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Electron probe microanalysis
Electron - Specimen
Interaction
Revised 1/19/13
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What’s the point?
Electrons from a source
interact with electrons in specimen
yielding a variety of photons and electrons
via elastic and inelastic scattering processes.
These are the “signals” that we use to make
images and measure to characterize the
composition of our specimens.
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Overview
•Elastic and inelastic processes
•Characteristic and continuum X-rays
•K,L,M etc: families of X-rays
•Energy versus wavelength
•Moseley’s relation
•Absorption or critical excitation energy
•Interaction volume and ranges
•Monte Carlo models
•Odds of X-ray production
•Distinction between X-rays and electrons
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Elastic and inelastic scattering
of HV electron by sample
Elastic (a): incident electron’s
direction altered by Coulombic field of
nucleus (Rutherford scattering),
screened by orbital electrons. Direction
may be changed by 0-180° (ave 25°) but velocity remains virtually
constant. <1 eV of beam energy
transferred.
E0 = accelerating voltage
(of electrons emitted from
gun); usually 15-20 keV
Inelastic (b): incident electron transfers
some energy (up to all, E0) to tightly
bound inner-shell electrons and loosely
bound outer-shell electrons. Direction
(Goldstein et al, 1992, p.72)
barely changes (<0.1°)
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Elastic and inelastic scattering
of HV electron by sample
This Monte Carlo program output represents 1000
electron trajectories (idealized), in a cross-section--both
elastic and inelastic scattering. Twenty years ago this
(Goldstein et al, 1992, p.72)
took a fair amount of computing power….
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Monte Carlo simulations are very useful
Today, you can simulate the “interaction volume” of scattered
electrons for whatever kV and whatever composition material
you may be interested in, in seconds. (above: using “Casino”)
Gopon et al, 2013
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Scattering lexicon
Cross section: a measure of the probability that an event of a
certain kind will occur, e.g. K-shell cross section. Defined as
Q = N/nint, where N=events of certain type/vol (sites/cm3),
ni=number incident particles/unit area (particles/cm2), and
nt=number target sites/vol (sites/cm3). Q has units of cm2 and
is thought of as an effective ‘size’ which the atom presents as
a target to incident particle. The Q for elastic scattering is
~10-17 cm2 and for K-shell ionization is ~10-20 cm2.
Mean free path: average distance an electron travels within a
specimen between events of a specific type. MFP=A/(NArQ)
where A is atomic wt (g/mol), NA is Avogadro’s number, r is
density (g/cm3).
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Elastic and inelastic scattering
Elastic :
Backscattering of electrons (~high energy)
Inelastic :
Plasmon excitation (in metals, loosely bound outershell electrons are excited)
Phonon excitation (lattice oscillations: heating)
Secondary electron excitation
Inner-shell ionization (Auger electrons, X-rays)
Bremsstrahlung (continuum) X-ray generation
Cathodoluminescence radiation (non-metal valence
shell phenomenon)
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Backscattered Electrons
High energy beam electrons may suffer single or multiple
elastic scattering events in the solid, escaping from the
material.
The fraction of beam
electrons that scatter back (h)
was found experimentally to
vary directly as a function of
composition (atomic number
Z). This provides a valuable
imaging tool: a rapid means
to discriminate phases that
have different mean Z values.
Intensity (grey level) varies from black (voids/epoxy), to
plagioclase, olivine, basaltic glass, with Ti-magnetite the
brightest phase.
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Secondary Electrons
Inelastic scattering of HV beam electron can promote loosely
bound electrons from valence to conduction band in
semiconductor or insulator with enough energy to move thru
the solid (in metals, promotion from conduction-band
directly). Backscattered electrons can also produce secondary
electrons.
By definition,
these secondary
electrons are
<50 eV, with
most <10 eV.
(Goldstein et al, 1992, p. 107)
a) Complete energy distribution of electrons emitted from target.
Region I and II are BSE, Region III secondary. b) Secondary
electron energy distribution, measured (points) and modeled (lines)
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SE images
Secondary electrons are generated
throughout the interaction volume, but
only secondary electrons produced near
the surface are able to escape (~5 nm in
metals, ~50 nm in insulators). For this
reason, secondary electron imaging
(SEI) yields high resolution images of
surface features.These have grey-scales,
though pseudo-coloring is sometimes
done.
20 mm
Pollen, cat flea, and Si nanowires on alumina sphere.
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SE and BSE coefficients
Coefficients for backscattered-electron (h) and secondary electron (d) as
function of Z. Tilt of specimen from 90° beam incidence (q) is 0.
E0=30 keV. Data from 1966; more recent views suggest the flat SE curve
may be due to carbon contamination on specimen hindering SE escape.
(Goldstein et al, 1992, p. 109)
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Inner-shell ionization:
Production of X-ray or Auger eTime
1
2
3
K shell
L shell
Blue Lines indicate
subsequent times: 1
to 2, then 3 where
there are 2 alternate
outcomes
(=photoelectron)
HV electron knocks inner shell
(K here) electron out of its orbit
(time=1). This is an unstable
configuration, and an electron
from a higher energy orbital (L
here) ‘falls in’ to fill the void
(time=2). There is an excess of
energy present and this is
released internally as a photon.
The photon has 2 ways to exit
the atom (time=3), either by
ejecting another outer shell
electron as an Auger electron
(L here, thus a KLL transition),
or as X-ray (KL transition).
(Goldstein et al, 1992, p 120)
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X-ray Lines - K, L, M
Ka X-ray is produced due to
removal of K shell electron,
with L shell electron taking
its place. Kb occurs in the
case where K shell electron
is replaced by electron from
the M shell.
La X-ray is produced due to
removal of L shell electron,
replaced by M shell electron.
Ma X-ray is produced due to
removal of M shell electron,
replaced by N shell electron.
(Goldstein et al, 1992, p 121)
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All possible K, L, M X-ray Lines
(Originally Woldseth, 1973,
reprinted in Goldstein et al,
1992, p 125)
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X-ray Lines with
initial + final levels
NB:not
Greek!
LN
LL
(Reed, 1993)
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Nomenclature of X-rays
There is some
movement now
to change the
way X-rays are
described, from
the traditional
Siegbahn
notation (e.g.
Ka1) to the the
IUPAC (K-L3).
(International
Union of Pure
and Applied
Chemistry). This
table is from
their 1991
recommendation.
(Reed, 1993)
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X-ray energies, Cu for example
Where do the values
for characteristic xrays come from: here
are the numbers for
Cu K x-rays:
Subtract the energy of
the L shell (binding)
energy from that of
the K shell (binding)
energy, and you have
the characteristic
value.
L3 2p3/2
933 ev
L2 2p1/2
952 ev
L1 2s
1097 ev
Ka1
K
1s
Ka2
8979 ev
8979 - 933 = 8046 ev (book says 8048)
8979 - 952 = 8027 ev (book says 8028)
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Or… Fe L lines
Ll = M1-L3 = 615.2 eV
Lα= M5-L3 = 705.0 eV
Lβ= M3-L2 = 718.5 eV
(Gopon et al., 2013)
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Absorption Edge Energy
Edge or Critical ionization energy:
minimum energy required to
remove an electron from a
particular shell. Also known as
critical excitation energy, X-ray
absorption energy, or absorption
edge energy. It is higher than the
associated characteristic (line) Xray energy; the characteristic
energy is value measured by our
X-ray detector.
Example: Pt (Z=78)
X-ray line energies and
associated critical excitation
(absorption edge) energies,
in keV
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Absorption Edge Energy
Edge or Critical ionization energy:
minimum energy required to
remove an electron from a
particular shell. Also known as
critical excitation energy, X-ray
absorption energy, or absorption
edge energy. It is higher than the
associated characteristic (line) Xray energy; the characteristic
energy is value measured by our
X-ray detector.
Example: Pt (Z=78)
X-ray line energies and
associated critical excitation
(absorption edge) energies,
in keV
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Overvoltage
Example: Pt (Z=78)
X-ray line energies and
associated critical excitation
(absorption edge) energies,
in keV
Overvoltage is the ratio of accelerating
(gun) voltage to critical excitation
energy for particular line*. U = E0/Ec
Maximum efficiency (cross-section) is
at 2-3x critical excitation energy.
Example of Overvoltage for Pt:
for efficient excitation of this line,
would be (minimally) thisß
accelerating voltage
• La -- 23 keV
• Ma -- 4 keV
* recall: E0=gun accelerating voltage; Ec=critical excitation energy
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Overvoltage
Example: Pt (Z=78)
X-ray line energies and
associated critical excitation
(absorption edge) energies,
in keV
Overvoltage is the ratio of accelerating
(gun) voltage to critical excitation
energy for particular line*. U = E0/Ec
Maximum efficiency (cross-section) is
at 2-3x critical excitation energy.
Example of Overvoltage for Pt:
for efficient excitation of this line,
would be (minimally) thisß
accelerating voltage
• La -- 23 keV
• Ma -- 4 keV
* recall: E0=gun accelerating voltage; Ec=critical excitation energy
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Fluorescence yield
Fluorescence yield (w) is fraction of ionizations that
yield characteristic X-ray versus Auger yield (a)
within a particular family of X-rays. w + a =1
(Goldstein et al, 1992)
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Fluorescence yield …
can cause misunderstanding
1. These are fractions, so each
one is normalized to one.
You cannot say anything
about absolute detected xray intensities.
2. Measured characteristic x-rays by WDS will additionally be
a function of (a) the crystal diffraction efficiency, (b) the gas
absorption efficiency, and c) the spectrometer sin theta
position (distance between detector and sample).
For example, from the above chart, you cannot predict
whether Hf La or Hf Ma will have higher count rates.
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Continuum X-rays
HV beam electrons can decelerate in the Coulombic field of
the atom (+ field of nucleus screened by surrounding e-). The
loss in energy as the electron brakes is emitted as a photon, the
bremsstrahlung (“braking radiation”). The energy emitted in
this random process varies up from 0 eV to the maximum, E0.
On an EDS plot of X-ray intensity vs energy, the continuum
intensity decreases as energy increases. The high energy value
where the continuum goes to zero is known as the DuaneHunt limit.
The Duane-Hunt
limit is very
important to
remember -- and
utilize continuously!
Duane-Hunt
Limit
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Kramer’s Law
Duane-Hunt
Limit
Kramer’s Law (or Relation) is a mathematical description
(formula) for the background or continuum shape and
intensity:
I = constant x Z (E0 - E) / E
Where I is the intensity of the continuum at any energy E, Z is
atomic number and E0 is the accelerating voltage
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Continuum and Atomic Number
At a given energy (or l), the intensity of the continuum
increases directly with Z (atomic number) of the
material. This is of critical importance for minor or trace
element analysis, and also lends itself to a timesaving
technique (Mean Atomic Number,“MAN”).
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X-ray units: A, keV, sin q, mm
l = hc/E0 where h=Plancks constant, c=speed of light
l = 12.398/E0 where is l is in Å and E0 in keV
also, the 2 main EMPs plot up X-ray positions thusly:
Cameca: n l = 2d sin q so for n=1 and a given 2d, an Xray line can be given as a sin value (or 105 times sin q)
JEOL: distance (L, in mm) between the sample (beam
spot) and the diffracting crystal, i.e. L= l R/d, where R is
Rowland circle radius (X-ray focusing locus of points) and
d is interlayer spacing of crystal.
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Moseley’s Relation
Moseley (1913, 1914)
found that there is a regular
relationship between the
atomic number of a
material and its
characteristic X-ray
wavelength.
l =B/(Z-C)2,
where B and C are
constants for each family
of X-rays.
(Goldstein et al, 1992, p. 123)
Cathodoluminesce
When insulators and semiconductors are hit by HV
electrons, long l photons (UV, visible, IR light) may be
emitted. The light may be bright enough to be seen in the
reflected light image (examples are benitoite, scheelite,
zircon, corundum, diamond, wollastonite, YAG, GaAlAs).
Incident electrons may promote valence shell electrons
across the band gap to the empty conduction band,
creating electron-hole pairs. With no bias to sweep the
electron away, it will recombine with the hole. The excess
energy (= gap energy) will be emitted as a long l photon.
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CL Images
CL image of zircon from Yellowstone tephra (Lava
Creek Tuff). Note faint oscillatory zoning
surrounding sector-zoned core, and healed fractures.
These are not visible in the BSE image. ~50 um
grain. (courtesy Ilya Bindeman)
Impurity atoms as well as
dislocations increase the
possibilities for
additional gap energies,
yielding different
wavelengths of emitted
light.These may be
valuable for production
of diagnostic images. CL
is a cheap way to view
overgrowths (inherited
cores) and healed
fractures in quartz and
zircons.
Electron interaction volumes
Effect of beam interaction (damage) in plastic (polymethylmethacrylate), from
Everhart et al., 1972. All specimens received same beam dosage, but were etched
for progressively longer times, showing in (a) strongest electron energies, to (g) the
region of least energetic electrons. Note teardrop shape in (g). Same scale for all.
(Goldstein et al, 1992, p 80)
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Ranges and
interaction
volumes
It is useful to have an
understanding of the
distance traveled by the
beam electrons, or the
depth of X-ray
generation, i.e. specific
ranges. For example: If
you had a 1 um thick
layer of compound AB
atop substrate BC, is
EPMA of AB possible?
Electron and X-ray Ranges
Several researchers have developed physical/mathematical
expressions to approximate electron and X-ray ranges. Two
common ones are given below.
Electron range. Kanaya and Okayama (1972) developed an
expression for the depth of electron penetration:
RKO=(0.0276 A E01.67)/(r Z0.89)
X-ray range. Anderson and Hasler (1966) give the depth of Xray production as:
RAH=(0.064)(E01.68 - Ec1.68)/ r
where Ec is the absorption edge (critical excitation) energy.
There are nomograms for these ranges, given on the next slides.
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Ranges
From Will Bigelow,
now emeritus U MI
(Ann Arbor)
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Monte Carlo simulations
With the development of PCs, Monte Carlo simulations of
electron-beam interactions have been very easy to perform.
You can input your specific sample composition and run
various “what if” scenarios, e.g. what is the maximum
penetration of the electron beam through a thin film, or
what is the smallest size crystal in a glass matrix that can be
analyzed.
You will be performing
some of these MC
simulations in a take
home exercise.
Each MC run has distinct conditions:
specific E0, specific composition (Atomic
wt and average Z), density, and
potentially different tilt angle.
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Specimen Heating
Castaing (1951) derived the maximum temperature rise in a
solid impacted by electrons of E0 energy and i current (in
mA) and beam diameter d (mm):
DT = 4.8 E0 i /kd
where k is thermal conductivity (W/cmK).
For E0=20 keV and 20 nA, d=1 um, in a metal (k=1), DT is
2 K. In a typical mineral (k=0.1), DT is 20 K. And in
organic material, (k=0.002), DT is 1000 K! (e.g. epoxy)
Difficult materials: carbonates, hydrated materials, halides,
phosphates, glasses, feldspars.
(Reed 1993, p 158)
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“Harper’s Index” of EPMA
1 nA of beam electrons = 10-9 coulomb/sec
1 electron’s charge = 1.6x 10-19 coulomb
ergo, 1 nA = 1010 electrons/sec
Probability that an electron will cause an ionization: 1 in 1000 to 1 in 10,000
ergo, 1 nA of electrons in one second will yield 106 ionizations/sec
Probability that ionization will yield characteristic X-ray (not Auger electron):
1 in 10 to 4 in 10.
ergo, our 1 nA of electrons in 1 second will yield 105 xrays.
Probability of detection: for EDS, solid angle < 0.01 (1 in 100). WDS, <.001
ergo 103 X-rays/sec detected by EDS, and 102 by WDS. These are for pure
elements. For EDS, 10 wt%, 102 X-rays; 1 wt% 10 X-rays; 0.1 wt % 1 X-ray/sec.
ergo, counting statistics are very important, and we need to get as high count rates
as possible within good operating practices.
Acknowledgement: I first encountered this treatment at the Lehigh Microscopy Summer School
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Sources of X-ray data
• J.A. Bearden, 1964 (NBS; AEC)
• White et al (“Penn State” 1965) tables
• main lines in tables in Goldstein et al, and Reed texts
• Probe for EPMA database (includes higher order lines for
WDS), also online at <epmalab.uoregon.edu/UCB_EPMA/xray>
• NIST database: click on “X-ray Database” at bottom of page:
www.cstl.nist.gov/div837/Division/outputs/DTSA/DTSA.htm
• Lawrence Berkeley National Lab online at xdb.lbl.gov for data
Electrons and X-rays …
don’t get them confused !
• X-rays have no mass, no charge; electrons have charge
(key!) and a small mass
• X-rays can be produced by accelerating HV electrons
in a vacuum and colliding them with a target.
• The resulting electron-generated X-ray spectra contains
(1) continuum or continuous background
(Bremsstrahlung), (2) occurrence of sharp lines
(characteristic X-rays), and (3) a cutoff of continuum at
a short wavelength/high keV.
• X-rays can also generate other x-rays, but unlike the
above process, NO Bremsstrahlung is produced!