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dissertation entitled

Resistance Imaging with 3 Scanning Electron
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presented by

Qifu Zhu

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RESISTANCE IMAGING WITH A SCANNING ELECTRON
MICROSCOPE

By

Qifu Zhu

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1994

ABSTRACT

RESISTANCE IMAGING WITH A SCANNING ELECTRON
MICROSCOPE

By
Qifu Zhu

This thesis describes two separate research projects. The first project is the
development of a technique, called electron beam resistance imaging (EBRI), to
measure electrical resistance variations along lithographic metal lines. With this
technique, we have studied the onset of failure of metal lines by electromigration
and local heating effects by imaging the resistance and then slowly increasing the
external current to the failure, recording the evolution of the resistance at hot spots.
A serious technical problem in the implementation of this technique is the
formation of carbonaceous contamination on sample surfaces under the action of
the electron beam in the scanning electron microscope. Several methods to
prevent and remove this contamination have been compared. In the second
project, a mechanically-controlled squeezable tunnel junction has been built to
study single-electron tunneling phenomena through a vacuum barrier. Using a
squeezable tunneling junction with a micron-sized sample, two-level fluctuations
of the conductance in the tunneling regime has been observed at liquid nitrogen

temperature.

T o my parents

iii

ACKNOWLEDGMENTS

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. I thank Professor Norman Birge, Philip Duxbury, Henrik
Weerts, and Eugene Capriotti for serving on my graduate committee. I thank Prof.
D. K. Reinhard for his stimulating discussions about the EBRI experiment.

There are several people to whom I own acknowledgment: the machine shop
staff, Thomas Palazzolo, Jim Mums, and Tom Hudson for their assistance in
construction of experimental apparatus and in teaching me machine shop skills;
Electronic shop staff, Barry Tigner and Bob Raine for their technical support in
building electronics; Dr. George Perkins for his professional help in PC network;
Reza Loloee for his efforts to deal with hazard chemical waste from our
lithography lab.

I would like to extend my thank to my fellow graduate students: Dr. Jeeseong
Hwang for sharing the oriental culture; Lowell Mch for reading one part of this
thesis; Dr. George J effers, for useful conversations regarding experiments and
sharing knowledge of editing work in his thesis.

I would like to thank my fellow Chinese students for friendships and happy
memories: Dr. Fan Zhu, Boyong Chen, Dr. Yong Cai, Dr. Nengjiu Ju, Dr. Weiqing
Zhong, Qing Yang, Hong Wang and Dr. J idong Chen.

My special thanks go to my special friend, Ping Shi for her patience and love

over years; Among Peng for her friendship and understanding.

iv

Finally, I want to thank Michigan State University, Center for Fundamental
Material Research, the National Science Foundation, Dr. Thomas Aton and Texas

Instrument for financial support during my graduate studies.

TABLE OF CONTENTS

LIST OF FIGURES ........................................................................................... ix
1 Introduction ..................................................................................................... 1
2 Sample Fabrication—Pbotolithography and E-beam Lithography ........... 4
2.1 Introduction ........................................................................................ 4
2.2 Contact Lithography and Projection Lithography ............................. 5
2.2.1 Photography of Mask Patterns ............................................. 5
2.2.2 Contact Photolithography .................................................... 7
2.2.3 Projection lithography ........................................................... 12
2.3 Metalization——Thin Film Deposition ................................................. 16
2.3.1 Substrate cleaning——Reactive Ion Etching(RIE) ................. 16
2.3.2 Metal Thermal Evaporation ................................................. 17
2.3.3 Thermal Deposition of Silicon Monoxide ........................... 19
2.4 Electron Beam Lithography by SEM ................................................. 20
2.4.1 Comparison of E-beam Lithography and
Photolithography ............................................................................. 20
2.4.2 Electron-Beam Exposure ..................................................... 23
2.5 Some Samples Fabricated .................................................................. 23
2.5.1 Al/SiOZ/Al and Au/SiOZ/Al Samples
for Resistance Imaging ................................................................... 24
2.5.2 Samples for Squeezable Tunnel Junction ............................ 30

vi

2.5.3 Sample for Crack Junction ................................................... 35

3 E-beam Induced Contamination and Efforts to Stop It .............................. 38
3.1 Contamination Problem and Decontamination Techniques ............... 38
3.2 PF PE Type Diffusion Pump Oils ....................................................... 39
3.3 Cold Shroud ....................................................................................... 42
3.4 Decontamination Using an Gas Jet Technique .................................. 45
4 Resistance Imaging with a SEM .................................................................... 54
4.1 Abstract .............................................................................................. 54
4.2 Introduction ........................................................................................ 55
4.3 Principle and Analysis of Measuring Circuits ................................... 56

4.3.1 Electron Beam Interaction with Metals and
Semiconductors ............................................................................... 5 6

4.3.2 Principle of Electron Beam Resistance Imaging

Technique ........................................................................................ 61
4.3.4 Experimental Apparatus ....................................................... 63
4.4 Experimental Results ......................................................................... 70
4.4.1 Sample Preparation and Sample Holder .............................. 70
4.4.2 Result and Discussion .......................................................... 73
5 Squeezable Tunnel Junction and Crack Tunnel Junction .......................... 84
5.1 Introduction ........................................................................................ 84
5.2 Coulomb Blockade Theory ................................................................ 87
5.2.1 General Tunneling Theory ................................................... 87
5.2.2 Coulomb Blockade Theory .................................................. 92
5.3 Apparatus and Techniques ................................................................. 95
5.3.1 Theoretical Calculation of Controlling Force vs.
Tunneling Gap ................................................................................ 100
5.3.2 Crack Junction ..................................................................... 102

vii

5.4 Experimental Measurement and Results ............................................ 104
5.4.1 Coulomb Blockade with a Crack Junction ........................... 104
5.4.2 Two Level Conductance Fluctuation in a Squeezable

Tunnel Junction ............................................................................... 109

viii

LIST OF FIGURES

Figure 2.1 This diagram shows the main steps of
contact photolithography for a positive resist. ...................................................... 8

Figure 2.2 Block diagram for UV exposure system: (A) lamp Housing,

(B) 100W mercury lamp, (C) reflecting mirror, (D) quartz collimating lens,

(E) reflecting mirror, (F) Shutter, (G) stage with sample and mask;

(I) glass or quartz cover plate, (11) metal bar held down with (111) 4-40

screw ..................................................................................................................... 10

Figure 2.3 A schematic diagram shows pattern edge profiles:
(i) over-cut; (ii) vertical-cut; (iii) under-cut.
An under-cut profile is ideal for lifi-off technique ................................................ 1 1

Figure 2.4 Optical path diagram for projection lithography:
(A) tungsten lamp, (B) collimating lens, (C) mask, (D) filter,
(E) collimating lens, (F) objective lens, (G) prism, (H) eyepiece ......................... 14

Figure 2.5 (Top) Photograph of the thermal evaporator, Coating System
E306A, made by Edwards High Vacuum International, Edwards, England.
(Bottom) Schematic block diagram of the thermal evaporator ............................. 18

Figure 2.6 Schematic diagram showing the region of

interaction between high energy electron beam and 3000 A thick
polymethylmethacrylate (PMMA). Such a droplet- shaped

interaction volume produces a natural undercut profile for

electron beam lithography if the e-beam resist coating layer is thin ..................... 22

Figure 2.7 (a) An optical microscope photograph of a sample line

under 400x magnification. The line width is 1.6 pm. (b) A sample

in the sample holder, with leads attached to the lithographically

defined metal films on a 1 cm2 substrate. ............................................................. 26

Figure 2.8 Schematic diagram of the sample shown in Fig. 2.7 (b) .................... 27

ix

Figure 2.9 The procedure for laying down
a metal stripe on a Si/Si02 substrate. .................................................................... 29

Figure 2.10 (a) An optical photograph of a micron-sized tunnel junction

under 150x magnification; (b) a sub-micron sized bridge for a tunnel

junction under 300x magnification, the sub-micron line at the center is 40

um long and 0.15 urn wide. .................................................................................. 31

Figure 2.11 An atomic force microscope (ATM) image of an e-beam
lithographic Au line on a glass substrate, taken by J eeseong Hwang
with a NANOSCOPE-III ....................................................................................... 34

Figure 2.12 Schematic layout of a sample for a crack junction. .......................... 36
Figure 2.13 Optical microscope photograph of a broken Au line

on a cracked glass substrate. The Au line is 30 um wide.

Although the crack in the glass is clearly visible, the break

in the Au line cannot been seen in this photo ........................................................ 36

Figure 3.1 Five-ring phenyl ether structure of
Santovac-S diffusion pump oil. ............................................................................. 40

Figure 3.2 F luorochemical Structure, Krytox perfluoroalkylpolyether. ............... 40

Figure 3.3 Arrangement of the cold shroud
in the sample chamber of the SEM ....................................................................... 44

Figure 3.4 Photograph of the cold finger installed
in the wall of the sample chamber ......................................................................... 44

Figure 3.5 A plot of pressure vs. time while the SEM chamber
is shut off from the pumping system. .................................................................... 46

Figure 3.6 Schematic diagram illustrates the gas-jet technique:
(A) 1" diameter clamp connector; (B) 1/8" quickconnect. .................................. 47

Figure 3.7 5+1] vs. time for an Al film with a 2 keV electron beam at a
pressure of 4x 10'4 torr: (a) Oz-jet; (b) Ar-jet ....................................................... 49

Figure 3.8 SEM images of decontamination spots: (a) Al film on an
oxidized Si substrate (image taken with a lkeV beam) (a) One more spot
made on the SiOz substrate (image taken with a 10keV beam). ........................... 51

Figure 4.1 Relationship of the diffusion range of electrons and the

electrons' accelerating voltage and specimen's density. A line drawn

between the density of a specimen and the accelerating voltage of the

electron beam intersects the diffusion axis, giving the diffusion length.

[ Reproduced from the J EOL electron microscope service manual.] ................... 59

Figure 4.2 Schematic illustration of the relationship between a primary

beam current 13, specimen current ISPECIMENa backscattered electron

current 185 and secondary electron current ISE as a high voltage electron

beam impinges on the surface of the sample: 13 = 188 + ISE + ISPECIMEN

The shaded area indicates interaction volume ...................................................... 60

Figure 4.3 Principle of electron beam resistance imaging (EBRI):

(a) Measuring the resistance between point x and ground by injecting

current with a SEM; (b) A plot of resistance vs. position;

(0) A plot of dR/dx vs. position ............................................................................. 62

Fig. 4.4 Experimental apparatus for resistance imaging with
a scanning electron microscope. The dark line is a GPIB
interface between computer and lock-in amplifiers. ............................................. 64

Figure 4.5 A plot of spot sizes (diameter) of electron beams vs.
measured beam currents. ....................................................................................... 66

Figure 4.6 A plot of the sum of backscattered and secondary

coefficients 1] + 6 vs. the beam accelerating voltage

for an Al film with and without secondary collection ring. .................................. 67
Figure 4.7 Experimental apparatus for measuring the position

derivative of resistance vs. position. (A) Low-noise voltage

preamplifier; (B) DC current amplifier. ............................................................... 69
Figure 4.8 Sample holder. .................................................................................... 72
Figure 4.9 A profile of current vs. position when a large

current beam crossing the sample line. ................................................................. 74

xi

Figure 4.10 A plot of resistance vs. position along the sample line ..................... 76

Figure 4.11 (A) Resistance vs. position after J=2.5x105A/cm2

for 24 horas, data taken without 02 jet. (B) Resistance vs.

position after 20 hour stress of J = 4.0 x105 A/cm2 and

2 more hours of J = 2.5 x106 A/cm2 , data taken with Oz jet ................................ 77

Figure 4.12 Sample current vs. position ............................................................... 79

Figure 4.13 SEM image of the void formed by electromigration
corresponds to the huge peak in Fig. 4.11 ............................................................. 81

Figure 4.14 dR/dx vs. position. ............................................................................ 82

Figure 5.1 A schematic diagram shows the Fermi energy
diagram for a basic tunneling process. .................................................................. 88

Figure 5.2 Energy diagram for a tunneling process,
where a bias voltage V is applied to the left side electrode. ‘
Fermi level is set to zero as a reference point ................................................. 89

Figure 5.3 Apparatus for single electron tunneling experiment.
40 kn resistor limits current in the case of tunnel junction short. ......................... 97

Figure 5.4 A schematic diagram of the mechanically controllable
squeezable tunneling junction. The diagram is not to scale. ................................ 98

Figure 5.5 A schematic diagram of a squeezable tunnel junction
sample with two electrodes on two glass substrates

separated by four thin metal film spacers. ............................................................ 100

Figure 5.6 Schematic diagram showing
the controlling mechanism for a crack junction. ................................................... 103

Figure 5.7 Photograph of a crack junction with indium pads .............................. 105
Figure 5.8 Data for a crack junction at T: 77 K.

Curve (A): plot of conductance G vs. bias voltage V;
Curve (B): plot of tunneling current I vs. time t. .................................................. 105

xii

Figure 5.9 Photograph of conductance vs. bias voltage
for a crack junction at room temperature. ............................................................. 108

Figure 5.10 Photograph of a typical micron-sized squeezable junction .............. 109

Figure 5.11 Plot of conductance vs. bias voltage
fora 1 pm sample atT=83 K ............................................................................... 112

Figure 5.12 Tunnel current vs. time
foralpmsampleatT=83K ............................................................................... 113

Figure 5. 13 Trace of a tunneling current vs. time to show
the controllable gap in the squeezable tunneling junction. ................................... 114

Figure 5.14 Two level conductance fluctuation
of a sample in a tunneling junction. ...................................................................... 115

xiii

Chapter 1

Introduction

This thesis describes two distinct research projects. The first project is the
development of a new technique to image resistance variations in lithographically
fabricated metal circuit lines with a scanning electron microscope (SEM). The
second project is a study of single electron timneling effects with two difi‘erent
mechanically-controlled, adjustable-gap tunnel junctions.

Scanning electron microscopy has been used in both the fabrication and testing
of semiconductor devices since the development of integrated circuits in the
1960's. With an electron beam spot size as small as 1 nm, the scanning electron
microscope (SEM) is now being used to fabricate sub-micron circuitry, producing
computer chips with higher transistor density, that are faster, cheaper, and more
energy efficient. The SEM can also be used to probe the function of a working
integrated circuit. When the high energy electron beam (typically 1-50 keV) of an
SEM strikes the surface of a metal or semiconductor, many reaction products are
produced including x-rays, backscattered electrons, and secondary electrons.
Secondary electrons have energies less than 50 eV and are emitted from parts of
the sample within 5 nm of the surface. The flux of these low-energy secondaries
is extremely sensitive both to the morphology of the sample surface and to local
electric fields. A surface with a positive voltage tends to pull secondary electrons
back to the surface and appears dark in a secondary electron image, while a
negatively charged surface appears bright. This phenomena has been exploited in
the technique of voltage contrast imaging, which is routinely used to test the
function of chips. Circuit lines on the chip are seen to alternate dark and bright as
the logic levels switch high and low. Although the 0-5V levels of standard TTL
logic is easily imaged with voltage contrast electron microscopy, the IR voltage

1

2

drop along metal circuit lines is much too small to be seen with this technique. In
this thesis, I describe the development of a technique to image this small IR
voltage drop along metal lines, a technique which has been dubbed electron beam
resistance imaging (EBRI). In this technique, the electron beam of the SEM
injects current at a point along the metal sample line, and the resulting voltage
drop is measured with external circuitry. This technique has a voltage resolution
of a few nanovolts, a resistance resolution of a fraction of an ohm, and a spatial
resolution approaching 0.1 um.

This technique was first used in 1965 by Watanabe and Munakata, who
measured variations in the resistivity of bulk semiconductors.1 Long and Slichter
used a variant of the technique to study organic semiconductors in 1979.2
However, both these groups studied non-metallic samples with very high
resistivity. The primary goal of my work was to extend the sensitivity of the
technique to allow characterization of metals. As a test, we studied the evolution
toward failure of an aluminum circuit as it was stressed with a large external
current. Electromigration is the primary cause of circuit failure in circuit lines and
is a subject of active investigation in the electronic industry. The technique of
EBRI may provide a powerful new probe of this phenomena.

One of the primary technical difficulties in implementing EBRI is the
formation of carbonaceous contamination on the surface of the sample due to
polymerization of contaminant molecules under the action of the energetic electron
beam in a SEM. We tried several different ways to eliminate this contaminatin
including replacement of the conventional diffusion pump oil by
perfluoropolyethers (PFPE) type diffusion oil, the construction of a coldshroud
around the sample and installation of a gas jet to clean the surface.

In the second research project, single-electron tunneling phenomenon were

studied with a home-built, mechanically-controlled squeezable tunnel junction and

3

a crack junction. The tunneling dynamics of a small junction with a very small
capacitance has become a topic of intensive investigation in last several years, both
theoretically and experimentally. In small capacitance junctions, there occurs a
new regime of tunneling, single electron tunneling Applications of single electron
tunneling include the fabrication of precision current meters that can count
electrons one-by-one. 3

The remainder of this thesis is organized in the following way. In Chapter 2, I
describe the procedures for use of photolithography and e-beam lithography to
fabricate the micron-sized and submicron-sized samples used in the two research
projects of this thesis. Chapter 3 and Chapter 4 describe the first research project
—electron beam resistance imaging (EBRI)——a technique to measure electrical
resistance variations along lithographic metal lines. A serious technical problem in
the implementation of this technique is the formation of carbonaceous
contamination on sample surfaces. In Chapter 3, I describe several methods
employed to prevent and remove this contamination. In Chapter 4, I describe the
principles of EBRI and the circuitry used to implement it, as well as some
experimental results on resistance imaging of a metal line damaged by
electromigration. In Chapter 5, I describe the second research project,
development of two types of mechanically-controlled tunneling junctions, a
squeezable junction and a crack junction. I also discuss some single-electron

tunneling phenomena that were observed with these junctions.

 

1 Hiroshi Watanabe and Chusuke Munakata, Japan. J. Appl., 51, 250 (1965).
2 James P. Long and Charles P. Slichter, Phys. Rev. B, 2;, 4521 (1980).

3 L. J. Geerling, V. F. Anderegg, P. A. M Holweg, and J. E. Mooij, Phys. Rev.
Lett, 64, 2691 (1990).

Chapter 2

Sample Fabrication—Photolithography and E-beam
Lithography

2.1 Introduction

Over the last several decades, the line width in integrated circuits has been
pushed down from 3 um to 0.6 um. Many new technologies, such as electron
beam lithography and soft x-ray lithography, have been simultaneously developed
in order to make smaller, faster and more energy efficient chips. Electron beam
lithography is widely used for the fabrication of master masks for contact
lithography because it is capable of writing submicron lines directly on a quartz
substrate coated with a Cr film. Contact lithography -g a method for transferring
patterns fiom a mask to a wafer - is still one of the most popular technologies in
modern integrated circuit industry due to its unique capability of fabricating chips
in a large scale. As a result, the CPU in modern personal computers, e. g. the “P6”
processor manufactured by Intel Corp. using contact lithography, has 0.6 um lines,
and has 5 million transistors in such a 0.5 inch by 0.5 inch areal.

In our lab, contact photolithography, projection photolithography and electron
beam lithography have all been used together to fabricate samples for the studies
of electromigration and the Coulomb blockade effect. These techniques have
differing resolution. In our lab, we use contact photolithography to fabricate 10 um
lines using a photographic negative as a mask. We use projection
photolithography to make lum lines, a resolution which is limited by the
wavelength of the Ultraviolet (UV) light source. And we have fabricated 0.1 pm

wide metal lines with e-beam lithography using a scanning electron microscope.

4

5

Once a pattern is transferred from the mask to the photoresist, layers of thin metal
films, such as Al/SiOz/Al and Au/Cr, are deposited by thermal evaporation at a
base pressure of 1x10'7 torr. This chapter describes these procedures for sample

fabrication in detail.

2.2 Contact Lithography and Projection Lithography

2.2.1 Photography of Mask Patterns

In our lab, contact photolithography is used to make 10pm wide metal lines on
silicon wafers, a line width which is limited by the minimum feature size in the
mask. A photographic negative is used as the mask, and an ultraviolet light source
is used to transfer the mask pattern to a silicon wafer which is coated with
photoresist. The following procedure is used to make a mask.

First, a desired pattern is drawn and printed out by a laser printer with contrast
and resolution as high as possible and with the pattem's edge as sharp as possible.
The pattem's dimensions are calculated according to the desired line width in the
final sample and the demagnification of the camera. For example, in order to
produce a negative with a 50 um wide line using a camera with a demagnification
of 20X, a line with a 1 mm width must be drawn on paper. Typically, laser
printers have a resolution 300 dpi (dots per inch), with some as high as 600 dpi.
These are ideal for making mask patterns. Before laser printers were available to
us, we used an HP plotter with a 0.5 mm diameter, special dark ink pen. The
hardcopies coming from such a plotter have two serious problems: (i) a line with a
dimension smaller than a plotter pen's diameter of 0.5 mm cannot be drawn; (ii)
even for a wide line, for example, 1 mm wide line, the edge is not sharp because

the ink diffuses in the paper. Later, using a sharp razor, we cut dark paper into

different shapes with the required dimensions and patched them together on white
paper as the background. We also used transfer decals ( trans-artype2 ) to produce
fine lines with a width of 0.5 mm, because it is almost impossible to cut such
narrow lines by hand with a razor. With the laser printers now available, it is
much easier to make and modify a mask using software, such as DrawPerfect,
HarvardGraphics, MicroSoftDraw, AutoCAD, etc. A laser printer produces
satisfactory masks with high contrast, uniformly dark area and sharp edge
definition, as desired.

The next step is to make a negative mask with a high contrast negative film,
Kodalith Orth Film 9656, Type III (ASA 6), manufactured by Kodak Corp..
Kodalith Orth 9656 has the highest contrast among commercial negative films,
with a resolution of a few um’s, which serves well for contact pads requiring
dimensions larger than 10 pm. When photographing the laser printer pattern, the
paper pattern is covered by a large glass plate, in order to keep the entire pattern in
the same focusing plane. (The paper tends to curl under the hot illumination
lamps.) A Micro-Nikor 55 mm f/2.8 lens is used together with an FM2 Nikon
camera body. For each pattern, several exposures are made by varying the
exposure time, the aperture stop, and the position of the light source. The
maximum demagnification that we use is 15X, limited by the maximum distance
between the camera and the mask pattern allowed by our Polaroid MP4 camera
stand. With 10X demagnification and without the glass cover plate, the
appropriate exposure conditions are as follows: f/4(aperture)—1/8 sec. exposure
time or f/5.6—1/4 sec., with two 150 watts tungsten-lamps illuminating the mask
pattern. When 15X demagnification is used, the exposure time is somewhat longer
with the same aperture and illuminating light because of the larger object distance.
We found that use of the glass cover plate reduces the exposure time because the

glass increases the reflection coefficient of the white paper. The best exposure

7

time is 1/ 15 sec. with the aperture set at f/4 and four 150 W-lamps illuminating the
sample. Shorter exposure times are preferred in order to reduce fuzzy edges
caused by vibration of the table.
The recipe for developing the high contrast films is:3
Kodalith Super RT developer(Part A & B): 2 min. 45 sec.;
Stop Bath: 30 sec.;
Kodak Fixer: 3 min.;
Water rinse: 30 min.;
Dry in air overnight.
A stop bath is a dilute acetic acid solution for stopping firrther development by the
developer, and a fixer is used to stabilize the image. For developing one roll of
film with 24 exposures, 8 oz (236 ml) of each solution is needed.
After developing the films, we view them with an optical microscope, looking
at the silver grains under 1000X magnification with transmitted light illumination.
This helps us to choose the best negative to use as a mask. We are now ready to

transfer the mask pattern to a substrate by contact lithography.

2.2.2 Contact Photolithography

The most frequently used method for transferring a pattern from a mask to a
sample substrate is contact lithography. This is a well-known technique, and there
are many excellent descriptions of this technique in the literature.4a5 Fig. 2.1
illustrates the basic procedure for contact photolithography.

A substrate is cleaned by a standard procedure:5

rinse in acetone for several seconds;
rinse in methyl-alcohol (methanol) for several seconds;

rinse in deionized water (DI) for two minutes;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a)
l l l l l l l
: t b)
I I; » c)
d)
I - 1 e)
O O
Photoresist Substrate

Photoresist coating the substrate

UV exposure with a mask

Development
Metalization
Lifi-off
. @
Mask Metal Film

Figure 2.1 This diagram shows the main steps of contact photolithography for a

positive resist.

dry with nitrogen gas.

After being prebaked at about 200°C for 30 minutes in a hot plate oven to remove
water from the surface, the substrate is coated with lum thick layer of positive
photoresist $1811 from SHIPLEY company7, using a spinner at a speed of 5,000
rpm. A positive photoresist is a cross-linked polymer with chemical bonds that
can be broken by exposure to UV light, and such an area with broken bonds can be
dissolved by a special solvent, called a developer. Conversely, a negative
photoresist has the opposite property, the exposed area is insoluble to the solvent.
The resist-covered substrate then goes through a sofibake procedure -- baking at
90-100°C controlled in the air for 30 min. to drive the carrier solvent out of the
photoresist.

The crucial step for contact lithography is the UV exposure. A block diagram
for this procedure is shown in Fig. 2.2. A 100W mercury lamp, with a collimating
lens, is used as the UV source.8 A simple camera shutter controls the exposure
time in this home-built exposure system. In order to get uniform illumination in
the 1 inch diameter of the field of view, a frosted glass plate is inserted into the
light path, just above the shutter. It acts to scatter light and reduces the intensity of
the UV light by half at the contact plane. With the frosted plate, the exposure time
is typically 10 seconds. Optimum edge definition is achieved when the side of the
negative coated with silver grains (the emulsion layer about 0.2um thick) faces the
photoresist on the substrate. The negative film acetate base substrate (about 0.15
mm thick) scatters light and makes the edge profile fuzzy when the acetate is
between the emulsion and the photoresist. In order to make good contact between
the mask and the photoresist, a glass or quartz plate is placed on the mask held in

place by two metal

f——_——J Glass cover plate

<— Substrate

    

II

Figure 22 Block diagram for UV exposure system: (A) lamp housing, (B) 100W
mercury lamp, (C) reflecting mirror, (D) quartz collimating lens, (E) reflecting
mirror, (F) shutter, (G) stage with sample and mask; (1) glass or quartz cover plate,
(11) metal bar held down with (III) 4-40 screws.

bars. This mimics the situation in a commercial mask aligner, in which a
mechanical pump is used to create a vacuum between the mask and the photoresist,
so that air pressure produces good contact. Of course, in this case, the mask must
be on a solid substrate instead of a floppy negative film. In the integrated circuit
industry, the mask is often made on fused silica (quartz). One side is coated by a
Cr or Fe203 film which is exposed with direct electron beam writing. Then the Cr
or Fe203 is etched during development so as to produce a master mask. In the
most of my work, samples were fabricated using floppy negative film masks; some

commercial Fe203 film masks were also used.9

11

 

Metal film

‘— Photoresist

 

 
 

 

‘— Substrate

 

 

 

(i) Over-cut

        

   

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(ii) Vertical-cut

 

 

 

 

 

 

 

 

 

(iii) Under-cut

 

 

 

Figure 2.3 Pattern edge profiles: (i) over-cut; (ii) vertical-cut; (iii) under-cut. An
under-cut profile is ideal for lifi-off.

12

Right after being exposed to UV light, the substrate with photoresist is placed
in Shipley Micro Developer 452 for 45 seconds, a development time which ofien
produces an over-cut edge profile. The pattern edge profile is described as over-
cut, vertical-cut, or and under-cut, as shown in Fig. 2.3. Obviously, the pattern
edge profile has to have an under-cut in order to produce clean patterns afier lift-
off. The lift-off technique is a process which removes the metal on the top of the
photoresist by dissolving the photoresist underneath with a solvent, such as
acetone. Achieving the desired under-cut profile requires a special treatment of
the photoresist in chlorobenzene, as discussed in section 2.5.1.

When we need to do projection lithography after contact lithography in order to
fabricate a 1pm sized samples, we partially develop the contact pattern for 2-3
seconds, just long enough so that a faint image of the pattern is barely visible with
an optical microscope. After the projection lithography exposure, the photoresist
is fully developed for 45 seconds. This procedure will be discussed in detail in the

following section on projection photolithography.

2.2.3 Projection lithography

With an acetate negative film used as a mask, contact lithography can only
produce 10pm wide lines due to the edge definition of the pattern on the negative
film. Over the past decades, scientists have developed and refined projection
lithography to reduce the dimensions in microlithography. Using an inorganic
resist/polymer bilayer scheme, Tai et al. have successfully fabricated 0.5 um lines
with a Perkin-Elmer projection printer photolithography system.10 Another research
group produced 0.2 mm metal patterns using projection photolithography.11 In the

latter experiment, the substrate was transparent to light, the mask was projected

13

through an oil-immersion objective lens and the substrate onto a single photoresist
layer. With this technique, the under-cut profile is obtained naturally.

The optical path in our commercial optical microscope12 is shown in Fig. 2.4.
The mask is an acetate negative held in a rigid frame. With a yellow filter, a
conventional W lamp can be used as both a visible light source for mask alignment
and as a UV source for exposure. The UV tail from a conventional W lamp is
intense enough to expose photoresist if the light is focused down to a small enough
area. There are three objective lenses in our microscope: 10X, 40X and 100X; the
corresponding fields of view are 1800 um, 450 um and 180 um. For the 100X
lens, the proper exposure time is 35~40 seconds when the voltage on the lamp
power supply is set to 6V and aperture position is at its minimum position. For the
40X lens, the exposure time is 2005 for the same mask with the same illuminating
power. For the 10X lens, the pattern does not show up in photoresist in a
reasonable time, because the UV intensity is not high enough to fully break the
polymer’s chemical bonds. All projection lithography in this work was done using
the 100X objective lens.

If the film mask has a 100 um wide line feature, and a 100X lens is used for

projection, then a fine line of loom/00:1“!!! is obtained in the resist. Usually this

size is near the resolution limit of projection lithography set by the wavelength of
the UV tail in the spectrum of a tungsten lamp. We routinely achieve lum
resolution, a resolution which is perhaps limited by the thickness of the photoresist
layer. We have found that the resolution of projection lithography is sensitive to
the reflectivity of the substrate. The photoresist profile of the pattern on some
transparent substrates, such as glass or quartz coated with F e203, are well-
controlled with sharp edge definition and good under-cut profile (shown in Fig.

2.3). However, the linewidth is slightly larger if

14

 

 

I
D\ E K "F —Photoresist
ni— gEye — Substrate

 

 

 

 

 

 

 

 

 

 

 

 

l
I
m

7 \ ‘ —Under-cut

 

 

 

 

 

 

 

 

m —Metalization

 

 

 

 

Figure 2.4 Optical path for projection lithography: (A) tungsten lamp, (B)
collimating lens, (C) mask, (D) filter, (E) collimating lens, (F) objective lens, (G)
prism, (H) eyepiece.

the substrate is a metal film with a high reflection coefficient. Just as in contact
lithography, the pattern profile turns out better when the side of the negative
coated with silver grains faces toward the substrate. Most of our samples are
fabricated on oxidized silicon substrates. In the resistance image study [Sec. 3.3],
the substrate is a strongly reflecting 2000 A Al film. This substrate yields a good
under-cut profile in 100X projection lithography, resulting in clean lift-off after
metal film thermal evaporation.

In contrast to projection lithography, with contact photolithography, one cannot
easily obtain the under-cut photoresist profile which is crucial to reliable sample
fabrication. Intense research over the years has led to several recipes to achieve
good undercuts with contact lithography. The most popular technique is the triple-
lay 61' method13 which uses two photoresist layers and one thin metal film layer

separating the two resist layers. In this technique, two UV exposures are required.

15

The bottom resist layer is exposed to UV without a mask (first exposure) and then
several hundred A of Al or Cr is thermally evaporated onto it. A Cr film is
preferred because photoresist developer 4522, which is a potassium hydroxide
solution(KOH), etches A1. A thin top layer of photoresist is spun on following the
metal thermal evaporation. Then the mask pattern is transferred to the top
photoresist layer (second exposure), which then developed. The opaque metal film
protects the bottom resist layer during this exposure. The Al / Cr film is then
etched away and the bottom layer of photoresist which was previously exposed is
developed to form an under-cut profile in this triple-layer system. The advantage
of this method is that the under-cut profile can be well controlled by the length of
the second development; the disadvantages are that it takes more steps than the
single layer resist method and can leave more residues on the substrate surface
after lift-off.

Instead of using the triple-layer method, we used a single photoresist layer and
a “chlorobenzene soak” of the photoresist to achieve the under-cut on profile in
contact lithography. 12 After UV exposure of the photoresist-covered substrate,
the substrate is soaked for eight minutes in chlorobenzene, which hardens the
positive photoresist which is not exposed to UV source, but has little effect on the
exposed photoresist area. This hardening is proportional to the time which
substrate is left in air after soaking and before its development. If it is developed
immediately after the chlorobenzene soaking, only several seconds in the
developer produces a faint image of the pattern; by contrast, it takes as long as 40
seconds to get a faint image if it is kept in air over night after chlorobenzene
soaking. After this partial development, the sample is processed by projection
lithography. The procedure for projection lithography is the same as described
previously, except that the exposure time is 45~50 seconds for the 100X objective

lens, 50% longer than before, because the photoresist surface is harder after

16

chlorobenzene soaking. The photoresist is then developed for 60~70 seconds.
Now that the mask pattern has been transferred to the photoresist layer on the

substrate, it is ready for the next process—metalization.

2.3 Metalization—Thin Film Deposition
2.3.1 Substrate cleaning—Reactive Ion Etching(RIE)

In thin metal film deposition, one is often concerned about the adhesion of the
evaporated metal film to the substrate. Usually metal films cannot form a strong
chemical bond with the substrate due to interfacial contamination from residual
photoresist. One solution is to install an ultra-high vacuum electron-beam
evaporator with in-situ plasma cleaning facilities. However, in our lab, a thermal
evaporator operating with a simple diffusion pump is used. Prior to the metal
deposition the substrate is cleaned of photoresist residue in a reactive ion
etching(RIE) system14 for 30 seconds with 02 base pressure = 50 mtorr and power
= 19 watts. The working principle of RIE is that 02 forms a reactive plasma and
chemically reacts with residues on the substrate. There is no evidence that this
short time RIE cleaning affects the photoresist profile. Within 10 minutes of RIE
plasma cleaning, the substrate is put into the evaporation chamber. This cleaning
process is crucial to the adhesion between the submicron-sized samples and
substrates.

In order to further improve adhesion between A1 or Au and a glass-like
substrate, we find it necessary to put a thin Cr layer between the sample and the
substrate. The Cr layer is usually about 5~8 nm for samples prepared in our
thermal evaporation system, and this has a negligible effect on the electron
transport properties measurement because it is much thinner than the sample

thickness of 200 ~ 300 nm

17

2.3.2 Metal Thermal Evaporation

In our lab, metalization for sample fabrication is done in a diffilsion pumped
vacuum system with a LNz coldtrap. The basic structure is shown in Fig. 2.5.
This thermal evaporator has one rotating stage with four source boat positions, so
we can evaporate up to four different materials on the same substrate without
breaking vacuum. In this way, we can fabricate samples while keeping their
interfaces as clean as possible. With the coldtrap filled with liquid nitrogen, the
base pressure is 1x10“7 torr. Usually the pressure rises to 2x10'6 torr during
evaporation of metal films. Tungsten boats are used to evaporate Al and Au. A
calibrated crystal thickness monitor, cooled by water, measures film thickness
during deposition. A shutter is carefully positioned between the source boat and
the sample so that the crystal monitor will never be blocked. Depending on the
location of the monitor, the sample film thickness may differ from the thickness of
the film on the monitor by a “tooling factor”. The tooling factor is determined by
comparing the reading of the crystal monitor and the thickness of a test sample,
measured by a Dektak 11 surface profile. The deposition rate is about 1 nm/sec for
Al and 0.1 nm/sec for Au or Cr. It is believed that fast deposition will produce
purer metal films because less contamination can be incorporated into the film.
However, fast deposition requires a higher boat temperature which raises the
pressure during evaporation. The Cr source is a Cr-impregnated W-rod15 so no
boat is needed for the Cr evaporation.

During the deposition of Au, the substrate's temperature rises to about 100°C
due to radiation heating from the hot boat without a Cu heatsink. Such a
temperature change is not a concern in sample fabrication because STM and
AF M's images indicate that metal film's morphology is not dramatically affected

by it.16

 

 

Heat sink (Cu block)
to keep resist cool

\ Crystal Monitor
Shutter

 

 

 

 

Source Boats

Figure 2.5 (Top) Photograph of the thermal evaporator, Coating System E306A,
made by Edwards High Vacuum International, Edwards, England. (Bottom)
Schematic block diagram of the thermal evaporator.

19

2.3.3 Thermal Deposition of Silicon Monoxide

In fabricating samples for electron beam resistance imaging, an insulating layer
has to be laid down just underneath the metal sample, and this is done by thermal
evaporation in the same vacuum chamber as the subsequent metal evaporation.
Silicon dioxide is used as an insulating layer by thermally evaporating silicon
monoxide in an 02 environment at a pressure of 1x10”4 torr.

A tungsten boat is used to evaporate silicon monoxide powder. Because silicon
monoxide is an insulator with very poor thermal conductivity, radiation from the
boat rather than conduction heats the silicon monoxide. This means that the
tungsten boat is very hot and is an intense radiation source during the deposition.
It is necessary to surround the boat with thermal shielding made of 0.01 inch thick
stainless steel shim stock in order to keep the vacuum chamber cool. Also, a one
inch diameter, half inch thick copper cylinder is placed on the back of the substrate
as a heat sink to keep the substrate cool. Otherwise, the photoresist will crack due
to overheating during silicon monoxide deposition. The deposition is carried out
in an 02 atmosphere with the pressure just above 1x10‘4 torr. Before admitting
the 02, the silicon monoxide outgased for several minutes with the shutter
covering the sample. The vacuum valve to the diffusion pump is then partially
closed and 02 gas is admitted through a needle valve. The pressure in the chamber
is maintained at 1x10'4 torr by adjusting the valve to the diffusion pump. The
deposition rate is very slow, less than 0.1 nm/sec because of the difficulty in
heating the silicon monoxide. As silicon monoxide vapor condenses on a cool
substrate in an oxygen environment, it becomes silicon dioxide. As a result, this

passive layer is 700~1000 A thick SiOx with l< x _<_ 2, which serves well as an

20

insulating layer with a resistance larger than 20 M!) because the resistance of the
sample is about 20 [2.

It is dangerous to use a diffusion pump to pump 02 gas because the hot silicon
or carbon-based oil can react explosively with the 02. To be safe, one should use

a PFPE type diffusion pump oil (a fluorine-based oil) which is inert to oxygen gas.

2.4 Electron Beam Lithography by SEM
2.4.1 Comparison of E-beam Lithography and Photolithography

The principle of electron beam lithography is similar to that of contact
photolithography schematically shown in Fig. 2.1 except that electron beam
exposure is used instead of UV exposure and the resist layer is e-beam sensitive
rather than photon sensitive. A UV photon is neutral and has kinetic energy of
only a few eV, so its interaction with a polymer is relatively simple. However, an
electron is charged and is accelerated to typically 30 keV in a SEM, so its
interaction with an e-beam resist, such as polymethylmethacrylate (PMMA) is
very complex, involving the production of X-rays, and backscattered and
secondary electrons, as shown in Fig. 2.5. These differences between e-beam and
photolithography determine their advantages and disadvantages, as well as their
resolution and applications.

Cost: An electron with an energy of a several keV has a mean fi'ee path in air
of a few microns. Therefore, a vacuum chamber is needed for the electron beam in
a SEM. Also, an electron beam in a SEM is focused with an expensive magnetic
lenses. In contrast, a UV photon can travel in air for long distances. An uv light
rays are relatively easily focused and collimated with quartz or glass lenses. As a

result, electron beam lithography often costs more than photolithography.

21

Resolution: The resolution of electron beam lithography is limited by the
beam spot size of about 3 nm-20 nm and by the effective interaction volume in the
sample, which depends on the substrate properties. If a substrate is electron-beam
opaque, there will be large flux of the backscattered electrons and X-rays,
producing an exposed region of resist about 100 nm diameter for a 30 kV electron
beam. In order to achieve the minimum exposure spot size in e-beam lithography,
a resist layer has to be thinner than 100 nm and the substrate has to be electron-
beam transparent in order to reduce the back-scattering electron effect as much as
possible. Photolithography's resolution is usually limited by the wavelength of UV
photons to about 0.5 um.

Obviously, the lift-off technique requires that resist layer is thicker than the
metal film. In photolithography, the resist layer is usually lum thick so that the
minimum linewidth obtained with single layer resist technique is about 1pm. In
electron beam lithography, the effective interaction region (~ 100 nm) is much
greater than the spot size of electron beam (~ 6 nm), hence, the minimum
linewidth obtained with single thick layer resist technique is about 100 nm. (Many
people get 30 nm lines using thin layer resist with dry etching.) In addition, the
effective interaction region is a droplet-like shape and naturally produces an under-
cut profile in electron beam lithography even using single resist layer method.

Throughput: E-beam lithography is a serial process while contact lithography
is a parallel process. Electron beam lithography writes directly on resist without a
mask. The disadvantage is that it takes a long time to write a large area with
complex patterns; also, e-beam lithography requires pattern alignment of 0.1um
for multipattem exposures. These are the challenges facing electron beam
lithography specialists in the integrated circuit industry. Fortunately, in this thesis
work, it is relatively easy to fabricate the samples needed because of the simple

patterns used.

22

e-bea

<i= PMlVIA layer

 

<l==| Si Substrate

 

Figure 2.6 Schematic diagram showing the region of interaction between a high
energy electron beam and 3000 A thick e-beam resist layer,
polymethylmethacrylate (PMMA). Such a droplet-shaped interaction volume
produces a natural undercut profile for electron beam lithography if the e-beam
resist layer is thin.

23

2.4.2 Electron-Beam Exposure

In our lab, electron beam exposure is done with a conventional scanning
electron microscope (181 model SX-40). Initially, a ramp generator was used to
control the electron beam scanning range and speed for writing a single line.
Later, a computer with a D/A board was used to control the x-y scanning coils and
the electron beam blanker during writing of more complex pattern.

The production of sub-um features by e-beam lithography requires careful
attention to details. First, a well focused beam with small astigmatism is crucial
for the production of a sub-micron line. Focusing of the electron beam is
facilitated by a droplet of silver paint placed very close to sample writing area,
which provides a focusing target. Second, the correct exposure dose of electrons is
important. For the 496K, 4% polymethyl-methacrylate (PMMA) used in this
work, the total charge deposited per unit area must be 1.6x10'4 C/cmZ. The dose
is determined by the primary electron beam current, the beam diameter, and the
exposure time which is controlled by the appropriate writing speed. A third
important factor is the SEM's accelerating voltage, which on our machine is
adjustable from lkV to 30 kV. Usually the maximum accelerating voltage is
chosen because a higher accelerating voltage will give smaller beam spot size and
better resolution. In addition, the sample stage should be clamped to the chamber

wall in order to reduce vibration and drift caused by.

2.5 Some Samples Fabricated

As discussed so far in this chapter, there are many techniques available for
sample fabrication. The main concern is how to choose one technique or another,
and how to wisely combine several techniques together. Here I present several

recipes for samples fabricated for different purposes in this thesis.

24

2.5.1 Al/SiOzlAl and Au/SiOzlAl Samples for Resistance Imaging

A sample for the resistance imaging experiment with a scanning electron
microscope is shown in Figs. 2.7 and 2.8. A lum wide metal line made with
projection lithography is separated from an Al substrate by a 0.1 pm thick
thermally evaporated Si02 layer. The Al substrate consists of a 0.5 mm wide,
2500 A thick Al stripe, which is embedded in a 0.8 um thick silicon dioxide layer
of a silicon substrate. Projection lithography and two stages of contact
photolithography are used in the sample fabrication.

The process begins with dry oxidation of Si substrates. Substrates are cut from
a 3" diameter (100) p-type polished silicon wafer with a resistivity of 10 Q-cm.17
Using a diamond cutter, the wafer is cut into 0.5" by 0.5" square pieces. These are
washed in an ultrasonic cleaner with acetone, methanol and de-ionized water in
order, followed by drying with nitrogen gas.

Prior to lithography, a thick native dioxide layer is grown on the silicon
substrates by thermal oxidation in an oxygen environment at high temperature.
The Si substrates are placed in a quartz tube through which oxygen from an O tank
flows. The flow rate of 0 gas is monitored by bubbling the exhaust through a
beaker of water, and the flow rate is set at about 5 standard cubic centimeters per
second (sccm/sec.), which corresponds to several bubbles per second in the water.
The quartz tube and substrates are heated in a tube furnace at 1100°C for 17 hours
while oxygen flows continuously. This procedure produces a 0.7~ 0.8 um thick
silicon dioxide layer which appears greenish under white light. The oxidation time
can be shortened to 3 hours by a wet oxidation process, in which oxygen gas flows
through 95°C hot water before flowing over the substrate. The silicon dioxide
layer grows faster during wet oxidation than during dry oxidation because water

molecules can diffuse through silicon dioxide layer more easily than oxygen gas at

25

the same temperature. In industrial processes, both wet oxidation and dry
oxidation are used to grow high quality passive oxidation layers.

After oxidation, a patterned trench is etched in the SiO and filled with an Al
film as shown in Fig. 2-9. The substrates are coated with Shipley S1811 (25%
concentration) photoresist. The substrates are prebaked at 95°C for 30 minutes in
air to drive the solvent out of the coating photoresist layer. Using an acetate film
negative as a mask, a stripe line pattern is transferred to the photoresist with
contact photolithography as shown in Fig. 2.2. After UV exposure, the photoresist
is developed in Shipley Micro Developer 452 for 50 seconds. The substrate is then
baked at 110°C for 30 minutes to harden the unexposed photoresist for further
processing (the so-called "hardbake"). After cooling, the substrate is placed in a
buffered HF solution for 3 minutes to partially etch away the silicon dioxide
unprotected by photoresist. This chemical reaction is as follows:

Si02 + 4HF 2) SiF4 + ZHZO (2.1)
Buffered HF is made from one part 50% hydrofluoric acid and seven parts 50%
NH3F; it etches SiOz at a rate of about 1000 A per minute. As a result, 3000 A
SiOz are removed from a 7000 A thick Si02 layer in three minutes. Only 3000 A
Si02 are removed because an Al film of that thickness will fill this trench.
Chlorobenzene soaking of the photo-resist is not necessary here because isotropic
etching with buffered HF indeed gives an undercut profile as shown in Fig. 2.9.

The resist-covered substrate is then coated with 2500 A A1 in a thermal
evaporator. After lift-off, a 0.5 mm wide, 2500 A thick Al stripe is embedded in
the thicker silicon dioxide layer. This Al film forms the substrate for samples used
in the resistance imaging experiment.

The reason for using such a metal stripe as a substrate will be explained in
detail in Sec. 4.4.1. Briefly, it is because the high energy electron beam of a SEM

interacts with silicon dioxide and generates electron-hole pairs. This pair

 

Figure 2.7 (a) An optical microscope photograph of a sample line under 400x
magnification. The line width is 1.6 mm. (b) A sample in the sample holder, with
leads attached to the lithographically defined metal films on a 1 cm2 substrate.

27

 
   
  

Top View

Side view

 
 

cross-section

 

 

 

Side View

Al(200nm)\ Si0x(70nm)

Al(300nm)

   

Figure 2.8 Schematic diagram of the sample shown in Fig. 2.7 (b)

28

production generates a large substrate current, which ruins the resistance imaging
measurements. A metal substrate eliminates such effects.

After the Al stripe is laid down in the SiOz, the contact photolithography
procedure shown in Fig. 2.2 is followed. A 1 pm thick S1811 photoresist layer is
spun on the Al stripe and substrate and is prebaked at 95°C for 30 minutes. An
acetate negative mask with the contact pad pattern is then aligned on the
photoresist, with the sample position over the 0.5 mm wide Al stripe. After a UV
exposure, the substrate is soaked in chlorobenzene for 8 minutes to achieve an
undercut profile. The substrate is baked at 75°C for 20 minutes to drive solvent
out of photoresist layer instead of leaving it in air overnight. In doing so, the
processing time is significantly shortened. After cooling, the contact pattern is
partially developed in Shipley developer CD-30 for about 10 seconds until the
contact pattern is barely visible. Then using projection lithography, a 2 pm wide
and 160 um long line is transferred to photoresist. As explained in sec. 2.2.3, the
line width is larger than lum because the substrate is a highly reflecting Al film.
After being fully developed for 60~70 seconds, the photoresist has an under-cut
profile ideal for metalization. Prior to loading the substrate into the thermal
evaporator, the substrate is cleaned by reactive ion etching in 02 gas for 30
seconds with a power of 19 W. Then following the procedure for thermal
evaporation of silicon dioxide and Cr/Al or Cr/Au described previously, 1000 A
SiOz, 50 A Cr and 2500 A A1 or 2000 A Au films are evaporated in sequence. (50
A Cr is unneccessary for adhesion here since we are deporting Al or Au directly on
fiesh SiOZ; it is for the consistence with the previous samples.) After lift-off, the

sample shown in Figs. 2.7 and 2.8 is produced.

29

 

 

 

 

Silicon substrate

 

 

—— Silicon dioxide
dry oxidation

 

 

 

 

 

 

\Photo-resist patterned by

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

contact lithography

-[ , ' ' ‘. Buffered HF etching
Emmy-fl: — Metalization
'5' After lift-off

 

 

 

 

Figure 2.9 The procedure for laying down a metal stripe on a Si/SiOz substrate.

30

2.5.2 Samples for Squeezable Tunnel Junction

In order to study single electron tunneling effects, it is necessary to fabricate
small tunnel junctions with small capacitance. To do this, we make a squeezable
tunnel junction, which consists of two metal stripes on two different substrates,
which are stacked over each other and separated by metal film spacers, forming a
very small gap, adjustable from zero (contact) to 0.5um. The junction capacitance

is related to the width of the metal stripes and their separation as follows:

c = a, .3 (2.2)

Where so is the dielectric constant, A is the surface area of the capacitor,
approximately the square of the stripe line width, and d is the separation between
the two metal surfaces. It is clear that A has to be small in order to reduce a
junction's capacitance because d cannot be larger than 100A for the purpose of
electron tunneling through a vacuum barrier. Two metal stripes with micron and
sub-micron sizes are shown in Fig. 2.9.

The substrates are 1 mm thick, optically flat, polished glass slides ordered fiom
Esco Products, Oakridge, NJ. The micron sized sample is fabricated by contact
lithography and projection lithography, using the procedures described in the
previous sections. All samples were made with 1500 A Au with a thin 50 A Cr
underlayer for improving adhesion. In the following section, I concentrate on the
fabrication of sub-micron sized tunnel junctions using electron beam lithography.

As purchased, the original glass slides are one inch wide and three inches long.
These are cut with a diamond saw into six sample substrates, each one inch long
and 3/8 inch wide with precautions to avoid scratching the polished substrate
surface. The substrates are cleaned in an ultrasonic cleaner with a detergent for

glass, followed by cleaning with acetone and methanol. Next, the substrates

31

 

Figure 2.10 (a) An optical photograph of a micron-sized tunnel junction under
150x magnification; The junction is viewed through one of the transparent glass
substrates. (b) a sub-micron sized bridge for a tunnel junction under 300x
magnification, the sub-micron line at the center is 40 um long and 0.15 um wide.

32

are baked at 200°C for 30 minutes to remove water from their surfaces. Now they
are ready for contact lithography and projection lithography to lie down contact
pads for electron beam lithography samples.

Next, the glass substrate is covered with lum thick photo-resist layer (Shipley
S1811), followed by a prebake at 95°C for 30 minutes to drive solvent out of
photoresist polymer. An acetate negative is used as a mask in contact lithography.
This mask defines two large contact pads leading to the junction area and four 2 x
2 mm2 squares for the mechanical spacers. A chlorobenzene soak is used to
harden the unexposed photoresist to get an under-cut profile for lift-off. After
partial development of the resist for about 30 seconds, the contact pad area are
visible. With projection lithography, a line 200 mm long and 2 pm wide, with a 40
um gap in its center, is registered with the contact pads and exposed. This 40 um
gap is the writing field for e-beam lithography, and a sub-micron line written by e-
beam lithography will fill this gap. After full development for 60 seconds, the
substrate with its patterned resist is placed into the thermal evaporator for
metalization. 50 A Cr and 1500 A Au are laid down as contact pads. After this
metalization, the vacuum chamber is opened, and a mechanical mask made of
stainless steel shim stock with four holes is placed against the substrate. The four
holes match the positions of the four square mechanical spacers. A 0.4 pm Al film
is evaporated and covers only the area of the spacers. After lift-off, the contact
pads have 50 A Cr and 1500 A Au, while the four mechanical spacers have 50 A
Cr and 1500 A Au plus 0.4 pm Al film, much thicker than the contact pads.

Now, electron beam lithography is needed to place a sub-micron sized line
between the two contact pads. For simplicity, a single layer resist method is used
here.

After cleaning, the substrate with contact pads and mechanical spacers is spin

coated with 300 nm polymethylmethacrylate (PIVHVIA) at 4000 rpm for 605. Then

33

it is prebaked at 170°C for 60 min. to drive the solvent out of the resist. Next, a 20
nm Al film is evaporated onto the PMMA to prevent charging during e-beam
lithography. This step is required because the glass substrate is insulating. The
thin Al film is nearly electron transparent and has little effect on SEM imaging of
Au contact pads underneath the PIVIMA. Such a metal coating is not necessary if
the substrate is a silicon wafer with silicon dioxide layer lum thick or less,
because a 30 keV energy electron beam can penetrate through such an oxide into
the Si substrate. A tiny droplet of silver paint is placed very close to the sample
area for adjusting focus and astigmatism.

Now the substrate is loaded onto the SEM sample stage, which is clamped to
the sample Chamber's wall. After the pressure inside the chamber is below about
10'5 torr, 30 kEV high voltage is turned on, and the SEM's filament warms up for
one hour to stabilize the electron beam current before the sample writing. Final
focusing the electron beam is done by imaging a filament of the silver paint droplet
with the minimum beam spot size at high magnification, usually fiom 50 kX to
100 kX. This step is crucial for reliable electron beam lithography. The specimen
current at minimum beam spot size is about 1.5 pA.

Sample alignment is achieved by imaging the two contact pads and the 40 um
gap in the line connecting the pads. At a low magnification of 600X, the two
contact leads are placed horizontally in the middle of the CRT viewing screen.
Then at a magnification of 2100X, the ends of the two contact leads are visible on
the two edges of the screen. This alignment procedure has to be done quickly in
order to avoid an unwanted exposure of e-beam resist during imaging.

Now electron beam writing is carried out by switching the SEM to computer
control. The computer contains the writing pattern(produced with HarvardGraphic
and stored in a data file) and controls the electron beam position and its writing

speed, i.e., its exposure time. A 40 um long. 0.2 pm wide single line is drawn in

34

chroscope

Setpoint
Scan rate
Number of sanples

View angle

light angle

X 0.200 un/diu
2 63.261 nn/div

 

Figure 2.11 An atomic force microscope (ATM) image of an e-beam lithographic
Au line on a glass substrate, imaged by J eeseong Hwang with a NANOSCOPE-III.

9.3 seconds with the specimen current of 1.5 pA. The electron dose for this line is
2x10'4 C/cm2, just over the critical exposure dose.

After electron beam exposure, the substrate is placed in 0.1 Mole NaOH
solution to remove the 20 nm Al coating on the PMMA. Then the sample is
developed for 65 seconds to get a clean profile of a sub-micron sized line. Before .
it is put into a evaporator, the substrate is cleaned in a reactive ion etching(RIE)
system for 30 seconds. 5 nm Cr and 100 nm Au are thermally evaporated onto the
substrate at a deposition rate of 1 A per second. During lift-off, the tiny droplet of
silver paint, as well as the PMMA resist, are removed by acetone. An AF M image

of a sub-micron sample is shown in Fig. 2.11. This high resolution AFM image

35

shows that a high quality Au line with a smooth morphology and sharp edge

definition is obtained by electron beam lithography and thermal evaporation.

2.5.3 Sample for Crack Junction

Among those samples fabricated lithographically, a sample used as a crack
junction in the Coulomb blockade experiment is the simplest. The sample shown
in Fig 2.13 is a single 30 um wide, 5 cm long line laid down by contact
lithography. The substrate is cut from a 1.2 mm thick, 1" by 3/4" glass slide.
There are two holes with a center to center separation of 3/ 16" which are drilled by
1/8" diameter ceramic tile drill. After a standard cleaning procedure, the pre-
drilled substrate is coated with a 1 pm photoresist layer. After a softbake at 95°C
for 30 minutes, a pattern in an acetate negative mask is transferred to the
photoresist by optical contact lithography. After development, the substrate is
hardbaked at 115°C for 30 minutes, then loaded into the thermal evaporator for
metalization. Again, 5 nm Cr film is used for improving the substrate adhesion
before 45 nm Au film is deposited. After lift-off, a single 30 um wide, 5 cm long
line stretches along the glass bridge between the two holes.

In the crack junction experiment, the metal line is broken in liquid nitrogen
vapor by making a crack in the glass substrate perpendicular to the metal film line,
connecting the two holes in the substrate; thus forming two electrodes for
tunneling. As described in chapter 5, the crack is made by bending the substrate,
and the broken metal line forms a tunnel junction whose gap can be adjusted by
adjusting the stress on the substrate. A typical crack junction sample with a crack
in the glass substrate is shown in Fig. 2.13. Because of the strong reflection from
the metal film, the break in the metal line is invisible, even though the crack in the

glass substrate is easily seen.

36

1/8" predn'lled holes

5 .31. t.
T—‘t t
l<— 1" —\>l\ Crack line

Sample

 

 

 

 

 

 

Figure 2.12 Schematic layout of a sample for a crack junction.

 

Figure 2.13 Optical microscope photograph of a broken Au line on a cracked
glass substrate. The Au line is 30 um wide. Although the crack in the glass is
clearly visible, the break in the Au line cannot been seen in this photo.

37

References for chapter 2

 

y—n

Computer Shopper Mar. 1994.

N

A product of Artype Inc., FT Myers, FL.

U)

Instructions from Manufacturer, Kodak Company.

.5

W. H. Henkels, Ph. D. thesis, Cornell University, 1974 (unpublished)

LII

John Michael Warlaumont, Thesis, Cornell University (1980).

6 Reinhard, D.K. Introduction to Integrated Circuit Engineering. Houghton
Mifflin company, 1987, Append. A9.

7 SHIPLEY COMPANY inc., Newton, MA. 02162
8 ORIEL corporation.

9 Fused silicon substrates coated with Cr or Fe203 films are commercial
available from Towne Laboratories Inc., NJ.

10 K.L. Tai, R.G. Vadimsky, C.T. Kemmerer, J .S. Wangner, V.E. Lamberti, and
A.G. Timko, J. Vac. Sci. T echnol., 11 1169, 1980.

11 Mark D. Feuer and Daniel E. Prober, IEEE Trans. on Electron Device, Vol ED-
28, 1375, Nov. 1981.

12 Model PME metallurgical microscope, Olympus Optical Co., LTD, Shinjuku-
ku, Tokyo, Japan.

13 Hunt, Brain Dominic, Thesis, Cornell University, 1985.

14 RF Plasma Products, Plasma-Therm I. P. Inc., USA.

15 Johnson. Mathey, Seabrook, NH 03874

16 Jeeseong Hwang and M. A. Dubson, J. Appl. Phys. 12 1852, 1992.

17 Wacker Siltronic Corp. Portland, Oregon.

Chapter 3

E-beam Induced Contamination and Efforts to Stop It

A sample surface bombarded by an energetic electron beam in a SEM quickly
develops a contamination layer made up of polymerized hydrocarbons and other
molecules from backstreaming diffusion pump oil and the chamber walls. This
surface contamination is a dark, electrically conducting, tar-like substance which
strongly absorbs secondary electrons and makes SEM images appear dark. In
attempting to overcome this problem, we have tried several different techniques,
including replacing the carbon-based diffusion pump oil with perfluoropolyethers
(PFPE) fluids, adding a cold shroud around the sample, and installing a gas jet.
Use of the fluorine-based pump oil and the cold shroud substantially reduced the
rate of sample contamination, but did not eliminate the problem. Our results
indicate that the gas jet eliminates the build-up of carbonaceous contamination, as
evidenced by the appearance of SEM images and measurements of the secondary
electron coefficient, but in place of the tar-like residue, the gas jet appears to

produce a bright, non-conducting surface layer of unknown composition.

3.1 Contamination Problem and Decontamination Techniques

Hydrocarbon molecules on the sample surface in a scanning electron
microscope (SEM) are polymerized under action of the electron-beam and form a
dark, conducting contamination layer. The details of the chemistry of formation of
such contamination remain unknown. Many researchers have made great efforts to
eliminate such contamination using different strategies. Conru and Laberge report

that contamination rates (determined by measuring the volume of contamination

38

39

spots) decrease by a factor of 40 when perfluoropolyethers (PFPE) type diffusion
pump oil replaces conventional silicon- and carbon-based diffusion pump oils.l
Duerr and Ogilvie discovered a gas jet technique to efficiently remove light
element contamination in an electron probe microanalyzerz. The review article by
Miller gives a systematic description of different decontamination techniques
attempted by a dozen different research groups.3

Contamination by polymerized hydrocarbon molecules is a problem in our
resistance imaging experiment primarily because the contamination layer is
conductive and shorts the sample to its metallic substrate when the sample is
exposed to the electron beam. Here I describe some decontamination techniques
used in our experiment and their effects on samples, in the order of their

implementation.

3.2 PFPE Type Diffusion Pump Oils

The instrument used in this experiment is an International Scientific
Instruments (ISI) Model SX-40 SEM, with a pumping system that consists of a
mechanical roughing pump, a diffusion pump with a liquid nitrogen (LN2)
coldtrap and a Zeolite baffle between the roughing pump and the diffusion pump
to prevent backstreaming from the roughing pump.

The diffusion pump oil originally used in the diffusion pump is Santovac-S, a
five-ring polyphenyl ether fluid, whose structure is shown in Fig. 3.1.4 It is well
known that such benzene ring fluids are polymerized under bombardment of the
electron beam in a SEM, leaving a tar-like residue on the specimen surface. This
hydrocarbon contamination layer has a strong secondary electron absorption

coefficient so that it looks dark in SEM images obtained fi'om the secondary

4O

electron signal. Moreover, such a contamination layer is conducting and can short

out electrically conducting components of a sample.
O— o (O—o)<>
3

Figure 3.1 Five-ring phenyl ether structure of Santovac-S diffusion pump oil.

Conru and Laberge have demonstrated the seriousness of this oil contamination
problem in a SEM. They found that a cone of contamination, a 1.6 pm high and
0.4 um wide, built up on a cleaved Si wafer after 5 minutes in the spot mode
(beam stationary on sample) with an electron beam of 25 keV and a specimen
current of only 5 pA.1

Diffusion pump oils are the main source of contamination of the specimen in a
SEM chamber, because such oils contain long-chain hydrocarbon molecules. In
order to reduce hydrocarbon contamination in a SEM, alternative diffusion pump
oils have been sought to replace the benzene-based oils. Fortunately, such
alternative pump oils have been found. They are perfluoroakyl-polyethers,
completely fluorinated fluids, which are called PFPE (perfluoropolyethers) for
short. A typical PFPE structure, shown in Fig. 3.2, consists of 20 to 30 repeating

C3F6O groups.

F —(C|F - CF2- 0),, c213S

CF3

Figure 3.2 Fluorochemical Structure, Krytox perfluoroalkylpolyether.

41

Holland et al. found that PF PE type fluids used in pumps are not polymerized
under an energetic electron or ion beam in high vacuum, thus avoiding specimen

contamination.5

The claim is that the fluorine-based polymers unzip under the
electron beam and form volatile species that desorb and are pumped away. All
other fluids smeared on a metal substrate and placed under electron bombardment
were found to form an insoluble tar-like residue. Moreover, even under ionized
gas conditions, PFPE is not polymerized by oxygen or other gases, with the
exception of pure hydrogen.

Because of the convincing evidence of the elimination of oil contamination by
the use of PF PE fluids in a SEM, we decided to replace Santovac-S used in our
diffusion pump by a PF PE oil, Krytox 1625, whose structure is shown in Fig. 3.2.

Replacing the diffusion pump oil in our SEM required that the system be
thoroughly cleaned in order to eliminate all traces of the old oil. The entire
pumping system and sample chamber of the SEM was dissembled, and the
diffusion pump was cleaned by trichlorethylene (TCE), acetone, and methanol; all
pipes, valves, and chamber walls were cleaned thoroughly with acetone and
methanol. Finally, the new pump oil Krytox 1625 was added and the system was
reassembled. A

A Micromaze foreline trap, made by Kurt J. Lesker company, was installed for
blocking the backstreaming of hydrocarbon molecules from the mechanical pump.
The Micromaze trap uses a ceramic, highly porous material which is non-metallic,
inorganic and inert, and has a surface area of 200 m2/ g with internal pores of
diameter 40-60 A. The Micromaze trap must be heated under vacuum at monthly
intervals to purge it of oil.

After the SEM was reassembled, a test of the pumping speed of the new pump
fluid was carried out by monitoring the pressure vs. pumping time. It was found

that the diffusion pump with the PF PE fluid works as efficiently as with Santovac-

42

5, with no significant decrease in its pumping speed. Then, a contamination test
was done with a fresh sample of Al film thermally evaporated on a silicon
substrate. After exposure to a 2 keV electron beam for a couple of minutes with
the beam in spot mode and a beam current of 10 nA (conditions similar to those of
the resistance imaging experiments) a dark spot appeared on the metal film. Thus,
the replacement of the old type diffusion pump oil had not eliminated the
contamination problem. A likely reason for such an unhappy outcome is that there
are other sources of hydrocarbon contamination such as outgassing of plastic and
rubber materials in the instrument such as "O"-rings, specimen mounting material
and electrical insulation, etc.. Therefore, other techniques were needed to further
reduce hydrocarbon contamination. A cold shroud around the sample was used to
reduce the partial pressure of hydrocarbon molecules and improve the vacuum

near the specimen in the SEM chamber.

3.3 Cold Shroud

Our SEM's base pressure is usually in the range of 10'5 - 10‘6 torr when the
liquid nitrogen coldtrap on the diffusion pump is filled. At such a pressure, a
specimen surface is struck by 1- 10 monolayers of contaminant molecules every
second. To eliminate hydrocarbon contamination altogether, one could switch to
an ultra-high vacuum system. However, because of the high cost and complexity
of an ultra-high vacuum system, this solution is seldom feasible.

Fortunately, some alternative solutions are available. One of them is to install
a liquid-nitrogen-cooled cold plate very close to the specimen surface. Such a cold
surface acts as a cryo-pump and reduces the partial pressure of hydrocarbon and
water molecules, but has no effect on light, non-polar molecules such as N2, 02,

and CH4. Flavio and Garuli demonstrated a striking reduction in contamination

43

with such a cryopump.6 Their results showed that almost no contamination could
be detected with their design of cold trap in their electron microprobe.

Fig. 3.3 and Fig. 3.4 show the cold shroud, which consists of an LNz-filled
copper tube and an attached copper plate. The large cold surfaces help to improve
vacuum. The ends of the coiled copper tube are soldered to two double-walled
stainless steel dewar tubes which are welded to the chamber wall. Liquid nitrogen
is poured into one dewar tubes and N2 gas is vented from the other.

A copper plate, located above the specimen stage, is attached to the copper pipe
by a copper adapter to ensure high thermal conduction between them. The
electron beam passes through a small hole in the plate. In order to maximize the
cold plate's solid angle as seen by the sample stage, one side of the plate is bent
down around the specimen stage, without significantly blocking the secondary
electron detector.

When the cold shroud and the diffirsion pump coldtrap are filled with liquid
nitrogen, the base pressure of the chamber obtained at a penning gauge located
away fiom the specimen stage is 1.0 x 10'6 torr. We believe that the local pressure
near the specimen stage is lower than the reading at the penning gauge. Moreover,
the partial pressure of water and hydrocarbon molecules is believed to decrease by
orders of magnitude because the temperature of the cold shroud (- 150 °C) is well
below their freezing point. It takes approximately 20 minutes for the cold plate to
achieve thermal equilibrium after pouring liquid nitrogen into the copper pipe, and
the copper pipe must be topped off with LN2 every 30 minutes. Prior to opening
the sample chamber to air, the copper pipe must be warmed by blowing dry
nitrogen through for several minutes, in order avoid condensation of water on the
pipe.

The efficiency of the cold shroud as a cryopump was measured by monitoring

the pressure while all valves connecting the chamber to the external pumps were

44

Gun Column

 
    
   

Copper plate
SE Detector

,, Coiled copper tube

 

 

SEM Chamber

Figure 3.3 Arrangement of the cold shroud in the sample chamber of the SEM

 

 

Figure 3.4 Photograph of the cold finger installed in the wall of the sample
chamber.

45

closed. Pressure vs. time is plotted in Fig. 3.5, which shows that the presence of
the cold finger reduces the pressure by a factor of two.

After installation of the cold shroud, another test for contamination was carried
out with a fresh sample of Al film, 2000A thick, thermally evaporated on a silicon
substrate. The result was that the cold shroud significantly reduced, but did not
eliminate the contamination. So far, we had replaced the difiusion pump oil by
PFPE fluid, installed a foreline trap, and installed a cold shroud very close to the
specimen surface. All of these measures helped to reduce the hydrocarbon
contamination rate, but not enough to carry out the resistance imaging experiment.

It was necessary to search for other solutions.

3.4 Decontamination Using an Gas Jet Technique

Decontamination by the use of a gas jet directed at the point of impact of the
electron beam on the specimen has been developed by other researchers.7’8 The
gas used may be 02, N2, air, or Ar, and must be at a pressure <10'4 torr to be
compatible with SEM operation. Castaining and Descamp directed a fine stream
of Oz and N2 gas at the point of electron beam bombardment, and showed that the
carbon concentration on the surface, measured by X-ray spectroscopy, decreased
sharply once the gas jet was on, and remained at a low leve19. When the gas jet
was turned off, the carbon intensity rose linearly with time, indicating the buildup
of contamination on the sample surface. 02 gas was the most effective. Their
results showed clearly that the gas jet not only prevents the buildup of
contamination but also removes any previously deposited material. Borile and
Garulli found that oxygen and air are effective in preventing contamination, but
not argon or nitrogen.6 Other work suggests that nitrogen, room air, as well as

10,11

other inert gases are effective, and that water vapor has a strong

Pressure (torr)

46

 

‘4.OE‘4-Irl'I'I'f*t‘1‘I'I
3.05-4------s--~-~;-----~:—-~~-5 ------ 5 ------ 2 ------ 3 ------ ¢-;.:sof~-

2.0E-4-~--§ ...... ...... ...... 13., ...... ______ ,,,,,, ______

 

 

 

 

1 .OE-4

 

 

 

 

00E0L1-1-1-1-L+n-n-n-n-

0 10 20 3O 40 50 60 70 80 90100

Time (s)

Figure 3.5 A plot of pressure vs. time while the SEM chamber is shut off from the

pumping system.

47

decontamination effect.12

We installed a gas jet, similar to Castaining's, in our SEM as shown in Fig. 3.6.
The flow of gas is controlled by a needle valve, a NUPRO B2-JNA with a 0.094
inch orifice and a 3-degree taper on the needle. The valve connects to a 1/8-inch
copper pipe by a Swagelok fitting. A 22-gauge stainless steel syringe tube was
glued into the other end of the 1/8" copper tube with a vacuum compatible epoxy.
The position of the fine SS tube can be adjusted by sliding the Cu tube horizontally
through a quickconnect vacuum seal. The fine SS tube is bent so that the gas jet is
pointed at the point of impact of the electron beam on the specimen. Fig.3.4 also

shows the gas jet tube inside the SEM chamber.

Gun [Column
fig

SE Detector Copper plate

 

 

 

Air, 02 or Ar gas \ '
"a: r
{i o-ring seal 2'

 

 

 

 

 

 

II— I
B _ 7; Copper Pipe
A 321.2.
Needle valve , ‘
I” in“ :; an,

 

epoiry -

sea

1/8" Cu 1 ‘

p be/ SEM Chamber
22 gauge SS tu

Figure 3.6 Schematic diagram illustrates the gas-jet technique: (A) 1" diameter
clamp connector; (B) 1/8" quickconnect.

48

Again, a decontamination test was carried out on a fresh Al film on a silicon
substrate. The build-up of surface contamination was monitored by measuring the
specimen current while the electron beam was focused on a stationary point on the
sample (spot mode) or a rastered over a small patch of the sample. As explained in
Sec. 4.3.1, the specimen current Ispec, the primary beam current 13, the secondary
electron current ISE, and the backscattered electron current IBS are related by 13 =

Ispec+ISE+IBS- Measurement of 13 and ISpec thus allows one to calculate the sum

I [BS 18 _Ispec

of SE and BS coefficients 5+1] = %+—= . The SE Coefficient 8 is

B IB 18

 

extremely sensitive to the level of surface contamination. In general, clean
surfaces have a larger 5 (appear bright in a SE image) and contaminated surfaces
have a smaller 8 (appear dark).

The procedure for using the gas jet is first to pump the SEM chamber down to a
base pressure of 1><10'6 torr with the cold shroud and diffusion pump cold-trap
filled with liquid N2. Then, 02 or Ar gas is admitted through the needle valve,
which is adjusted until the pressure rises to 4><10"4 torr. The sum 5+r] for Ar-gas
jet and Oz-gas jet with a 2 keV electron beam is plotted vs. time in Fig. 3.7. The
data show that the ratio rises more rapidly with a 02 jet than with a Ar jet, even
though the final values are very close. With the gas jet on, 5+r] remains high and
darkened regions on the sample surface do not occur. With no gas jet, 5+1] falls
continuously as the surface contaminates and the SEM image becomes more and
more dark. We believe, therefore, that both the 02 and Ar gas jets prevent
carbonaceous contamination. However, with the gas jet, the ratio 6+r] becomes
too high, higher that previously reported for clean surfaces (for clean Al, 5+1] =
1.2) , indicating that some kind of surface layer is forming, but not a conducting
carbonaceous one. The bright layer is transparent when viewed with optical

microscopy, and our resistance imaging data (Chap.4) indicates that the bright

(lb-Is)/Ib = 8 :t n

2.0

1.5

1.0

0.5

0.0

Figure 3.7 8+1] vs. time for an Al film with a 2 keV electron beam at a pressure of

 

49

 

""'-'I ' U "U'. 'V'I'V'I I I "I'. ' """'

. 250 nm thick Al on Si02

 

For a 2 keV electron beam

P. ...........................................................
O

    

- ...........................

 

 

 

 

 

.
--n__g-- l I‘ll-l --_n_--n lALl-i --n----

 

 

 

1‘2345 10 234 1.0623

Time (s)

4><10'4 torr: (a) Oz-jet; (b) Ar-jet

50

layer is non-conducting. One might argue that A1203 is forming in the highly
reactive oxygen plasma formed by the Oz jet and the e-beam, but then it is hard to
understand why a similar bright layer is formed with a non-reactive Ar jet.

An SEM image of decontamination spots formed under the 02 gas jet is shown
in Fig. 3.8. In Fig. 3.8 (a),which was imaged with a lkeV beam, the bright stripe
is an Al film and the darker background is the oxidized silicon substrate (0.8 um
thick SiOz). Because the secondary coefficient 5 of Al is higher than that of
silicon for a 1 keV electron beam, the Al film is brighter than the substrate in this
image. The two bright squares were made by a 2 keV electron beam in scanning
mode with the 02 jet on. The dark dot on the Al film is a hole in the film
revealing the SiOz substrate. We believe that the dark regions surrounding the
bright squares are hydrocarbon contamination. We do not know the composition
of the surface in the dark regions and in the bright squares because of our lack of
in situ analytical capability, such as Auger spectroscopy or X-ray spectroscopy.
Transporting the sample for Auger analysis would probably yield inconclusive
results because of contamination during transportation. In F ig.3.8 (b), another
bright square was produced by a 2 keV electron beam with 02 jet on the surface of
the Si substrate, and this bright square is also surrounded by a dark region. This
image was taken with a 10' keV electron beam, an energy at which 8A] is very
close to 58i , so that the Al stripe no longer appears brighter than the substrate.
However, the bright squares appear similar in the two SEM images, indicating that
the bright areas are not simply clean surfaces.

A highly undesirable result of the 02 gas jet technique is that the average
lifetime of the tungsten filament of the electron gun is reduced fiom 100 hours to
10 hours due to oxidation of the filament. For this reason, we used the 02 jet on

only a few occasions and then switched to the Ar jet. One solution to this problem

51

 

Figure 3.8 SEM images of decontamination spots: (a) Al film on an oxidized Si
substrate (image taken with a lkeV beam) (a) One more spot made on the Si02
substrate (image taken with a 10keV beam).

52

would be to keep the filament in a separate high vacuum chamber, as is done in
field-emission SEM’s.

No clear microscopic picture exists of how the gas jet modifies the surface
chemistry. Borile7 used ion milling and Auger analysis to measure the depth
profile of oxygen and carbon in an iron sample that had been imaged while under
an Oz gas jet. He observed an enhanced oxygen concentration down a depth of
45A. Evidently, use of the 02 gas jet impregnated the sample surface with
oxygen. Borile's conclusions are consistent with the speculation that the bright
areas on our Al samples are A1203, and yet there remains the puzzle of why bright
areas form with the Ar gas jet. In any case, the bright surface layer is non-
conducting, and therefore, should not significantly affect the results of our
resistance imaging experiments.

In summary, we have attempted to eliminate carbonaceous contamination in our
SEM with increasingly heroic measures. We replaced the diffirsion pump oil by a
PFPE fluid, then installed a liquid N2 cold shroud around the sample, and finally
installed a gas jet. Use of PFPE pump oil and the cold shroud reduced, but did not
eliminate, the contamination. The gas jet apparently eliminated carbonaceous
contamination, but produced a "bright" non-conducting contamination of unknown

composition.

53

References for chapter 3

 

1 H. w. Conru and P. C. Laberge, J. Phys. E. s, 136 (1975).

N

J. S. Duerr and R. E. Ogilvie, Analytical Chemistry, 44, 2361 (1972).

U)

D. E. Miller, Scanning Electron Microscopy, Vol. 1, 513 (1978).

4 John F. O'Hanlon, A User’s Guide to Vacuum Technology, 2nd ed., John Wiley
& Sons, Inc. New York, 1988, p. 220.

5 L. Holland eLaL, " T he behavior of perfluoropolyether and other vacuum fluids
under ion and electron bombardment', Nuc. Inst. Methods, 111, 555-560 (1973).

6 Flavio Borile and Alberto Garuli, X-ray Spectrometry, vol. 7, 125 (1978).

7 J. Rouberol, M Tong and C. Conty, GAMS Conference in Paris, France, 8 June
1966.

8 S. H. M011 and G. W. Bruno, Gas jet Sample decontamination in the electron
microprobe, EPASA 2, Paper No. 57.

9 R. Castaining and J. Descamps, C. R. Acad. Sci, 218, 1506 (1954).

10 G. W. Bruno and S. H. Moll, Second National Microprobe Conference, Boston,
Mass., June 1967.

11 R. Theisen, "Quantitative Electron Microprobe Analysis, " Springer, Berlin,
1965.

12 A. J. Campbell and R. Gibbons in "The Electron Microprobe," T. D.
McKinley, K. F. J. Heinrich, and D. B. Wittry. Ed., pp 75-82, 1966.

Chapter 4

Resistance Imaging with a SEM

4.1 Abstract

A technique, similar to one described by Long and Slichter], has been
developed to measure electrical resistance variations along lithographic metal
lines. In this technique, called electron beam resistance imaging (EBRI), an
electron beam from a conventional scanning electron microscope is used to inject
current into a metal line sample which has one end attached to ground through a
current meter and the other end connected to a voltmeter. Current 1(x) and voltage
drop V(x), where x is the distance fi'om the point of current injection to the end

grounded, are recorded simultaneously while the electron beam is scanning along

the thin metal film line. The resistance R(x) is calculated by R(x) = 38)) . With

this technique, we have measured R(x) vs. x along Au and Al lines 1 pm wide,

 

150 um long, and we have achieved a spatial resolution of 0.5 pm and a resistance
resolution of 0.2 Q. We expect that the technique can achieve 0.1 pm and 0.05 0
resolution. We have studied the onset of failure of metal lines by electromigration
and local heating effects by imaging the resistance and then slowly increasing the
external current to the point of failure, recording the evolution of the resistance at
hot spots. In addition to the linear ohmic voltage from the specimen current, we
observed an extra voltage which we suspect is generated by the bombardment of
the electron beam on the interface between the metal and semiconductor substrate
(the barrier electron voltaic effect) at some pinholes produced by electromigration

in the samples.

54

55

4.2 Introduction

The steadily increasing density of transistors in integrated circuits has been
achieved by reducing the size of each transistor and the metallic circuit lines which
connect them. The reliability of those conductor lines determines the lifetime of
the chip. In order to fabricate more reliable conductor lines, it is necessary to
understand the mechanism of the failure of those conductor lines.

When there is a high current density through a conductor line, there is a strong
electron wind force in the direction opposite to the current. This electron wind
strongly interacts with the ions or defects in the metal lattices and drives those
defects away from their original positions. This phenomena is called
electromigration, and it is the primary mechanism for the failure of conductor lines
under the stress of a high current density. Scanning electron microscopy has been
used to study electromigration by imaging the evolving morphology of conductor
lines under the stress of high current density which causes the formation of voids
and hillocks in the lines.

Here, I describe a technique called electron beam resistance imaging (EBRI),
which uses an electron beam from a SEM as a movable injection current source,
allowing measurements of local sample resistance with sub-micron resolution.
Using this technique, we have measured the local resistance of micron-sized
lithographically fabricated metal lines before and after the stress of a high current
density.

In this chapter, a review of the interaction between an electron beam and metal
samples is presented. The principles of EBRI and the details of the electronic
circuitry are presented. Finally, some data from Al samples are discussed at the

end of the chapter.

56

4.3 Principle and Analysis of Measuring Circuits

4.3.1 Electron Beam Interaction with Metals and Semiconductors

A large number of complex interactions occur when a focused electron beam
penetrates a specimen surface. Among the signals produced are secondary
electrons, backscattered electrons, characteristic and continuum x-rays, Auger
electrons, and photons of various energies. These signals are obtained from a
specific interaction volume within the sample, and this interaction volume strongly
depends on the electron beam energy E0 and the atomic number of the specimen Z.
In fact the resolution of an image from a scanning electron microscope is primarily
determined by the excitation volume and not by the electron beam size.

Electrons having kinetic energies in the range 1-50 keV exhibit very complex
behavior as they impinge on the surface of a solid sample. The energetic electrons
undergo elastic scattering (change of direction with negligible energy loss) and
inelastic scattering (energy loss with negligible change in direction). Elastic
scattering is caused mainly by close collisions with the nuclei of atoms and in this
case significant deviations fiom the incident direction occur. Inelastic scattering is
caused by interaction with the atomic nuclei and with the bound electrons..

Inelastic scattering is primarily responsible for producing signals other than
backscattered electrons. The incident primary electrons interact with the Coulomb
field of the nuclei of the atoms and lose energy by emitting continuum x-ray
radiation. Inelastic collisions also occur between the loosely bound outer electrons
and the incoming electrons, and in this case loosely bound electrons are ejected.
The ejected electrons have an energy typically less than 50 eV and are called
secondary electrons. If these secondary electrons are produced close to the sample

surface and their energy is greater than the surface barrier energy ( a sample's work

57

function of 2-6 eV), then these secondary electrons have a high probability of
escaping from the surface. In contrast, those secondary electrons produced at
depths much larger than 100 A from the surface of the sample are likely to lose
their energy by inelastic collisions before reaching the surface. In some materials,
if the secondary electrons recombine with the holes formed during the scattering
process, a photon is produced in the visible or near-infrared range. Inelastic
collisions can also result in the production of characteristic x-rays and Auger
electrons when the K, L, or M shell electrons are ejected during collision.

Elastic scattering by the Coulomb field of atomic nuclei is the most probable
mechanism of large-angle scattering of primary electrons. The scattering consists
of two parts: (a) Rutherford scattering, whereby a single scattering event results in
a large change of the direction ( greater than 90°), and (b) multiple scattering,
composed of many small-angle scattering events. Multiple scattering may also
result in a large change of direction of the primary electrons. After changing
direction, the primary electrons may travel back to the surface and escape. This is
the process of backscattering. The backscattered electrons leave with somewhat
reduced energy due to inelastic processes. At some depth within the target, the
original direction of the electron beam is lost and the electrons diffuse through the
material at random. The position at which this occurs is the depth of complete
diffusion xd. Cosslett and Thomas have given a rather complete discussion of
scattering theory and experiments in a series of papers.2

In a high atomic number sample, there is considerable (single and multiple)
scattering close to the sample surface and a large fraction of the incoming
electrons are backscattered. In the case of heavy elements, such as gold, diffusion
sets in much nearer the surface than for a light element, such as aluminum. In fact,

the penetration depth (diffusion range) of 10 keV electrons is about 0.1 pm, for Au

58

and 1 pm for Al. Fig. 4.1 is a diagram showing the relationship among
accelerating voltages, density of specimen, and diffusion length of electrons.

When the primary electron beam impinges on the surface of a specimen, there
exists a secondary electron current and a backscattered electron current, while
some electrons absorbed by the specimen flow to ground forming the specimen
current. The diagram shown in Fig. 4.2 illustrates quantitative relationship among
them.

To further characterize these relationships, two ratios 8 and n are defined as

follows:
1..
8 = i (4.1)
[B
n = 11A (4.2)
B

The secondary electron coefficient 8 depends strongly on specimen surface
topology and on surface contamination as well as on the primary beam energy. 8
has been used to characterize specimen surface contamination processes in a SEM.
In contrast, the backscattered electron coefficient 11 is almost independent of the
primary electron energy, is not very sensitive to sample topology, and increases
gradually with increasing specimen atomic numbers. For Al, n = 0.15 while for
Au, r] = 0.5.3 for 30 keV electrons.

It is convenient to use the sum 11 + 8 to monitor the buildup of surface
contamination. n + 8 can be determined very easily by directly measuring both the

primary beam current and the specimen current.

 

5+1] = Isa +1113 = In — [SPECIMEN (4.3)

In 13

59

Density 9 (g/ctn’)

 

 

    

05 I 10 20
;~--::‘A : ”1"L::.;“;“:
I
An 41
I
Diffusion range ()1)
0.1 ' I 0
A——A A, A A. A A annI A LLAI 1.. A—Ll A n L; A
“V I I ITV‘VV' V v 'i' vvvv' v v V 'Ivvv' ——-fi

 

Figure 4.1 Relationship of the diffusion range of electrons and the electrons'
accelerating voltage and specimen's density. A line drawn between the density of
a specimen and the accelerating voltage of the electron beam intersects the
diffusion axis, giving the diffusion length. [Reproduced from the JEOL electron
microscope service manual. ]

60

BS

 

 

 

 

 

 

/ , ._
j A.
I A

Specimen

Figure 4.2 Schematic illustration of the relationship between a primary beam
current 113, specimen current ISPECIMENa backscattered electron current 188 and
secondary electron current ISE as a high voltage electron beam impinges on the

surface of the sample: 13 = IBS +1313 + ISPECIMEN- The shaded area indicates
interaction volume.

61

Variations in n + 8 are due almost entirely to variations in 8, since n is nearly
independent of beam energy and sample surface conditions. Generally, metal
surfaces that are contaminated with hydrocarbons have a low 8 and appear dark in

SEM images, while atomically clean metal surfaces are more bright.

4.3.2 Principle of Electron Beam Resistance Imaging Technique

The goal of this research is to develop a practical technique for measuring
resistance variations along a thin metal film line fabricated by lithography, and to
study the failure of metal lines by electromigration.

F ig. 4.3 illustrates the principle of electron beam resistance imaging. An
electron beam from a scanning electron microscope is used to inject current at a
point x in a metal line. One end of the metal line is grounded through a current
meter, and the other end is attached to a volt-meter. The specimen current created
by the electron beam cannot flow through the high-impedance voltmeter, and
instead flows to ground through the low-impedance current meter. By measuring
specimen current and the voltage drop independently, the resistance R of the
specimen between the point of current injection and ground is determined by R =
W]. As the beam is scanned along the line, the resistance R(x) is mapped out.

Note that when 8+1] = 1, then from eqn. 4.3 the specimen current is zero.
Consequently, the voltage drop is zero and the R cannot be measured. Since
Ispec =In_Iss-Ias’ the specimen current may be either positive or negative,
depending on whether 11 + 8 is greater than or less than one. 11 + 8>1 means that
for every electron entering the sample from the primary beam more than one
electron leaves the surface as a secondary or backscattered electron. In this case,
one should not think of the beam as a current injector, it is really a current

extractor.

62

(a) e-beam curren

<1 X {>
1' s

Specimen current I

 

 

 

 

0
v

‘9

(b) R

 

 

(C) dR/dX A

X

 

 

 

Figure 4.3 Principle of electron beam resistance imaging (EBRI): (a) Measuring
the resistance between point x and ground by injecting current with a SEM; (b) A
plot of resistance vs. position; (c) A plot of dR/dx vs. position.

63

4.3.4 Experimental Apparatus

We devised two different ac lock-in techniques for electron beam resistance
imaging. In the first technique, which was used most often, the electron beam is
chopped and the sample resistance from the point of beam penetration to ground is
measured. In the second technique, which was used only a few times, the electron
beam is not chopped. Instead, the position of the beam is dithered, and the
position derivative of resistance dR/dx is measured.

The apparatus for the beam chopping technique is shown in Fig. 4.4. A
conventional scanning electron microscope (ISI Model SX-40) is used as a current
source. In most of our measurements, a relatively low accelerating voltage of 2 kV
was chosen both to reduce sample damage and to maximize specimen current (see
Fig. 4.6).

An ac lock-in technique is used for maximum sensitivity . The dc electron
beam is chopped by a beam blanker with a frequency of 510 Hz, a frequency
chosen to optimize the noise figure of the lock-ins and to be well away from 60 Hz
and its multiples. A single phase lock-in amplifier (Stanford Research SR 510)
with current preamplifier is used to measure the specimen current from the sample
to ground. A dual—phase lock-in amplifier (SR 560) with a low-noise differential
voltage preamplifier is used to measure the voltage drop from the beam impact
spot to ground. The low-noise voltage preamplifier (SR 512) has a gain of 100 and
a noise figure of 0.5 dB with a source impedance of 100 Q in frequency range of
100 Hz-l kHz. The resistance of a typical sample used in our experiments is about
10 Q. An IBM compatible 286-class personal computer is interfaced to both lock-
in's through GPIB interface cards, and calculates the resistance at every point

according to

64

 

Electron gun -—> |_U_|

lst Condenser lens-b a a
| 1

Beam blanker ——-—-

 

1 I
, Reference signal
2nd Condenser lens-t- .

 

 

 

 

 

 

 

  
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(disabled for greater
beam current) . R( )
. . x
Scanning corls-F [:3 9 1 D/A 6:9 Computer F‘
i Y
Objective lens —>
Final aperture R f f
- e .
+ 300 V rlng T Lock-in for I |__.‘I(x)
Sample f f
Re . *
f E >9_l— Lock-in for V l—VQ‘L
Voltage
pre-amp

Fig. 4.4 Experimental apparatus for resistance imaging with a scanning electron

microscope. The dark line is a GPIB interface between computer and lock-in
amplifiers.

65

V(X)
I (x)

 

R(x) = (4.4)

The computer also controls the location (x) of the electron beam by supplying the
voltage of the scanning coils through a D/A board.

Obtaining a good signal-to-noise ratio with this scheme is not easy. Under
normal operating conditions, a well-tuned SEM has a small electron beam current
of 5 pA to 100 pA and a small electron beam spot diameter of 60 A to 100 A.
With a 10 0 sample, this small beam current produces a voltage of less than 1 nV.
In order to increase the beam current, we have disabled the 2nd condenser lens and
removed the final aperture of our SEM. These measures increase the beam current
to 50-100 nA but greatly degrade resolution, producing a spot size of about 0.1 u
m. The spot size verses beam current is shown in Fig. 4.5. The size of the beam
was measured fi'om the secondary electron signal profile as the beam was scanned
across the sharp edge of a Faraday cup.

A collection ring biased at +300V to ground was fixed over the sample to
collect secondary electrons and prevent their return to the sample and current
detection circuitry.l Without a collection ring for capturing stray secondary
electrons, these secondaries can reenter the specimen at positions away from the
beam spot, changing the specimen current, and causing errors in the measurement
of the resistance. Watanabe and Munakata have performed an experiment similar
to ours, using the electron beam of a SEM as a current injector and measuring the
voltage drop along a series of resistors used as a test sample.4 Their results show
that stray secondary electrons have a strong effect on the measurement of the
resistance. They found that, with the sample carefully shielded from stray
secondaries, the relative errors in the resistance measurements were less than 2%,
while without shielding, the results were wildly inaccurate, often incorrect by more

than an order of magnitude. Fig. 4.6 is a plot of n + 5 vs. accelerating

Spot Size D (um)

66

 

0.30 - r - . - . - . - . 4
0.25 - o o -
o

0.20 r- 0 -

0.15 - -
r O

0.1 0 - o o o .
r O.

0.05 P -

0.00 ‘ ' J

 

 

 

0 20 40 60 80 1 00 1 20
Beam Current (nA)

Figure 4.5 A plot of spot sizes (diameter) of electron beams vs. measured beam
currents.

67

 

     
   
     

 

 

 

--.|.--

 

“DIS OtteE'v 2 338:4” .

 

 

 

 

.....................

(ls‘lb)/lb = 5 + 1]

...........

 

Collection ring V = 0v

0.0 l l - n - n - n - 14+-1-1-n 1 L1 1 J
103 2 3 4 5 67 104 2 3

Beam voltage (V)

 

Figure 4.6 A plot of the sum of backscattered and secondary coefficients n + 8

vs. the beam accelerating voltage for an Al film with and without secondary
collection ring.

68

voltage for an Al film both with and without voltage applied to the collection ring,
clearly showing the effects of stray secondaries.

Fig. 4.7 is the circuit we used to measure the position derivative of resistance.
The primary beam is not chopped by the beam blanker. Instead, the beam's
position along the sample is modulated with a small sinusoidal deflection voltage.
As long as the sample current is constant, the voltage measured by the lockin is

proportional to the position derivative of resistance.

The position x of the beam, controlled by voltages fed to the SEM scan coils, is
given by

x = x0 +Axsin(o)t+(p) (4.4.1)
where x0 is the mean position of the beam controlled by a large (0—5V) voltage
fiom the computer's D/A converter and Ax is the amplitude of a small ac
modulation generated by coupling a small ac voltage through a transformer to the

scan coils of the SEM. The voltage drop along the sample is then given by

 

dV 1 d2V 2
V(X)=VO+E.AX+§.EZ_.(AX) +...
2 — o
=I-Ro+(I-§-Ax)sin(mt+¢)+ 14.2.sz .1 cos(2(o1t+¢))+m
dx 2 dx2 2

where we have assumed that the specimen current I does not vary rapidly with
position x, an assumption which is only valid if the sample has a relatively smooth

topology and slow variations with position of the secondary electron coefficient 8.

The lock-in measures the voltage at fi'equency co which has amplitude Inc-15M.

The dc specimen current I is measured with a dc picoammeter, and the amplitude

of the beam dither Ax can be computed from the known characteristics of the

69

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

Electron gun ——> LU _| A
lst condenser lens—I» fll
Transformer
Beam blanker -——-— || x+ x
' E x

2nd condenser lens-k a l dx '
(disabled for high D/A -—J Computer

current) 49
Scanning coils—D E D— Reference

srgnal 1(x)

Objective lens —-> l H

+ 300 V ring |I(x) ! E ‘ AID

Sample

Ref. f V
Lock-in for V (x

 

 

 

 

 

 

 

 

Figure 4.7 Experimental apparatus for measuring the position derivative of

resistance vs. position. (A) Low-noise voltage preamplifier; (B) DC current
amplifier.

70

SEM's scan coils. Both current and voltage are recorded by the computer, which
computes the derivative of resistance dR/dx as the beam is scanned along the
sample, point by point, under computer control. Typically, for a 100 sample and a
beam current of 50 nA, the position dither Ax was 101m and the co-voltage was 33
nV.

4.4 Experimental Results
4.4.1 Sample Preparation and Sample Holder

Our final samples consist of Al or Au lines 2000 A thick, 1.9 pm wide and 160
um long separated from an Al metal substrate by a 700 A thick thermally-
evaporated silicon dioxide(See Fig. 2.8). The Si02 layer exists only under the
metal and is not exposed directly to the electron beam. The Al substrate is a thick
Al film thermally evaporated onto a polished silicon wafer. The detailed procedure
for the fabrication of these samples was presented in the section 2.5.2.

Originally, we tried using samples consisting of metal lines separated from a Si
substrate by a thermally grown 7000 A thick silicon dioxide layer which covers the
Si wafer everywhere. However, we encountered two serious problems with these
samples. The thick silicon dioxide layer charged up under the electron beam,
producing a large local electric field which distorted the focused beam and the
SEM images. An even more serious problem was caused by interaction of the
electron beam with the silicon substrate. When a high energy electron beam
strikes a semiconductor such as Si, copious electron-hole pairs are generated.
Only a few eV are required to make a single electron-hole pair in Si, so a high
energy electron of several keV energy can create thousands of electron-hole pairs.
Many of these carriers recombine after diffusing several micrometers (the

diffusion distance in Si). However, those e-h pairs which are near the Si interface

71

are pulled apart by the strong electric field in the depletion layer and produce a
spurious specimen current that may be many times larger than the beam current.
We found specimen currents as large as 50 times greater than the beam current,
and current multiplications of more than 1000 are reported in the literature. These
huge currents were very noisy and always overloaded our lockin amplifiers. To
solve this problem, we replaced the semiconducting substrate with a metal one,
eliminating both the production of electron-hole pairs and the charging problem.
The sample holder consists of a 0.5" diameter aluminum cylinder surrounded
by a tight fitting Teflon ring, as shown in Fig. 4.8. Electrical leads to the sample
are held by eight SS syringe tubes (gauge #22) which fit snugly in vertical holes in
the Teflon ring. Electrical leads from the SEM's electrical feedthrough are
soldered to the SS tubes. Each SS tube contains a fine brass wire bent to form a
simple clip which presses against the sample, making good electrical contact with
both the metal film and the SS inner tube. This simple scheme allows rapid

changing of samples with minimum damage to the sample's contact pads.

72

 

brass clip
‘- I Stainless steel
III/IIIIIIIIIA

     

tube (1 of 8)

 

Figure 4.8 Sample holder.

73

4.4.2 Result and Discussion

Fig. 4.9 is a plot of sample current and substrate current as the electron beam
was scanned along the substrate, perpendicular to the sample line, crossing back
and forth once over the sample line. The sample is an Al line is 1.9 pm wide,
separated from an Al substrate by a 700 A thick SiOz layer. The 2 kV electron
beam was chopped at 507 Hz and the average beam current was 51 nA. (The beam
current was 113 nA with the AC modulation off.) A new data points was taken
every 3 seconds and the lock-in's time constant was 300 ms. The secondary
electron collection ring was biased at +300 V, and the 02 gas jet was on with a
pressure of 4x10'4 torr for decontamination, as described in the section 3.3. In
considering these data, it is well to recall that the specimen current is not, in
general, equal to the beam current.

When electron beam is far from the sample, the sample current is negligible,
compared with the substrate current, indicating that the silicon dioxide layer
effectively insulates the sample from the substrate. However, when the beam is at
the center of the sample, the substrate current does not decrease to zero although
the sample current is at a maximum. Also, the current profile is very wide, much
wider than the sample. A likely explanation of this is that the effective spot size is
very large, more that 5 um. Apparently, the ac modulation of the beam blanker
greatly increases the spot size. It is also possible that the 8102 layer becomes
somewhat conductive when it is under bombardment by the electron beam, due to
electron-hole production. Although the mean penetration depth of 2 kV electron in
Al is about 0.1 um, shorter than the sample's thickness of 0.25 pm, nevertheless, a
portion of the beam current will reach the SiOz layer and may open a conducting

channel.

74

 

75 'I'lfiI'I'Ifil'l

63- -

p

50- -

b

38 - Al / Si02/Al, lb=51nA SUDSVate'
r 1.9um wide, 250nm thick l

Current (nA)

 
   

25

<}—— sample I

    
  

 

 

   

I 1.. I l

-o -15 -1o -5 o 5 1015 20
Position(um)

'Figure 4.9 A profile of current vs. position when a large current beam crossing
the sample line.

75

F ig.4.10 is a plot of resistance to ground vs. position along 3 Al sample line,
measured using the circuit in Fig. 4.5. The average sample current was 35.6 nA
with the beam chopped at 507 Hz. The 02 gas jet and +300 V collection ring
were on, as usual. The data were taken while the beam swept forward and back
once along the sample line, over a 5 minute period, which is about 38 for each data
point. The time constant for the lock-in's was 300 ms. The plot is nearly linear,
as expected from Ohmic law. The two traces agree to within about 0.1 O This
plot indicates that the total resistance of the sample is 10.1 O, which agrees well
with a 2-terminal ohmmeter measurement of the resistance, which yielded 11 Q
and includes lead resistance.

In an effort to observe electromigration effects, the sample was then stressed
with an external current of 1 mA for 24 hours while under vacuum in the SEM
chamber at 1x10'5 torr. The current density was J = 2.5 x105 A/cmz. After 24
hours, the external current was removed, and the resistance vs. position was
measured again. The data are shown in Fig. 4.11 and were taken with the gas jet
off. (A single sweep of the sample does not result in significant contamination.
Only when repeated sweeps of the beam across the sample are performed is the
contamination severe and the gas jet necessary.)

The data of Fig.4.11 show very puzzling behavior. After the 24 hours,
J=2.5x105A/cm2 stress, the computed resistance to ground vs. position is non-

monatomic, showing two spots on the metal film line where R=V/I goes up and

down. This behavior is inconsistent with R = [3% and clearly shows that, in this

sample, W] is not equal to sample resistance. For this reason, we have relabeled
the y-axis as V/I. The non-monotonic bumps reproduce well and, away from these
bumps, the sample appears to show ohmic behavior with a total resistance of about

11.5 Q, slightly greater than before the current stress.

Resistancelfl)

76

 

 

 

 

 

1 5 1 . 1 I r V l I I f
12 . Au on Si02, Sample I = 35.6 nA ..
1.9um wide, 250nm thick
10 - -
l
7 - .
5 - .
2 - .
0 1 - l . 1 .. n L - l .. l L
0 23 45 68 90 113 135 158 180

Position(um)

Figure 4.10 A plot of resistance vs. position along the sample line.

VII

77

 

20 ' I ' I ' I ' I ' I ‘ T ' I r I '

I
I
1 I
1 3‘. ' I
C: I

16......-.: ....... : .......... 3.; .............................. ,- .........
: : :—' ' : : ' :
O

I u
' n a
‘ 1 I
a u I
12.. ................................. , .............. , ..............
I o
' c ' o h . .
I. , I '
a c " u

 

1.91m wide, 250nm thick: - a l 6 0
. : '2 I 9 : I
:3"; : é , ' :
:g '; : ? l :
-,e ........ . ............ , ....... .l
8 : '5 :{r : V :
: 1.! Z’.\ I
r : qt: :
rt A?
’0: , ’: 1
................... ..' ..:- ...
4 E 2?:
. E ,7 Z 3%} .
. ' 9;:
WU .

 

O . 3' n - L - i - i - J A i - L L L -
0 20 40 60 80 100 120 140 160 180
Position(um)

 

Figure 4.11 (A) Resistance vs. position after J=2.5x105A/cm2 for 24 hours, data
taken without 02 jet. (B) Resistance vs. position after 20 hour stress of J = 4.0
x105 A/cm2 and 2 more hours of J = 2.5 x106 A/cm2, data taken with 02 jet.

78

This same sample was then stressed with a current density of J = 4.0 x105
A/cm2 for 20 hours, followed by 2 hours of J = 2.5 x106 A/cmz. After this
treatment, the V/I of the sample was again mapped out, this time with the gas jet
on. The data are plotted in Fig. 4.11, which shows a new huge anomalous peak
appearing besides the previous two bumps. Obviously, this plot no longer
indicates the resistance of the sample. We cannot explain this anomalous data
entirely, however, we believe that the interaction between the energetic electrons
and the SiOz/metal interface plays an important role here.

Recall that the resistance R = V/I is calculated from the measured voltage and
sample current in this EBRI technique. The sample current profile for the most
stressed sample of Fig. 4.11 is shown in Fig. 4.12. It is clear that the sample
current is nearly constant with small fluctuations, except at the two ends of the
sample line, where the larger contact pads increase the effective area for collecting
electrons and cause a big jump in the sample current there. Since the sample
current is almost constant, the anomalous resistance changes in Fig. 4.11 are
primarily caused by the anomalous changes of the voltage signal.

Prior to current stressing, the Al sample line was smooth and of uniform width.
After current stressing, the morphology of the Al line was rough and the line width
was non-uniform as shown in Fig. 4.13. There were holes in the film (seen as dark
areas to the right and left of center in Fig.4.13) whose positions corresponded to
the locations of the anamolous voltage bumps in Fig.4.] 1. Clearly, much of the
damage to the film was caused by electromigration during current stressing.
However, some of the damage could have been caused by reaction with the oxygen
plasma formed by the interaction of the Oz gas jet and the electron beam. The
holes in the Al film expose the SiOz underlayer. It is known that when a
metal/semiconductor interface is exposed to an energetic electron beam, a voltage

appears at the interfaces. This phenomena, known as the barrier electron voltaic

Spec. Current(A)

79

 

5-05'8'1'7'1'1'1'F'7'!
éAloinSi02,10:nA/;02§ ; g
4.0E-8 - ...... .......

3.0E_8. ...... ...... ....... ...... ...... .' ...... .......

205-3; ..... ...... g ....... g ...... g _______ z .......

'54-. e flaw ~ ; -------

 

 

 

1.0543
0 20 40 60 80100120140160180

Position(um)

Figure 4.12 Sample current vs. position.

80

effect, is probably the cause of the anamolous voltage. Note that the thickness of
the Al film (250nm) is larger than the penetration depth of 2keV electrons in
Al(150nm - see Fig.4.]) and so the Al/SiOz interface is not ordinarily exposed to
the electron beam. Fig. 4.13 shows a SEM photo corresponding to the huge peak
in Fig. 4.11.

Shown in Fig. 4.14, is a scan of the position derivative of resistance dR/dx of
this same current stressed sample. The scan was made with the circuit shown in
F ig.4.7 , after the first current stress of 2.5x105 A/cm2 for 24 hours, but before the
second larger current stress. Note the coincidence of the large voltage bumps in

Figs.4.ll and 4.14.

 

81

 

Figure 4.13 SEM image of the void formed by electromigration corresponds to
the huge peak in Fig. 4.11.

DR/ome Oum)

82

 

1.0

0.8

0.6 r

0.4

.... ................_ .............................................

Alon 31112, 56 nA No 022 , _ _
1.9um Wide, 250nm thick 3 3 E .

..... ' ..............I---...u‘.-....-..-...-I......-‘-.... ~'.-u.¢-
I u I
a

 

- ...............................

 

0.2

0.0

0

  

 

 

 

 

 

 

 

C :21: . A
L 4 J

j 1 -

4o 60 80 10120140160180
Position(um

 
    

20

Figure 4.14 dR/dx vs. position.

 

83

References for chapter 4

 

1 James P. Long and Charles P. Slichter, Phys.Rev.B 21, 4521 (1980).

7- v. E. Cosslett and R. N. Thomas, Brit. J. Appl. Phys, 15, 883 (1964). ibid.,
Brit. J. Appl. Phys, 15, 1283 (1964). ibid., Brit. J. Appl. Phys, 16, 779 (1965).

3 D. B. Wittry, In X—Ray Optics and Microanalysis, I VInternational Congress on
X-Ray Optics and Microanalysis, Orsay, 1965 (R. Castaing, P. Deschamps, and J.
Philibert, eds.), Hermann, Paris (1966), p. 168.

4 Hiroshi Watanabe and Chusuke Munakata, Japan. J. Appl. Phys, 4, 250
(1965).

5 P. Rappaport: Phys. Rev. 93 246 (1954).

Chapter 5

Squeezable Tunnel Junction and Crack Tunnel Junction

A mechanically controlled squeezable tunnel junction and a crack tunnel
junction, similar to Morland’s “squeezable” and break junctions, have been built to
probe single electron tunneling phenomena through a vacuum barrier. Both of
these can work in the temperature range from 4.2 K to room temperature. In the
squeezable and crack junctions, two electrodes are formed in two different ways:
(i) by evaporating metal films onto two glass substrates in the squeezable tunnel
junction; (ii) by breaking a narrow metal film by cracking a glass substrate in the
crack junction. When the tunneling gap between the two electrodes, controlled by
bending the glass substrates, is in the nanometer range, electrons can tunnel
through the small gap. However, if the capacitance C of the junction is very small,
single electron tunneling will be blocked by the Coulomb energy of 9%: as long as
the applied voltage is smaller than %c and the Coulomb energy 97% is much larger
than thermal energy kT. Such a Coulomb blockade effect is observed using a
crack junction at liquid nitrogen temperature. Using a squeezable nmnel junction
with micron-sized samples, two-level fluctuation of the conductance in the

tunneling regime has been observed at liquid nitrogen temperatures.
5.1 Introduction

Since the experiment of electron tunneling through superconductor structures
of Al-A1203-Al was done by Giaever in 1961,1 it has been known that electrons
can tunnel through an oxide barrier if two metal films are separated by a thin
insulating layer, about 1~5 nm thick Although it would be more interesting to
study electron tunneling through an adjustable vacuum barrier instead of a fixed

84

85

thin oxide layer, this was not feasible until the scanning tunneling microscope
(STM) was invented by Binnig, Rohrer et al.2 in 1982. They implemented a
negative feedback loop in the STM's electronic circuit to control the vacuum gap
between the tunneling tip (one electrode) and the sample surface (the other
electrode) as well as the tunneling current. In that feedback loop, the tunneling
current fiom the tip to the sample is the feedback signal to control a high voltage
output which either contracts or expands a piezoelectric material, thus controlling
the vacuum gap between the tip and the sample surface, in turn, keeping the
tunneling current constant as set.

The working principle of a scanning tunneling microscope is a quantum
mechanical efl‘ect: if the gap between two electrodes is in the nanometer regime,
wave functions of electrons in the two electrodes will overlap, and the electrons
can tunnel through the vacuum gap. The probability of an electron tunneling
depends exponentially on the vacuum barrier's height and its width, as well as
electron's effective mass and charge. Because of such an exponential relationship
between the tunneling current and the tunneling gap, a STM has an extremely high
resolution and can often directly image atoms on a sample surface. It is one of the
most efi‘ective instruments available to studies of surface science. Unfortunately,
the tunneling tip and sample surface obviously have to be electrically-conducting
materials, a serious limitation. In other words, a STM can only be used for
observing surfaces of metal and semiconductor materials, not insulating materials,
even not metals with a thick oxide layer. Fortunately, the atomic force microscope
(AFM), developed after the STM, has no such limitation for observing material
surfaces.

In addition, a STM can also serve as a spectroscopic tool if its feedback loop is
turned off. For example, after an image is obtained the STM's tip is placed at an

interesting position, at which a characteristic I-V curve can be recorded quickly

86

while the feedback loop is turned off. An I-V curve contains information about
electronic density of states (DOS) in the conduction band of the sample. The time
for measuring an I-V characteristic has to be short because of the vibration of the
STM body and the drifting of the tunneling tip while the feedback is turned off.
Due to such a sensitivity to vibration, the STM has so far played a limited role as a
spectroscopic tool for superconducting materials and normal metals. Therefore, it
is desirable to develop a device with both an excellent stability and a
mechanically-adjustable tunneling gap without the feedback loop in its electronic
circuit.

Two years later after the invention of a STM, Morland and his coworkers
designed a “squeezable” tunnel junction, which consists of two evaporated
electrodes on two glass slides which are separated by four thin metal film spacers
and pressed towards each other with an electro-magnetic squeezer until electrons
can tunnel through the gap.3 Later, They employed another scheme to form a
clean tunneling interface by breaking Nb-Sn filaments in liquid helium.4 Both the
squeezable tunnel junction and the “break” junction have the extreme stability
required for tunneling spectroscopy. Such a stability is achieved by sacrificing the
transverse scanning capability. In this chapter, I describe a squeezable tunnel
junction and a crack junction, similar to Morland’s, with which both Coulomb
blockade of single electron trmneling in a junction with an ultra-small capacitance

and two level conductance fluctuation are observed

87

5.2 Coulomb Blockade Theory

5.2.1 General Tunneling Theory

In Quantmn mechanics, it is well known that an electron can tunnel through a
barrier with a finite probability, which depends on the barrier’s height and width,
as well as the electron’s effective mass in the conduction band For instance,
when two electrodes are placed very close without contact, i.e., less than a few
nm's, an electron in one electrode can tunnel through the vacuum gap and arrive at
the opposite electrode if a small voltage is applied between the two electrodes,
thus resulting in a current flowing through the vacuum gap between the two
electrodes. This trmneling current is related to the applied voltage. Generally
speaking, the relationship between the tunneling current and the bias voltage is
determined by quantum mechanics and it is complicated However, at a small bias
voltage, the tunnel junction is nearly ohmic and can be characterized by a
tunneling resistance Rt, without considering the effect of the junction’s
capacitance, which will be considered in the next section 5.2.2.

In Fig 5.1, a schematic diagram shows the Fermi energy diagram in a basic
tunneling process. The two electrodes can be two different metals with different
work functions. The work function (p is defined as the energy required to remove
one electron out of its conduction band to the vacuum. For most metals, the work
fimction is in the range of 3-5 eV. When the two metals are placed very close,
about 10 - 30 A apart, electrons will tunnel between them, resulting in equalization
of the Fermi levels of the two metals. [5.1(b)] With a bias V applied to the
electrode on the left side, electrons on the right side electrode with the energy level
higher than the opposite Fermi level can tunnel to the left, thus producing a current

flowing in the circuit.

0 l
rer->
N

\ F2
F1

a) Two neutral metals separated by a large gap.

I I

b) Two metals in equilibrium separated by a tunneling gap.

ml IMF
C¢1 _ §
£Fl ¢ .......... s

C) Tunnel junction with an applied bias voltage V.

 

 

Figure 5.1 a schematic diagram shows the Fermi energy diagram for a basic
trmneling process.

89

By mean the I-V characteristic, one can obtain information about the
electron density of states (DOS) and the phonon spectrum. Usually, such
experiments are done at low temperature because thermal energy smears out small
non-linear features in the I-V characteristic. In the following, we are going to
employ quantum mechanics to derive a quantitative expression for I-V in the
simplest case: both electrodes are normal metal even at low temperature.
Nevertheless, the result can be modified easily for a mixed structure with a
superconducting electrode and a normal metal electrode. In cases involving
superconducting electrodes, quasi-particle tunneling plays an important role. At
low enough temperature, if both of the electrodes are superconducting and the
tunneling gap t is smaller than about 20 A, a Cooper pair can tunnel through the
vacuum barrier, thus causing a supercurrent flow in a Josephson tunneling
junction. For simplicity, this case will not be discussed here even though it is a
very interesting research field now.

In Fig 5.2, the electron density of states is plotted vs. the energy, and the

Fermi levels are offset by an applied voltage V. We seek a quantitative expression

FIT!
Dar

0 ----- Fermi Level

_____ 0 $

eV

T

Figure 5.2 Energy diagram for a tunneling process, where a bias voltage V is
applied to the left side electrode. Fermi level is set to zero as a reference point.

 

5N1.

 

 

90

for the tunneling resistance in terms of physical quantities, such as the work
function of the electrodes as well as the tunneling gap.

From “Fermi’s golden rule number 2”, the probability of an electron tunneling
from the right side to the left side can be written:

WU)...=(2%)|<L1H(‘>|R>|'.N,(g) (5.1)

where I < Llflm I bf is the tunneling matrix element, denoted by |T,I|2 and N,(g) the

density of states on the left.

Now, taking into account the Fermi distribution for T120, the flow rate of
electrons from the right to the left is (F e)r—)13

(FL)...=(ZMA)T|721r'N.(£)-N.(s—eV)-f,(s—eV)~l1-f,(s)]dg (5.2)

-Q

where A is the cross section area of the junction, 8 the electron’s energy above the
Fermi level (a = E - EF), and f is the F ermi-Dirac distribution function

f(g)=%l+exp(fl6)) (5'3)

with [3 = l/kT.
On the other hand, the flow rate of electrons from the left to the right is
(Fe)I—-)r3

(173)“,=(ZMA)TIT;,F°N,(£)-N,(£-eV)': f,(£)'[l-f'(£—eV)]ds (5-4)

So the current— the net electrons — flowing from the right to the left is:

1 =”4(5),...“(ELF(2%)71712-N,(s)-N,(s-eV)-[fl(s)-f'(s—eV)]dg (5.5)

where it is assumed that ITIr|2 = |T,I|2 = ITIZ.
When eV (< 50 mV) is relatively small compared with Fermi level (4 eV), we

have, approximately,

91

[f,<a)-f,(s -eV)]=[f(e)-f(£ —eV)]= 4/54 -(eV)
Also, when the temperature is very low, [3 is very large so
”7 a; 6(a) (5.6)

is a good approximation, where 6(8) is the well-known Dirac Delta function. Then
eq.(5.5) can be further simplified as follows:

I =(WAmfi-NM-N.<s—eV)-07/,,,lM-<ews

1 =(Wm-(emTlle'Nxa-N.<e-eV>’6<e>d€
Finally,

I =(Zm’A%)-|Tf-N,(0)-N,(—eV) (5.7)

It is natural to characterize tunneling junction by a tunneling resistance Rt defined
as:5

R. 4% =(%m.A)~|T|"-[N,(o)- N,(—eV)r‘ (5-8)
where the tunneling matrix element can be written specifically:6

unfligfgfle—im—‘w-m (5.9)

 

where E and V are the Fermi energy EF and the barrier hight of the metal
respectively. The work function of the metal is defined as:

¢ = V — EF
So we have: I '1 ~ 165,43 -§«fz-To
(E, +¢)’ e
| zmerw (5.10)
1613,45

Replacing |T|'2 in eqn.(5.8) with eqn. (5.10), we get
R: =Roem(A'\/$d) (5-11)
Where A'=1.025eV"/2 A", and

92

R0 = [Wir- + ¢%E,¢m2A].[N’(O). N,(‘eV)]-1 (5.12)

In terms of conductance, this can be written as
§= G. = R: «IN.<0>-N.<—eV>1 (5-13)

It is clear that the first derivative of tunneling current with respect to bias
voltage is proportional to the electron density of states in the conduction band
Furthermore, it can be shown that second derivative gives phonon spectroscopic
information. So far, we have ignored any effect due to junction capacitance
because this effect is negligible if the junction capacitance is 2. 10'13 F. However,
such an effect cannot be neglected if the junction cross section area is small,

( S (1 um)2), and its capacitance is smaller than 10'15 F. Such a small-capacitance

effect is the subject of the next section.

5.2.2 Coulomb Blockade Theory

In a current biased normal metal—Insulating layer—normal metal (N-I-N)
junction with a junction capacitance C and tunnel resistance R,, the initial charge
Q is a classical, continuous variable, and can be a fraction of an electron charge e
because it is treated as a polarized charge in a capacitor. When an electron tunnels
through the junction, the charge Q is changed by an electron charge e, which is a
discrete quantum number. In such a semi-classical theory, the Coulomb energy
varies:

magi: 3
AE' 2C 2C C(QiZ)

when the initial charge is in the following range,

e e
——< <— 5.14
2 Q 2 ( >

93

the energy change is always positive for any sign of AQ = :1: e,
AE > 0
Therefore, the tunneling process is forbidden at low temperature when its
initial charge Q is between i e/2. This effect is called the Coulomb blockade of
single electron tunneling The physical origin of this blockade is electron’s strong
Coulomb interaction in a junction with a small capacitance C.
For such a junction, its 1- V characteristic curve is strongly non-linear, because

of the Coulomb blockade effect.7 The junction I-V is parabolic at small bias

voltage:
1 =(2C/1rR,e)V2 for M S e/2C (5.15a)

and approaches the linear asymptote

. _L- f V >> /2C 5.151)
I—)G' (V 2CsrgnV) 01" I e ( )

The above two equations show that the Coulomb blockade effect has
dramatically changed the characteristic I-V curve in two regions: at small bias
voltage, an I-V is parabolic and conductance of the N-I-N junction is linear to the
applied bias voltage:

a%,V=(4C/1zR,e)V (5-15a)'

Actually, the dynamic conductance in eqn.(5.15a)' is smaller than the junction
conductance without the Coulomb blockade effect. In an ordinary tunnel junction,
the conductance is constant at a small bias voltage. At a large bias voltage, the
junction I-V is linear to tunnel conductance, but with a voltage offset of e/2C. In
fact, those features are experimental evidences for the existence of the Coulomb
blockade of single electron tunneling

Only under some appropriate conditions, can this Coulomb effect be observed
in experiments. Three kinds of energy scales play roles in single electron

timneling junction: charging energy EC 6:“ e'Z/ZC; thermal energy E T = kBT; and

 

94

quantum fluctuation energy AE ~ Znh/r, where ‘t is the discharging time and
equals R,C for the junction. The condition for observing the coulomb blockade
effect in such an experiment is:
EC >> AE >> ET

i.e.

e2//2C >> 21rfr/t = 211'h/R,C

R, >> 41rh/e2 = RQ = 26 k!)
where RQ is known as the quantum resistance.

For example, if a junction timnel resistance is about 100 kn and its capacitance
C is about 3x10‘15 F with a cross section area A as 1 m2, the temperature has to
be in S 1 K so as to observe the Coulomb blockade effect in such a junction, in
which the offset voltage is around e/C z 50 uV, large enough for being observed at
0.3 K. However, such a requirement of low temperature can be relaxed at certain
situations. For instance, if a junction has a much smaller capacitance C =5 3x10‘18
F, where the cross section area S m 0.001 umz, the offset voltage e/C z 50 mV, so
that the Coulomb blockade effect can be measured even at room temperature!

The first experiment to show clear evidence of the Coulomb blockade effect
was performed with a double tunnel junction structure by Fulton and Dolan.8 So
far most experiments have been done in similar structures with a multi-junction
array. These results of Coulomb staircases as well as microwave coupling data
demonstrate Coulomb blockade of single electron tunneling 9’10,“ The reason for
such a situation is because the electrodynamic environment profoundly efi‘ects the
behavior of small-capacitance tunnel junction . The stray capacitance in an
electronic circuit lead is usually about 10"12 F, which lowers the offset voltage to
0.1 uV, thus reducing the Coulomb blockade effect dramatically. In a double
junction structure or a multi-junction arrangement, the central junction is isolated

from its electrodynamic environment by the nearest neighbor junctions, those

95

neighbor junctions are shielding away the eflect of the large stray capacitance. As
a result, the Coulomb blockade effect has been observed most frequently in such
multi-junction array structures. Instead of using junctions to reduce the
environment's electrodynamic influence, a high resistance lead with a resistance
larger than the quantum resistance 26 k9 placed very close to a junction region
has been shown to effectively isolate the junction from its electrodynamic
environment both theoretically and experimentally. 12,13

However, some controversial experimental results for a single tunnel junction
should be mentioned here also. Using a STM as a probe above a stainless steel
surface as well as a superconducting material, Bentum et. observed the Coulomb
blockade efl‘ect of single electron tunneling in a voltage-biased single junction
formed by the STM’s tip and the conducting material surface. 14 Later, in a single
tunnel junction formed by two tiny metal filaments, Gregory also reported
experimental evident for the Coulomb blockade of single electron tunneling in
such a voltage-biased junction. 15 In both cases, no higher resistive leads were
used to isolate the single junction fiom its electrodynamic environment as
suggested by the theory. There has been speculation that there could be a tiny
metal defect embedded between the STM’s tip and the clean metal surface in the
former experiment or between the two filaments in the latter case, so that these
single junction were actually double junction structure. In the section 5.4 of this

chapter, I will present experimental evidence for the Coulomb blockade effect in a

voltage-biased tunneling junction.

5.3 Apparatus and Techniques

A standard ac lock-in technique in the electronic circuit shown in Fig 5.3 was

used to measure the differential conductance G = d! /dV of a single junction verse

96

the biased voltage. The dc bias voltage supply is simply a ramp generator with an
adjustable amplitude and ramp scanning time. A small ac modulation voltage is
coupled to the dc bias voltage through a 1:1.25 transformer so as to break the
ground loop between different power sources. The ac current signal is magnified
with a current amplifier, then measured by a lock-in. Then the output fiom the
lock-in goes to an x-y recorder, which has an inline buffer memory for storing
data Finally, a computer reads data from the recorder for further data processing
One 40 k0 resistor is inserted in the circuit to limit the maximum current and
protect the current amplifier in case the tunnel junction shorts.

The above circuit for measuring the differential conductance G = d] /dV is

based on the following relationship between the current and the biased voltage.
V=V0+AV (5.3.1)
AV =vSin(wt+¢o) (5.3-2)

where V0 is the dc biased voltage from the ramp generator, and AV is the ac
modulation voltage coupled through the transformer. The current I (V) in this
circuit will vary with the voltage as:

1(V)=10+%.AV+1.31

2 5V2 -(AV)2+---

 

= Io+%-v-Sin(at + ¢o)+%-%-(v-Sin(ax+ ¢l,,))2 +---

I(V)=Go~Vo+(%-v)-Sin(wt+¢o)+[l- 3’1

 

2 W2-v’)-(Sin(at+¢o))2+m

 

131,2). 1‘C"~‘(2("’“‘¢o)) +...
2 072

d .
=Go-Vo+(W-v)~Sm(ax+¢o)-t~[— 2

_ . 1.21.2 31. . - _ 1.21.. 2 . (5-3-4)
I(V)—Go V0+[4 5V2 v ]+(0"V v) Sm(ax+¢o) [4 6V: v J Cos(2(rx+2¢o)+

97

 

1

T Q) ac Modulation signal

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

——~ _ K’ 40 kilo-ohm Resistor
-7- W-
Transformer (1 B‘ lta
(l : 1.25) c rasvo ge
F>— Lock-in Amplifier
I preamp. X (V)
Y Computer
“1de) X-Y recorder
Junction's body, see diagram on next page for detail

 

 

 

/

 

 

 

 

Figure 5.3 Apparatus for single electron tunneling experiment. 40 k9 resistor
limits current in the case of tunnel junction short.

 

98

 

 

 

Aluminum

 

S
a

Metal Film Spacer

 

 

 

 

Glass Substrate

E

2-64 Screw

Spring
Stainless Steel Shim

 

Ball Bearing

 

 

 

Hole for Observing

Figure 5.4 A schematic diagram of the mechanically controllable squeezable
tunneling junction. The diagram is not to scale.

 

99

The coeficients in front of the first harmonic a) sine and the second harmonic
20) cosine are proportional to differential conductance and its derivative
respectively. As a result, using a lock-in amplifier to pick out the first harmonic a)
term or the second harmonic 20) term, we can obtain either the first derivative of
current verse voltage a/aV (differential conductance) or its second derivative
521/62V respectively.

The mechanical squeezer shown in Fig 5.4 is the basic device for controlling
the tunneling gap in our tunneling measurements. The squeezer consists basically
of a spring and one piston. The piston is guided along a smooth cylinder and
driven up or down with little fiiction by a 2-64 screw, thus compressing or
relaxing the spring The other open end of the spring is attached to an aluminum
plug attached to a thin stainless steel shim, in which a 1/32" diameter ball bearing
is embedded in one hexagonal screw. The 10 mil thick cross-shaped shim is so
flexible that it can moves up and down easily. However, it prevents lateral
movement of the spring because its four corners are attached to the body of the
squeezer. A ball bearing is used for two reasons. First of all, it has a small contact
area (point contact) with the glass substrates so that the applied force is
concentrated on the junction area Second, its spherical surface always keeps
applied force vertical to the glass substrate, thus largely eliminating a horizontal
force.

The entire mechanical squeezer assembly was attached to one end of a long
tube, and placed inside a liquid nitrogen Dewar. A long 8.8. shaft is used to turn
the 2-64 screw so as to compress or relax the spring for controlling the tunneling

gap from outside of the Dewar.

100

5.3.1 Theoretical Calculation of Controlling Force vs. Tunneling Gap

A schematic diagram of our squeezable tunnel junction is shown in Fig 5.5.
Two 3/8"><l" glass substrates are separated by four thin metal film spacers and
forms a stiff spring The lithographically-fabricated sample consists of two
thermally-evaporated thin metal films on the glass substrates. The tunneling gap
between those two electrodes is controlled by pressing the glass substrates with the
squeezer shown in Fig 5.4. The spring constant for such a system depends on its

spacers’ positions as well as on the glass substrate’s thickness.

T”? We“ Side View

 

 

“‘\“ (\\\\\\\\\\\\\\\‘

 

’I/I/I/Il/I/Il. 7. ll/ltr

 

 

 

 

 

\ .
. \_‘
K537 m\\\\\\\\\\\\\\\ \\“.

 

 

 

 

 

.\ J, j
r \_ ’7 I

l
t — ,,,,,,
T A————— zit—1‘

Figure 5.5 A schematic diagram of a squeezable tunnel junction sample with two
electrodes on two glass substrates separated by four thin metal film spacers.

 

 

 

101

In order to calculate this spring constant, the sqeezable junction can be
modeled as a beam which is supported on the two ends and pressed at the center
by an external force F. The Young’s Modulus Y of the beam is related to the force
F and the deflection a:

_ F13 _ F12
4st3w 4st3

where I is the distance between the two supporting bars, or the two spacers, w is
the length of the bar and equal to 1 approximately, t the thickness of the glass
substrate. Its effective spring constant K, is:

Obviously, K, is very sensitive to the thickness of the substrate and spacer’s
position. K, is proportional to the cube of the thickness of the glass substrate, and
inversely proportional to a square of the separation distance between two
supporting bars.

In our experiment, the glass substrate t is 0.1 cm thick, and the four 0.2 cm
square spacers are 0.4 cm apart from center to center, Y = 7.8 x 1010 N/mz, the
spring constant K, for such a geometry is:

K, = 3.2 x 107 N/m
The spring constant for the steel spring in our sqeezer is K,’ = 28 N/cm = 2800

N/m. the ratio for the displacements of these two springs is:

5 K' 2.8 103
y =----,-=—L=-——x—7~10—4
5 K, 3.2x10

The maximum deflection e of the beam's center is:

_ F73
8 " 481’]

where I is the moment of inertia of the beam,

102

where w and t are the length and the thickness of the bar respectively.

5.3.2 Crack Junction

A diagram of a crack junction is shown in Fig. 5.6. The crack junction is
similar to Morland's "Break junction".4 A 30 um wide Au line is fabricated by
photolithography on a glass substrate with two predrilled holes. The detailed
procedure for sample fabrication by photolithography was described previously in
chapter 2, section 5.4. A force is provided by the same squeezer shown in Fig
5.4, and redirected to one end of the glass substrate by a L-shape lever shown in
Fig 5.6, while the other end of the substrate is held by the base which is bolted
solidly to the squeezer. An aluminum bar supports the substrate just underneath
the narrow glass bridge between the two holes. When a small force is applied, the
substrate will be bent just like the squeezable tunnel junction shown in Fig 5. 5.
As the force increases and approaches a critical point, the glass substrate will
crack along the supporting bar because a higher strain is built up there, thus
breaking the metal film line above. Usually, such a crack line propagates through
its glass substrate and reaches to the other side. However, by controlling the force
through compressing the spring, it is possible that the crack line would stop at the
middle of the glass substrate instead of going through. It is not crucial to the
experiment.

After the thin metal film line is broken, it forms a tunnel junction with a very
small capacitance because of the very small cross section of the thin metal film.
By backing off the spring to reduce the force, the tunneling gap decreases until a
tunnel current signal appears. Because the edges of the glass substrate are still
continuous they produce a restoring force, just like in a bent beam, to overcount

external force from the compressed spring

 

103
1/8" Predrilled holes

//

//

       
 

   

l///

3/16"

 
 

Crack line

 

Small Force

(controlled by compressing spring)

  

Figure 5.6 Schematic diagram showing the controlling mechanism for a crack
junction.

104

Unlike the squeezable tunnel junction, where the force is placed down at the
center of the junction area, a crack junction has more complicated geometry
arrangement and is more difficult to be modeled in a simple way. We have not

calculated the tunneling gap verse the controlling force due to such complexities.

5.4 Experimental Measurement and Results

5.4.1 Coulomb Blockade with a Crack Junction

A photograph of a crack junction is shown in Fig 5.7. The detailed procedure
for sample fabrication by photolithography is described in section 2. 5 of chapter 2.
The sample is a thermally-evaporated 45 nm thick, 50 um wide, 1.2 cm long Au
film above a 5 nm thick Cr layer for improving Au adhesion to the glass substrate,
and has a 218 Q resistance before cracking The two electrical leads are attached
to the two contact pads of the metal line by simply pressing indium (In) dots in the
following procedure. First, a sample is cleaned by acetone and methanol; then,
after a 1 mm diameter In wire is cut to several thin slabs by a razor, one piece of In
is pressed down to the contact pad of the sample with the round end of a tweezers;
then, with one electrical lead placed on the top of the pressed In pad, 3 second
piece of In is placed over it, and pressed firmly, thus forming a solid electrical
contact. This so-called cold-solder method produces excellent lead contacts for
low temperature electronic measurements. Leads are 20 mil diameter Cu-Zn alloy
wire.

After lead attachment, the squeezer with the sample is slowly lowered into the
liquid nitrogen dewar. The sample is not immersed in the liquid nitrogen; instead,

it remains in the cod nitrogen vapor, where T = 83 K at equilibrium.

105

 

Figure 5.7 Photograph of a crack junction with indium pads

 

  

 

 
 

 

‘et ,.. Y‘ .¢.~

 

 

 

 

 

. aging- ,.-,_.,-_,,, ..

 

 

 

 

 

 

 

 

.l pi i 1 l i
“‘ ““w

 

Figure 5.8 Data for a crack junction at T= 77 K. Curve (A): plot of conductance
G vs. bias voltage V; Curve (B): plot of tunneling current I vs. time t.

106

The force on the sample is increased by turning the long screw driver of the
sample stick until the metal line is broken, and the current decreases to zero in the
electronic circuit, shown in Fig 5.3.

A reference frequency of 510 Hz was chosen to minimize the Lock-in
amplifier's intrinsic noise figure. 16 The root mean square (rms) of ac modulation
voltage is about 0.7 mV, and the typical range of a ramp voltage is from -0.3 V to
+0.3 V.

In Fig 5.8, a conductance is plotted vs. ramp voltage as curve A, and curve B
is a time trace of the tunneling current, both at T = 83 K. The ramp voltage rate is
about 10 mV per second, while the time constant of the lock-in amplifier is 300
ms. From curve B, it can be seen that the tunneling current is very stable, with a
fluctuation of i 1%, at a low bias voltage region. For curve B, the full ranges of
tunneling current and time axes are 1 nA and 120 seconds respectively.

From curve A, it is clear that conductance vs. bias voltage is linear at a low
bias voltage in the range of M s 0.1 V. Above this range, the conductance sigral
becomes flat and more noisy at higher bias voltages. This can be explained by
Coulomb blockade theory as mentioned previously in section 5. 3. From curve A,
the intercept of the linear line with plateau is about 0.12 V, where the tunneling
current is 0.598 nA at the bottom and 0.8 nA at the intersection point. The
corresponding conductances are 0.87 [S and 1.16 uS since the rms modulation
voltage is 0.69 mV. The resistance R, of the plateau is 0.86 MQ, so the
capacitance C of the crack junction is, according to the eqn. (5.15a)’:

[(dI/dV),. ‘ (“U/W), V" = fig;

“7% = [116- 0.87]pS/0. 12V = 2.42m / V

 

107
£=4sz4zm=0w
This large offset voltage shows that the effective capacitance C of this crack
junction is very small:
C = 3 X 10'19 F
However, this capacitance is much smaller than the capacitance calculated
fi'om the known geometry of the crack junction as follows:

C=£~fi
d

where the cross section area isA = 0.05 pm x 50 um = 2.5 m2, 8 = 8.8 x 10"12
szm'2 is the permitivity of free space. Assuming a reasonable value of 20 A for

the tunneling gap (1, we have:

-12
C = a-fi = 8.8-10'” 3431—0,— =1.1x10'“ F
d x10

Gregory found a similar discrepancy in his data 15 As pointed out before in
section 5.2.2, this result is not expected for a single junction that is not isolated
fiom its electromagnetic environment by nearby large lead resistance. A possible
explanation for such a strange finding is that there is a tiny impurity defect in the
tunneling gap, forming a double tunnel junction structure. However, we did not
observe any Coulomb staircase as shown in other literature. 13

Fig 5.9 shows similar plot for another crack junction. The metal film line was
broken in air at room temperature, and then the data were taken. This time, the
linear regime obviously continues beyond the range of ramp voltage. At higher
bias, tunneling current becomes more noisy. Moreland's squeezable tunnel
junction showed the same noisy behavior at high bias voltage.9:12 The reason for

such behavior remains unknown.

108

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5.9 Photograph of conductance vs. bias voltage for a crack junction at
room temperature.

109

5.4.2 Two Level Conductance Fluctuation in a Squeezable Tunnel

Junction

A photograph of an aligned sample for a squeezable tunnel junction is shown
in Fig 5.10. The sample is formed by two 1 pm wide thermally evaporated metal
lines facing each other on two glass substrates. The glass substrates are 1.2 mm
thick, 1 inch long and 0.4 inch wide. It is a challenge to put such a pair of
substrates together, and put the 1 um2 junction area right underneath of the tip of
the ball bearing This is done with the help of an optical microscope.

The procedure for assembling the squeezable junction requires an inverted
optical microscope. An inverted microscope is one in which the objective lens
points up at a sample which faces down and is supported along its edges by the
sample stage(see Fig2.3). A 1" long, thin-walled Al cylinder with an inner

 

Figure 5.10 Photograph of a typical micron-sized squeezable junction

110

diameter of 3/ " fits snugly on the x10 objective lens of the microscope which has
an X-Y—Z sample stage. The first substrate is placed on the top of the cylinder
with the metal film sample facing upward and the cylinder is positioned on the
objective lens so that the sample, viewed through the glass substrate, is in sharp
focus. Then the second substrate, supported by the sample stage with its metal
film sample facing down, is positioned over the first one and moved down slowly
until both samples are in the focus, but still not touching The sample stage and
the top substrate are then positioned so that the two substrates are aligned with the
four spacers on both substrates matching and the two metal stripes perpendicular
to each other. Finally, the top substrate is lowered until the two substrates touch
and adhesive tape is used to prevent slipping of the matched substrates. Then, four
electrical leads are attached to the four pads of the junction by pressing In slabs.
No other better way has been found for attaching the leads after assembling the
squeezer in our design.

Now, the junction with attached electrical leads has to be placed underneath
the ball bearing of the squeezer in the mechanical squeezer shown in Fig 5.4.
This is done using a ruler and an optical microscope. A plastic ruler inserted into
the path of illuminating light provides an one-dimensional coordinate in the field
of the view. Using the ruler, the positions of the junction and the ball bearing can
be located easily through the observing hole at the center of the bottom of the
squeezer, even though the junction and the top of the ball bearing cannot be seen
at the same time because of the limited depth of focus of the objective lens. As a
result, the tunnel junction can be placed right at the center of the ball bearing's
contacting area to the substrate by adjusting the junction's position carefully.

The mechanical squeezer is "top-loaded" in the following order: first, the
aligned junction with electrical leads are placed onto the base of the squeezer; then
the cross-shape stainless steel shim with the ball bearing is placed down along the

111

four long bolts at the top; next, the spring is placed with piston at the top of the Al
plug in the shim; finally, the top base with the smooth guiding cylinder and the #
2-64 screw is lowered down and four bolt nuts are tightened to make the entire
squeezer solid

The squeezer with the tunnel junction is then attached to one end of the sample
stick, and lowered down into a liquid nitrogen dewar. Again, the tunnel junction is
in the cold nitrogen vapor. It takes about two hours for the junction to come to
equilibrium with the cold vapor. By turning a long S.S. shaft outside, the
tunneling gap is decreased by the squeezer, until a tunneling current appears in the
lock-in's monitor.

Fig 5.11 shows the plot of conductance vs. bias voltage for a squeezable
tunnel junction at 83 K. This curve is approximately parabolic, and varies slowly
at low bias voltage, a behavior typical of a conventional tunnel junction with a
large junction capacitance. At high bias voltage, the signal becomes noisy as
mentioned previously in the crack junction's section. The reason for such a
behavior remains unknown.

The tunnel current vs. time at low bias voltage is plotted in Fig 5.12. This
curve indicates that the mechanically-controlled squeezer has a very good stability,
:1%. The curve in Fig 5.13 shows the tunneling current trace vs. time while the
tunneling gap is adjusted by the long S.S. shaft. First, the tunneling current is
initially set to A1. After a while, the tunneling gap is decreased by turning the
shaft, the tunneling current increases and goes off scale. However, the two
electrodes do not contact. Then the screw shaft is turned to increase the tunneling
gap, the tunneling current decreases, but it is still larger than the initial setting A
moment later, the tunneling gap is increased further, the tunneling current became
smaller than the initial value. The horizontal axis is 2 minutes in full scale, the Y-

axis is arbitrary unit. It is clear that our mechanical squeezer has good

Conductance (S)

112

Conductance vs. Bias-Voltage

 

7-05'5 '1'1fififi—Tfi—F'I'F
6.0E'5
5.0E-5'
4.0E'5.
3.0E'5.

2.0E-5

 

1 .0E-5

 

 

0.0E0
-o.4 -o.3 -o.2 -o.1 0.0 0.1 0.2 0.3 0.4

Bias-voltage (V)

 

Figure 5.11 Plot of conductance vs. bias voltage for a 1 pm sample at T = 83 K.

Conductance (S)

4.0E-5

3.0E-5

2.0E-5

1 .OE-5

0.0E0

Figure 5.12

113

Conductance Fluctuation

 

I 1 I r ' I I '
--------------------------------------------------------------- -
P ........................................................... ‘
I
............................................................ .-

i

 

 

 

0 2O 40 60 80 100 120 140

Time (s)

Tunnel current vs. time for a 1 pm sample at T = 83 K

114

 

 

 

Figure 5. 13 Trace of a tunneling current vs. time to show the controllable gap in
the squeezable tunneling junction.

Conductance (S)

115

Two-level Fluctuation of Conductance

 

4-05'5 '7'1'1'7'1'?

305-5» ----------- -~ ~ - --------------- .
U . . . '

-r

ZOE-5' ....... ......... ........ _________ _______ ,,,,,,, ‘

1.05-5-~--~~§ ......... ...... ........ ........ ......... ....... ,

 

 

; l .

 

0.0E0‘i*i-1Pir‘
0 2o 40 60 so 100 120 140
Time(s)

Figure 5.14 Two level conductance fluctuation of a sample in a tunneling
junction.

116

controllability as well as stability during the entire process of the adjustment.

Finally, a two-level conductance fluctuation vs. time is show in Fig 5.14. The
data were taken at T = 83 K. Even though there is a background noise, it is clear
that two level system shows up in the tunneling conductance fluctuation. We
cannot identify the microscopic origin of this two-level conductance fluctuation
yet. Nevertheless, it is speculated that there could be nanometer scale defect
migrating near the tunneling area on the sample surface. When the defect jumps in
or out of the tunneling area, it could modulate the tunneling gap, thus causing
tunneling conductance fluctuation at two levels. Several minutes after the trace of
Fig 5.12 was taken, this two-level conductance fluctuation was gone. Either the
tunneling area shifted away fiom the defect or the defect migrated away from the
tunneling area

It should be pointed out that we conducted such experiments for a large
number of micron-sized squeezable tunnel junctions. However, none of them
showed Coulomb blockade of single electron tunneling as the crack junctions did
Some effort was made to fabricate 0.1 pm tunnel junctions. Unfortunately, they
were always destroyed by the lead attachments due to static electrical discharge
because the sub-micron microbridges were not protected by shorting bridges.
There was difficulty to scratch those lines in the squeezable tunneling junction
because of the junction arrangement.

In conclusion, I have presented the design for the crack junction and the
squeezable tunnel junction in this chapter. Both the crack junction and the
squeezable tunneling junction demonstrated excellent mechanical controllability
and stability. The experimental data from the crack junctions showed Coulomb
blockade of single electron tunneling and the squeezable tunnel junctions showed
two-level conductance fluctuation at T = 83 K.

117

References for chapter 5

 

1 Ivar Giaever and Karl Mergerle, Phys. Rev. B E2, 1101 (1961).

2 G. Binnig, H. Rohrer, Ch. Gerber and E. Weibel, Appl. Phys. Lett. Q, 178
(1982); ibid, Phys. Rev. Lett. 49 (1982) 57; ibid, Physica B 1_09_-1_IQ, 2075
(1982)

3 John Morland and P. K. Hansma, Rev. Sci. Instrum. 5_5, 399 (1984).

4 John Morland and J. w. Elkin, J. Appl. Phys. 58, 3889 (1985).

5 J. G. Simmons,J. Appl. Phys. 3_4_, 1793 (1963).

6 Zeng Jingxian, Quantum Mechanics, Science Publisher Cop. 1989.

7 D. V. Averin and K. K. Likharev, J. Low Temp. Lett. 6_2, 109 (1986).
8 T. A Fulton and G. J. Dolan, Phys. Rev. Lettfi, 109 (1987).

9 R Wilkins, E. Ben-Jacob, and R. C. Jacklevic, Phys. Rev. Lett., Q, 801
(1990)

10 K. Mullen, E. Ben—Jacob, R. C. Jacklevic and Z. Schuss, Phys. Rev. B. 32, 98
(1988)

11 L. J. Geerlings, V. F. Anderegg, P. A. M Holweg and J. E. Mooij, Phys. Rev.
Lett., g, 2691 (1990).

12 K. Flensberg, S. M Girvin, M Johnson, D. R Penn, and M D. Stiles, call

13 P. Delsing, K. L. Likharev, L. S. Kuzrnin, and T. Claeson, Phys. Rev. Lett., _6_3,
1180 (1989).

14 P. J. M Von Bentum and H. Van Kempen, Phys. Rev. Lett., @, 369 (1988).
15 Stephen Gregory, Phys. Rev. Lett., 64, 689 (1990).

16 Lock-in amplifier, SR510, Standford Research Corp.

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