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IIIIIIIIIIII III IIIIIII IIIIIIIIII

009114 0108

This is to certify that the

dissertation entitled

"Scanning Tunneling Microscope Study of Surface Diffusion

and Dislocation Mot ion in Atomically Flat Gold Films"

presented by

Jeeseongﬂvang

has been accepted towards fulﬁllment
of the requirements for

Ph-D- degree in Bhysi gs

 

Major professor

Date 1993

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MSU Is An Affirmative Action/Equal Opportunity Institution
emulation

 

 

 

SCANNING TUNNELING MICROSCOPE STUDY
OF SURFACE DIFFUSION AND DISLOCATION MOTION
IN ATOMICALLY FLAT GOLD FILMS

By

Jeeseong Hwang

A DISSERTATION

Submitted to
Michigan State University
in partial ﬁilﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1993

i
.1

ABSTRACT

SCANNING TUNNELII‘{G MICROSCOPE STUDY
OF SURFACE DIFFUSION AND DISLOCATION MOTION
IN ATOMICALLY FLAT GOLD FILMS

By

Jeeseong Hwang

A simple scanning tunneling microscope (STM) which works well from room
temperature to 4K is described. It is relatively easy to build, repair or modify, and works
very reliably. With this STM, we study mass ﬂow on (111)Au and ﬁnd that the rate of
decay of the area of monolayer islands produced by STM lithography is linear in time.
We demonstrate by Monte Carlo simulations that a proper accounting of the detachment
and reattachment rates of kink site atoms produces a linear decay. To observe the decay
rate of a monolayer gold island, one needs a sample with large isolated grains with large
facets showing atomically ﬂat terraces separated by monatomic steps. We ﬁnd that
thermal evaporation of Au onto heated glass substrates satisﬁes these conditions. At
room temperature in air, these ﬁhns show low angle grain boundaries and other
dislocation arrays which move under an applied stress introduced either by handling the

sample or by crashing an STM tip on the sample surface.

To my parents

iv

ACKNOWLEDGEMENTS

I wish to thank Michael A. Dubson for his invaluable guidance, inspiration,
assistance, and encouragement as a supervisor, a teacher, and a friend in all aspects of
my graduate years. In, particular, he taught me how to create exciting, and enjoyable
moments out of long and dry-looking physics. I thank Professors Norman Birge, Phillip
Duxbury, William Hartmann, and Michael Thoennessen for serving on my graduate
committee.

There are several people to whom I owe acknowledgement: Martine Kalke for
writing the Monte Carlo simulation program for the cubic lattice solid-on-solid model;
the machine shop staff, Thomas Palazzolo, Jim Muns, and Tom Hudson for their
assistance in construction of experimental apparatus and in teaching me machine shop
skills; Electronic shop staﬁ‘, Barry Tigner and Bob Raine for their technical support in
building electronics and cleaning notorious viruses in my PC; Reza Loloee for his efforts
to teach various measurement skills and organize a hazard-free chemical room.

I would like to extend my thanks to my fellow graduate students; Qifu Zhu, for
useful conversations regarding experiments and sharing the spirit of the orient; Lowell
McCann who is a creative participant in the 'STM next generation', for his assistance of
measurements, useful discussions in small particle experiments and critical proof reading
of this manuscript; George Jeffers, for divulging his own secrets in making thin ﬁlms
and careful reading of this thesis; Sangil Hyun, for drawing the STM shop drawings in
the appendix; and all the graduate students in department.

I am also grateful for the encouragement and support that I received from my
parents, parents-in-law, brothers and sisters. Their many prayers and support on my
behalf are appreciated.

My special thanks go to my wife, Miyoung for her prayers, patience, sacriﬁce,
and love over the last six years.

Finally, I want to thank MSU and the National Science Foundation for ﬁnancial
support during my graduate studies.

TABLE OF CONTENTS

1. INTRODUCTION

2. THE MICROSCOPE
Simple, Variable Temperature Scanning Tunneling Microscope
2.1 ABSTRACT
2.2 INTRODUCTION
2.3 DESIGN AND CONSTRUCTION
2.4 OPERATION
REFERENCES FOR CHAPTER 2

3. SAMPLE PREPARATION
Atomically Flat Gold Films on Hot Glass Substrates

3.1 ABSTRACT
3.2 INTRODUCTION
3.3 PROBLEMS WITH MICA SUBSTRATES
3.4 SAMPLE PREPARATION
3.5 RESULTS
REFERENCES FOR CHAPTER 3

17
22

24

24
25
26
28
33
55

4. STM OBSERVATIONS OF SURFACE SELF DIFFUSION

ON THE Au (111) PLANE 57
4.1 ABSTRACT 57

4.2 INTRODUCTION 5 7

4.3 EXPERIMENTAL TECHNIQUES 60
4.3.1 Sample Preparation 60

4.3.2 STM Lithography 63

4.4 RESULTS 68
4.4.1 Linear Decay in Time of the Monolayer Island 68

4.4.2 Measurement of the Diffusion Coeﬁicient
from a Diffusing Mound 81

4.4.3 Measurement of the Difﬁrsion Coefﬁcient
from Moving Terrace Edges 83
REFERENCES FOR CHAPTER 4 98

5. MONTE CARLO SIMULATION OF THE LINEAR DECAY

OF ISLANDS ON METAL SURFACES 99
5.1 ABSTRACT 99
5.2 INTRODUCTION 99
5.3 MODELS AND RESULTS 102
5.3.1 A Hybrid Lattice-Continuum Model 102
5.3.2 A Cubic Lattice Solid-On-Solid Model 104

REFERENCES FOR CHAPTER 5 115

vii

6. STM STUDY OF THE PLASTIC DEFORMATION OF
STRESSED THIN GOLD FILMS ON GLASS SUBSTRATES
6.1 ABSTRACT
6.2 INTRODUCTION
6.3 RESULTS AND DISCUSSION
REFERENCES FOR CHAPTER 6

7. STM STUDIES OF SMALL PARTICLES ON FLAT SUBSTRATES
7.1 ABSTRACT
7.2 INTRODUCTION
7.3 SAMPLE PREPARATION

116
116
116
125
149

150
150
150
152

Searching for the Recipe to Fabricate Flat Metal-Oxide Barrier Substrates

7.4 RESULTS OF STM SPECTROSCOPY AND DISCUSSIONS
7.4.1 Coulomb Staircase
7.4.2 Coulomb Blockade
7.4.3 Other I-V Measurements

REFERENCES FOR CHAPTER 7

8. OTHER OBSERVATIONS AND FUTURE EXPERIMENTS
8.1 A sample cleaning technique at low temperature
8.2 STM observations of graphite surfaces radiated by high energy
charged nucleons
8.3 High resolution AF M images of a submicron Au wire
8.4 STM observations of recrystallized gold on W boat
REFERENCES FOR CHAPTER 8

viii

165
165
170
173
176

178
178

179
182
185
189

9. SUMMARY OF CONCLUSIONS 190

A. Shop drawings for STM Body 193

B. List of Publications 197

ix

LIST OF TABLES

Table 4.1 Features formed by voltage pulse under various conditions.

LIST OF FIGURES

Figure 2.1 Photographs of the STM. (a) fully assembled. (b) with sample 6
stage removed for easy sample loading.

Figure 2.2 Schematic diagram of theSTM setup. 7

Figure 2.3 Thermal expansion coefficients of Invar and other metals. 10
Figure 2.4 Tip-sample gap change on cooling the invar-body STM. 11
Figure 2.5 l6Ax16A scan of graphite at 77K. 13

Figure 2.6 250nmx250nm scan ofAu(111) at room temperature showing 13
monatomic steps of 2.4A.

Figure 2.7 Piezoceramic tube with O-ring lead attachment. 14
Figure 2.8 Plate/Piezo tube/tip structure . 16
Figure 2.9 SEM pictures of STM tips. (a) cut Pt-Rh tip. (b) pulled Nb tip. 18

Figure 2.10 67Ax67A scan of (1 1 1) gold with a pulled Nb tip at room 19
temperature in constant height mode.

Figure 2.11 The power spectrum of the tunneling current showing the STM 20
resonating at 2.8 kHz.

Figure 3.1 SEM photograph of a 200nm-thick gold ﬁlm grown on mica at 27
350C.

Figure 3.2 The sample heater block. 29

Figure 3.3 Increase in temperature of the sample surface vs. time of 31
exposure to the hot tungsten evaporator boat.

xi

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.8

Figure 3.9

Figure 3.10

Figure 3.11

Figure 3.12

Figure 3.13

Figure 3.14

Figure 3.15

Figure 3.16

Figure 3.17

STM image showing multiple-tip artifacts (inside the boxes).

Average grain size in gold ﬁlms evaporated onto glass as a
function of substrate temperature during growth.

Height-height autocorrelation functions for 80nm thick gold
ﬁlms grown at 20C and 105C.

(a-b) STM images of 20nm thick gold ﬁlms grown on glass
substrates of (a) 20C, (b) 105C. (c) A SEM image of a 20nm
thick gold ﬁlm grown on a glass substrate of 185C.

STM images of 40mm thick gold ﬁlms grown on glass
substrates of (a) 20C, (b) 105C, (c) 185C, (d) 300C, (e) 400C,
and (i) 465C.

STM images of 60nm thick gold ﬁlms grown on glass
substrates of (a) 20C, (b) 105C, (c) 185C, ((1) 300C, (e) 400C,
and (t) 465C.

STM images of 80nm thick gold ﬁlms grown on glass
substrates of (a) 20C, (b) 105C, (c) 185C, (d) 300C, (e) 400C,
and (t) 465C.

Typical scan proﬁles for 80nm thick ﬁlms.

Measured rms surface roughness vs. substrate temperature for
40nm, 60nm, and 80nm thick ﬁlms.

Grains showing ﬂat tops with terraces separated by multi-
atomic steps.

The hexagonal faceting of gold crystal.

Terraces separated by monatomic steps on clearly developed
top facet.

STM image of an 80nm-thick ﬁlm grown at 300C showing a
large grain with terraces separated by monatomic steps.

Large step-free region bounded by a 60° hexagonal facet which
is the characteristic of Au(1 1 1) face.

xii

34

35

36

37

39

41

43

45

46

48

49

50

51

Fgure 3.18

Figure 3.19

Figure 4.1

Figure 4.2

Figure 4.3
Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11

Figure 4.12

Figure 4.13

Figure 5.1

STM image of a 60nm-thick gold ﬁlm annealed at 485C for 3
hours.

A monolayered wormy sreucture on ﬂat top of the grain in the
annealed gold ﬁlm.

X-ray 29 scan of the 80nm-thick gold ﬁlm of 300C glass
substrate.

A pair of STM images of a 6 month old sample showing no sign
of activity.

Images of tip-crashes.
Pits and mound formed by voltage pulses.

Time-sequential STM images showing linear decay of two layer
system.

A schematic illustration showing the effect of a double tip.

Areas vs. time for both top island and second island shown in
Figure 4.5.

Time-sequential STM images showing linear decay of two layer
system.

(a) The plot of the area vs. time for each island in two layer
system of Figure 4.8. (b) A plot of total area of top and second
island vs. time.

The time lapse images of diffusing mounds and healing pits.

The time sequential STM images of the contaminated sample
showing wandering of terrace steps due to surface diffusion.

A schematic illustration of the diffusing terraces.
Time series STM images showing the shrinkage of stacked
monolayer gold mesas in the sample prepared by clean

procedure.

Potential near a monatomic step.

xiii

53

53

61

64

67

69

73

75

76

79

82

85

92

94

101

Figure 5.2

Figure 5.3
Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

Decay of an island of radius 20 with outer absorbing circles of
reﬂection coefﬁcient k=0.

Decay of an island with outer absorbing circles of reﬂection
coeﬁicient k = 0.95.
Two stacked mesas in the cubic lattice solid-on-solid model.

Plot of log of the number of active sites vs. log of total number
of remaining atoms in a mesa during the simulation.

Decay of the top mesa in a three mesa system of starting sizes
200, 800, and 2500 atoms with several diferent values of k = 0,
0.5, 0.85, and 0.9.

Decay of the top and middle mesas in a three mesa system of
starting sizes 400, 1600, and 6400 atoms, respectively. The
reﬂection coefficient, k = 0.9.

(a) A model of a simple cubic lattice. (b) A positive edge
dislocation DC formed by inserting an extra half-plane of atoms
in ABCD. (c) A left-handed screw dislocation DC formed by
displacing the faces ABCD relative to each other in direction
AB. ((1) A spiral of atoms adjacent to the line DC in (c).

(a) Burgers circuit around an edge dislocation. (b) Burgers
circuit in a perfect crystal; the closure failure is the Burgers
vector.

(a) Burgers circuit around a screw dislocation. (b) Burgers
circuit in a perfect crystal; the closure failure is the Burgers

VCCIOI‘.

A low angle grain boundary consisting of a sheet of equally
spaced dislocations.

Motion of a dislocation as a glide along the slip plane.

A screw dislocation produced during the evaporaion of a 80nm
thick gold ﬁlm onto a 300C glass substrate.

Time lapse STM images showing the attenuated motion of the
low angle grain boundary.

A surface proﬁle of the image 6.7(d).

xiv

105

106

108

110

112

113

118

120

120

121

123

126

127

129

Figure 6.9

Figure 6.10

Figure 6.11

Figure 6.12

Figure 6.13

Figure 6.14

Figure 6.15

Figure 6.16

Figure 6.17

Figure 7.1

Figure 7.2

Figure 7.3

Figure 7.4

Figure 7.5

Figure 7.6

The plot of the distance that the low angle grain boundary
shown in Figure 6.7 moves vs. elapsed time.

(a) The FCC system showing one of the {111} planes and three
slip directions in the plane. (b) A close-up view of the (111)
plane-low angle grain boundary system.

A series of STM images showing that the tip crash causes the
low angle grain boundary motion.

A plot of the distance that the low angle grain boundary in
Figure 6.11 moves vs. time.

Time lapse STM images showing that the motion of a high
angle grain boundary reverses direction.

(a) A surface proﬁle of the boundary line of the image shown in
Figure 6.13 (t). (b) A close-up view of the boundary line.

A plot of the distance that the low angle grain boundary in
Figure 6.13 moves vs. time.

Sequential images showing that two low angle grain boundaries
show an oscillatory behavior.

A plot of the distance that each low angle grain boundary in
Figure 6.16 moves vs. time.

The experimental arrangement of the small particle experiment.

Topographic mode STM image of a 12nm thick gold ﬁlm
evaporated on a 240C mica.

SEM photograph showing that evaporated Al does not wet the
gold surface.

SEM photographs of well isolated compact indium islands with
faceted tops. (a) top view. (b) side view of the same sample.

(a) STM image of the surface of Si wafer etched with a HF
solution. (b) A STM image of the surface of an etched Si wafer
with a buffered HF solution.

A STM image of percolating gold islands on a Si surface.

XV

130

132

135

136

138

141

142

144

146

153

155

155

157

160

162

Figure 7.7

Figure 7.8

Figure 7.9

Figure 7.10

Figure 7.11

Figure 7.12
Figure 7.13
Figure 7.14

Figure 8.1

Figure 8.2

Figure 8.3

Figure 8.4
Figure 8.5
FigureA.1
Figure A.2
Figure A.3

Figure A4

(a) A SEM photograph of isolated lead islands on SiOz. (b) A
SEM photograph showing how thermally evaporated lead wets
a gold surface.

A STM image of isolated gold islands on PbOx.

A schematic illustration of the variation in sample bias during
the I-V measurement.

I-V spectrum of the coulomb staircase at room temperature.

(a) The experimental arrangement of the small particle
experiment. (b) The equivalent circuit of the N-I-N-I-N double
junction.

I-V spectrum of the coulomb blockade at T = 83K.

A STM I-V spectrum of a NIN tunnel junction.

A STM I-V spectrum of a NIS tunnel junction.

(a) A STM image of HOPG bombarded with high energy
ionized Kr nucleons. (b) A close-up view of the regular
triangular pits.

(a) An AF M image of a submicron gold wire fabricated by
electron beam lithography. (b) A close-up view of top of the
wire clearly showing gold grains.

(a) An AFM image of a thin gold ﬁlm and thick gold leads
fabricated by the triple layer method. (b) A close-up view of
the thick lead with tapered edge.

A STM image of recrystallized gold surface on a W boat.

A STM image of recrystallized gold surface on a W boat.

STM bottom plate.

STMright hand side plate.

STM back plate.

The ﬁnal assembly of the STM body.

xvi

163

164

166

168

169

171

174

175

181

183

184

186

187

193

194

195

196

Chapter 1

INTRODUCTION

Atomic resolution observations of mass ﬂow on a metal surface provide
important clues about the microscopic mechanism of surface self diffusion. Direct 3-D
observations of diffusing atoms or molecules on metal surfaces have been accomplished
using a Field Ion Microscope (FIM), Scanning Tunneling Microscope (STM), and
Atomic Force Microscope (AF M). A direct measurement of the surface self diffusion
coefﬁcient can be made by observing the motion of an individual atom diffusing on an
atomically ﬂat surface. If the surface is ideal the atomistic motion can be considered as a
2-D random walk amongst sites separated by potential barriers.

At room temperature in air, however, the motion of the individual atom is too fast
to observe with an STM. Another technical problem for the observation of individual
atoms is that it is very hard to obtain atomic resolution in air due to surface
contamination. Instead, in this research, the surface self diffusion coefﬁcient is
measured from sequential STM images which show wandering monatomic steps or from
the shape change of a gold mound.

At room temperature in air, we also observe that the area of single monolayer
gold island decays linearly with time. A linear decay of island is puzzling at ﬁrst sight.
If the rate of mass loss is proportional to the circumference of the island then the decay is
parabolic, not linear. We have found, by Monte Carlo simulations, that a proper
accounting of the kink atom detachment and reattachment rates leads to a linear decay.

To observe the decay rate of a monolayer gold island, one needs a sample with

grains with large facets showing atomically ﬂat terraces separated by monatomic steps.

Gold ﬁlms evaporated on hot glass satisfy these conditions. One might be tempted to
assume that epitaxial growth is a requirement for making atomically ﬂat ﬁlms. But our
results for Au on amorphous glass substrates show that epitaxy is deﬁnitely not
necessary for the production of large, ﬂat regions.

In our experiment, since not every layered structure created by the evaporation
undergoes surface diffusion, we lithographically fabricated small mounds or islands with
an STM using the voltage pulse technique. There are several advantages to making
small structures artiﬁcially. First, in most cases, we can expect the features to change
because they are in a metastable state. Secondly, a small system is desirable so that we
can collect enough data in a short period of time before the STM image degrades due to
build-up of surface contamination. Thirdly, a system of appropriately small size can be
exactly modeled by the Monte Carlo simulation with the limitations in array size.

During this surface self diffusion measurement, low angle grain boundaries and
other dislocation arrays were observed. We also found that these low angle grain
boundaries move under an applied stress introduced either by handling the sample or by
crashing an STM tip on the sample surface. These dynamic features usually accompany
a deformation of part of the sample.

In a perfect crystal, atoms are arranged in a regular periodic pattern. However, in
the real world, a crystal may contain various kinds of defects such as point defects
(impurities, vacancies, etc.) and line defects (edge dislocations, screw dislocations).
Since the macroscopic behavior of crystalline solids strongly depends upon the species
and number of defects, an understanding of defects in a crystal is very important. For
irreversible plastic deformation of a crystalline solid, it is well known that the
deformation is induced by the atoms sliding over one another along a well—deﬁned slip
plane instead by uniform shearing of the crystal. Some characteristics of observed

dislocations can be explained by this model.

Originally, before this subject of surface self diffusion drew our attention, our
principle goal was investigating discrete charging and quantum size effects in single
small metal particles with the STM. This investigation involves the attempt to correlate
the I-V characteristics of various tunneling junctions which include a small metal particle
and the STM tip.

The understanding of the electronic properties of small pieces of metal is a
subject of growing importance as the microelectronics industry pushes toward smaller
and smaller circuitry. As the size of a block of metal diminishes, new effects, not visible
in large samples, arise and eventually dominate the simple ohmic metallic behavior.
Some important I-V curves including the Coulomb Staircase at room temperature and the
Coulomb Blockade at T = 83K were obtained.

For this study, we built a STM which works reliably ﬁ'om room temperature to
4K. The design and construction of our STM is described in Chapter 2. Let us brieﬂy
discuss the basic concept of STM before we close this chapter.

A STM can provide direct images of conducting surfaces with atomic resolution.
A STM consists of a sharp metal tip held several angstroms above a sample surface by
piezoelectric ceramic supports. An applied voltage between the sample surface and tip
results in a tunneling current which depends exponentially on the tip-to-sample distance.
With a tunneling barrier height of a few electron-volts, a change of the turmeling barrier
width by one angstrom changes the tunneling current by an order of magnitude.

A STM can be operated in either the topographic mode (constant current mode)
or the current mode (constant height mode). In the topographic mode, as the tip is
scanned over the surface by the piezo supports, feedback electronics hold the tunneling
current constant by adjusting the tip-sample distance. The resulting plot of tip height vs.
position is a map of the electronic wavefunctions on the sample surface. Alternatively,

in the current mode a tip is scanned over the surface at constant height while the current

is monitored. In this mode the variations in tunneling current due to surface corrugation
are mapped vs. tip position. Each mode has its own advantages. The topographic mode
gives direct topographic information of the surface over large structure and rough
surfaces. On the other hand, current mode allows faster scans for relatively ﬂat surfaces
so that the fast imaging minimizes noise due to thermal driﬁ, vibration and piezo creep.
Consequently, this current mode is usually used for obtaining images with atomic
resolution.

STM is also capable of doing spectroscopic measurements to observe surface or
subsurface electronic properties. The applicable subjects involve characterization of

superconductors, phonon spectroscopy, quantum size effects, etc.

Chapter 2

THE MICROSCOPE

Simple, Variable Temperature Scanning Tunneling Microscope

2.1 ABSTRACT

We describe a simple scanning tunneling microscope (STM) which works well
from room temperature to 4K. It is relatively easy to build, repair or modify, and works
very reliably. An unusual feature of our STM is that it is assembled without glues or
solders. A list of suppliers of the components used in our STM is included in the

references.

2.2 INTRODUCTION

Several designs for variable-temperature and low-temperature scanning tunneling
microscopes (STM's) have been published.1’2,3a4 In this chapter, a single-tube STM
with a differential spring coarse-approach mechanism, similar to that described in ref] is
described. The instrument, shown in Figure 2.1, has a box-shaped body, chosen for ease
of machining and so that the microscope can be quickly disassembled for repair or
replacement of any component. The schematic diagram of entire STM setup is given in
Figure 2.2 and the shop plans of STM body is shown in Appendix A. Our STM has the
unusual feature that it is constructed without glues or solders, and it functions very

reliably in the temperature range 4-300K.

 

Figure 2.1 Photographs of the STM. The scale on the ruler is centimeters. (a) fully
assembled. (b) with sample stage removed for easy sample loading.

Long screw driver

Brass Quick-Connect

 

 

piezo bias (+X,+Y,-X,-Y)

 

 

sample bias CONTROLLER

POMONA
BOX

 

 

 

PREAMP tunneling
current

  

 

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COMPUTER

 

 

 

ﬁx Phenolic Tube

Wooden POStS Fork at the end of long screw driver

to turn top screw of the STM in situ

 

STM NOTE : Figure not to scale.
HEAD See Figure 2.2 (b) for the detail
of inside circle.

 

 

 

 

Figure 2.2 (a) Schematic diagram of the STM setup

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Figure 2.2 (b) Schematic diagram of the STM head

2.3 DESIGN AND CONSTRUCTION

The differential spring coarse-approach mechanism consists of a steel spring
pressing against a 1/16" thick aluminum plate supported along two edges. Aluminum,
rather than steel, was chosen for the plate because, for a given spring constant, an
aluminum plate has a resonant frequency twice as great as that of a steel plate, resulting
in better vibration immunity.5 The motion of the plate and tunneling tip is about 3 pm
per turn of the 2-64 screw at the top of the STM body. The screw and the screw plate
must be made of the same material (brass, in our case) to avoid binding at low-
temperature due to differential thermal contraction. A plastic barrel surrounds the spring
to prevent transverse movement during compression.

The main body of the STM is made of Super-lnvar5, a F e-Ni alloy which has a
near-zero coefﬁcient of thermal expansion at room temperature7. The thermal expansion
coefﬁcient of Invar is plotted in Figure 2.3 along with several different metals in the
temperature range 0-300K. In earlier designs, we made the STM body of aluminum,
chosen for ease of machining, and because A1 is strong and light, with a (Young's
modulus/density) ratio equal to that of stainless steel. The aluminum body STM
ﬁmctioned very well both at room and cryogenic temperatures. However, during cooling
to <100K, contraction of the aluminum body causes the tip-sample distance to shrink by
more than 60pm, requiring about 20 turns of the coarse-approach screw to keep the tip in
tunneling range. With the Invar body, on cooling ﬁ'om room to cryogenic temperatures,
the tip-sample distance increases by about 20pm, due to contraction of the sample stage
and the piezo tube The increase of the tip-sample gap due to cooling is plotted in Fig
2.4. Not only is the thermal driﬁ much reduced, but the increasing tip-sample distance
upon cooling reduces the possibility of tip crash.

A difﬁculty with Super-Invar is that it is available only in 3/ " thick plates which

10

 

 

4'50 I l I i l I i l 1 CE] I I T
DATA SOUR -
‘ BRASS. STAINLESS AND INVAR
400 \V— BEENAKKER JJ.M.. SWENSON C.A. —
*"\ REV. SCI. INST. 26 No. 12 DEC 1955 P. 1204
'- \ COPPER. IRON AND ALUMINUM -
WADD. TECH. REPORT 60 - 56 PART II

 

350 , V [ +1
---- \ +ALUMIN -
300 —- I
.. *BRASS -
250 \ ~ 1
.. Weeping. -
200 3\ \1
- mask \ \\\ -
150
STAIN. S. .
_ 304.316 ﬁ\ STAIN. S. 302 -
100 \
\

 

 

 

 

 

 

 

 

 

(L293-LT ) / L293 (multiply value by 105)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50 ‘
- INVARJ\\. -
0
-50 1 L l l | 1 L l T
0 50 100 150 200 250 300 350 400
Temperature (K)

Figure 2.3 Thermal expansion coefﬁcients of Invar and other metals.

11

 

 

 

 

25 . r . r
E?
3 20— 0 ° .
to
o o
2%
(:5 15b 0 o q
CL 0 1
25 0
Lu 10- ° -
af 0"
Ex 0
m o
1 5'- 00 T
E
I— oo

o
O O a I a l l
300 200 100 O

TEMPERATURE(K)

Figure 2.4 Tip-sample gap change on cooling the invar-body STM. The tip-sample
separation increases during cool-down.

12

must be sliced up into thinner plates. This job is best performed with an electrical
discharge wire cutter. Another drawback of this Fe-Ni alloy is that it is ferromagnetic,
which complicates any magnetic ﬁeld work.

The sample stage is made of G-lO (ref. 9), ﬁber glass and epoxy compound
which has a high value of (Young's modulus/density) ratio. At the comer of the sample
stage a 10 mil brass wire clip is clamped with 0000-160 miniature bolt and nutle. The
clip holds the sample in place and provides electrical contact for the bias voltage. The
sample stage is attached to the bottom plate of the STM body by the following
mechanism: Three 2-64 stainless steel screws in the bottom plate support the sample
stage while a ﬁne steel spring11 holds the stage and the bottom plate together. Initial
coarse-coarse approach is performed by advancing those three screws independently
while monitoring the tip-sample gap with an optical microscope. A diagram of the
sample stage is shown in Figure 2.2 (b). A modiﬁcation of the sample stage for a
cryogenic UHV system is discussed in chapter 8.

The 1/2" long, 1/4" diameter piezoelectric-ceramic tube12 has a response of
95AN in x,y motion, 47A/V in z motion, and a maximum x-y range of about ilum at
room temperature. The x-y motion is calibrated by imaging graphite; the z motion is
calibrated by imaging monatomic steps on (111) gold (see Figure 2.5 and Figure 2.6)
The x-y response drops to 33A/V at 77K and to about 12A/V at 5K13. The reduced
piezoelectric response at cryogenic temperatures increases the probability of tip crash
during the ﬁnal mechanical approach. To improve the sensitivity of the mechanical
approach, the plate in the differential spring mechanism can be easily replaced with a
slightly thicker one. (The spring constant of a plate rises as the cube of the plate
thickness.)

Figure 2.7 is a photograph of the piezo lead attachment scheme. Each of the four

piezo leads consists of a length of number 30 poly-therrnaleze coated Cu wire which is

 

Figure 2.5 16Ax16A scan of graphite at 77K. Topographic mode, current = 1.0nA,
bias = +0.41V

 

Figure 2.6 250nmx250nm scan of Au(1 1 1) at room temperature showing
monatomic steps of 2.4A. Tunneling current = 1.0nA, sample bias = +0.20V

14

 

 

5 6

Figure 2.7 Piezoceramic tube with O-ring attachment. The scale is in centimeters.

15

wrapped around a Viton O-ring14. To make electrical contact, the insulation on the wire
on the inside of the O-ring is sanded off with a ﬁne ﬁle. The O-ring Size is chosen to be
a snug ﬁt on the piezo tube so that all four leads make good contact to their quadrants. It
is important to use a Viton O-ring; the more readily available Buna-N O-rings have a
leakage resistance of about 1M0 which shorts the high-voltage quadrants.

Figure 2.8 is a diagram of the plate/piezo tube/tip structure. A ﬁne steel spring
inside the piezo holds the entire assembly together, yet does not degrade the performance
of the microscope”. The aluminum ﬂange on the top of the tube touches the inside
electrode of the tube and provides electrical contact to ground. The tunneling tip is held
in a 3mm long SS syringe tube (O.D.=32mil, I.D.=20mil) inserted through a phenolic
disc on the bottom of the piezo tube. The tip is slightly bent before inserting into the
tube to prevent slipping.

In earlier versions of our STM, we attempted to hold the plate/piezo/tip structure
together with cyanoacrylac glue ("Superglue") which is very convenient because it is
strong and completely reversible (acetone dissolves the glue in minutes). Although the
behavior of this glue is excellent at room temperature, it cracked during thermal cycling
between room temperature and 77K. There are glues, such as "Stycast"16, which
survive thermal cycling, but these are so difﬁcult to dissolve that they are essentially
permanent.

In most experiments, our tunneling tip is a 10 mil Pt-Rh wire17 which is cut, by
hand, at a 45° angle, with a clean pair of scissors. We ﬁnd that this simple procedure
yields atomic resolution on graphite almost every time. We also tested a 10 mil Nb wire
as a tunneling tip with a view toward future experiments with superconducting tips.
Cutting the Nb wire with scissors failed to produce a sharp tip and good images. Instead,
we produced Sharp Nb tips by ﬁrst scribing a shallow indentation around the wire with a

razor and then pulling the wire apart so that it breaks at the indentation and forms a sharp

r2—

1. 0-80 screw
2.aluminum plate

. clearance hole

. inner electrode (Al)

. 0-80 tap

. Piezo tube (PZT-SH)
. SS Syringe tube
Pt/Rh tip

. miniature spring

oogoqcnmaw

. Phenolic disc E
7

16

he

J

 

0103

to
war

 

Figure 2.8 Plate/Piezo tube/tip structure

 

 

17

tip at the pulled cross-sectional surface. This pulled Nb tip performs reliably, producing
good images at room temperature. F igure2.9 shows Scanning Electron Microscope
(SEM) pictures of cut Pt-Rh tip and pulled Nb tip. An atomic resolution image of gold
was obtained once at room temperature with the Nb tip in constant height mode. (see
Figure 2.10) In this ﬁgure, the average distance between neighboring atoms is 2.95 A
which agrees well with the known value, 2.88A.

As seen in Figure 2.1, the STM is attached to the end of a cryogenic stick with 4
wooden posts. The stick itself is a phenolic tube18. These ﬁbrous materials help
dissipate mechanical vibrations traveling down the stick. Electrical leads to the STM are
miniature 500 coax cables”. The tunneling current lead is particularly susceptible to
noise from triboelectric currents due to mechanical movement3. To prevent such
movement, this lead is threaded through a tight-ﬁtting stainless steel syringe tube which

is clamped at several points along the inside of the phenolic tube.

2.4 OPERATION

With commercial electronics and softwarezo, our STM performs very reliably,
routinely giving atomic resolution on graphite and showing terraces and monatomic
steps on gold. (see Figure 2.6 and 2.7). The lowest mechanical resonance of the STM is
2.8 kHz, due to vibration of the sample stage. Figure 2.11 is the power spectrum of the
tunneling current showing the STM resonating at that frequency. With no special
temperature control precautions, the thermal drift at room temperature is typically lA/ sec
after a 10 minute settling period. At 77K or lower, the thermal drift is very small, less
than SA/hour.

For cryogenic operation the STM is lowered down the throat of a Helium storage

1 of: 1:1 I'
_

 

Figure 2.9 SEM pictures of STM tips. (a) cut Pt-Rh tip. (b) pulled Nb tip.

 

Figure 2.10 67Ax67A scan of (1 1 1) gold with a pulled Nb tip at room temperature
in constant height mode. Sample bias = +68mV.

20

Signal Test PUUEH SPECTRUM

Signal Test (log UoltS/JHZ)

”I ‘iii"*.l'irtrl-Iirtitmutt I:I'I'I'I'v*uqn~a III , Ira-III...

l

Z8 25 38
Frequency (x 188 ”2)
I ; :ia‘jnIIl i! HHIII i

’ I Iii‘I ”-

 

Figure 2.11 The power spectrum of the tunneling current showing the STM
resonating at 2.8 kHz.

21

dewar21. The STM, which is enclosed in a grounded steel can with small ventilation
holes, is operated in the vapor just above the bath. We ﬁnd very poor operation in the
liquid, presumably because of vibration due to bubbling.

For vibration isolation, we suspend the entire dewar by large rubber bands from a
steel frame. Our experience is that noise due to building vibrations is relatively easy to
eliminate. A more difficult problem, in a non-vacuum system such as ours, is vibration
due to acoustical noise (from fan motors, etc.)

The quality of images taken at low temperatures depends critically on the
cleanliness of the sample surface. Layered materials, such as graphite, do not acquire
surface contaminants and can be imaged well at any temperature. However, metal
surfaces such as Au, Ni, Pb, Ag, etc. acquire one or more monolayers of hydrocarbon
contamination after several minutes of exposure to air. This hydrocarbon layer does not
seem to degrade STM images taken at room temperature. However, we ﬁnd that when
an air-contaminated sample is cooled to below about 240K, the STM images become
extremely noisy, apparently because the hydrocarbon layer freezes and produces an icy
coating which disrupts tunneling. To produce good images of metals at low
temperatures, we ﬁnd it necessary to take freshly evaporated samples directly from the
vacuum evaporation chamber to the low-temperature STM as quickly as possible, with
no more than 5 minutes of exposure to air. Schemes to circumvent this problem will be
discussed later in chapter 8 in detail.

In summary, we have described the design and operation of a simple STM which
functions reliably from room temperature to 4K. The STM is assembled without glues

and solders and can be quickly and easily disassembled for repair or modiﬁcation.

22

REFERENCES FOR CHAPTER 2

 

1 AP. Fein, J .R. Kiltley, and RM. Feenstra, Rev. Sci. Instrum. 58, 1806 (1987).

2 H.G. LeDuc, W.J. Kaiser, and J.A. Stein, Appl. Phys. Lett 50 (26), 1921 (1987);
W.J. Kaiser and RC. Jaklevic, Surface Sci., 55 (1987).

3 J.W. Lyding, s. Skala, J.S. Jubacek, R. Brockenbrough, and G. Gammie, Rev.
Sci. Instrum. 59, 1897 (1988).

4 MD. Kirk, T.R. Albrecht, and CF. Quate, Rev. sci. Instrum. 59, 833 (1988).

5 The resonance frequency of a plate supported underneath along two edges is
proportional to (E/p)1/2, where E is the Young's modulus and p is the density of the
plate. The value, E/ p of aluminum is about 4 times as great as that of a steel.

6 Burleigh Instruments, Inc., Burleigh Park, Fishers, NY 14453, (716) 924-9355.

7 Super-Invar is a 65% Fe/ 35% Ni alloy with a room temperature coefﬁcient of
thermal expansion of less than 1 x 10'6 K'l; it is like Invar, but with a more precisely
controlled Fe/Ni ratio, designed to give a smaller thermal coefﬁcient. In this
ferromagnetic material, at room temperature, the positive coefﬁcient of thermal
expansion is nearly canceled by a negative magneto-constrictive coefficient. The total
linear contraction between 300K and 4K is 5x10'4, about 1/6 that of stainless steel. See
"Physics Vade Mecum", H.L.Anderson, ed., American Institute of Physics, New York,
p.131.

8 Burleigh sells Super-Invar in 3/4" thick plate and in solid rod of various
diameters.

9 Almac Plastic Inc., 47-42 37th Street Long Island City, NY 11101

10 Fine bolts and nuts are available from J.I.Morris Co., Southbridge, Massachusetts
01550

11 Extremely small steel springs are available from Lee Spring Co., 1462 62 St.
Brooklyn, NY 11219.

12 PZT-SH piezo tube from Staveley/E.B.L. Div. Crystal Products, 91 Prestige Park
Cir., East Hartford, CN 06108, (302) 289-5428.

13 We have found that the piezo response drops by nearly a factor of 10 between

23

 

room temperature and helium temperatures, in contrast to other workers who reports a
factor of 5. See ref. 1.

14 A 1/4" ID - 3/8" OD Viton O-ring provides a snug ﬁt around a 1/4" diameter

piezo tube.
15 The mass of our 1/4" long Spring is 0.019 gm, small compared to the 0.912 gm
mass of the piezo tube.

16 Emerson & Cuming, Inc., Woburn, MA 0188, (617) 938-8630.

17 Thermocouple wire from Omega Engineering Inc., P.O.Box 4047, Stamford, CT
06907, (800)-TC-OMEGA.

18 Grade L phenolic tubes from Almac Plastics Inc., 26400 Growsbeck Highway,
Warren, MI 48090, (313) 773-9050.

19 S-l miniature stainless steel coaxial cable from LakeShore Cryotronics, Inc., 64
E. Walnut St., Westerville, OH 43081, (614) 891-2243.

20 RHK Technology Inc., 1750 W. Hamlin Rd., Rochester Hills, MI 48309, (313)
656-3116.

21 Cryofab, Inc, 540 North Michigan Ave., P.O.Box 485, Kenilworth, NJ, 07033
(210) 686-3636. This company makes storage dewars with special wide necks. Our 60
liter dewar has a 2" neck and a boil-off rate of 1.5 liters liquid helitun per day.

Chapter 3

SAMPLE PREPARATION
Atomically Flat Gold Films Grown on Hot Glass

3.1 ABSTRACT

In this chapter, the results of a scanning tunneling microscope (STM) study of the
morphology of Au ﬁlms thermally evaporated onto heated glass substrates are discussed.
Au ﬁlms of thickness 20nm-80nm were evaporated onto Corning glass cover slips at
temperatures of 20C-465C. Before the evaporation, the glass substrates were pre-baked
at 300C-400C for 12 hours to remove surface contamination. We have measured grain
size and surface roughness of the ﬁlms, and our best results were obtained with Au ﬁlms
80nm thick evaporated onto 300C substrates. These ﬁlms have 250nm diameter grains
with large, atomically ﬂat tops exhibiting step-free terraces as large as 200nm x 200nm.
These results are comparable to the best reported results for Au grown on heated mica
and show that epitaxial growth is not required for the production of ﬁlms with large
atomically ﬂat regions. This study of Au on glass was motivated by our failure to
produce ﬂat ﬁlms of gold on mica using recipes in the literature. Possible reasons for

our poor results with mica are discussed.

24

25

3.2 INTRODUCTION

In this chapter, the results of a scanning tunneling microscope (STM) study of
gold ﬁlms thermally evaporated onto heated glass substrates are reported. We ﬁnd that
gold ﬁlms grown on glass cover slips held at 300C exhibit large, faceted grains with
atomically ﬂat tops as large as 200nm x 200nm. The production of such large,
atomically ﬂat regions is comparable to the best results obtained for Au on heated
mica1a2a3a4 and for faceted Au balls made by melting Au wires.

We have also made several attempts to grow ﬂat Au ﬁlms on heated mica
substrates using the recipes reported in the literature, but the resulting ﬁlms are of very
poor quality. We will argue that our poor results are due to the decomposition of the
mica during the deposition.

Since the growth of Au on mica is epitaxialé, one might be tempted to assume
that epitaxial grth is a requirement for the making of atomically ﬂat ﬁlms. Our results
for Au on amorphous glass show that epitaxy is deﬁnitely not necessary for the
production of large, atomically ﬂat regions.

There have been previous STM studies3a7a8 of Au evaporated onto glass, but for
the most part, these have dealt with Au ﬁlms evaporated onto room temperature
substrates. However, Putnam et. al.3 report that a 100nm Au ﬁlm evaporated onto a
glass slide at 430C showed no atomically ﬂat regions. This result is consistent with our
ﬁnding that the optimum temperature for the production of large facets is about 300C;
we ﬁnd that higher substrate temperatures result in rough ﬁlms.

26

3.3 PROBLEMS WITH MICA SUBSTRATES

Our study of gold on glass was motivated by our failure to reliably produce good
ﬁlms of Au grown on heated mica. Although other groupsltza394 have reported the
production of atomically ﬂat Au ﬁlms grown by thermal evaporation on heated mica
substrates, our attempts to reproduce these results produced ﬁlms that are extremely
rough and have a milky appearance. Figure 3.1 is an SEM photograph of one of our
rough Au ﬁlms. This ﬁlm, grown by evaporation on cleaved mica9 held at 350C, is
200nm thick and has an rms surface roughness of about 100nm. Before evaporation the
mica was baked in vacuum for 23 hours at 370C. We ﬁnd that rough ﬁlms result when
the temperature of the pre-bake and deposition is in the range 320C-500C. Films of
moderate quality result when the temperature of the pre-bake and deposition is less than
280C. Our results are in marked contrast to the results of others4 who report excellent
ﬁlms when the temperature of the pre-bake and deposition is about 500C.

We believe that the discrepancy between our results and those of other groups is
due to the variable quality of commercially available mica. Mica is a naturally occurring
silicate mineral with a complex layered structure“). This silicate undergoes
dehydroxylation at elevated temperatures, losing internal OH groups and giving off
water. The dehydroxylation process in muscovite mica occurs very gradually over an
extremely broad temperature range extending from roughly 100C to 900C1 1,12,13.
Typically, mica samples show a weight loss that is linear with temperature in the range
100-500C and amounts to l - 3% at 500C. In the temperature range 500-900C, the
weight loss is somewhat more rapid, with samples losing 3 - 5% of their weight over this
range. The exact weight loss depends on the rate of the temperature increase and on the
sample. It is quite difﬁcult to completely dehydroxylate mica unless the temperature is

raised above 1000C or the sample is baked for many hundreds of hours at lower

27

.f’
381

 

Figure 3.1 SEM photograph of a 200nm-thick gold ﬁlm grown on mica at 350C.

28

temperaturesl 1. The poor quality of our Au ﬁlms indicates that the dehydroxylation of
the mica is proceeding during the evaporation and that the substrate is continuously
producing water under the growing ﬁlm. Given the wide range of dehydroxylation rates
reported in the literature, we expect that the success of mica as a substrate for Au ﬁlms

will vary markedly depending on its exact impurity content, defect structure, etc.

3.4 SAMPLE PREPARATION

Our substrates are 0.15mm thick glass cover Slips (Coming #0211 cover glass).
According to the manufacturer, this glass has a softening point of 720C, and will
undergo slow creep at temperatures as low as 508C”. The cover slips were cut into
lOmmxlOmm squares and cleaned by ultrasonic wash in acetone, methanol, and de-
ionized water, followed by drying in a stream of dry nitrogen. Our evaporation chamber
is diffusion-pmnped with a LNz cold trap and a base pressure of 2 x 10'7 mbar. In the
evaporator chamber, the substrates were held with stainless steel clips on a copper block
which contains a resistive heater and a platinum resistance thermometer”. The setup
for the sample heater block is shown in Figure 3.2. Before deposition, the sample block
and glass substrates were pro-heated to 300-400C in vacuum for at least 12 hours, after
which time the system attained its base pressure. The temperature of the sample block
was then brought to the ﬁnal substrate temperature of between 20C and 465C. After
brieﬂy outgassing the tungsten evaporator boat, a Shutter was opened and gold was
evaporated onto the heated glass substrate at 0.1nm/sec. During the evaporation the
pressure remained below 2 x 10’6 mbar. The thicknesses of the ﬁlms were measured
with a quartz crystal thickness monitor which was calibrated against a surface proﬁler.

After the evaporation, the samples were allowed to cool in vacuum to room temperature.

29

 

 

   
 
 
    

screwed down with -1" "C-

/

SS 0-80 screws 5—

 

 

 

 

 

 

Cover Glass
Cover Glass
Cu Block Q Q
/ // 1 cm
/ /
/ 7
/ Cryogenic PT102 Thermometer

/

Omega Cartridge Heater
CIR-1020

Figure 3.2 The sample heater block.

30

During the evaporation, the temperature of the growing ﬁhn increases above that
of the copper sample stage due to radiation from the evaporator boat. In our evaporator,
the distance between the evaporator boat and the sample is 8.5 cm and 200 watts power
is supplied to the boat during evaporation. We have measured the temperature rise of the
surface of the sample by clipping a thin-ﬁlm resistance thermometer16 to a glass cover
Slip on the copper sample stage which is then exposed to a heated evaporator boat.
Figure 3.3 is a plot of the temperature rise vs. exposure time in seconds. Two curves are
shown, for starting temperatures of 26C and 201C. At higher starting temperatures, the
sample radiates more efﬁciently and the temperature rise is less. Recall that the Au is
evaporated at 0.1nm/sec, so the horizontal scale in Figure 3.3 can also be interpreted as
thickness of the Au ﬁlm in writs of 0. lnm. From the curve, we see that in the worst case,
that of an 80nm thick ﬁlm with a starting temperature of 20C, the temperature rise is
13C. An 80nm thick ﬁlm at a starting temperature of 400C has a temperature rise of less
than 8C.

Aﬁer evaporation the samples were stored in a nitrogen-ﬁlled desiccator.
Samples were transferred to an air STM”, and all imaging data were collected within 3
hours of exposure to air. The tunneling tip is a 10 mil Pt-Rh wire cut with clean scissors.
Such tips routinely produce atomic resolution on graphite. All images in this work were
taken in topographic mode, with a tunneling current of 1.0nA and a bias voltage in the
range 100 - 300mV (sample positive). The STM images shown in this chapter all have
256 scan lines and are displayed as if illuminated by a distant point source. Occasionally,
the STM images showed tip artifacts, recognized as regularly repeated features in the

image as seen in Figure 3.4. In these cases, the tip was re-cut until the artifacts

disappeared.

31

 

 

 

 

 

 

 

 

16 F —T I l l I ﬁ— l l
A God
X ooo
I: I Starting Temperature 0 0 ° .
([112 ' 000° -
Li " 0 26C oxoo J
0: r o 2010 0° Doug.
0 0°° 13‘3".“3
2 0° 13° 0
— 8 - 00 can '1
'61-] 0° our:
0 an .1
3 0°00 Donna .
I— O a
< O on .4
QC 4 '- o°°°o°°an -
E o°g°°°a
a .
2 a398
Lﬁ—J n‘° ,
”a j
0 l 1 J I l 1 L l J

0 100 200 300 400 500 600 700 800 900 1000
EXPOSURE TIME (seconds)

Figure 3.3 Increase in temperature of the sample surface vs. time of exposure to the hot
tungsten evaporator boat.

32

 

Figure 3.4 STM image showing multiple-tip artifacts (inside the boxes). T=300C,
80nm sample. Scan area = 0.5um x 0.5um.

33

3.5 RESULTS

Figure 3.5 is a plot of average grain Size vs. substrate temperature for Au ﬁlms of
thicknesses 20, 40, 60, and 80nm. Because of the radiative heating discussed above, the
temperature of the growing ﬁlm increased above that of the sample stage by typically 5
to 10C during the evaporation (in the worst case the increase is 13C). The 20nm thick
samples grown at temperatures above 150C were not electrically continuous and so
could not be imaged with an STM. For these samples, the grain size was determined
from SEM photographs.

To measure the average grain size from the STM images, we computed the angle-
averaged height-height autocorrelation ﬁutnction1 8. The distance between the ﬁrst two
bumps in the autocorrelation function is a good measure of the grain diameter (see
Figure 3.6). For some of the ﬁlms the autocorrelation function did not Show clearly
deﬁned bumps. In these cases, we determined the average grain diameter from the
average grain area, which we obtained by dividing the scan area by the number of grains
counted by eye.

STM or SEM (for electrically discontinuous ﬁlms) images of the 20, 40, 60, and
80nm thick ﬁlms grown at the substrate temperatures of 20C, 105C, 185C, 300C, 400C,
and 465C for each thickness are shown in Figure 3.7, 3.8, 3.9 and 3.10 respectively. The
ﬁgures show the evolution of the grain morphology as substrate temperature is increased.

Figure 3.11 displays typical scan proﬁles for the 80nm thick samples, and Figure
3.12 is plot of the measured nns surface roughness as a function of substrate temperature
for samples of average thicknesses 40nm, 60nm, and 80nm. The rms surface roughness
is 1 standard deviation of the pixel height histogram (taken over 0.25x0.25um2 for the
20C sample and over 1.0xl .Oum2 for all other samples.) With the exception of the 60nm
sample grown at 180C, which displays an anomalously large roughness, the overall trend

34

 

 

 

 

 

300 T I I I l l l l
Thickness

250 - : a ,
A O 80 nm .
E D 60 nm '
5 200 - A 40 ”m —_- a .
0.1 O 20 nm
E
m s
z 150 - . -
a = °
0 100 ’-
LLl " - 3 .1
2 ./ .
o:
g L- /
< 50 a .

O I I I I I L I l I

 

 

 

o 50 100 150 200 250 300 350 400 450 500
SUBSTRATE TEMPERATURE (c)

Figure 3.5 Average grain size in gold ﬁlms evaporated onto glass as a function of
substrate temperature during growth.

35

 

 

 

 

 

 

 

 

 

 

O
' o T=2oc 1
a o T=105C
t:
Z l- ..
D
3‘:
< 1. D O ..
E; 118
m _ ..
0C
I<
0. AI. 00000000a
000 I _L I l
0 so 100 150 200 250 300

DISTANCE (nm)

Figure 3.6 Height-height autocorrelation ﬁmctions for 80nm thick gold ﬁlms grown at
20C and 105C.

36

 

Figure 3.7 (a-b) STM images of 20nm thick gold ﬁlms grown on glass substrates
of (a) 20C, (b) 105C. (c) A SEM image of a 20nm thick gold ﬁlm grown on a glass
substrate of 185C.

37

 

Figure 3.8 STM images of 40mm thick gold ﬁlms grown on glass substrates of (a)
20C, (b) 105C, (c) 185C, (d) 300C, (e) 400C, and (t) 465C.

38

(ch-1011111 , 300C

 

Figure 3.8 (cont'd).

39

 

Figure 3.9 STM images of 60nm thick gold ﬁlms grown on glass substrates of (a)
20C, (b) 105C, (c) 185C, (d) 300C, (e) 400C, and (f) 465C.

40

((1)6011111 .

 

Figure 3.9 (cont'd).

41

(3)8011111 . 20C

(b)80mn. 105C 1, '

“a.

(0)8011111 . 185C

 

Figure 3.10 STM images of 80nm thick gold ﬁlms grown on glass substrates of (a)
20C, (b) 105C, (c) 185C, (d) 300C, (e) 400C, and (f) 465C.

42

((1)8011111 _. 300C

 

Figure 3.10 (cont'd).

43

 

 

 

 

 

T= 300C
30
20
10
O I I I I I l I I I I
T=- 1 85C
20
10 W
o J l I I I I I I I I
T=- 1 05C
20
10 W
o L I I I L I I L l l
0 1 00 200 300 400 500 600 700 800 900 1 000
T- 20C
20
10 W
o I n r 1 I
O 250
DISTANCE (nm)

Figure 3.11 Typical scan proﬁles for 80nm thick ﬁlms. (The vertical scale is expanded.)

in Figure 3.12 is a gradual increase in roughness with increasing substrate temperature.
The unusually rough 60nm sample is shown in Figure 3.9 (c) and appears to have no
other unusual features. We suspect that its measured roughness was large because it was
scanned with an unusually sharp tip and that the other samples show smoother surfaces
because they were scanned by more blunt tips. A blunt tip cannot reach into the depths of
the trenches between grains and will produce an erroneously smooth proﬁle. Clearly, the
roughnesses displayed in Figure 3.12 are lower limits.

The samples grown at room temperature all Show an average grain size of about
30nm, independent of ﬁlm thickness. As seen in Figure 3.7 (a), 3.8 (a), 3.9 (a) and 3.10
(a), the grains are all of about the same size and have smoothly rounded surfaces with no
evidence of faceting. The surface roughness of these T=20C ﬁlms increased slightly
with sample thickness from 2.0nm for the 20nm ﬁlm to 3.0nm for the 80nm ﬁlm. We
also grew a set of ﬁlms at room temperature with no substrate pre-bake. Compared to
the ﬁlms with the substrate pre-bake, the no-prebake ﬁlms exhibited a larger spread in
grain sizes, a slightly larger average grain size, and rougher surfaces with roughness
varying from 2.6 to 4.0nm. Evidently, pre-baking removes light molecular-weight
contamination ﬁom the glass substrates and results in smoother ﬁlms.

The ﬁlms grown with a substrate temperature of 105C all have an average grain
size of about 100nm, independent of ﬁlm thickness, and all have a surface roughness of
about 3.9nm. Some of the grains show ﬂat tops with terraces 10 or 20nm wide separated
by multi-atomic steps. (See Figure 3.13.)

Samples grown at temperatures at or above 185C all show a grain size that
increases with both the sample thickness and the substrate temperature. At these elevated
temperatures, ﬁlms of 20nm thickness are discontinuous and break up into isolated
islands. SEM examination shows that each island contains only a few grains and that the

island size is comparable to the grain size. The break-up of the ﬁlm into isolated islands

45

 

 

 
   

 

 

 

 

10 I I I I I I I I
Thickness
121.,
A 0 80 nm .'
E D 60 nm
5 40 nm /
m
3 5
z I I
I
O F
D
o ..
0: ..-',
El",’
5 4
O I I l I I J I l

 

 

O 50 100 150 200 250 300 350 400 450
SUBSTRATE TEMPERATURE (C)

Figure 3.12 Measured rms surface roughness vs. substrate temperature for 40nm,
60nm, and 80nm thick ﬁlms.

46

 

Figure 3.13 Grains showing ﬂat tops with terraces separated by multi-atomic steps.
Scan size = 1016A x 1014A. A 60nm-thick gold ﬁlm on a 105C glass substrate.

47

is the reason for the decrease in average grain size seen in the 20nm thick ﬁlm in going
from 105C to 185C.

Films grown at 185C show grains with clearly developed top facets, which we
believe to be the (111) face. We occasionally observe the hexagonal faceting
characteristic of the (1 1 l) face.3a4 (See Figure 3.14) Terraces 10-100nm wide, separated
by monatomic steps, are seen. (See Figure 3.15 )

Films grown at 300C exhibit the largest step-free terraces. 80nm thick ﬁlms
grown at this temperature have an average grain size of 250nm. As seen in Figure 3.16,
the tops of the grains typically show a few terraces 20-40nm wide and 100-200nm in
length, separated by monatomic steps. About 1 out of 20 grains has a step-free terrace of
area 100nm x 100nm or larger, and occasionally a large grain is seen with a 200nm x
200nm atomically ﬂat region. Figure 3.17 shows such a large region bounded by a 60°
hexagonal facet. The rms roughness of step-free regions seen in Figs. 3.16 and 3.17 is
less than 0.03nm. The STM images show the trenches between grains to be 10 - 20nm
deep and 50 - 100nm wide. (Again, we cannot rule out the possibility that the trenches
are actually deeper and are not accurately proﬁled by a blunt tunneling tip.) The
measured overall roughness of these 80nm ﬁlms grown at 300C is 6 - 7nm. We expect
that even larger grains and larger terraces will appear in ﬁlms with thickness greater than
80nm.

Films grown at 400C are similar to the 300C ﬁlms but the tops of the grains are
frequently marred by small, round bumps, about 6am in diameter and lnm high, rising
above the otherwise atomically ﬂat terraces. In ﬁlms grown at 465C, these protrusions
are larger (lOnm high and 30nm in diameter) and densely cover the tops of the grains,
destroying the terraces. We speculate that, at these elevated temperatures, the glass has
begun to creep, causing strains to build in the growing ﬁlms and ruining the development

of facets.

48

 

Figure 3.14 The hexagonal faceting of gold crystal. The angle between any two of
the three faces 1, 2, and 3 are 120°. A 60nm-thick gold ﬁlm on a 185C glass
substrate.

49

 

Figure 3.15 Terraces separated by monatomic steps on clearly developed top facet.
Scan size = 2521A x 2520A. A 60nm-thick gold ﬁlm on a 185C glass substrate.

50

 

Figure 3.16 STM image of an 80nm-thick ﬁlm grown at 300C showing a large
grain with terraces separated by monatomic steps.

51

 

Figure 3.17 Large step-free region bounded by a 60° hexagonal facet which is the
characteristic of Au(1 1 1) face. The substrate temperature during growth was 300C.

52

We also studied Au ﬁlms grown at room temperature and then annealed at high
temperature. Films grown at 26C were heated to 485C in vacuum for 3 hours. The
annealed samples have properties Similar to those of ﬁlms grown at high temperatures.
Figure 3.18 is an image of an annealed 60nm thick sample showing atomically ﬂat grains
of 250nm size with some monatomic steps. Again, surface was marred by small, round
bumps. Occasionally, we observe monolayer or bilayer worrny channels with the width
of 20-50A on ﬂat top of the grains. (See Figure 3.19)

We made one attempt to grow Au ﬁlms on quartz substrates at 500C. Clear fused
quartz has a softening point of 1665C and a strain point of 1070C and so it may be
expected to provide a stable substrate at high temperatures. The quartz substrates19
were pre-baked at 500C for 6 hours and then Au ﬁlms of thickness 45nm and 80nm were
deposited at 0.1nm/sec. The resulting ﬁlms were extremely poor; they had a milky
appearance very similar to the failed Au-on-mica ﬁlms. The average grain size was
about 100nm and the surface roughness was comparable to the sample thickness. We do
not understand these poor results, but we speculate that differential thermal contraction

during sample cool-down may damage the ﬁlm.

3.6 SUMNIARY

Thermal evaporation of Au onto heated glass substrates is an extremely reliable
technique for the production of ﬁlms with large, atomically ﬂat regions. We ﬁnd that
80nm thick Au ﬁlms evaporated onto glass substrates held at temperatures of 300C
exhibit large faceted grains of about 250nm diameter. The tops of the grains are
atomically ﬂat with step-free terraces as large as 200nm x 200nm. The grains are

separated by trenches 10-20nm deep and 50-100nm wide, leading to an overall rrns

53

 

Figure 3.18 STM image of a 60nm-thick gold ﬁlm annealed at 485C for 3 hours.
The ﬁlm was evaporated at 26C before annealing.

 

Figure 3.19 A monolayered wormy structure on ﬂat top of the grain in the annealed
gold ﬁlm. Scan area = 1003A x 1004A.

54

surface roughness of 6nm or greater. In comparing our ﬁlms with the best reported
results for gold ﬁlms grown on mica4, our ﬁlms exhibit larger step-free, atomically ﬂat
regions, but have an average roughness that is greater than the Au-on-mica ﬁlms. We
ﬁnd that mica is unreliable as a substrate, apparently because of the variable quality of

commercial supplies.

55

REFERENCES FOR CHAPTER 3

 

1 C.E.D. Chidsey, D.N. Loiacono, T. Sleator and S. Nakahara. Surface Sci. 200, 45
(1988)

2 R. Emch, J. Nogami, M.M. Dovek, C.A. Lang, and CF. Quate, J. Appl. Phys. 65,
79(1989)

3 Albert Putnam, B.L. Blackford, M.H. Jericho, and MO. Watanabe, Surface Sci.
217, 276 (1989).

4 J .A. DeRose, T. Thundat, L.A. Nagahara, and SM. Lindsay, Surface Sci. 256,
102 (1991).

5 J. Schneir, R. Sonnenfeld, O. Marti, P.K. Hansma, J .E. Demuth, and RJ. Hamers,
J. Appl. Phys. 63, 1 (1988).

6 K. Reichelt and H.O. Lutz, J. Crystal Growth 10, 103 (1971).

7 J. Vancea, G. Reiss, F. Schneider, K. Bauer, and H. Hoffmann, Surface Sci. 218,
108(1989)

8 Tzer-Shen Lin and Yip-Wah Chung, Surface Sci. 207, 539 (1989).

9 Green muscovite mica supplied by Asheville-Schoonmaker Mica Co., 900
Jefferson Ave., P.O.Box 318, Newport News, VA 23607.

10 Thomas .I. Pinnavaia, Science 220,365 (1983).
11 Ralph E. Grimm, Clay Mineralogy, McGraw-Hill Book Co. (1953), pp.233-238.

12 Stephen Guggenheim, Yu-Hwa Chang, A.F. Koster Van Groos, American
Mineralogist 72, 537 (1987).

13 The Spruce Pine Mica Company, a major supplier of mica, speciﬁes 400-500C as
the "Maximum temperature with no decomposition."

14 The glass has a softening point of 720C, an armealing point of 550C and a strain
point of 508C. The softening point is the temperature at which the glass deforms under
its own weight; the annealing point is the temperature at which internal stresses relax
within 15 minutes; the strain point is the temperature at which internal stresses relax
within 4 hours.

56

 

15 Lake Shore PT-102 platinum resistance thermometer
16 Omega model TFD thin ﬁlm platinum resistance thermometer.

17 The electronics and software are made by RHK Technology, 1750 West Hamlin
Rd, Rochester Hills, MI 48309. The seaming head is home-built and is described in
M.A.Dubson and Jeeseong Hwang in Rev.Sci.Instrum. 63 (7), July 1992.

18 This function is deﬁned as follows: if z(r) is the height as a function of x-y
position r, the angle-averaged autocorrelation function is a function of scalar r and is

C(r) = <z(r') z(r'+ r)>rv,9, where <--->r',9 indicates an average over all vectors r' and an

average over all angles 9 of the position vector r, keeping the length of r ﬁxed.

19 Cut from quartz microscope slides made by Esco Products, 171 Oakridge Ave,
Oakridge, NJ 07483.

Chapter 4

STM OBSERVATIONS OF SURFACE SELF DIFFUSION ON THE
Au (111) PLANE

4.1 ABSTRACT

STM lithography, the technique to fabricate small structures with an STM tip on
an atomically ﬂat surface, is demonstrated. At room temperature in air, an STM study
shows that the area of the monatomic gold island on (111) Au decays linearly in time.
The surface diffusion constant is also measured ﬁ'om sequential STM images showing
wandering monatomic steps or from the shape change of a gold mound. We ﬁnd that the
mass diffusion is faster in a heavily contaminated sample compared to a relatively clean

sample.

4.2 INTRODUCTION

The problem of mass transport by surface self diffusion on metal surfaces was
ﬁrst considered by Volmer and Estermann, who observed the growth dynamics of a
mercury crystal by the condensation process from its vapor state.1 Since then, several
methods to study the problem have been developed: a theoretical approach using surface
potentials and adatom mobilities, and experimental approaches including semi-
microscopic observations of mass transportation and direct observations of mobile

surface atoms (molecules) on an atomic (molecular) scale. One of the accomplishments

57

58

of the theoretical approach is the introduction of the terrace-ledge-kink (TLK) model.2
The details of this model will be discussed in chapter 5 along with the Monte Carlo
Simulation explaining our STM data.

Although several measuring techniques such as Auger Electron Spectroscopy
(AES), Low Energy Electron Diffractometer (LEED), and workfunction measurement
provide important information on surface structure, none of these gives direct real-space
information on an atomic scale. The conventional method of directly observing surface
morphology is to investigate the two dimensional projection of the 3-D conﬁguration of
a sample using a transmission electron microscope (TEM)3. Direct 3-D observations of
diffusing atoms or molecules on metal surfaces has been accomplished using a Field Ion
Microscope (FIM)495’°, STM7, and Atomic Force Microscope (AF M).

Atomic resolution observations of mass ﬂow on a metal surface provide
important clues about the microscopic mechanism of surface self diffusion. Peal and
Cooper have reported8 that, using an STM at room temperature in air, the area of single

monolayer gold island decays linearly with time, i.e.

N(t) = N(to) - m(t-to) (4-1)

where to is the initial time, N(t) is the number of atoms in the island at time t, and m is
the loss rate of atoms. In this chapter, time-sequential STM images are presented
showing the same linear decay. The microscopic picture of this decay process will be
discussed in detail in Chapter 5.

A direct measurement of the surface self diffusion coefﬁcient can be made by
observing the motion of an individual atom diffusing on an atomically ﬂat surface. If the

surface is ideal, i.e. without any local defects, the atomistic motion can be considered as

59

a 2-D random walk from one site to another site which are separated by a potential

barrier. In this case we can deﬁne a diffusion coefﬁcient9 as

_ 1 F2
D — 4(7) (4.2)

where f , the mean square displacement of the adatom, and t, the duration of the
observation, are measurable parameters. At room temperature, the adatom on a Au(1 11)
surface diffuses ten's of nanometers in about 10'7 seconds so that the motion of the
individual diffusing atom is too fast to observe with an STM since typical data
acquisition time for one STM image is a few seconds at best. Lowering the ambient
temperature can slow down the diffusive motion since the temperature dependence of the

diffusion constant is expected to be

where Do is a prefactor and Eb is the activation barrier for diffusion. Another technical
difﬁculty is that it is very hard to obtain atomic resolution in air because one or more
layers of water and hydrocarbon contamination build up on the metal surface after
several minutes of exposure to air. This problem can be eliminated by operating the
STM in Ultra High Vacuum (UHV).

In this experiment, the surface diffusion coefﬁcient is measured either from the
time-sequential STM images showing decaying monolayer islands or from the shape
change of a gold mound which was lithographically fabricated by an STM.

60

4.3 EXPERIMENTAL TECHNIQUES

4.3.1 Sample Preparation

To observe the decay rate of a monolayer gold island, one needs a sample with
large isolated grains with large facets showing atomically ﬂat terraces separated by
monatomic steps. As discussed in chapter 3, the evaporated gold ﬁlms on hot glass
satisfy these conditions. We also ﬁnd that the <111> direction is perpendicular to the
ﬂat surface of the layers. Figure 4.1 is an x-ray 20 scan10 of the 80nm-thick, T=300C
sample showing a strong {111} peak. The x-ray shows that the measured lattice constant
between two {111} planes is 2.3509A which is in accord with the monatomic step height
of 2.36A on gold {111}. All of the samples in this experiment are prepared by thermal
evaporation of 60-80nm thick gold ﬁlms on 300C glass substrates as described in chapter
3. Large-grained samples with large terraces and monatomic steps are produced almost
every time with the recipe.

All the images in this experiment are obtained within a few days after the sample
were made. We have not seen any surface diffusion in samples older than a month. We
ﬁnd that samples reach a static state after approximately one month. Figure 4.2 is a pair
of STM images of a 6 month old sample showing no sign of activity even after 13 hours
and 50 minutes. We reclean old samples by rinsing them in a ﬂow of clean acetone and
methanol followed by drying with clean N2 gas. Even after the cleaning, sometimes
tough greasy contamination on the old sample surface is identiﬁed ﬁ'om the streaky or
fuzzy STM images. In that case we use the ultraviolet (UV) ozone cleaner to remove the

tough organic contamination from the surface.

61

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Figure 4.1 X-ray 29 scan of the 80nm-thick gold ﬁlm of 300C glass substrate. The
peaks are identiﬁed as the orientations of a gold crystal: 2(111},3{200}, 4{220}, etc.
The broad peak in position 1 is a contribution from an amorphous glass substrate.

62

 

Figure 4.2 A pair of STM images of 6 month old sample showing no sign of
activity. Scan area = (250nm)2. (a) Image at time = 0. (b) Image aﬁer 13 hours
and 50 minutes.

63

4.3.2 STM Lithography

All the images in this chapter are taken at room temperature in air in a constant
current (topographic) mode using our home built STM described in chapter 2. Emch et.
a!“ and Schneider et (11..12 used an air STM to produce controlled features by applying
voltage pulses to the tip. They also exhibited that at ambient temperature the written
features disappeared on a time scale of hours. In our experiment, since not every layered
structure created by evaporation undergoes surface diffusion, we lithographically
fabricated small mounds or islands with an STM using the voltage pulse technique.
There are several advantages to making small structures artiﬁcially. First, in most cases,
we can expect the features to change because they are in a metastable state. Secondly, a
small system is desirable so that we can collect enough data in a short period of time
before the STM image degrades due to build-up of surface contamination. Thirdly, a
system of appropriately small size can be modeled by the Monte Carlo simulation with
the limitations in array size.

Now we describe our STM lithography procedure. The STM tip was scanned
over the sample surface to ﬁnd a grain with an atomically ﬂat surface. The tip is then
moved far away ﬁ'om the grain and crashed several times onto the gold surface so that
the tip picks up gold atoms from the surface. Figure 4.3 demonstrates that the tip is not
ruined even aﬁer several crashes or dragging it along the surface. The tip is sent over the
atomically ﬂat area again and a step pulse of +3-4V (sample at + voltage, tip at virtual
ground) is applied to the sample for a period of 1-10msec to produce a pit or a mound.
The feedback circuit maintains the constant tunneling current during the pulse. This
procedure sometimes produces mounds, sometimes pits. As shown in Table 4.1, mounds
tend to form with a preset tunneling current of below 1.05nA while pits tend to form

above 1.05nA for a tunneling current. At high tunneling current (above 2.0 nA), the tip

64

 

Figure 4.3 Images of tip-crashes. Scan area = (30nm)2. (a) The ﬁrst crash (b) The
second crash. (c) The tip was being dragged between the two crash sites before
imaging. Note that the monatomic gold steps are still visible even aﬁer the tip
crashes several times.

65

Table 4.1 Features formed by voltage pulse under various conditions.

 

 

 

 

 

 

 

 

 

 

 

 

 

Preset Tunnel Current (nA) Pulse height (V) Pulse width (msec) Feature
0.91 +3.0 5 mound
0.97 +3.0 20 mound
1.00 +3.0 10 mound
1.02 +3.0 5, mound
1.02 +3.0 5 mound
1.05 +3.0 10 mound
1.05 +3.5 10 pit
1.38 +4.0 5 pit
1.62 +3.0 20 pit
1.67 +3.0 20 pit

 

 

 

 

66

makes several pits and mounds on the surface. The pits and mounds fabricated by the
voltage pulses are presented in Figure 4.4. Note the multiple-tip artifact in the images.

A reproducible way of controlling the size of fabricated features is not available
at present. In most cases, a smooth, rounded gold grain with a size of a few nanometers
in height and a few tens of nanometers in width is formed by the voltage pulse with a
tunneling current below lnA. In some cases, however, a layered structure of gold
islands is produced. We believe that the features are made of gold atoms because the
deposited island has a faceted crystalline Shape and the height of the island equals the
height of a monatomic terrace of Au(1 11} layer within the error bound.

Once interesting features such as mounds, well deﬁned islands, and layered pits
are found, the shape change is followed by imaging at regular intervals in time. For the
measurement of number of atoms vs. time, the area of the island or pit is measured by
counting the number of pixels inside the boundary of the feature then converting the
image area to actual area. Finally, the number of atoms corresponding to an area is
calculated simply by dividing the area by the unit area of the Au(1 l 1) plane. To deﬁne
the boundary of a feature, we use the differential image which shows the curvature of the
pixel intensity. Since the boundary also takes up a certain number of pixels in the image,
the number of atoms corresponding to the pixels of the boundary is calculated. Half of
this value is assigned as an upper bound of the error and half for the lower bound. To
follow the shape change of a mound, the height and width are obtained from the surface
proﬁle.

67

 

Figure 4.4 Pits and mound formed by voltage pulses. Scan area = (120nm)2. (a)
Large, atomically ﬂat area on top terrace. (b) The ﬁrst pit (inside the box) formed
after a pulse of (+3V, 20msec), tunnel current = 1.62nA. (b) The second pit formed
under the same condition (inside the box 1). Note the repeated image of the pit (in
box 2) due to a double tip. The ﬁrst tip does not repeat since its distance from the
terrace edge is greater than the distance between the double tips. (0) A mound
formed after a pulse of (+3V, 5msec), tunnel current = 0.91nA.

68

4.4 RESULTS

4.4.1 Linear Decay in Time of the Monolayer Island

Figure 4.5 shows time-sequential STM images of a bilayer gold island. Figure
4.5(1)-(6) are images with the surface illuminated by a point light source at inﬁnity,
while Figures 4.5(7)-(9) are grayscale images with brightness representing the height.
Figure 4.5(1) shows a large atomically ﬂat area before a voltage pulse. The tip was then
set at a spot on the ﬂat surface and a pulse (+3Volt, lOmsec.) was applied to the sample
to make the mound shown in Figure 4.5(2). We can claim that the mound is deposited
from the tip because we do not see a moat around the mound which is a Sign of 'lifting'
the mound out of the surface. 8 minutes after the pulse, the area was scanned again and
the decay process was observed by comparing this image to the previous one. We
zoomed in on the area around the mound and found that the mound is actually a layered
structure of two monatomic gold islands. Figures 4.5(3)-(9) are additional time lapse
images of the structure.

One might argue that the top island is a just tip artifact because the image shows
that there is a triple tip. But, we can rule out this concern by following argument:
Looking at the image, we can easily tell the triple tip is aligned in the south-north
direction because the repetition of image occurs in that direction (the line scans in the
east-west direction.) Furthermore, we can tell the tip at the south end is closest to the
sample since the STM constructs the image starting from the line at the north. First, the
closest tip at the south scans over the top terrace. Right after the scan over the top
terrace is ﬁnished, the tip moves to the lower terrace and is then pushed downward to
maintain a constant current. But, as soon as the tip is pushed downward, the neighboring

tip takes over the tunneling. Since this second tip is still over the top terrace, it images

69

Figure 4.5 Time-sequential STM images showing linear decay of two layer system.
Frame (1) and (2) are images before and after a voltage pulse. Scan area :
(150nm)2 for (l) and (2), (40mm)2 for (3)-(9). The time index of each image is as
follows (minutezsecond) : (3) (00:00) (4) (09:23) (5) (24:17) (6) (34:48) (7)
(37:05) (8) (48:30) (9) (50:43).

70

 

Figure 4.5

71

 

Figure 4.5 (cont'd).

72

the top terrace again, and so on. Figure 4.6 shows an illustration explaining the triple
image. We now know there is no tip artifact in the ﬁrst image of the highest terrace.

In Figure 4.7, the areas vs. time for both the top island and the second island are
plotted. The data for the top island Shows that the area decays linearly in time and it ﬁts
very well to a simple line given in formula (4.1) with the slope, m of -0.13 atoms per
second (aps). The area of the second island increases during the decay of the top island
then decreases after the top island disappears. Initially, the rate at which the second
island is being fed by the atoms diffusing from the top island is greater than the rate at
which the second island itself decays. D.R. Peal has suggested possible reasons for this
difference in rate”. One possibility is that if the island edge is in contact with a line
defect, the ﬂow of atoms is obstructed along this contact zone. The other possibility is
that since the mass ﬂow is observed in air and not in UHV condition, the decay rate may
be enhanced by adsorbates on the surface which lower the diffusion barrier in surface
potential. In this case, the nonuniform coverage or the difference in the species of the
adsorbates alter the decay rates for the different layers. The historical review and the
experimental justiﬁcation of the increase of the diffusivity on contaminated surfaces
compared to non-diffusive behavior in UHV systems is well addressed in Reference 15.

Figure 4.8 is another series of STM images showing linear decay in a two layer
system. In this case, a voltage pulse of +3Volt was applied for 10 milliseconds with a
tunnel current of 2.0nm so that the tip produces pits and mounds on the surface. After
the pulse, the tip was sharpened to produce a cleaner image compared to the image
before the pulse.

The plot of the area vs. time for each island in the two layer system is presented
in Figure 4.9 (a). A linear ﬁt yields a decay rate of -0.27 aps for the top island. The
decay rate of the second island during the decay of top layer is +0.01 aps and then

changes to -0.27 aps as soon as the top island disappears. The same argument for

73

Figure 4.6 A schematic illustration showing the effect of a double tip. Arrows
represent the tunneling site. The solid contour shows the image with a single tip.
The repeated image due to a double tip is drawn with a dotted line. (Tip position 1)
STM is imaging with a tip2. (Tip position 2) After this moment the tip is pushed
downward to maintain a constant tunnel current. (Tip position 3) Tip] takes over
tunneling and images a part of the top layer again. (Tip position 4) Tip2 takes over
the tunneling again and images the lower terrace.

74

 

 

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76

Figure 4.8 Time-sequential STM images showing linear decay of two layer system.
Scan area = (40nm)2. Frame (12) shows the location of the top island and the
second island The time index of each images is as follows (minutezsecond): (1)
(00:00) (2) (02:13) (3) (16:22) (4) (20:27) (5) (22:42) (6) (29:55) (7) (38:46)
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previous data can be applied for this case also. It is worth pointing out that the total area
of the top and second islands also decays linearly since any atom diffused from this two

layer system must have left from the edge of the second island. (See Figure 4.9 (b).)

4.4.2 Measurement of the Diffusion Coefﬁcient from a Diffusing Mound

Schneider et a1. 12 made a rough estimate of the diffusion constant on a gold
surface at room temperature in air ﬁom the diffusing mound, assuming a gaussian shape
of the mound which consists of non-interacting atoms. If we take h, the local height of
the mound as a measurement of concentration of atoms, then we can write down the

relation as

h(r)oc exp(-r2/4Dt) (4.4)

where t is the time passed since the formation of the mound (modeled as a delta peak at
t=0), D is the diffusion constant, and r is the distance ﬁ'om the center of the mound.

The time lapse STM images of several diffusing mounds and healing pits are
presented in Figure 4.10. The mounds and pits were produced by a voltage pulse of
+4Volt with a duration of 10 milliseconds with a tunneling current of 2.0 nA. About 4
hours later, the pits are completely healed and the mounds have dispersed in the radial
direction. At each time, the width, w of the biggest mound (width=3.32nm,
height=17.54nm at t=0) is measured from the STM images. Here, the width of the
mound is measured at the point where the height of the mound drops to He times the
mound peak height. From (4.4), we get -w2/(16Dt) = -1 so that D=(w2/16t)1/2, and ﬁnd
D to be approximately 10'16 to 10'17 cmZ/sec.

82

 

Figure 4.10 The time lapse images of diffusing mounds and healing pits. Scan area
= (200nm)2. The time index of each image is as follows (hour:minute:second): (1)
(before the formation of structures) (2) (00:00:00) (3) (01:11:21) (4) (02:01:25)
(5) (03:02:37) (6) (04:14:39).

83

Conventionally, a quantitative measurement of the surface self diffusion was
made at high temperatures. In those experiments, the experimental value of the diffusion
coefficient on a metal surface is different from author to author and depends on the
orientation of the crystalline surface. However, all the data fall within a narrow band in
the plot of ln(D) vs. Tm/T, where Tm is the absolute melting temperature of the metal.9
Accordingly, we can extrapolate the diffusion constant at room temperature and our
measured value is within the range although this non-interacting particle model is
unrealistic. A more realistic measurement of the surface self diffusion coefficient from

wandering monatomic terraces will be described in the next section.

4.4.3 Measurement of the Diffusion Coefficient from Moving Terrace Edges

The ﬁrst direct STM observation of moving gold steps at room temperature were
reported by Jaklevic et a1. 14 in 1988. They produced monolayer pits on Au(1 1 1) surface
by crashing the tip to the surface then found that the pits are ﬁlled by the diffusive
atoms. Holland-Moritz et 01.15 also reported a more comprehensive study of moving
gold steps on gold ﬁlms evaporated on hot mica substrates. They concluded that the
speed of step motion is very sensitive to levels of contamination during the sample
preparation process.

Adopting their idea, we intentionally prepared a contaminated sample to see if
there is active step motion. For the preparation of clean samples, we prebake a
evaporation chamber for 12 hours at high temperature and pre-melt gold wire in the
tungsten boat with the sample shutter closed before evaporation. To make an
intentionally dirty sample, however, we evaporated 80nm of gold on 300C glass

substrates without either prebaking the chamber or pre-melting the gold in the boat.

84

Another few monolayers of gold were evaporated after the sample was cooled to room
temperature.

Figure 4.11 is a series of STM images of this contaminated sample showing the
wandering of terrace steps due to surface diffusion. It is clear that thermodynamics is
ﬂattening the surface so that atoms in top terraces are ﬂowing to lower terraces to ﬁll the
valleys. One interesting feature of these images is that the terraces split into small
islands and the islands then disappear due to surface diffusion. In STM lithographically
fabricated samples, however, the terrace decays by evaporating atoms from the perimeter
sites isotropically in all directions. In heavily contaminated samples, atoms around
contaminant sites may evaporate faster so that the terraces break into small islands ﬁrst
before they decay. The decay process of the second terrace in the frame (00:48:17) and
(00:52:23) of Figure 4.11 clearly shows this.

We can estimate the surface diffusion constant from this data by a simple model
as follows: Consider a system of monatomic layers whose neighboring adjacent steps are
separated by an average distance I and the average distance between the active kink sites
along each step is d. For the reasons discussed in Chapter 5, the atoms diffuse only from
the higher layer to the lower layer. When an atom diffuses, an atom on the edge of the
higher terrace detaches on a time scale of tdet and performs an unbiased random walk on
the terrace between the higher and lower edges and eventually it either goes back to the
home terrace and reattaches or falls downstairs and attaches to the lower edge. Let the
time scale that the atom falls downstairs and attaches to the lower edge be tesc- (See
Figure 4.12 for the illustration of the system.)

The mass transfer diffusion coefﬁcient is deﬁned by9

I)M = (n/N)Do (4-5)

85

Figure 4.11 The time sequential STM images of the contaminated sample showing
wandering of terrace steps due to surface diffusion. The time index of each image
is (hour:minute:second). Scan areas : (00:00:00)-(00:29:47);(120nm)2, (00:31:52)-
(00:34:43);(150nm)2, (00:36:54)-(00:41:03);(120nm)2, and (100nm)2 for the rest
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Figure 4.12 A schematic illustration of the diffusing terraces. The steps move Al
after At. The greyscale represents the height of each terrace at time of At (the
darker, the higher).

93

where n is the density of diffusers, N is the density of available diffusion sites, and Do is
a diffusion constant for one diffuser which is approximately 12/4tesc. Since we know
that N=1/a2 and n=l/ld with a as a lattice constant and l,d as parameters deﬁned above,
(4.5) can be rewritten as DM=(a3/d)(1/4tdet). It can be shown that a 1D random walker,
taking steps of unit length and starting at x=l, has a probability l/xo of reaching x>xO

before returning to origin.16 Consequently, we obtain the relation

tesc = tdet (I/a). (4.6)

In the STM pictures in Figure 4.11, we observe that the steps move an average
distance of 6.2 nm in 120 seconds, i.e. AI = 6.2x10"7 cm and At = 120 seconds. Using

(4.6), the time, At for a step to retreat a distance AI is rewritten as

Ald Ald I [AM
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a a a a

Accordingly, DM is expressed with our observable parameters of AI and At as
DM=(AI)2/4At . (4.7)

here we used the approximation of Al~l based upon the STM images. The estimated
value of the mass transfer diffusion coefﬁcient is 8.0x10‘16 cmZ/s.

A time series of STM images of a ﬁve days old gold ﬁlm evaporated by the clean
procedure is displayed in Figure 4.13. Though not all the spots we imaged showed the
surface diffusion, the shrinkage of the stack of gold monolayers was seen in one spot of
the sample. After two and a half hours, the top terrace area reduced to a quarter of the

initial area. We also observe a strong anisotropy in the surface diffusion so that

94

Figure 4.13 Time series STM images showing the shrinkage of stacked monolayer
gold mesas in the sample prepared by clean procedure. The time index of each
image is (hour:minute:second). Scan area = (100nm)2.

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originally well rounded terraces end up with elongated terraces. As shown in the decay
of the two terrace system in section 4.4.1, the decay rate of each terrace gets smaller as
we go to lower terraces since higher terraces feed the lower ones with diffusive atoms.
In this relatively clean sample, the surface diffusion is considerably slower than in the
contaminated sample. Using the average values of A1 = 4.5 nm and At = [100 seconds,
equation (4.7) yields the mass diffusion constant of 4.6x10‘17cm2/sec, one order of
magnitude lower than the D of the contaminated sample.

In summary, we fabricated small gold islands and pits on an atomically ﬂat gold
surface by a voltage pulse. The sequential STM images of the fabricated structures show
that the area of the monolayer gold island decays linearly in time at room temperature in
air. To measure the surface diffusion constant, the relaxation of the stepped gold surface
toward equilibrium is observed. From the series of images showing moving monatomic
steps, we obtain a diffusion constant of 6.2x10'17cm2/sec for the clean samples, while
the heavily contaminated sample yields 8.6x10‘15 cmZ/seconds. These values are in

good agreement with reference 17.

98

REFERENCES FOR CHAPTER 4

 

1 M. Volmer and I. Estermann, Z. Physik 7, l (1921)

2 w. Kossel, Nach. Ges. Wiss. Gottingen K1 135 (1927); IN. Stranski, z. Phys.
Chem. 136, 259 (1928)

3 Jan-Olle Malm and Jan-Olov Bovin, Surf. Sci. 200, 67 (1988)

4 J.A. Panitz, J. Phys. E15 1281 (1982)

5 G. Ehrlich and F.G. Hudda, J. Chem. Phys. 44, 1039 (1966)

6 H.W. Fink and G. Ehrlich, Surf. Sci. 143, 125 (1984)

7 1.x. Gimzewski, R. Berndt, and RR. Schlitter, Surf. Sci. 247, 327 (1991)
8 DR. Peale and EH. Cooper, J. Vac. Sci. Tech. A 10, 2210 (1992)

9 HP. Bonzel, edited by NATO Adv. Study Inst. Ser. Sec. B 86, 195 (1983)

10 The x-ray diffraction was performed on a Rikagu Diffractometer using Cu K0!
radiation.

11 RE. Emch, J. Nogami, M.M. Dovek, C.A. Lang and CR Quate J. Microscopy
152, 129 (1988)

12 J. Schneider, R. Sonnenfeld, O. Marti, P.K. Hansma, J .E. Demuth, and R.J.
Hamers, J. Appl. Phys. 63(3), 717 (1988)

13 DR. Peal, Ph.D. Thesis, Cornell University, 1992 (unpublished)
14 RC. Jaklevic and L. Elie, Phys. Rev. Lett., 60(2), 120 (1988)

15 E. Holland-Moritz, Joseph Gordon 11, G. Borgers, and R. Sonnenfeld, Langmuir
7, 301 (1991)

16 Eugene Capriotti, private communication.

17 P. Wynblatt and N.A. Gjostein, Surf. Sci. 12, 109 (1986)

Chapter 5

MONTE CARLO SIMULATION OF THE LINEAR DECAY OF
ISLANDS ON METAL SURFACES

5.1 ABSTRACT

STM studies of mass ﬂow on (111) Au have shown that the rate of decay of the
area of monolayer islands is linear in time. We demonstrate by Monte Carlo simulation
that a proper accounting of the detachment and reattachment rates of kink Site atoms
produces a linear decay. In our simulation, adatoms emitted from kink sites on mesa
edges execute an unbiased random walk and may reattach to the home mesa or be
absorbed by an outer ledge, possibly after several reﬂections from the step down at the
outer ledge. The linear decay of mesa areas is found to be rather insensitive to variations

in the probability of reﬂection from the outer ledge.

5.2 INTRODUCTION

In an STM study of surface mass ﬂow on (111) gold, Peale and Cooper have
reported1 ,2 that, at room temperature in air, the area of Single monolayer islands decays
linearly with time. We have done similar experiments and ﬁnd the same results3 as
shown in Chapter 4. A linear decay of island areas is puzzling at ﬁrst sight. If the rate of
mass loss is proportional to the circumference of the island (a natural assumption if the

number of kink sites per unit length along the perimeter is constant), then the number N

99

100

of atoms decays as dN/dt oc -(N)1/2, and the decay is parabolic, not linear. In this
Chapter we Show, by Monte Carlo simulations, that a proper accounting of the kink atom
detachment and reattachment rates leads to a linear decay.

We have developed two distinct computer models, which produce nearly
identical results. Our models are based on the assumption that the potential near a
monatomic step has the form shown in Figure 5.1 with a deep well at the base of the
step (site B), small activation barriers between shallow wells far ﬁ'om the step, and a
somewhat higher shallow well at the site on the top terrace adjacent to the step (Site A).
Site A is somewhat higher because it lacks a second nearest neighbor. As a consequence
of the asymmetry in this potential, a kink site atom in the deep well B is more likely to
activate out onto the lower terrace than up onto the higher terrace. Also, an adatom
approaching the step ﬁ'om the left has some tendency to be reﬂected, while an adatom
approaching the step from the right has no such tendency and will be captured in the
deep well B. The qualitative form of this potential is supported by embedded atom
method calculations“. Also, reﬂection of an adatom by a step down has been observed
on metal surfaces by ﬁeld ion microscopy5.

Because the terrace corrugation is small, the time for an adatom to random walk
between ledges is very fast compared to the mean time for a kink site atom to detach6r7.
The atoms at the surface of a perfect crystal are vibrating at some frequency VD which
can be estimated by the relation th=kTD, where TD is the Debye Temperature of the
solid, h is a Planck's constant, and k is Boltzmann's constant. For gold, VD ~3x1012
sec"l is obtained with a value of TD=165K.8 Sometimes thermal energy gives the atom
sufﬁcient energy to leave its initial site and hop to a neighboring site. The frequency v
with which an atom will jump from the original site is expected to be v=vDexp(-Eb/kT),
where Eb is the energy barrier for the atom to surmount during the hopping.

Accordingly, the time Scale for the atom to hop from one Site to its nearest neighboring

101

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site is T=V'1=(1/VD) exp(Eb/kT). For (111) Au at room temperature, the mean time for
a kink atom to detach is 10‘5 to 10% depending on the depth of the well at point B (Eb
= 0.45-0.65 eV). On the other hand, with an activation barrier Eb=0. leV, the time for an
adatom to random walk a distance of one lattice constant is about 10'1 1s so that an
adatom on a (111) surface wanders ten's of nanometers (i.e. hundreds of lattice
constants) in about 10"11x(100)2 = 10'7s. Consequently, at low temperatures (T < 0.25
Tmelting)a the rate-limiting step in mass ﬂow is the detachment of kink atoms and there
is rarely more than one adatom on a given terrace at any time.

The linear decay may be understood qualitatively as follows. An adatom emitted
from a kink site on' the edge of a mesa is quite likely to reattach somewhere along the
mesa's perimeter after a brief random walk. Only occasionally do adatoms wander to the
outer ledge of the terrace before encountering the perimeter of the home mesa. However,
this high reattachment rate drops as the mesa shrinks, because the wandering adatoms are
less likely to encounter the smaller mesa. The dropping reattachment rate
counterbalances the dropping emission rate as the perimeter shrinks and nearly linear

decay results.
5.3 MODELS AND RESULTS
5.3.1 A Hybrid Lattice-Continuum Model
In our ﬁrst model, we assume that the number of kink sites on the perimeter of an
island is proportional to the perimeter length. We also assume that all kink sites have the

same constant probability per unit time to detach so that the mean time between

detachment events is inversely proportional to the perimeter length. In this model,

103

which is a hybrid lattice-continuum simulation, a mesa is represented by a circle I of
radius Ri centered on the origin. Ri is determined by an integer N representing the
number of atoms in the mesa: Ri = (N/Tr)1/2. A larger circle 0 of ﬁxed radius R0, also
centered on the origin, represents an outer ledge which can capture adatoms emitted by I.
A walker, representing an atom detached from a kink on the perimeter of I, is released
from the smallest positive integer position on the x-axis outside I and begins an unbiased
random walk on the xy lattice, jumping to one of its 4 nearest neighbors in each step. If
the walker crosses the outer circle 0 before crossing I, then it may be absorbed with
probability (l-k) or it may reﬂect with probability k and continue its meandering trek. If
it is absorbed by O, the time is advanced by At = N'l/2 (the inverse of the mesa
circumference), N is then reduced by 1, the radius of I is reduced accordingly, and a new
walker is released from the smallest integer position on the x-axis outside the now-
smaller circle I. The time increment At represents the mean time between detachment
events, assumed inversely proportional to the circumference of I and the number of kink
sites.

During its random walk, the adatom may undergo multiple reﬂections from 0
before being absorbed by O, or it may return to I after one or more reﬂections from O, or
(most likely) it may return to I without reaching 0. If the walker crosses the inner circle
I, it is immediately absorbed, the time is advanced by At = N'l/z, N is unchanged, and a
new walker is released from the starting point just outside I. The process repeats until I
completely evaporates, while N is recorded as a function of time.

Note that our model assumes that successive walkers do not interact, which is the
case if the time between detachment events is long compared to the time of the random
walk. Also, duration of the random walk does not affect the advancement of time in the

simulation. The total time in the simulation is the sum of the times between successive

104

detachment events. The random walk proceeds "in parallel" with the wait until the next
detachment event.

Figure 5.2 displays the results of this simulation for an inner circle of starting
radius near 20 (N=1257), outer circles of radius 25, 50, 100, and 200, and a reﬂection
coefﬁcient k=0 (walkers always absorbed upon contact with the outer circle). For outer
circles large compared to the inner circle, we see that the mesa area decay is very nearly
linear, but as Ro approaches the inner circle's starting radius Ri, the mesa decay becomes
more parabolic. A smaller outer circle captures adatoms more effectively, resulting in a
lower reattachment rate and a net evaporation rate which is more dominated by the rate
of emission, leading to a more parabolic decay.

Figure 5.3 displays the results of the same simulations, but with a reﬂection
coefﬁcient k=0.95. For larger outer circles, the decay is only slightly slower than the
k=0 case and is still nearly linear. The linear decay is insensitive to k because once the
walker has wandered to the outer circle, it is very likely to undergo multiple reﬂections

and be absorbed by 0 before ﬁnding the small inner island.

5.3.2 A Cubic Lattice Solid-On-Solid Model

Next we describe a cubic lattice solid-on-solid model, similar in spirit but more
realistic in detail than the ﬁrst model. The initial conﬁguration is a stack of mesas,
concentric circular terraces separated by monatomic steps. To specify the condition of
each atomic site, two two-dimensional arrays, T(x,y) and E(x,y) are used. T(x,y)
represents the occupied site at position (x,y), and E(x,y) represents the empty site right
above each occupied one. Introducing E(x,y) is essential since the coordination numbers
for the neighboring empty sites are to be speciﬁed before an atom makes any movement

toward one of its nearest neighboring sites. We then assign a value to each array

105

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variable according to the physical situation of each site as follows. The ﬁrst two digits
of the value show a local coordination number of an atom which is calculated by
weighting lst, 2nd, and 3rd nearest neighbors 9:3:1 (approximately the ratio in a Van der
Waals solid). In three dimensional lattice cubic model, the ﬁrst nearest neighbors are
adjacent atoms that share a side of the cube, the second nearest neighbors share an edge,
and the third nearest neighbors share a comer. The third digit of the array variable
represents the terrace number, deﬁned as l is for the top terrace, 2 is for the next lower
terrace, and so on.

During the simulation, a list of "active" sites on the perimeters of the mesas is
maintained. Active sites are those with a coordination number fewer than 49, in other
words, fewer than 3 in-plane nearest neighbors including kink and corner sites as shown
in Figure 5.4. At the start of the simulation, an atom is chosen at random from the list of
active sites. The atom detaches from its mesa by jumping one step away from the
perimeter and begins an unbiased random walk, stepping to any of its empty in-plane lst
or 2nd nearest neighbor sites. An atom is detached from a mesa if it has no nearest
neighbor in-plane, even though it may have a second nearest neighbor in-plane. As in
the lattice-continuum model, a detached atom may re-attach to its home mesa, or it may
attach to the perimeter of an outer mesa by jumping down one level, possibly after
several reﬂections from the step. Hops up onto higher terraces are not allowed; hops
down to lower terraces are allowed with probability (1 -k).

When the meandering atom attaches to a mesa, it explores the perimeter for some
time, searching for a highly coordinated site, and comes to rest when it ﬁnds a local
maximum in bond number (i.e. local maximum of the coordination number). This
perimeter search procedure is required to keep the mesas compact as the simulation
proceeds. If the wandering atom were to stick where it ﬁrst hits a mesa, the mesas would

develop a highly ramiﬁed, fractal shape, as in diffusion limited aggregation. Again, in

108

    

   
       

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marked with a dot.

109

computing the local coordination of a perimeter atom, we weight lst and 2nd nearest
neighbor bonds 3 to 1. In searching for a ﬁnal resting place along the perimeter, the
atom random walks for up to 50 steps (an arbitrary number) and is allowed to
temporarily reduce its second nearest neighbor count by one in order to move around
comers. If the atom has not found a local bond number maximum after 50 steps, as in
the case of a atom exploring the edge of square mesa, the atom stops.

When the walking atom ﬁnally comes to rest, the time is advanced by At = l/B
where B is the total number of active Sites in the system of mesas. The list of active sites
is then updated, and a new walker is chosen at random from the updated list.
Maintaining the list of active sites requires some ingenuity, since old active sites
disappear (either evaporate or are covered by new atoms) and new ones appear as the
simulation proceeds. In this cubic lattice simulation, as in the simpler continuum-lattice
model above, we assume a constant probability per unit time that an active site will
detach. Hence, the mean time between detachment events is inversely proportional to
the number of active sites. Note that, in this lattice model, we do not need to assume that
the number of kink sites is proportional to the mesa circumference.

The number of active sites, log of N(t)active vs. log of total remaining number of
atoms, N(t) is plotted in Figure 5.5 from the simulation of the decay of an initially
circular mesa with a beginning size of 3800 atoms. From this plot, to avoid an error due

to a size effect of the small island, we ﬁt the data down to N(t)=400 and obtained
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Here, the number of active sites is proportional to the island perimeter.

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110

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111

for reasons of simplicity, we make no such distinction. We note that for the (111) face
of an fcc lattice, comer and kink sites have very similar local coordinations, each with 3
nearest neighbors in-plane. Occasionally, an active site with a single in-plane nearest
neighbor is produced. This occurs when one of two adjacent kink sites detaches, leaving
behind a ledge atom (see the lower left of the bottom mesa of Figure 5.5). Our
simulation makes no distinction between such ledge atoms and other active sites,
although it would be more realistic to allow ledge adatoms to explore the mesa
perimeter, seeking a kink site. We believe that because such ledge active sites are rare,
their occurrence does not signiﬁcantly effect our results.

This cubic lattice model produces results which are nearly identical to the results
of the simpler lattice-continuum model. The area of a single isolated mesa decays nearly
linearly with time if it is on top of a larger mesa with a radius at least twice the starting
radius of the smaller top mesa. As before, this result is rather insensitive to the value of
the reﬂection coefﬁcient k, at least for k < 0.95. Figure 5.6 displays areas vs. time for
the top mesa of a three mesa stack with beginning sizes of 200, 800, and 2500 atoms
with several k values of 0, 0.5, 0.85, and 0.9. Only k=0 case shows a slight parabolic
behavior.

Our lattice model produces interesting behavior for a series of stacked mesas.
Figure 5.7 shows area vs. time for the top two mesas of a three mesa stack with
beginning sizes of 400, 1600, and 6400 atoms. The bottom mesa (not shown in the
ﬁgure) is surrounded by an absorbing circle of radius 1.5 times the radius of the bottom
mesa. The reﬂection coefﬁcient k = 0.90. While the top mesa decays linearly, the
middle mesa decays slowly at ﬁrst and then more rapidly when the top one has
disappeared. This is because the middle mesa is at ﬁrst fed by the top one. This is
precisely the behavior that has been observed experimentally for stacked mesas on (I l 1)

112

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114

Au2a3r9. Our STM data shows the same behavior as shown in Figure 4.7 and 4.9 in
Chapter 4.

In summary, we have shown, by Monte Carlo simulation, that the linear decay of
monolayer islands on metal surfaces arises from a competition among the rate of
emission of adatoms by kink sites, the rate of absorption by an outer ledge, and the rate
of reattachment to the home mesa. Linear decay is found when the distance to the outer
absorbing ledge is more than 2 or 3 times the starting radius of the mesa, and it is rather

insensitive to variations in the probability of reﬂection from the outer ledge.

115

REFERENCES FOR CHAPTER 5

 

1 DR. Peale and B.H. Cooper, J. Vac. Sci. Tech. A10, 2210 (1992).
2 David R. Peale, Ph.D. Thesis, Cornell University, 1992 (unpublished).
3 Jeeseong Hwang and MA. Dubson (in preparation).

4 Chun-Li Liu and James B. Adams, Surf. Sci. 265, 262 (1992)

5 Hans-Werner Fink and Gert Ehrlich, Surf. Sci. 143, 125 (1984).

6 Claude A. Roulet, Surf. Sci. 36, 295 (1973).

7 P. Wynblatt and NA. Gjostein, Surf.Sci. 12, 109 (1968); P. Wynblatt, Phys. Stat.
Sol. 36, 797 (1969).

8 C. Kitell, Introduction to Solid State Physics, 6th ed., John Wiley & Sons
(1986)

9 B.H. Cooper, D.R. Peale, J .G. McLean, R. Phillips, and E. Chason, in Evolution
of Surface and Thin Film Microstructure: Materials Research Society Symposium
Proceedings, Vol. 280, 1992 (in press); D.R. Peale and B.H. Cooper (in preparation).

Chapter 6

STM STUDY OF THE PLASTIC DEF ORMATION OF STRESSED
THIN GOLD FILMS ON GLASS SUBSTRATES

6.1 ABSTRACT

With an STM, at room temperature in air, low angle grain boundaries and other
dislocation arrays are observed in thermally stressed gold ﬁlms evaporated on heated
glass substrates. We ﬁnd that these low angle grain boundaries move under an applied
stress introduced either by handling the sample or by crashing an STM tip on the sample
surface. From time lapse STM images, we also observe that the motion may slow to a
stop, reverse direction, or show oscillatory behavior. These dynamic features usually
accompany a deformation of a part of the sample. Possible explanations for this

behavior are discussed along with STM observations.

6.2 INTRODUCTION

In a perfect crystal, atoms are arranged in a regular periodic pattern. However, in
the real world, a crystal can contain various kinds of defects such as point defects
(impurities, vacancies, etc.) and line defects (edge dislocations, screw dislocations).
Since the macroscopic behavior of crystalline solids strongly depends upon the species
and number of defects, the understanding of defects in a crystal has been very important.

For an irreversible plastic deformation of a crystalline solid, it is well known that the

116

117

deformation is induced by the atoms sliding over one another along a well-deﬁned slip
plane instead by uniform shearing of the crystal. Many systematic studies of this
behavior have revealed that the dislocations play a major role in the deformation.

Before we discuss the role of dislocations in a plastic deformation, let us ﬁrst
describe basic geometry of the edge and screw dislocations. Here, the deﬁnitions of

those two dislocations and the Burgers vector are borrowed from Reference 1.

Figure 6.1(a) shows the atomic arrangement and bonding in a simple cubic
lattice. Figure 6.1(b) and Figure 6.1(c) Show an edge and screw dislocation,
respectively. Suppose that all the bonds across the surface ABCD are broken and the
faces of the crystal are separated so that an extra half-plane of atoms can be inserted in
the slot, as illustrated in Figure 6.1(b). The faces of the slot will have been displaced by
one atom spacing, but the only large disturbance of the atoms from their normal
positions relative to their neighbors is close to the line DC. The deﬂection and distortion
of the interatomic bonds decreases with increasing distance from the line. This line DC
is called a positive edge dislocation and is represented symbolically by the symbol J..
A negative edge dislocation would be obtained by inserting the extra plane of atoms
below plane ABCD and is represented by the symbol T. The arrangement of atoms
around a screw dislocation can be simulated by displacing the crystal on one side of
ABCD relative to the other side in the direction AB as in Figure 6.1(c). Examination of
this model shows that it can be described as a single surface helicoid, rather like a spiral
staircase. The set of parallel planes initially perpendicular to DC have been transformed
into a single surface, and the spiral nature is clearly demonstrated by the atom positions
shown in Figure 6.1(d). DC is a screw dislocation. Looking down the dislocation line, if
the helix advances one plane when a clockwise circuit is made round it, it is referred to

as a right-handed screw dislocation, and if the reverse is true it is left-handed.

118

 

 

 

((1)

Figure 6.1 (a) A model of a simple cubic lattice. The atoms are represented by ﬁlled
circles, and the bonds between atoms by springs, only a few of which are shown. (b) A
positive edge dislocation DC formed by inserting an extra half-plane of atoms in ABCD.
(c) A left-handed screw dislocation DC formed by displacing the faces ABCD relative to
each other in direction AB. (d) A spiral of atoms adjacent to the line DC in (c). [Taken
from Hull and Bacon (reference 1)]

119

The most useful deﬁnition of a dislocation is given in terms of the burgers
circuit. A burgers circuit is any atom-to-atom path taken in a crystal containing
dislocations so that the path forms a closed loop. Such a path is illustrated in Figure
6.2(a), i.e. MNOPQ. If the same atom-to-atom sequence is made in a dislocation—free
crystal and the circuit does not close, then the ﬁrst circuit, Figure 6.2(a) must enclose one
or more dislocations. the vector required to complete the circuit is called the Burgers
vector. It is essential that the circuit in the real crystal passes entirely through "good"
parts of the crystal. For simplicity consider the Burgers circuit to enclose one dislocation
as in Figure 6.2(a). The sequence of the circuit MNOPQ in this Figure. The enclosed
failure QM is the Burgers vector and is at right angle to the dislocation line. When the
Burgers circuit is drawn around a screw dislocation(Figure 6.3), again with a closed
circuit in the crystal containing the dislocation, the Burgers vector QM is parallel to the

dislocation line.

Usually, in a crystalline solid, there are a large number of randomly oriented
single crystal grains separated by grain boundaries. When the disorientation between the
adjacent grains is small, the boundary is called a low-angle grain boundary. A model
that describes the low-angle grain boundary between adjoining crystallites or crystal
grains as an array of edge dislocations was ﬁrst proposed by Bragg2 and Burgers3. The
model was conﬁrmed experimentally by Gronsky who observed low-angle grain
boundaries in molybdenum crystals on an atomic scale by Transmission Electron
Microscope (TEM).4a5 Figure 6.4 shows such a low-angle grain boundary consisting of
a sheet of an array of equally spaced edge dislocations lying in the vertical direction. If

the spacing of the dislocations is D, then the following relation is satisﬁed.

120

(a)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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III-"J
ll
\\~__

 

lu

 

 

 

 

 

 

 

 

(b) “—

Pl L_ M0

 

 

 

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-n-

 

 

 

 

 

 

 

 

T

Figure 6.2 (a) Burgers circuit around an edge dislocation. (b) Burgers circuit in a perfect
crystal; the closure failure is the Burgers vector. [Taken from Hull and Bacon
(reference 1 )]

 

 

 

 

 

 

Figure 6.3 (a) Burgers circuit around a screw dislocation. (b) Burgers circuit in a prefect
crystal; the closure failure is the Burgers vector. [Taken from Hull and Bacon (reference

1)]

121

to‘
O

ooooooooooooooooooooooooo

o
o
o

o

o
o

o

OOOOOOOOOOO
i

H
I

 

l

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oooooooooooooooooooooooo

Figure 6.4 A low angle grain boundary consisting of a sheet of equally spaced
dislocations.

122

where 9 is the small tilt angle in radians, and b is the magnitude of the burgers vector. If

the angle 9 is small enough, then

D=—. @2)

Washburn et al.6 did an x-ray study to Show that, in a zinc single crystal,
dispersed dislocations created by bending the crystal at low temperature tend to turn into
planar arrays upon annealing at high temperature. In most cases, annealing results in a
network of the planes of dislocation arrays with relatively dislocation free volumes
enclosed by this network. The edge of the low-angle grain boundary plane is observable
on the crystal surface where the plane meets with the crystal surface. Consequently, two
crystal surfaces are bounded by the edge line and form a small tilt angle. In Figure 6.4,
the tilt angle is presented as 9. We call the intersection of the low-angle grain boundary
plane and the crystal surface a 'boundary line'.

The idea that the low-angle grain boundary consists of arrays of dislocations is
also supported by the observed motion of a dislocation array on the crystal surfaces. (If
the low-angle grain boundary were just an amorphous barrier, under some shear stress,
then the subgrains would Slide over each other along the low-angle grain boundary and
the motion of a dislocation array on the crystal surface would’not be observed.)

There are two types of dislocation movements; in its slip plane (glide), and
normal to the slip plane (climb). The slip plane is the plane which is perpendicular to the
low-angle grain boundary plane and contains the dislocations. The glide of low-angle
grain boundary under the applied stress was ﬁrst predicted by Schockley713. As shown
in Figure 6.5, consider a stress (T's) applied on the surface of a crystal which contains a

low-angle grain boundary. The shearing stresses moves the atoms above the slip plane

123

 

 

 

 

Figure 6.5 Motion of a dislocation as a glide along the slip plane (a horizontal bar
of the T symbol). A system of shear stresses are represented as four arrows going
around the crystal. As the motion of the low angle grain boundary (a vertical bar of
the T symbol) proceeds, the atomic bond a is breaking and a' is forming. b is the
Burgers vector.

124

to the right and the atoms below the slip plane to the left. The slip plane is represented
as the horizontal bar of the symbol T, the low-angle grain boundary as the vertical bar.
In fact, in a crystal, the glide starts at a local region and steps along (in this case to the
left) instead of shearing the two pieces each other along the slip plane. Figure 6.5 shows
one step of this glide process where the low-angle grain boundary plane moves to the left
by one lattice constant. The black and gray dots represent the atoms before and after the
motion respectively. As the motion of the low-angle grain boundary proceeds, the
atomic bond a is breaking and a' is forming.

The motion of this low-angle grain boundary has been observed by J. Washburn
et a1.4 with an optical microscope. In their experiment, a zinc bicrystal was clamped at
one side and stress was applied to the un-clamped side of the crystal. Under the
inﬂuence of the applied stress, they observed a 2 degree low angle low-angle grain
boundary move back and forth according to the direction of the applied stress. It is
worth pointing out that the motion was observed with an external stress approximately
equal to the crystal's yield stress.

With a home built STM described in Chapter 2, we observed similar behavior in
thin gold ﬁlms on glass substrates. Most of the samples in this experiment are prepared
by evaporating 40 to 200nm-thick gold ﬁlms on heated glass substrates at 300C and
annealed at 300C for a few hours following deposition. The samples were then allowed
to cool in vacuum to room temperature. All of the STM images presented in this
Chapter are taken at room temperature in air with a tunneling current of 1.0nA and a

sample bias in the range of +100mV to +300mV. (The STM tip is at virtual ground.)

125

6.3 RESULTS AND DISCUSSION

In Chapter 3, we showed that thermal evaporation of gold on hot (about 300C)
glass substrates yields growth of layers of gold which are (111) planes. We ﬁnd that
such ﬁlms exhibit many dislocations and defects. Figure 6.6 shows a right-handed screw
dislocation developed during the growth. To produce this sample, 80nm of gold was
evaporated on 300C glass without annealing after the evaporation. Since this kind of
screw dislocation is rarely found in annealed samples, we believe the dislocations tend to
annihilate (for the dislocations with opposite signs) or turn into a more stable
conﬁguration by thermal activation during the annealing. If the dislocations are random,
then they will collect to make a low-angle grain boundary plane during the annealing.4

Figure 6.7 displays time-lapse STM images showing a boundary line on a 80nm-
thick Au ﬁlm thermally evaporated on a 300C glass substrate and annealed. This sample
was recleaned and imaged 5 days after the preparation. The low-angle grain boundary
emerges from the crystal to form a straight boundary line on the surface. By measuring
the tilt angle from the sample surface proﬁle (see Figure 6.8), we ﬁnd that the two
subgrains meet with an angle of 5.1:05 degrees which is maintained throughout the
sequence of images. The images are illuminated by a point light source at infinity with
an appropriate angle so that the surface of the tilted subgrain (the portion on the right
side of the low-angle grain boundary) appears darker. Measuring the position of the
boundary line on the sample surface, we ﬁnd that the low-angle grain boundary moves to
the left and ﬁnally stops. The step structure seen on the surface provides a steady
reference mark relative to the motion of the low-angle grain boundary. The plot of x(t),
the distance that the low-angle grain boundary moves vs. time in seconds shown in

Figure 6.9 demonstrates that the motion is attenuated and ﬁnally stops.

126

 

Figure 6.6 A screw dislocation produced during the evaporation of a 80nm thick
gold ﬁlm onto a 300C glass substrate. A ramp with a monatomic height is going
around from top to bottom. Scan size = (100nm)2.

127

(a) (00:00) (b)(03:21)

(c) (09:2 1) (<,1)(l3:22)

(DOW-10')

 

Figure 6.7 Time lapse STM images showing the attenuated motion of the low
angle grain boundary. Scan size = (180nm)2. The time index of each image is
(minutezsecond).

128

(ammo) (h)(31:lll

(j) (39:37)

 

Figure 6.7 (cont'd).

129

62 = 58.8888 5

 

Figure 6.8 A surface proﬁle of the image 6.7(d). The surface proﬁle along the line
on the image is displayed in the plot at the right hand side. The cross mark at one
end of the line corresponds to the origin of the plot. The proﬁle shows that the
surface of the subgrain (darker gray scale) rises from the horizontal plane with an
angle of about 5.1 degrees. Note that the scale of the y axis is expanded.

130

 

140

r'1

120

100-

 

DISTANCE (run)
3

’ X11) . 140m (1- owl-09200043»

 

 

o a I n l a
0 1 000 2000 3000
TIME (seconds)
Figure 6.9 The plot of the distance that the low angle grain boundary (shown in

Figure 6.7) moves vs. elapsed time. Note that the motion is attenuated and ﬁnally
stops. A trial ﬁt of x(t) is displayed along with the data.

131

Assuming the low-angle grain boundary is a plane, we can measure its
orientation relative to the surface. If the crystal surface were perfectly ﬂat, then the
boundary line would appear as a straight line no matter how the low-angle grain
boundary was oriented. The orientation of the low-angle grain boundary is not resolved
in this case. With some corrugations on the surface, however, a top-down view of the
boundary line will be a straight line if the low-angle grain boundary cuts the sample
vertically; the boundary line will not be straight if the low-angle grain boundary plane
intersects with the surface at other than 90 degrees. From Figure 6.7(a)-(d), we measure
the angle of 69:5 degrees between the ﬂat (111)Au surface and the low-angle grain
boundary.

It is well known that the face centered cubic (fcc) crystal glides primarily on the
close-packed {111} plane in three <110> directions in {111} plane. Figure 6.10(a)
illustrates the fcc system showing one of the {111} planes and three slip directions in the
plane.9 The Figure also shows a possible low-angle grain boundary plane (plane ABD)
which is another {111} plane and whose orientation corresponds to the STM
observations in Figure 6.7. Figure 6.10(b) displays that the low-angle grain boundary
(plane ABD) meets at an angle of 72.8 degrees with the (111) plane (plane ABC). This
angle corresponds to the value obtained from the STM images within the error bound.

Once we know the orientation of the low-angle grain boundary plane, we can
calculate the spacing D of the dislocations shown in Figure 6.3. From Equation 6.1, we
obtain D = 29.63 13.22 A, using 9=5.1:0.5 deg. and b = 2.64A which is the length of
the bond AD in Figure 6.5. This means that there is an edge dislocation about every 11
lattice constants.

If the yield shear stress is the minimum stress required to move a dislocation, a
larger shear stress should be applied to assure the motion of a dislocation. The

calculation of the yield shear stress was ﬁrst done by Peierls and Nabarrolo. They

132

[011]
(a)

[101]

  
   

low angle
grain boundary

 

 

 

0=72.8 deg.

(b)

 

B

Figure 6.10 (a) The FCC system showing one of the {111} planes and three slip
directions in the plane. (b) A close-up view of the (111) plane-low angle grain
boundary system. The plane ABC is a (111) plane, and the plane ABD is a possible
low angle grain boundary observed with an STM. The low angle grain boundary
meets the (111) plane with an angle of 72.8 degrees.

133

calculated the change in energy due to the dislocation motion from one local equilibrium
position to the next. From this, they found the stress, O'm necessary to move a

dislocation to be

20
0'," =
(I‘V)

 

exp[—21ta/b(l — v)] (6.3)

where G is a shear modulus, v is a Poisson's ratio, and a and b are the lattice constants in
a low-angle grain boundary plane and in a slip plane respectively. If we put the values9
G = 2.0lx1010 N/m2, v=0.42, and a/bzl, then we obtain am a 6.8lx10'5 G =
1.3711106 N/mZ.

Now we ask the question "What is the source of the stress to move the
dislocation?" After deposition, during the cooling of the sample, thermal stresses are
introduced to the gold ﬁlm since the thermal expansion coefficients of gold and glass are
different. By using a simple l-D approximation, we estimate the stress, 0' introduced to
the gold ﬁlm. During the cooldown, the strain, E of the gold ﬁlm due to a differential

thermal expansion coefﬁcient is

where 0: Au and “glass are thermal expansion coefﬁcients of gold and of glass
respectively, and AT is the temperature change during the cooldown. Using 0: Au
=14.2x10-6, 6131,53 = 7.4x10-6, and AT=280K, we obtain 6 = 1.6711103 which is one
minus ratio of stretched length to the original length of a gold. (i.e. during cooldown to
room temperature, the gold ﬁlm does not shrink as much as it would be like.) In the

simple case of uniaxial tensile stress and in an elastic limit, the stress can be expressed as

134

0=Ee (6”

where E is the Young's modulus of gold. (More precisely, this should be the biaxial
modulus of gold in (111) plane.) Using E=7.45x1010 N/m2 for gold (Reference 11), we
obtain 0' = 1.24x108 N/mz. This thermal stress is certainly large enough to move the
dislocation by glide since it is two orders of magnitude greater than the yield shear
stress.

One might be tempted to believe that the attenuated motion of the low-angle
grain boundary is due to the relaxation of this thermal stress. However, recalling that the
images were taken 5 days after the sample preparation, it is unlikely that the relaxation of
the thermal stress still persists since the time scale of the attenuation of the low-angle
grain boundary motion is order of 10 minutes. (See Figure 6.8.) Since the motion has
such a short lifetime, it is more likely that the stress was introduced just before taking the
STM images. We believe that the stress was introduced when the sample was handled4
with tweezers as it was loaded onto the STM sample stage. Actually, the images were
taken within in a few minutes after loading the sample in the STM. Once the sample is
loaded in the STM sample stage, the sample is imaged in a stress-free state so that the
relaxation of the stress can occur.

Another clue that a small stress can cause low-angle grain boundary motion is
demonstrated in Figure 6.11. This series of images from a sample of 80nm thick gold
ﬁlm on a 300C glass substrate shows that STM tip crash can cause a enough stress to
initiate the low-angle grain boundary motion. After obtaining an image of a ﬂat top
grain with an indented area at the center, the feedback circuit of the STM is disabled
momentarily so that the thermal drift of the tip can cause the tip to crash on the sample.

Several mounds shown in the images in the upper right are formed by tip hitting the

135

(:1) (00:00) (b) (06:49)

(0) (10:54)

(e)(23:5(1)

 

Figure 6.11 A series of STM images showing that the tip crash causes the low
angle grain boundary motion. The horizontal streaky lines in (e) and (f) are noise
signals. Scan area = (200nm)2. The time index of each images is (minutezsecond).

136

 

100 ' I ' I ' I ' I ' I ' I ' I ' I
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slope - 0.05 urn/sec

USTANCEII'IHI)
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O
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j ' I

 

nLnL

1

A

 

n I L l a I n l l n l n l n l
0 200 400 000 800 1 000 1200 1400 1 000
TIME (seconds)

Figure 6.12 A plot of the distance that the low angle grain boundary in Figure 6.11
moves vs. time. The velocity of the motion is measured to be 0.05nm/sec.

137

surface. Immediately after the tip-crash, the feedback circuit is reactivated and the same
area is imaged at regular intervals.

From the series of STM images, we ﬁnd that a sharp buckling of the sample
surface with an angle of 45:03 degrees on the upper left comer of the image starts
moving toward the lower right. The angle is determined from the surface proﬁles of
each image and found to be invariant through the measurement. In this case the surface
is buckled down viewing from the top. The distance that the boundary line moves is
measured and is displayed in Figure 6.12 as a function of time in seconds. From this
plot, we measure the velocity of the dislocation's motion to be 0.05 nm/sec.
Unfortunately, in this experiment, we did not follow the motion long enough to see any
attenuation.

A striking feature in these images is that there is a noticeable plastic deformation
of the features on the surface. On the surface behind the moving boundary line, the
mounds elongate and ﬂow toward the top and the surface indentation also deforms in the
same direction.

Another observation of the similar activity of deformation or elongation is
displayed in Figure 6.13 which are 7 sequential images selected out of total 20 images
of a 40nm-thick sample taken over 100 minutes. Note the straight boundary line running
across the image. A tilt correction was made before displaying the image so that the
surface shown as bright gray is ﬂat. After the tilt correction, the surface as dark gray is
found to rise up with an angle of 2012 degrees from the horizontal plane. (This angle is
also preserved throughout the measurement.) Assuming the low-angle grain boundary is
a ﬂat plane, we ﬁnd the tilt angle between the low-angle grain boundary and the
horizontal (111) plane to be 151-2 degrees. This angle corresponds to the angle between
(111) plane and (221). The simple picture that the low-angle grain boundary (or

whatever) is just an edge dislocation boundary plane might be unrealistic in this high

138

Figure 6.13 Time lapse STM images showing that the motion of a ln'ghangle grain
boundary reverses direction. Scan Size = (300nm)2 for images (a) to (e), (330nm)2
for the rest. The surface appearing darker rises up with an angle of about 20
degrees from the horizontal plane which is the bright surface. Note that the part of
the sample where the low angle grain boundary has passed elongates and the
original Shape is restored as the low angle grain boundary passes again during its
reverse motion. The time index of the images is (hour:minute:second).

139

00211402“ ) (b) (00;: 3:30)

((1) ((10:34:40)

(c)(00;53:28) ”5%? _ (f)(01:03:31)

 

Figure 6.13

140

Q
4,

)(‘l‘llz07;50) . g (11) (01:12:25)

.13 (01:16:36)

 

Figure 6.13 (cont'd).

141

(a)

62 = 158.8888 13

 

(b)

    

 

33 :2 deg.

I
M deg. j 0.5nm

Figure 6.14 (a) A surface proﬁle of the boundary line of the image shown in Figure 6.13
(f). (b) A close-up view of the boundary line. The surface proﬁle along the line on the
image is displayed in the plot at right hand side. The cross mark at one end of the line
corresponds to the origin of the plot. A close-up view of the boundary line reveals that
there are actually three boundary lines.

 

142

 

 

 

 

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" U
I
'5', 50 - i .
5
I I I
0 l "'
I .
-50 7 1 r . r . r . r . r .
0 1 000 2000 3000 4000 5000 0000
TIME (seconds)

Figure 6.15 A plot of the distance that the low angle grain boundary in Figure 6.13
moves vs. time. The letters for data points correspond to the sequence of images in
Figure 6.13.

143

angle boundary case. Actually, a close look of the surface proﬁle near the intersection
reveals that there are in fact three kinks in the intersection. (See Figure 6.14.)

Surprisingly enough, we ﬁnd that the boundary line proceeds from lower left
comer of the image toward upper right comer until it stops and moves backward. A
heart-shaped monatomic island on top of the grain provides a nice steady reference mark
relative to the motion. (See Figure 6.15 for a plot of distance vs. time.) From Figure
6.15, It is observed that the backward motion is about 3 times faster than the motion
before the reverse.

A more striking feature of this observation is that, as the low-angle grain
boundary proceeds, the portion of the sample where the low-angle grain boundary has
passed stretches about three times toward the opposite direction of the motion. This
stretch occurs not only in a horizontal plane but also in a lateral direction. The surface
proﬁle of the stretched part shows that the monatomic step becomes about three times
higher after the boundary line passes. Moreover, during the backward motion of the
intersection, the original unstretched shape is restored as soon as the intersection passes
again.

One might raise an issue that there is a problem of mass conservation since the
tilted part of the sample requires a large inﬂow of mass. Although a precise explanation
is unavailable at present, we can think of several possible reasons for this. The atoms
inside the bulk can be exposed by the climb of dislocations or an extrusion of a slip
bandl2 Other possibilities are buckling of the glass substrate or peeling off the gold
ﬁlm from the substrate.

Sequential STM images in Figure 6.16 demonstrate another observation showing
that low-angle grain boundary motion reverses (actually oscillates) its direction. Six
images in this Figure are part of a sequence of 59 images of an 80nm-thick sample taken

over 3 hours and 20 minutes. From the vertical view of the images, we ﬁnd that two

144

Figure 6.16 Sequential images Showing that two low angle grain boundaries show
an oscillatory behavior. Six images are part of a sequence of 59 images. Scan size
= (300nm)2. From the top down view of the image, the distance in the plot of
Figure 6.17 increases when the low angle grain boundary 1 moves to the left or
when low angle grain boundary 2 moves upward. The boundary line running in the
vertical (horizontal) direction is due to the low angle grain boundary 1 (2). The
time index of the images is (hour: minutezsecond).

145

(:1) (00:51:26)

(1)) (01:01:41)

(0) (01:10:23) ((1) (01:24:31)

1 (e) (01:31:45)

(i) (01:39:51)

 

Figure 6.16

146

 

 

 

 

 

 

 

 

30° ' l V I v I v 1 v I
no
a 1: 0° 0% a
.6 0% D 0% DD
.1 200 l- l “3° 0° Q12) :1“ .
E a. Q a a AA AA 0
9 0' 0' ADD :1 A A D
i .. ... he. ..
A % A ‘5 “A A ‘F
g, D t AMA AA ‘8
10° " g t A A‘A 1
g a ﬂoat
. a 11002 4
DE 1 1 1 1 1 L 1 1 1 1 n
0 2000 4000 0000 0000 10000 12000
“(mortal

Figure 6.17 A plot of the distance that each low angle grain boundary in Figure
6.16 moves vs. time. Line] and line2 represent the motion of boundary lines due to
the motion of low angle grain boundaries 1 and 2 respectively. The data points are
from the original sequence of the Figure 6.16. Six data points corresponding to
images in Figure 6.15 are indicated with 6 arrows.

147

com (surface is buckling upward from the top view) boundary lines are crossing each
other at an angle of about 60 degrees. This implies that two sub boundaries with a same
sign are crossing each other inside the bulk. When two dislocations with opposite signs
meet, they tend to annihilate each other to relieve a internal stress. In this case, however,
they do not annihilate since they are of the same sign.

The plot of the position of these two sub boundaries move vs. time is displayed in
Figure 6.17. The boundary line due to the low-angle grain boundary running in the
vertical direction (from top-down view) are named as linel and the other is line2. The
data points indicated by arrows correspond to images displayed in Figure 6.16 in
sequence. In this plot, we ﬁnd that the motion is oscillating with a period of about 1
hour and with an amplitude of 100nm. The observation was stopped while the motion
was continuing. It is worth noting that this oscillatory behavior is not induced by the tip
scanning effect since the oscillation is continuing even when we are not imaging during
a coffee break. (See the break near at t=9500 seconds.)

I now present a possible explanation of the reversible motion of the low-angle
grain boundary. A series of dislocations constantly emitted from a dislocation source
(due to an applied stress) can be piled up against an obstacle barrier such as grain
boundary so that they interact elastically with each other by reducing the spacing.
Consequently, there will be an internal backward stress due to the repulsion of the
dislocations. When the applied stress is eliminated, the backstress might initiate the
dislocation motion backward. This explanation is nothing but speculation at present.
Further experiments such as an STM observation on an atomic scale might reveal a
precise mechanism.

Although the observations in this Chapter still need more rigorous explanations,

we conclude this Chapter by raising following questions based on the observations.

148

o How are the dislocations introduced during the ﬁlm growth so that they collect into a
low-angle grain boundary plane during the annealing process?

4 In a thin ﬁlm, how does the velocity of a moving dislocation depend on the applied
stress?

. What causes the abrupt change in a surface feature (the factor of 3 stretch) after a
low-angle grain boundary passes?

o How can a moving dislocation stop and reverse the direction of its motion?

a What is the driving force of the oscillatory behavior of a low-angle grain boundary?

4 How can we explain the motion of the high angle grain boundary showing the shape

memory and the stretching behavior?

Possible answers for some of these questions have already been discussed in the
text. To give a clear answer of those questions, however, we may need more
experimental investigations which involve observations during the annealing, atomic
scale observations of the dislocation, a stress controlled experiment, and the study of the

effect of the substrates with an AF M.

149

REFERENCES FOR CHAPTER 6

 

1 D. Hull and DJ. Bacon, Introduction to Dislocations, 3rd. ed., Pergamon Press,
1984

2 W.L. Bragg, Proc. Physical Soc. 52, 54 (1940)
3 J .M. Burgers, Proc. Physical Soc. 52, 23 (1940)
4 R. Gronsky, Images of Materials, Oxford, 1991

5 C. Kittel, Introduction to Solid State Physics, 6th. ed., John Wiley & Sons,
1986

6 J. Washburn and ER. Parker, Trans. AIME (1952); Journal of Metals (October
1952)

7 W. Schockley, Cold Working of Metals, Amer. Soc. Metals (1949)
3 W. Schockley, Trans. AIME (1952); Journal of Metals, (August 1952)

9 R.W.K. Honeycombe, The plastic Deformation of Metals, 2nd. ed., Edward
Arnold, 1984

10 R. Peierls, Proc. Phys. Soc., 52, 34 (1940); F .R.N. Nabarro, Proc. phys. Soc., 59,
256 (1947)

11 EA. Avallone and T. Baumeister, Mark's Standard Handbook for Mechanical
Engineers, 9th. ed., McGraw—Hill, 1978

12 John E. Dorn, Mechanical Behavior of Materials at Elevated Temperatures,
McGraw-Hill, 1961

Chapter 7

STM STUDIES OF SMALL METAL PARTICLES ON FLAT
SUBSTRATES

7.1 ABSTRACT

A variable temperature STM is used to study discrete charging effects in small
normal metal particles on substrates which are so ﬂat that the particle shape can be
clearly imaged with an STM. Samples consist of a support substrate (cleaved mica,
etched Si, glass), a base electrode (Au, Ag, In, Sn, Pb, etc.), a tunneling barrier (A1203,
InOx, PbOx, etc.), and ﬁnally small particles of Au. Several attempts to make a ﬂat
metal-oxide barrier substrate are presented. Our most successful recipe involves
oxidized Pb on top of Au ﬁlm evaporated on SiOz. Finally, small gold particles are
prepared by thermal evaporation of a discontinuous ﬁlm onto the PbOx-Au-SiOz
substrate. A home-built STM, operating in the range 4K-300K, both images the particles
and performs I-V spectroscopy. I show I-V curves which exhibit a coulomb staircase at

room temperature and a coulomb blockade at 83K.

7 .2 INTRODUCTION

Understanding the electronic properties of small metal samples is a subject of
growing importance as the microelectronics industry pushes toward smaller and smaller
circuitry. As the size of a block of metal diminishes, new effects, not visible in larger
samples, arise and eventually dominate the simple ohmic metallic behavior. For sizes
less than roughly 1000A, at least three small size effects must be considered: weak

localization, discrete charging effects, and quantum size effects. In this small size

150

151

regime, the distinction between bulk and surface physics fades away: nearly every atom
is on or near the surface.

Each of the three small size effects - weak localization, discrete charging effects,
and quantum size effects - becomes apparent in distinct regimes of sample size and
temperature.

Weak localization effects become apparent when the sample dimensions are
smaller than the electron inelastic diffusion length (about 0.1 - lum at 4K). This
"mesoscopic regime" has come under intense scrutiny (for a review, see reference 1) and
a fairly clear picture of coherent backseattering and universal conductance ﬂuctuations
has emerged. The work here focuses on the study of particles and structures smaller still
(typically lO-lOOA) than this mesoscopic regime. Discrete electron charging effects
appear when the coulomb charging energy exceeds the thermal energy, kBT. This
charging energy is the energy required to add an extra electron to a metal particle or,
more generally, the energy to transfer an electron across a capacitive junction. The
charging energy is e2/2C where C is an appropriate capacitance, a particle-substrate
capacitance, for instance. The condition e2/2C > kBT is satisﬁed for a 1000A particle at
T < 10K. In this regime, charge ﬂuctuations via tunneling are suppressed. The charging
energy is then the dominant energy scale, determining the timneling dynamics of small
particle systems and of small-area Josephson junctions},3

In very small particles, of size less than 100A, the discreteness of the electronic
energy level spectrum is expected to produce a variety of unusual effects, commonly
referred to as quantum size effects (QSE). The separation in energy between adjacent
energy eigenstates is roughly 5=EF/N where E}: is the fermi energy and N is the total
number of conduction electrons in the sample. When the sample is so small that 5 >
kBT, one expects the particle to act more like a big molecule than a metal with a quasi-

continuum of states. At T=4K the condition 5>kBT is met for particles less than 100A

152

in diameter.

Most experiments to date on small particle systems have involved many-particle
samples and an inevitable smearing of measured properties over the particle distribution.
In contrast, the main goal of this Chapter is to investigate small size effects in single
small metal particles with the variable temperature STM described in Chapter 2. The
STM can both image the particles and perform electron energy-level spectroscopy,
allowing investigation of a size regime (lO-lOOOA) as yet inaccessible to lithography
while avoiding the ambiguities of ensemble averaging.

Such efforts as described here are essential to further our understanding of
tunneling dynamics and transport in granular materials and other small electronic
systems. This knowledge will be necessary for the design of future quantum electronic
devices -- devices whose function involves movements of single electrons. Quantum
devices now envisioned will rely on the ﬁeld effect to detect single electronic charges,
and will lead to new extremes in packing density and speed of integrated circuits.
Examples already being developed are a quantum electrometer which measures current
by counting the passage of electrons one-by-one, or a small particle memory element

whose quantum charge state, controlled by tunneling, deﬁnes the memory.

7.3 SANIPLE PREPARATION

Searching for the Recipe to Fabricate Flat Metal-Oxide Barrier Substrates

The experimental arrangement of the small particle experiment is illustrated in
Figure 7.1. Samples consist of a support substrate (cleaved mica, etched Si, glass), a
base electrode (Au, Ag, In, Sn, Pb, etc.), a tunneling barrier (A1203, InOx, PbOx, etc.),
and ﬁnally small particles of Au which are prepared by thermal evaporation of a

153

m
V

7-v

 

Jr 1 metal particle

 

 

Figure 7.1 The experimental arrangement of the small particle experiment. This is
a N-I-N-I-N double tunnel junction with the upper junction being the adjustable
vacuum gap (between the STM tip and the small metal particle).

154

discontinuous ﬁlm on top of the oxide layer. Fixed in Space above a particular particle is
the tunneling tip of an STM. We then have a N-I-N-I-N double tunnel junction with the
upper junction the adjustable vacuum gap (between the STM tip and the small metal
particle), the lower junction the ﬁxed oxide barrier, and the small particle in between.
We then investigate the I-V characteristics of this two-terminal structure.

To locate the STM tip above a particular particle, the substrate must be ﬂat so
that the particle shape can be clearly imaged with the STM. Several attempts were made
to achieve the ﬂat metal-oxide barrier substrates.

Our ﬁrst attempt involved the fabrication of an atomically ﬂat gold ﬁlm
evaporated on a hot mica substrate. After we obtain an atomically ﬂat gold ﬁlm on a
mica substrate, we then evaporate a few monolayers of aluminum to be oxidized.

As discussed in Chapter 3, the evaporation of a gold ﬁlm onto a heated mica
substrate results in very poor quality ﬁlms if the temperatures of the pre-bake and
deposition are in the range 320-500C. However, ﬁlms of moderate quality result when
the temperature of the pre-bake and deposition is less than 280C. Figure 7.2 is an STM
image of 120nm-thick gold ﬁlm evaporated on 240C mica substrate. The images shows
that the ﬂat-top gold grains with an average grain Size of about 100 nm are formed on the
mica substrate. The freshly cleaved mica substrate was baked in vacuum for 16 hours in
the temperature range 235-265C. During the evaporation the pressure remained below 2
x 10"6 mbar. (The base pressure was 1 x 10'7.)

After the gold ﬁlm has cooled to room temperature in vacuum, another lnm of
aluminum is evaporated at a rate of 0.1-0.3nm/sec. The aluminum ﬁlm is then exposed
to a pure oxygen gas at a pressure of about 5x10‘2 mbar for a few minutes. We chose
aluminum expecting it to wet gold since aluminum has the same crystal structure (fee)
and it has a similar lattice parameter as gold (Au: 4.08 A, A1: 4.05A). However, the

SEM picture of the resulting ﬁlm shows that Al does not wet the gold surface. (Figure

155

 

A)? 9; ’h K' I%\ ‘

Figure 7.2 Topographic mode STM image of a 12nm thick gold ﬁlm evaporated on
a 240C mica. Scan Size = (750nm)2. Sample bias = 255mV, tunneling current =

0.3nA.

 

Figure 7.3 SEM photograph showing that evaporated Al does not wet the gold
surface. The evaporated aluminum forms spherical droplets (bright dots in the
picture) with diameter of a few tens of nanometers to a few micrometers.

156

7.3) We ﬁnd that the evaporated aluminum forms isolated spherical droplets with
diameters of a few tens of nanometers to a few microns.

Our second attempt was inspired by the morphology of indium evaporated on an
oxidized Si wafer. Below a critical thickness, an indium ﬁlm evaporated onto $102 at
room temperature produces isolated, compact islands (droplets) with ﬂat faceted tops.
The SEM photograph in Figure 7.4 illustrates such a ﬁlm which consists of faceted
droplets prepared by evaporating 111nm of indium at a rate of 10nrn/sec. Our hope was
that, after oxidizing the surface of the indium sample, the faceted surface could be used
as a platform for small metal particles.

The oxide barrier must be thin enough to conduct the tunneling current of the
STM. Otherwise, the isolated metal particles are not observable since they would be
placed on top of insulator which does not provide a conducting path to the particles. To
see the possibility of tunneling, a 450nm thick indium ﬁlm (beyond the percolation limit)
was evaporated on room temperature Si02 and oxidized by the same procedure as in the
case of aluminum. We found that a very high bias (sample voltage> 3.3 volt) was
required to obtain a tunneling current of 1.0 nA. Moreover, the tunneling current was
suspiciously stable and did not respond to acoustic noise or mechanical vibrations. We
believe that the tunneling tip was buried in the oxide layer. Consequently, we found that
this recipe is not useful since the oxide layer of the indium is too thick to tunnel through.

We also tried to fabricate a ﬂat SnOx surface by oxidizing Sn evaporated on a
silicon substrate at room temperature. We found results similar to those of indium.

A commercially available silicon wafer has a native oxide layer on its surface
with a thickness of about 4 nanometers. This oxide layer is usually too thick to obtain a
tunneling current on a silicon substrate with an STM. The technique of hydrogen
passivation has been widely used41516 to remove the surface oxide so that an STM can

image a bare Si surface. Several studies show that the etching process results in not only

157

 

Figure 7.4 SEM photographs of well isolated compact indium islands with faceted
tops. The sample is 111nm of indium evaporated on a room temperature oxidized
Si substrate. (a) top view. (b) side view of the same sample. Note the difference in
the scales in two photographs. (This sample and pictures were produced by G.
Jeffers.)

158

the removal of the surface oxide but also leaves a ﬂat surface terminated by hydrogen
atoms.7

Our substrate was a n-doped (Arsenic) Si(l l 1) wafer with resistivity varying
from 0.01 to 0.02 .Qcm. Before the etching process, the silicon wafer was cut into
10mmx10mm squares and cleaned by an ultrasonic wash in acetone, methanol, and
deionized water (DI), followed by cleaning in hot MICRO solution8 for about 5 minutes
and recleaning with DI for several minutes. The sample was then dipped into a dilute
HF (36% in H20) for 1 minute to etch the oxide layer. These concentrations and the
dipping time were conﬁrmed to be appropriate by observing how the etched surface
becomes hydrophobic. (After dipping the etched substrate into DI and we remove and
observe the surface of the substrate. If DI wets the surface, then we need to immerse the
substrate in the HF solution again since the oxide surface is hydrophilic.).

Higashi et al. reported that samples etched in basic buffered HF (pH=9-10)
produces an ideal hydrogen-passivated Si(111) surface which is microscopically
smoother than samples etched in an acidic HF solution.7 We followed their recipe to
prepare a smooth Si surface. Ammonium ﬂuoride was added to 10% HF solution as a
buffering agent (NH4F :HF = 7:1) to increase the pH and maintain it constant at pH~5.0.
Using this buffered HF solution as the starting point, the pH was raised by adding
ammonium hydroxide (NI-14011) or lowered by hydrochloric acid (HCl).

Now we give a step-by-step procedure for etching Si wafers with the buffered HF

solution.9

The etching procedure uses three beakers. One contains the buffered HF solution and the
other two contain DI for sequential rinses and are referred to as DH and DI-2. Use
plastic beakers and plastic tweezers since the HF is so strong that it etches glass beakers

and metal tweezers.

159

l. Immerse the wafer into the buffered HF solution. The etch rate depends on the
concentration of the solution (typically 100nm/min). To avoid overetching, initially
leave the wafer in the solution for somewhat less than the estimated required time based
on the oxide thickness.

2. Remove the wafer ﬁ'om the etching solution and immerse it in Dl-l for a few seconds,
to stop the etching procedure, and then in DI-2. Observe the surface. If it is wet, then
Si02 is still remains since the oxide is hydrophilic. However, if the SiOz is completely
etched away, there will be only a few isolated drops since the silicon is hydrophobic.

3. If SiOz remains, immerse the wafer in the buffered etch again for another 30 seconds.
Check the surface of the wafer as before. Continue until the oxide is removed.

4. Rinse in running DI.

5. Dry with N2 gas.

Following the procedure above, the silicon wafer was etched in the buffered HF
solution for 45 seconds. The etched samples were then stored in methanol until the STM
imaging was performed. The surface proﬁles of STM images shown in Figure 7.5
compare the results between the etching in HF solution and in buffered HF solution.
While a HF etched surface shows the surface corrugation of about 4nm (Figure 7.5(a)), a
buffered HF etched sample displays the surface corrugation of 1.0-1.5nm (Figure 7.5(b)).
Our result that etching in buffered HF solution results in a smoother surface is consistent
with the results in reference 7.

To grow a thin oxide layer on the etched surface, the etched sample is stored in
D1 for 10 hours since half a monolayer equivalent of oxygen is known to be taken up by
the etched surface after expose to D1 for ~3 hours. 10 The sample is then transferred to a
vacuum chamber to evaporate Snm of gold at room temperature so that the evaporation

produces isolated gold particles on the surface. (We expect the formation of isolated

160
62 : 158.8888 6

l
122....

5888 5

62 : 58.8888 5

 

Figure 7.5 (a) STM image of the surface of Si wafer etched with a HF solution.
Scan size = (250nm)2, topographic mode (sample bias = -3.757V, tunneling current
= 0.52nA). The surface proﬁle along the line has a corrugation of about 4nm. (b)
A STM image of the surface of an etched Si wafer with a buffered HF solution.
&mﬁm=aﬂmmzmmgwMHm®Gmmkﬁa=Q2MMummmymmm
= 0.26nA). The surface proﬁle along the line has a variation of about 1.0-1.5nm.

161

islands since metal usually does not wet an insulating surface at room temperature.)
However, as displayed in Figure 7.6, the STM image shows that the gold islands are very
small (~7 nm in diameter) and form a percolating network.

Our ﬁnal successful recipe involves the fabrication of small gold islands on an
oxidized thin lead ﬁlm. An SEM photograph in Figure 7.7(a) shows 10 nm of lead
evaporated on an oxidized Si wafer, producing small islands on the surface. On the other
hand, the SEM photograph in Figure 7.7 (b) shows that 5nm of evaporated lead wets the
gold surface produced by evaporating 30nm of gold onto a room temperature oxidized Si
wafer. If lead did not wet gold, it would form spherical droplets and would show up as
in the case of aluminum on gold. (See Figure 7.3.)

For the sample preparation, 30nm of gold was evaporated onto a room
temperature Si wafer at a rate of 0.2nm/sec, followed by evaporating Snm of lead at a
rate of 0.1nm/sec. The pressure was maintained below lxlO‘6 during the evaporations.
The base pressure was 2x10'7 mbar. The sample is then exposed to a pure oxygen gas at
a pressure about 5x10"2 mbar for 5 minutes. The vacuum chamber was then pumped
down until it returned to the original base pressure. Finally, an additional 0.5nm of gold
was evaporated at a rate of 0.1nm/sec. (The pressure was maintained below 6x10'7
mbar for this evaporation.)

An STM image of this sample is illustrated in Figure 7.8. In this Figure, gold
islands with diameters of 5-7 nm and heights of 3-5nm are visible on the lead oxide
surface. The existence of the oxide layer is signaled by a moderately high sample bias
(1.35 V) required to obtain a tunneling current of 1.09nA. (i.e. The tunneling resistance
in this case is an order of magnitude larger than the case of imaging an oxide-free metal

surface.)

162

 

Figure 7.6 A STM image of percolating gold islands on a Si surface. This image
shows that Sum of gold evaporated on Si etched with a buffered HF solution forms
percolating islands with an average diameter of 7nm and a height of 8nm. Scan
size = (104nm)2, topographic mode (sample bias = -1.509 V, tunneling current =
0.21nA).

163

p.
4“.
‘

 

Figure 7.7 (a) A SEM photograph of isolated lead islands on SiOz. The sample is lOnm
of lead evaporated on a room temperature oxidized Si substrate. (b) A SEM photograph
showing how thermally evaporated lead wets a gold surface. The sample is 5nm of lead
evaporated on gold on oxidized Si wafer.

164

 

Figure 7.8 A STM image of isolated gold islands on PbOx. Scan area =
(55.5nm)2, topographic mode (sample bias = -1.35V, tunneling current = 1.09nA).
An I-V characteristics were measured on the gold island indicated with an arrow.

165

7.4 RESULTS OF STM SPECTROSCOPY AND DISCUSSIONS

7.4.1 Coulomb Staircase

After obtaining the image of small metal islands, I-V characteristics were
measured by the STM on an interesting island. For the I-V measurement, a special
voltage waveform is applied to the sample while the feedback circuit is disabled
momentarily. Figure 7.9 illustrates a schematic diagram of the waveform in the time
domain. At the moment (point A) when the I-V measurement starts, the feedback circuit
is disabled and the bias voltage starts ramping up from a preset minimum value (B) with
small steps of size AV. During the rarnping-up of the voltage, the tunneling current is
measured after every At time step. (Here, the sampling frequency is given by 1/ At.) If
more than one sampling is required, the rarnping voltage is held at every step for a
moment while a desired number of measurements is reached. (In Figure 7.9, the black
dots between the points B and C represent the measuring points, and 4 samplings per
voltage are shown in this case.) The measurements obtained at every step are averaged.
Once the voltage reaches a preset maximum value, it starts ramping down again and the
same measurements are performed. When the voltage returns to point C, the feedback
circuit is reactivated and stabilizes the tip-sample distance. The same measurement
repeats from point F if more than one spectrum is needed.

After obtaining the image displayed in Figure 7.8, at room temperature in air, we
measured the I-V characteristics on the gold island indicated with an arrow in the Figure
7.8. The resulting I-V measurement is displayed in Figure 7.10. The measurement was
performed with a sampling rate of 40kHz averaging 16 samplings per voltage step and 4
consecutive spectra. The tip-sample distance was stabilized during every time interval

between the spectra for 5 msec. In this l-V measurement, two curves are presented since

166

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167

each case for ramping up and ramping down is plotted separately.

In the I-V spectrum in Figure 7.10, a few steps with widths of about 170mV are
observed. The signal is rather noisy, probably due to a contamination of surface
contamination and vibration.

The samples in this experiment can be modeled with the equivalent circuit
consisting two junctions11 in series as shown in Figure 7.ll(b). Ct and Rt are the
capacitance and tunneling resistance, respectively, between particle and tip. Cb and Rb
are the capacitance and tunneling resistance between particle and substrate. To obtain a
current through the circuit, the capacitances of the junctions must ﬁrst be charged up to
certain threshold voltages so that an electron can tunnel through the junctions thereafter.

The threshold voltage is,12

Vt = e / 2 max{Ct , Cb} = e/2C. (7.1)

From the experimental data in Figure 7.10, we obtain Vt = 85mV which is half of the
step width. From this we get C = e/2vt = 941111019 F.
The capacitance, C in this expression corresponds to capacitance of a small metal

particle separated by an oxide barrier from the metal substrate1 3 as

C = KeoA/d (7-2)

where 60 is a permittivity of free Space, K is the dielectric constant of the oxide barrier,
A is the area of the particle, and d is the oxide barrier thickness. From the STM image in
Figure 7.8, we can measure the dimensions of the island from which the I-V
characteristic was obtained. Using A = 1T(35A)2, d =20A, and K = 10, we obtain C =

2.4x10"l8 which is in good agreement with the measured value. It is not surprising to

168

Tunnel Grip Bins—Unitary: Spectrum

Tunnel Current (x 8.1 110)

~1 ~8 1
Tip Bias (x 8.1 U)

 

Figure 7.10 I-V spectrum of the coulomb staircase at room temperature.

169

m
V

7-v

 

.1. 1 metal particle

 

 

0))

Ct

O
\J

 

WW

Cb Rb

 

V

Figure 7.11 (a) The experimental arrangement of the small particle experiment.
This is a N—I-N-I-N double tunnel junction with the upper junction being the
adjustable vacuum gap (between the STM tip and the small metal particle). (b) The
equivalent circuit of the N-I-N-I-N double junction.

170

see the coulomb staircase at room temperature in this system since the thermal energy
corresponding to room temperature (kBT = 2.5x10'2 eV) is less than the fundamental
macroscopic charging energy of the small particle (e2/2C = 3.3x10'2 eV, with C =
2.4x10’18 F for this system).

7.4.2 Coulomb Blockade

We also measured the I-V characteristics of the same sample at 83K. The STM
was lowered down into a dewar ﬁlled with liquid nitrogen and placed in the cold vapor
without touching the liquid surface to prevent mechanical vibration due to the boiling of
the liquid. At 83K, during the attempt to image, the tip crashed into the sample surface
several times and we were unable to obtain an image. Just maintaining the tip in the
tunneling range, I-V measurements were performed with a sampling rate of lkHz
averaging the of 16 samples per voltage step and 4 consecutive spectra. The resulting I-
V is displayed in Figure 7.12. The I-V curve in this ﬁgure shows that the curve is
quadratic in V at low voltages. At high voltages, the curve tends to converge to an
asymptotic line which is displaced from the origin by AV = 60.5 mV.

This behavior has already been observed by Fulton and Dolan13tl4 and
explained by Averin and Likharev15 who model the system as a current biased single
electron tunnel junction. Adopting this model, the displacement in the asymptotic line
can be considered as a result of coulomb blockade due to a charging of the capacitance
junction. The capacitance of the junction is estimated from C = e/ AV = 2.6 x 10‘18 F.
Note that the charging energy of this capacitance junction, e2/2C = 3.1x10‘2 eV is larger
than the thermal energy , kBT = 7.2x10‘3 eV at T=83K so that the condition e2/2C>kBT
is satisﬁed.

For a signal small current -biased tunnel junction, the analytical solution of 1(V)

171

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172

is available at small voltages as15

I(V) = (2C/TrRte)V2 (7.3)

where C is the capacitance of the junction and Rt is the tunneling resistance. From the
experimental I-V plot in Figure 7.12, Rt = 2.0x108 [2 is obtained by measuring the slope
of the asymptotic line to which the I-V curve converges at high voltages. (See dotted
lines shown in the inset of the ﬁgure.) Using our values of C and Rt, equation (7.3)
yields the predicted I(V) as I(V) = 52.5 V2 in nanoamperes.. The inset of the I-V plot in
Figure 7.12 displays this predicted I(V) ﬁt as a solid line at low voltages and shows good
correspondence to the data.

However, this picture of single capacitance junction seems problematic since the
real circuit is voltage biased and the stray capacitances due to the leads to the junction
are typically much larger than the junction capacitance. Why then is the charging energy
effect not destroyed by the stray capacitance? One proposed answer is that the stray
capacitance is effectively decoupled from the system if the impedance of the leads is
larger than the quantum of resistance, RH = h/e2 = 4.1 “116,17 This condition is
satisﬁed in the case that the STM tip forms a point contact junction with a sample
surface.

On the other hand, Wilkins et 01.18 found that any metal oxide involved in the
junction region can have a dominant effect on the observed tunneling characteristics.
They observed that a double junction system in series which has ' a single metallic
impurity embedded in the oxide layer sometimes imitate a single junction coulomb
blockade. Unfortunately, we cannot say which model is compatible with our system
since we do not have the information on the state of the sample and the STM tip

location.

173

7.4.3 Other l-V measurements

Figure 7.13 displays a STM I-V spectrum taken over a gold sample at 82K in
cold nitrogen vapor. The gold sample is 25nm thick ﬁlm evaporated onto 77K glass
substrate. This I-V curves shows a typical behavior in a normal metal-insulator-normal
metal (NIN) tunneling junction. At low voltages the curve shows a linear ohmic
behavior. As the voltage becomes comparable to the work function voltage, the I-V
becomes non-linear. The I-V was measured at a sampling frequency of 40kHz and
averaged over 16 samplings and 8 spectra. Pt-Rh (10%) wire was used as the STM tip.

Figure 7.14 is an I-V curve of the buffered HF etched Si sample taken at T =
82K with a sampling rate of 40kHz. The signal was averaged over 16 samplings. The
sample is a n-type Arsenic doped Si wafer with a resistivity of 0.010-0.020 0cm. The
diodelike curve shows characteristic of the normal metal-insulator-semiconductor (NIS)
tunneling junction19 and illustrates the expected dependence of the doping.

While experiments described in this chapter were being performed, we
discovered a reliable technique to fabricate atomically ﬂat gold ﬁlms on glass substrates
as described in Chapter 3. The fabrication of small metal particle samples using this

technique to make large ﬂat platform substrates is very promising for future experiments.

174

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176

REFERENCES FOR CHAPTER 7

 

1 S. Washburn and RA. Webb, Adv. Phys. 35, 375 (1986)
2 B. Abeles, P. Sheng, M.D. Coutts, and Y. Arie, Adv. Phys. 24, 407 (1975)

3 M. Iansiti, A.T. Johnson, W.F. Smith, H. Rogalla, C.J. Lobb, and M. Thinkam,
Phys. Rev. Lett. 59, 489 (1987)

4 W. Kern, Semicond. Int. April, 94 (1984)
5 F .J . Grunthaner and P.J. Grunthaner, Mater. Sci. Rep. 1, 69 (1986)
6 M. Grundner and H. Jacob, Appl. Phys. A 39, 73 (1986)

7 GS. Higashi, Y.J. Chabal, G.W. Trucks, and Krishnan Raghavachari, Appl.
Phys. Lett. 56, 7 (1990)

8 MICRO solution is supplied by the Micro International Products Co., PO. Box
70 Burlington, NJ 08016 (Ph: (609) 386-8770). The supplier claims that the solution

removes grease residue on the surface and dissolves oxide layers of various metal
surfaces.

9 D.K. Reinhard, Introduction to Integrated Circuit Engineering, Houghton
Miﬁlin, 1987

10 M. Grundner, D. Graf, P.O. Hahn, and A. Schnegg, Solid State Technology,
February, 1991.

11 The analytic solution for the I-V characteristics of this circuit is presented in M.
Amman, R. Wilkins, E. Ben-Jacob, P.D. Maker, and RC. Jaklevic, Phys. Rev. B 43,
1146 (1991)

12 P.J.M. van Bentam, R.T.M. Smokers, and H. van Kempen, Phys. Rev. Lett. 60,
2543 (1988)

13 T.A. Fulton and 0.1. Dola, Phys. Rev. Lett. 59, 109 (1987)

14 P.J.M. van Bentum, H. van Kempen, L.E.C. van de Leemput, and AA.
Teunissen, Phys. Rev. Lett. 60, 369 (1988)

15 D.V. Averin and K.K. Likharev, J. Low Temp. Phys. 62, 345 (1986)

177

 

16 K.K. Likharev, IBM J. Res. Develop. 32, 144 (1988)

17 SM. Girvin, L.I. Glazman, M. Jonson, D.R. Penn, and MD. Stiles, Phys. Rev.
Lett. 64, 3183 (1990)

18 R. Wilkins, M. Amman, E. Ben-Jacob, and RR. Jaklevic, Phys. Rev. B 42, 8698
(1990)

19 SM. Sze, Physics of Semiconductor Devices, 2nd. ed., John Wiley & Sons
(1981)

Chapter 8

OTHER OBSERVATIONS AND FUTURE EXPERIMENTS

8.1 A sample cleaning technique at low temperature

As discussed in Chapter 2, the quality of images taken at low temperatures
depends on the cleanliness of the sample surface. The surface of gold acquires one or
more monolayers of water and hydrocarbon contamination after several minutes
exposure to air. When an air contaminated sample is cooled to below about 240K the
STM images becomes noisy.

To circumvent this problem, a high or ultra high vacuum system for the STM is
under construction. The scheme is to transfer samples from the evaporator to the STM in
air. The STM vacuum system is then pumped down to 10'7 torr at room temperature and
sealed. When cooled to low temperature, residual gases condense on the inside walls of
the vacuum system so that cryopumping produces a high vacuum (less than 10‘13 torr at
liquid helium temperature).

Aﬁer the system is cryopumped, a heater wire wrapped around the STM sample
stage brieﬂy heats the sample to higher temperature, driving off surface contamination
which condenses on the cold surrounding surfaces.

Under these circumstances, G-lO (glass ﬁber reinforced epoxy) is not an
appropriate material for a sample stage since it outgases in the vacuum and can not
survive high temperature. There is a good substitute called 'lavite' (an aluminum silicate
ceramic). Lavite is a soﬁ, machinable ceramic that we can easily use to make the STM

sample stage. After machining, it is ﬁred at high temperature so that it hardens. To ﬁre

178

179

lavite, we ﬁrst bake it at 200F for 1 hour. Then the temperature is increased by steps of
200F degrees every hour to maximmn temperature of 2000F. (For a thick block, an extra
bake for one more hour at 1100F is needed.) When the temperature reaches ZOOOF, hold
it at that temperature for 1 hour for each 0.25 inches of thickness. This ﬁring recipe is

from the MacMaster-Carr catalog.

8.2 STM observations of graphite surfaces radiated by high energy charged nuclei

In early experiments, point defects or dislocations caused by neutron radiation
were observed by conventional methods such as the etchpit techniques and diffraction
electron microscopy. 1’2 The dynamic behavior of defects in radiation damaged samples
can also be monitored by several indirect measurements which include the change of
electrical resistance during the annealing of the defects or the change in mechanical
properties of the crystal under applied stresses.

Highly oriented pyrolytic graphite (HOPG) is a material which easily yields an
atomic resolution image with a STM in air. Its layered structure is also of great use since
we can easily expose the internal structure by peeling off the outermost layers without
damaging the bulk structure.

To observe the radiation damage in a HOPG sample, the HOPG with a thickness
of 1.28 mm is cut into lOmmxlOmm size and exposed to an 84Kr (with a charge of +17)
beam for 52 min using the K1200 machine at the National Superconducting Cyclotron
Laboratory (N SCL). The total number of charged Kr nucleons, the beam energy, and the
beam intensity were measured to be 2.2x1013, 35MeV/nucleon, and 17nA respectively.
The beam energy was chosen so that the Kr ion stopped in the sample. The STM images

were taken over the central region of the surface where the beam was incident. The

180

beam diameter was approximately 2mm. Before imaging the sample with the STM,
several layers of irradiated side HOPG were peeled off 20 times with a piece of scotch
tape to expose the fresh surface in the bulk and to reduce the radioactivity of the sample
by removing those layers exposed to high energy Kr beam. Typically 1-10 microns are
lost every time the surface is peeled.

STM images were made at several spots on the resulting graphite surface on both
sides of the sample. Most of the images showed a perfect undamaged hcp lattice.
However, one spot on the sample exhibited a strange triangle pattern shown in Figure
8.1. The regular triangular pits with a depth of lnm and a side of 40-80 nm are clearly
visible in the ﬁgure. Note that the density of the pattern is inhomogeneous. A more
interesting feature in this sample is that the triangular pits disappear aﬁer peeling off
several more layers of HOPG.

It is possible that the Kr-damaged layer of the sample was completely removed
during the peeling procedure. Further STM measurements on irradiated graphite are

currently underway.

181

 

Figure 8.1 (a) A STM image of HOPG bombarded with high energy ionized Kr
nucleons. (b) A close-up view of the regular triangular pits. The images were
obtained with a topographic mode (sample bias = 227mV, tunneling current =
1.3nA). Images were obtained with a NanoscopeIII STM. The sample was
prepared by Michael Thoennessen, at the National Superconducting Cyclotron
Laboratory, Michigan State University.

182

8.3 High resolution AFM images of a submicron Au wire

Submicron size metal wires fabricated by photolithography or electron beam
lithography have many applications. Understanding failure mechanisms involving
electromigration or local Joule heating in these small metal wires are of great importance
in designing reliable VLSI circuits with a long lifetime. Direct imaging of defects or
grain boundary motion along with electrical measurements may provide this
understanding. Using the STM for this application is problematic since the bias voltage
can have an undesirable effect on measurements of interest. Another technical problem
arises from the fact that locating the STM tip over the sample is very hard since the small
wire is fabricated on an insulating surface.

An AF M image displayed in Figure 8.2 shows a submicron gold wire with a
width of 0.3 micrometer and a height of 80nm. Note that the gold grains are clearly
visible on top of the wire. These grains are a few tens of nanometers in width and about
7-8 nanometers in height.

To make an electrical measurement on a submicron wire, we have to attach thick
electrical leads to make good electrical contact. A very useful lithographic technique
called the triple layer method can alleviate this problem.

Figure 8.3(a) displays an AFM image of a thin wire and thick leads. The thin
ﬁlm wire was evaporated alter the leads were fabricated by the triple layer method
(sample made by D. W. Hoadley). The bright, thick features in the image are 120nm
thick gold leads fabricated by the triple layer method and the thin ﬁhn sample with a
thickness of 50nm is visible between the leads. A close-up view of one of the thick
leads, displayed in Figure 8.3(b), shows that the lead has a tapered edge with an angle of
about 9 degrees to the horizontal plane.

183

X 0.200 [In/d“;
2 83.331

run/div

 

Figure 8.2 (a) An AFM image of a submicron gold wire fabricated by electron
beam lithography. (b) A close-up view of top of the wire clearly showing gold
grains. The image was taken with a NanoscopeIII AF M. The sample was made by
Qifu Zhu.

184

X 5.000 Im/diu
2 296.983 I‘m/div

 

Figure 8.3 (a) An AFM image of a thin gold ﬁlm and thick gold leads which was
fabricated by the triple layer method. (b) A close-up view of the thick lead with
tapered edge. Note the visibility of the grains on top of the lead. The sample was
prepared by David William Hoadley.

185

8.3 STM observations of recrystallized gold on W boat.

During thin ﬁlm fabrication by thermal evaporation, a piece of pure gold wire is
melted in a tungsten boat by resistive heating and evaporated onto a substrate. We
brieﬂy heat the tungsten boat in order to turn the solid gold into a liquid form and
stopped applying current through the boat. The tungsten boat then was cooled down to
room temperature in the vacuum chamber so that the gold recrystallizes. After several
minutes, the recrystallized gold on the boat was transferred in air to the STM and
imaged. Figure 8.4 shows a STM image of the gold surface. This image shows the clear
hexagonal faceting which is characteristic of the (111) closed packed plane of FCC
metals}:4 This result is similar to that obtained by evaporating gold on heated mica at
500C (reference 4).

Figure 8.5 is another STM image taken at a different spot on the gold surface.
The image shows evidence of the uniform shear motions in the crystal. (In the ﬁgure,
the slip planes are bright surfaces parallel to the horizontal plane of the staircase
structure.) In Chapter 6 we found that, under a reasonably small stress, the slip motion
in a crystal is induced by local rearrangements of atoms along the slip plane instead of
uniform shearing of the crystal as observed in this case.

As in Chapter 6, we can estimate the thermal strain introduced in the gold ﬁlm.
During the cooldown, the strain, 6 of the gold ﬁlm due to a differential thermal

expansion coefﬁcient is

5 = (“Au ' aw) AT

where or Au and “w are the thermal expansion coefﬁcients of gold and of ttmgsten,

respectively, and AT is the temperature change during the cooldown. Using 0: Au

186

 

Figure 8.4 A STM image of recrystallized gold surface on a W boat. The
discreteness in the grayscale in the image represents each (111)Au planes separated
by a monatomic step. The image was obtained with our STM in a topographic
mode (sample bias = 240mV, tunneling current = 1.3 nA).

187

 

Figure 8.5 A STM image of recrystallized gold surface on W boat. The image
shows the uniform shear caused by slip in the crystal. The slip planes are bright
surfaces parallel to the horizontal plane. The sample was imaged with our STM in
a topographic mode (sample bias = 240mV, tunneling current = 1.2nA).

188

=14.2x10‘6, aw = 4.5x10'6, and AT=1337K(melting point of gold)-293K(room
temperature) = 1044K, we obtain 6 = 1.00x10'2 which is an order of magnitude larger
than the case of Au on glass. We speculate that this large strain combined with the

sudden temperature change might have caused a catastrophic shearing of the crystal.

189

REFERENCES FOR CHAPTER 8

 

1 JJ. Gilman and w.o. Johnston, J. Appl. Phys. 29, 877 (1958)
2 LG. Greenﬁeld and H.G.F. Wilsdorf, J. Appl. Phys. 32, 827 (1961)
3 K. Reichelt and H0. Lutz, J. Crystal Growth 10, 103 (1971)

4 J .A. DeRose, T. Thundat, L.A. Nagahara, and SM. Lindsay, Surface Sci. 256,
102 (1991)

Chapter 9

SUMMARY OF CONCLUSIONS

c We have described the design and operation of a simple STM which functions
reliably from room temperature to 4K. The STM is assembled without glues and

solders and can be quickly and easily disassembled for repair or modiﬁcation.

0 Thermal evaporation of Au onto heated glass substrates is an extremely reliable
technique for the production of ﬁhns with large, atomically ﬂat regions. We ﬁnd
that 80nm thick Au ﬁlms evaporated onto glass substrates held at temperatures of
300C exhibit large faceted grains of about 250nm diameter. The tops of the grains
are atonrically ﬂat with step-free terraces as large as 200nm x 200nm. The grains are
separated by trenches lO-20nm deep and 50-100nm wide, leading to an overall rrns
surface roughness of 6nm or greater. In comparing the our ﬁhns with the best
reported results for gold ﬁlms grown on mica, our ﬁlms exhibit larger step-free,
atomically ﬂat regions, but have an average roughness that is greater than the Au-on-
mica ﬁlms. We ﬁnd that mica is unreliable as a substrate, apparently because of the

variable quality of commercial supplies.

0 We fabricated small gold islands and pits on an atomically ﬂat gold surface by a
voltage pulse. The sequential STM images of the fabricated structures show that the

area of the monolayer gold island decays linearly in time at room temperature in air.

190

191

We have shown, by Monte Carlo simulation, that the linear decay of monolayer
islands on metal surfaces arises from a competition among the rate of emission of
adatoms by kink sites, the rate of absorption by an outer ledge, and the rate of
reattachment to the home mesa. Linear decay is found when the distance to the outer
absorbing ledge is more than 2 or 3 times the starting radius of the mesa, and it is

rather insensitive to variations in the probability of reﬂection from the outer ledge.

To measure the surface diffusion constant, the relaxation of the stepped gold surface
toward equilibrium is observed. From the series of images showing moving
monatomic steps, we obtain a diffusion constant of 6.2x10'17cm2/sec for the clean

samples, while the heavily contaminated sample yields 8.6x10‘16 cmZ/seconds.

With an STM, at room temperature in air, low angle grain boundaries and other
dislocation arrays are observed in thermally stressed gold ﬁlms evaporated on heated
glass substrates. We ﬁnd that these low angle grain boundaries move under an
applied stress introduced either by handling the sample or by crashing an STM tip on
the sample surface. From time lapse STM images, we also observe that the motion
may slow to a stop, reverse direction, or show oscillatory behavior. These dynamic

features usually accompany a deformation of a part of the sample.

The STM was used to study discrete charging effects in small normal metal particles
on substrates which are so ﬂat that the particle shape can be clearly imaged with an
STM. Our most successful recipe involves oxidized Pb on top of Au ﬁlm evaporated
on SiOz. Small gold particles are prepared by thermal evaporation of a
discontinuous ﬁhn onto the PbOx-Au-SiOz substrate. The STM, operating in the
range 4K-300K, both images the particles and performs I-V spectroscopy. We

192

showed I-V curves which exhibit a coulomb staircase at room temperature and a

coulomb blockade at 83 K.

APPENDIX

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197

B. List of Publications

B.1 "Simple, variable-temperature scanning tunneling microscope", M.A. Dubson
and J. Hwang , Rev. Sci. Instrum. 63(7), 1992 ....... (described in chapter 2)

B2 "Atomically ﬂat gold ﬁlms grown on hot glass", J. Hwang and MA. Dubson,
J. Appl. Phys. 72(5), 1992 ....... (described in chapter 3)

B3 "The linear decay of islands on metal surfaces", M.A. Dubson, Martine Kalke,
and Jeeseong Hwang (to be published in Phys. Rev. B) ....... (described in chapter 5)

BA "STM observations of surface diffusion of gold on Au (111)", J. Hwang and
MA. Dubson (in preparation) ....... (described in chapter 4)

B5 "STM observations of dynamics of low-angle grain boundaries and

dislocations in stressed thin gold ﬁhrrs on glass substrates", J. Hwang and MA.
Dubson (in preparation) ....... (described in chapter 6)

B6 "An atomic view of mass transport by surface diffusion", M.A. Dubson, J.
Hwang (in preparation)
Contributed Papers

B.7 "STM study of atomically ﬂat Au on glass", J. Hwang and MA. Dubson, Bull.
Am. Phys. Soc. 37, 112 (1992)

B8 "STM study of small metal particles on ﬂat substrates", J. Hwang and MA.
Dubson, Bull. Am. Phys. Soc. 35, 505 (1991)

"‘111111111111111“