electronic transitions
between q u a n t u m mechanical states separated by energy levels of less than
1 eV to more than several electronvolts. Luminescence emission spectra can be
divided between (i) intrinsic, fundamental or edge emission and (ii) extrinsic,
activated or characteristic luminescence. Intrinsic luminescence, which appears at ambient temperatures as a near Gaussian-shaped band of energies
Cathodoluminescence characterization of semiconductors
377
with its intensity peak at a p h o t o n energy hv = £ , is due to recombination of
electrons and holes across the fundamental energy gap; so it is an "intrinsic"
property of the material. (The recombination may occur via the formation of
excitons but their binding energies are generally much less than kT at room
temperature.) This edge emission band (arising from essentially conductionband to valence-band transitions) is produced by the inverse of the mechanism
responsible for the fundamental absorption edge. Thus, any change in E with
an external perturbation (for example, temperature), or with a change in
crystal structure in polymorphic materials, or with high doping concentrations, can be monitored by measuring hv (Davidson, 1977; D a t t a et al,
1977; Holt and Datta, 1980; Warwick and Booker, 1983).
Energy and m o m e n t u m (hk) must be conserved during the electronic
transitions. When the maximum of the valence band and the minimum of the
conduction band occur at the same value of the wavevector k (Fig. 8.1a),
transitions are direct, or "vertical", and the material is a direct gap
semiconductor (for example, GaAs, I n P , CdS). In materials with a direct gap,
the most likely transitions are across the minimum energy gap, between the
most probably filled states at the minimum of the conduction band and the
states most likely to be unoccupied at the maximum of the valence band.
Radiative recombination between electrons and holes is likely in such
transitions. If the band extrema d o not occur at the same wavevector k
(Fig. 8.1b), transitions are indirect. T o conserve m o m e n t u m in such an indirect
gap material (for example, Si, Ge, GaP), p h o n o n participation is required.
Thus, the recombination of electron-hole pairs must be accompanied by the
simultaneous emission of a photon and a phonon. The probability of such a
g
p
g
p
Conduction
(a)
(b)
Fig. 8.1 The energy transitions in direct (a) and indirect (b) gap semiconductors
between initial states E and final states E . For indirect transitions (b) the participation
of a phonon (£ ) is required.
{
ph
f
378
D . B . Holt and B . G . Y a c o b i
T a b l e 8.1 Values of bandgaps and types of some semiconductors (after
Pankove, 1971 and Sze, 1981)
Ge
Si
InP
GaAs
AlAs
GaP
A1P
GaN
CdTe
CdSe
ZnTe
CdS
ZnSe
ZnO
ZnS(ZB)*
ZnS (W)t
Energy Gap
Eg
(OK)
(eV)
E (300K)
0.74
1.17
1.42
1.52
2.24
2.34
2.50
3.50
1.60
1.85
2.39
2.56
2.80
3.44
3.84
3.91
0.66
1.12
1.35
1.42
2.16
2.26
2.43
3.36
1.50
1.74
2.28
2.42
2.58
3.35
3.68
3.75
g
Type
(eV)
Indirect
Indirect
Direct
Direct
Indirect
Indirect
Indirect
Direct
Direct
Direct
Direct
Direct
Direct
Direct
Direct
Direct
*ZB = zinc blende.
= wurtzite.
process is significantly lower as compared with direct transitions. Therefore,
fundamental emission in indirect gap semiconductors is relatively weak,
especially when compared with that due to impurities or defects. Bandgap
values and types of fundamental transitions for some semiconductors are
given in Table 8.1.
The emission spectra (in both direct and indirect semiconductors), which
depend on the presence of impurities, are of "extrinsic" nature. C L emission
bands in these cases are "activated" by impurity atoms or other defects and the
emission features are "characteristic" of the particular activator. Such
radiation can be made much more intense than intrinsic C L at ambient
temperatures even in direct gap materials. This is the aim of phosphor
technology and it is the reason for regarding the desired "activated" emission
as characteristic.
A simplified set of radiative transitions that lead to emission in semiconductors containing impurities is given in Fig. 8.2. General properties of
these transitions will now be discussed briefly. Process 1 is an intraband
transition: an electron excited well above the conduction-band edge dribbles
C a t h o d o l u m i n e s c e n c e c h a r a c t e r i z a t i o n of s e m i c o n d u c t o r s
379
F i g . 8.2 Schematic diagram of radiative transitions between the conduction band
(E ) the valence band (E ) and exciton (E ), donor (E ) and acceptor (E ) levels in a
semiconductor.
c
v
E
D
A
down and reaches thermal equilibrium with the lattice. This thermalization
process may lead to (i) phonon-assisted p h o t o n emission, or (ii) more likely, the
emission of p h o n o n s only. Process 2 is an interband transition: "intrinsic" CL;
recombination of electrons from the conduction b a n d and holes in the valence
band. Process 3 is the exciton decay observable at low temperatures; both free
excitons and excitons b o u n d to an impurity may undergo such transitions.
Processes 4, 5 and 6 arise from transitions which start a n d / o r finish on
localized states of impurities (e.g. donors and acceptors) in the gap; these
produce "extrinsic" C L (Table 8.2). Similar transitions from deep d o n o r and
deep acceptor levels can also lead to recombination emission with p h o t o n
T a b l e 8.2 Ionization energies of some
impurities in GaAs at liquid helium
temperatures (after Casey and Trumbore,
1970 and Ashen et al, 1975).
Donors
(meV)
Si
Ge
S
Se
Te
Sn
C
Acceptors
(meV)
5.8
6.1
6.1
5.9
5.8
6.0
6.0
C
Si
Ge
Zn
Be
Mg
Cd
Sn
26.0
35.0
41.0
31.0
28.0
29.0
35.0
171.0
380
D . B . Holt and B.G. Y a c o b i
energies well below the bandgap. Transition 7 is the radiative de-excitation of
a center such as a rare earth ion.
Recombination of electron-hole pairs may occur via non-radiative processes as well, as is the case, for example, for process 1 in Fig. 8.2. Examples of
non-radiative recombination processes are: multiple phonon emission, i.e.
direct conversion of the energy of an electron to heat; the Auger effect, in which
the energy of an electron transition is absorbed by another electron, which is
raised to a higher energy state in the conduction band, with subsequent
emission of the electron from the semiconductor or dissipation of its energy
through emission of phonons (thermalization) (Pankove et al, 1971); and
recombination due to surface states and defects.
In the case of a degenerately doped semiconductor, in which the impurity
concentration exceeds a certain level, the energy levels broaden out into a
band. If such a band, for example, is near the top of the valence band, it might
even overlap with valence states. The energy gap in such cases depends on the
doping concentration and the photon energy of the previously "intrinsic"
emission will depend on the concentration of impurities (see, for example,
Pankove, 1971).
In principle, the shapes of the absorption and emission bands of luminescent
point defects can be obtained from configuration coordinate models (for
detailed accounts see Klick and Schulman, 1957 and M a r k h a m , 1959). The
quantum-mechanical configuration coordinate theory of phonon-coupled
emission predicts, assuming the harmonic approximation for lattice vibrations, a Gaussian emission band. Experimental studies, however, have
indicated that the shapes of both the intrinsic (edge emission) and extrinsic
emission bands in various materials (Casey and Kaiser, 1967; Yacobi et al,
1977; D a t t a et al, 1979) are not entirely of Gaussian form. At elevated
temperatures (above 77 K) emission bands generally have an asymmetric
Gaussian form around the peak, followed on either side by low- and highenergy exponential tails. The experimentally derived low-energy exponential
tail of the fundamental edge emission band in GaAs, as well as other CL
emission parameters such as intensity, peak position and half-width have been
correlated with the impurity concentration (Cusano, 1964; Pankove, 1966;
Casey and Kaiser, 1967). These correlations provide a method of carrier
concentration measurement in a semiconductor.
In order to explain the shapes of the emission bands, M a h r (1962,1963) and
Toyozawa (1959) proposed a two-mode model for coupling of the electronic
transitions to the lattice vibrations in ionic crystals. Both linear and quadratic
modes are assumed to interact with the electronic transitions, and this leads to
both a Gaussian shape around the maximum (linear interaction) and an
exponential function at the edge (quadratic interaction). Keil (1966) later
Cathodoluminescence characterization of semiconductors
381
presented q u a n t u m - m e c h a n i c a l modifications to the semiclassical model
proposed by M a h r a n d Toyozawa.
In some cases the wide luminescence bands which appear to deviate from a
Gaussian shape, are, in fact, composed of several Gaussian bands associated
with different transitions (Koschek a n d Kubalek, 1983). Thus, a knowledge of
band shape makes possible a deconvolution procedure for luminescence
bands, especially at ambient temperatures, a n d so is of great importance.
The low-energy exponential tail in the edge emission band corresponds to a
similar exponential dependence in the absorption edge that is observable in a
wide variety of semiconductors. D o w a n d Redfield (1972) explained the
exponential form of absorption edges in terms of internal electric field assisted
broadening of the lowest excitonic state. The sources of these internal
microfields can vary from material t o material and may involve phonons (LO
and LA), ionized impurities, dislocations, surfaces a n d other defects (Dow and
Redfield, 1972).
The relation between absorption and emission can be derived from the
principle of detailed balance (van Roosbroeck a n d Shockley, 1954), which
enables one to calculate the shape of the emission band from the experimentally determined values of the absorption coefficient. The relation between the
(8|BOS 8A|;B|8J) ABjeue IUBJPBH
Corrected
for
absorption
Emergent
.5
1.7
1.9
W a v e l e n g t h (/ym)
2.1
F i g . 8.3 Observed luminescence in germanium (solid line), and luminescence
obtained by correcting for self-absorption (dashed line). (After Haynes, 1955.)
382
D . B . H o l t and B . G . Y a c o b i
absorption coefficient oc(hv) and the equilibrium emission intensity L(hv) at a
photon energy hv was found to be
L(hv) = oc(hv)B(hv) [exp(hv/kT)
2
- 1]"
(8.1)
where B = &nn /h c
contains the refractive index n, the speed of light c and
Planck's constant h.
The effect of self-absorption on the shape of the luminescence spectrum
should be taken into consideration (see, for example, Pankove, 1971 and Holt,
1974). Figure 8.3 shows the effect of a correction for the absorption performed
for Ge (Haynes, 1955). It is clear that self-absorption virtually eliminates the
shorter wavelength, direct gap recombination radiation leaving only the
longer wavelength, indirect gap recombination band to emerge.
As was mentioned earlier, the information in the broad luminescence bands
observed above liquid nitrogen temperatures is difficult to interpret. At liquid
helium temperatures, however, as the thermal broadening effects are minimized, C L spectra in general become both much sharper and more intense.
This leads to an improved signal-to-noise ratio and to a more unambiguous
identification of luminescence centers (see, for example, Fig. 8.4).
The "edge" (near bandgap) emission (Fig. 8.4a) at liquid helium temperatures
is often resolved into emission lines (Fig. 8.4b). These can be due to, for example,
excitons, free carrier to d o n o r or acceptor transitions and their phonon
replicas (or sidebands), and/or d o n o r - a c c e p t o r pair lines.
Two models of excitons have been considered. O n e is a strongly bound,
closely localized exciton represented by the Frenkel model, and the other is a
weakly bound exciton of the W a n n i e r - M o t t type with wave function spread
over many interatomic distances. W a n n i e r - M o t t excitons are usually present
in materials with high dielectric constants. At and below liquid nitrogen
temperatures these excitonic lines may be resolved from the lower energy side
of the bandgap emission. The energy levels can be described by a hydrogenlike expression:
2
3
2
(8.2)
where n = 1,2,3,... is the principal q u a n t u m number and E is the excitonic
binding energy, E = iie*/2h e , containing the reduced effective mass
=
e h / ( e + h)
d the dielectric constant e. Frenkel and W a n n i e r - M o t t
excitons are two limiting models differing in the degree of pair separation.
Intermediate separations of electrons and holes are also possible. A detailed
discussion of these intermediate cases, as well as the ranges of validity of
Frenkel and W a n n i e r - M o t t exciton models and the proper choice of the
dielectric constant is given by Knox (1963). The exciton emission line shapes
can be analysed using two limits of phonon-broadened line. F o r small values
of the e x c i t o n - p h o n o n coupling constant a quasi-Lorentzian shape descripB
2
B
m
m
m
m
a n
2
C d S R T 30 kV
o
400 r
(a)
o o o o
PHOTON COUNT PER SEC (x 1C
~
320
400
480
560
640
720
800
W A V E L E N G T H (nm)
o
CdS
L H E30 kV
(b)
o o o o o
PHOTON COUNT PER SEC (x
2
10 )
~
320
1400
480
560
640
720
800
W A V E L E N G T H (nm)
F i g . 8.4 Uncorrected count rate spectra from a CdS crystal (a) at room temperature
and (b) at liquid helium temperature. There is a change of scale between the two. The
near bandgap emission in (b) has a peak count rate about 4.5 times that of the
fundamental band in (a) and is resolved into a series of narrow lines, known as the "edge
emission". The broad impurity peak, on the right, in contrast, has the same peak count
rate and full width at half maximum at both temperatures. (After Holt, 1981.)
384
D . B . H o l t and B . G . Y a c o b i
tion is valid, while for larger coupling constants the line is of Gaussian form
(Knox, 1983).
At low temperatures, when the p h o n o n occupation number is close to zero,
one can also observe p h o n o n replicas (or p h o n o n sidebands). These are series
of lines, which are separated by a photon energy hco (see, for example, Dean,
1983).
Series of emission lines can also arise from d o n o r - a c c e p t o r pairs. An
electron captured by a donor (which is positively charged when ionized)
recombines with a hole similarly captured by an acceptor. The energy of the
emitted photons is
hv(r) = E -{E
g
+ E ) + e /er
2
A
D
(8.3)
where E and E are the binding energies of the acceptor and donor,
respectively and e is the dielectric constant. The last term arises from the
coulombic interaction of the carriers and depends on the pair separation r
which can only have values corresponding to integral numbers of interatomic
spacings. Thus, a fine structure, consisting of sharp emission lines, is expected.
Two extreme cases are the widely separated (or distant) d o n o r - a c c e p t o r pairs
and associated d o n o r - a c c e p t o r pairs. The number of distant pairs is large and
for these pairs the last term in eqn (8.3) is small. Consequently, a broad,
unresolved (distant) d o n o r - a c c e p t o r pair (DA or DAP) band is what is seen in
SEM C L (e.g. Myhajlenko, 1984; Wakefield et al, 1984b). This is because the
low total intensity characteristic of S E M C L limits the spectral resolution to
values that are modest by P L standards as yet. F o r the distant pair case the
static dielectric constant would be used, while for the associated pair case, it is
the optical dielectric constant. This equation does not contain the van der
Waals term, which may become important for small r (for more details, see, for
example, Dean, 1966; Pankove, 1971; Bebb and Williams, 1972). A characteristic feature of d o n o r - a c c e p t o r recombination is the shift of the peak as a
function of the excitation intensity. This follows from the reciprocal dependence of the peak energy hv on the pair separation r and the reduction in
the transition probability with increasing r. At higher excitation intensities,
widely separated pairs will be saturated because of the lower transition
probability, and a larger portion of pairs with smaller r are excited and decay
radiatively because of their higher transition probability. Therefore, a relative
increase in the intensity due to pair transitions with smaller r is expected as the
excitation intensity increases. This leads to a shift of the peak to higher
energies. D o n o r - a c c e p t o r pair recombination emission also occurs near the
band edge. At very low temperatures, however, very large numbers of sharp
lines are observable, at least in P L studies, which also distinguishes this
emission from other mechanisms. This fine structure can be resolved for pair
separations r up to about 50 lattice spacings.
A
D
Cathodoluminescence characterization of semiconductors
385
The results of low temperature P L studies of a wide variety of luminescence
centers in semiconductors are available in the literature a n d the data can help
in the identification of emitting centers.
8.2.2
R e c o m b i n a t i o n processes
The carriers generated in the semiconductor will undergo diffusion, followed
by recombination including that which gives rise to C L emission. Thus,
generation, diffusion and recombination are important for describing luminescence phenomena. The diffusion of the stationary excess minority carriers for a
continuous irradiation can be treated in terms of the differential equation of
continuity. F o r electrons in p-type semiconductors this can be written
DV {An)-
— + g(r) = 0
2
T
(8.4)
where D is the diffusion coefficient, An is the excess minority carrier density per
unit volume, x is the minority carrier lifetime, and g(r) is the generation rate of
excess carriers per unit volume. This equation is valid under the conditions
that T is independent of An and that the motion of excess carriers is purely
diffusive. T h e former condition is satisfied if An is small compared to the
majority carrier density p (for p-type material); this low injection condition
can usually be satisfied by using low electron beam currents. The condition
that the motion of excess carriers is purely diffusive is valid for sample regions
without depletion zones or applied fields.
Recombination centers with energy levels in the gap of a semiconductor are
radiative or non-radiative depending on whether they lead to the emission of a
p h o t o n or not. These centers are characterized by a rate of combination
R cc T~ \ where T is a recombination time. The diffusion length is related to the
lifetime by L = ( D T ) , where D is the diffusion coefficient. When competitive
radiative and non-radiative centers are both present, the observable lifetime is
given by
0
1 / 2
1/T=l/T +1/T
r r
N R
(8.5)
where r a n d r are the radiative a n d non-radiative recombination lifetimes,
respectively. Here i , in general, is the resultant of different non-radiative
recombination processes ( T " = £ - T ~ ) . The radiative recombination efficiency (or internal q u a n t u m efficiency) n, which is defined as the ratio of the
radiative recombination rate R to the total recombination rate R, is (using
eqn (8.5)):
r r
n r
n r
1
1
I
F
rr
(8.6)
386
D . B . H o l t and B . G . Y a c o b i
Hence *7 = T / i when, as is often the case, r » T . For a material that
contains only one type of radiative and one type of non-radiative recombination center one can write, using x = (N<rv)~ :
n r
r r
r r
n r
1
(8.7)
where N and N
are the densities of the radiative and non-radiative
recombination centers, respectively; o and a are the radiative and nonradiative capture cross sections and v is the carrier thermal velocity. The rate of
C L emission is proportional to rj, and eqn (8.7) indicates that in the observed
CL intensity we cannot distinguish between radiative and non-radiative
processes in a quantitative manner. It is possible to ensure that JV > N in
some cases, but a is usually much larger than a .
The major electron-hole recombination pathways between the conduction
and valence bands involve donor and/or acceptor levels, recombination via
deep level traps and recombination at the surface. The last two are expected to
be non-radiative at any rate in the near bandgap spectral region. Recombination through a single dominant type of trap can be described by H a l l Shockley-Read recombination statistics (Hall, 1952; Shockley and Read,
1952), which can be applied to a wide variety of conditions. F r o m H a l l Shockley-Read statistics it follows that deeper traps act as efficient recombination centers. In a simple case, when one radiative recombination center is
dominant, the luminescence efficiency will depend on the ratio of the radiative
recombination rate to the non-radiative recombination rate (eqn (8.7)). For
cases in which a distribution of traps is present, the statistics described by Rose
(1963) should be considered. More recent work by Simmons and Taylor (1971)
presents statistics for an arbitrary distribution of both the traps and trap cross
sections.
As mentioned above, one of the basic difficulties involved in luminescence
characterization is the lack of information on the competing non-radiative
processes present in the material. The most widely used technique, which
complements luminescence spectroscopy for the assessment of non-radiative
levels, is deep level transient spectroscopy (DLTS) (Lang, 1974), which is based
on the capture and thermal release of carriers at traps. The application of an
analogous SEM technique, scanning deep level transient spectroscopy
(SDLTS) was developed by Petroff et al. (1978) for determining both the
energy levels and spatial distribution of deep states in semiconductors. While a
voltage bias pulse is used to fill the traps in the D L T S technique, an electron
beam injection pulse is employed in the SDLTS method. Recently, the
introduction of a more sensitive detector (Breitenstein, 1982) has made the
technique more widely applicable (Heydenreich and Breitenstein, 1985). (For
details, see Chapter 7.)
rr
nr
rx
nT
rr
nr
rr
m
Cathodoluminescence characterization of semiconductors
8.3
387
Cathodoluminescence
8.3.1
Introduction
The mechanisms leading to p h o t o n emission in semiconductors are similar for
different types of excitation energy. So, cathodoluminescence a n d other
luminescence phenomena, for example photoluminescence, yield similar
results. However, differences associated with the details of the excitation
processes may arise. Electron beam excitation in general leads to emission by
all the luminescence mechanisms present in the semiconductor. P L emission
may strongly depend on the excitation p h o t o n energy, which can be used for
selective excitation of particular emission processes. C L analysis of materials,
on the other hand, can provide depth-resolved information by varying the
electron beam energy.
The C L mode of the S E M has attracted great interest in recent years (see, for
example, recent reviews by Holt, 1974; Balk a n d Kubalek, 1977; Davidson,
1977; Holt and Datta, 1980; Pfefferkorn et a/., 1980; Davidson and Dimitriadis, 1980; Booker, 1981; Hastenrath and Kubalek, 1982; Lohnert a n d
Kubalek, 1983; Wittry, 1984; Holt a n d Saba, 1985; Yacobi and Holt, 1986). A
discussion of C L S E M techniques and the characterization of semiconductors
using C L S E M will be provided in subsequent sections. In this section we will
discuss the basic principles underlying the interpretation of C L processes.
8.3.2 Generation of t h e CL signal a n d its d e p e n d e n c e o n excitation
c o n d i t i o n s a n d materials properties
The analysis of the electron energy dissipation a n d generation of carriers in
the solid is of great importance. This subject was reviewed in detail in
Chapter 2. T o summarize, as the result of the scattering events within the
material, the original trajectories of the electrons are randomized, with the
range of the electron penetration being a function of the electron beam energy
E , R = (k/p)El, where p is the density of the material; k depends on the
atomic number of the material and is also a function of energy; a depends
on the atomic number and the electron beam energy E (see, for example,
Everhart and Hoff, 1971). The most important method of dealing with these
processes a n d computing S E M signals is that of M o n t e Carlo simulation
(see Chapter 2). This h a s n o t been applied t o C L , however. Alternatively,
analytical approximations can be used as follows. O n e can estimate the
so-called generation volume (or excitation volume) in the material. According
to Everhart a n d Hoff (1971), K = (0.0398/p)£^ ( um), where p is in g / c m
and E is in keV. This result was derived for the electron energy range of
h
e
h
75
e
h
3
i
388
D . B . Holt and B . G . Y a c o b i
5 - 2 5 k e V and atomic numbers 1 0 < Z < 1 5 . A more general expression
derived by Kanaya and O k a y a m a (1972) was found to agree well with
experimental results in a wider range of atomic numbers (see, for example,
Goldstein et al, 1981). The range according to K a n a y a and O k a y a m a is
(8.8)
where E is in keV, A is the atomic weight in g/mol, p is in g/cm , and Z is the
atomic number. The shape of the generation volume depends on the atomic
number, varying from a nearly pear-shaped volume for a low atomic number
material, to a spherical shape for 1 5 < Z < 4 0 , to hemispherical for larger
atomic numbers.
The generation factor, i.e. the number of electron-hole pairs generated per
incident beam electron is given by:
3
b
(8.9)
where E is the electron beam energy, e is the ionization energy (i.e. the energy
required for the formation of an electron-hole pair), and y represents the
fractional electron beam energy loss due to the backscattered electrons. (The
Monte Carlo method, in effect, computes y for any particular case.) The local
generation rate has been determined experimentally for silicon by Everhart
and Hoff (1971), who proposed a universal depth-dose function g(z). This
function, shown for different electron beam energies in Fig. 8.5, represents the
number of electron-hole pairs generated by one electron of energy E per unit
depth and per unit time.
In order to analyse the generation of the C L signal, we need to know the
excess minority carrier concentration An. The solution of eqn (8.4) for an
arbitrary generation function presents a challenging problem (Lohnert and
Kubalek, 1983, 1984), since no analytical expression for this function is
available. The solution of the continuity equation can be greatly simplified by
considering a point source generation function, or sphere of uniform
generation. F o r a spherically symmetric distribution and far from a point
source, the solution of the continuity equation is:
h
{
An = const. e x p ( - r/L)/r
(8.10)
where L = J D T is the minority carrier diffusion length. The depth distribution
of An(z) can be obtained by rewriting this solution and assuming that the total
number of carriers generated per second is Glje (where I is the electron beam
b
Cathodoluminescence characterization of semiconductors
1
1
Si
AlOkeV
3
g(z),(Pairs//im><10 )
1
389
—
120keV
A
V 3 0 keV
\
\
1
15
10
5
Penetration depth {jjm)
F i g . 8.5 The depth-dose curves for Si. These curves are calculated using a universal
depth-dose function g(z) which represents the number of electron-hole pairs generated
by one electron of energy E per unit depth and per unit time. (After Everhart and Hoff,
1971.)
current and e is the electronic charge):
(8.11)
where f is a radial coordinate in the plane of the layer, r = £ + z . Assuming
the C L intensity is proportional to the excess carrier concentration An (this
can be verified by measuring the dependence of the C L intensity on I ), which
is valid for low excitation conditions, the luminescence intensity due to
radiative recombination in a layer of thickness dz at a depth z is:
2
2
2
h
(8.12)
The actual n u m b e r of p h o t o n s generated per second at a depth z can be
derived noting that L = Dx a n d rj = i / T
2
r r
(8.13)
390
D . B . Holt a n d B . G . Y a c o b i
where f and f are factors which account for the fact that not all the photons
generated in the semiconductor are able to leave through its surface. The
absorption loss factor, f , arises from a decrease in intensity of the form
exp (— ad), where a is the absorption coefficient and d is the length of the
photon path in the interior of the material; this correction factor can be
shown (Holt, 1974) to be / = (l + a L ) . The reflection processes at the
semiconductor/vacuum interface, characterized by the total reflection of a
portion of photons, can be described (Reimer, 1985) as
A
R
A
_ 1
A
(8.14)
where n is the refractive index, which varies between 2 and 4 for typical
semiconductors (see Table 8.3). F o r example, for n = 3, / ^ 2% i.e. the C L
intensity can be significantly reduced by internal reflection losses. It is
important to know what happens to the major part of the C L that is totally
internally reflected. Is it lost by absorption, or does it emerge to be detected
after repeated reflections (and the absorption of the higher photon energy
components)? In the latter case, "ghost peaks" may be formed in the emission
spectrum. Precautions must then be taken to prevent the detection of multiply
reflected C L (Warwick and Booker, 1983).
It should be emphasized that, in addition to these loss mechanisms, the
observed luminescence efficiency varies with such factors as temperature, the
presence of defects (e.g. dislocations), particular dopants and their concentrations, and specifics of the recombination process (e.g. whether it is a
monomolecular or bimolecular process). The necessity to account for these
factors makes the use of C L intensity as a quantitative characterization tool
R
difficult.
Non-radiative surface recombination is an additional loss mechanism of
great importance, especially for materials like GaAs. This effect, however, can
T a b l e 8.3 Refractive indexes of some
semiconductors (after Pankove, 1971).
n
Si
InP
GaAs
GaP
CdTe
CdS
ZnO
ZnS
3.44
3.37
3.40
3.37
2.75
2.50
2.02
2.40
C a t h o d o l u m i n e s c e n c e c h a r a c t e r i z a t i o n of s e m i c o n d u c t o r s
391
be minimized by increasing the electron beam voltage V to produce a greater
electron penetration range. Analytically, surface recombination can be
expressed by the appropriate boundary condition for diffusion to the surface:
h
sAn = D
(8.15)
where s is the surface recombination velocity (in units of cm/s). The fraction of
minority carriers lost by surface recombination for a point source was derived
by Van Roosbroeck (1955) for the one-dimensional case as:
An =-
exp(-z /L)g(z )dz
s
s
(8.16)
s
where S = sz/L is the reduced surface recombination velocity and g(z ) is the
source depth distribution of excess carriers per unit depth. Equation (8.16)
indicates that the loss due to surface recombination increases with S/(S + 1)
and decreases as exp( — zJL). In other words, the loss due to surface
recombination will decrease if the generation range is increased and/or the
diffusion length is decreased.
In general, the brightness dependence of C L on the electron beam current
and voltage can be described as L = f{I )(V — V ) , where V is the "dead
voltage" and n may vary as 1 ^ n < 2. Naturally, this relationship is of great
importance for C L phosphor applications, and many reports on phosphors
were published. However, only a few similar studies on semiconductors have
been reported.
Early analytical models of C L in semiconductors were provided by Kyser
and Wittry (1964), Wittry and Kyser (1966, 1967) and Rao-Sahib and Wittry
(1969). F o r the case of direct, intrinsic recombination in GaAs, Kyser and
Wittry (1964) provided a description of the recombination process as a
function of excitation conditions and the main conclusions are as follows. The
C L intensity is proportional to the excess carrier generation rate g {gocI V ).
F o r constant V , the dependence of C L intensity on the electron beam current
may shed some light on the dominant type of transition. As discussed earlier,
L is proportional to gT (z + T ) , where g = GIJe
F r o m the W i t t r y Kyser model it follows that for T « T , when radiative recombination is
dominant, the C L intensity should be proportional to the beam current only.
F o r t « t , when non-radiative recombination is dominant, low and high
excitation cases should be considered. In the former case the C L intensity is
proportional to the equilibrium carrier concentration rc , while at higher
excitation levels the C L is proportional to ll and independent of n (assuming
that r is constant). In general, however, C L intensity may depend on g ,
where m ^ 1. As pointed out by Wittry and Kyser (1967), if m does not remain
constant due to changes in the occupation of recombination centers, a different
s
n
C L
h
0
0
h
h
h
_ 1
C L
nT
TT
r r
n r
v
n r
n r
r r
0
0
m
n r
D . B . H o l t and B . G . Y a c o b i
392
treatment has to be developed. T o the best of our knowledge this has not been
done yet.
The dependence of the C L intensity on the electron beam voltage was
calculated by Wittry and Kyser (1966,1967), who concluded that the electron
beam voltage dependence of the C L could be explained by invoking a "dead
layer" of thickness d at the surface. This layer, where radiative recombination
is reduced, was interpreted as being due to the existence of a space charge
depletion region, which is caused by the pinning of the Fermi level by surface
states. By assuming that only non-radiative recombination occurs in the "dead
layer", and noting that the luminescence intensity is proportional to the net
excess carrier concentration, the C L efficiency in this case can be written as
(neglecting absorption):
g(z )dz
*7CL =
s
s
(8.17)
These results calculated by Wittry and Kyser (1967) for a Gaussian
approximation of g(z ) are shown in Fig. 8.6, assuming no "dead layer"
(Fig. 8.6a) and a "dead layer" of thickness d = 0.1L (Fig. 8.6b), as a function of
the reduced electron range R/L (absorption is not included). These plots
indicate that for C L excitation, a threshold electron beam energy would be
required in order to penetrate the "dead layer". Experimental measurements
(Wittry and Kyser, 1967) for electron beam voltages in the range between 5 and
50 kV were fitted to this model in order to obtain values for the diffusion length
L, the reduced surface recombination velocity 5, and the reduced "dead layer"
depth D/L. However, as they remark, caution must be exercised in this type of
fitting since equally good agreement can be obtained for various choices of
these parameters.
The condition of linear dependence of L Q on I is not always valid. In p-type
GaAs, for example, the superlinear dependence was observed (Rao-Sahib and
Wittry, 1969), i.e. L Q OC J£ (1 ^ n ^ 2). The analysis outlined above would not
be applicable in this case. This problem was treated by Rao-Sahib and Wittry
(1969) who modified both the theoretical curves and the experimental method.
Thus, using the method of voltage dependence of C L with a defocused electron
beam, values of diffusion lengths for p-type GaAs were obtained.
The temperature dependence of the C L intensity in direct gap semiconductors was analysed by Jones et al (1973) by developing a theoretical
model based on the Van Roosbroeck-Shockley theory. Thus, the temperature
variation of C L intensity was estimated with assumptions related to the
temperature dependence of the absorption coefficient, diffusion length and
minority carrier lifetime. G o o d agreement between the experimental observations and theoretical calculations was obtained for GaAs (Jones et al, 1973).
In a recent analysis of recombination for materials like GaAs, in which
s
L
L
H
393
Relative intensity
Relative intensity
C a t h o d o l u m i n e s c e n c e c h a r a c t e r i z a t i o n of s e m i c o n d u c t o r s
R/L
-
F i g . 8.6 Relative CL intensity for n-type GaAs as a function of the reduced electron
range R/L and reduced surface recombination velocity 5, (a) assuming no "dead layer"
and (b) assuming a "dead layer" of thickness d = 0AL. (After Wittry and Kyser, 1967.)
^ T , it was also shown that the effect of re-absorbed recombination
radiation (RRR) has to be taken into consideration (Von Roos, 1983) for a
material with high doping levels. This effect, i.e. repeated emission and
absorption in the bulk of the semiconductor, will essentially diminish the
contribution due to the radiative recombination process and the total
recombination rate will depend on t only.
i
r r
n r
n r
394
8.3.3
D.B. Holt and B.G. Yacobi
Interpretation of
cathodoluminescence
As mentioned earlier, n o unified interpretation of C L in terms of a simple law is
possible. The influence of defects, of the surface and of various external
perturbations (such as temperature, electric field or stress) also have to be
taken into consideration in the analysis of C L spectra. F o r example, the
luminescence intensity may depend strongly on dislocation densities; thus, in
order to compare luminescence intensities, knowledge of the defect concentrations in each case may become essential. Although it is possible to
estimate the dislocation densities from C L images, there is still a need to
determine such quantities as, for example, the recombination cross sections of
both the radiative and non-radiative centers and the concentration of nonradiative centers as well. In simple systems, with well-characterized centers, it
would be feasible to account for these factors. This would become realistic with
the refinement and application of such techniques as, for example, timeresolved cathodoluminescence (Steckenborn et al, 1981a, b; Bimberg et al,
1985a, b, 1986). Using the latter one can determine such important properties
as the combination capture cross sections for charge carriers of ionized donors
and acceptors. But even in the most favorable cases, one must consider nonradiative recombination channels as well. Using carefully characterized
standards would appear a more feasible and desirable approach for quantitative C L analysis. But even in this case one should also take account of the effect
of defects on the luminescence efficiency of the material. F o r example, the effect
of dislocations on the luminescence efficiency of an optoelectronic device was
considered by Roedel et al (1977), who correlated the luminescence efficiency
t] with the dislocation density N as rj/t] = 1/(1 + Lln N /4),
where t] is the
efficiency without dislocations (see Fig. 8.7). Thus, in any quantitative
analysis of luminescence intensities it is important to know the defect
densities.
3
D
0
D
0
The information in the peak of the fundamental emission or edge emission
band ("intrinsic" C L at ambient temperatures) is relatively easy to interpret
because hv is approx. £ a n d the variation of E with various materials
parameters and external perturbations is comparatively well understood.
However, the information in the broad "extrinsic" C L bands (which arise from
transitions that start and/or finish on localized states of impurities in the gap)
observed above liquid nitrogen temperatures is difficult to interpret because of
the lack of any generally applicable theory for the wide variety of possible
types of luminescence centers and radiative recombination mechanisms.
Experimentally, the thermal broadening effect can be minimized by using
liquid helium temperatures at which C L spectra will generally consist of a
series of sharp lines corresponding to transitions between well-defined energy
levels. These processes can then be identified with particular C L emission
g
g
395
••J.x
•
• \
• • \
o
V/V
Relative efficiency
7
o
Cathodoluminescence characterization of semiconductors
Calculated
values
Experimental
values
•
10
L_
10<
J
Dislocation density
10
10
E
€
(cm )
2
F i g . 8.7 Electroluminescent efficiency as a function of dislocation density for
GaAs light-emitting diodes. The dashed line represents the calculated efficiency
using rj/rj = 1/(1 + L n N /4).
(After Roedel et al, 1977.)
2
0
3
0
d
phenomena, for example, excitonic lines, p h o n o n replicas and d o n o r - a c c e p t o r
pair lines.
It should be emphasized that, compared to E P M A analysis, quantitative C L
is in its infancy. The major limitations in quantitative C L analysis include the
difficulties involved in accounting for non-radiative processes and the various
factors that affect the C L intensity. A wide variety of theoretical models
describing the luminescence processes a n d centers are reviewed in the
luminescence literature. However, n o universal theoretical approach is
available to describe the luminescence centers, a n d thus n o unified theory of
quantitative C L analysis can be presented a n d correlated with experimental
data at this juncture. T h e difficulties involved in the quantitative analysis of
C L intensities can be circumvented by C L band-shape analysis (Cusano, 1964;
Pankove, 1966; Casey a n d Kaiser, 1967).
Despite all the difficulties involved in accounting for all the factors that
affect the C L intensity, one has to begin somewhere. Warwick (1987) proposed the so-called MAS-corrections (in analogy with the ZAF-correction
procedure for X-rays). M A S stands for Mixed level injection, Absorption and
Surface recombination. Because of the presence of the competitive recombination channels in most luminescence phenomena, the luminescence intensity is
not a simple function of the impurity concentration, but it also depends on the
minority carrier lifetime (Warwick, 1987). Thus, measurements of both the
luminescence intensity a n d the luminescence time decay will be required.
396
D . B . H o l t and B . G . Y a c o b i
Mixed level injection implies that the excess carrier density is greater than the
ionized impurity concentration near the electron probe and less than that
concentration away from the probe. It should be noted that the reflection
losses should also be included in the correction procedure of the C L signal.
Further work along these lines will be both desirable and important.
8.3.4
Spatial resolution a n d the detection limit
The spatial resolution of the C L mode of the S E M is determined by three
parameters. These are the electron probe size, the size of the generation volume
which is related to the beam penetration range in the material, and the
minority carrier diffusion length. Thus, depending upon the properties of the
material and the electron energy, one of these factors, or their combination,
would determine the spatial resolution of the C L (see Davidson, 1977 and
Davidson and Dimitriadis, 1980).
The size of the electron beam decreases with decrease of the beam current
and increase of the beam voltage (see, for example, Goldstein et a/., 1981). It
should also be noted that for the same beam current and voltage the probe
diameter for the tungsten filament is about twice as large as that obtained
using the L a B gun. F o r the latter, for example, the probe diameter for 30 kV
beam is about 240 A at the probe current of 10" A, and it is about 40 A at the
probe current of 1 0
A. In practice, the resolution is often essentially given
by the beam penetration range.
The sensitivity of C L analyses was demonstrated to be in some cases at least
1 0 times better than that attainable by X-ray microanalysis. In other words,
impurity concentrations as low as 1 0 cm ~ can be detected (see, for example,
Holt and Saba, 1985). In the case of P L (and arguably C L as well) in the most
favorable cases of strongly luminescent impurities which emit at energies
undisturbed by other emission or absorption mechanisms in the host material,
it should be possible to detect impurities down to the 1 0 c m level (Dean,
1982).
6
9
- 1 1
4
1 4
3
1 2
8.3.5
- 3
Artifacts
Spurious signals in C L analyses may arise, for example, from luminescent
contaminants, from incandescence from the electron gun filament reaching the
detector, or from scintillations caused by backscattering electrons striking
components of the C L systems. M a n y of these background contributions may
be eliminated by chopping the electron beam and detecting the C L signal in
phase with a lock-in amplifier.
C a t h o d o l u m i n e s c e n c e c h a r a c t e r i z a t i o n of s e m i c o n d u c t o r s
397
Prolonged electron beam irradiation may also cause changes in the C L
intensity (see examples given by Holt and Saba, 1985). These changes,
naturally, should be taken into consideration in quantitative analyses of C L
intensities.
An artifact in the C L emission spectrum, a "ghost" C L peak in I n P , was
reported by Warwick and Booker (1983). This was due to the rays that are
totally internally reflected before emerging from the specimen, after selfabsorption.
Caution should be exercised during C L contrast observations of defects.
Balk et al (1976) reported contrast inversion at a single dislocation in Sedoped G a A s by increasing the electron beam current from a b o u t 1 0 " A to
about 1 0 " A. This was explained as being due to the localized heating effects
at higher beam currents, which leads to enhanced non-radiative recombination and a decrease of the C L signal.
6
5
8.4
Cathodoluminescence analysis techniques
There are two basic types of C L analysis systems for materials characterization. One naturally involves an electron microscope, for example, an SEM,
which can be equipped with various C L detecting attachments. Using C L
S E M enables one to obtain C L spectra and images and display, for example,
defect maps. The significant differences between S E M - and STEM-based
systems, and also between these and systems attached to a T E M will be
discussed below. The other approach employs a simple high-vacuum system
containing an electron gun for the excitation of a material; n o scanning or
transmission microscopic capability is provided, so no image of a sample can
be obtained; thus it is limited to spot mode C L only. The use of large-area,
high-power beams results in high C L intensities and makes high spectral
resolution possible. In general, spectral and spatial resolution vary inversely.
In this section we will review some basic principles and systems of C L
techniques.
8.4.1
C a t h o d o l u m i n e s c e n c e s c a n n i n g electron m i c r o s c o p y
The essential requirements for C L detection system designs are a high
efficiency of light collection, transmission and detection. Two types of signal
from the photomultiplier can be extracted to produce micrographs or spectra.
F o r a constant m o n o c h r o m a t o r setting a n d a scanning electron beam
condition, m o n o c h r o m a t i c micrographs can be obtained. W h e n the m o n o c h r o m a t o r is stepped through the wavelength range of interest and the
398
D . B . Holt and B . G . Y a c o b i
Cooled
Photon
counter
PM
Housing
Data converter
SEM
video
screen
Multichannel
analyzer
Monochromator
collector
(semi-ellipsoidal
mirror, l e n s a n d
fiber o p t i c s )
^ - O u t p u t to
computer
F i g . 8.8 Schematic diagram of a typical early CL SEM detection system for the
visible range.
electron beam is stationary or scans a small area, spectral information for a
point analysis can be derived. When the grating of the m o n o c h r o m a t o r is bypassed, photons of all wavelengths fall on the photomultiplier giving the
panchromatic (integral) C L signal.
Recent designs (e.g. Steyn et al, 1976 and references therein) utilize a semiellipsoidal mirror for C L collection (Horl and Mugschl, 1972; Giles, 1975) and
a fiber-optic guide for signal transmission (see Fig. 8.8). In these designs the
electron beam is incident on the sample at the first focus of a semi-ellipsoidal
mirror, which concentrates the emitted light through the second focus of the
mirror where it is collimated by a lens and transmitted via a fiber-optic guide
into the entrance slit of the monochromator. Light with a narrow range of
wavelengths then falls on the photomultiplier, the output of which is a train of
pulses corresponding to the incident photons. The output of the p h o t o n
counter, which provides noise rejection and amplification, can then be fed
through a video amplifier to a cathode-ray-oscilloscope display to produce C L
images, or alternatively, subjected to computer analysis.
The calibration of the detection system for its spectral response characteristics is of great importance (Steyn et al, 1976). Significant changes in the CL
intensity, the shape of the luminescence band and the value of the peak photon
energy are observed with the correction of such spectra (Datta et al, 1977,
1979). Specifically, it was found that broad emission bands undergo larger
correction effects than do narrower bands. This leads, for example, in the case
of the "self-activated" (SA) luminescence in ZnS:CI, to a sign reversal of the
temperature coefficient of the SA peak (Datta et al, 1979). In other words,
while the peak of the SA uncorrected luminescence band shifted towards
C a t h o d o l u m i n e s c e n c e c h a r a c t e r i z a t i o n of s e m i c o n d u c t o r s
399
higher energies with the increase in temperature, after the correction it shifted
in the opposite direction (similar to the shift of the fundamental edge). Thus,
the frequently reported temperature shift anomaly, which was thought to be
characteristic of the SA emission peak in ZnS:Cl, was found to be an artifact of
uncorrected spectra in this particular material. T h o m a s et al (1984) found
that the sign of the temperature shift of this peak depends also on the
concentration of Cu in the material.
While the m o n o c h r o m a t o r - p h o t o m u l t i p l i e r system provides a sequential
detection of each wavelength of the C L spectrum, a different system, which
utilizes a silicon intensified target (SIT) vidicon camera and an optical
multichannel analyser (OMA) was also developed recently for simultaneous
observation of all wavelengths in a CL-spectrum ("parallel" detection as
compared to "serial" spectral detection by the systems described above) (see,
for example, Lohnert et al, 1981).
Solid-state detectors have been used recently for transmission C L (TCL)
and emission C L (ECL) infrared panchromatic microscopy (Chin et al, 1979;
G a w and Reynolds, 1981; Cocito et al, 1983; Marek et al, 1985; Yacobi and
Herrington, 1986). A more recent design for E C L imaging utilizes a donutshaped Si detector mounted on the pole-piece of the objective lens (essentially
replacing the backscatter detector) (Marek et al, 1985). In these designs a glass
cover of the photodetector blocks backscattered electrons that could also
contribute to the detector signal. To avoid charging, the glass is coated with a
thin layer of indium-tin-oxide.
Monochromatic infrared C L detection methods have attracted increasing
interest in investigations of semiconductors with energy gaps below the
detection range of photomultipliers. Although photoconductive and p h o t o voltaic semiconductor detectors can be used with m o n o c h r o m a t o r s in this
range (Myhajlenko et al, 1984), the optimum method in the infrared range is
Fourier transform spectrometry (FTS). This is generally based on the
Michelson interferometer, which produces the interferogram of the C L
emission as one mirror is moved. The interference pattern is later converted
into the C L spectrum by computing the Fourier transform of these data (Holt
and Saba, 1985).
C L decay measurement set-ups, which attracted increasing interest in recent
years, can be utilized for carrier lifetime mapping. This can be achieved by
using a microprocessor-controlled boxcar integrator system for data acquisition (Steckenborn, 1980; Steckenborn et al, 1981a, b), or alternatively, using
computer-controlled C L acquisition with an optical multichannel analyser
(Hastenrath et al, 1981). A paper by Myhajlenko and Ke (1984) describes the
technique of delayed coincidence for analysis of minority carrier lifetime. One
such system was described recently by Bimberg et al (1985a, b). A block
diagram of this C L S E M system for time-resolved measurements is shown in
D . B . H o l t and B . G . Y a c o b i
400
ELECTRONGUN
DCPOWERSUPPLY
BEAM-BLANKING
UNIT
1
r
-D
J
L D-
PULSE GENERATOR
X-Y
RECORDER
Fig. 8.9 Schematic diagram of a liquid helium CL SEM system for time-resolved
studies. (After Bimberg et al, 1985a.)
Fig. 8.9. In this system electron pulses of rise and decay times ^ 2 0 0 p s with
widths variable between 1 ns and 10 /is and a repetition rate of 1 k H z to 1 M H z
are used for excitation. A liquid He cryostat allows the temperature to be
varied from 5 K to 300 K. The pulse generator triggers both the beam blanking
unit and photon counting system via a delay line. The pulse-height distribution is evaluated by a computer-controlled multichannel analyser and the
data are stored on a magnetic tape. This method allows simultaneous
acquisition of 14 spectra taken at different times relative to the start of the
exciting pulse. An example of a 800-ns electron pulse excitation is shown in
Fig. 8.10. U p to 14 time windows, indicated by hatched regions, can be
simultaneously set during the onset of the CL, the quasi-equilibrium, and the
C L decay. It should be emphasized that such a system is essential for analysis
of the lifetime in a complex system containing more than two levels (one initial
and one final state). Utilization of such an acquisition system to compare a
number of decay spectra covering the wavelength range of interest, would
allow the interpretation of results in multilevel systems (Bimberg et al,
1985a, b).
8.4.2 C a t h o d o l u m i n e s c e n c e s c a n n i n g transmission electron
microscopy
Petroff etal (1977, 1978, 1980) and Pennycook et al (1977, 1980) have
developed C L collection systems in STEM. This enables a direct correlation
to be made between structural and physical properties of individual defects.
luminescence intensity
quasiequilibrium
onset
400
600
decay
800
1000
t i m e (ns)
Fig. 8.10 Schematic CL response to 800-ns electron pulse; time windows which are
simultaneously set during onset, quasi-equilibrium and decay of the CL are indicated
by the hatched regions under the curve. (After Bimberg et al, 1985a.)
5 0 - 2 0 0 KeV
ELECTRONS
B
E
A
M
CTEMOR STEM
Fig. 8.11 Schematic diagram of a CL STEM system; the distance between the two
halves of the objective pole-piece is 8 mm. (After Petroff et al, 1978.)
402
D . B . H o l t and B . G . Y a c o b i
In one of these designs (Petroff et al, 1978), shown in Fig. 8.11, an elliptical
mirror is used for efficient light collection. F o r transmission of the C L signal,
two planar mirrors are used to bring it to an optical fiber. The signal, taken
out of the microscope column by the optical fiber, is passed through a
m o n o c h r o m a t o r and detected by a photomultiplier or a solid-state detector.
The C L system can be manipulated in order to bring the focal point of the
mirror and the sample into coincidence. This arrangement also allows for
simultaneous S T E M analysis of structural properties. Impressive evidence
of the power of this technique was presented by Cibert et al (1986a) and
Petroff et al (1987) who correlated the structural and optical properties of
individual GaAs q u a n t u m wells and interfaces.
G r a h a m et al (1986) described modifications of their T E M C L system for
the visible to include the infrared region using both a Ge photodiode and a
Fourier transform spectrometer.
8.4.3 N o n - s c a n n i n g c a t h o d o l u m i n e s c e n c e
systems
Cathodoluminescence systems with no scanning capability are relatively
simple, but, nevertheless, powerful characterization tools, especially for the
analysis of interfaces and ion-implanted materials, because of their ability to
obtain depth-resolved information.
MANIPULATOR
ELECTRON
F i g . 8.12 Schematic arrangement of ultrahigh-vacuum CL system. (After Brillson
et al, 1985.)
C a t h o d o l u m i n e s c e n c e c h a r a c t e r i z a t i o n of s e m i c o n d u c t o r s
403
In general, such a system consists of a high-vacuum chamber with optical
ports and a port for an electron gun. In these applications, the incident electron
energies are usually varied between a b o u t 0.5 keV a n d several keV in order to
obtain a near surface penetration.
O n e example of such a system, shown in Fig. 8.12, was published by Brillson
et al (1985) and effectively used for the analysis of metal-semiconductor
interfaces (Viturro et al, 1986). This system has an ultrahigh-vacuum chamber
with a base pressure of 5 x 1 0 " torr. A sample is positioned at the c o m m o n
focal point of both a glancing incidence electron gun a n d the optical detection
system. The C L signal is focused by a quartz lens inside the chamber and
transmitted through a quartz window into the m o n o c h r o m a t o r . In order to
avoid light emitted from the electron gun filament, the electron beam is
chopped and a photomultiplier or a solid-state detector is used with a lock-in
amplifier.
1 1
8.5
Applications
This section reviews some practical applications of C L analysis in the
assessment of electronic properties of various materials. M o r e detailed
discussion of specific cases of C L applications to Si and various I I I - V and I I VI c o m p o u n d s have been given in several reviews (for example, Holt, 1974;
Davidson, 1977; Holt and Datta, 1980; Lohnert a n d Kubalek, 1983; Wittry,
1984; Holt and Saba, 1985; Yacobi and Holt, 1986). The purpose of this section
is to outline the basic features of C L applications to semiconductors.
There is a growing n u m b e r of reports of the application of C L microscopy to
the analysis of q u a n t u m wells (Cibert et al, 1986a; Petroff et al, 1987). Using
m o n o c h r o m a t i c imaging, the distribution of individual q u a n t u m wells can be
observed. The spatial resolution in S T E M observations is basically determined by the carrier diffusion length, a n d thus these measurements should be
considered with great caution (Petroff et al, 1987).
8.5.1
Defect contrast s t u d i e s
Two modes of the S E M , C L and EBIC, are frequently used for the
characterization of electrically active defects in semiconductors a n d semiconductor devices. An advantage of the C L m o d e is that it is a contactless
microcharacterization tool with n o requirements for device fabrication steps.
C L is of great value in providing an assessment of a starting material, and it
thus m a y help to eliminate problems associated with processing steps that
cause device failure. In C L imaging of defects, dark contrast is due to the
404
D . B . H o l t and B . G . Y a c o b i
enhanced non-radiative recombination at irregularities in the crystal. Thus,
the defect sites can be readily identified. Several papers describe the
mechanisms of C L defect contrast formation in semiconductors (Schiller and
Boulou, 1975; Davidson, 1977; Booker, 1981; Lohnert and Kubalek, 1984;
Holt and Saba, 1985; Jakubowicz, 1986; Pasemann and Hergert, 1986).
Jakubowicz (1986) and Jakubowicz et al. (1987) have demonstrated that
simultaneous C L and EBIC contrast studies may provide a powerful method
for characterizing the orientation, shape and depth of dislocations in
semiconductors. This is accomplished by comparing experimental results with
theoretical curves derived for the ratio of the C L and EBIC contrast:
I
QL/ EBIC =
C
_
| _
E
e
- H ( a - l / L )
- H * - i / L )
( - 8)
8
1
where H is the position of the defect, h is the penetration depth of the electron
beam, a is the absorption coefficient and L is the minority carrier diffusion
length. By obtaining the best fit to the experimental line scans for different
inclination angles of an extended defect in the semiconductor, the geometrical
properties of the defect can be obtained.
In recent years, the dislocation-induced electronic levels in the gap and their
effects on electrical and optical properties have attracted increasing fundamental interest (see, for example, Lax, 1978; Labusch and Schroter, 1980;
Marklund, 1983; Farvacque et al, 1983). Several C L studies have also greatly
contributed in elucidating the recombination properties of the dislocations
(see, for example, Petroff et al, 1980; Dupuy, 1983; Lohnert and Kubalek,
1984; Myhajlenko et al, 1984; Holt and Saba, 1985). It appears that
dislocations may introduce two types of levels in the gap: (i) narrow energy
bands near the middle of the gap, which are associated with dangling bonds,
and (ii) shallow levels, which are introduced by the localized deformation
potential due to the elastic strain field of dislocations.
Dislocation contrast frequently appears as dots (due to threading dislocations) or as lines (due to misfit dislocations). In the former case, two types of
dislocation contrast have been observed: "dark dot" contrast in more lightly
doped semiconductors and "dot and halo" contrast in more heavily doped
materials. The crucial question in analysing the dislocation contrast is whether
the recombination is due to the inherent structure of the dislocation (i.e.
dangling bonds associated with the dislocation core, or a dislocation core with
reconstructed dangling bonds), or, for example, to a Cottrell atmosphere of
point defects around the dislocation. Experiments indicate that both dislocation core effects and Cottrell atmospheres might be involved in the observed
dislocation C L contrast (see, for example, Davidson, 1977; Davidson and
Dimitriadis, 1980; Dupuy, 1983; Holt and Saba, 1985).
Booker (1981), Lohnert and Kubalek (1984) and Holt and Saba (1985) gave
C a t h o d o l u m i n e s c e n c e c h a r a c t e r i z a t i o n of s e m i c o n d u c t o r s
405
comprehensive reviews of the analysis of C L contrast produced by dislocations. C L contrast was defined as
(8.19)
C = (L -L )/L
CL
CLD
CLi
is the C L intensity away from a defect and L
is the C L
where L
intensity at the defect. Lohnert and Kubalek (1984) analysed the C L
contrast formation due to the defects in semiconductors using an extension
of Donolato's model for the EBIC contrast of dislocations. The dislocation
was treated as a cylinder of radius R with a uniform C L q u a n t u m
efficiency n < n. The generation function was represented by a point source.
An exponential rise of the C L intensity with distance from the dislocation was
obtained for x > 2L. These calculations were shown to be in a good agreement
with the experimental observations of the "dark dot" dislocation contrast in
GaP.
Recent studies have demonstrated the usefulness of the C L mode in the
C L
C L D
0
d
EBIC
CL
A-790nm
STEM
F i g . 8.13 (A) EBIC, (B) CL and STEM micrographs of a misfit dislocation network
in G a i ^ A f . A S i - y P j , epitaxial layers. Dl in the STEM micrograph is a sessile edge
dislocation which does not give EBIC and CL contrast unlike the other dislocations,
which are all 60° type. (After Petroff et al, 1980.)
406
D . B . H o l t and B . G . Y a c o b i
analysis of luminescence properties of individual dislocations. Petroff et al
(1977, 1978, 1980) and Pennycook et al (1977, 1980) utilized C L attachments
to an S T E M and Booker et al (1979), Myhajlenko et al (1984) and G r a h a m
et al (1987) used C L and T E M for the analysis of both the structural and
electronic properties of defects in various semiconductor compounds. These
results (see, for example, Fig. 8.13) clearly indicate that certain types of
dislocations produce C L and EBIC contrast, while others do not. These
observations provide strong evidence that the dislocation core is involved in
enhanced recombination. C L studies of individual dislocations and dislocation tangles in ZnSe and I n P were reported by Myhajlenko et al (1984) and
Batstone and Steeds (1985). Luminescence at 2.60eV (Y band) and 2.52eV (S
band) in ZnSe were related to dislocations with an indication that in the case of
the Y band impurity-dislocation associations are involved. Some of these
results for O M C V D (organometallic chemical vapour deposition) Al-doped
ZnSe deposited on GaAs substrates are presented in Figs 8.14 and 8.15, which
show the spectra acquired from a dislocation tangle and corresponding
CL INTENSITY (ARBITRARY UNITS)
Y
2.3
2.4
2.5
2.6
2.7
2.8
2.9
ENERGY (eV)
F i g . 8.14 CL spectra (30 K) acquired from a dislocation tangle in Al-doped ZnSe; (a)
probe away from tangle, (b) and (c) probe on tangle. (After Batstone and Steeds, 1985.)
D°X, 2-79eV
2pm
D A P , 2-68eV
Y, 2-60eV
Fig . 8 . 1 5 Monochromatic CL images from the dislocation tangle in Al-doped ZnSe
(compare with Fig. 8.14). (After Batstone and Steeds, 1985.)
408
D . B . H o l t and B . G . Y a c o b i
monochromatic C L images. The donor-bound exciton (D°X) emission at
2.79 eV and F E (free exciton) (ls-2s) at 2.78 eV are reduced in the dislocation
tangle region, Y emission is localized along the tangle, together with the
strongly localized d o n o r - a c c e p t o r pair (DAP) emission at 2.68 eV. In the case
of InP, however, no dislocation-induced emission band was detected.
Observation of infrared C L from dislocations in deformed Si was recently
reported by G r a h a m et al (1987). C L emission localized at defects produces
bright C L contrast in monochromatic C L micrographs recorded at that
wavelength.
Examples of the C L applications in uniformity characterization of semiinsulating GaAs were reported by Kamejima et al (1982), Chin et al (1984),
Wakefield et al (1984a), Wakefield and Davey (1985) and Warwick and Brown
(1985). The segregation of various impurities, like oxygen, silicon, chromium
and carbon, at cellular dislocation tangles was observed. The major conclusion of these observations is that inhomogeneous distribution of impurities
may lead to non-uniform electrical transport in the material, which would be
undesirable for such applications as GaAs integrated circuits (Warwick et al,
1985).
Observations by Warwick and Brown (1985), who used PbS and Ge
detectors for deep-level C L imaging of undoped semi-insulating GaAs,
confirmed the segregation of the dominant intrinsic defect EL2 (which is
believed to be associated with an A s antisite-related defect) from the cell
interior to the dislocation cell walls. Wakefield et al (1984b) observed an
emission line (at 1.36 eV) in epitaxial I n P which was due to an exciton bound
to a defect suggested to be a complex involving a phosphorus vacancy.
Myhajlenko (1984) observed a deep-level band, which was ascribed to a
phosphorus vacancy complex in L E C I n P annealed at 750°C. These results
demonstrate the power of C L analysis in detecting point defects and their
complexes in semiconductors.
Magnea et al (1985) have demonstrated the usefulness of C L in characterizing defect traps at I I I - V compound heterostructure interfaces. They shifted
the edge of the depletion zone of an avalanche photodiode by applying a
reverse-bias voltage and observed selective quenching of C L at the interfaces
due to the electric field-induced modification of carrier distributions. This they
called "electric field dependent CL".
C L studies were also instrumental in attempts to explain the phenomenon
of "self-compensation" in I I - V I compounds (for a summary, see, for example,
Yacobi and Holt, 1986) and to elucidate the nature of C L variations in faulted
ZnS crystals (Williams and Yoffe, 1968; Yoffe et al, 1973; Holt and Culpan,
1970; D a t t a et al, 1977). It was found, for example, that the local variations in
C L emission from structurally complex ZnS crystals (see Fig. 8.16) are due to
changes in structure, impurity segregation, and/or internal electric fields.
G a
F i g . 8.16 Micrographs of a striated ZnS platelet with the common c axis running
horizontally, (a) Low-magnification polarized light micrograph of the whole platelet,
showing the polytypic bands running vertically. The remaining micrographs are all of
the area in the rectangle outlined in the center of the platelet, (b) Enlargement of the
area outlined in (a), (c) Panchromatic CL SEM micrograph. The remaining pictures are
monochromatic CL SEM micrographs (the width of the area is 308 fim) recorded at the
following emission wavelengths: (d) 328 nm (3.78 eV), (e) 334 nm (3.71 eV), and (f)
344 nm (3.60 eV). (After Datta et al, 1977.)
410
D . B . H o l t and B . G . Y a c o b i
C L assessment of I I I - V L E D materials (Booker, 1981; Trigg and Richards,
1982; Lohnert and Kubalek, 1983) was instrumental in elucidating device
degradation, which was explained on the basis of the changes of the
concentration of vacancies and/or antisite defects in the vicinity of dislocations
(Frank and Gosele, 1983).
The value of C L in the assessment of fluorescent lighting phosphor powders
was demonstrated by Richards et al (1984). In recent applications of these
materials in fluorescent lamps, for example, mixtures of various narrow-band
emitters are used. These multicomponent blends consist, for example, of
phosphors that emit in the blue, green and red. By varying the proportions of
the components, light emission with various colours can be produced. The
spectral and spatial resolutions of the C L analysis of these phosphors were
essential in locating and identifying components of low efficiency and relating
the problem to the processing procedure.
8.5.2
Time-resolved
cathodoluminescence
In this technique a C L decay time is measured by employing a beam blanking
system and a fast detector (for a review, see, for example, Hastenrath and
Kubalek, 1982). If the decay of the luminescence intensity L(t) is exponential,
i.e.
L(0 = L ( 0 ) e x p ( - r / i )
(8.20)
a minority carrier lifetime can be obtained. Caution should be exercised in this
type of experiment because of the effect of surface recombination. The
measured values are actually effective lifetimes (Shockley, 1950),
T
eff
1
=
T
bulk +
T
(8.21)
surf
Observations of the variation of a C L decay time with electron beam energy
make possible calculations of both the minority carrier lifetime and the surface
recombination velocity. Hastenrath and Kubalek (1982) analysed, for
example, C L decay time measurements as a function of electron beam energy
to derive the surface recombination velocity S from
S = L (T V-To )
(8.22)
1
p
e
where L is the hole diffusion length, and r and T are the effective lifetime
and bulk lifetime, respectively. Thus they estimated the value of S, which was
well within the typical range of values of the surface recombination velocity for
GaAs.
A theoretical analysis of the cathodoluminescence decay was presented by
Boulou and Bois (1977), who used the difference in the shape of the decay with
p
e f f
0
C a t h o d o l u m i n e s c e n c e c h a r a c t e r i z a t i o n of s e m i c o n d u c t o r s
411
short and long excitation pulses for the determination of both the surface
recombination velocity and the bulk minority carrier lifetime in G a P . M o r e
recently Jakubowicz presented a theoretical analysis of transient C L with the
conclusion that the initial part of the decay depends on the surface
recombination velocity, the excitation range and the absorption coefficient,
while at longer times the near-exponential decay is controlled by the bulk
lifetime (Jakubowicz, 1985).
C L decay analysis has also been applied to Si (Davidson et al, 1981;
Cumberbatch et al, 1981; Myhajlenko et al, 1983) to measure the carrier
lifetimes at and away from a grain boundary in that material (see Fig. 8.17).
The reduction of the minority carrier lifetime at single dislocations in G a P was
also determined by using C L decay measurements (Rasul and Davidson, 1977;
Davidson and Rasul, 1977).
An impressive demonstration of the value of this technique for the study of
the kinetics of relaxation and recombination processes of non-equilibrium
1
1
0
i
I
I
I
I
I
I
200 400 600 n s
TIME
Fig . 8 . 1 7 Minority carrier lifetimes derived from CL decay rates in ribbon silicon at
( O ) and away ( • ) from a grain boundary. (After Myhajlenko et al, 1983.)
412
D . B . H o l t and B . G . Y a c o b i
carriers in GaAs and GaAs multiple q u a n t u m wells is provided by the work of
Bimberg et al. (1985a, b, 1986). These results demonstrate the power of timeresolved C L in elucidating the question of the distribution of competing
recombination channels and determining such important parameters as the
capture cross sections of charge carriers by ionized donors and acceptors. In
these experiments, the lifetimes of non-equilibrium carriers in their different
band and impurity states are analysed and subsequently capture cross sections
are derived from the lifetimes. Thus, cross sections of c o n d u c t i o n - b a n d acceptor transitions, as well as of hole capture by the ionized acceptors
(carbon and tin), and of electron capture by ionized donors are derived. In
these experiments, C L spectra and transients were found to depend strongly
on pulse lengths up to 1 fis. The capture cross sections of electrons and holes by
ionized donors and acceptors are derived from these luminescence onset
results. Further analysis of the decay from a metastable excited state as a
function of excitation intensity, temperature, and doping using pulse lengths of
the order of 1 /xs, provides additional information for interpretation of
recombination kinetics. The excitation pulse length dependence of the C L
spectra in both n- and p-type GaAs is shown in Fig. 8.18. Luminescence peaks
from the free exciton (X), from the donor- and acceptor-bound excitons
( D ° X , D X , A°X), from acceptor-tin-bound exciton (Sn°X), from the freeelectron-acceptor recombination (eA°), and from the d o n o r - a c c e p t o r pair
+
1.49
1.50
1.51
photon energy (eV)
1.52
1.49
1.50
1.51
1.52
photon energy (eV)
Fig . 8 . 1 8 CL spectra of (a) a lightly Sn-doped n-type GaAs, and (b) a high-purity ptype GaAs. The values of the excitation pulse length of 2,50 and 500 ns are indicated for
each spectrum. (After Bimberg et al, 1985a.)
C a t h o d o l u m i n e s c e n c e c h a r a c t e r i z a t i o n of s e m i c o n d u c t o r s
413
recombination (D°A°) are present. It is evident from this figure that the
spectral distribution of the emission depends on the length of the exciting
pulse. (It should be noted that no analogous observations were reported in
time-resolved P L experiments using pulsed lasers, since the width of a laser
pulse cannot be adjusted independently of its rise and decay time. As was
pointed out by Bimberg et al (1985a), the failure to consider the effect of the
shape of the exciting laser pulses on quantities derived from luminescence
transients may lead to erroneous conclusions.)
Bimberg et al (1985a, 1986) also reported results of time-resolved C L on
undoped and Be-doped GaAs multiple q u a n t u m wells ( M Q W ) of various
thicknesses. These results demonstrated that the excitonic decay channels
dominate the carrier recombination in a q u a n t u m well for excess carrier
densities less than 1 0 c m " , and that the structural localization induces an
increase of intrinsic excitonic recombination probabilities as compared to
carrier capture by impurities or traps, which are increasingly bypassed with
decreasing q u a n t u m well width. This effect is illustrated in Fig. 8.19, which
shows the transients of q u a n t u m wells taken at r o o m temperature for samples
with different width and acceptor concentration. The radiative recombination
probability increases with decreasing L , which is manifested by the decrease
of lifetime (in agreement with theoretical predictions). Doping leads to the
decrease of the luminescence lifetime due to the participation of the additional
excitonic radiative recombination channels. In contrast, the recombination in
bulk epitaxial GaAs occurs stepwise via impurities (Bimberg et al, 1985b).
1 7
3
lum. intensity ( a.u.)
z
time (ns)
F i g . 8.19 Room temperature CL decay (after long pulse excitation) of quantum
wells with different width L . (After Bimberg et al, 1985b.)
z
414
D . B . H o l t and B . G . Y a c o b i
8.5.3
Depth-resolved
cathodoluminescence
Depth-resolved information obtained from C L analysis of semiconductors is
one of the most attractive features of this technique as compared to P L
analysis. The non-destructive depth-resolved information in C L analysis is
obtained by varying the range of electron penetration (which is dependent on
the electron beam energy) in order to excite luminescence from different depths
of the material. This technique is particularly useful for studying ionimplanted materials. In this case, since the penetration depths of ions that are
implanted using energies of the order of 50-300 keV are comparable with the
ranges of electrons with energies of l - 2 0 k e V , the analyses can be performed
using commercial scanning electron microscopes, or relatively simple dedicated systems for depth-resolved studies. This technique provides information
on the redistribution of impurities and lattice damage defects during annealing
of ion-implanted samples. This, in conjunction with the spatially resolved
information available in a scanning electron microscope, should, in principle,
provide a three-dimensional mapping of impurities and defects in the material.
These studies are often performed using a constant total electron injection rate
(i.e. constant electron beam power) in order to obtain greater signal from
shallower depths at low energies (Norris et al, 1973,1977; Norris and Barnes,
1980). In some cases, in order to maintain a constant level of excitation at the
surface of the sample and keep the relative peak of the electron-hole pair
density at a constant level (compare with Fig. 8.5 which represents the relative
density of electron-hole pairs for a constant electron beam current 7 ), the
ratio I VJR
is kept constant in depth-resolved C L measurements. This
method is useful in comparing electron-hole pair profiles with calculated
profiles of implanted ion concentration as a function of penetration depth
(Norris et al, 1973; Pierce and Hengehold, 1976).
b
h
e
As mentioned earlier, depth-resolved C L studies can be performed in a
relatively simple high-vacuum system equipped with an electron gun. Several
reports of such C L depth-resolved studies of implantation-induced damage
profiles in various I I I - V and I I - V I compound semiconductors were published, for example, by Norris et al (1973,1977), Pierce and Hengehold (1976),
Norris and Barnes (1980), and Cone and Hengehold (1983). These C L studies
indicate, for example, that implantation-induced damage in the material
occurs beyond the projected ion range of implants. This effect has important
implications for the fabrication of ion-implanted devices. Such a case is
illustrated in Fig. 8.20, which presents the depth-resolved C L spectra of a 100keV X e - i m p l a n t e d In-doped CdTe sample which was etched to a depth of
about 1400 A. The presence of the implantation-induced 1.2-eV band in this
case is indicative that the defects associated with that band are present at
depths of several thousand angstroms beyond the projected ion range (Norris
+
Cathodoluminescence characterization of semiconductors
415
SAMPLE CTH-24D (CdTe: In)
IMPLANTED AND ETCHED 140 nm
RELATIVE INTENSITY (PMT CURRENT, 1.75 x 10 " A F.S.)
E
B
= 20 keV
(x 1)
jtim
8
DEPTH = 1.44
E
B
= 7.368 keV
(x 54.5)
DEPTH = 0.25 fim
E
= 2.714 keV
675)
DEPTH = 44 nm
B
(x
Eg = 1 keV
1911)
DEPTH = 7.6 nm
(x
1.2
1.3 1.4 1.5 1.6
ENERGY (eV)
F i g . 8.20 CL spectra (at 80K) of 100-keV Xe -implanted and etched In-doped
CdTe as a function of the electron beam energy. Note the implantation-induced 1.2-eV
band in this sample, even though it was etched to a depth of about 1400 A, which
indicates its presence at depths beyond the projected ion range of 1100 A. (After Norris
et al, 1977.)
+
et al, 1977). It should also be noted that the appearance of the implantationinduced band at 1.2 eV is accompanied by quenching of the so-called "native"
luminescence in CdTe at about 1.4 eV. (This "native" luminescence is believed
to be due to transitions involving defect-impurity complexes.) These results
were explained as being primarily due to Te vacancies which are responsible
for the anomalous deep introduction of both the 1.2-eV centers and those that
cause quenching of the "native" luminescence (Norris et al, 1977). Similar
anomalous (post-range) implantation-induced introductions of defects were
416
D . B . H o l t and B . G . Y a c o b i
I
10
•
I
1.4
•
I
•
I
1.8
•
I
I
I
L_J
2.2
,
I
2.6
I
I i 1
3.0
E n e r g y (eVI
F i g . 8.21 CL spectra of UHV-cleaved CdS before and after in situ deposition of 50 A
Cu, and after in situ laser annealing with energy density 0.1 J/cm . The electron beam
energy is 2keV. (After Brillson et al, 1985.)
2
also observed in other compound semiconductors, and it was suggested that
this process may be due to the interaction of ionization with the dynamic
stresses or p h o n o n flux effects during ion implantation (Norris et a/., 1977;
Norris and Barnes, 1980).
In a more recent development, Brillson et al. (1985) and Viturro et al. (1986),
who used an ultrahigh-vacuum (UHV) C L system (see Section 8.4.3),
demonstrated the power of C L depth-resolved analysis in characterizing
subsurface metal-semiconductor interfaces. F o r example, Fig. 8.21 shows C L
spectra of UHV-cleaved CdS before and after 50 A Cu deposition and pulsed
laser annealing. The deposition of Cu produces only a weak peak at about
1.3 eV in addition to band-edge emission at 2.42 eV. Pulsed laser annealing
with an energy density of 0.1 J / c m leads to an intense (relative to band-edge
emission) peak at 1.27 eV which can be related to C u S compound formation.
These results indicate that this C L technique can be effectively used in the
2
2
C a t h o d o l u m i n e s c e n c e c h a r a c t e r i z a t i o n of s e m i c o n d u c t o r s
417
o
LUMINESCENCE INTENSITY
_
_ _
LUMINESCENCE INTENSITY
analysis of chemical interactions at metal-semiconductor interfaces which
produce new interfacial phases. It should be noted that, in contrast to the C u
case, similar experiments with Al layers indicate the formation of bulk defects
due to lattice damage (Brillson et al, 1985).
Viturro et al (1986) investigated the formation and evolution of interface
states for various metals deposited on I n P and GaAs. C L spectra in these
studies reveal the energy levels which are localized at the interface. The energy
0 8
10
12
14
PHOTON ENERGY(eV)
0.8
10
12
14
PHOTON ENERGY(eV)
F i g . 8.22 CL spectra of (a) Au, (b) Cu, and (c) Al on clean, mirror-like n-InP (110),
and (d) Pd on clean, mirror-like p-InP (110) as a function of a metal layer thickness.
(After Viturro et al, 1986.)
418
D . B . H o l t and B . G . Y a c o b i
distributions of the interface states were found to depend on the particular
metal, the semiconductor and its surface morphology. F o r example, Fig. 8.22
illustrates the changes in the C L spectra of I n P with the deposition of various
metals. In these cases, the C L spectrum of clean I n P exhibits one peak at
1.35 eV corresponding to a near bandgap transition. Deposition of Au on n - I n P
(Fig. 8.22a), which leads to new peaks at 0.8 and 0.96 eV, reduces the relative
C L intensity at higher energies with increasing thickness of the deposited layer.
In contrast to Au, interface states due to Cu deposition on n - I n P (Fig. 8.22b)
evolve faster with the layer thickness. Deposition of Al on n - I n P (Fig. 8.22c),
on the other hand, does not cause a significant relative reduction in the nearb a n d g a p emission. The low-energy emission is again observed for Pd
deposition on p - I n P (Fig. 8.22d), but the near b a n d g a p emission is reduced.
The metal-deposition-induced reduction in the near b a n d g a p emission in all
these cases can in part be due to electron beam attenuation by the metal layer
and formation of a surface "dead layer". Increasing band bending, which
depends on the particular metal, and the width of the surface space charge
region, leads to the reduction of the bulk radiative recombination (Wittry and
Kyser, 1967). The changes in the near b a n d g a p C L intensity were found to
correlate with the metal-deposition-induced Fermi-level movement measured
by photoemission. This explains the relatively strong reduction in the near
b a n d g a p emission due to the deposition of Au, Cu and Pd, which causes large
Fermi-level movement and correspondingly large band bending. Al deposition, on the other hand, causes both smaller band bending and relatively
smaller reduction in the near b a n d g a p emission. The observed metaldeposition-induced emission peaks were explained as being due to metal
indiffusion and semiconductor outdiffusion leading to the formation of defect
complexes that are responsible for the interface states. The observed C L results
were also found to be consistent with the Schottky barrier heights of different
metals on these semiconductors (Viturro et al, 1986).
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9 The Electron Acoustic Mode
LJ.
BALK
Universitat
Duisburg,
Kommandantenstrasse
Fachgebiet
Werkstoffe
der
60, 4100 Duisburg
1, FRG
List of symbols
9.1 Introduction
9.2 Origin of SEAM signals and contrasts
9.2.1 Generation of SEAM signals
9.2.2 Origin of SEAM contrast
9.3 Experimental conditions for SEAM
9.3.1 SEAM detection
9.3.2 Set-ups for SEAM
9.3.3 Special problems with SEAM analysis of semiconductors
9.4 Application of SEAM to semiconductor characterization
9.4.1 Gallium arsenide
9.4.2 Silicon
9.4.3 Metallizations on semiconductors
9.5 Conclusions
Acknowledgements
References
Elektrotechnik,
.
.
.
425
426
427
427
430
431
432
433
435
436
437
438
442
444
444
444
List of s y m b o l s
d
/
K
u(f)
V
W
a
T
0
thermal decay or thermal diffusion length
frequency
thermal conductivity
ultrasonic wave amplitude (magnitude)
a constant
the absorbed primary electron beam energy
linear thermal expansion coefficient
SEM Microcharacterization of Semiconductors
ISBN 0-12-353855-6
Copyright © 1989 Academic Press Limited
All rights of reproduction in any form reserved
L . J . Balk
426
p
co(=2nf)
cr
9.1
material density
the modulation frequency
Introduction
The electron acoustic mode, often referred to as scanning electron acoustic
microscopy (SEAM), is based on the production of acoustic waves due to the
interaction between a solid and the primary electron beam. The frequency
range of these waves is determined by the operating conditions of the scanning
electron microscope (SEM) and by the properties of the material investigated.
It may extend from low sound frequencies up to very high ultrasound. As
an acoustic wave is not a steady-state quantity but a temporal variation of
the mechanical situation within a solid, the interaction between primary
electrons and the sample must be of a similar temporal dependence. The first
SEAM experiments, introduced by Brandis and Rosencwaig (1980) and by
Cargill (1980), brought out such a time dependence by chopping the primary
electron beam into a square wave or sine waveform. The sound signal
generated was then determined at the same frequency as the chosen chopping
frequency / . A first and certainly universal theoretical approach attributed
the generation of acoustic waves by high-energy electrons to an intermediate
production of thermal waves due to a periodical heating of the sample within
and close to the primary electron dissipation volume and to a subsequent
conversion of so-called thermal waves into elastic waves via the linear thermal
expansion coefficient a. This m o d e is sometimes also called thermal wave
microscopy. Although this theoretical model has proven to be adequate for
the interpretation of SEAM micrographs in many materials, in semiconductors a more complicated situation arises. This is due to the fact that more
than one interaction mechanism may contribute to the SEAM signal
generation; various coupling phenomena between electron beam and acoustic
wave may occur at the same time. Such a mechanism may be generation of
an inhomogeneous space charge within the semiconducting material, which
then may couple into a sound wave via either the piezoelectric or the
electrostrictive effect. Accordingly, S E A M signals not only occur at the beam
modulation frequency / , but also at other frequencies, preferably at the
second harmonic If (Balk and Kultscher, 1983).
As a result of the manifold possibilities of generating SEAM signals,
various SEAM instrumentations have been developed which do not only use
a periodic beam modulation and a production of so-called linear SEAM
micrographs taken at the frequency / . Apart from non-linear SEAM images
taken at even harmonics of the modulation frequency, other techniques have
been developed. Use of short electron beam pulses allows the analysis of the
The electron acoustic mode
427
SEAM frequency response up to gigahertz frequencies and the production
of time-resolved SEAM micrographs with high temporal resolution (Balk
and Kultscher, 1984a). A modulation of the electron beam interaction with
the solid can be obtained without the need for beam chopping by modulating
the S E M scan generator current and by this the electron beam position at
the sample (Balk, 1986). All these different operating conditions for S E A M
add up to a set of experiments which deliver often quite different data for
the sample and which help to improve the understanding of the principal
mechanisms for SEAM signal generation.
In spite of this present uncertainty about the relative magnitude of the
various possible interaction mechanisms, SEAM has already shown its great
applicability to the investigation of semiconducting materials and devices.
SEAM has been applied to a large variety of different materials, mainly
silicon and I I I - V compounds, and it has been used not only to image
microscopic structures directly at the sample surface, but also to deliver
information on subsurface features, especially if these are buried by an upper
layer like, for instance, a passivation.
9.2
Origin of S E A M signals and contrasts
The generation of SEAM signals can be caused by various physical effects
within a semiconductor. These are a coupling between a time-dependent beam
intensity and the acoustic waves by an intermediate generation of thermal
waves, a direct coupling by means of piezoelectricity and electrostriction and a
mismatch between the concentration of free and fixed charge carriers.
Unfortunately it is a complicated process to separate these mechanisms
quantitatively concerning their relative magnitudes. First experimental and
theoretical proofs are gained by comparing the different frequency responses
and by the various contributions of signal amplitudes and phases. The
interpretation of SEAM micrographs becomes even more difficult, as the
reason for a given contrast may not be associated with the main source for an
SEAM signal. That means that even if non-thermal properties dominate the
signal generation, the contrast-gained may be of a thermal nature, and vice
versa.
9.2.1
Generation of S E A M s i g n a l s
The typical frequencies of modulation for a periodic excitation of SEAM are in
the approximate range from 100 k H z up to 1 M H z , although much lower and
much higher frequencies are also usable. The question of which S E A M signal
L . J . Balk
428
generation process dominates is strongly governed by the chosen frequency.
F o r all mechanisms one has to mention, however, that the corresponding
signal generation volume is primarily defined by the electron energy
dissipation volume, which can be of several micrometres in diameter within a
semiconductor. Depending on the physical nature of the dominant coupling
mechanisms a contribution of a somewhat larger volume has to be taken into
account. In any case the sound generation occurs mainly below the sample
surface, which creates the possibility of imaging subsurface features and gives
the technique an apparent insensitivity to surface corrugations, an advantage
over conventional scanning acoustic microscopes.
Thermal wave generation as an intermediate mechanism for the production
of acoustic waves was the first mechanism within SEAM to be discussed
theoretically in detail (Opsal and Rosencwaig, 1982). As the modulated
electron beam loses its energy within the sample partially under heat
production, a periodic temperature variation results within the primary
electron energy dissipation volume. This periodic temperature profile, however, is not limited to this volume, but it may extend further with the decay
length of this thermal signal, which is referred to as thermal waves. These
waves can be treated like scalar waves with a rapidly decaying magnitude.
The thermal decay or diffusion length d is dependent on frequency as
T
d =
(2K)^(ojp C )-"
2
T
CT
th
where K is the thermal conductivity of the material, co = 2nf is the modulation
frequency, p is the material density, and C its specific heat.
Beyond a distance d away from the primary dissipation volume the thermal
waves are converted into acoustic waves by means of the linear thermal
expansion coefficient a. Thus the generation volume for SEAM is defined by
2d in diameter for large d values which should be the case for low operation
frequencies, whereas the primary dissipation volume limits the spatial
resolution for small d values as for high frequencies. F o r metals the validity of
this model could be proven by varying the modulation frequency from 80 Hz
up to about 20 M H z . F o r / < 1 M H z a pure dependence of the spatial
resolution on f~
could be measured, whereas for the megahertz range a
saturation of the attained resolution occurred (Balk et al, 1984). F o r
semiconductors similarly clear experimental evidence for the thermal wave
model has not been shown yet.
c r
t h
T
T
T
T
i/2
The SEAM magnitude u(f) should be given by
u(f)=v w( c fy
1
0
PcT
th
where V = const, and W is the absorbed primary energy (Ikoma et al, 1984).
This shows that both thermal and elastic (via p ) material properties may
contribute to an S E A M signal variation.
0
cr
429
The electron acoustic mode
The thermal wave model as discussed so far has not been able to explain
many SEAM results in semiconductors. One problem, which already arises
within the thermal wave approach, is caused by the fact that thermal wave
generation is not only given by the energy dissipation but to a large extent by
the recombination of excess charge carriers via non-radiative transitions
(Sablikov and Sandomirskii, 1983). As any primary electron produces within a
semiconductor a huge number of electron-hole pairs, the contribution of such
a "recombination heating" cannot be neglected. If one discusses a spatial
resolution of SEAM with this modified model, one can easily see that the
minority carrier diffusion length L is dominating, if it is larger than the primary
dissipation volume and than d . As Lis not dependent o n / as d , a pronounced
frequency dependence of the spatial resolution might not be visible at all. As
heating of the sample due to non-radiative excess carrier recombination
occurs after a preceding carrier diffusion, it is temporarily shifted by a delay of
a carrier lifetime with respect to the heating due to the primary electron
impact. This situation means that the signal contributions cannot be added in
a simple manner, and that quite complicated SEAM signal waveforms may
result. F r o m photothermal theory and experiment (Fournier et al, 1986) it
could be shown that the relation of the two signal contributions depends
strongly on frequency. F o r / > 10 kHz heat generation by excess carrier
recombination should be dominant, whereas primary electron heating should
be of importance only at frequencies far below those typically used in SEAM
experiments.
T
T
Within a semiconducting material the injection of high-energy electrons can
cause the generation of an inhomogeneous space charge within the generation
volume of excess charge carriers, especially if in this specimen volume there is
no a priori existing electric field. One explanation of this effect is that the
minority carriers are trapped by locally fixed impurities. The excess majority
carriers, which are excited thermally any way, diffuse away from their original
generation site. Together with the charged impurities they then contribute to
an internally generated space charge (Sasaki et al 1986). This space charge
can be directly recalculated into an electric field, the extension of which should
be given by the primary dissipation volume plus the carrier diffusion. As any
semiconductor is a dielectric medium, two different sources for an SEAM
signal generation are given without the need for additional heat production:
these are piezoelectricity and electrostriction (Kultscher and Balk, 1986). The
piezoelectric coupling should be dominant in those semiconductors which
have a considerable piezoelectric stress constant. This is the case for most III—
V compounds, especially InP. As the piezoelectric effect is linear and as the
electron beam-generated field is the source for the SEAM signal, polarity
effects within the SEAM signal, especially in its phase behaviour, have to be
considered.
9
L.J. Balk
430
Electrostriction on the other hand is a universal property occurring in any
dielectric material. Though being of relative small magnitude, it may
contribute to SEAM signals significantly if other coupling possibilities are also
small. This is the case, for instance, in silicon, which has a very low thermal
expansion coefficient. A main difference between electrostrictive coupling and
other mechanisms is that it is inherently non-linear, because the acoustic wave
magnitude depends on the square of the electric field. This means that a
harmonic modulation of the primary electron beam at a frequency/ will cause
an electric field variation at the same frequency, which subsequently leads to
an acoustic signal response at the second harmonic frequency If. By
frequency-selective experiments this electrostrictive contribution can be
separated quantitatively from the other SEAM generation mechanisms.
In a further theoretical model one can show that a periodic fluctuation of the
excess carrier concentration can cause a mechanical strain and thus be the
direct origin of an acoustic wave (Stearns and Kino, 1985). This effect is
especially important for low doped material, in which the excess carrier
concentration close to the beam entry point may considerably exceed the
equilibrium carrier density. F o r very low doped silicon it can be shown that
this signal contribution may be greater than, for instance, the thermal heating
effect.
9.2.2
Origin of S E A M contrast
According to the preceding discussion many material parameters may be
involved in SEAM signal generation and thus may introduce a contrast within
an SEAM micrograph. These may be thermal and elastic properties as well as
electronic parameters like excess carrier transport properties or equilibrium
carrier density. Unfortunately, many of these parameters only vary along with
alteration of other properties, too. F o r instance, a change of the free carrier
concentration can induce a strong increase of the elastic moduli (Averkiev
et al, 1984). The thermal coupling is in any case affected by the anisotropy of
the elastic behaviour of crystals. In this context it can be shown that different
crystal orientations will lead to various SEAM magnitudes for identical
excitation conditions (Hildebrand, 1986).
Although quite often only S E A M magnitude images are produced, the
recording of either phase-resolved micrographs for harmonic SEAM excitation or time-resolved micrographs for pulsed excitation gives additional
information on a sample. Phase contrasts may occur, for instance, with
changes in the material stiffness, as softer material reacts on an acoustic
excitation with a certain delay compared to hard material. Further, phase or
The electron acoustic mode
431
time delays may be due to the excess carrier diffusion process preceding the
final conversion of the interaction products into elastic waves. Crucial
experiments need to be carried out in future to separate all these different
contrast effects from each other.
Contrast within SEAM micrographs may be due not only to an altered
SEAM signal generation; under certain circumstances propagation effects
must also be taken into account. Propagation may influence both the thermal
wave and the acoustic wave. A thermal wave may create an S E A M signal
before reaching its decay length. This may occur if it passes a scatterer site
which directly converts the thermal into an acoustic wave without the need for
a thermal expansion coefficient (Favro et al, 1984). Any temperature-sensitive
structure may act in this sense as a membrane. This could be shown, for
example, for martensite structures in brass (Balk et al, 1984). The acoustic
waves are typically of a long wavelength compared to the sample thickness
and to usual specimen structures. Therefore, a changed propagation of the
acoustic wave only occurs for large scatterers. These are often twodimensional crystal imperfections, like grain boundaries, or even more severe
defects such as delaminations, which are possible at the interface between
semiconductor and a conduction line within an integrated circuit, or cracks
(Holstein, 1985). Such contrasts are strongly pronounced in phase or timedelay contrast images, as they induce a changed travelling time of the acoustic
wave from its origin towards the detector.
9.3
Experimental conditions for S E A M
The most important choice in SEAM instrumentation is the selection of an
appropriate acoustic transducer to detect the SEAM signal emitted by the
sample. Typical detection techniques of S E A M employ piezoelectric materials
to transduce the acoustic wave into an electrical signal. Secondly it is
important to achieve a suitable modulation of the primary electron beam
current at the investigated specimen location. This can be done either by
electron beam chopping or by electron beam position modulation. Depending
on the waveform used for modulation, various amplification techniques may
be used, such as lock-in amplification or boxcar integration. As in electronic
devices, electrical field are present, for example, at p - n junctions, electron
beam-induced currents (EBIC) may be generated which may counterpart the
SEAM generation. Furthermore, one has to make sure that such signals are
not detected by S E A M incidentally, as this may cause artefacts within the
SEAM image. Finally, semiconductors may be piezoelectric themselves and
may therefore act as their own sound transducers.
432
9.3.1
L . J . Balk
S E A M detection
The most commonly used transducers in SEAM instrumentation are devices
which make use of a piezoelectric ceramic of lead zirconate titanate (PZT), as
this ceramic exhibits a very wide band response. Figure 9.1 shows schematically such a detector arrangement. The transducing material is mechanically
contacted to the bottom surface of the sample. The sound acting on the
transducer causes a voltage d r o p over the two opposite surfaces of the P Z T
ceramic, which can be determined by the connected amplifying circuitry. F o r a
properly designed arrangement a flat band with an accuracy of better than
3 d B can be gained from 50 kHz to 1 MHz, which is the usual range of the
modulation frequency / (Proctor, 1982). Although beyond 1 M H z the signal
magnitude of the P Z T material rolls off, it can still be used up to 1 G H z .
However, if one wants to extend the application of SEAM into the high
megahertz range, the polymeric material polyvinylidene difluoride (PVDF)
achieves better results, as its bandwidth extends to about 2 G H z and the signal
levels are on average larger by a factor of 3 than those for P Z T (Domnik et al,
1987). Besides these two materials, other piezoelectric media can be used in
theory for SEAM detection, such as barium titanate or zinc oxide. In any case
electron beam
electrical
shielding
transducer
specimen
brass
electrode
electrical
insulation
to
F i g . 9.1
•
SMA vacuum
feedthrough
SEAM specimen stage with piezoelectric transducer.
The electron acoustic mode
433
it is essential to ensure perfect electrical shielding of the transducer, to avoid
spurious signals, often of the same frequency as the chopping frequency,
falsifying the S E A M signal.
There are m a n y other methods of detecting ultrasound, but they must be
applied within the vacuum chamber of the S E M and therefore many of them
are not convenient. Recently a transducer has been developed which does not
contact the sample at all and which does not need any material property to
transduce sound into an electric signal. This is the so-called capacitive
transducer, in which an electrode is placed in the direct vicinity of the b o t t o m
surface of the sample, giving a defined capacitance between the electrode and
the sample. As soon as a sound wave arrives at the sample surface, this
capacitance is disturbed, the magnitude of disturbance being directly proportional to the sound magnitude. The advantages of such a transducer are that it
operates contactlessly and that its response is not modified by the frequency
response of the transducing material like, for instance, P Z T (Balk et al, 1987).
9.3.2
S e t - u p s for
SEAM
As discussed above, any generation of sound by means of electrons relies on a
temporal modulation of the electron beam current at the investigated
specimen location. This can be achieved either by modulating the position of
the primary electron beam with a frequency which is high compared to the
saw-tooth frequency of the S E M scan generators or by chopping the primary
electron beam within the electron optical column. Modulation of the beam
entry point position, as already applied to EBIC experiments (Balk et a/.,
1975), delivers a relatively small signal, as the effective modulation of energy
dissipation is low compared with beam chopping (Balk, 1986). The technique
typically delivers the first, or if amplification occurs at 2f, the second
derivative of the S E A M signal with respect to the modulated spatial
coordinate. Such information may be of advantage if vague structures have to
come off the background. This technique could also be applied in cases where
installation of a beam chopper into the S E M column has to be avoided.
Modulation of the primary electron beam intensity is best achieved by
means of rectangular waveforms, which are square waves or pulses. Use of
sinusoidal beam modulation is difficult to achieve, as clean waveforms are
needed. Furthermore, for most beam chopping arrangements it would involve
considerable chopping degradation. If a harmonic, i.e. a square wave
modulation, is used, it is essential to realize a precise duty cycle, as the Fourier
components of the primary beam modulation may only consist of odd
harmonics of the modulation frequency / . Otherwise, amplification of SEAM
at even harmonics would not reveal non-linear signal behaviour, but would
L.J. B a l k
434
electron beam
prelens
square
wave
generator
•
•
frequency
standard
word
generator
I—1__
I—I
display
1st
lens
2nd
lens
scan K
coils E
video
amplifier
scan
generator
condensor)
lens
«— specimen
J — transducer
f
2f
4f
preamplifier
J
f
lock-in
amplifier
Q_n_
arum
F i g . 9.2
0
A
• A sin 0 '
" A cos 0 "
differential
amplifier
SEAM set-up using lock-in amplification.
only be an experimental artefact. Control of the waveform is best achieved by
means of a F a r a d a y cage and a digital recording system. T w o different
principal set-ups are described in the following: these are the use of lock-in
amplification and the application of boxcar techniques.
Lock-in amplification
of SEAM
signals
Figure 9.2 is a schematic block diagram of an S E A M arrangement which can
be used for any experiment to analyse both magnitude and phase response of a
SEAM signal. Beam chopping is achieved by means of a pair of plate
condensors which are mounted in the crossover of a pre-lens. The chopping is
controlled via a square wave generator which is triggered by a frequency
standard to allow precise frequency adjustments. An intermediate word
generator is used to enable jitter-free triggering of the lock-in amplifier at
various frequencies, like / , 2 / , and so on. The lock-in amplifier can be used to
deliver any of the four outputs: magnitude A or phase <j> relative to the exciting
beam waveform, and the mixed quantities (as the direct outputs of a lock-in)
Asmcj) and A c o s ^ . Preamplification is critical in those cases where the
transducer impedance varies within the used frequency range. Especially in the
high frequency range (up to 50 MHz) precise impedance matching has to be
obtained.
435
The electron acoustic mode
electron beam
prelens
pulse
generator
square
wave
generator
frequency
divider
•
•
1st
lens
2nd
lens
scan
generator
scan
coils 13
sampling
head
display
video
amplifier
condensor
lens
— specimen
J — transducer
preamplifier
boxcar
integrator
differential
amplifier
F i g . 9.3 Experimental arrangement for time-resolved SEAM.
SEAM
by means of boxcar
integration
In Fig. 9.3 two ways of using boxcar integration with an S E A M system are
shown. O n e employs square wave chopping as in Fig. 9.2. The boxcar
integrator than allows the analysis of the responding SEAM waveform. If the
time delay of the preamplifying window amplifier or of a sampling head (used
instead of a gated preamplifier for high temporal resolution) is fixed, timeresolved S E A M micrographs can be recorded. This is also true when applying
a pulse generator for chopping. But, if the pulse repetition rate is chosen to be
low enough to give a quasi-single pulse experiment, any sound wave
interferences can be avoided and - if a digital boxcar system is used - detailed
frequency analysis of SEAM becomes possible. Furthermore, by scanning the
time delay for a fixed electron beam position time-of-flight experiments can be
carried out, enabling the determination of layer thicknesses. With present
instrumentation time resolutions u p to 200 ps are achievable (Domnik et al,
1987) resulting in an apparent depth resolution of less than 1 pm.
9.3.3
S p e c i a l problems w i t h S E A M a n a l y s i s of s e m i c o n d u c t o r s
The investigation of semiconductors with S E A M involves much more care in
experiments than for any other material group. There are two points which are
436
L . J . Balk
of importance in this respect. O n e is that in any inhomogeneous semiconductor, especially in any device or integrated circuit, electrical
space charges may exist which cause the generation of considerable EBIC
signals. These signals may add to the original SEAM signal, as they are also
frequency modulated by the beam chopping and as the transducer impedance
may be low enough at / to allow such an additional signal pick-up. This
situation may become quite complicated, as SEAM and EBIC signal are
usually shifted by a time delay, possibly causing different phase shifts at
various frequencies, which may lead to significant signal misinterpretation.
Therefore, it is sometimes convenient to shunt such structures by applying an
ohmic metallization onto the sample surface.
The second problem with SEAM of semiconductors is due to the fact that
many semiconducting materials, especially those of the I I I - V or I I - V I
compounds, may be piezoelectric on their own. They can thus operate as their
own transducers. This can be made an advantage, as the voltage apparent at
the bottom surface is directly proportional to the acoustic wave magnitude.
N o extra transducer is needed in that case. However, according to the
preceding discussion, precautions have to be taken to avoid mixing of E B I C
into the signal. Shunting of both sample surfaces to earth, by the way, will
counteract the piezoelectric action of the crystal bulk and will therefore cause a
diminishing of the achievable magnitude. If an additional transducer is
attached to these materials, the two piezoelectric materials may interact
causing signal deteriorations, and a high-frequency S E A M signal, as is
possible, for instance, in I n P or GaAs, may be lost by the low pass properties of
the detecting device. It may be worthwhile to follow this consideration more
closely, especially as use of the semiconductor as its own transducer may offer
the possibility of establishing SEAM as an in situ control within a technological process.
9.4
Application of S E A M to semiconductor characterization
In spite of the extremely complicated situation in interpreting SEAM
micrographs for semiconducting samples, serious efforts have been put into
the development of SEAM as a method for non-destructive characterization
and for process control. It could be shown that due to the versatility of the
SEAM signal generation nearly all solid-state parameters relevant to semiconductor research can be imaged, like doped regions, p - n junctions,
metallization thicknesses and so on. O n e main advantage of SEAM within
these applications is that essentially n o specimen preparation is needed, which
is especially important for in situ control during a process. Even thin
The electron acoustic mode
437
passivations d o n o t matter, as long as they can be penetrated by the primary
electrons. Although time-resolved SEAM has also been applied to semiconductors, most of the experiments were aimed at an understanding of the
mechanisms involved (Balk a n d Kultscher, 1984a; Balk 1986). T h e majority of
experiments up to date have made use of lock-in amplification. Therefore, the
examples given in this section will be restricted to this technique. SEAM has
been applied to a large number of semiconductors; apart from silicon and
GaAs materials like I n P (Balk and Kultscher, 1983), G a A s P (Ikoma et al,
1984) and C u I n S e (Takenoshita, 1986) have been investigated. The following
discussion, however, will only show results for silicon a n d GaAs, as these are
the most important semiconductors of today's technology. As a third topic
some remarks will be given on the investigation of conduction lines within
integrated circuits.
2
9.4.1
G a l l i u m arsenide
GaAs is a piezoelectric semiconductor a n d so, as described above, all
mechanisms may happen simultaneously. This disadvantage may at first sight,
appear a profit, as a high signal level may be involved and many features will
show up. As the penetration of a primary electron of, say 30 keV energy, into
GaAs extends to a b o u t 5 jum into the bulk, subsurface information can also be
gained. Figure 9.4b is a linear SEAM magnitude image showing dislocation
networks in a semi-insulating L E C GaAs wafer (Davies, 1986). The corresponding secondary electron micrograph in Fig. 9.4a does not reveal any
information on these structures. It is important to mention that results similar
to those shown in Fig. 9.4b can be achieved by EBIC but only if a Schottky
contact is deposited on t o p of the sample. Cathodoluminescence will also be
able to show similar results. However, as shown in Figs 9.4c and d, S E A M
can image the dislocation networks, even if they are buried below a layer. In
this example the t o p surface has been implanted with silicon, and additional
metallizations have been brought onto the sample. Neither EBIC nor
cathodoluminescence would have been able to produce a comparable result.
The high sensitivity of SEAM against variation of doping concentrations is
indicated by Fig. 9.5, in which striations within a G a A s wafer are clearly
visible. Again this detection is not significantly hindered by upper layers,
as can be seen by the darker arc shaded area which is part of an evaporated,
1 /mi-thick circular Al electrode (Davies, 1985).
In similar m a n n e r the influence of subsurface defects in GaAs on the
behaviour of devices has been analyzed by SEAM experiments (Kirkendall
and Remmel, 1984).
438
L . J . Balk
F i g . 9.4 Dislocation networks in semi-insulating LEC GaAs (courtesy of D.G.
Davies, University of Cambridge, UK), (a) Secondary electron image of a wafer;
(b) linear SEAM magnitude image of same area as (a) ( / = 250 kHz, primary
electron energy = 30 keV); (c) secondary electron image of a wafer with metallizations and a Si-implanted layer; (d) linear SEAM magnitude image of same
area as (c) ( / = 250 kHz, primary electron energy = 30 keV).
9.4.2
Silicon
Silicon wafer material (Rosencwaig, 1984) and silicon transistor devices
(Takenoshita et al, 1985) have been explored by linear SEAM. However, as
silicon has a very low thermal expansion coefficient and is not a priori
piezoelectric, a significant contribution of electrostriction occurs leading to a
strong non-linear component within the signal at the second harmonic of the
The electron acoustic mode
439
F i g . 9.5 Linear SEAM magnitude image of striations in a GaAs wafer (courtesy of
D.G. Davies, University of Cambridge, UK).
modulation frequency. This is shown by the following examples taken from the
analysis of polycrystalline solar silicon (Balk and Kultscher, 1984b). Figure 9.6
shows high magnification images taken at the site of a grain boundary. The
secondary electron image (Fig. 9.6a) demonstrates the high surface corrugation and shows a scratch, but does not reveal any important material
parameter. In the non-linear SEAM magnitude image (Fig. 9.6b) two features
are clearly shown: the position of the grain boundary as a black line
surrounded by an approx. 20-/mi-wide bright region on both sides. The
contrast can be explained in terms of the model for this non-linear signal
origin. As signal generation is dominated by the excess carrier recombination,
any electric barrier within the sample will affect the SEAM magnitude. The
various grains are differently doped and barriers of up to several tens of volts
are usual. Thus, instead of SEAM, an internally generated EBIC signal occurs
as a competing process, which finally yields the dark line as an essential E B I C
negative. The white regions on either side of the boundary are due to a change
in carbon and oxygen concentration. Especially oxygen contents tend to
440
L . J . Balk
F i g . 9.6 Grain boundary in polycrystalline solar silicon, (a) Secondary electron
image; (b) non-linear SEAM magnitude image at If (f = 100 kHz, primary electron
energy = 30 keV); (c) non-linear SEAM phase image corresponding to (b).
stiffen silicon mechanically without affecting its electronic properties too
much. The white regions are so-called denuded zones of low oxygen
concentration compared to the grain interior. With, to a first approximation,
unchanged electronic properties the contrast is given solely by a low stiffness.
The phase of SEAM signals is dependent on the local doping situation within
the electrostriction model, as the transport and recombination properties of
the excess carriers are affected by dopant variation. Therefore the non-linear
phase image of Fig. 9.6c locates the grain boundary position precisely without
The electron acoustic mode
(c)
surface
signal (arb.units)
electron acoustic
generation volume
30keV 5keV
441
beam position
F i g . 9.7 Non-linear SEAM magnitude imaging of grain boundaries at If
( / = 1 0 0 k H z ) . (a) Primary electron energy = 15 keV; (b) primary electron
energy = 30 keV; (c) interpretation of contrast variation for images (a) and (b).
being affected by the d r o p in signal magnitude. Similarly, although the
magnitude image is only slightly disturbed by topography due to a changed
backscattering yield, the phase image is nearly insensitive against it.
As in GaAs, subsurface information can also be gained by S E A M in silicon.
This effect may, however, cause artefacts when images are interpreted
quantitatively. This is illustrated by Fig. 9.7. The two non-linear S E A M
magnitude images are taken for an identical specimen area under equal
operation conditions, but with different primary electron energies of 15 and
30keV. T w o differences are immediately noticeable between them: the
442
L . J . Balk
apparent width of the denuded zone is smaller for 15keV and the actual
location of the b o u n d a r y is shifted to the left with lower energy. Further, in
both images the width of the denuded zone a r o u n d the boundary is
asymmetrical. These effects are due to a small angle inclination between the
grain boundary and the specimen surface. This means that the primary
electrons reach the denuded zones at various depths according to their energy
dissipation (Fig. 9.7c).
9.4.3
Metallizations on s e m i c o n d u c t o r s
EA- signal
When primary electron energies are used for SEAM experiments that are low
enough to limit the energy dissipation to the metallization itself, the contrasts
obtained are of solely thermal wave origin. The underlying semiconductor
then merely acts as a sound transmitter. In Fig. 9.8 a typical contrast for an
aluminum metallization is sketched in a line scan (Ikoma et al, 1984). As soon
as the metallization has no direct contact with the thermally conducting
semiconductor, for instance due to an intermediate passivation layer, a higher
signal arises caused by an effectively lower thermal conductivity adjacent to
the aluminum line. F o r high-frequency SEAM it becomes possible to
determine the thickness of a metallization by a sort of time-of-flight
experiment. Figure 9.9a is a secondary electron image of a crossing of
conduction lines. Figures 9b and c are the corresponding SEAM phase
images. However, these images are modified by tuning an internal reference
F i g . 9.8 Contrast variation in linear SEAM magnitude images of Al conduction
lines due to an altered effective thermal conductivity. (After Ikoma et al, 1984.)
The electron acoustic mode
443
F i g . 9.9 Investigation of Al conduction lines by linear SEAM phase images
( / = 2 MHz, primary electron energy = 30 keV). (a) Secondary electron image;
(b) phase image with internal reference set to 86°; (c) phase image with internal
reference set to 83°.
angle so that a monitor peak supplied by the lock-in amplifier at a 0° phase
difference td this internal reference is displayed. This shows up in these images
as a ripple-like effect. The thickness of the pads can be determined by this
technique if the peak is adjusted to come up to the conduction line and at the
substrate (or at the crossing). The phase difference between the images at the
operation frequency correlates to the metal thickness via the velocity of
longitudinal ultrasound waves in the respective semiconductor.
L . J . Balk
444
9.5
Conclusions
SEAM techniques can be applied to the analysis of semiconductors with great
success, as many material parameters relevant to semiconductor research
affect the signal generation. Nevertheless, quantitative interpretations of
SEAM micrographs are only possible in favourable cases. Therefore, it is
important to increase the level of understanding of SEAM signal and contrast
mechanisms by means of crucial experiments and by the development of more
detailed theories. The ease with which SEAM can be applied makes it a
prominent candidate for non-destructive evaluation of semiconducting
materials and devices.
Acknowledgements
The author wishes to express his thanks to Professor D r -Ing. E. Kubalek, who
encouraged the development of S E A M within his department, to D r D.G.
Davies from Cambridge University for many discussions, and to N . Kultscher
for assisting in experiment and theory.
References
Averkiev, N.S., Ilisavskiy, Y.V. and Sternin, V.M. (1984). Sol State Commun., 52,17-21.
Balk, L.J. (1986). Can. J. Phys., 64, 1238-1246.
Balk, L.J., Domnik, M. and Bohm, E. (1987) SPIE, 809, 151-157.
Balk, L.J. and Kultscher, N. (1983). Inst. Phys. Conf. Ser. 67, 387-392.
Balk, L.J. and Kultscher, N. (1984a). J. Phys. (Paris), Colloque C2, C2-873-876.
Balk, L.J. and Kultscher, N. (1984b). J. Phys. (Paris), Colloque C2, C-869-872.
Balk, L.J., Menzel, E. and Kubalek, E. (1975). IITRI Proc. Scanning Electron
Microscopy, Part I, 447-455.
Balk, L.J., Davies, D.G. and Kultscher, N. (1984). Phys. Stat. Sol, a82, 23-33.
Brandis, E. and Rosencwaig, A. (1980). Appl. Phys. Lett., 37, 98-100.
Cargill III, G.S. (1980). In Scanned Image Microscopy, ed. Ash, E.A., Academic Press,
New York, p. 319.
Davies, D.G. (1985). PhD thesis, University of Cambridge.
Davies, D.G. (1986). Phil. Trans. R. Soc. Lond. A, 320, 243-255.
Domnik, M., Schottler, M. and Balk, L.J. (1988). In: Springer Series in Optical Sciences
58, Ed. P. Hess and J. Pelzl), pp. 292-293, Springer Verlag, Heidelberg.
Favro, L.D., Kuo, P.K., Lin, M.J., Inglehart, L.J. and Thomas, R.L. (1984). Proc. IEEE
Ultrasonics Symp., pp. 629-632.
Fournier, D., Boccara, C , Skumanich, A and Amer, N.M. (9986). J. Appl Phys., 59,
787-795.
Hildebrand, J.A. (1986). J. Acoust. Soc. Am., 79, 1457-1460.
Holstein, W.L. (1985). J. Appl. Phys., 58, 2008-2021.
T h e electron a c o u s t i c
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Ikoma, T , Murayama, M. and Morizuka, K. (1984). Japan J. Appl. Phys., 23, Suppl.
23-1, 194-196.
Kirkendall, T.D. and Remmel, T.P. (1984). J. Phys. (Paris), Colloque C2, C2-877-880.
Kultscher, N and Balk, L.J. (1986). J. Scanning Electron Microscopy, I, 33-43.
Opsal, J. and Rosencwaig, A. (1982). J. Appl. Phys., 53, 4240-4246.
Proctor, T.M. Jr (1982). J. Acoust. Soc. Am., 71, 1163.
Rosencwaig, A. (1984). J. Scanning Electron Microscopy, IV, 1611-1628.
Sablikov, V.A. and Sandomirskii, V.B. (1983). Sov. Phys. Semicond., 17, 50-53.
Sasaki, M., Negishi, H. and Inoue, M. (1986). J. Appl. Phys., 59, 796-802.
Stearns, R.G. and Kino, G.S. (1985). Appl. Phys. Lett., 41, 1048-1050.
Takenoshita, H. (1986). Solar Cells, 16, 65-89.
Takenoshita, H , Managaki, M. and Mizuno, K. (1985). Japan J. Appl. Phys., 24, Suppl.
24-1, 93-96.
Index
Abbe theory of resolution, 10
absorbed electron, 48
ABT E-beam tester, 191
ADVICE project, 237
Airey's disc pattern, 22
analog-to-digital converter. (ADC), 141
'atomic number' contrast, 37
automatic test equipment (ATE), 235-6
backscattered concentric scintillator,
127
backscattered electron, 48
barrier electron voltaic effect (barrier
EVE), 246-9
BCC crystal, 85, 87
beam blanking, 193-200
beam voltage, 23-4
jS-conductivity, 245, 327-33
constant voltage bias, 328-9
experimental verification, 330-3
Bethe expression, 44-5, 50
Bethe range, 255
Bloch waves, 72-4
Bragg angles, 73, 76-7, 93, 95, 113
Bragg's Law, 142
braking radiation see bremsstrahlung
bremsstrahlung, 41-2, 138
bulk contrast, 6
bulk modes, 10, 14
Burgers vector, 321
capacitatively coupled voltage contrast
(CCVC), 227-8
carrier distribution models, 258
carrier lifetimes, 411
cathode ray oscilloscopes (CROs), 6
cathodoluminescence, 373-423
analysis techniques, 397-403
artifacts, 396-7
generation, 387-93
interpretation of, 394-6
spatial resolution, 396
cathodoluminescence scanning electron
microscopy, 397-400
cathodoluminescence scanning
transmission electron
microscopy, 400-2
charge collection (CC), 245
mode, 5, 10, 14
probability, 264
charge collection scanning electron
microscopy, 57
inverse transform in, 265
CL contrast
bright dislocation, 314-17
dislocation, 310-11
CL mode, 5, 14
CL mode monochromators, 9
closed-loop operation, 162, 163, 170
CMOS, 171, 207, 211, 223
'compositional contrast', 37
computer-aided design (CAD), 204
computerization, 24-5, 205
of E-beam testing, 205
of voltage contrast methods, 218-23
conductive mode
basic physical principles, 245-60
barrier electron voltaic effect
(barrier EVE), 246-9
bulk electron voltaic effect, 250-3
hole-electron pair generation, 2549
plasma regime effects, 259-60
time resolution, 260
^-conductivity, 253-4, 327-33
detection systems and contacts, 2602
SEM CC microscope optimization,
262
EBIC and CL defect contrast theory,
296-326
EBIC and EBIV measurements,
262-96
448
Index
charge collection by a Schottky
barrier, 263-8
EBIC current collected by p - n
junction or Schottky barrier
normal to the beam, 286
EBIC current collected by p - n
junction or Schottky barrier
parallel to the beam, 268-85
heterojunctions and barriers in
striated ZnS platelets, 295
modelling in defect-free material,
263
plasma effect contrast, 296
Schottky barriers height
determinations, 294
time-resolved EBIC, 285-6
confocal scanning laser optical
microscope, 8
contrast theory
linear dislocation EBIC, 298-301
physical dislocation, 319-26
plasma effects on dislocation EBIC,
305-6
second-order dislocation, 301-5
dislocation EBIC strength, 302-3
and dislocation strengths, 303-4
EBIC dislocation studies, 301-2
Monte Carlo simulations, 304-5
dark dot contrast, 404
DC servo motors, 202
deep level transient spectrometer, 341
deep level transient spectroscopy,
(DLTS), 340-1
Dember potential, 327
depth varying minority carrier diffusion
lengths, 290-2
design validation, 219
detector system limiting factors, 24
device geometry, 164
Dirac delta function, 263
Donolato theory of EBIC contrast, 245
doped silicon semiconductors, 216
dot and halo contrast, 404
DRAMs, 220-3
E-beam lithography systems, 27
E-beam testers, 27, 155
EBIC (electron beam-induced current),
6, 14, 15, 57, 245, 246
and CL defect contrast theory, 296326
contrast of precipitates, 309-10
and EBIV measurements, 262-96
charge collection by a Schottky
barrier, 263-8
EBIC current collected by p - n
junction or Schottky barrier
normal to the beam, 286
EBIC current collected by p-n
junction or Schottky barrier
parallel to the beam, 268-85
heterojunctions and barriers in
striated ZnS platelets, 295
modelling in defect-free material,
263
plasma effect contrast, 296
Schottky barrier height
determinations, 294
time resolved, 285-6
grain boundary EBIC contrast, 3069
linear dislocation EBIC contrast
theory, 298-301
dislocation resolution, 300-1
dislocation strength, evaluating,
299-300
phenomenological theory of, 297-8
plasma effects on dislocation EBIC
contrast, 305-6
dislocation EBIC strength, 302-3
EBIC dislocation studies, 301-2
Monte Carlo simulations, 304-5
of precipitates and stacking faults,
309-10
temperature dependence of EBIC
contrast, 317-19
EBIV measurements, 262-96
EELS (electron energy loss
spectroscopy), 9, 26, 63-8
electric field dependent CL, 408
electroacoustic mode, 10, 15, 425-45
electron backscattering patterns, 113-4
electron beam diameter and current,
17-22
electron beam induced conductivity see
EBIC
electron channeling patterns (ECP)
449
Index
channeling micrographs, 98-100
contrast
angle of scan, 76-7
beam collimation, 77-8
beam current, 79-80
sample preparation, 81-3
signal collection, 80-1
signal processing, 81
theory, 71-6
electron backscattering patterns, 113—
4
information in
crystal perfection, 95-8
lattice parameter determinations,
93-5
microanalysis, 95
orientation, 83-92
Kossel patterns, 93, 115-16
selected area (SACP), 100-5
application to microerystalline
orientation, 105-8
studies of crystalline perfection,
108-13
electron energy loss spectroscopy
(EELS), 9, 26, 63-8
electron probe microanalysis, 5, 9, 24-6
electron scattering, 31-44
cross sections, 33-4
elastic scattering, 34-8
inelastic, 38-44
continuous energy loss
approximation, 43-4
multiple electron excitations, 41-3
single electron excitations, 39-41
fast secondary electrons, 39-40
inner-shell ionization, 40-1
low-energy secondary electrons,
39
process of, 31-2
electron voltaic effects (EVEs), 245
emissive mode, 5, 9, 14
backscattered imaging modes, 134-8
backscattered modes, 134
channeling, 138
magnetic contrast, 135-8
Z-contrast and topography, 134-5
detectors for imaging, 123-8
quantitative microanalysis, 140-4
secondary electron imaging modes,
128-33
magnetic, 132-3
topographic contrast, 128-30
voltage contrast, 130-2
signals in, 120-3
X-ray microanalysis, 138-40
qualitative, 144-6
quantitative, 146-8
energy dispersive spectrometers (EDS),
24, 140-2
energy dispersive spectroscopy, 340
EPMA (electron probe microanalysis),
5,9
dedicated, 26
ZAF corrections, 24-5
equipotentials, 164
ETEC, 101
Everhart-Hoff depth-dose function,
256-7, 265
Everhart-Thornley (E-T)
collector, 186, 216
Everhart-Thornley (E-T) detector, 123—
5
configuration, 126
secondary electron detector, 81
Faraday cage, 186
FCC crystal, 85, 86
Fermi-Dirac statistics, 321
Feuerbaum energy filter, 186-90
field effect transistor (FET), 141
field-emission guns, 21-2
filling pulse width scan, 357
Fourier transform spectrometers, 9
fringing fields, 164
FWHM, 142, 177
Gaussian spot diameter, 22-3
Gaussian spot size, 17
Green's function, 264
Grun range, 256
HB-5, 26
hemispherical electron energy filters,
182-3
heterojunctions, 6, 295-6
450
Index
ideality factor, 247
image processing, 204-5
indium phosphide electrode, 59, 60
instrumentation, 16-25
inverse transform in charge collection
microscopy, 265
isothermal DLTS, 361
JEOL, 101
Kikuchi patterns, 71
Kossel patterns, 93, 115-16
K-shell ionization cross sections, 41, 43
Lambert's Law, 129
Langmuir's law, 20
lanthanum hexaboride guns, 21
lateral-dose function, 258
light optical microscopes (LOMs), 10
linear dislocation EBIC contrast theory,
298-301
dislocation resolution, 300-1
evaluating dislocation strength, 299300
plasma effects on, 305-6
Lintech energy filter, 186-90
local DTLS, 344
Lorentz deflection, 135
L-shell ionization cross sections, 43
luminescence
applications, 403-18
defect contrast studies, 403-10
depth-resolved
cathodoluminescence, 414-18
time-resolved cathodoluminescence,
410-13
mechanisms and centres, 376-85
native, 415
recombination processes, 385-6
MAS-corrections, 395
metal-oxide semiconductor (MOS), 8,
207-13
method of moments, 275-6
micrometre and sub-micrometre
diffusion lengths, 285
Miller indices, 83, 84, 88, 93, 94
minimum attainable spot size, 22-3
modulation spectroscopy, 15
Monte Carlo electron trajectory
simulation technique, 31, 139,
258-9
applications to semi-conductors, 5261
calculation of charge collection
microscopy images, 57-61
calculation of line width, 52-3
effect of fast secondary electrons
on photoresist resolution, 55-7
exposure of photoresists, 53-4
calculations, practical aspects of, 4 8 52
incorporating secondary processes,
48-9
statistics, 50-1
targets with special geometry, 51-2
testing, 49-50
double, 56
and EBIC, 304-5
formulation, 46-8
general principles, 45-6
Mott cross sections, 37
multiexponential DLTS, 361
multiple quantum wells (MQW), 413
NMOS, 207, 223
non-scanning cathodoluminescence
systems, 402-3
OBIC (optical beam-induced current),
7, 8
ohmic contacts, 261
open-loop waveform, 170, 173
photoinduced capacitance transient
spectroscopy (PICTS), 362
photoluminescence (PL), 79, 375
physical dislocation contrast theory,
319-26
planar collector geometry, 289
planar electron energy filters, 182-3
plasmon scattering, 42-3
point analysis, 15
Index
PMOS, 207
p - n junctions, 6
EBIC current collected by, normal to
the beam, 286
EBIC current collected by, parallel to
the beam, 268-85
point defect image, 360
polycrystalline silicon channeling
patterns, 91
polycrystalline silicon (polysilicon)
semiconductors, 216
polyimide, 217
polymethylmethacrylate, 55
Powell constants, 31
rate window, 342
scan, 359-61
re-absorbed recombination radiation
(RRR), 393
Read model, 319-21
recombination at dislocations, 321-2
recombination heating, 429
resolution, 8-16
point, 12-13
signal (spectral), and contrast, 15-16
spatial
and contrast, 10-15
horizontal, 14
and magnification, 15
vertical, 14
'Rowland' circle, 143
Rutherford elastic scattering cross
section, 34, 35, 50
scanning Auger microscopy (SAM), 9
scanning deep level transient
spectroscopy (SDLTS), 8, 340-70
applications, 365-9
capacitance versus current, 350-2
excitation process, 347-50
instrumentation, 352-5
optimization of the imaging
conditions, 355-8
on semi-insulating materials, 362-5
signal identification, 358-62
scanning electron microscopes (SEMs)
general purpose, 25
mini, 25-6
numbers manufactured and sold, 4
as a two-component system, 5-8
451
scanning optical microscope (SOM),
353
Schottky barriers, 6
EBIC current collected by, normal to
the beam, 286
EBIC current collected by, parallel to
the beam, 268-85
Schottky contacts, 261
S-curves, 161-6
SEAM
analysis of semiconductors, problems
with, 435-6
application to semiconductor
characterization, 436-43
detection, 432-3
experimental conditions for, 431-6
gallium arsenide semiconductors, 437
generation of signals, 427-30
lock-in amplification of signals, 434
by means of boxcar integration, 435
metallizations on semiconductors,
442-3
origin of contrast, 430-1
origin of signals and contrasts, 42731
set-ups for, 433-5
silicon semiconductors, 438-42
secondary ion mass spectrometry
(SIMS), 340
second-order dislocation contrast
theory, 301-5
SEM CC microscope optimization, 262
semi-insulating (SI) GaAs, 330, 333
signal gating, 175-7
silicon controlled rectifier (SCR), 227
silicon crystal, 90
silicon dioxide, 216
silicon nitride, 216
solid-state detector, 127
SOMSEM, 6-8
specimen stages, 200-4
'spray apertures', 19
stacking faults, 309-10
stand-alone energy filters, 186-91
STEM, 14-15, 191, 341
dedicated, 26
mode, 9
stepping motors, 202
Stereoscans, 25
stroboscopy, 167-75
452
Index
surface acoustic wave devices (SAWs),
234-5
surface recombination, 272-5
effects of surface oxide charging by
the beam, 277-8
reverse bias and its verification, 27884
velocity, 268-9, 288
swirl defects, 296
TEMSCANS, 27
through-the-lens (TTL) filters, 186
transmission electron microscopes
(TEMs), 10
numbers manufactured and sold, 4
trap population statistics, 345-7
tungsten, 21
'unit triangle', 85
voltage contrast
applications, 206-35
application-specific integrated
circuits (ASICs), 223-6
CMOS latch-up, 226-30
junction location and leakage,
230-4
microprocessors and memories,
218-23
operating conditions, 206-13
passivation removal, 216-17
passivated devices, 213-16
surface acoustic wave devices
(SAWs), 234-5
instrumentation, 177-205
beam blanking systems, 193-200
combined lens/energy filters, 191-3
electron energy filters, 182-93
stand-alone energy filters, 186—
191
electron probe, 178-82
general resolution considerations,
177-8
origins, 153-5
principles, 155-77
boxcar averaging, 175-7
stroboscopy, 167-75
voltage measurement, 155-67
recent developments, 235-8
VMOS, 207
Van Roosbreck-Shockley theory, 392
Wannier-Mott excitons, 382
wavelength dispersive detectors, 142-4
wavelength dispersive spectrometers
(WDS), 24
Wehnelt (grid), 17
Wehnelt modulation, 194
wet chemical analysis, 139
Wilshaw and Booker model, 322-3
X-ray energy dispersive spectrometer,
25
X-ray microanalysis, 138-40
qualitative, of an unknown, 144-6
quantitative, 146-8
X-ray mode, 5, 9
X-ray spectroscopy systems, 6
Z contrast' 37, 134-5
'ZAF method, 24, 147-9
ZnS platelets, 295-6