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The Pennsylvania State University
The Graduate School
Department of Chemistry
NANOSCOPIC ANALYSES:
SINGLE MOLECULE CHARACTERIZATION IN
MOLECULAR ELECTRONICS AND SURFACE SCIENCE
A Thesis in
Chemistry
by
Brent Allen Mantooth
⃝c 2005 Brent Allen Mantooth
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
August 2005
∗
The thesis of Brent Allen Mantooth was reviewed and approved by the following:
Paul S. Weiss
Professor of Chemistry
Professor of Physics
Thesis Adviser
Chair of Committee
Thomas E. Mallouk
Professor of Chemistry
DuPont Professor of Materials Chemistry and Physics
A. Welford Castleman, Jr.
Evan Pugh Professor of Chemistry and Physics
Eberly Distinguished Chair in Science
Vincent H. Crespi
Professor of Physics
Professor of Materials Science and Engineering
Ayusman Sen
Professor of Chemistry
Head of the Department of Chemistry
∗
Signatures are on file in the Graduate School
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Abstract
Time-resolved scanning tunneling microscope (STM) measurements of single molecules are
used to determine the behavior and interactions of adsorbed species. This thesis describes the cus-
tom design of the scanning tunneling microscope hardware and software used to acquire molecular-
resolution images. Using this instrument, two systems are characterized: the conductance switching
of oligo (phenylene-ethynylene) (OPE) molecules inserted in n-alkanethiolate self-assembled mono-
layers (SAMs), and the motion of benzene adsorbed on Au{111} at 4 K. For both systems, the
use of digital image processing was applied to the analysis of time-resolved sequential images to
determine changes in topographic features or overlayer structure. From these analyses we can
determine the mechanism for conductance switching and quantify the weak adsorbate-adsorbate
substrate-mediated interactions present in benzene overlayers. These types of analyses must be exe-
cuted at the single molecule level, as no ensemble technique can observe the discrete, heterogenious
behaviors observed by STM in these systems.
One of the ultimate miniaturizations in nanotechnology is molecular electronics, where elec-
tronic devices will potentially consist of individual molecules. Some of the molecules being inves-
tigated for application in molecular electronics are a family of OPE molecules. Ensemble mea-
surements of these molecules have yielded hysteretic switching and negative differential resistance,
both useful properties that enable memory and logic operations. We investigate these systems by
inserting the molecule of interest in an inert SAM to isolate single molecules, probing each molecule
with the STM tip on a single-molecule basis. We acquire time-resolved sequences of STM images
over periods of up to several days or acquire real-time measurements at a rate of 10 kHz for 15
seconds, and observe that these molecules exhibit conductance switching such that their apparent
height changes. Due to properties of the materials used to acquire STM images, the field of view
may drift. A digital image tracking algorithm based on Fourier transform cross-correlation has
been developed to correct for instrumental drift in STM images. Analyzing the apparent height
of different molecules in variable SAM matrices as a function of time has enabled us to propose
that conductance switching is the result of hybridization and/or conformational changes at the
metal-molecule interface.
iv
Using similar analyses, we have applied scanning tunneling microscopy to probe and to quan-
tify the weak substrate-mediated interactions in benzene overlayers on Au{111} at 4 K. We observe
that benzene molecules exhibit three types of motion, including 2D desorption, 2D adsorption, and
simultaneous dislocations of many molecules (molecular cascades). Correlating the probability of
2D desorption with the number of nearest neighbors of the desorbing molecules enables the calcula-
tion of the magnitude of the adsorbate-adsorbate substrate-mediated interactions. We also observe
chains of up to 12 molecules simultaneously moving in the same direction at the same time in an
event we refer to as molecular cascades. These cascades are the result of translation of the overlayer
structure and are highly correlated with 2D desorption and 2D adsorption.
v
Table of Contents
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Ensemble and Single Molecule Measurements . . . . . . . . . . . . . . . . . . . 1
1.2 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2. Ambient Condition Scanning Tunneling Microscopy . . . . . . . . . . . . . . . . 6
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Electron Tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Piezoelectric Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Beetle-style STM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.1 Coarse Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.2 Sample Holder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.3 Current Preamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.4 Vibration Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 Control Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Chapter 3. Development and Design of Instrumentation Control Software:
WinSTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1 Program Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.1 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.2 Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.3 Scanning Probe Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Operating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4 High-Precision Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.5 Class Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5.1 Class Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5.2 CWinSTMApp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.3 CInstrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5.4 CRaster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5.5 CSpectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5.6 CDlg ScanAcq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5.7 CWinSTMDoc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
vi
3.5.8 CWinSTMView . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5.9 Other Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Chapter 4. Molecular Electronics:
Fabrication, Assembly, and Characterization . . . . . . . . . . . . . . . . . . . 46
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Self- and Directed Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Molecular Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4 Measuring Molecular Electronic Components . . . . . . . . . . . . . . . . . . . 58
4.4.1 Mercury Drop Junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.4.2 Break Junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4.3 Nanopores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4.4 Metal Nanowires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.4.5 Bridging Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4.6 Crossed Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4.7 Scanning Tunneling Microscopy . . . . . . . . . . . . . . . . . . . . . . . 67
4.4.8 Contact Conductive Probe AFM . . . . . . . . . . . . . . . . . . . . . . 73
4.4.9 Nanoparticle Coupled CP-AFM . . . . . . . . . . . . . . . . . . . . . . . 74
4.5 Conclusions and Future Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Chapter 5. Lateral Drift Correction for Adsorbate Analysis . . . . . . . . . . . . . . . . . . 78
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2 Drift Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3 Monitoring Single Molecule Topography . . . . . . . . . . . . . . . . . . . . . . 85
5.4 Single Molecule Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Chapter 6. Single Molecule Switching with
Real-Time Topographic Measurements . . . . . . . . . . . . . . . . . . . . . . . 99
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.2 Real-Time Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.3 Topographic Switching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.4 Temporal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Chapter 7. Analyzing the Motion of Benzene on Au{111}:
Substrate-Mediated Interactions and Cascade Motion . . . . . . . . . . . . . . . 122
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.2 Benzene on Au{111} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.3 Digital Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.4 Two-Dimensional Desorption/Adsorption of Single Molecules . . . . . . . . . . 137
7.5 Cascade Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
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Chapter 8. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
8.1 Instrumentation and WinSTM . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
8.2 Drift Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
8.3 Real-Time Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
8.4 Digital Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Appendix A. Scientific Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Appendix B. Instrumentation Schematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
B.1 Electronics Schematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
B.2 Hardware Schematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
B.2.1 Sample Holder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
B.2.2 Preamplifier Elevator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
B.2.3 STM Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Appendix C. Matlab Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
C.1 WinSTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
C.2 Image Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
C.3 Calculating Apparent Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
C.4 Real-Time Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
C.5 Analyzing Benzene Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
viii
List of Tables
3.1 Comparison of the features and capabilities of WinSTM, PSCan, and RHK (com-
mercial) software. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Comparison of resources for PSCan and WinSTM. . . . . . . . . . . . . . . . . . . 27
3.3 High-precision timing results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Class structures in WinSTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1 Experimental characteristics of several molecules and selected papers that address
these properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 Various β values expressed in ˚A−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.1 Topographic height differences for common surface features. . . . . . . . . . . . . . 109
7.1 Data for motion events as a function of number of nearest neighbors and region. . 138
B.1 Jumper descriptions for the feedback loop board, corresponding to Figure B.1. . . 176
B.2 Jumper descriptions for the bias coupler board, corresponding to Figure B.2. . . . 178
B.3 Jumper descriptions for the interpro board, corresponding to Figure B.3. . . . . . . 180
B.4 Jumper descriptions for the ramp generator board, corresponding to Figure B.4. . 182
B.5 Jumper descriptions for the X and Y scan and walker amplifier boards, correspond-
ing to Figure B.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
B.6 Jumper descriptions for the X and Y offset amplifier boards, corresponding to Fig-
ure B.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
B.7 Jumper descriptions for the diplex boards that filter the X and Y offset signals,
corresponding to Figure B.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
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List of Figures
2.1 Energy level diagram for electron tunneling. . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Schematic of a piezoelectric scanning tube. . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Photograph of a beetle-style STM head. . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Schematic of the STM tip assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 Schematic of electrical signals applied to the STM head. . . . . . . . . . . . . . . . 12
2.6 Photographs of the sample holder. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.7 Photographs of the preamplifier and assembled instrument. . . . . . . . . . . . . . 16
2.8 Schematic of a scanning tunneling microscope. . . . . . . . . . . . . . . . . . . . . 18
2.9 Example of a typical molecular resolution STM image. . . . . . . . . . . . . . . . . 19
2.10 Electronics schematics for custom control hardware. . . . . . . . . . . . . . . . . . 21
3.1 STM image showing the results of atom manipulation. . . . . . . . . . . . . . . . . 25
3.2 Hierarchy of applications, operating systems, and hardware . . . . . . . . . . . . . 28
3.3 Characterization of high-precision timing. . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 WinSTM Class Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 Raster and sub-step trajectories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.6 Simplified schematic of integrator electronics. . . . . . . . . . . . . . . . . . . . . . 40
3.7 Pseudo-code listing of the steps for acquiring an STM image. . . . . . . . . . . . . 41
3.8 Data acquisition interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.9 Data visualization and analysis interface. . . . . . . . . . . . . . . . . . . . . . . . 44
4.1 Potential molecules for use in molecular electronics. . . . . . . . . . . . . . . . . . . 48
4.2 STM image of a SAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3 I-V curve for a SAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 Methods for measuring molecular electronics components. . . . . . . . . . . . . . . 59
4.5 On/Off states as imaged by STM. . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.6 Height vs. time characterization by STM. . . . . . . . . . . . . . . . . . . . . . . . 70
5.1 Real-space calculation parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2 Cross-correlation images. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.3 Drift track analysis using key frames. . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.4 Key frame analysis for simulated image sequence. . . . . . . . . . . . . . . . . . . . 85
5.5 Drift simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.6 Extraction of single OPE molecules from an image for topographic analysis. . . . . 87
5.7 Definition of apparent height. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.8 Simulated image showing regional maximum detection. . . . . . . . . . . . . . . . . 90
5.9 Simulated images to test apparent height calculation methods. . . . . . . . . . . . 91
5.10 Comparison of height calculation techniques on real data. . . . . . . . . . . . . . . 93
5.11 Structure of a fcc{110} surface face. . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.12 Surface diffusion tracking for benzene on Ag{110}. . . . . . . . . . . . . . . . . . . 96
6.1 Molecular resolution STM images and corresponding cross-sections of OPE molecules
exhibiting switching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2 Response of the FBL as a function of frequency. . . . . . . . . . . . . . . . . . . . . 103
x
6.3 STM image and corresponding real-time measurements of OPE molecules. . . . . . 105
6.4 Real-time topographic measurement of an OPE molecule demonstrating Z-drift
subtraction and time resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.5 Multiple real-time topographic height traces. . . . . . . . . . . . . . . . . . . . . . 108
6.6 Real-time topographic height traces of OPE molecules showing multiple discrete
heights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.7 Real-time topographic height traces of OPE molecules showing drift-like behavior. 110
6.8 Real-time topographic height traces of the SAM. . . . . . . . . . . . . . . . . . . . 111
6.9 Histogram of topographic height differences detected by real-time topographic mea-
surements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.10 Dependence of the apparent height on tunneling current and bias. . . . . . . . . . 114
6.11 Single-molecule state lifetimes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.12 Autocorrelation of real-time topographic measurements. . . . . . . . . . . . . . . . 118
6.13 Real-time topographic height traces acquired over the OPE that diffuses up and
down atomic step edges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.1 STM image of 0.9 ML of benzene on Au{111}. . . . . . . . . . . . . . . . . . . . . 125
7.2 Overlayer structures for hcp and fcc regions of benzene on Au{111}. . . . . . . . . 127
7.3 STM perspective image of near monolayer coverage of benzene on Au{111}. . . . . 129
7.4 Drift track for image sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.5 Digital image processing steps to locate molecules and detect motion. . . . . . . . 133
7.6 Visualization of the data obtained from image processing. . . . . . . . . . . . . . . 134
7.7 Radial distribution functions for the fcc and hcp regions for 0.9 ML coverage of
benzene on Au{111}. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.8 Probability per frame of 2D desorption as a function of number of nearest neighbors
and region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.9 Spatial histograms indicating the location of 2D adsorption or 2D desorption events. 143
7.10 Multidimensional histograms for the fcc region that represent 2D adsorption events,
2D desorption events, and number of molecules as a function of distance from the
soliton wall and number of nearest neighbors. . . . . . . . . . . . . . . . . . . . . . 144
7.11 Multidimensional histograms for the hcp region that represent 2D adsorption events,
2D desorption events, and number of molecules as a function of distance from the
soliton wall and number of nearest neighbors. . . . . . . . . . . . . . . . . . . . . . 145
7.12 STM images that show cascade motion. . . . . . . . . . . . . . . . . . . . . . . . . 147
7.13 Spatial histogram of cascade motion. . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.14 State diagram for molecules that undergo cascade motion. . . . . . . . . . . . . . . 150
7.15 Structural changes resulting from cascade motion. . . . . . . . . . . . . . . . . . . 152
7.16 Histogram of the ‘lifetimes’ of cascade states for both configurations for αβ and αγ
cascades. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.17 State diagram for the occupation states of adsorbate sites along the soliton region. 155
7.18 Correlation coefficients for cascade state and soliton occupation. . . . . . . . . . . 156
7.19 Correlation coefficients between cascade states and soliton site occupation. . . . . . 157
A.1 FE-SEM images of the molecular ruler process. . . . . . . . . . . . . . . . . . . . . 167
A.2 FE-SEM image of a circular nanostructure generated by the molecular ruler process. 168
A.3 STM image of the electron density of a triangular island on a Au{111} surface,
demonstrating the quantum mechanical properties of a particle in a triangular box. 169