A VERSATILE, MULTIMODE SCANNING PROBE
MICROSCOPE
by
Christoph Hebeisen
Vordiplom (Universität Stuttgart, Germany, 1998)
T HESIS SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
M ASTER OF S CIENCE
IN THE DEPARTMENT
OF
P HYSICS
c Christoph Hebeisen 2002
SIMON FRASER UNIVERSITY
April 26, 2002
Copyrights are not reserved.
Permission is hereby granted to
reproduce this work in whole or
in part provided that proper credit is
given to the original author.
APPROVAL
Name:
Christoph Hebeisen
Degree:
Master of Science
Title of Thesis:
A Versatile, Multimode Scanning Probe Microscope
Examining Committee:
Dr. Howard Trottier, Professor
Department of Physics, SFU (Chair)
Dr. John Bechhoefer, Professor
Department of Physics, SFU
Dr. Karen Kavanagh, Professor
Department of Physics, SFU
Dr. Michael Wortis, Professor
Department of Physics, SFU
Dr. Simon Watkins, Professor
Department of Physics, SFU
Date Approved:
April 26, 2002
ii
Abstract
The superior resolution capability of scanning probe microscopy (SPM) makes it an ideal
tool for investigations beyond the diffraction limit of ordinary optical microscopy. We
have designed and built a scanning probe microscope that combines atomic force microscopy (AFM), near field scanning optical microscopy (NSOM) and scanning tunnelling
microscopy (STM) with simultaneous optical far field detection. The simultaneous use
of AFM and NSOM or STM and optical detection has potential applications in molecular
biology and biophysics.
iii
Acknowledgments
I would like to thank my supervisor John Bechhoefer for his encouragement, helpful discussions and suggestions throughout this project. Russell Greenall deserves credit for software
and many other important contributions. I also want to thank Vincent Fourmond and Bram
Sadlik for their help with this project.
I want to thank the German Academic Exchange Service for financial support and for
making my studies at SFU possible in the first place.
Last but not least I want to thank my family and Lana Fong for patience, encouragement
and love.
iv
Contents
Approval
ii
Abstract
iii
Acknowledgments
iv
Contents
v
List of Tables
viii
List of Figures
ix
1 Introduction
1
1.1
Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Scanning Probe Microscopy . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2.1
Scanning Tunnelling Microscopy . . . . . . . . . . . . . . . . . .
2
1.2.2
Atomic Force Microscopy . . . . . . . . . . . . . . . . . . . . . .
3
1.2.3
Near Field Scanning Optical Microscopy . . . . . . . . . . . . . .
4
2 Theory
6
2.1
Vacuum Electron Tunnelling . . . . . . . . . . . . . . . . . . . . . . . . .
6
2.2
Forces Involved in AFM . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.2.1
Tip-Surface Interaction Forces . . . . . . . . . . . . . . . . . . . .
8
2.2.2
Static Bending of a Cantilever . . . . . . . . . . . . . . . . . . . .
9
Near-Field Optical Imaging . . . . . . . . . . . . . . . . . . . . . . . . . .
10
2.3.1
12
2.3
NSOM Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
CONTENTS
2.3.2
2.4
vi
Signal Estimation for NSOM . . . . . . . . . . . . . . . . . . . . .
12
The Digital PID Controller . . . . . . . . . . . . . . . . . . . . . . . . . .
15
3 Technical Implementation
3.1
3.2
3.3
3.4
18
Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
3.1.1
Sources of Mechanical Disturbances . . . . . . . . . . . . . . . . .
19
3.1.2
Countermeasures . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
3.2.1
Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
3.2.2
Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
3.3.1
Detection and Signal Conditioning, AFM . . . . . . . . . . . . . .
27
3.3.2
Sample Emission Detection . . . . . . . . . . . . . . . . . . . . .
29
Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
3.4.1
Detection and Signal-Conditioning, STM . . . . . . . . . . . . . .
29
3.4.2
Positioning Driver Electronics . . . . . . . . . . . . . . . . . . . .
30
3.4.3
Supplementary Electronics . . . . . . . . . . . . . . . . . . . . . .
32
4 Results
33
4.1
AFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
4.2
NSOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
4.3
STM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
5 Conclusions and Further Projects
38
5.1
AFM -translation Modification . . . . . . . . . . . . . . . . . . . . . . .
38
5.2
Photon Emission from Inelastic Tunnelling . . . . . . . . . . . . . . . . .
39
Appendices
A Electronic Circuits
40
A.1 STM Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
A.1.1 IV-converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
A.1.2 Second Stage Amplifier . . . . . . . . . . . . . . . . . . . . . . .
40
A.1.3 Stable Power Supply . . . . . . . . . . . . . . . . . . . . . . . . .
42
CONTENTS
vii
A.2 Vernier Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
A.3 Close-Approach Motor-Control . . . . . . . . . . . . . . . . . . . . . . . .
48
B Optics
51
B.1 AFM detection optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
B.1.1
Laser Spot Size . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
B.1.2
Lever Deflection Signal Conditioning . . . . . . . . . . . . . . . .
51
B.2 Sample Emission Detection Optics . . . . . . . . . . . . . . . . . . . . . .
54
C Controller
56
C.1 Controller Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
C.1.1
The Fast Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
C.1.2
The Slow Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
D Scanner Calibration
62
E Dynamic Characterisation of the STM
64
List of Abbreviations
66
Bibliography
67
List of Tables
A.1 Noise and common mode response (RMS) of the vernier and buffer circuits.
48
D.1 The SPM scanner calibrations. . . . . . . . . . . . . . . . . . . . . . . . .
62
viii
List of Figures
1.1
Schematic drawing of an AFM. . . . . . . . . . . . . . . . . . . . . . . . .
2.1
The potential of a tunnelling barrier between two metals; (a) Two different
3
metals with a bias voltage applied between them; (b) two identical conductors with no bias voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.2
An AFM Cantilever. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2.3
The SPM feedback system. . . . . . . . . . . . . . . . . . . . . . . . . . .
15
3.1
a) Damping system for insulating the SPM from building vibrations; b)
Model of the SPM for vibration analysis. . . . . . . . . . . . . . . . . . . .
21
3.2
A harmonic oscillator with different damping coefficients. . . . . . . . . .
22
3.3
Mechanical design of the instrument, STM configuration. . . . . . . . . . .
25
3.4
The AFM head (closeup on the right side), the bungee cord vibration damping system and the acoustic and thermal shielding system. The inside of the
shielding box is coated with aluminum foil for additional protection against
electrical interference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
3.5
Schematic drawing of the AFM detection optics . . . . . . . . . . . . . . .
28
4.1
a) An SPM test grating; black to white range
. b) Atomic step on
graphite; -range ca. Å. . . . . . . . . . . . . . . . . . . . . . . . . . .
34
4.2
AFM and NSOM images of a test sample with fluorescent microspheres. . .
35
4.3
AFM/NSOM images taken with a damaged NSOM tip. . . . . . . . . . . .
36
4.4
STM images Gold evaporated on a microscope slip. a), b) Two images
taken during the same scan as left and right image. c) closeup of the same
sample. Bias voltage .. . . . . . . . . . . . . . . . . . . . . . . .
ix
37
LIST OF FIGURES
4.5
x
Typical result of an attempt to image freshly cleaved HOPG surface. Bias
voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
A.1 Block diagram of the electronics . . . . . . . . . . . . . . . . . . . . . . .
41
A.2 The STM signal conditioning circuits - IV-converter (left) and second-stage
amplifier (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
A.3 The measured transfer function of the STM signal-conditioning electronics;
second-stage amplifier (solid) and (dashed). . . . . . . . . . . . .
43
A.4 Stable power supply for STM signal conditioning. . . . . . . . . . . . . . .
43
A.5 The idea of the vernier circuit. . . . . . . . . . . . . . . . . . . . . . . . .
44
A.6 The -vernier circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
A.7 The transfer functions of the
coarse (solid) and fine (dashed) channels of
the vernier circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
A.8 DC-motor speed control circuit. . . . . . . . . . . . . . . . . . . . . . . .
49
A.9 Close approach speed vs. control voltage. . . . . . . . . . . . . . . . . . .
50
B.1 The quad photodetector;
is the detector radius,
the radius of the
laser spot and the offset of the laser spot. . . . . . . . . . . . . . . . . .
B.2
right left
vs.
52
; solid: numerical calculation; dashed: linear approximation. 53
B.3 The sample emission pickup optics, NSOM configuration. . . . . . . . . .
54
C.1 Flowchart of the fast task. Splits in the execution path mean alternating
execution of the different targets. . . . . . . . . . . . . . . . . . . . . . . .
57
C.2 The principle of the -feedback system. . . . . . . . . . . . . . . . . . . .
59
tunnelling current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
D.1 Calibration of the piezoelectric positioners. . . . . . . . . . . . . . . . . .
63
E.1 The system transfer function of the STM. . . . . . . . . . . . . . . . . . .
64
C.3 The STM approach algorithm; is the fine -piezo control voltage, is the
Chapter 1
Introduction
1.1 Objective
The goal of this project is to build a multimode scanning probe microscope especially for
biophysical applications; the particular application that motivated it is high-resolution imaging of fluorescently labelled DNA [1].
Our main requirements for the instrument are
Atomic Force Microscopy (AFM);
Near Field Scanning Optical Microscopy (NSOM);
Scanning Tunnelling Microscopy (STM);
Efficient optical detection suitable for fluorescence experiments;
Large scan range and positioning reproducibility to allow detailed scans of small
areas that were previously identified in an overview scan.
Although instruments that combine AFM and NSOM or AFM and STM are commercially available, we are not aware of any SPM that implements all of the above features in
one instrument.
1
CHAPTER 1. INTRODUCTION
2
1.2 Scanning Probe Microscopy
At the heart of any of the various SPM methods is some type of short-range interaction
between a probe and a surface. The nature of this interaction is specific to each type of
SPM.
By scanning the probe over the sample, one can obtain a map of the sample in terms
of the interaction. Often, a feedback system is used to keep the interaction at a specific
strength by controlling the tip-sample separation. The image obtained in this way is usually
referred to as “sample topography,” although this is not entirely correct since it shows a
surface of constant interaction strength that depends both on topography and material properties. Obviously, high-precision imaging requires ways of carefully positioning the sample
relative to the probe tip in all three dimensions. In addition, an SPM needs a close-approach
mechanism to bring the probe within range of the positioning mechanism that controls the
tip-sample separation.
1.2.1 Scanning Tunnelling Microscopy
STM is historically the oldest SPM method [2]. It relies on the ability of electrons to tunnel
through a very narrow vacuum gap between two conductors. A sharp tunnelling tip is
brought near a (conducting) surface. If a voltage bias is applied between the surface and the
tip, a tunnelling current flows across the gap between the sample and the tip. Its magnitude
changes roughly exponentially with the distance between the tip and the surface.
The tunnelling current also depends on the electronic structure and the bias voltage;
this dependence may be used to examine the properties of semiconductors (tunnelling spectroscopy).
STM routinely reaches true atomic resolution. However, the sample must obviously be
at least moderately conducting for STM. This rules out the use of STM on many interesting
surfaces. Also, STM cannot be used in a conducting solution, which makes it unsuitable
for many biological applications.
CHAPTER 1. INTRODUCTION
3
1.2.2 Atomic Force Microscopy
AFM [3] can use different types of surface forces (e.g., electric and van der Waals) to image
a surface. It uses attractive, repulsive or lateral (friction) interatomic forces (see Ch. 2.2.1)
between a sharp tip and the sample in its different modes of operation.
Close−
approach
mechanism
Position−
sensitive
photodetector
Laser
Cantilever
and tip
sample
z
xyz translation
stage
y
x
Figure 1.1: Schematic drawing of an AFM.
We use only the “contact mode,” where the tip actually touches the surface and repulsive
forces between the sample and the tip dominate the interaction. Fig. 1.1 is a schematic
drawing of a contact-mode AFM with optical detection.
The cantilever acts as a spring that bends when a force acts on the tip. A laser beam
is reflected off the back side of the lever, and hence the beam is deflected when the lever
bends. This can then be detected with a position-sensitive photodetector.
In non-contact mode, the tip oscillates horizontally (shear- or lateral-force microscopy)
or vertically just above the surface. The tip-surface interaction influences the behaviour of
this oscillator, which can be detected by examining the amplitude, phase or frequency of
the oscillations. A hybrid between contact and non-contact mode is the “tapping mode,” in
which the lever also oscillates vertically but the tip lightly hits the surface during every cycle
of the oscillation. Material properties of the sample (such as elasticity and “stickiness” on
a microscopic level) strongly influence the data obtained in this mode.
CHAPTER 1. INTRODUCTION
4
In contrast to STM, AFM does not need conducting surfaces, and operation in solution
is not a problem. It has thus become an important tool for many fields. Its resolving
capabilities are not as good as STM; although the lattice structure of crystals can be resolved
[4], AFM does not normally reach true atomic resolution. Because of the finite interaction
area between tip and sample, one observes a convolution between the tip shape and the
sample topography that smears out details on the surface [5, 6]. Under ultra high vacuum
(UHV) conditions, however, true atomic resolution has been reported [7].
1.2.3 Near Field Scanning Optical Microscopy
A significant limitation of classical optical microscopy is that the wavelength of light sets
its resolution. An object that scatters light creates a diffraction pattern that spans the whole
solid angle around it. Since no optical microscope can capture all diffraction orders, information about the object is lost and the image reconstruction is incomplete, leading to finite
resolution [8]:
,
(1.1)
NA
where is the minimum distance at which two objects can still be distinguished, NA
is the numerical aperture of the microscope objective ( with the index of
refraction of the medium between object and lens and the half-angle of the cone of rays
captured by the lens) and is the wavelength of the light used. A good oil immersion
objective with NA of can resolve two objects down to about
if visible light
is used. Although other methods clearly offer higher resolution, optical
microscopy has retained its importance because of its versatility: Many techniques, such as
fluorescence microscopy and polarising microscopy, still have wide application.
In 1928, Synge [9] suggested that one could overcome the diffraction limit by illuminating the sample through a sub-wavelength ( ) aperture that is brought extremely close
( "!# ) to the sample. The light transmitted from the near-field probe through the sample
can then be collected in the far field by a conventional microscope objective and detected
with a sensitive photodetector, such as a photomultiplier tube or avalanche photodiode. The
size of the area of the sample that is illuminated essentially depends only on the size of the
aperture.
Obviously, some mechanism is required to maintain the small distance between the near
CHAPTER 1. INTRODUCTION
5
field probe and the sample. Typically, AFM (shear force or contact mode) is used for this
purpose [10]. This combination of AFM and NSOM also allows to obtain topographical
and optical information of the surface simultaneously.
The aforementioned DNA samples require dual labeling for distinguishing different
sections of the strands when standard optical microscopy is used. This is because the DNA
strands are not visible without labeling. In a combined AFM/NSOM, however, the topography information can be used to “see” the DNA while the photon count identifies tagged
regions. Therefore only one dye is necessary, which simplifies the sample preparation.
Since the topographic data obtained from shear force microscopy is not reliable [11], we
use contact mode AFM.
Chapter 2
Theory
In this chapter, we discuss the probe-sample interactions of different SPM methods and
the discrete PID (proportional, integral, differential) controller as a means of maintaining a
constant tip-sample interaction.
2.1 Vacuum Electron Tunnelling
The quantum-mechanical phenomenon of tunnelling arises because the wave function
describing a particle can extend into areas where classically it would be forbidden. The
Fermi energy
of a typical metal is about
below the vacuum potential. Two pieces
of metal separated by a vacuum gap will therefore have a
energy barrier between them.
,
(2.1)
Since electrons follow the Fermi-Dirac distribution,
it is extremely unlikely for them at room temperature to have enough energy ( !
) to pass this barrier classically by thermal fluctuations.
The one-dimensional potential
of a tunnelling gap is shown in Fig. 2.1. It is
instructive to look at the case of electrons tunnelling between two identical conductors with
no bias voltage (Fig. 2.1b). For a detailed treatment of this problem, see [12].
The time-independent Schrödinger equation for this simple tunnelling system is
! #" %)$'( & * & ,+-! * &
6
,
(2.2)
CHAPTER 2. THEORY
V
7
V
Gap
∆V
V gap
Metal 1
Metal 2
e−
EF
0
z
0
z
d
(a)
(b)
Figure 2.1: The potential of a tunnelling barrier between two metals; (a) Two different
metals with a bias voltage applied between them; (b) two identical conductors with no bias
voltage.
where is the potential energy of the electron:
We will assume
regions of the potential are
! gap .
gap
.
(2.3)
Then the solutions to the Schrödinger equation in the three
$
$ $
$
)(
( $ gap .
(2.4)
We will only look at electrons tunnelling from the left side to the right side and ignore the
more, we replace
, where by
term describing electrons approaching the barrier from the right side (
! and
! ). Further-
is the tunnelling matrix element for electrons
tunnelling from the left to the right side.
The conditions that
be continuous at
and
yield four
equations. Since we have five parameters and all equations are linear, we may choose the
CHAPTER 2. THEORY
8
amplitude of the incoming electron wave to be
$
. Solving the equations yields
.
$
& $& &
The probability of transmission of an electron through the barrier .
&
&
If the decay length of the electron wave function, ( ), we can simplify Eq. 2.6 to read
!
gap
gap
"
"
gap
is
(2.6)
gap
, is much smaller than the gap width
+ " ( gap
$ + (2.5)
gap
gap
'+
(2.7)
(2.8)
)( ! Å .
&
Hence, the tunnelling probability (and, therefore, the tunnelling current) depends expo , we expect the
nentially on the distance between the metal pieces. Assuming
where
gap
is the tunnelling barrier height and
tunnelling current to change by a factor of for every Å change in the tunnelling distance.
A more detailed calculation that takes the bias voltage into account [13] yields
where
,
is the bias voltage applied between the tip and the sample and
(2.9)
is the average
tunnelling barrier height.
2.2 Forces Involved in AFM
In normal force AFM, the attractive and repulsive forces between the tip and the surface are
balanced by the spring force of a bent cantilever.
2.2.1 Tip-Surface Interaction Forces
In contact-mode AFM, the dominating force is the repulsive interaction between two atoms
whose electron clouds overlap. Although there is no general expression that describes their
CHAPTER 2. THEORY
9
distance dependence, they can be modelled empirically [14]. The simplest model for the
interaction force is the “hard-sphere model”, which completely ignores any compressibility
of the atoms:
where
,
(2.10)
is the sum of the radii of the two atoms and is the distance between them. Other
approaches use a power-law potential or an exponential potential. However, the exact shape
of the potential does not matter, given that the potential rises very steeply when the distance
decreases below a certain distance, that is on the order of two atomic radii, and it only acts
on very short distances.
The other important force is the attractive van der Waals interaction
. Once
the tip is in contact with the surface, it will be compensated by the repulsion. However, this
increases the force of the tip on the surface where they are in contact. In reality, neither
tip nor surface is infinitely stiff. This causes the tip to be in contact with the sample over a
finite contact area instead of a single point [5].
2.2.2 Static Bending of a Cantilever
The cantilever in a contact-mode AFM holds the tip and acts as a spring that compensates
the forces between the tip and the surface and allows their measurement.
α
∆z
z
x
F
y
Figure 2.2: An AFM Cantilever.
Fig. 2.2 shows a lever that is rigidly mounted on one side and bent upwards by a force
applied to the other end. For small forces, the lever takes the shape [15]
&
,
(2.11)
CHAPTER 2. THEORY
where
10
is the force acting on the end of the lever,
material,
is the Young’s modulus of the lever
is the area moment of inertia (a constant that depends on the geometry of the
lever) and is the lever length. The spring constant at
is:
.
(2.12)
Since the spring constant is a parameter of commercial cantilevers that can experimentally
be determined [16], we rewrite Eq. 2.11 as
& .
(2.13)
In AFM, we use the deflection of a laser beam reflected off the back side of a cantilever
for detecting bending of the lever. Hence, the angle of deflection of the cantilever is much
more useful than the displacement. For small angles we can write
"!
and, assuming that the laser is focused on the end of the beam ( (2.14)
For biological samples, forces of !
), we obtain
.
(2.15)
or less must be used to avoid damage to the
specimen. With the soft contact mode cantilevers that we use ( , TM Microscopes (Veeco) Microlever “C”), we therefore expect angles around
!
,
. The optical detection system (see App. B.1.2) allows detection down to about
.
2.3 Near-Field Optical Imaging
A simple definition of near-field optics is given by Paesler and Moyer [17] who define
“near-field optics as that branch of optics that considers configurations that depend on the
passage of light to, from, through or near an element with subwavelength features and the
coupling of that light to a second element located a subwavelength distance from the first”.
In illumination NSOM, laser light is coupled through the probe tip and used to illuminate the sample. The tip takes on the role of the sub-wavelength emitter whose near
CHAPTER 2. THEORY
11
field probes the sample details that can convert evanescent modes into propagating waves
that can then be detected in the far field. This can happen either by scattering or by other
processes such as fluorescence.
Modes with high spatial frequencies, i.e., the ones that carry information about subwavelength details, decay exponentially with increasing distance from the object [18, 19].
While inaccessible to traditional far-field microscopy, they can be used to image in NSOM
and to boost the resolution beyond the diffraction limit.
The exponential decay of these modes and their detection at short distances is closely
analogous to electron tunnelling through a vacuum gap (see Ch. 2.1), which is why nearfield optical microscopy is sometimes dubbed photon tunnelling microscopy 1 .
The resolution of NSOM is essentially limited by the size of the near-field aperture.
This, however, cannot be made arbitrarily small. One limitation is the difficulty in funnelling enough light through the aperture to detect a signal. A second limitation comes
from the finite skin depth of the material used to make the “opaque” wall of the aperture.
Electromagnetic radiation penetrates even good conductors (typically, metals are used to
shield the light) to a certain depth, known as the skin depth. It sets the limit for the res-
olution2 in aperture NSOM (ca. [22]). Since the coating is somewhat dissipative,
this process heats the NSOM probe which can be destroyed if the power coupled into it
becomes too high.
For completeness, we mention a variant of NSOM, apertureless NSOM, that does not,
at least in theory, suffer from the above mentioned resolution limitations. Different methods
have been tested, including scattering techniques in which light is scattered by a sharp tip
which enhances the intensity in the vicinity of the tip [23] and illumination of the sample
using a single molecule in a crystal that has been glued to a conventional NSOM tip [24].
However, these techniques are not only very complicated to use but also so far have failed
to produce resolutions that are better than those routinely achieved in conventional aperture
NSOM.
1
In the literature (e.g. [20]), sometimes the term PSTM is used to describe what we call collection mode
NSOM while NSOM is used referring to illumination mode NSOM.
2
When light near the surface plasmon resonance is used, as is typically the case, light will penetrate much
longer than the simple skin depth ( for aluminum at !!
) [21] suggests.
CHAPTER 2. THEORY
12
2.3.1 NSOM Probes
The most popular probes for NSOM are tapered fiber probes. To produce them, a singlemode optical fiber is pulled in a pipet puller while heated by a laser [22]. Alternatively
& diameter with [25].
the taper can be achieved by etching the fiber to the desired aperture
To prevent light from escaping from the fiber in the taper, thus creating far field background,
the fiber is coated by evaporating a layer of aluminum onto it. These NSOM tips are commercially available3 as straight tips for shear force microscopy and as cantilevered tips for
normal force microscopy [26, 27] as distance feedback mechanism. The manufacturers
claim typical light transmission coefficients for tapered fiber probes on the order of .
Another type of commercially available NSOM probes are pyramidal AFM tips with a
hole through their center4 . A laser, focused on the hole in the back of the cantilever, can be
used to illuminate the sample. The transmission coefficient is on the order of .
2.3.2 Signal Estimation for NSOM
As a design goal for NSOM performance, we want to be able to observe single fluorophores
[28]. To demonstrate the feasibility of this, we estimate the expected signal [29]. As a
typical fluorescent molecule, we will assume the example of fluorescein, excited by the
line of an -ion laser.
The problem that limits most single molecule fluorescence measurements is photobleaching. In the excited state the molecule is more susceptible to reactions with its environment [30]. At high intensities, however, double excitation of the fluorophores becomes
a problem. In this process, a molecule that is already in an excited state gets excited to a
higher state when it is hit by another photon. The molecule then irreversibly bleaches with
high probability.
To estimate the optical signal we can expect, without bleaching the sample too fast,
we calculate the probability for this process. Assuming identical photon absorption cross
sections for the first and second excitation and using the Poisson distribution, we calculate
the probability that the molecule is struck by no other photon within the lifetime of the
3
4
e.g. Nanonics Imaging Ltd.; Jerusalem, Israel; http://www.nanonics.co.il
e.g. Witec GmbH; Ulm, Germany; http://www.witec-instruments.com/
CHAPTER 2. THEORY
13
excited state :
(2.16)
with the average rate of excitation and the lifetime of the excited state. In a time interval
, the molecule is excited bleached after is
times. Therefore the probability that the photon has not
With the lifetime of the excited state
of
max &
.
(2.17)
[31] we estimate a maximum excitation rate
life
! (2.18)
of the molecule before photobleaching.
[31] a molecule excited at this rate emits
At the quantum yield of fluorescein photons. A objective captures about of the emitted
emission
for a lifetime of
life
photons assuming spherical symmetry of the emission. The avalanche photodiode we use
for detection has detection efficiency at the emission wavelength of fluorescein .
As an example, we assume a image with pixels scanned at a
speed of (line scan frequency: "! ). Without fluorescent molecules in the image
we expect an average of count per pixel, while a molecule in the center of the pixel would
$# counts. The molecule is only exposed to the light for , therefore the
cause and a dark count of dark
bleaching probability is extremely low. By using slower scan speeds the signal-to-noise
ratio can easily be increased.
In practice, we expect a somewhat lower signal because of losses from the fluorescence
filters and other parts of the optics, as well as an increase in the dark count caused by stray
fluorescence.
We have shown that the detection of single molecules is possible provided that we can
reach the excitation rate that we assumed. To estimate the excitation rate of a single dye
molecule, we need to know its effective absorption cross section
to the excitation light.
Since normally only the bulk behaviour of most dyes is known, we need to relate the absorption cross section to the bulk extinction coefficient ( % [30]).
&
('*),+-
for fluorescein
CHAPTER 2. THEORY
14
The number of photons absorbed of dye molecules per unit volume
is proportional to the photon density, the number
, the absorption cross section and the distance element
the light travels:
.
(2.19)
By integrating this equation, we get
and for the intensity "
(2.20)
+
.
(2.21)
Comparing this to the familiar law of absorption,
% ,
(2.22)
where is the molarity of the solution, we determine (after changing units)
& %
,
(2.23)
is Avogadro’s number. For fluorescein and an excitation wavelength of ,
.
we obtain an effective absorption cross section of & &
The maximum input power into the cantilevered fiber tips we are using is in .
Using its transmission , aperture area
for a diameter
where
&
aperture
tip, and the wavelength, we estimate a photon flux of
in
aperture
&
&
(2.24)
through the aperture, assuming that the intensity distribution over the aperture size is uniform. From this we calculate the maximum possible excitation rate a dye molecule as
absorption . This is almost three orders of magnitude above the necessary
and safe level. Therefore the power density in the near field is certainly sufficient and has
to be reduced to prevent excessive photobleaching.
CHAPTER 2. THEORY
15
2.4 The Digital PID Controller
In all SPM methods, one measures some type of interaction between the surface and the
probe tip that depends on the tip-sample distance. For imaging the topography of the sample, it is desirable to keep the distance between the surface and the tip constant. This can be
achieved by employing a feedback system. Fig. 2.3 shows such an SPM feedback system
[32];
h
r
e
u
Controller K
Actuator G
x
y
z
Sensor H
Figure 2.3: The SPM feedback system.
For this discussion, we assume the dependence of the interaction strength of the tipsample distance
to be linear5 , at least for small deviations. The tip-sample distance de-
pends on the height
of the sample at the current
-position and the actuator extension .
The interaction is measured with a sensor with a response
and compared to the setpoint
to calculate the error input.
When the feedback is engaged, the controller’s task, for which its transfer function
has to be designed, is to zero the error signal, i.e., to keep the measured interaction strength
at the setpoint. Ideally, the controller would stabilize the tip-sample distance but this is not
directly accessible. Via its output , the controller operates the -actuator whose dynamic
behaviour is described by
. A detailed discussion of a feedback system for STM can be
found in [33].
5
An exception is STM in which the tunnelling current varies roughly exponentially with the distance.
Linearization can be achieved by using the logarithm of the tunnelling current and setpoint instead of the
actual values.
CHAPTER 2. THEORY
16
Proportional Controller
The simplest controller is the proportional controller. Its action is
.
(2.25)
is called the proportional gain. Obviously the sign of
has to be chosen so that the
effect of the controller action is counteracting the error of the system instead of increasing
it. For a fixed setpoint , the error Therefore, this steady state error does not go to zero but is
In the DC limit (zero frequency),
.
(2.26)
and
are just real, finite constants.
only vanishes if is infinite. In practice, is limited
because dynamic systems become unstable at high gain.
Integral Term
The problem of the steady state error can be solved by adding an integral term in the controller:
or
(2.27)
(2.28)
in frequency space. The gain for zero frequency now becomes infinite, solving the problem
of the steady state error.
System Stability
The output of real systems is never purely immediate but also depends on the history. This
can seriously interfere with the controller action. If the system is subjected to a disturbance
at frequency
, where
is the loop delay time, the controller action is in phase with
the oscillations and& will therefore enhance them. If the controller gain is high enough, the
system becomes unstable and starts oscillating spontaneously.
CHAPTER 2. THEORY
17
Differential Term
The integral term introduces a phase lag in the controller which adds to the total sys-
tem delay. This makes the system more susceptible to feedback oscillations. To compensate
for this, one can introduce a differential term into the controller:
or
in frequency space. The differential term has a
(2.29)
(2.30)
phase lead and therefore effectively
damps the system, making faster feedback possible.
However, in noisy systems adding the differential term normally leads to an increase in
the noise levels because it especially increases the response to high frequency fluctuations
of the error signal.
Discretisation
So far we have discussed continuous systems in which there are no discrete timesteps. This
is obviously not possible when the feedback controller is implemented in software. The
discretisation of Eq. 2.29 is
,
(2.31)
where is the time interval between two controller iterations and and are the error
signal and the controller output signal at time step .
Since the digital controller only examines the error signal at discrete times and sets its
output accordingly, it discards some of the available information. This leads to slightly
lower performance of digital controllers when compared to analog controllers with respect
to overshoot and settling time [32]. Obviously, the performance of the digital controller
will approach that of an analog controller if the execution frequency of the control loop is
much higher than the frequencies of the disturbances the feedback needs to compensate.
Despite the disadvantages, the much greater flexibility of a digital controller makes it the
much more suitable solution for our application.
Chapter 3
Technical Implementation
In any SPM, the control over the position of the tip relative to the sample in the lateral (
)
directions as well as in the axial ( ) direction has to be better than the desired resolution.
This criterion is clearly the dominating factor in the design of all components [34].
To define the “desired resolution”, we consider highly oriented pyrolitic graphite
(HOPG), a standard STM sample. The apparent nearest neighbour distance 1 is
Å and
the corrugation is around Å, depending on the bias voltage. To be able to resolve this
lattice, we need better than Å lateral resolution.
The necessary control over the displacement is dictated not only by the desired resolution but also by the stability of the tunnelling gap. As a rough rule of thumb, the tunnelling
current changes by one order of magnitude when the tunnelling gap width changes by Å.
Therefore, control over the
position to
Å is needed.
3.1 Mechanical Design
The quality of the mechanical setup is of paramount importance for achieving good results with an SPM since precision positioning obviously cannot exceed the steadiness of its
mounts that act as a reference. Since the requirements for the -positioning are the highest,
the system is most sensitive to changes in this direction. We will therefore focus on issues
1
The real nearest neighbour distance in graphite is
but since the atoms are alternatingly either directly
above an atom in the layer below or above the center of a hexagon of atoms [35], the obvious periodicity in
STM images of graphite is Å
18
CHAPTER 3. TECHNICAL IMPLEMENTATION
19
that affect the tip-sample distance. However, the basic considerations are the same for the
- and -axes.
3.1.1 Sources of Mechanical Disturbances
There are different disturbances that should be considered in the design with the goal of
making the instrument immune to them, or at least minimising their effect.
Thermal Drift
While the body and most of the rest of the instrument are made from aluminum with thermal expansion coefficient2
Al
[36], the piezoelectric actuators are made
from ceramic materials that have a much lower expansion coefficient piezo
.
Therefore, overall changes in the instrument temperature will cause changes in the tipsample position. A long piezoelectric stack causes a change of
piezo
Al
piezo
!
(3.1)
in the tip-sample distance when the temperature of the instrument changes uniformly. Assuming a rate of change of , we expect about
Å drift due to these temperature
changes.
Thermal drift is a very slow process caused by overall changes in room temperature.
Provided there are no periodic disturbances (caused, for example, by an air conditioner),
typical variations occur on the scale of hours.
Localised Thermal Fluctuations
Air currents and other effects can cause local temperature changes that alter the length of
parts of the setup thereby changing the tip-sample position. Between the sample and the
probe tip, the instrument forms a large loop through the
-stage, the instrument body and
the probe head. The characteristic vertical length of this setup is difference
2
. If a temperature
occurs between a part of the instrument body and the rest of the setup, the
Different parts of the setup might actually be made from different aluminum alloys that have slightly
different expansion coefficients
CHAPTER 3. TECHNICAL IMPLEMENTATION
tip-to-sample distance will change by 20
! Al
. Obviously, the instrument
is very sensitive to small temperature differences.
These temperature differences are evened out by heat conduction. The time constant
for this process [37] is
where
&
with
is the distance over which the temperature difference occurs,
diffusivity,
(3.2)
is the thermal
is the density, the specific heat capacity and the heat conductivity of the
material.
Substituting values for aluminum [38], and the characteristic length of the instrument,
we find that the time constant is on the order of ten minutes. Obviously, temperature
changes that happen much slower than this can be treated as overall temperature changes
while very fast fluctuations get damped strongly because they cannot penetrate the material
deeply. Thus, it is important to minimise temperature variations that occur at about this
most dangerous time scale.
Building Vibrations
Building vibrations are caused by many different sources such as fans and machines as well
as people walking nearby. The typical frequency range for these disturbances is !
and peaks in the spectrum frequently occur around the subharmonics of the line frequency
[34].
Acoustic Noise
Another source of vibrations that can cause problems is sound. Talking, music and noisy
equipment have caused problems. These sources cover a wide frequency spectrum from
below "!
to several "! .
Intrinsic Sources
All movements of positioning elements in the setup itself can to some degree couple to
other axes and cause displacements there. The main source for this type of vibrations is
CHAPTER 3. TECHNICAL IMPLEMENTATION
21
the approach motor with gearhead (Diamond Motion, 1200-1-1616-1670) but we have also
observed signs of crosstalk between the three piezo actuators.
3.1.2 Countermeasures
Thermal and Acoustic Insulation
For imaging, we are typically not interested in overall slope, i.e. features that cover the
whole image with one shape. With a line scanning frequency between "! , signals
much slower than this can be ignored and are simply filtered out by a high-pass filter.
However, if thermal drifts or fluctuations are too violent, they may cause the instrument
to run out of range on the -positioning or cause image distortion when a drift in lateral
direction occurs. For this reason, and also to reduce acoustic vibrations, we built a box
from insulating material that contains the instrument and protects it from air currents, lowpasses thermal changes and reduces acoustic influence.
Vibration Isolation
a)
b)
Mass m
Damper λ’
x(t)
Spring k
Head
x(t)
Tip
Spring k
Sample
f(t)
Base
f(t)
Figure 3.1: a) Damping system for insulating the SPM from building vibrations; b) Model
of the SPM for vibration analysis.
To shield the SPM from building vibrations, we use damping systems as shown in Fig.
3.1.a to decouple it from the floor. The damping system is a damped harmonic oscillator
with a low resonance frequency. The differential equation describing such a system is
( ,
(3.3)
CHAPTER 3. TECHNICAL IMPLEMENTATION
where
is the offset of the floor and
22
is the offset of the load (SPM). By Fourier
transformation, we obtain the system transfer function
,
(3.4)
&
is the frequency normalised to the resonance frequency of the undamped
and is a dimensionless damping parameter.
system
where
The absolute value of the system transfer function is called transmittivity. It is the ratio
of the amplitudes of the oscillation of the mass and the oscillation of the floor:
& & & &
& &
.
(3.5)
Figure 3.2: A harmonic oscillator with different damping coefficients.
Fig. 3.2 shows transfer functions for different damping coefficients . There are clearly
distinguishable frequency regimes in this transfer function: At low frequencies, the transmittivity is unity. Around the resonance frequency, there is resonant enhancement, so the
vibrations in this frequency range actually get worse than without the damper. The lower
the damping coefficient, the stronger the resonant enhancement. Obviously, the resonance
frequency has to lie well below the frequencies the instrument is sensitive to.
CHAPTER 3. TECHNICAL IMPLEMENTATION
23
At higher frequencies, we achieve the desired damping of the vibrations. It is obvious
in Eq. 3.5 that for very high frequencies, a system with finite damping ( the behaviour of a first-order system ) approaches
. However, for lower damping there is
&
two regimes is clearly visible in the curve in Fig. 3.2.
a transition region in which the system shows
behaviour. The transition between the
In the regime where these systems reduce vibrations, lower damping coefficients are
therefore favourable. However, systems with very low damping take a long time to attenuate accidental excitations which are unavoidable during manipulations on the instrument.
Therefore, the damping coefficient should not be too low.
We are currently using two damping systems; the first one is an optical table on air
springs with a vertical resonance frequency of about
bungee cords (
table
"!
and the second is a set of
! ) with which the instrument is suspended from a frame that sits
on top of the optical table. A commercial damping system with "! was ordered but
bungee
did not arrive in time for this thesis.
Instrument Design
The SPM itself forms an oscillator as well (Fig. 3.1.b). An infinitely stiff instrument would
not be affected by external vibrations. The design goals are quite the opposite to those of
the damper elements: the desired behaviour is that the tip moves with the same amplitude
and in phase with the sample to keep the relative position constant. Therefore, we redefine
the transmittivity for the instrument as
&
& &
& &
,
(3.6)
describing the ratio between the tip-sample position oscillation amplitude and the excitation
amplitude. Since the system is made mostly of metal which has very low dissipation, we
can ignore its damping term. Then we can see from Eq. 3.6 that it will perform well for
i.e.
. Obviously, the resonance frequency of the setup should be made as
high as possible.
To estimate the range of frequencies that the system rejects, we look at the lowest reso-
CHAPTER 3. TECHNICAL IMPLEMENTATION
24
nance frequency of a rectangular plate whose edges are supported [39]:
Here,
&
is the Young’s modulus, the density and
& &
.
(3.7)
is the Poisson ratio of the material,
is the thickness and the length of the longer side of the plate.
Substituting the values for aluminum for ,
with aspect ratio
(3.8)
. Obviously, there are two ways to increase the resonance fre
quency of a part: reduce its size
and [38], we get
or decrease the aspect ratio
.
The element that dictates the minimum size of the instrument is the
-stage with
. After two failed attempts to build the instrument out of relatively
thin ( and respectively) plates in which vibrations of the instrument body made
!
accurate -positioning basically impossible, we changed the design to an L-shape made out
of aluminum bar stock as shown in Fig. 3.3.
Using Eq. 3.8 we obtain a lowest resonance frequency of ca. !
for the vertical piece
of the instrument body. Although this is certainly lowered by the weight of the head and the
bottom piece, no increase of noise is observed in the
!
frequency range so we assume
that the vibration damping and acoustic insulation are working effectively.
3.2 Controller
3.2.1 Hardware
Modern SPM designs use digital controllers to control the instrument and image acquisition. This allows the user to adapt the controller to a wide range of instruments and
situations by simply changing parameters or the code. Although there are several commercial turnkey solutions available, we decided to develop a controller especially for this
instrument mainly because we wanted to implement a number of nonstandard features such
as DC approach motor control using a DC voltage. As the source code of the controlling
software is normally not provided with the commercial solutions, the extra flexibility of a
home-built controller is essential.
CHAPTER 3. TECHNICAL IMPLEMENTATION
25
Close Approach
Motor
3"
STM
Head
7"
xy−stage
3"
6.5"
Figure 3.3: Mechanical design of the instrument, STM configuration.
Apart from the obvious necessity of a sufficient number of high-resolution analog inputs
and outputs, it is essential to be able to control the timing of the feedback loop for the
tip-sample distance control and that this feedback provides high bandwidth. Therefore it
is necessary to use a device that is capable of fast real-time processing of analog data.
Furthermore, image acquisition requires high-speed data transfer to the computer and a
sufficient amount of memory to buffer data on the real-time system.
We decided to use an ADwin Gold system as the controller hardware (Jäger Messtechnik GmbH) that, apart from the previously mentioned features, can be programmed in a
simple, high-level programming language (ADbasic) that allows fast software development
and easy maintenance by future users. It connects to a personal computer via a universal
serial bus interface.
3.2.2 Software
The SPM software consists of two main parts: The real-time part, running on the SHARC
CPU of the ADwin Gold system and the user interface, running on the PC under IGOR Pro
CHAPTER 3. TECHNICAL IMPLEMENTATION
26
Figure 3.4: The AFM head (closeup on the right side), the bungee cord vibration damping
system and the acoustic and thermal shielding system. The inside of the shielding box is
coated with aluminum foil for additional protection against electrical interference.
4.0 (WaveMetrics Inc.). Both parts of the software were initially written by RTS Consulting.
We later heavily modified them to adapt them to changes in the setup.
The software allows data acquisition on up to 5 channels simultaneously. The user can
choose each channel independently to be any of the analog inputs of the controller, one
of the four counters, the -piezo position or the error for the feedback and derived values
depending on the currently active SPM mode. All channels allow a maximum sampling
rate of "!
. There are three basic modes for acquiring data:
static mode:
CHAPTER 3. TECHNICAL IMPLEMENTATION
27
hunt mode;
scan mode.
In static mode, the tip sits over one point of the sample. Active channels can be displayed
as a time series or as a power spectrum. In hunt mode a single scan line is continuously
scanned and the data is presented versus the position along the scanline. This mode also
allows space-time diagrams that repeatedly record the same scanline to make changes visible. Finally, in scan mode a two dimensional area of the sample is scanned and the acquired
data is represented as a contour plot.
3.3 Optics
3.3.1 Detection and Signal Conditioning, AFM
The detection of the cantilever deflection in AFM is realized with a laser beam deflection
system: A laser beam, focused on the back of the cantilever, is deflected to twice the cantilever angle when the cantilever bends. By measuring the shift
of the light-spot at a
distance from the lever, we can determine the change in angle . Assuming get
Since the levers are very narrow (
.
we
(3.9)
), the laser beam needs to be focused to a small spot.
Ordinary laser diodes typically suffer from astigmatic aberrations and cannot be focused to
the diffraction limit. Therefore we use laser diodes with integrated correction optics (Blue
Sky Research, Circulaser).
The light-spot position is detected using a split photodiode. The difference between
the photocurrents from its segments is a measure of the displacement of the light spot.
However, since the difference scales with the overall intensity of the light, we also measure
the sum of the photocurrents. By dividing the difference by the sum, we can compensate
for intensity fluctuations of the laser diode.
Since we are only interested in the deflection in one direction, a one-dimensional diode
(split into two segments) would be sufficient. However, for practical reasons (easier centering of the beam on the photodetector) we chose to use a quad-photodiode module with
CHAPTER 3. TECHNICAL IMPLEMENTATION
28
integrated sum and difference amplifiers for both lateral directions (Pacific Silicon Sensor,
PSS-QP50-6SD).
CCD
camera
Quad
photodiode
Polarising
beamsplitter
λ/2 waveplate
Laser
diode
λ/4 waveplate
Collimator
19mm EFL
achromat
Lever
Figure 3.5: Schematic drawing of the AFM detection optics
Fig. 3.5 shows the principal setup of the AFM detection scheme. The light from the
laser diode with correction optics is collimated into a parallel beam and reflected by a polarising beamsplitter. It then passes through a waveplate at , which turns the linearly
polarised light into circularly polarised light. The laser beam is then focused on the back
of the cantilever using an achromat. The reflected light from the cantilever is collimated
again by the same lens and passes the waveplate again so that the linear polarisation of
the resulting beam is rotated
with respect to the original beam. Therefore it passes
the beamsplitter without being reflected back into the laser diode. A rotates the polarisation by another
waveplate at before the beam gets reflected onto the detector by
another polarising beamsplitter. The setup allows lateral (with respect to the laser beam)
movement of the lever to place it in the focus of the beam, axial displacement of the achromat for focusing and lateral movement of the sensor for centering the beam on the quad
photodiode. A camera mounted on top of the assembly can be used to support positioning
the laser spot on the cantilever and for focusing.
CHAPTER 3. TECHNICAL IMPLEMENTATION
29
We use gold coated silicon nitride cantilevers (TM Microscopes (Veeco) sharpened Microlever) with sharpened pyramidal tips. Their tip radius of curvature is
. They are
mounted to the tip holder by gluing the chip attached to the cantilevers to the tip holder
with an instant adhesive.
3.3.2 Sample Emission Detection
Light that is emitted by the sample (either excited with an NSOM tip or by STM) can be
detected through transparent and semitransparent samples. To achieve high efficiency in
the detection of the light, we use a , microscope objective (Zeiss Jena,
Achromat). The setup allows insertion of filters in the optical path, viewing of the sample
through a CCD camera and focusing of the collected light into an optical fiber that can
deliver it to a photomultiplier tube (Hamamatsu, H6180) or to an avalanche photodiode
(Perkin Elmer Optoelectronics, SPCM-AQR-14-FC). For a more detailed description of the
pickup optics see App. B.2.
3.4 Electronics
The electronics in the setup can be divided into three major parts:
Detection electronics
Driver electronics for piezoelectric elements
Supplementary electronics
Because the detection and driver electronics directly influence the image by controlling the
lateral position and the tip-sample distance, their noise levels greatly affect the resolution
of the instrument.
3.4.1 Detection and Signal-Conditioning, STM
In STM, the tunnelling current (nA) has to be measured with high accuracy (pA). Since the
inputs of the controller allow to , this current has to be converted to a voltage in
CHAPTER 3. TECHNICAL IMPLEMENTATION
30
that range. To achieve a flat frequency response in the targeted frequency range, we split the
signal-conditioning electronics into a current-to-voltage converter (see App. A.1.1) with a
conversion factor of and a x10 or x100 amplifier (see App. A.1.2) that boosts the
signal to
or respectively.
The IV-converter converts the tunnelling current into a proportional voltage [40]. Often,
logarithmic IV converters are used because they cover a greater range of currents [41] and
linearise the tunnelling interaction. However, their bandwidth is severely reduced by the
capacitance of the diodes used in the feedback.
Since the circuit is designed to detect very small currents ( ), it must be well-shielded
from electromagnetic noise in the environment. This is done by integrating it into the STM
head which is made from an aluminum block. This placement also keeps the connections
to the STM tip short which further prevents noise pickup. To prevent electrical interference
from the power supply, we initially powered the circuit by batteries. After draining many
batteries in a relatively short time, we replaced them with a very stable power supply (see
App. A.1.3).
3.4.2 Positioning Driver Electronics
Lateral Translation Stage
A common problem with many SPMs is that the reproducibility of the
positioning is
very poor because of hysteresis, creep [42] and thermal drifts of the piezoelectric stacks
that are typically used for positioning. A way to avoid these problems is to use position
sensors and a closed-loop feedback circuit to compensate these effects.
There are several commercial products available that use position sensors and a feedback system. They differ mainly in the type of position sensors (optical, piezoresistive and
capacitive) they use. The stage we are using (Mad City Labs, Inc., Nano H100) uses flexure hinges to ensure straightness of motion and orthogonality, has piezoresistive sensors
and comes with a variable bandwidth feedback- and driving circuit (NanoDrive). Its scan
range is , and it claims sub-nanometer accuracy.
CHAPTER 3. TECHNICAL IMPLEMENTATION
31
-Translation
The requirements for the vertical translation are very different from the
translation stage.
Since SPM is normally used on relatively flat surfaces, the range required is much smaller
than in the lateral direction. The bandwidth of the -translation has to be much higher
though, because it is part of the
feedback loop and therefore directly changes the tip-
sample separation. Hence, the moving part of the -translation must be light and stiff so it
will not cause any resonances within the target bandwidth.
In STM-mode, we use a piezoelectric stack (Thorlabs AE0203D04) with
over its range
drive-voltage range to drive a small tip-holder so that the tip is moving in
the -direction instead of the much heavier sample. However, in AFM this is not possible
because of the optical detection system. By moving the tip vertically it would go out of
focus of the laser beam. Currently, the tip-sample control is realized by moving the sample
using three piezoelectric actuators (Thorlabs AE0505D08) with range.
To produce the high voltage required to drive the piezoelectric actuators, we use a highvoltage amplifier. On the one hand it needs to provide large currents to allow high slew
rates despite the relatively large capacitances of the piezoelectric stacks and a large smallsignal bandwidth. On the other hand the noise on the output must be low enough to allow
(Piezomax PMDRV) has
Å. The driver we are using
RMS output noise over its "! bandwidth.
controlling of the tip-sample distance in STM down to
Vernier Circuits
Given the ranges of the
and positioning devices, the resolution of the analog outputs of
the controller are not sufficient to reach the desired resolution of and
, respectively. The
vernier circuits combine two analog outputs of the controller into one with higher precision.
The concept and their implementation are discussed in App. A.2.
In addition to the vernier, these circuits buffer all outputs of the controller with differential amplifiers to eliminate interference from common-mode voltages on the outputs of
the controller.
CHAPTER 3. TECHNICAL IMPLEMENTATION
32
3.4.3 Supplementary Electronics
For the operation of the SPM, several additional electronic circuits are necessary. However,
most of them are not directly related to the SPM operation or are just serving interfacing
purposes. I will therefore abstain from describing them here.
Approach Motor Controller
Although not directly involved in imaging, the approach motor control circuit is crucial for
SPM operation. This is because for a reliable close approach, control over the speed of
the approach motor down to very low speeds as well as fast spin-up and spin-down control
are necessary. Concretely, motor steps smaller than the range of the -piezo are necessary.
Because of the algorithm that is used for the close approach in STM, this is limited to the
range of the fine control of the -piezo (ca.
).
We developed a circuit that controls the speed of a DC-motor without the need for a
tachometer by using the countervoltage induced in the motor coils. This circuit is described
in detail in App. A.3.
Chapter 4
Results
Since this project constitutes the design and setup of a new instrument, the images presented
here have to be viewed as tests of the instrument capabilities and therefore not as the primary
fruits of the project.
4.1 AFM
AFM was the first SPM method we implemented. Hence, the images shown here were taken
with a very early setup. As is obvious in the image of the calibration grating Fig. 4.1.a (diagonal lines), there was a periodic signal, probably caused by a ground loop, superimposed
on the image.
Fig. 4.1.b was obtained on a freshly cleaved HOPG surface at very low bandwidth to
circumvent interference problems.
Since these images were taken with a Park Scientific AFM control unit (SPC400 and
SFM-BD2-210) that had to be severely altered to interface with our AFM / NSOM head,
neither the lateral calibration nor the -calibration is reliable.
4.2 NSOM
To produce test samples for NSOM imaging we used
fluorescent polystyrene micro-
spheres (Bangs Labs, Estapor Uniform Dyed Microspheres) that we attached to the surface
33
CHAPTER 4. RESULTS
34
4µm
a)
350nm
b)
4µm
350nm
Figure 4.1: a) An SPM test grating; black to white range
. b) Atomic step on graphite;
-range ca. Å.
of a microscope coverslip by heating the sample to . Fig. 4.2 shows an image of such
a sample. The -scale of the AFM image is and the scale of the NSOM image is
from black to white. The tip we used had a aperture.
Cantilevered optical fiber NSOM tips are extremely fragile. Fig. 4.3 shows images
taken with a tip that consistently delivered a good optical signal as well as AFM feedback.
However, it is obviously damaged since the features in the two images are offset. We
assume that a piece of the aluminum coating of the tip broke off and light leaked out the
side of the tip, illuminating an area of the sample that was not in contact with the tip.
4.3 STM
Since STM has the simplest setup and is also the method most sensitive to vibrations, we
used it for most of the debugging of the instrument. Many of the improvements such as
the dual -feedback (App. C.1.1) and the sturdy instrument body were only tested with the
STM setup but are expected to improve the performance of the other modes in the same
way.
Fig. 4.4 shows gold evaporated on a microscope slip (sample courtesy of Brian
Leathem), imaged at tip bias with a Platinum-Iridium clipped wire tip.
CHAPTER 4. RESULTS
35
AFM
NSOM
10 µ m
10 µ m
10 µ m
Figure 4.2: AFM and NSOM images of a test sample with fluorescent microspheres.
Obviously, features on the order of several laterally as well as in -direction can be
resolved. However, these images were taken without the
voltage amplifier causes lateral oscillations at
-piezo driver because its high
"! , the sixth harmonic of the line fre-
quency. This is probably because of poor power supply design in the Nanodrive (
-stage
feedback circuit and high voltage amplifier). These horizontal oscillations have an ampli-
tude on the order of , making stable tunnelling impossible. Running the instrument
without the driver solves the problem of the oscillations but deprives the instrument of the
closed-loop feedback, which normally compensates thermal drift, piezo hysteresis, creep
and the like in the
-stage.
Fig. 4.4.a and 4.4.b were taken in the same scan. However, the scanning direction is
from left to right (sample moving left) in Fig. 4.4.a and reversed in Fig. 4.4.b. The two
images exhibit an -offset with respect to each other caused by bandwidth limiting of the
piezo actuator voltages. Fig. 4.4.c is a closeup of the same surface. The grain structure
that is visible in these images is caused by the fact that gold does not wet glass unless a
chromium layer is applied first.
To test the limits of the instrument on a reference surface, we tried imaging the lattice of
HOPG. Although some of the images showed some structure and might even be interpreted
as a badly distorted atomic resolution image, this is certainly not the case since the “lattice”
CHAPTER 4. RESULTS
36
AFM
NSOM
5µm
5µm
5µm
Figure 4.3: AFM/NSOM images taken with a damaged NSOM tip.
one can sometimes see does not scale with the size of the raster scan but does scale with the
scan frequency. This is strong evidence for periodic interference. The amplitude for those
noise oscillations is about Å peak-to-peak while the expected periodic variations of the
graphite lattice are Å. We assume that this Å interference stems from the
amplifier whose output noise is periodic with !.
high-voltage
CHAPTER 4. RESULTS
37
a)
b)
c)
Figure 4.4: STM images Gold evaporated on a microscope slip. a), b) Two images taken
during the same scan as left and right image. c) closeup of the same sample. Bias voltage
.
Figure 4.5: Typical result of an attempt to image freshly cleaved HOPG surface. Bias
voltage .
Chapter 5
Conclusions and Further Projects
Although the design goals for the positioning control have not all been reached, the instrument should be capable of carrying out the tasks that motivated its construction. DNA has
a height of when imaged with AFM [43]. This is clearly above the noise level of the
instrument. The instrument is also capable of maintaining a stable tunnelling current in
STM mode, which is an important prerequisite for experiments in which one expects to see
photon emission induced by the tunnelling current.
Apart from the obvious imperative to hunt down and eliminate the noise source that
currently limits the resolution of the SPM, I would like to suggest a change in the setup that
would improve the AFM capabilities of the instrument considerably. Also, a project that
combines STM and the efficient light collection seems worthwhile.
5.1 AFM -translation Modification
The design of the AFM requires that the tip stay fixed with respect to the rest of the head
because of the change in the laser spot position if the cantilever is at an angle. Hence,
the current design implements the -translation on top of the
-stage, thereby moving the
relatively heavy sample holder with the reaction force acting on the soft
causes resonances in the ’s of "! (compared to !
-stage. This
in STM mode where only the tip
is moved, see App. E), leading to a very low feedback bandwidth.
The dual feedback leads to a natural way out of this dilemma: while the slow feedback,
which is limited to max. "! , still moves the sample, small, fast movements are done
38
CHAPTER 5. CONCLUSIONS AND FURTHER PROJECTS
39
by a piezoelectric actuator that moves the tip by small amounts. By splitting the feedback
this way, much higher gains and therefore better tracking of the surface and faster scanning
should be possible. This configuration would also allow easy implementation of intermediate and non-contact modes by adding another very small piezoelectric element to excite
oscillations of the cantilever.
5.2 Photon Emission from Inelastic Tunnelling
With its efficient light detection system consisting of the high NA microscope objective
and the PMT/APD photon counters, this instrument is made for detection of light emission
caused by the tip-sample interaction. Apart from the obvious case of NSOM, photon emission can be caused by electron tunnelling. This is commonly observed in metals [44] and
semiconductors [45]. Obviously, since the instrument detects light from below the sample,
we can detect light only from (semi)transparent sample substrates.
One interesting project is that it might be possible to excite dye molecules by a tunnelling current [46]. Since the sample substrate has to be at least moderately conducting for
STM, a thin metal layer or a layer of a conducting oxide such as which is partially
&
transparent needs to be deposited on the sample carrier. Although a conducting
surface is
an efficient quencher of fluorescence, the increased photostability caused by the vicinity of
the metal surface may allow a sufficient number of photons to be detected [47]. The reason
for both, the fluorescence quenching and the reduction of bleaching (see Ch. 2.3.2) is the
shorter lifetime of the excited state, caused by energy dissipation in the metal. This allows
higher excitation rates that can at least partially compensate for the decrease in quantum
yield. If this technique works, it could provide much higher resolution than NSOM because
it is not aperture limited.
Appendix A
Electronic Circuits
A.1 STM Signal Conditioning
A.1.1 IV-converter
The IV-converter converts the tunnelling current from the STM tip into a voltage. The
circuit is shown in Fig. A.2.
A test of the circuit without bandwidth limiting showed that when the supply voltage
dropped below the circuit started to oscillate at troduced in the feedback to limit the bandwidth to
"!
!
. Hence a capacitor 1 was in-
. While cutting off well below
the self-oscillation frequency of the circuit, this filter does not change the behaviour of the
circuit significantly within the frequency range of the instrument ( "!
).
The operational amplifier is a low-noise, precision model, optimised for low bias current
(Burr-Brown OPA111/BM). To reduce noise further, we used a metal-film resistor as
the feedback resistor [48].
A.1.2 Second Stage Amplifier
The second amplifier boosts the voltage from the IV-converter by a factor of 10 or 100 to
reach a signal of
and , respectively. Additionally, this amplifier limits the
The required, extremely low capacitance ( ) was obtained by using conducting traces on opposite
sides of a printed-circuit board.
1
40
APPENDIX A. ELECTRONIC CIRCUITS
AFM
41
STM
IV
Sensor
Sum
Approach
Difference
Motor
xyz−Stage
PMT
APD
Converter
Piezo and
STM Tip
xy−Stage
Amplifier
Amplifier
Power
1
Supply
2
3
4
5
7 9 11 13 15
2 4
Odd Row
Analog Inputs
Digital I/O
Counter Buffers
1
3
2
z−Vernier
8 10 12 14 16
Even Row
ADwin Gold
4 Counters
1
6
3
Buffer
Analog Outputs
4
5
Buffer
6
x−Vernier
7
8
y−Vernier
Piezomax
PMDRV
Mad City Labs
Motor
Nano Drive
Controller
Figure A.1: Block diagram of the electronics
signal bandwidth to !
to prevent aliasing in the digitisation.
Fig. A.3 shows the transfer function of the two signal conditioning circuits together.
The phaseshift approaches for high frequencies because both the IV-converter as well
as the second stage amplifier are bandwidth limited with a first-order RC-filter. The input
noise of the circuits is .
APPENDIX A. ELECTRONIC CIRCUITS
42
100K
+18V
+
1.5nF
10K
0.5pF
−
+
−
−18V
15nF
10M
OPA27
−
−
+
1k
OPA111/BM
Signal out
+
Sample Bias in
STM Tip
Sample Bias out
Figure A.2: The STM signal conditioning circuits - IV-converter (left) and second-stage
amplifier (right).
A.1.3 Stable Power Supply
As a replacement for the batteries that powered the STM signal conditioning circuit, we
built a double-stabilised power supply (Fig. A.4).
The AC voltage ( V) from the secondary coil of the transformer is divided into a
positive and negative half-cycle, smoothed by a capacitor and stabilised to
# . To further
reduce ripple on the output, we use another pair of voltage regulators that reduce the voltage
to
#
.
Each of the voltage regulators claims a ripple rejection of at least combined ripple rejection of the two stabilisation stages should be around . Therefore the
. However,
the real circuit is very close to the transformer and therefore subject to stray magnetic fields.
Under our typical conditions (
), the oscilloscope image of the AC component of
APPENDIX A. ELECTRONIC CIRCUITS
43
Figure A.3: The measured transfer function of the STM signal-conditioning electronics;
second-stage amplifier (solid) and (dashed).
7818
+
+15V
7815
1µ F
1µ F
+
1000 µ F
4700 µ F
+
0
+
4700 µ F
117V
60Hz
1µ F
7918
1µ F
7915
24V
1000 µ F
−15V
Figure A.4: Stable power supply for STM signal conditioning.
the output voltage ( loads (
RMS) has no obvious correlation with the line frequency. Higher
) caused the output to show some ripple of about peak-to-peak.
A.2 Vernier Circuits
As introduced in Ch. 3, the desired resolution in the lateral direction is about Å while it
Å control over the tip to sample distance to maintain a stable
and tunnelling current. Given the ranges of and
, the number of bits is necessary to have about
needed are
&
&
Å
!
Å
!
(A.1)
,
APPENDIX A. ELECTRONIC CIRCUITS
44
respectively. The analog outputs of the controller are 16-bit and therefore do not seem
suitable for these tasks. Since adding high-resolution DACs would require much effort, we
use a trick to achieve the required resolution.
Rc
Vc
V
Vf
Rf
Figure A.5: The idea of the vernier circuit.
For the three high resolution outputs, we use two DAC outputs each and create a
weighted sum voltage via an analog circuit. One analog output is used as “coarse” con-
and the second one as “fine” control . The circuit is shown in Fig. A.5. For the
trol output voltage of the circuit we get
If
, we can rewrite this as
"
(
(A.2)
+ (
(A.3)
Hence, the result is a kind of vernier drive with an advantage of for the fine control.
Since the full range of the DACs is
an input range of
for the
voltage steps smaller than
, one step is -controller and the
for the
#
Å
!
. With
high-voltage amplifier, we need
(A.4)
Å
!
(A.5)
-control voltages and
for the -control voltage which results in minimum vernier advantages of
spectively.
and , re-
APPENDIX A. ELECTRONIC CIRCUITS
45
However, this calculation completely ignores the noise on the outputs. Noise measure-
ments show that the output noise on all DACs is below Assuming white noise, this is a noise density of RMS on "! &
advantages !
bandwidth.
per channel. For vernier
, only the noise on the coarse input has to be considered.
While this noise can safely be ignored on the ! bandwidth of the
controller 2
(
! & ! ! RMS), it will obviously be higher than the stepsize on the
! bandwidth of the high-voltage amplifier. The bandwidth of the signal therefore
"! "! to lower the RMS of the
has to be limited to less than
& &
noise below the desired resolution. Obviously, this is not an acceptable bandwidth for the
tip-sample distance regulation feedback. As mentioned earlier, though, because the noise
of the coarse control voltage dominates in the final signal, there is no need to limit the
bandwidth of the fine control voltage.
To be able to make use of the lower noise in the
controller, we choose a vernier advantage of !
bandwidth setting of the
-
. For the -vernier, we have to take the
impact of the bandwidth limit on the imaging into account; the calculation of the actual
output voltage from the fine voltage and the coarse voltage and history would require relatively CPU-intensive operations on the ADWIN controller and is therefore not a favourable
solution3. To circumvent this, we place the cutoff-frequency for the coarse voltage so that
it is below the frequencies of expected image features. We can then use the data from the
fine voltage as image data, less overall slope and drift. On the one hand, this suggests a
very low cutoff frequency; on the other hand, the fine voltage can only vary the
position
in a relatively small range, so a low bandwidth in the coarse setting might cause crashes
due to overall slope of the sample or thermal drift. We chose the
-cutoff frequency to
be 10Hz. While this cutoff causes the noise of the coarse control to be much lower than
necessary and therefore suggests using a higher vernier advantage than calculated earlier, it
does not make sense to reduce the noise of the control voltage much below the input noise
of the high-voltage amplifier (see Ch. 3.4.2). Furthermore, a high vernier advantage results
in a small range of fine control. A vernier advantage of is a good compromise.
The possible bandwidths are , and ; we typically use the setting because of
detector-noise induced position-noise
3
Acquiring the data of both the coarse and the fine control should, together with the system transfer
2
function of the vernier circuit, allow the reconstruction of the complete image information, including slow
components.
APPENDIX A. ELECTRONIC CIRCUITS
50nF
150pF
Vernier/
separate
−
100
−
10K
10K
324K
324K
Vc
10Hz/
full BW
46
V1
+
+
324K
10Hz/
full BW
324K
75pF
50nF
324K
Vf
−
5K
−
100K
100K
324K
V2
+
+
324K
324K
Figure A.6: The -vernier circuit.
The circuit for the -vernier is shown in Fig. A.6; the inputs are buffered by inverting
differential amplifiers (gain: ) to prevent common mode problems that result from poor
grounding design in the ADWIN Gold controller4 . The coarse-control channel has two
capacitors to limit the bandwidth. These capacitors are not present in the - and -circuits.
The signals from the input amplifiers are then combined into the sum signal using the
vernier circuit ( and for , and for
and ) and buffered by two
inverting output amplifiers (gain: ).
The two outputs are needed for the automatic vernier calibration; to execute the calibration, the output from the vernier circuit is fed back into an ADC input of the controller.
Then the controller outputs different voltages on the coarse and fine output to determine the
advantage of the vernier circuit. Separate buffering is necessary to eliminate interference
4
The digital and analog ground are not properly separated [49]; this leads to a
signal on some of the analog outputs during memory access bursts.
common mode
APPENDIX A. ELECTRONIC CIRCUITS
47
because the ADC multiplexer circuit in the ADWIN controller changes the impedance of
an input drastically when it is activated.
The coarse and the fine channel can also be operated separately; the two outputs are
then the coarse and the fine channel, respectively. This might be used, for example, for two
different piezoelectric elements for the coarse and the fine tip-to-sample distance control.
In all channels, the second amplifiers are bandwidth limited to
!
as shown in the
second channel in the circuit diagram, except for one of the channels (first channel). Since
!
high-voltage amplifier only has a bandwidth of the
, a bandwidth limit to reduce
noise is not necessary at this point and would introduce unnecessary phase shift. In practice,
it is still preferable to use a feedback capacitor to prevent amplifier oscillations. We chose
it so that the bandwidth of the amplifier is "!
. In this circuit, different resistor values
were chosen to reduce thermal or Nyquist noise of the feedback resistors [50]:
where is the RMS noise voltage of the noise,
constant, is the temperature of the resistor and ,
(A.6)
is the resistance, is the Boltzmann’s
is the bandwidth over which the noise
is detected. In a unity-gain inverting amplifier, both resistors contribute equally to the noise
on the input. For two resistors we get (corresponding to
at room temperature. Although this is below the acceptable noise ( dangerously close. Therefore, we chose to use ) RMS noise
) it is perhaps
resistors. Although, strictly speaking,
Eq. A.3 only holds for very high input impedances of the following amplifiers, it can still
be used; a more detailed calculation shows that the reduces the range of the vernier circuit by about ( All resistors used are input impedance of the amplifier
.
metal film resistors. They were sorted to obtain better matches
) for the resistor quadruples of the input amplifier and the resistor pairs of the output
amplifiers in order to have high common-mode rejection and nearly unity gain. Each channel is grounded separately to avoid cross-talk, and the operational amplifiers amplifiers are
low-noise precision amplifiers (OP27GP).
The output noise and common mode response are listed in Tab. A.1. For measuring
the amplifier noise, we shorted and floated the inputs. The common mode response was
measured by imposing a RMS, "!
inputs. The detection bandwidth was square wave signal on both leads of the amplifier
"!
and the verniers were deactivated.
APPENDIX A. ELECTRONIC CIRCUITS
Channel
Input
Output
48
Noise [
]
CMR [
]
1
coarse
HV-Amplifier
14
900
2
fine
calibration
52
240
3
approach motor
33
2130
4
STM bias voltage
39
270
controller
44
490
calibration
33
350
controller
53
330
calibration
53
680
5
6
coarse
fine
7
8
coarse
fine
Table A.1: Noise and common mode response (RMS) of the vernier and buffer circuits.
Figure A.7: The transfer functions of the
coarse (solid) and fine (dashed) channels of the
vernier circuit.
A.3 Close-Approach Motor-Control
At very low speeds, DC motors typically do not run reliably, tending to “stall” because of
stiction. To overcome this, one can use different strategies. A very common one is to pulse
the voltage supply, controlling the speed by varying the duty cycle. The disadvantage of this
method is that the speed of the motor depends on the load. To get a more reliable control,
one can use a tachometer that controls the voltage of the motor via a feedback mechanism.
However, this is relatively costly because it requires additional hardware. Our solution uses
the same principle as the latter possibility while not requiring a separate tachometer.
A real motor can be modelled as an “ideal” motor, i.e. one without ohmic loss, in
series with a resistor . While the voltage across the ideal motor is proportional to its
APPENDIX A. ELECTRONIC CIRCUITS
49
angular momentum, the current through it, , is proportional to the torque. Of course, the
only values that are accessible to us are the voltage across the terminals of the real motor
and the current . But since , the resistance of the motor coils, can
be measured, we can calculate . This voltage can then be compared to a
setpoint and feedback can be employed.
Control Voltage
R=R m
M
Motor
Rm
Figure A.8: DC-motor speed control circuit.
The principle of the circuit we are using to control the motor speed is shown in Fig. A.8.
A resistor with resistance identical to the motor coils
motor. The voltage across it
motor:
is used in series with the
is measured and subtracted from the voltage across the
. The difference between this and the setpoint is used to control the
motor voltage through an amplifier, turning the circuit into a simple proportional controller.
fit
, where
. For . The coefficients for the linear
is the speed and is the control voltage, are and
The approach speed can be controlled down to
, the motor stalls.
APPENDIX A. ELECTRONIC CIRCUITS
Figure A.9: Close approach speed vs. control voltage.
50
Appendix B
Optics
B.1 AFM detection optics
B.1.1 Laser Spot Size
As pointed out in Ch. 3.3.1, it is important to design the optical AFM detection system
so that the laser spot diameter on the cantilever is smaller than the cantilever diameter. In
practice, the spot should be made as small as practically possible because in the case of a
bent-fiber NSOM probe, the laser is reflected by a curved surface.
The diameter of the laser beam is
, and the focal length of the lens is . Using
the laws for the propagation of a Gaussian laser beam [21], we determine after a lengthy
calculation a spot diameter of . If the cantilever is not perfectly in focus, the spot
size becomes larger. The calculation yields a tolerance of about
#
for a spot size
.
B.1.2 Lever Deflection Signal Conditioning
By combining Eqs. 2.15 and 3.9, we can calculate the offset of the spot on the detector
Here, laserspot on the detector. Hence,
tip
tip
.
is a displacement of the tip in -direction and
(B.1)
is the displacement of the
is called “amplification” of the optical system.
51
APPENDIX B. OPTICS
52
the amplification is
With the working distance .
and the length of a cantilever ∆p
1
3
2
4
RL
RD
Figure B.1: The quad photodetector;
is the detector radius,
spot and the offset of the laser spot.
the radius of the laser
Fig. B.1 is a schematic drawing of the split photodetector that is hit by an off-center
. The
laser beam. Each of the four detector segments creates a current , top bottom
and right left .& We are primarily interested in right left & .
& of the beam the power density of the spot is
Assuming a Gaussian intensity profile
" & +
(B.2)
& &
where is the distance from the center of the laser spot,
is the total laser power and
available outputs are sum
is the radius of the beam. If we ignore the finite size of the detector, the power received by
left side
&
and the right side
&
&
and
of the detector is
& &
,
(B.3)
respectively. Using the symmetry of the Gaussian, we write the difference between them as
& &
.
(B.4)
APPENDIX B. OPTICS
53
Since we are only interested in small deviations, we expand this expression to first order
around :
!
"
& The difference voltage is therefore
right left
!
& +
&
tip
.
Fig. B.2 shows this linear approximation and a numerical calculation of tip offset for a
Figure B.2:
right left
vs.
long cantilever at (B.5)
(B.6)
right left
versus the
laser power.
; solid: numerical calculation; dashed: linear approximation.
According to the manufacturer, the RMS noise voltage on the output of the quad pho-
todiode module is !.
On "!
detection bandwidth this results in , under aforementioned conditions, detector noise.
or
APPENDIX B. OPTICS
54
B.2 Sample Emission Detection Optics
Fig. B.3 shows the principle of the light collection optics. The light emitted from the
sample is collected by the microscope objective, filtered and focused into an optical fiber
that delivers it to the photomultiplier or avalanche photodiode.
NSOM Tip
Fluorescent
Molecules
Sample
APD / PMT
Microscope
Objective
Optional
Filters
Optical
Fiber
Mirror
Removable
Beamsplitter
CCD Camera
Figure B.3: The sample emission pickup optics, NSOM configuration.
When the beamsplitter is inserted, one can obtain a spatially resolved image of the sample with a CCD camera. This is especially helpful for selecting interesting areas of the
sample and for alignment. Filters can be inserted before or after the beamsplitter. Since the
objective is infinity corrected, no other changes are necessary when filters or the beamsplitter are inserted, removed or changed.
The optical fiber that delivers the light to the photon counting modules has a core diameter of . Since the microscope objective and the tube lens that focuses the light on
the fiber produce a magnification of about 50, the area of the sample from which the light
reaches the photon counter has a diameter of
. This limitation of the detection area is
APPENDIX B. OPTICS
55
very desirable in illumination NSOM to reduce photon counts from fluorescent molecules
that get excited by far-field radiation. Also, stray fluorescence in the optical system (i.e.
photons that do not originate from the sample surface) has very low detection efficiency
because this light does not get focused on the fiber end.
Appendix C
Controller
C.1 Controller Software
The ADwin Gold system is a real-time DSP system and the software that runs on it is in
some ways fundamentally different from “usual” programs. Most of the code is within
the “event” part of a program; the event is called in regular time intervals and therefore
should not take longer than the time interval to the next event. The ADwin system can run
up to eight processes, one of which is a high-priority process. The event of this process
will interrupt any other process that is currently running and override all other events to
guarantee a very regular execution of this task. The ADwin system also allows processes
whose events are not run regularly but triggered by an external event but we are not using
this capability.
For communication to the computer, 80 integer parameters and the same number of
floating point parameters and 80 arrays or FIFOs are available.
C.1.1 The Fast Task
The high-priority process is executed at a rate of "!
in the SPM control software which
is the reason why we call it the “fast task”. The SHARC DSP in the ADwin Gold is running
! which makes one clock cycle and therefore the execution
at a clock frequency of
time of most commands . Hence, we have a maximum of clock cycles of the CPU
per fast task. Fig. C.1 shows a flow-chart of the fast task.
56
APPENDIX C. CONTROLLER
57
80kHz
Fast Task
Entry Point
40kHz
40kHz
Read Both ADCs
20kHz
Start ADCs
20kHz
Set MUX of Odd ADC
to Fast Channel
10kHz
Set MUX of Odd ADC
to next slow Channel
z−Feedback
10kHz
x−Control
y−Control
10kHz
z−Feedback
10kHz
FIFO5
Scan
Housekeeping
40kHz
Set MUX of Even ADC
to next Channel
10kHz
FIFO1
10kHz
FIFO2
10kHz
FIFO3
10kHz
FIFO4
Figure C.1: Flowchart of the fast task. Splits in the execution path mean alternating execution of the different targets.
The ADwin system has only two ADCs for its sixteen analog inputs. The inputs with
odd numbers are multiplexed to ADC1, the inputs with even numbers to ADC2. Therefore
the voltages on the inputs cannot be read simultaneously. The analog multiplexer has a
settling time of
and the ADC takes to perform the conversion. Therefore, in
each event we either initiate the conversion of both ADCs (right flowpath) or we read the
results and switch the multiplexer to the next pair of analog inputs we want to read (left
flowpath). While all even channels are treated equally, they are all read at , one of
the odd channels, the fast channel, is acquired at . This channel is used for the
-feedback (i.e. tunnelling current in STM mode). Because of this, the other seven odd
channels can only be acquired at about .
The -feedback code is executed in two of the four slots in the right flowpath and hence
has an execution rate of . The - and -control functions output the control voltages for the lateral translation, that are calculated by the scan function. The housekeeping
function was introduced for load balancing away from the feedback controller. It mainly
contains the code to prevent integral wind-up in the z-feedback.
The acquired data is transported to the computer through FIFOs. For load balancing
APPENDIX C. CONTROLLER
58
reasons, the five FIFO feeding procedures have been distributed over the flowpaths with the
shortest execution times.
Lateral Control
For slow SPM modes such as NSOM it is interesting to allow non-rectangular scans of
regions of interest. Therefore we use a non-conventional way to define the scan region:
A scan is defined by two lists that we call - and -vector. While the -vector contains
the scan information for one scan line, the -vector defines the position of each scanline
relative to a separately defined center point. The -vector not only contains information
about the shape of the scanline but also about the scan speed and which data points are to
be fed into the FIFOs. Furthermore, it allows fields for additional control commands such
as setting the bias voltage for tunnelling spectroscopy.
While the creation of the - and -vectors is typically considered a high-level non-real-
time task and therefore should be executed on the PC, for simple rectangular scans it is
done on the ADwin controller in order to eliminate lengthy uploads of these lists to the
controller.
-Feedback
The -feedback is realized in two stages as shown in Fig. C.2. The first stage, called the
fast feedback, controls the fine -control and therefore has a high bandwidth but only a
relatively limited range. It tracks image features and vibrations. The second stage or slow
feedback controls the coarse -control. It uses the position of the fast feedback as its input
and a setpoint of
so it stabilizes the average of the fast feedback to the center position.
The slow feedback mainly tracks overall slope of the sample and drifts.
Both feedback stages are PID controllers. For practical use in the controller, we rewrite
Eq. 2.31:
" ,+ . (C.1)
Here we introduced the integral and differential time constants and and the previous
APPENDIX C. CONTROLLER
59
SPM
Fast Feedback
1/50
Setpoint
Slow Feedback
Lowpass
Controller Software
Vernier Circuit
Figure C.2: The principle of the -feedback system.
integral term . After simplifying Eq. C.1
" + " + (C.2)
we arrive at a form that contains very few mathematical operations and is therefore suitable
for use in a fast algorithm [32]:
(C.3)
with the coefficients
" + " +
and
.
(C.4)
In real controllers, one of the problems is the initialisation of the previous integral term
when the controller is activated. The goal is to create a smooth transition from manually controlled operation to feedback control. In practice it turned out to be sufficient to
use although this initialisation might still create a step in the controller output
when the controller is activated at non-zero error.
C.1.2 The Slow Tasks
The slow tasks take care of various less time-critical issues such as building the - and vector, controlling the approach motor and calibrating the vernier circuits. There are three
slow tasks; the - and -vector building task, the millisecond task and the centisecond task.
APPENDIX C. CONTROLLER
60
Close Approach Motor Control
The close approach motor control is located in the centisecond task. It is capable of two
different approach modes:
In AFM approach mode, the motor is simply run at a specified control voltage and
automatically stopped when the force on the cantilever passes the setpoint. This will also
activate the feedback.
The STM approach mode is more complex because the tip must be brought extremely
close (on the order of ) to the surface without touching it. The vibrations caused by the
motor are too large for the feedback to be able to efficiently prevent the tip from crashing
into the surface. Therefore the approach algorithm shown in Fig. C.3 is used for the close
approach in STM mode.
Ramp up
z-Piezo Voltage
until
V>V0
I>I0
Activate Feedback
Fully Retract Piezo
Run Motor for t 0
Figure C.3: The STM approach algorithm;
is the fine -piezo control voltage,
is the
tunnelling current.
With the coarse
piezo control voltage set to the middle of its range, the fine
control
voltage is ramped from minimum to maximum extension. If the tip current crosses the
threshold current
during this ramping process, the ramping is stopped and feedback is
activated. Otherwise the motor will be run for a specified time
to move the head closer to
the sample. It is important that the motor advance step is smaller than the range of the fine
APPENDIX C. CONTROLLER
control to prevent tip crashes during motor advance. Typical values are ) for the motor control voltage and .
61
(roughly
The active feedback used to control the motor speed causes vibrations when the motor
is stopped. The power to the motor control circuit is therefore cut off with a relay after the
motor has stopped.
Appendix D
Scanner Calibration
The
-translation stage as well as the -piezos initially are provided with very big toler-
ances on the information about their extension at a certain voltage. Therefore we calibrated
them using a “linear variable differential transformer” (LVDT) (Schaewitz, LVDT Type
500 and Analog Transducer ATA-101) to obtain a scale for all image dimensions. The displacement was measured versus the controller output voltage ( range) so that the
calibrations include the effects of the high-voltage amplifier and position feedback where
used. The data and linear fits to it are shown in Fig. D.1 and the calibration results are listed
in Tab. D.1.
Name
Calibration
(with Nanodrive)
(with Nanodrive)
(without Nanodrive)
(without Nanodrive)
(AFM with PMDRV)
(STM with PMDRV)
Table D.1: The SPM scanner calibrations.
Although these values are certainly much better than the vendor provided data, all these
calibrations can only be regarded as clues; the dynamic behaviour of piezoelectric elements
includes hysteresis and creep, which, especially for the -piezos, cannot be ignored during
62
APPENDIX D. SCANNER CALIBRATION
63
Figure D.1: Calibration of the piezoelectric positioners.
imaging. The only exception to this is the
stage when the Nanodrive (position feedback)
is used, since the feedback eliminates these effects.
Appendix E
Dynamic Characterisation of the STM
Resonances and other strong variations in the system transfer function of a system can cause
difficulties controlling it (see Ch. 2.4). Therefore, it is important to design the -positioning
system in a way that it exhibits as little dynamic behaviour as possible.
The system transfer function is measured by imposing a small reference signal from a
lock-in amplifier on the -piezo control voltage of the controller. We cannot abandon feedback completely because thermal drift makes it impossible to maintain a constant average
tunnelling gap width for the duration of the measurement without feedback. Therefore we
reduce the feedback gain and increase the integration time constant so we can ignore the
reaction of the feedback to the reference signal. Then the reference signal can be swept
through the frequency range of interest and the amplitude and phase of the response in the
tunnelling current can be measured1 .
Figure E.1: The system transfer function of the STM.
1
This measurement includes the IV-converter and the second stage amplifier and the -piezo driver.
64
APPENDIX E. DYNAMIC CHARACTERISATION OF THE STM
65
The system transfer function is shown in Fig. E.1. In this setup the first resonance
frequency occurs above !
. Since the tip holder and the tip are the moving parts, this
value depends on the length of the tip wire and how it is mounted.
List of Abbreviations
AC
Alternating Current
ADC
Analog-to-Digital Converter
AFM
Atomic Force Microscopy
APD
Avalanche Photodiode
CPU
Central Processing Unit
DAC
Digital-to-Analog Converter
DC
Direct Current
DSP
Digital Signal Processor/Processing
FIFO
First In First Out buffer
HOPG
Highly Oriented Pyrolytic Graphite
IV-converter
Current-to-Voltage Converter
LSB
Least-Significant Bit
LVDT
Linear Variable Differential Transformer
NSOM
Near Field Scanning Optical Microscopy
PC
Personal Computer
PMT
Photomultiplier-Tube
PSTM
Photon Scanning Tunnelling Microscopy
RMS
Root-Mean-Square
SFM
Scanning Force Microscopy
SPM
Scanning Probe Microscopy
STM
Scanning Tunnelling Microscopy
SNOM
NSOM
UHV
Ultra High Vacuum
USB
Universal Serial Bus
66
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