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THESIS

7
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31293 01712 9028

This is to certify that the

dissertation entitled
H igh 9‘63me Eflecfrimi Baperttes
(9% P0 Hcrgstqm no Di cum 0 noL

presented by

Mokanmad M Baton/wok

has been accepted towards fulfillment
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Major professor

Date 0.5146. [OJ/997

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1/96 mumps-ma

HIGH FREQUENCY ELECTRICAL PROPERTIES OF
POLYCRYSTALLINE DIAMOND

By

Mohannad M. Bataineh

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Electrical Engineering

1997

ABSTRACT

HIGH FREQUENCY ELECTRICAL PROPERTIES OF
POLYCRYSTALLINE DIAMOND

By

Mohannad M. Bataineh

Diamond is a material of great interest for various high frequency electronic
applications stemming from its constellation of material properties, including large
energy gap, high breakdown field, and high free carrier saturation velocity, among
others. However, there are several outstanding questions regarding the frequency
dependent electrical properties of diamond. For example, it is not clear whether
observed frequency dependencies are mainly due to inter-grain or intra-grain
effects. Also it is not clear whether grain boundary effects on frequency dependent
conductivity is mainly due to hopping or to potential barrier capacitive effects. This
dissertation addresses these basic questions by analyzing results over a broad
frequency range so as to separate the roles of these phenomena.

The impedance spectroscopy method is used to study electrical conduction
in diamond over a frequency range from dc to lGHz. Both thick, free-standing
films (200 to 400 um thickness) and thin films on silicon (3 to 6 pm thickness) are

investigated. Experimental results fit well to an electrical model which includes

 

both a hopping conduction path and a path representing cross-grain—boundary
conduction. For finer-grain, thin film samples, the data indicates that hopping plays
the larger role. However, this was not the case for the larger-grain, thick film
samples for which the cross-grain-boundary path dominated the frequency
dependent admittance between 1 MHz and 100 MHz.

Correlations are investigated between the do and ac electrical properties of
diamond, and the input and output growth parameters. The study of the relationship
to deposition parameters implies that the hydrogen flow rate is the single most
dominant parameter in determining the dc as-grown electrical resistivity. As for the
ac properties, the effects of annealing and temperature on electrical conductivity
and on the ac circuit model parameters suggest that the incorporation of hydrogen
in the diamond fihns takes place at the grain boundaries, and not within the
crystallites themselves.

In conclusion, the study shows that the frequency dependent electrical
properties of polycrystalline diamond, beyond those expected as a result of the
samples geometric capacitance, are principally associated with grain boundaries.
Both hopping and cross-grain boundary conduction paths play important roles in

the total conduction process of the diamond films.

 

Copyright by
Mohannad M. Bataineh
1997

To my wonderful parents and my sweet wife.

iv

ACKNOWLEDGMENTS

This publication would not be possible without the assistance and guidance
of Professor Donnie K. Reinhard in the Department of Electrical Engineering at
Michigan State University. His combined years of research and experience in this
field have given me a better understanding of this exciting work. I would like to
thank my doctoral committee members, Professor J. Asmussen, Professor D.
Aslam, and Professor B. Golding, for all the valuable comments and suggestions
they have provided, and for the helpful discussion of all aspects of this research
which we have had. Appreciations expressed to Dr. Joerg MoBbrucker for
providing the Raman analysis and to Dr. Saeid Khatami for providing the thin-film
samples.

Special thanks go to my mom and dad for their love and endless prayers. I
would also like to thank all of my family and family-in-law for their continuous
encouragement and support they have given me throughout the past years. Many
thanks go to my close friends who have been a very important part of my life.

Finally, I would like to thank the person who gave me the love and care I

needed to get through this work, the one who helped make my dreams come true,
many thanks go to my wonderful wife, Eman, for her patience and understanding.
This work was sponsored in part by the National Science Foundation Grant
ECS-9413727 and by the Michigan Research Excellence Fund through the Center
for Fundamental Materials Research and the Electronic and Surface Properties of

Materials Center.

vi

TABLE OF CONTENTS
LIST OF TABLES .................................................................................................... x
LIST OF FIGURES .................................................................................................. xi
CHAPTER 1
INTRODUCTION .................................................................................................... 1
1.1 Motivation .................................................................................................... 1
1.2 Objectives ..................................................................................................... 3
1.3 Preview of Thesis .......................................................................................... 4
CHAPTER 2
BACKGROUND ...................................................................................................... 5
2.1 Introduction and General Facts ..................................................................... S
2.2 Electrical Properties of Single Crystal Diamond ......................................... 10

2.3 DC Electrical Conduction in Polycrystalline Semiconductors:
General Considerations ........................................................................... 14

2.4 Frequency- and Temperature-Dependent Electrical Conduction in

Polycrystalline Semiconductors: General Considerations ...................................... 19
2.5 Electronic Properties of Polycrystalline Diamond ...................................... 28
2.5.] DC Properties of Polycrystalline Diamond .................................................... 28

2.5.2 Frequency and Temperature-Dependent ac Properties of Polycrystalline
Diamond ............................................................................................................................. 32

vii

CHAPTER 3

EXPERIMENTAL METHODS .............................................................................. 36
3.1 Introduction ............................................................................................... 36
3.2 Equipment ................................................................................................... 36
3.3 Sample Preparation ..................................................................................... 43

3.3.1 Measurement Setup ........................................................................................... 45

CHAPTER 4

MODELING TECHNIQUE ................................................................................... 49
4.1 Introduction ............................................................................................... 49
4.2 Impedance Spectroscopy Technique ......................................................... 50
4.3 Basic Four Path Model .............................................................................. 55
4.4 Model Fitting ............................................................................................. 58

CHAPTER 5

APPLICATION OF THE FOUR-PATH MODEL TO THIN- AND THICK-FILM

DIAMOND AT ROOM TEMPERATURE ............................................................ 64
5.1 Introduction ............................................................................................... 64
5.2 Thin-Film Diamond ................................................................................... 65

5.2.1 Film Growth And Structural Properties ......................................................... 65
5.2.2 Instrumentation Setup and Results for Thin-Film Diamond Samples ............ 67
5.3 Results of Thick-Film Diamond Samples ................................................. 81
5.4 Results Analyses ........................................................................................ 83
5.5 Relative Role Of The Model Components ................................................ 92
5.6 Sensitivity Of Model to Changes in Parameter Values ................................. 97
CHAPTER 6
EFFECTS OF GROWTH CONDITIONS AND FILM ATTRIBUTES ON AC
ELECTRICAL CONDUCTION IN CVD DIAMOND FILMS ............................ 100

viii

 

6.1 Introduction .............................................................................................. 100
6.2 Sample Description And Experimental Procedure .................................... 101
6.3 Relationship of As-Grown Electrical Properties to Film Attributes and
Deposition Parameters .......................................................................................... 1 12

6.4 Annealing and Temperature Effects on Electrical Conductivity and ac

Circuit Model Parameters ..................................................................................... 126
CHAPTER 7

DISCUSSION AND FUTURE WORK ................................................................ 144
BIBLIOGRAPY .................................................................................................... 148

ix

LIST OF TABLES
Table 2.1: Chronology of Carbon Technology .......................................................... 6
Table 2.2: Electrical and Related Properties of Diamond ........................................ 11
Table 5.1: Deposition Conditions for Thin Diamond Films ..................................... 66
Table 5.2: Best-Fit Model Parameters For Thick Diamond Films ........................... 78

Table 5.3: Model Parameters For Sample SK-13 Using Different Error Calculation

Methods .................................................................................................................. 82

Table 5.4: Best-Fit Model Parameters For Thick Diamond Films ........................... 87
Table 5.5: Normalized Cumulative Percent Error, E ............................................... 93
Table 5.6: Sensitivity Results for Thin Film Sample SK-13 .................................... 98
Table 5.6: Sensitivity Results for Thick Film Sample TDF-18 ................................ 98
Table 6.1: CVD Thin Diamond Films’ Key Properties .......................................... 1 1 1
Table 6.2: Samples’ Contact Properties and as-grown dc Resistivities .................. l 13
Table 6.3: IS Model Parameters for as-grown Films at Room Temperature .......... 121
Table 6.4: Resistivity of Selected Films Before and After Annealing .................... 131
Table 6.5: Best-fit Parameter Values for Two Thin Film CVD Samples ............... 135

LIST OF FIGURES

FIGURE 2.1: Raman spectrum of diamond and polycrystalline graphite .................. 8
FIGURE 2.2: Schematic diagram of diamond cubic structure ................................. 9
FIGURE 2.3: Energy band structure of n-type polycrystalline thin film ............... 17
FIGURE 2.4: Kuznicki’s electrical model of polycrystalline thin film .................. 18
FIGURE 2.5: Street’s model of the bulk material and the leads ............................... 23
FIGURE 2.6: Space charge limited current flow ..................................................... 31
FIGURE 3.1: HP—4l45B source/monitor unit circuit diagram ............................... 38
FIGURE 3.2: HP-4192A test signal terminals ........................................................ 40

FIGURE3.3:Circuitdesignofthereflectioncoefficientimpedancemeasurementrnethod

and the I-V measurment method .............................................................................. 42
FIGURE 3.4: Schematic diagram of diamond samples configurations .................. 46
FIGURE 3.5: Schematic diagram of conduction paths in a diamond film ............. 48
FIGURE 4.1: Flow chart for IS characterization process ......................................... 52
FIGURE 4.2: Two equivalent circuits with same impedance response ................. 53
FIGURE 4.3: Impedance spectroscopy results of a parallel R-C circuit ................ 56
FIGURE 4.4: Schematic diagram of an equivalent grain boundary path .............. 59

FIGURE 4.5: Impedance Spectroscopy Sample Circuit Model ............................. 60

FIGURE 4.6: Matlab sample program to produce model parameters with minimum

percent error ............................................................................................................ 62
FIGURE 5.1: Raman spectra thin diamond films ................................................... 68
FIGURE 5.2: Top surface SEM pictures thin diamond films ................................. 69
FIGURE 5.3: Schematic daigram of dc measurement setup .................................... 70
FIGURE 5.4: Schematic diagram of ac measurement setup .................................. 72

FIGURE 5.5: Schematic diagram of ac measurement setup .................................... 73
FIGURE 5.6: I-V Characteristics of thin-film samples ............................................ 75
FIGURE 5.7: Comparison of modeled and measured IS results ............................ 76
FIGURE 5.8: Comparison of modeled and measured IS results ............................ 79
FIGURE 5.9: Comparison of modeled and measured IS results ............................ 80
FIGURE 5.10: I-V characteristics of thick diamond films ..................................... 84
FIGURE 5.11: Raman spectra of thick diamond films ........................................... 85
FIGURE 5.12: Top surface SEM pictures of thick diamond films ................ . ........ 86

FIGURE 5.13: Results of modeled and measured IS for TDF-12 ............................ 88
FIGURE 5.14: Results of modeled and measured IS for TDF-12 ............................ 89
FIGURE 5.15: Effect of model parameter Rc on IS results ...................................... 91
FIGURE 5.16: Individual model paths contributions to total admittance ................ 96
FIGURE 6.1: Top surface SEM pictures of (a) SK-182 (b) SK-183 ...................... 102

xii

FIGURE 6.2: Top surface SEM pictures of (a) SK-l2 (b) SK-179 ........................ 103

FIGURE 6.3: Top surface SEM pictures of (a) SK-62 (b) sK-72 .......................... 104
FIGURE 6.4: Top surface SEM pictures of (a) SK-209, and (b) SK-177 ............... 105
FIGURE 6.5: Top surface SEM pictures of sample TKB ...................................... 106
FIGURE 6.6: Raman spectra of (a) SK-12 (b) SK-179 .......................................... 107
FIGURE 6.7: Raman spectra of (a) SK-62 (b) SK-72 ............................................ 108
FIGURE 6.8: Rarnan spectra of (a) SK-209 (b) SK-l77 ........................................ 109
FIGURE 6.9: Raman spectra of (a) SK-183 (b) TKB ............................................ 1 10
FIGURE 6.10: Schematic diagram showing the investigated correlations ......... 114

FIGURE 6.11: Correlation between as-grown dc resistivity and growth

parameter ............................................................................................................... 116
FIGURE 6.12: Relationship between fihns’ as-grown dc resistivity and (a) flow rate,
in sccm, (b) substrate temperature, Ts, in OK .......................................................... 1 17
FIGURE 6.13: Relationship between films’ as-grown dc resistivity and (a) growth
parameter, or, (b) full-width-at—half-maximum (FW HM) ............................... 118
FIGURE 6.14: Relationship between films’ as-grown dc resistivity and (a) Id/Ig
Raman signal ratio, (b) grain size, um ................................................................... 119
FIGURE 6.15: Relationship between ac hopping admittance and [(1/18 ................. 122
FIGURE 6.16: Relationship between ac hopping admittance and grain

size ........................................................................................................................ 123

xiii

FIGURE 6.17: The relationship between cross-grain boundary conduction and grain
Slze ............................... 125
FIGURE 6.18: dc I-V behavior of SK-72 in the as-grown state versus temperature,
showing annealing effect at higher measurement temperatures ............................. 127
FIGURE 6.19: I-V characteristics (a) before annealing, and (b) after

annealing ............................................................................................................... 129
FIGURE 6.20: dc Resistance as a function of temperature for (a) sample SK-62, and
(b) sample SK-72 .................................................................................................. 131
FIGURE 6.21: ac Conductance for samples in the as-grown, annealed, and annealed
and tested at higher temperatures. (a) SK-62, and (b) SK-72 ................................. 133
FIGURE 6.22: Individual path contribution to the total admittace for as-grown
sample SK-62 ........................................................................................................ 137
FIGURE 6.23: Individual path contribution to the total admittace for as-grown
sample SK-72 ........................................................................................................ 138
FIGURE 6.24: Comparison between experimental and modeled ac conductance for
annealed samples, (a) SK-62, and (b) SK-72 at measurement temperature of 550
°K .......................................................................................................................... 140
FIGURE 6.25: Comparison of ac conductance for sample SK-62 with both hopping
and cross-grain-boundary paths of the ac circuit model in two frequency regions: (a)

100 Hz to 1 MHz, and (b) 10 MHz to 100 MHz ..................................................... 141

xiv

FIGURE 6.26: Comparison of ac conductance for sample SK-72 with both hopping
and cross-grain-boundary paths of the ac circuit model in two frequency regions: (a)

100 Hz to 1 MHz, and (b) 10 MHz to 100 MHz ..................................................... 142

XV

 

CHAPTER 1

INTRODUCTION

1.1 Motivation

There is a considerable interest in the electrical properties of diamond
stemming from its constellation of material properties. These include a large
energy gap, a large breakdown field, and a high thermal conductivity which
provides a potential for high-temperature, high-power electronic device operation.
Diamond’s hardness and chemical inertness offer the possibility of device
operation in hostile environments. Diamond is also considered a material of
potential interest for certain high frequency electronic applications because of its
high carrier saturation velocity. However, the ac properties of diamond have
received less attention in the literature than the dc properties. It is the frequency
dependent electrical properties that are the subject of this dissertation.

There are several questions regarding frequency dependent electrical

properties of polycrystalline diamond and diamond devices which need to be

2

answered if diamond is to be effectively used in electronic devices. For example, it
is not currently clear whether the observed frequency dependencies are primarily
due to inter-grain or intra-grain effects [1][2] [68]. This research study attempts to
answer these questions by developing a physical model which includes multiple
paths of conduction through the grains and the grain boundaries. The individual
contribution of conduction paths to the total ac electrical conductivity of a wide
variety of chemical vapor deposited (CVD) diamond samples is investigated over a
frequency range from dc to 1 GHz.

For many electronic applications, it is important to understand the dc and ac
electrical properties of diamond films over a wide range of frequencies and
temperatures, and correlate them to the input and output parameters of the growth
process. Other researchers have studied and characterized diamond films in terms
of input parameters of growth processes [70] [71][72]. However, many questions
remain unanswered. For example, does crystalline orientation play any role in
determining the electrical resistivities of diamond films, and if so, how? Does
higher Raman quality films imply better diamond insulators at high frequencies?
What are the major relationships between the growth input parameters and the
film’s electrical properties? These and other questions need to be answered from
both an electrical and a physical point of view. This research study aspires to

answer and explain such inquiries.

 

1.2 Objectives

The main objective of this study is to add to the current understanding of
electronic conduction mechanisms in both free-standing, thick polycrystalline
diamond samples and in thin diamond films on silicon. To accomplish this
objective, both the dc and the ac electrical impedance is measured and analyzed

over a frequency range from dc to 1 GHz, with temperatures varying from 300 to

550 °K. The measurements are designed to generate experimental data in a form
that can be fitted into an electrical circuit model. It is important that this model
corresponds to a physical understanding. The impedance spectroscopy (IS)
technique is found to be a useful tool for obtaining a model which explains the
relative role of contributors to the frequency dependent conductivity in diamond.
The second objective of this study is to add to the experimental
understanding of the relationship between the electrical properties of diamond and
the growth input and output parameters. The films are analyzed in the as-grown and
annealed states. As part of this task, the as-grown dc resistivity of the films is
correlated to four growth output parameters, namely average grain size, Full-
Width-at-Half-Maximum (FWHM), diamond to graphite signal ratio, and growth
parameter, or. In addition, the ac properties are analyzed in terms of the developed

model.

 

1.3 Preview of Thesis

Chapter 2 reviews previous studies of dc and ac conductivities in
polycrystalline materials, and more specifically in diamond, and examines the
electrical and physical models proposed by other researchers.

Chapter 3 describes the experimental setup and equipment used in this
study. Also included in this chapter is a description of the sample preparation
process.

Chapter 4 provides detailed background on the impedance spectroscopy (IS)
technique used to analyze experimental results, and describes the modeling method
used to fit the data into an electrical circuit model.

Chapter 5 presents the IS results of both free-standing, thick diamond
samples and thin diamond films on silicon. Also included in chapter 5 is an analysis
of how the results obtained are explained by the model developed in chapter 4.

Chapter 6 explains the relationship between the as-grown electrical
properties of CVD thin diamond films and the growth input and output parameters.
Also investigated in this chapter are the annealing and temperature effects on
electrical conductivity and ac circuit model parameters for the as—grown and
annealed diamond films.

Chapter 7 concludes this study with an analysis of the presented results and

a discussion of the open research issues and identifies ideas for future work.

 

CHAPTER 2

BACKGROUND

2.1 Introduction and General Facts

Carbo, latin for carbon, is one of the most diverse elements on earth. It has
several material forms with different physical structures known as allotropes. One
of them is the form of diamond. Table 2.1 gives a historical perspective of carbon
and its allotropes and several important dates in the development of carbon
technology.

In nature, diamond is often found in combination with other carbon
allotropes. To identify it as a separate material from all other forms of carbon,
different techniques can be used. One of them is the x-ray diffraction technique
which reveals the crystalline structure of bulk diamond or graphite. However, when
the material is composed of a mixture of diamond, graphite, and amorphous
constituents, the diffraction technique has to be interpreted cautiously because the

electron diffraction patterns of polycrystalline diamond are very similar to those of

 

Table 2.1: Chronology of Carbon Technology [33]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

First “lead” pencils 1600’s
Discovery of carbon composition of diamond 1797
First carbon electrode for electric are 1800
Graphite is recognized as a carbon polymorph 1855
First carbon filament 1879
Chemical vapor deposition (CVD) of carbon patented 1880
Production of first molded graphite (Acheson process) 1896
Carbon dating with 14C isotope 1946
Industrial production of pyrolytic graphite 1950’s
Industrial production of carbon fibers from rayon 1950’s
High Temperature /High Pressure synthesis of diamond by GE 1955
Development of production of vitreous carbon 1960’s
Development of PAN -based carbon fibers 1960’s
Development of pitch-based carbon fibers late 1960’s
Discovery of low pressure diamond synthesis 1970’s
Production of synthetic diamond suitable for gem trade 1985
Development of diamond-like carbon (DLC) 1980’s
Discovery of the fullerene molecules late 1980’s
Industrial production of CVD diamond A 1992

 

 

7
basal-plane oriented polycrystalline graphite. An alternative way to identify

diamond is by using a laser-optical technique called Raman spectroscopy. This

technique can determine the bonding states of the carbon atoms by displaying their

vibrational properties [33][34]. The sp2 bonding yields graphite, and the sp3

bonding yields diamond. Other forms of carbon, such as fullerenes, may contain

mixtures of sp2 and sp3 bondings. Figure 2.1 shows the distinction in Raman

spectra between diamond and graphite samples. The single crystal diamond shows
a sharp Raman peak at 1332 cm'1 (wave numbers) while the graphite shows a

broader peak at 1570 cm'l.

The diamond structure is cubic and may be considered as two face-centered

interpenetrating cubic lattices, one with origin at (0,0,0) and the other at (211211211) ,

with parallel axes. In Figure 2.2, two different representations of the diamond
structure are displayed [35][36]. The carbon atom bond in diamond has a very high
bond energy of 711 KJ/mol, and a small bond length of 0.154 nm [33][35].

Thus, the diversity of carbon materials has led to diverse and significant
applications. This study is concerned with a particularly interesting form of carbon,

namely diamond.

8

Diamond

 

.0
O)
r

Intensity au.

.0
A
I

 

I j I T I T I I T

 

 

 

l L 1 l l

 

0
1000

1 1 00 1 200 1 300 1 400 1 500 1 600 1 700 1 800 1 900 2000
Shift Wavenumber in 1 /cm

Graphite

 

.0
01
r

Intensity a.u.

p
A

0.2 -

 

I I I T I T Y r T

 

L

 

0
1000

1 1 00 1 200 1 300 1 400 1 500 1 600 1 700 1 800 1 900 7 2000
- Shift Wavenumber in 1/cm '

FIGURE 2.1: Raman Spectrum of diamond and polycrystalline graphite[42]

Polycrystalline Graphite film was grown on Cobalt substrate. Recording parameters:

spectral resolution=1.6 cm'1 and laser wavelenght=514.5 nm.

 

 

 

 

 

 

FIGURE 2.2: Schematic diagram of the diamond cubic structure.

 

 

10
2.2 Electrical Properties of Single Crystal Diamond

Single crystal diamond is considered one of the best known materials
because of its fame as a gem and because of its unparalleled hardness. However it is
also has a combination of electronic properties which in principle may offer
performance advantages for electronic application. Some of these electrical and
related properties are listed in Table 2.2. Single crystal diamond has a 5.5 eV
bandgap and is considered one of the best solid electrical insulators. The strong
electron bonding in diamond makes it unlikely for an electron to jump out of the

valence band even at elevated temperatures. Consequently, as listed in Table 2.2,

the resistivity of pure diamond can exceed 1018 ohm-cm. However, the presence of
impurities and the inclusion of graphite can considerably change the resistivity of
diamond, and can be reflected on the material’s electronic properties.

The question that comes to mind here is what so special about those
properties listed in Table 2.2? And what specifically makes diamond an attractive
material for a variety of electronic applications? Let us tackle some of those
properties individually. The wide bandgap is mainly responsible for the high
breakdown fields in diamond [83] which when combined with the high carrier
mobilities at both room and elevated temperatures makes diamond an excellent

material for high temperature electronic devices which require high current driving

capabilities and speed [61][69][82]. The high saturated electron velocity (2.7 x 107

11

Table 2.2: Electrical and Related Properties of Diamond

 

 

 

 

 

 

Energy gap 5.5 eV
Resistivity, ohm-cm Type Ila 1018
Dielectric constant @ 300 K 5.7i0.05
Dielectric strength, V/cm 107
Saturated electron velocity, 107 cm/s 2-7
Carrier mobility, cm2/V.s

Electron 2200
Hole 1600

 

 

Thermal conductivity @ 293 K, W/m.K

 

Type Ia 600 - 1000
Type Ila 2000 - 2100

 

 

 

12

curls) and the dielectric strength (107 V/cm) are other advantages of diamond. As
defined in [65] by Johnson, Equation 2.1 results in Johnson’s figure of merit (JFM)

for diamond to be much higher than that of silicon. The ratio of (JFM)diamond to

(JFM)Silic0n equals to 8206 [62] [63][64].

ECDS
JFM = Zn (2.1)

 

EC is the breakdown field, which is for diamond equals to 107, and Us is the charge

carriers saturation velocity, which is for diamond equals to 2.7x107.
Another important figure of merit which researchers use to estimate a
material’s potential for digital integrated circuits is Keyes figure of merit [66]

(KFM.) As defined by Keyes, Equation 2.2 gives the meaning of that figure.

1

2
KFM = 161:) (2.2)

 

where 7t is the thermal conductivity, c is the velocity of light in vacuum, and e, is
the dielectric constant of the material. With Keyes’ measures, the ratio of
(KFM)diamond to (KFM)Smcon came out to be equal to 32.2 [61]. Indeed, diamond,
as compared to other semiconducting materials, has excellent material electrical

properties to be considered unique. For example, the Keyes figure of merits for

 

13
gallium arsenide (= 0.456) and silicon carbide (= 5.8) are much lower than that of

diamond. Also comparing the numbers for Johnson’s figure of merit for those two

materials with diamond shows that J FMdi amond is over a thousand times higher than

that of GaAs, and over ten times higher than that of SiC.

On the other hand, doped diamond also possesses excellent semiconducting
properties, and has good potential as a semiconductor material [37]. It has the
widest indirect bandgap of any other semiconductor material, which makes it a
perfect semiconducting material to be used at high temperatures when long carrier
lifetime is important [61][69] [73][74] [75][76] [81]. Compared to other
semiconductors, such as silicon and GaAs, diamond has a low dielectric constant

(5.7) which reduces capacitive effects. And unlike silicon or gallium arsenide,

diamond has an upper limit semiconductor temperature of 500°C or higher. Those
excellent properties of diamond have motivated many researchers to try to form
synthetic diamond under economical conditions on non-diamond substrates with
areas large enough for electronic applications. To date, this has resulted primarily
in polycrystalline diamond rather than single-crystal diamond. The properties of
polycrystalline semiconductors can differ considerably from those of single-crystal
materials. In the following section, first issues related to polycrystalline
semiconductors in general are described, then in particular polycrystalline

diamond.

14
2.3 DC Electrical Conduction in Polycrystalline Semiconductors:

General Considerations

Most of the transport mechanisms for electrical conduction in
polycrystalline, semiconducting films in general, that have been proposed by
researchers in past years, have focused on the effect of the inherent intercrystalline
boundaries, or grain boundaries [3]. Although researchers have described
generalized techniques to explain the electrical conduction behavior due to grain
boundaries, the techniques must be viewed as models which correctly explain the
electrical behavior of the films under an explicit set of conditions of experimental
and material circumstances.

The most cited theoretical analysis of transport mechanisms in
polycrystalline thin. films is that of Petritz [8] who based his model on the
assumption of energy barriers between crystallites. In this case, the conductivity of
polycrystalline semiconductors is dominated by the thermionic emission of carriers
over the barriers between grains [3][8]. The current-voltage relationship for the

barrier in his model was expressed, analogous to simple diode theory, as
j = Moneeer-qiib/kT) [6Xp(qu/kT)-1] (2.3)

where j is the current density, n is the mean majority carrier density in the grains, ¢b

15
is the potential height of the barriers, Vb is the voltage drop across the barriers, and

M is a factor that is barrier dependent but independent of rib and is given by
M=ubnckT, where r1C is the number of grains per unit length along the film. If the

film has many barriers (i.e small grain sizes), the voltage drop across any one is

small compared to kT/q, and the equation 2.1 may be written as
j = M-n-exp(—q¢b/kT) . (qu/kT) (2.4)
Thus, the conductivity can be expressed as
0 = 178 = qubn exr)(-q¢p/kT) (2.5)

where e is the electric field. Figure 2.3 shows the energy band structure of an n-type

polycrystalline semiconductor thin film with grain size 11, grain boundary width 12,
and grain boundary barrier potential qob. Petritz explicitly derived an equation for

the mobility in the film, “g, as

ug=ub exp<—q¢b/1<T> (2.6)

where uh is the bulk or single-crystal mobility value, and q¢b is defined to be equal
to kT ln(n1/n2), where n1 and n2 are the carrier densities in the grain and grain

boundary regions, respectively.

 

 

 

 

 

16
I
,1 214 T
(1%
EC
_____________________ Ir}
J E,
|< >1
’1

FIGURE 2.3: Energy band structure of n-type polycrystalline thin film.

17

A simpler model was proposed earlier by Volger [9] to explain the electrical
conductivity mechanism in polycrystalline semiconductor films. He based his
model on that the polycrystalline films consist of two separately homogenous
regions, the grains and the grain boundaries, in which no space charge regions
exist, and where the grain boundaries region has a higher electrical resistivity than

that of the grains region. Defining 11 and 12 as the grain and the grain boundary

widths, he derived an expression for the effective mobility as follow

ug=ub {[1+(12/11)eXI>(q<l>b/I<T)l‘l +(12/1m (2.7)

where rig is the film mobility, and (Pb is the barrier potential due to the

concentrations in the grain and grain boundary.

Several other models have been proposed to interpret the electrical
conductivities in polycrystalline semiconductor films, and among them are more
complicated approaches based on electrical component modeling of the
polycrystalline films. Kuznicki [10] has proposed an equivalent electrical model to
represent the grains and the grain boundaries in the films as shown in Figure 2.4.
The model was used to numerically verify the static electrical characteristics of
CdSe films. The simulated results of this model fitted well with his experimental
data.

In summary, a variety of conduction models for polycrystalline

18

 

AAA
V

   

 

 

 

 

9

i“ i

FIGURE 2.4: Kuznicki’s electrical model of polycrystalline CdSe thin film.

19

semiconductors have been proposed in the literature, however a key feature of all is
the role of the grain boundaries. Additional insight is obtained by considering the

frequency and temperature dependent of conductivity.

2.4 Frequency~ and Temperature-Dependent Electrical Conduction in

Polycrystalline Semiconductors: General Considerations

The temperature and frequency dependent electrical conductivities of

polycrystalline materials have been studied by several researchers [1][3][ll][12].

The frequency dependent electrical conductivity in hopping systems, 6(9), was
first observed and reported by Pollak and Geballe in 196l[l8][l9]. Pollak has
observed in his study of the non-steady-state (i.e. ac) band and hopping
conductions that the two conduction mechanisms have basically different ac
behaviors. Band conduction current is carried by electrons (or holes) in Bloch
states, and so, it is necessary only to disturb the equilibrium distribution of the
electrons to achieve a finite current. However, in the hopping conduction process,
the states are localized and there is no current associated with any electronic state.
In this case, the conduction current is a result of transition of electrons from state to
state, i.e. the hopping of electrons produces the current. In his study, Pollak derived
formulas for the real parts of the band and hopping conductions, and they are given

in the following equations

20
Eliobandm) or ——1—2——2- (2.8)
1 + (o r
ERG (w) or (”21 (2 9)
h .
0p (1 + (0212)

where 12 is the Boltzman transport equation’s relaxation time and is usually in the
order of pico-seconds for band conduction, and a) is the angular frequency of the

applied field. The first equation clearly shows that for frequencies less than 1011

Hz, (1)212 will be much less than unity, and the conductivity due to band

conduction will not show any considerable dependence on frequency. However, in

the higher ranges of frequencies (> 1011 Hz), the first equation predicts that the real
part of conductivity will be a decreasing function of frequency.

Jonscher [20] also experimentally studied the frequency dependence of
conductivity in hopping systems, mainly non-metallic solids, in which the flow of
current occurs by hopping of localized carriers, whether electrons or ions. He
pointed out that the same dependence is found in semiconducting amorphous

systems and in a broad group of insulators. He observed in his study that at
sufficiently low frequencies and down to dc there is a constant level, 00, of

conductivity, and there follows a region where conductivity is an increasing

21
function of frequency. He expressed this dependence, supporting Pollak and

Geballe’s observation, by the empirical relation

oaw" (2.10)

where 11 takes values in the range 0.5 < n < 1.0, depending upon temperature.
Jonscher added, however, that the principal drawback of the various theories lies in
the difficulty of obtaining an adequate physical insight into the suggested
conduction mechanisms, especially in view of the extremely wide range of systems
involved [21]. Even though Jonscher’s results do not agree completely with
Pollak’s, similar observations were reported by other researchers

[1][2][3][4][l1][22][23][24][25] for different types of polycrystalline materials.

2

However, the appearance of 0) -dependent conductivity was also reported by

Jonscher and by other researchers [20][26][27]. Jonscher related the (02

dependency to a possible spurious effect of even very small resistance and

inductance associated with the leads external to the films. Street, et al.[26] clarified

the (1)2 -dependence of A82583 amorphous films with the aid of the circuit model
shown in Figure 2.5. The parameters CL and RL are the lead capacitance and
resistance, and CS and RS are the capacitance and resistance of the sample,

respectively. The equivalent capacitance and resistance of the circuit are given by

22

 

 

 

RP, c, a1>

 

 

 

FIGURE 2.5: Street’s model of the bulk material and the leads.

23
the following equations:

 

Rs

RP=RL+1+03212

R
(R /(R +R ))2C
C =C + S L C S

P L 2 2

1+(o TC

where
2 2 2

TR = (CS RS RL)/(RS+RL)

2 2 2 2 2
TC =( SRS RLj/(RL+RS)

(2.11)

(2.12)

(2.13)

(2.14)

Under the assumption that R5 >> RL, they divided the frequency-dependent

electrical conductivity into three different regions. For the low-frequency region

where (1) <<1/1:R,one finds RP z RS and CP z CL + CS' For the mid-frequency

region where lltR < 0) < lltC one finds RP= IlmngRL and sz CL + C3.

Note that in this caSe the meaSured Rp shows an (1) dependence which is an artifact

due to the presence of RL. And finally, in the high-frequency region where (D >>

24

i , R P 2 R L and C P s: C L + (C3/ (021%). Consequently, the frequency

TC
dependence of the measured Rp may not reflect the actual behavior of the sample
resistance, R5, at sufficiently high frequencies.

In a similar study of the electrical conductivity in amorphous materials by
Elliot [28], an equation for the ac electrical conductivity was derived. He proposed
a model, correlated barrier hopping (CBH), to interpret the dependence on both
frequency and temperature of the ac electrical conductivity. In his model, he
assumed that an electron in a charged defect state hops over a potential barrier of

height W given by

 

4 2
“W” = w — "e (2.15)

where Wm is the maximum energy required to take an electron from a hopping site

to the conduction band, a is an effective dielectric constant which may be taken to
be the same as the bulk dielectric constant, e is the electronic charge, 11 is the

number of electrons that hop, and R is the distance between the hopping sites. He

eventually derived the final expression for the o Adm) to be equal to:

 

25

2 2 2 s
GAc(0)) = [In 21:; 8L8; Jff—B] (2.16)
m

 

where B=6kT/Wm, s=l-B, N = concentration of localized states and t is of the

order of an atomic vibrational period, 10'135. This model, in disagreement with
Pollak’s theoretical model, shows that the exponent, 3, cannot be greater than unity.

However, both models did not take into account the effect of lead resistances and

inductances. Moreover, Elliot’s model shows that the exponent of (1) directly
depends on the temperature and the maximum energy height.

On the other hand, other researchers [8] [9] [29] [47] [48] directly related the
frequency-dependent electrical conductivity of polycrystalline semiconductor
materials to the electrical properties of grain boundaries rather than hopping.
Werner [29], in his study of the electronic properties of grain boundaries, suggested
that the application of a small ac voltage leads to a time periodic change of the
potential barrier between grains which leads to a periodical variation in the hole
concentration at the interface between grains. This change drives a periodic capture
and emission of holes by the interface states. The difference between the capture

and emission rates produces a displacement current given by:

26
J = Yeti (2.17)

where Y is the characteristic admittance of the traps, and 5(1) is the applied ac
voltage.

Concerning the temperature dependent electrical conductivity, Elliot and
other researchers [12][30][31][32] showed that both the dc and the ac electrical
conductivities are functions of temperature. However, Elliot did not explicitly show
in his model how the temperature affects each individual conductivity path within
the polycrystalline materials he studied. It has been subsequently shown by other
researchers [1][11][44][45][46] that the dc electrical conductivity can be expressed

as a sum of three components:

0 = 01 exp(—E1 lkT) + 0'2 exp(—E2 IkT) + 63 exp(-E3 IkT) (2.18)

where E], E2, and E3 are the activation energies for the high, medium, and low

temperature ranges, respectively. Researchers have also studied the ac temperature
dependent electrical conductivity in different materials systems, and found out that
temperature plays a major role in hopping conductions as well as in conductions
within the grain boundaries [21][32]. It has been shown by many researchers that
the exponent n in the empirical relation of equation 2.10 is a function of

temperature, approaching unity at low temperatures and decreasing to 0.5 or less at

27
higher temperatures. In a recent study by Hari, et al.[32], the complex impedance

of n—BaTiO3 ceramics have been studied. They explicitly studied and analyzed the

contributions of grains and grain boundaries to the total resistance of the samples,
and they have concluded that the observed Positive Temperature Coefficient of
Resistance (PT CR) in dc resistivity is mainly due to the increase in grain boundary
resistivity. They have clearly showed that the grain boundary resistivity jumps are
relatively high compared to the change observed in the grain resistivities versus
temperatures, confirming the major contribution to the PTCR effect is from the
grain boundaries, not the grain interiors.

In summary, it seems that the frequency-dependent electrical conductivity,
particularly in amorphous semiconductors and non-metallic polycrystalline solids,
can be related either to hopping, which can occur either as a bulk phenomena or via
states between grains, or to a grain boundaries’ electronic potential properties.
Hopping between localized states within a crystallite, for example, is considered to
be a pure bulk phenomena where the SCL currents and currents due to the capture
and emission of holes by the interface states are related to changes in the grain
boundaries potential barriers. Finally, the ac electrical conductivity measurements
versus temperature, of different semiconductor materials, were very helpful in
differentiating between variable-range hopping conduction through the films’

surface conducting layers and through paths along the grain boundaries, and

28

conduction due to the thermal excitation energy of electrons.

2.5 Electronic Properties of Polycrystalline Diamond

2.5.1 DC Properties of Polycrystalline Diamond

Concerning polycrystalline diamond, several researchers have studied the
static and dynamic electrical conduction mechanisms in both thin and thick
diamond films grown by different techniques and under different conditions
[l][3][4][11][12][13][14][77][78][80]. Ohmic and non-ohmic current flow
behavior has been reported and in some cases diamond films, with different
electrode materials and sample geometries, show both ohmic and non-ohmic
portions of the current-voltage characteristics [15][79]. Iwasaki et al. [15]
concluded, in their study of the formation of ohmic contacts on semiconductor
CVD diamond, that the current-voltage characteristics of All and Mg/p-type
diamond contacts change from ohmic to non-ohmic as the resistivity of the

semiconductor diamond films increases, while the Au/p-type diamond contact
shows good ohmic behavior. Also, a contact resistance, RC, of less than 103 51cm2

was found to be necessary for obtaining ohmic contacts on semiconductor CVD

diamonds regardless of the metal. However, it should also be noted that other

29
researchers [17] have successfully fabricated Schottky diodes using gold contacts

on thin diamond films obtained by plasma assisted CVD process.

Muto et a1. [7] have studied the electrical conduction along conducting
layers between grains in CVD polycrystalline diamond films and have concluded
that the conductivity in the ohmic region in the as-grown films is mainly caused by
variable range dc hopping along the disordered graphitic region between diamond
grains. This type of hopping has often been observed in amorphous semiconductors
with dense localized defects. They have also observed that the conductivity
decreased drastically after the sample was annealed at 670 K. This decrease in the
conductivity was related to the removal of the disordered graphitic region.
However, in their study of the nonlinear portion of the current-voltage
characteristic of thin diamond films (1-2 1.1m), they suggested that the electrical
conduction in this region is more likely due to the Poole-Frenkel emission as
opposed to the Schottky emission. This conclusion is consistent with those of
Huang and Reinhard [16] who investigated the voltage dependence of the
photoconductivity and showed that the high-voltage increase in polycrystalline
diamond thin films’ conductance is due to an increase in dark carrier concentration
rather than an increase in mobility. And this, theoretically, agrees with the Poole-
Frenkel mechanism of electrical conduction. Thus, the currents, at sufficiently high

voltages, may no longer be determined by only the bulk carrier densities that were

30

present in the absence of the applied voltage.

At reasonably high voltages, excess carriers, injected from one of the
electrodes, may also have a considerable contribution to the total current flowing in
the bulk material. These currents, arise from a space charge of excess carriers, are
called Space-Charge-Limited (SCL) currents [23][56][57][58][59][60]. Figure 2.6
shows a bulk insulator with two contacts where the low work function cathode is
assumed to supply electrons in the conduction band. Those electrons will be drawn
into the space between the cathode and the anode by the applied voltage.

The current-voltage relationship of this type of currents flow is given by the

following equation

I = cvrrr (2.19)

where C is the geometric capacitance, V is the applied voltage, and Tr is the transit

time of an electron from cathode to anode, and is a function of the applied voltage.
This type of currents’ contribution can also be responsible for the increase in the
material’s electrical conductivity at high dc voltages.

Even though the steady-state measurement techniques, i.e. dc methods, are
very helpful in determining and understanding the different conduction
mechanisms of polycrystalline materials including diamonds, such as Poole-

Frenkel emission as opposed to space-charged-limited current, they do not easily

31

 

 

Cathode

+V

FIGURE 2.6: Space Charge Limited current flow.

32

reveal the information whether the conduction in the materials happens in a band or
by hopping of electrons from localized states. Therefore, the need for an extensive

study of the frequency and temperature dependent electrical conductivity comes up.

2.5.2 Frequency and Temperature-Dependent ac Properties of

Polycrystalline Diamond

The frequency dependent electrical conductivity, 0' (0)), of CVD diamond
films has been the subject of investigations by Sugino and Muto et a1. [2][3][7][22]
and by Sokolina and Ermakova et al. [1][4][11]. Both groups experimentally find

that the electrical conductivity of as-deposited CVD diamond depends on

frequency at sufficiently high frequencies greater than 104 Hz. However, the

annealed films showed a frequency dependence at lower frequency ranges, less

than 104 Hz.

Sugino and Muto et al. studied and analyzed the frequency-dependent
electrical conductivity of thin CVD diamond films (1-2 11 m) and concluded that the
conductivity in the as-deposited polycrystalline diamond films is caused by
conduction through disordered graphitic regions between grains and at the surface
of the films. This conclusion was reached from the correlation between the

electrical characteristics of the films and Raman spectra. It was also reported by

33

them that the ac electrical conductivity decreases drastically by several orders of
magnitude on thermal annealing. However, hydrogenation after annealing did not
change their results as much.

The frequency-dependent electrical conductivity of polycrystalline diamond

films was expressed by the known empirical relation 0(a)) or to", where the
exponent, n, was believed to be a function of temperature approaching unity at low
temperatures and decreasing to 0.5 or less at higher temperatures. However, a
frequency-independent conductance was observed, on some of their samples, at
high temperatures, which suggests that thermally activated band conduction is
dominant in the higher temperature region. They suggested that the total ac

conductivity consist of three types of conduction:

o = oo+oh+ot (2.20)

where 60, 0’ h and o" are the band, hopping and conduction related to thermal

emission of carriers, respectively. The 0 is a frequency dependent conductivity

I

caused by the thermal emission of carriers from traps, and is obtained as a broad

peak centered at a frequency f0 [2]. The reciprocal of that frequency, 1/fo, represents
the time constant, to, for the thermal emission of carriers from relevant trap levels,

and is given by Arrhenius relation:

34

(E /(kT))
3 Je ‘ (2.21)

where B is a constant determined by the effective mass and the capture cross
section of traps.
Sokolina et. al and Ermakova et. al also studied the temperature and

frequency dependence of the electrical conductivity of diamond films in vacuum at

temperatures in the range T = 150 - 900 0K. The films were grown on a tungsten

substrates, and the films’ thicknesses varied from a few microns to tens of microns.
After plotting the measured conductivity as a function of frequency, log 0'“ vs. log

f, they observed a power dependence of the ac electrical conductivity on frequency.
In agreement with Sugino and Muto, they found that the power dependence of the
electrical conductivity decreases, approaching 0.5 or less, on increase in
temperature. Nevertheless, they hypothesize that polycrystalline diamond films
consist of conducting grains and coherent scattering regions of different sizes and
shapes. They considered that at the boundaries between the grains and the coherent
scattering regions the structure of the crystal is distorted and impurities can
accumulate. This, as a result, gives rise to localized electron states in the band gap.

They proposed a model consisting of a bulk resistance, Rb, of a micro grain in

series with a parallel combination of a barrier capacitance, Cw, and a barrier

35

resistance, Rw. Consequently, a polycrystalline film can be represented by a set of

such chains.

In conclusion, the electrical conductivity of diamond films have shown a
frequency dependence as well as a temperature dependence. It has been proposed
by different researchers that the frequency dependence electrical conductivity could
be either due to hopping conduction within the crystalline grains or within the grain
boundaries or due to conduction across grain boundary potential barriers. However,
it has not been clearly shown how each individual part contributes towards the total
ac electrical conductivity of the films, and in what capacity. In this research work,
we will propose a physical model which distinguishes between the two types of

frequency dependent conductions within the diamond films.

CHAPTER 3

EXPERIMENTAL METHODS

3.1 Introduction

This chapter describes the do and ac equipment used to perform the
necessary measurements for this investigation. The sample preparation techniques

are described, and the details of the measurements’ setups are also discussed.

3.2 Equipment

HP4145B Semiconductor Parameter Analyzer: The Hewlett Packard model
41458 semiconductor parameter analyzer was used to measure and graphically
display the dc current-voltage characteristic of the diamond samples. It is equipped
with four programmable Source/Monitor units (SMU’s). Each SMU can be set up

to function as a voltage source/monitor, current source/monitor, or source common.

36

37
A simplified circuit diagram of an SMU is illustrated in the Figure 3.1. Two

SMU’s, one as a variable voltage source and the other as a common current source,
are used in setting up a two—probe circuit for the sake of measuring the dc current-
voltage characteristic of the diamond films. The HP4145B monitors currents as low
as 0.05 pA and up to 105 mA divided over nine different ranges. The resolutions of
the measurements are different from range to range.

HP4192A LF Impedance Analyzer: The Hewlett Packard Model 4192A LF
Impedance Analyzer is a fully automatic, high performance test instrument to
measure a wide range of impedance parameters as well as gain, phase, and group
delay. The internal frequency synthesizer provides a sinusoidal wave test signal that
has an accuracy of 55 ppm and can be set to measuring frequency within the range
from 5 Hz to 13 MHz with l mHz maximum resolution. The instrument has four

UNKNOWN terminals: chp Lcur, Hpov and Lpot. The test signal is output from the
OSC OUTPUT connector, chr of the UNKNOWN terminals as shown in the
Figure 3.2, and its level can vary from 5 mVrmS to 1.1 Vms. The purpose of the

current terminals is to cause a measurement signal to flow through the sample,
where the potential terminals are to detect the voltage drop across the sample. The
four terminal method, as shown in the configuration of Figure 3.2, provides the
shielding required for high-impedance, high-frequency measurements. Since the

same current flows through both the center conductors and the outer shield

38

Current Monitor
Voltage

Source]

V
Common
0 \ Source {SMU
* Monito out

Current Source ?1

 

 

Common

 

 

 

 

Voltage Monitor

FIGURE 3.1: HP4145B Source/Monitor Unit Circuit Diagram

39

Vector
Ammeter

——.’—+ 1

OSC chr

 

 

DUT

 

 

 

 

 

 

 

r411

T

Hpot Vector Voltrneter Lpot

 

 

FIGURE 3.2: HP4192A Test Signal Terminals

4O

conductors (in opposite directions), no external magnetic fields are generated
around the conductors. In this research, the HP4192A is used to measure the
conductance, G, and the susceptance, B, of different diamond samples over the
range of frequency from 5 Hz up to 13 MHz. The measurement’s range of G/B for

this instrument is ms to 12.9998. Consequently, samples with resistances greater

than 109 Q will not be accurately and stably measured with this instrument.
Signatone S-1160 High-Frequency Probing System: The S-1160 is a general

purpose analytical probe station designed for probing various geometries from 10

mils to 1 micron. It is equipped with a Signatone QuieTemp DC Hot Chuck System

model S-1060. The system is capable of conducting measurements in a temperature

range from room temperature to 300°C. This specific system is controlled by an
ATHENA temperature/process controller model XT-25, and a NESLAB
recirculating chiller model CFT-33. Multipurpose, high speed, passive, model 10
GGB picoprobes are used with this probing station to conduct high-frequency
measurements. The range of operation for those specific picoprobes is dc to
3.5GHz. The whole system is shielded with a Signatone Light-Tight box model
PSDB-l 160 to protect the measurements from any noise signals (photoconductive)
that may disturb the accuracy of the output measurements.

HP16191A Side Electrode SMD Test Fixture: The Hewlett Packard model

16191A high frequency test fixture is used in conjunction with the HP4291A

41

impedance analyzer, described below, to accommodate and measure the
conductance, resistance, susceptance, and reactance of the diamond films over the
frequency range from 1 MHz to 1 GHz. The unwanted electrical properties of the
fixture, such as the phase rotation due to the physical length of the electrodes and
other unwanted stray parasitics between electrodes, can be fully compensated for
by automated calibration techniques.

HP4291A RF Impedance/Material Analyzer: The Hewlett Packard model
. 4291A RF impedance analyzer is an integrated package designed to provide testing
at higher frequencies than the previously described HP4192A unit. It uses the RF I-
V method, as apposed to the conventional reflection coefficient method, to measure
impedance as a one-port, lumped element from a ratio of voltage and current.
Figure 3.3 shows the circuit design for both measurement techniques. The RF I-V
method ensures higher measurement accuracy through a wide frequency and
impedance range.

The RF impedance analyzer operates at frequencies from 1 MHz and up to
1.8 GHz with a frequency resolution of 1 mHz. The ac voltage oscillation level

varies between 0.2 mes to 1 Vrms with an ac voltage resolution between 0.002
mes to 2 mes. The RF analyzer has been extensively used in this research

work with two different measurement configurations. One uses the S-1160 probing

station with the model 10 picoprobes, and the other uses the HP16191A high

42

Directional Bridge

 

 

Reflection Coefficient Method

4?) DUT

I-V Method

 

 

l-l"
Zx - SOTTI‘
F=V,/V,-

V9
Zx = Roi/-

FIGURE 3.3: I-V method and reflection coefficient impedance method

43
frequency test fixture. With either configuration, the system is calibrated (short/

open/load) at the probes’ tips very close to the device under test to eliminate the
unwanted stray parasitics. The results are displayed on the HP4291A monitor and

stored on disks for later analyses.

3.3 Sample Preparation

Thin and thick diamond films, synthesized under different growth
conditions, are used in the impedance spectroscopy study. The thin diamond films
are provided by Dr. Jes Asmussen and Dr. Saeid Khatami at Michigan State
University. The thick, free-standing films were provided to us by a commercial

supplier. The sandwiched configuration, shown in Figure 3.4, is used for both thin

and thick diamond films. Large area contacts, in the range of 0.1 cm2 to 0.7 cm2,
are used to reduce the sample resistance to within the range of measurement
apparatus.

For the thin diamond films (3 to 6 pm), grown on silicon substrates, the
samples are sandwiched between two conducting layers. One is attached to the
back of the films, on the silicon side of the sample, and the other is in the form of
dot contact at the top surface of the films. Contact materials are selected to provide
ohmic I-V behavior over the voltage range of interest. In the impedance

spectroscopy study of thin films, two types of methods are used to form ohmic

44

Silver Paint

(.s

 

  
 

 

Diamond
Silicon

:t 4 ; . up *rs."- , .1 ,~.~.r :1 y .3 fiv w» .3. ’fi‘."'7 1. .‘aI‘-.°~‘~ V.‘ -w,_. -7v_n.,~.~_.~.~.
V _- vflvgflm ‘fiéru‘t‘ Ifl' t'tm‘f‘ewt ~ 'tflt-Q')” , i‘fl‘ “Mm. ‘ '

Silver Paint

 

a. Low resistive thin diamond film on silicon

Sputtered Gold

'.'.'.'-'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'-'-'.'.'.'.‘

Diamond
Silicon

 

.5 “'72J:.1.;§ummgfizlm . ;;-.- 3‘ "
O 0
Silver Paint

 

b. High resistive thin diamond film on silicon

 
 
 
  

Silver Paint

“201(25):- .., ,,

 

“5H

      
 

Diamond

 
  

 

"1""

Silver Paint

c. Free-standing, thick diamond film

FIGURE 3.4: Schematic diagram of diamond samples configurations

45
contacts to CVD diamond. On samples with low resistivity, less than approximately

1 x 106 Q-cm, silver paint produced linear current—voltage characteristics. On the
higher resistivity samples, however, non-linear characteristics resulted with silver
paint, and sputtered gold contacts are used to generate linear I-V characteristics.

The thick, free-standing diamond samples were synthesized by the arc-jet
method. The samples are 1 cm x 1 cm with thickness ranging from approximately
200 to 400 um and of gray to dark-gray visual appearance. Large area silver paint
contacts on opposing sides of some samples were adequate to produce linear
current-voltage (I-V) characteristics. On other samples, gold was needed.

In the sandwiched type samples, measurements may include a considerable
inter-grain conduction as apposed to intra-grain conduction. Figure 3.5 shows a
schematic diagram of two possible paths for the conduction current flow through a
diamond fihn in the vertical direction.

Samples did not receive any special cleaning to remove conducting surface
layers. However, the applied conducting contacts covered a large fraction of the
surface area, in any case. Some of the samples were annealed as part of the process
to study the effect of annealing on the dc and ac electrical properties of the films as
well as on the films’ ac electrical circuit model parameters. The annealing process
was taken place in a class-100 clean room using a furnace with a nitrogen gas

ambient.

46

 

 

Top conducting layer

 
  

Grain
‘ Boundaries

 

 

.,
I a

. Hg.
‘ ‘i .

Back conducting layer

FIGURE 3.5: Schematic diagram of conduction paths in a diamond film

47
3.3.1 Measurement Setup

In order to determine the complex impedance as a function of frequency, this
study used instruments which apply a single frequency signal to the sample and
measure the ratio of the voltage and current, in terms of both phase and amplitude,
to determine the real and imaginary parts of the impedance. Three instruments and
two sample connection methods were used to cover the frequency range from dc to
1 GHz. For the dc I-V measurements, a Hewlett-Packard model 4145B
semiconductor parameter analyzer was used. Hewlett-Packard model 4192A and
' model 4291A impedance analyzers were used to measure the real and imaginary
parts of the small signal impedance from 5 Hz to 1 MHz and 1 MHz to 1 GHz,
respectively. The small signal rms amplitude was less than or equal to 1 V, well
within the linear range of the I-V characteristics. From dc to 1 MHz, the sample
electrodes were contacted by coaxial probes on a micro-probing station. From 1
MHz to 1 GHz, a test fixture, model HP16191A, designed specifically for high
frequency probing with the HP4291A was used.

Both impedance analyzers have frequency-dependent upper limits on the
measured impedance which affect sample selection, particularly for thicker
samples. The upper impedance limit on the low frequency impedance analyzer is 1

M9. Considering for example a 500 pm thick sample with contact areas on the

order of 0.5 cm2, the system places an upper limit on resistivity of 107 Q-cm.

48

Consequently, higher resistivity thick samples were not within the scope of this
study. At 1 GHz, the upper impedance limit drops to 1K9. However this limit
places less restrictions on sample selection, since the sample capacitance is

sufficient to keep the impedance less than the high frequency limit.

CHAPTER 4

MODELING TECHNIQUE

4.1 Introduction

This chapter begins with a description of the general basics of the
impedance spectroscopy technique which is used in the physical modeling of thin
and thick diamond films. Later, some circuit model examples will demonstrate how
this technique can be ambiguous if the results are not carefully interpreted in a way
which agrees with the physical properties of the material. Section 4.3 introduces
the basic four path ac circuit model which is used for data fitting. Finally, in section
4.4, a sample Matlab program shows how the modeling optimization process is
achieved by calculating the minimum error between experimental and modeled

results.

49

 

50
4.2 Impedance Spectroscopy Technique

Impedance spectroscopy (IS) is considered a powerful technique to measure
and analyze many properties of electronic materials. It can be used to investigate
the ac electrical properties of liquids as well as solid materials: ionic,
semiconducting, mixed electronic-ionic, and insulators [49]. One of the very first
papers to deal with IS was that of Buerle in 1969. He applied the technique to
accurately determine the conductivity of solid electrolytes [50]. More recently,
researchers [51][52][53][55][84][85] have used the technique to study and analyze
the ac electrical conductivity of polycrystalline and single crystal electronic
materials, and to derive equivalent circuit models to describe the different ac
conduction mechanisms in materials.

The IS technique can be used in either the time domain or the frequency
domain [49]. Appropriate Fourier transforms can also be applied to go from one
form to the other. In the time domain measurement, a step function of voltage may
be applied to the system under test, and the time-varying current measured. The
ratio of voltage to current can then be used to define what is called time-varying
impedance. However, this would not be the same impedance defined in the IS
technique. A Fourier transform is needed to convert the results from the time to the
frequency domain to be used in the IS analyses.

The most common approach nowadays in the IS analyses is to measure

 

51

impedance directly in the frequency domain. This can be accomplished by applying
a small ac voltage signal of fixed frequency and measuring the real and imaginary
parts of the impedance directly as the frequency is stepped from one value to the
next. The availability of sophisticated commercial instruments which automatically
measure the impedance as a function of frequency makes this approach the method
of choice for researchers to accomplish their goals. Macdonald and Johnson [49]
have proposed a flow chart to present the general characterization process using IS.
The details are shown in Figure 4.1. After impedance results for a given material
have been obtained experimentally, data fitted to an existing mathematical model
based on a valid physical theory, or an empirical equivalent circuit can be
developed which predicts results similar to the experimental ones.

One disadvantage of this technique is associated with potential ambiguity in
choosing the appropriate equivalent circuit which believed to be the most consistent
with the expected behavior of the material under test. This difficulty comes from
the possibility that more than one electrical equivalent circuit may result in a
particular impedance response. Take for example the two circuits shown in Figure
4.2 [54]. They both produce the same impedance response for all frequencies when
the values of their elements are properly chosen and related. However they would
represent different physical phenomena and structures. For example, the circuit in

Figure 4.2 (a) could represent an ac model for a sample with a Schottky barrier

52

 

Materials under test

 

 

 

l 7

 

IS Experiment, Ze((u)

 

 

 

//

 

Theory

 

4 V

 

 

Physical Model

 

 

‘ v //

 

 

Mathematical Model, Zt((1)) r

 

 

\

\X

 

Equivalent curcuit, Zec((o)

 

 

 

 

 

Curve fitting

 

Y

 

 

System Charaterization

 

 

FIGURE 4.1: Flow chart for IS characterization process.'[49]

53

(a)

C1 C2

—+— ——1(—

 

 

 

 

 

R1 R2

0))
R1

Cl
1\

WE

R2 C2

 

 

 

FIGURE 4.2: Two equivalent circuits which can have the same impedance response

at all frequencies if parameters were chosen properly.

54

contact at one end. In this case, C1 and leould represent the barrier and C2 and
R2 would represent the bulk material. Figure 4.2 (b) would represent the model of a
sample with a dc bulk current path represented by R1 and a bulk capacitance Cl. In
addition, a cross-grain polycrystalline path would be represented by R2 and C2.
However, this ambiguity could be resolved by other measurements, in this case dc
measurements. For the cases illustrated in Figure 4.2, if a Schottky barrier did exist,
as suggested by part (a), then non-linear, rectifying characteristics would result as
opposed to the linear characteristics expected for a dc conduction path.

In this research study, the IS technique was used in the frequency domain
where both the real and the imaginary parts of the complex impedance were
measured as a function of frequency. Data are presented as a plot of the imaginary
part of the impedance vs. the real part of the impedance. Consider the simplest
possible case where the diamond is considered to have a frequency independent
conductivity and permittivity. In that case, the sample impedance is represented as
the parallel combination of a resistor and a capacitor. The resistor value is R = d/oA
where A is the cross sectional area of the sample, dis the sample thickness, and 0' is
the electrical conductivity. The capacitance value is C = eA/d where e is the
permittivity. R may be obtained experimentally from the measured dc resistance
and C may be calculated from geometric considerations, using a relative dielectric

constant of 5.5 for diamond. The combined impedance is

55

2: R _l. (1)RC (4.1)

l + (1)2R2C2 1 + (1)2R2C2
where (1) = 27tf is the frequency in radians per second and i is the imaginary
unit. An impedance spectroscopy plot of the imaginary part of the impedance on
the vertical axis and the real part of the impedance is shown in Figure 4.3 for the

hypothetical case of R = 100 Q and C = 10 pF.

4.3 Basic Four Path Model

The impedance spectroscopy results of thin and thick diamond films were
more complex to analyze and model than the simple case of a parallel combination
of a resistor and a capacitor. Previous reports in the literature have identified either
hopping or, alternatively, grain-barrier effects as contributors to frequency
dependent electronic conduction in diamond. Another question to be answered is
whether the electrical properties of grain boundaries are likely to be similar to or
significantly different from those of the grains themselves. The answer may depend
on whether the properties are intrinsic or extrinsic to the material under test. With
such questions, the impedance spectroscopy instrumentation comes to offer the
possibility of a comprehensive characterization of the films and in particular, the
characterization of the ac electrical conduction. Consider first hopping. It has been

very well established for many years that the frequency dependent electrical

56

 

55 I *I I I I I I I T I

 

 

 

 

FIGURE 4.3: Impedance Spectroscopy Results of a Parallel R-C Circuit

57

conductivity in many electronically and ionically conducting materials shows a
frequency independent dc component at low frequencies and a frequency
dependent ac component at high frequencies [38][39][40][41]. As discussed in

chapter 2, the conductivity dependence on frequency is of the form

0(a)) = Ba)" (42)

where B is a constant depending on the particulars of the sample and the value of n
is generally between 0.5 and unity, as also described in chapter 2. Frequency
dependent conduction in diamond which is indicative of hopping with n = 0.8 has
been previously reported by Sugino et a1. [2] [22], while Sokolina et al. [1][4][l l]
have proposed that conduction can be modeled by a path consisting of a series of
grains, each consisting of a bulk resistance in series with a grain-boundary potential
barrier. The latter group proposed a model consisting of a resistor, representing a
micro-grain’s bulk resistance, in series with a parallel combination of a barrier
capacitance and a barrier resistance.

There are always difficulties associated with choosing a circuit model to
represent the complex impedance data as explained earlier and shown in Figure 4.2.
Once an equivalent circuit model has been chosen, it is always necessary to make a
link between the circuit model elements and the region of the sample responsible

for each.

 

58

In our study of the frequency dependent electrical conduction in both thin
and thick diamond films, the impedance response can not be represented with a
simple RC circuit model. Consequently, it is necessary to add to the impedance
model in order to represent frequency dependent phenomena in the diamond. Since
the literature suggests evidence for both hopping and grain-boundary potential
barrier effects, it was decided to incorporate both effects in an IS equivalent circuit

model. As a result, to the basic model of a parallel combination of a capacitor and a

resistor, a frequency dependent conductance equal to BCDn was added. In addition, a

path consisting of a grain resistance Rg in series with a grain capacitance Cg was

added in parallel with the other paths in order to compensate for conduction across
the grain boundaries. It is necessary to note here that if multiple grains are in series
in a conduction path, the individual resistance and capacitance associated with each

grain can be combined into an equivalent circuit consisting of Rg and Cg as shown

in Figure 4.4. A sample model which contains both hopping and grain-barrier

containing paths is shown in Figure 4.5.

4.4 Model Fitting

The model of Figure 4.5 contains six parameters (R, C, B, n, Rg, and Cg)

which may be fit to the experimental IS data. The first two parameters are obtained

59

RgicgiRgzcgz
“mew—9W4 —- Rg Cg
-- wet—we -- —: Omar—o
I
R C

-——vw—)1—W—)1—ug§»—ii——-

FIGURE 4.4: Schematic Diagram Of An Equivalent Grain Boundaries Path

consisting of an equivalent resistor, Rg, in series with an equivalent capacitor, Rg.

60

 

 

 

R
dc Resistance Path W
C
Geometric Capacitance :€
H q

 

Hopping Path ___.| B 0)" |.__

Grain Boundaries Path I€__Wv____,
I

 

 

 

FIGURE 4.5: Impedance Spectroscopy Sample Circuit Model

consisting of four paths: dc resistance, geometric capacitance, hopping, and grain boundaries.

61

independently. The parameter R is obtained from the frequency independent
measured dc resistance, and the parameter C is obtained from the frequency
dependent geometric capacitance calculated based on the thickness of the sample
and the area of the metal contact. In order to obtain best fit values for the remaining
five, the parameters were systematically stepped through a range of values. Figure
4.6 shows a sample program used in calculating best fit for the model parameter
values. The exponent n, for example, was stepped through a range of values from
0.5 to 1 with an increment of 0.1. This range of values for n is reasonable and
experimentally reported by researchers studying the ac conductivities of
polycrystalline materials at room temperature. However, at higher temperatures, the
exponent n can reach values lower than 0.5. The rest of the parameters were also
stepped through a wide range of relevant values to produce a large number of
combinations for the model parameters. In the case of the sample Matlab program
shown in Figure 4.5, we considered over 3.5 million different combinations in
order to come up with the best parameter values to produce the minimum
percentage error. For each set of parameter values, a net difference between
experimental and modeled IS results was calculated by determining the normalized
cumulative percent error, E. This difference between experimental and modeled IS

results can be defined in several ways. Equation 4.3 defines the error, E, as follow:

62

load datafile.m; °/ccontains measured resistance and reactance
f=datafile(:,1); °/efirst column contains frequency values
r=datafile(:,2); °/csecond column contains resistance data
x=datafile(:,3); °/cthird column contains reactance data
ze=sqrt(r’\2+x’\2); °/etota| experimental impedance

w=2*pi*f; °/cangu|ar frequency
Rb=1e3; °/emeasured dc resistance
Cb=1e-12; °/ccalculated geometric capacitance

for a1=0.5:0.1 :1 .5;%to precisely find the grain capacitance value

for a2=0.5:0.1 :1 .5;°/cto precisely find the hopping coefficient value
Cg=a1 *1 e-12; %starting value for the grain capacitance
B=a2*1e-12; %starting value for hopping admittance coefficient
for n=0.5:0.1 :1; %exponent n steps through 6 values

for Rg=0210z1000; °/cRg steps through 1000 values

while Cg <= 1e-6; °/ethe highest allowed value for grain capacitance
while 8 <= 1e-6; %the highest allowed value for hopping coefficient
y1 =1 / Rb;

y2=i*w*Cb;

y3=B*w’\n;

y4=(i*w*Cg)/(1+i*w*Rg*Cg);

ym=y1+y2+y3+y4;%total modeled admittance

zm=1jym; °/ototal modeled impedance

for l=1 :1 :m; %m is the total number of points measured
error(|)=abs((zm(I)-ze(l))/zm(l));

end;

tota|_error=0;

for l=1 :1 :m;

total_error=total_error+error(l);

end;

percent_error=100*(total_error/m); °/cmust be minimized
end; %B-while statement

end; %Cg-while statement

end; %Rg-for loop

end; %n-for loop

end; %a2-for loop

end; °/ca1-for loop

FIGURE 4.6: Sample Program To Produce Model Parameters With Minimum Percent Error

63

pkg/922ml (4.3)

(t)

 

 

 

Zm

where the summation is over the frequency range from dc to 1 GHz, with N

representing the several hundred points between these limits. At each value of (on,
26 is the magnitude of the experimental impedance, including both real and
imaginary parts, and Zm is the magnitude of the modeled impedance. This equation

is used later in chapter 5 to calculate and minimize the error and choose the
parameters for the IS circuit model. There are other ways to define the cumulative
percent error. For example, one can calculate and minimize the difference between
the real parts of experimental and modeled IS data. The same can also be applied to
the imaginary parts of the complex impedances. However, our results showed that
the set of parameters used is not sensitive to the method of calculating the error.
More detailed examples will be discussed in chapter 5 when we describe the error

calculation of specific sample results.

CHAPTER 5

APPLICATION OF THE F OUR-PATH MODEL TO THIN- AND

THICK-FILM DIAMOND AT ROOM TEMPERATURE

5.1 Introduction

This chapter describes the application of the four-path circuit model to
interpret the impedance spectroscopy results. It describes how the model fits to
experimental results for a specific population sample of two thick-films and two
thin-films. Although the model parameter numerical values are found to vary
appreciably from one sample to another, the same basic model is successful in
matching experimental results for all four samples, even though they differ

considerably in their physical structure and growth conditions.

65
5.2 Thin-Film Diamond

5.2.1 Film Growth And Structural Properties

Thin films on silicon are used in this study to investigate the high frequency
electrical properties of CVD diamond. In this section, two representative samples
are considered in the analysis and modeling of the frequency dependent
conductivity study of thin diamond films on silicon, namely SK-l3 and SK-l79.
These films were grown by Dr. S. Khatami at Michigan State University. The films
were prepared on <100> oriented, p-type silicon substrates with resistivities
ranging from 1-10 Q—cm by microwave plasma assisted CVD. Table 5.1 shows the
deposition conditions for these undoped polycrystalline thin diamond fihns. Prior
to conducting any electrical measurements, it was necessary to determine whether
the films are in fact diamond, and to characterize the films qualities. Two different

techniques were used to accomplish this task. The Raman spectroscopy technique

was used to ascertain sp3 carbon bonding in the films. A 514.5 nm light source,
argon ion laser [42] was used to determine Raman scattering from 1200 to 1600
wavenumbers and to determine the presence of diamond and any non-diamond
carbon contents in the films. This helps in predicting any conduction that may be

caused by the presence of graphitic regions in the polycrystalline material. The

66

Table 5.1: Deposition Conditions for Thin Diamond Films

 

 

 

 

 

 

 

Sample SK-13 SK-179
Flow Rate, sccm 400 400
%CH4/H2 1.75 1.5

Ts, °c 1000 850
Deposition Time, 8 8

hours

Pressure, Torr 70 41
Thickness, 1.1m 5.97 3.68

 

 

 

 

 

67

films structural properties were investigated by the Scanning Electron Microscopy
(SEM) technique. Microscopic pictures of the growth surface of the films were
taken to define the film morphology including the dimensions of grains and the

crystal orientation. The Raman spectra of the film samples, as shown in Figure 5.1,
show the characteristic diamond peak at 1332 cm'1 for both samples. However, the

Raman spectrum for sample SK-13 shows a wide peak around 1580 cm’1 which
indicates the presence of graphite content in the sample. This resulted in a lower dc
resistance compared to the other thin film sample as will be discussed a later
section. Figures 5.2 show the surface morphologies of the two films grown at
different temperatures, as indicated in Table 5.1. Both the SEM pictures and the

Raman results were provided by S. Khatami.

5.2.2 Instrumentation Setup and Results for Thin-Film Diamond

Samples

The samples were prepared for the electrical conductivity measurements by
adding circular shape silver paint contacts on the top surface of the films, the
diamond side, as well as on the bottom side, the silicon wafer side, as shown in the
sample configuration of Figure 4.3(a). The HP4145B Semiconductor Parameter

Analyzer was then used to conduct dc I-V measurements. Figure 5.4 shows a

68

(a)

35 l I l T l I l

 

 

 

 

1 l l l l l l 1

 

1200 1250 1300 1350 1400 1450 1500 1550 1600

 

1.5 I T I I I l I

1.4- r

1.2’ -

1.1- *

 

 

 

1
1200 1250 1300 1350 1400 1450 1500 1550 1600

FIGURE 5.1: Raman Spectra of Two Thin Diamond Films
(a) SK-l3, (b) SK-l79

Measured with an argon laser at 514 nm.

69

 

FIGURE 5.2: Scanning Electron Microscopy Picture of The Thin Diamond Films
(3) SK—l3, (b) SK-179 [43]

70

HP4145B Semiconductor Parameter Analyzer

 

SMUl SMU2 SMU3 SMU4

O O

 

 

 

 

 

    

Silicon wafer Diamond

Silver-paint

Sliver'Pauu ‘— , \““““‘

    

 

 

Gold-plated
metal
Gold-plated chuck

 

FIGURE 5.3: Schematic diagram of the dc measurement setup
using two Source/Monitor units, SMUl and SMU2

71

schematic diagram of the dc measurement setup. Two Source/Monitor Units
(SMUs) were used to accomplish this purpose. SMU] was used as a variable
voltage source, and SMU2 was used as a common current return path. The dc
current-voltage relationship of both samples were found to be linear within the
voltage range of interest. To conduct the ac measurements on the samples, two
different impedance analyzers were used with two different sample contact setups.
HP4192A and HP4291A impedance analyzers, described in chapter 3, were used to
measure the real and the imaginary parts of the complex impedance of diamond
fih'ns in the frequency domain to cover the frequency range from 5 to 1 MHz and
from 1 MHz to 1 GHz, respectively. Figure 5.5 shows the low frequency
measurement setup for the frequency range from 5 Hz to 1 MHz using the
HP4192A instrument. The frequency was increased systematically from the 5 Hz
low frequency limit of the instrument up to 1 MHz, while the values of the
resistance and the reactance of the film under test were measured and stored in a
floppy disk. Note that the probes used in this type of measurement were special
high frequency coaxial probes. For the higher frequency range, the films were
placed in the HP16191A high-frequency test fixture, which is connected to the
HP4291A analyzer as shown in the schematic diagram of Figure 5.6. This
instrument is able to cover the range of frequency from 1 MHz to 1 GHz. Both

instruments operate so as to measure and plot both the resistance and the reactance

72

HP4192A LF Impedance Analyzer

 

High High Low Low
Pot. Cur. Pot. Cur

 

 

 

    

Diamond

Silicon wafer \ Silver-paint
Silver-pain

 

 

 

Gold-plated
metal

Gold-plated chuck

 

FIGURE 5.4: Schematic diagram of the ac measurement setup

for the frequency range from 5 Hz to 1 MHz

73

Diamond

Silicon wafer fl

— Silver-paint

 

 

 
 

HP 4291A RF Impedance / Material Analyzer

 

 

 

 

 

    

 

HP 16191A High-Frequency *
Test Fixture

FIGURE 5.5: Schematic diagram of the ac measurement setup

for the frequency range from 1 MHz to 1 GHz

74

(modeled in parallel) versus frequency. The amplitude of the applied ac voltage

signal was fixed for both analyzers at 1 Vrms.

The current—voltage relationship of thin diamond samples are shown in
Figure 5.6. The applied voltage was gradually changed from -2 to +2 volts with an
increment of 0.02 volt. The dc measurements were taken at room temperature, and
show essentially ohmic behavior for both fihns. The value of the resistance of the
films was calculated from the slope of a first-order best-fit polynomial. The ac
measurements {of the real and the imaginary parts of the complex impedance of the
samples were stored in floppy disk and imported into a mathematical software,
Matlab, then plotted and compared to the four path electrical model over the
complete frequency range from dc to 1 GHz.

Consider the thin film sample SK-l3 which has a resistance, R, of 2.4 KS) as
obtained from the dc current-voltage characteristics shown in Figure 5.7(a) and a
capacitance, C, calculated from the area and thickness to be 73 pF. Figure 5.8
shows that the experimental IS results differ considerably from those predicted by a
simple R—C parallel combination. Consequently, it was necessary to add to the
impedance model in order to represent frequency dependent phenomena in
diamond.

This research study assumes that the total ac conduction in diamond consists

of three types, namely band, hopping, and conduction through the grain

 

75

(a)

 

Current, mA

 

 

 

 

 

Current, mA

 

 

 

 

Voltage, volts

FIGURE 5.6: The Current-Voltage Characteristics of Thin-Film Samples.
(a) SK-l3, (b) SK-179

76

 

 

 

1200 I I+-I- + I
+++++ +
++
+ +
+
+
Jr+
1000 - +++ +
+
+
+
++
.1.
J
800 - +
+
it
+
+
+
+
+
_ if
600 + a
400 - 0 _
O O O
o 00
OO o
+
O +
200 + ..
+
+
+
I l l l
0 500 1 000 1 500 2000 2500

FIGURE 5.7: Comparison Between Measured [o] and Model {-1-} IS Results

Based on The Measured dc Resistance and The Geometric Capacitance for SK-13.

 

77

boundaries. The experimental results were compared with a circuit model which
includes, in addition to the basic RC circuit, two parallel paths of conduction. One
represents hopping and the other represents conduction through grain boundaries,
as described in more details earlier in chapter 4. Our investigations, however,
illustrated the necessity to add to the chapter 4 model a series contact resistance,

RC. This may be expected since all metal-semiconductor contacts have a finite, non-

zero, contact resistance. Later in this chapter, the importance of this contact
resistance component in the circuit model will be discussed in more details.
Although the two thin-film diamond samples have different Raman qualities
and different surface morphologies, our suggested model was adequate in best
fitting the experimental IS results of both samples by minimizing the cumulative
percent error, as described in chapter 4, and assigning relevant values to circuit
model components. Table 5.2 shows the chosen model parameter values for each of
those samples. Figure 5.8 and 5.9 show a comparison of model results with
measured results for the thin film samples, SK-13 and SK-179, respectively.
Earlier in chapter 4 the issue of error calculation methods was discussed,
and it was stated that the set of model parameters is not sensitive to the method of
calculating the error. Take for example the thin diamond sample SK-13. We ran
three simulation programs were run to obtain the best fit model parameters using

three different methods to minimize the cumulative percent error. The first is by

78

Table 5.2: Best-Fit Model Parameters For Thin Diamond Films

 

 

 

 

 

 

 

 

Parameter SK- 1 3 SK- 179
R (Q) 2.4x103 3.02x104
c (pF) 73 103
Rg (r2) 9 65
Cg (pF) 100 24
B (0") 1.1 x 10'9 2.2x10'9
n 0.9 0.8
RC (:2) 0.7 1.9

 

 

 

 

79

 

 

 

 

450 I I T I
0 o
400 O ‘
O
350 '- O + + _.
+ o
O + o
_ O ..
300 + +
+ + O
+
+ —I
O
O -I
+
0+
1 1 1 1 QL
500 1 000 1 500 2000 2500

 

Figure 5.8: Comparison of Model [0] and Measured [+] IS Results

For Thin-Film Sample, SK-l3.

 

5000

4500

4000

3500

3000

2500

2000

1500

1000

500

80

 

I I I I I I
0
40
+0
+0
d—C)
+0
1 l l l l J

I

I

 

 

x10

Figure 5.9: Comparison of Model [0] and Measured [+] IS Results

For a Thin-Film Sample, SK- 179.

81

minimizing the difference between the real parts of the complex impedance,
E_real, the second is by minimizing the difference between the imaginary parts
only, E_imag, and the third is calculating the error as described in equation 4.3.

Table 5.3 shows the resultant model components from each of the above methods.

5.3 Results of Thick-Film Diamond Samples

The thick diamond films used in this study, synthesized by the arc-jet
method, were provided by a commercial supplier and were free-standing, thick
films ranging between 200 to 400 um in thickness. Since we do not have any
information about the growth conditions of the films, the films were categorized by
colors ranging from white to dark grey. However, due to some instrument
limitations, as described in chapter 3, we were not able to obtain any impedance
measurements on the white type of films.

In this section, the results of two representative samples, TDF-12 and TDF-
18, will be presented to show the dc and the high frequency ac behaviors of this
type of sample. Both samples were categorized as dark grey. The sample TDF-12 is
198 um in thickness, and ohmic contact is obtained by evaporating a layer of gold
on the back side of the sample, which was the nucleation (smoother) side, and by
adding a circular-shape silver paint contact on the top side, the growth side.

However, for sample TDF-18, it was necessary to sputter gold on the top surface of

 

Error Calculation Methods

Table 5.3: Model Parameters For Sample SK-13 Using Different

 

 

 

 

 

 

 

 

 

 

E_real E_imag E
B (12") 1x10'9 1x10'9 1.1x10‘9
n 0.9 0.9 0.9
Rg (o) 8 10 9
Cg(F) 1.2x10'10 1x10'10 lxlO’lO
Rc (Q) 0.6 2 0.7
%Error 0.54 3.1 1.1

 

 

 

 

83

the sample to achieve that. The dc and ac measurement setups were similar to those
of thin-film diamonds. Figure 5.10 shows a linear current-voltage relationship for

both samples. As shown in Figure 5.11, the Raman spectra on both samples shows

a diamond peak at 1332 cm'] and shows no signs of any graphite layers associated
with the films. Figure 5.12 shows the surface morphologies of the free-standing
thick diamond films. Although the Raman qualities and the surface morphologies
of both films look very similar, the resistivity of the films were considerably
different. Table 5.4 lists the best—fit model parameter values which gives the
minimum cumulative percent error as calculated from equation 4.3. Figures 5.13
and 5.14 show the comparison between the measured and the calculated results of

the impedance spectroscopy.

5.4 Results Analyses

It is of interest to consider the relative role of the various model components
in fitting modeled IS results with experimental results. Considering the sample SK-
13, when only the dc resistance, R, and the geometric capacitance, C, are included
in the model, as is the case for Figure 5.7, the E value is 62%. By adding only a

hopping path the best fit E value is 9.7% as obtained with hopping prefactor B = 1.4

x 10'9 Q" and frequency power 11 = 0.9. By adding only a grain-barrier conduction

84

 

 

 

 

 

 

 

 

 

 

Figure 5.10: Current-Voltage Relationship of Two Thick Diamond Films

(a) TDF-12, (b) TDF-l 8

85

(a)
2.5 I I I I I I I

 

1.5-

 

 

 

I l J L l l I

1
1200 1250 1300 1350 1400 1450 1500 1550 1600

 

(b)
2.5 I I I I I I I

 

I

1.5

 

 

 

l l l l I l I

1
1200 1250 1300 1350 1400 1450 1500 1550 1600

 

Figure 5.11: Raman Spectra of Two Thick Diamond Films

(3) TDF-12, (b) TDF-18

86

 

Figure 5.12: Scanning Electron Microscopy of Thick Diamond Films

(a) TDF—12, (b) TDF-l8

87

Table 5.4: Best-Fit Model Parameters For Thick Diamond Fihns

 

 

 

 

 

 

 

 

Parameter TDF-12 TDF- 1 8
R (o) 149 822
c (pF) 8.8 3.3
Rg (o) 35 320
cg (pF) 900 11
3(9'1) 1.1x10‘6 3.8 x 10'12
n 0.5 0.9
RC (12) 0.4 2.0

 

 

 

88

 

 

 

 

 

I I I

50— _
X
40- 0 x -
0
X
30- 0 .
X
20- % -
0
%
0’;
Ox
10- (8)); -
X
0x

‘8‘
o- 8 .

_1o 1 l l

o 50 100 150

Figure 5.13: Comparison of Modeled [o] and Measured [+] IS Results

For Thick Diamond Sample, TDF-12

89

 

350 I a I I I I I I

250

200

150

100

 

 

 

 

Figure 5.14: Comparison of Model [0] and Measured [+] IS Results

For Thick Diamond Sample, 'IDF-18

 

90
path the best fit E value is 12.3% as obtained with Rg = 2 Q and Cg = 180 pF. By

adding both the hopping and grain-barrier conduction paths, the best fit E value is
7.1% as obtained with model values ofn = 0.9, B = 1.1 x 10'9 (2'1, Rg = 9 Q and Cg
= 100 pF. Finally, using the entire model adding a best fit RC value of 0.7 Q, the E

value is reduced to 1.1%.
Now, consider one specific component of the circuit model, the contact

resistance, RC. Note that although RC is quite small it plays an important role at high

frequencies, above approximately 500 MHz, as shown in Figure 5.15. The

importance of RC comes from the fact that at high frequencies the real part of the

equivalent impedance of the circuit model will be dominated by the value of the
contact resistance, as shown in the series of Equations 5.1 through 5.5. If we
substitute the values of the model circuit components for the diamond sample SK-
13, as given in Table 5.4, at the high frequency limit of 1 GHz, we conclude that the
real part of the total equivalent impedance converges to the value of the contact

resistance, RC. At 1 GHz, the total equivalent value of the real part of the
impedance equals to 0.8 9, which is dominated by the Rc value of 0.7 Q.

T1+T2

Real(ZT) = 737?;

+12, (5.1)

where,

20

15

—s

—10

20

91

 

 

 

 

1O

10

 

15'-

-5-

 

 

 

 

--10

Figure 5.15: The Effect of Model Parameter, Rc,on IS Results

(a) Without Adding Rc to The Model, (b) \Vrth RC

10

 

 

92

T1 = Bm"R" — (02R2CRgCg (5.2)

T2 = wZRRgCg(RgCg+RC+RCg+RgCgBm") (5.3)
T3 = (B 0)"R — mzRCRgCg)2 (5.4)

T4 = (02(RgCg + RC + RC8 + 18303123652 (5.5)

Similar results were obtained for the other samples. Table 5.5 shows the best
E values obtained by considering five different models: (1) the basic R-C model,
(2) R-C with the addition of hopping only, (3) R-C with the addition of a grain-
barrier path only, (4) R-C with the addition of both a hopping path and a grain-

boundary path, and (5) with the full model.

5.5 Relative Role Of The Model Components

A strong frequency dependence of electronic conduction in polycrystalline
diamond was observed for both sample types. Such a result can be indicative of
hopping via localized sates or of current transport across potential barriers
associated with grain boundaries. When dc conduction involves paths through

potential barriers at grain boundaries, non-linear characteristics result. However,

93

Table 5.5: Normalized Cumulative Percent Error, E.

 

Model

TDF-12

TDF-18

SK-13

SK-l79

 

R and C
only

70.6%

32.0%

61.5%

15.5%

 

With only

hopping
added

16.6%

11.1%

9.7%

8.6%

 

With only
grain-
barriers
(G.B) added

18.4%

3.6%

12.3%

4.8%

 

With hop-
ping and
GB. added.

6.6%

2.8%

7.1%

4.6%

 

 

With full
model

 

6.3%

 

2.8%

 

1.1%

 

2.7%

 

 

94

the samples in this study were limited to those with essentially linear dc I-V
characteristics. Consequently, electrode to electrode paths exist which do not
involve transport across significant potential barriers. Such paths can have a
substantial number of defect states as evidenced for example by Poole-Frenkel
emission at high electric fields [16] and it may be expected that such states would
contribute to frequency dependent conduction [3][4]. However this does not
preclude the role of carrier flow across interfaces at higher frequencies where the
potential barriers are shorted by capacitive currents. The results indicate that both
transport across grain barriers and hopping contribute to the impedance
spectroscopy results for these samples. The inclusion of both types of frequency
dependent conduction paths in the IS model give better agreement with experiment
than either one alone.

It is instructive to consider the relative roles of the various contributors. On
the thin film samples, the admittance due to the hopping path was an order of
magnitude or more higher than the admittance due to the grain-boundary path over
the entire frequency range. This was not the case, however, for the thick-film
samples. Figure 5.16 shows the relative contribution of the parallel conduction
paths for thick-film sample TDF-12. From approximately 1 MHz to 100 MHz, the
frequency dependent admittance due to the grain-boundary path was larger than

that due to hopping. Above 100 MHz, the hopping path dominated the frequency

95
dependent admittance.

It has been suggested [3][4], that the localized States that contribute to
hopping are associated with grain-boundaries. This would be consistent with the
dominant role of hopping in the thin-film samples since for the finer grain, thin-film
samples, grain-boundaries make up a larger fraction of the total sample volume. If
the hopping states are principally associated with the grain boundaries, then it may
be stated that the frequency dependent current-voltage characteristics for
polycrystalline diamond, beyond those expected as a result of the sample’s
geometric capacitance, are principally associated with grain-boundaries, either due
to hopping conduction within the boundaries or due to capacitive effects associated
with grain-boundary potential barriers.

Thus far, all measurements were conducted at room temperature (T2300

0K.) One may question whether the proposed circuit model, used successfully to fit
the experimental IS results of both thin and thick diamond film samples at room
temperature, is valid at higher temperatures. It is also of interest to further
investigate the relationship between the structural properties of the films and the
model results. Chapter 6 addresses these relationships and tries to find answers to
other temperature related questions by studying the correlation of model reSults
with sample morphology and Raman quality, and by testing the validity of the

circuit model at higher temperatures.

96

 

-1

10

1"

 

 

Admittance, 1/Ohm

 

I T1 rT

1
.
1

 

 

 

/'/
-3 / .
10 ' / I ./ 1
t / / .
/ ’ /
I ’ /
ix ./
./
./ ......... EUR
-4 .’
10 F/ -.-.-. GB. 1
E.
---- Hopping
Experimental
10-5 1 141.1111 4 . 11111.1 . 41.1.1.1 . i lrlnrrl .3441
4 5 6 7 8
10 1O 10 10 10 1
Freq, Hz

Figure 5.16: Individual Model Contributions to The Admittance

For Thick Diamond Sample, TDF-12

97
5.6 Sensitivity of Model to Changes in Parameter Values

This section investigates the effect of changing a parameter value on the
simulated results of the model. This is done by fixing one parameter value, obtained
as an output result for a similar sample, and running the simulation model to
determine the other values. Tables 5.6 and 5.7 show the results obtained after fixing

the values of n, Rg, and Cg, for two samples, namely SK-13 and TDF-18. The

values at which the parameters are fixed at for sample SK-13 are obtained from the
output results of the thin film sample SK-179, as listed in Table 5.2. Similarly, the
fixed values used for testing TDF-18 are acquired from the results of the other thick
film sample, TDF-12. The first row in both tables shows the original values
obtained by the model for each sample, as described earlier. The next three rows
display the model’s output values, including the percentage error, when each of the
three parameters is fixed separately. Note that the values of R and C for each
sample are fixed for all runs.

From Table 5.6, it is observed that forcing even a slight change in n, from
0.9 to 0.8, causes the error value for the thin film sample to more than double. This
is consistent with our previous observation of the dominant role of hopping in thin
film samples. It also suggests that the variations in n values among the thin film
samples are significant. In Table 5.7 however, a large force change in n, from 0.9 to

0.5, does not cause much change in the error value. This is consistent with our

98

Table 5.6: Sensitivity Results for Thin Film SK-13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fixed Parameter B (52“) n Rg (Q) Cg (PF) Re (9) %Error

none (original 1.1,(10-9 0.9 9 100 0.7 1.1

run)

n 4,1041 0.8 2 160 1.2 2.7

Rg 1,2,10-9 0.9 65 70 0.1 6.4

Cg 1x10'8 0.8 30 24 0.4 13.7

Table 5.7: Sensitivity Results for Thick Film TDF-18

Fixed Parameter B (9'1) Rg Cg Re %Error

Tone (original 38,1043 0.9 320 11 2 2.8

run)

11 15,109 0.5 338 10 0.1 3.1

Rg 17,109 0.6 35 0.9 30 8.3
1,3,10-9 0.7 888 900 0.1 17.4

 

 

 

 

 

 

 

 

 

99

previous observation that hopping is not dominant in thick film samples. These
results suggest that the model variation of n in the thick film samples may not be
significant. Interestingly, force variation in Rg and Cg produce significantly larger

error in both thin film and thick film samples.

CHAPTER 6

EFFECTS OF GROWTH CONDITIONS AND FILM
ATTRIBUTES ON AC ELECTRICAL CONDUCTION IN CVD

DIAMOND FILMS

6.1 Introduction

In this chapter, our effort is focused on correlating the do and ac electrical
properties, especially conductivity, of a wide selection of polycrystalline diamond
films to four other key fihn properties, namely (1) the Raman diamond to graphite
signal ratio (Id/lg), (2) the Full-Width-at-Half-Maximum of the diamond Raman
signal, (3) the crystalline morphology as quantified by the growth parameter, or, and
(4) the average grain size. The electrical properties are also correlated to two
deposition parameters, namely substrate temperature and gas flow rate. The effect
of test-temperature on as-grown and annealed films’ electrical behavior is also

carefully considered.

100

 

101
6.2 Sample Description And Experimental Procedure

Three sets of thin CVD films, grown on silicon wafers, are considered for

this study. Each set includes three films grown at the same hydrogen flow rate and

three different substrate temperatures of 850, 900, and 1000 OC. The samples are

chosen to have the same percent methane concentration, %CH4/Hz, of 1.5%.

Figures 6.1 through 6.5, and Figures 6.6 through 6.9 display the SEM and Raman
spectra for all samples, respectively. The samples, the Raman data, and all the SEM
pictures were provided by Dr. S. Khatami, a former Ph.D. student of Dr. J.
Asmussen, at Michigan State University. Table 6.1 shows the deposition
parameters and some other key properties of the samples. Included in Table 6.1 are
the average grain size, determined by the method of linear intercepts, the full width
at half maximum (FWHM) of the diamond Raman peak, and the diamond to

graphite peak ratio, Id/Ig. The latter is calculated from the peak at 1332 (diamond)
divided by the peak at 1580 (graphite) Figure 6.6(a) shows the method of obtaining

this value. Even though this method of calculation does not yield the actual ratio of

sp3 to sp2 bonds, it gives a simple and consistent measure of the graphite content in

V100

the samples. The growth parameter or is defined as ”EV
111

, Where V100 and V111

are the growth rates in the <100> and <111> directions, respectively [89] [90] [91].

The a values ranges between 1 for a cube and 3 for an octahedron.

102

 

FIGURE 6.1: Top Surface SEM Pictures of (a) SK-182 (b) SK—l83 [43]

[See Table 6.1 for growth conditions and film attributes]

103

 

FIGURE 6.2: Top Surface SEM Pictures of (a) SK-12 (b) SK-179 [43]

[See Table 6.1 for growth conditions and film attributes]

   

FIGURE 6.3: Top Surface SEM Pictures of (a) SK-62 (b) SK—72 [43]
[See Table 6.1 for growth conditions and film attributes]

105

 

FIGURE 6.4: Top Surface SEM Pictures of (a) SK-209, and (b) SK-177

[See Table 6.1 for growth conditions and film attributes]

   

FIGURE 6.5: Top Surface SEM Pictures of Sample TKB

[See Table 6.1 for growth conditions and film attributes]

107

 

 

 

 

x 104 Raman spectrum for SK12 sample
1.6 I T r I 1 I I I
‘ .
15rr I ..
1.4- -l .4
1.31— ........... I ..... . . ...; ................. -q
I Id/Ig = l.6/0.84 =. 1.9
1_2.. ...... ....l.. ................. _.
gm I _
e ' ‘
1,. .-
8 ' 1
0.90' ' ._(
. _ I
0.8-...WW ........ _
. . aI 3' i
0.7 $2.. :2. _.
I . l ;
0.6 1 1 .4 r i 1 1 j i
1 200 1 250 1 300 1 350 1 400 1 450 1 500 1 550 1 600 1 650

Shift Wavenumber 1/cm

(a)

 

 

 

 

x 104 Raman spectrum for SK179 sample
2-2 I I I I f I I
2.11...... .. . ,. .- ....... ...... .. . ..... ;.. ...... ..l
2r- _
$1.9... ................................. ....
1'3
51.8- ..... _
1.7... ....... . . L ..... . ..... ....... ........... ..
1.6- ..... ..5 ............ L ..... . ..... : .......
1.5 L l l l 1 l I
1200 1250 1300 1350 1400 1450 1500 1550 1600

Shift Wavenumber 1/cm

FIGURE 6.6: Raman Spectra of (a) SK-12 (b) SK-l79

Counts per second

108

 

 

 

 

 

x 1 0‘ Raman spectrum for SK62
1.7 r r r I I v I
,6- ..... .. x g ......
,,5___, .. ,. 5 A
1.4— .4
13- ............................... ..
1_2_ ..............................
11200 1 250 1 S00 1 3:0 1 400 1 4:50 1 5:30 1 5:50 1 600

Shift Wavenumber 1/cm

 

 

 

 

x 104 Raman spectrum for SK72 sample

155 I ' r f 3 7 f f

,5. ' ‘ ‘ ............ _
1.45_ ............................... 2

1.4 t. ......................................... a
1.35_ ................................................... _

1.3,. .......................................................... l
1.25 ~ ~~~~ ‘

1.2 _ ................................................................................ a
1.15.. ................................................ _,

1_1 .......................................................... a
1 015200 1250 1 300 1 3150 1400 14:50 1500 1 5150 16100 1 650

Shift Wavenumber 1/cm

FIGURE 6.7: Raman Spectra of (a) SK-62 (b) SK-72

 

109

 

Counts per second

Counts per second

x 1 0‘ Raman spectrum of SK209r sample
1 .4 I I I Ti I T I I
1 .3 t- . ..... —.
1 .2 - ...... _
1.1-..... 1.... ................. —t
1 ,_ .................... _.
0.9 ... ............................
0.8 _. . .............................. t
0.7 1 1 1 l_ 1 1 L L
1 200 1 250 1 300 1 350 1 400 1 450 1 500 1 550 1 600 1 650
Shift Wevenumber 1/cm
(a)
x 104 Raman spectrum for SK1 77 sample
1 .6 f I I I I I fl
1 .5 ... ........................................................ _.
1 .4 .. ...................... _,
1 .3 - -
1 .2 - -
1 .1 b ,
1 L l l 1 l l 1
1 200 1 250 1 300 1 350 1 400 1 450 1 500 1 550 1 600

 

 

 

 

 

 

 

 

(b)

Shift Wavenumber 1/cm

FIGURE 6.8: Raman Spectra of (a) SK-209 (b) SK-l77

 

110

Raman spectrum for SK183 sample
8000 I T I I f I I W.

 

7500p. .H .. .. .... ..M,H.l H.. H.,._,. . ... .x .4..H...g...m-._

 

7000

0001118 per second
a)
‘8

6000

5500

 

 

 

5000 l t l 4 1 I 1 L
1 200 1 250 1 300 1 350 1 400 1 450 1 500 1 550 1 600 1 650
Shift Wavenumber 1 /cm
(a)

 

x 1 0“ Raman spectrum for TKb sample
2.6 I I I I T I I I

 

2.4- ........ ............. .1

22— ............................ ...,
. .

Ixmmsmuaxam

1.6 ....... ‘ ..... _

1_4_..

 

 

1 . 1 I l 1 4L 4 J l
1200 1 250 1 300 1 350 1 400 1 450 1 500 1 550 1 600 1 650
Shift Wavenumber 1 /cm
0))

 

FIGURE 6.9: Raman Spectra of (a) SK-l83 (b) TKB

 

111

Table 6.1: CVD Thin Diamond Films’ Key Properties

 

 

 

 

 

 

 

 

 

 

 

 

Flow Grain
Sample %CH4/H2 Rate, Ts, "C on FWHM 1.1/lg Size, W“
sccm
SK-62 1.5 60 850 l 9.09 1.3 1.14
SK-72 1.5 60 900 3 9.67 1.3 1.1
SK-182 1.5 60 1000 mixed ----- —--- 2.4
SK-177 1.5 200 850 1 7.05 1.3 1.5
SK-183 1.5 200 900 3 10.5 1.3 1.23
SK-209 1.5 200 1000 3 7.05 1.5 1.98
SK- 179 1.5 400 850 3 12.04 1.2 0.65
TKB 1.5 400 900 3 12.9 1.4 0.42
SK-12 1.5 400 1000 3 11.2 1.9 1.1

 

 

 

 

 

 

 

 

 

4 -—.'1 r1" .l .h‘l_
I
- I
. .

 

112

All films were prepared for measurement in a similar way as described
earlier in chapter 5. Two types of metals are used to form the top surface contacts,
sputtered gold and silver paint. The back side of the sample, the silicon wafer side,
is placed on a gold-plated metal piece. Both dc and ac measurements are conducted
in the direction perpendicular to the surface of the film. Table 6.2 lists the metal
contact type and behavior as related to the dc resistivities of the films.

The ac complex impedance was measured from dc to 100 MHz over a broad
temperature range. The ac measurement setup is slightly different from the one
described in chapter 5 due to equipment limitations, namely that the HP 16191A
high frequency test fixture was not designed to operate at temperatures higher than
room temperature. As a result, the high frequency coaxial probes were used to

conduct the ac measurements.

6.3 Relationship of As-Grown Electrical Properties to Film Attributes

and Deposition Parameters

This section discusses the correlations investigated in this study, which are
depicted in Figure 6.10. The information about the samples’ deposition parameters
and other key properties are listed in Tables 6.1 and 6.2. There are two objectives in
this investigation. The first discusses the correlation between the films’ dc electrical

resistivity, ode, and the deposition parameters, namely the substrate temperature,

 

113

Table 6.2: Samples’ Contact Properties and as-grown dc Resistivities

 

 

 

 

 

 

 

 

 

 

 

 

Sample Metal Type 5:13:31. Thiflknrliess, gifiifity’
SK-12 Gold ohmic 5.28 8.1x107
SK-209 Gold ohmic 4.68 1 3,1103
SK-l77 Gold ohmic 3.77 13,1106
SK-62 Gold ohmic 3.15 1 3,1109
SK-72 Gold ohmic 3.82 25,1109
SK- 179 Gold ohmic 3 .68 6.4x 106
SK-182 Silver ohmic 4.202 7x108
SK-183 Silver ohmic 4.42 15,1103
TKB Silver ohmic 4.196 1.8x 1o6

 

 

 

 

 

 

114

 

I Simulated sac]

 

Growth Input Parameters

   

  
      
 

Substrate
Temperature, Ts

 

Measured Gdc Flow Rate

 

 

      
   
   

(1

Grain Size
FW HM

141.

Growth Output Parameters

 

Figure 6.10: Schematic Diagram Showing The Investigated Correlations

115
T5, and the hydrogen flow rate, and the selected film attributes. The second part of

the investigation of as-grown films at room temperature deals with the correlation

between the ac electrical conductivity, (Sac, specifically hopping, (Shop, and grain-
boundary, GGB, conductivities, and the films’ deposition parameters and growth

output properties.

Regarding O'dc, Figure 6.11 displays a map with the substrate temperature

and the hydrogen flow rate as inputs, and the measured resistivity and the
morphology measure, a, of all samples as outputs. Figures 6.12 through 6.14
display the as-grown dc resistivity versus the individual CVD film properties listed
in Table 6.1. Looking at these Figures, it appears that the clearest relationship that
can be concluded is that the as-grown dc resistivity of diamond films decreases as
the hydrogen flow rate increases. The decrease in resistivity at higher flow rates
may be attributed to the incorporation of more hydrogen atoms in the film during
the CVD growth process [61][69][87][92][93]. Landstrass et a1. [92] [93] believe
that the presence of atomic hydrogen in diamond films results in the passivation of
electrically active interband defect states which leads to lower film’s resistivity. As
for the relationship between the as-grown dc resistivity and other properties, there
may be suggestion of an increase in resistivity with increasing grain size and
decreasing FWHM. However, the single most dominant parameter appears to be

flow rate.

 

116

Substrate Temperature,0 C

 

 

 

 

850 900 1000
1.8x109 2.5x109 7x108
60
I A I A
E
g 13 106 8
. - X 1.5x10 13,1108
g 200 .
a; I A A
2
h 7
4 6 . 6 8.1X10
400 6 x10 18x10
A A A

 

 

 

 

 

A equivalent to (100) morphology, i.e. on = 1

- equivalent to (111) morphology, i.e. CL = 3
Resistivity, shown numerically, is measured in Q—cm

Figure 6.11: Correlation between as-grown dc resistivity, shown numerically, and growth

parameter, shown by symbol, and growth input parameters

117

(a)

10

 

 

 

 

 

 

 

 

10 :fi r T I W7 I I I :
o .
o 4
1O9 - 3
t 0 ‘
B
,, 10 E o 3
>5
H
.-
9.
.-
H 7
.a 10 E’ —:
a E °
0 0
10° F 1
1
l L I l 1 I I l
50 100 150 200 250 300 350 400
Flow Rate, sccm
1010.. v I I I
1 ° 1
0
0
10° :- O -:
a E o ‘
G) I
d '
G
.2» . °
0- ‘0 E- .5
> » :
.-
1, .
m 1
O- 4
an
§
107 — a
0
O O 1
105 I r 1 I
800 850 900 950 1000 1050

Substrate Temperature, 0K

Figure 6.12: Relationship between films’ as-grown dc resistivity and (a) Flow rate, in sccm,

and (b) Substrate temperature, Ts, in 0K.

118

(b)

10

 

 

 

 

 

 

 

 

‘0 E I I I I I I I j
o 4
8 1
10° .— ° 4,
9
c3
. 1 o i
3’ 10° .- 1
«II : I
> 1
._ ‘
H .
m 1
o—
W 1
Q)
a 107 :- 1
. O 2
O o J
100 1 1 1 1 1 1 1
0 0.5 1 1.5 2 2.5 3 3.5 4
Growth Parameter, on
10“); I I I r I I I
I 0
O 0
10° ,- 0 1
5 I 1
d k 4
'~ 0
r? ‘0’ ' ‘:
§ 2
O- 4
H .
.21
in
Q
a ‘107 :- 1
5 ° ‘
p
L
>- 0 o 4
‘0. 1 1 1 1 1 J 1
6 7 8 9 10 11 12 13 14

Full Width at Half Maximum, FWHM, cm'1

Figure 6.13: Relationship between films’ as-grown dc resistivity and (a) Growth parameter, a,

and (b) Full Width at Half Maximum, FWHM.

 

 

 

 

 

 

 

 

 

119
(a)
1010, I I I I r f j I
E
L
b O
o
0
10° — 0 1
5 i i
C} . o
B
:3 1Oa :- 1
O- ’
> F
o- 1
a; r w
.5 r- J
o 1
m ‘07 I. —.
t o
O 0
10° 1 1 1 1 1 1 1 1
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
Id/IgRatlo
(b)
10’°E . i . i . 1
i 0 ’
. 8
10. .- 0 .1.
E ° 1
C) I
I 4
Ci .
" 0
it? 1°” r 1
.2 3
u I
in
O-
to
5‘2
‘0’ r 1
C O
1.
0 0
10° 1 1 1 L 1
0.5 1 1.5 2 2.5
Grain Size, um

Figure 6.14: Relationship between films’ as-grown dc resistivity and (a) Id/Ig ratio, and (b)

Grain size, 11m

120

To study (Sac, six Matlab simulation programs, similar to the one showed in

Figure 4.6, were run to obtain the best fit parameter values, with minimum percent
error. Table 6.3 shows a list of the IS simulation results at room temperature.
Sample SK-182 is omitted because its Raman data is not available and it has a
mixed morphology (0:1 and 01:3) which makes it harder to fully compare its
results with any of the other samples.

First, consider the hopping conduction path. Two correlations were observed

in the investigation of thin films with similar morphology, on. The first relates the ac
hopping conductivity, Chop = Ba)", to the Id/Ig ratios, and the second relates it to the
grain size of the films. Plotting Chop versus the other parameters showed no

conspicuous correlations. Figure 6.15 shows how hopping, at high frequencies,

increases as Id/Ig decreases. The data points were calculated at 100 MHz frequency

for each of thin film sample using the Bo)n relation and the numbers listed in Table

6.3. Moreover, Figure 6.16 indicates that the (Shop is also inversely proportional to
the film’s grain size. However, the crystal size and the Id/Ig ratio of the films are not

clearly related. The first observation may suggest that hopping is mainly caused by
conduction along the graphitic region between diamond grains and the surface of
the films. This coincides with the conclusions of Sugino et a1. [3][22]. The second
observation indicates that the smaller the film’s grain size, the higher the role of

hopping admittance. This is again consistent with the fact that the finer grain films,

 

Table 6.3: IS Model Parameters for as-grown Films at Room Temperature

121

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample R (Q) C (pF) B (9'1) 11 R3 (Q) Cg (F)
TKB 9.5x103 92 1x108 0.7 87 40x10'12
SK-179 3.02x104 103 2.2x10'9 0-8 65 24111012
SK-IZ 3.38x105 116 6x10’8 0-5 4800 13:110'10
SK-72 3x107 41 5x10'9 0-7 389 17110'12
31962 1.85x107 47-3 9x109 0-7 171 9x10'“
SK-183 1.61x106 45-7 55x10“ 0-8 540 31110-12
SK-177 16,1104 39.6 1x10“ 0.5 39330 1x109
$19209 4.2311105 138-2 1.7x10'9 0-7 10145 26x10'”

 

 

 

ac Hopping Admittance

122

 

10 l I T T I I I I

Frequency = 100 MHz

 

 

 

 

.3
10 1 1 L 1 1 1 1 1

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Id/I g R3110

Figure 6.15: The Relationship Between ac Hopping Conduction And Id/Ig

 

ac Hopping Admittance

123

 

10 F I I I I I I I I I
b

Frequency 2 100 MHz

10'2 ~

 

 

 

 

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Grain Size, urn

Figure 6.16: The Relationship Between ac Hopping Conduction And Grain Size

2.2

 

124

grain boundaries make up a larger fraction of the total sample volume. This was
previously noted in chapter 5, comparing large grain free-standing films with
MWPCVD films. It is informative to note that for one of the film samples, SK-177
with morphology growth parameter or = 1, it was observed that the film exhibited a
low hopping conduction relative to other {111} films at all frequencies. This could
be related to the alignment of the grains at the grain boundary. The other on = 1 film
in this study does not have low hopping, however it has a smaller grain size.

Now, consider the other ac conduction .path, namely the cross-grain
boundary path, and its correlation with film properties and deposition parameters.
Figure 6.17 displays the relationship between the conductivity of the cross-grain-
boundary path and the film’s grain size. It can be stated that the higher the film’s
grain size, the lower the admittance of the cross-grain boundary path. A
comparison of the data indicates that at 100 MHz this is mainly due the fact that

larger grain size have larger Rg values. With regard to correlations with other film’s
attributes, such as the Id/Ig and the growth parameter 0:, and the deposition
parameters, such as T8 and the flow rate, again no confirmative conclusions were

derived.

 

ac Grain Boundary Admittance

 

 

 

 

 

 

125
-1
10 > r r r I 1 1 I l I
; 1'11
» Frequency = 100 MHz
, .
10.2 r 1 l I.
I 1
- 1
p 4
104 r 1
104 ~ 1
1
4
+ '1
I I I I l 4 I I I
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

Grain Size, 11m

Figure 6.17: The Relationship Between Grain Boundary Conduction and Grain Size

126
6.4 Annealing and Temperature Effects on Electrical Conductivity and

ac Circuit Model Parameters

It is important to study the electrical conductivity of semiconducting
materials at various temperatures in order to add to the understanding, and to better
characterize the electrical behavior of different conduction mechanisms. This
section discusses the annealing and temperature effects on the electrical
conductivity and the ac circuit model parameters for four selected samples. Two of

those samples, namely SK-62 and SK-72, are grown at the same flow rate of 60

sccm but at substrate temperatures of 850 °C and 900 0C, respectively. The other

two samples, namely SK-209 and SK-12, are grown at the same substrate

temperature of 1000 0C but at flow rates of 200 sccm and 400 sccm, respectively.
When the samples, in the as-grown state, were tested at elevated temperatures, they
showed time-varying behavior. Figure 6.18 shows the resistivity behavior in the

case of sample SK-72. In fact, this behavior was caused by annealing carried by the

measurement temperature. Sugino et al. showed that temperatures as low as 300 0C

were sufficient to anneal their films and to cause a sharp increase in resistivity. As a

result, our samples were annealed in a hydrogen furnace at 400 °C for one hour in
order to stabilize the film’s behavior at elevated temperatures. After annealing the

samples showed a sharp increase in do resistivity. The literature suggests that the

 

13

127

 

10

I rrvvvv

1’1

Resistivity, fl—cm
8

108 g

10 g

 

1O

 

I I I I J

Ll].

lAlAu‘l 411111

A ALLA“ 4 1 AAAIA“

 

 

250

Figure 6.18: do I-V Behavior of SK-72 in the as-grown state versus temperature, showing

300 350 400 450 500

Temperature, 0K

annealing effect at higher measurement temperatures.

550

600

 

 

128

increase in dc resistivity after annealing could be due to the removal of hydrogen
atoms from the films. Figure 6.19 shows the dc I-V characteristics before and after
annealing, and Table 6.4 lists the calculated resistivity for all four samples. It is
worth noting that two of the samples, namely SK-12 and SK-209, have lost the
linear behavior of their contacts after annealing. This, in turn, may have a
substantial effect on the ac measurements, especially at high frequencies, if a
significant voltage drop develops across the contact [86][88]. It is the higher flow
rate films that become non-ohmic. After annealing, all the films showed stable
behavior at elevated temperatures, and the measured dc resistance showed a
decrease as temperature increases.

To study the effect of annealing on the ac circuit model, consider the two
thin film samples, SK-62 and SK-72, which have {100} and {111} morphologies,
respectively, and which maintained ohmic characteristics after annealing. Figure
6.20, first, shows the after annealing temperature dependent behavior of the dc
resistance for both thin film samples, SK-62 and SK-72. The activation energies
illustrated in the lines shown in the plots of Figure 6.20 are calculated and found to
be approximately equal to 0.5 eV for the {100} film and 0.7 eV for the {111} film.
There is not a big difference between the activation energies of the two samples

considering the uncertainty of the experimental measurements. A plot of the log of

conductivity versus Tm to check for the characteristic temperature dependence of

 

 

 

Current, A

Current, A

129

SK—209

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Voltage, volts

Figure 6.19: I-V characteristics (a) Before Annealing, and (b) After Annealing

 

130

Table 6.4: Resistivity of Selected Films Before and After Annealing

 

 

 

 

 

 

 

Sample Resistivity Before Resistivity After
Annealing, Q-cm Anneallng, Q-cm
SK-12 31,1107 9.8x109
SK-209 13,1108 1.8x1010
SK-62 1.8x109 2.1x1012
SK-72 25,1109 1.2111012

 

 

 

 

131

(a)

10 : I I I I I I
.
D

 

10

10 f

A A AAAALl

AAIAI A L] AAALAI 4

Resistance, (2
3

 

 

 

 

10 I 1

I 1

> 4
10° :— .1

: i

r 1

1- 4
105 1 1 1 1 1 1

250 300 350 400 450 500 550 600

Temperature, °K

 

 

 

 

 

1 o I I ‘Ii I I I
1 0‘°
E 1
t 1
1 <
9
1 0 5' '1
c. . h 1
. 1 0 g- 1:
0 ’ :
g . I
7
3 1 O r '1
tn ' :
O- 1
8 b 1
0
a 1 0 g- 3
5
1 0 g- E
1 o‘ E- 1
1 03 1 1 1 1 1 1 '
250 300 350 400 450 500 550 600

Temperature, 0K

Figure 6.20: dc Resistance as a function of temperature for (a) sample SK-62, and (b) sample

SK-72

 

132

hopping would require more data points and less experimental uncertainty. In
comparison with other researchers’ results, Sugino et a1. [68] have observed three
trap levels with activation energies of 0.62, 1.38, and 0.95 eV for their annealed
samples, while only one trap with activation energy of 0.95 was observed after a
hydrogenation treatment of the samples. Sugino’s observation, again, supports the
theory of Landstrass et a1. [93] in which they stated that the incorporation of atomic
hydrogen in CVD films results in the passivation of electrically active traps leading
to the enhancement of the films’ conductivity. Figure 6.21 demonstrates how the

conductance for both CVD thin films changes after annealing, and at different

temperatures from 300 to 550 0K. Similar results have been reported in the
literature, and there has been disagreement among researchers on the main cause of
this behavior [2][4][78]. Sugino et a1. [3][77] have observed that the frequency
dependent conductance of annealed films are less frequency dependent at higher
temperatures. They concluded that thermally activated band conduction dominates
in the conduction process in the low frequency region. On the other hand, Fiegl et
a1. [78] have disagreed and reported that conductivity in polycrystalline diamond
films can be completely understood in terms of hopping conductivity within grain
boundaries. As for the results shown in Figure 6.21, the following ac observations
can be deduced. First, and in support of the dc measurements, there was

considerable decrease in conductivity at low frequency between the as-grown and

 

 

 

133

 

 

 

   

 

 

 

 

(a)
10-2: ‘ ' ' "VY'T ' ' Y ""'I I ' ' ""'1 ' ' ' V'err f
—3
1O 5-
(73 _,
. 1o —
8
g - . ° °°°°
-5 o o <>049 ,..r
U 10 E‘ ’ -
,, /
= . ,1
15 - I.
= u
I
O 104?. ..— /'
L) t , " o 00ch
F I
1 I ’ .. A A A Aafi
- _ .— -' ’ 06’ 'l’
10 75” O O O A I»
E o A .,
‘ .A
ab * *q'-
10" 11 111111 1 1 1 111111 1 1 1 111111 1 1 1111111 1
10‘ 102 103 10 105
(b) Frequency, Hz
10‘2 V ‘ ‘ "VVfI ' ' I r""r T fiV—frvw'T ' ' ' "'fiI
4
10 E-
t
m 1’
“ 1O :-
23 :
= I
a _.
’
g 10 Er .".
h I
I .000
2 . /°’
O 1o"[— ()0 / /
U E o o O 0 0 ’ I at
. fl __ 2 " ’ r:
a.
10”? a
‘0’. i 441 11111112 1 1 1 1111113 1 1 L11111l‘ 1 1 L111_1115
10 1o 10 1o 10
Frequency, Hz

Figure 6.2]: ac Conductance for samples in the as-grown, annealed, and annealed and tested at
higher temperatures, (a) SK-62, and (b) SK-72

 

-.-. As-grown and tested at 300 °K O Annealed and tested at 425 °K
A Annealed and tested at 300 0K 0 Annealed and tested at 550 °K
9K Annealed and tested at 350 °K

134

annealed samples. Second, at higher frequencies, the samples seem to be only
weakly dependent on temperature. This may indicate, as reported by Ermakova et
a1. [1][4], that polycrystalline diamond films are thermally stable at high
frequencies, that is, at high frequencies the conductivity of the films does not vary
as much with changing temperature. The third observation is related to fitting the
data to the four path ac circuit model, described earlier in chapter 4. Again, the 18
experimental results are compared with the four path ac circuit model, and the
model best-fit parameter values are obtained. The individual contribution of each
path in the model is looked at separately. Table 6.5 lists the parameter values for

two CVD thin film samples, SK-62 and SK-72, in the as-grown, annealed, and

annealed and tested at 550 0K states.

According to the listed data in Table 6.5, the exponent n tends to have higher
values for the annealed films than for the as—grown ones. This may support similar
observations reported by other researchers [2][3][7][22][68][77]. However, and in
disagreement with the work of Muto et a1. [2], it is also observed that the exponent
n is a temperature dependent variable decreasing with increasing temperature.

Although Table 6.5 shows a value of 0.1 for the exponent n in the case of sample

SK-62 when tested at 550 OK, it is believed that this is a result of the parameter
best-fit method used in simulation, and does not have any physical significance.

Figure 6.21 (a) shows that the conductance is almost independent of frequency in

135

Table 6.5: Best-fit Parameter Values For 'leo Thin Film CVD Samples

 

 

 

 

 

 

 

 

 

 

SK-62 I SK-72

Annealed Annealed
Parameter As-grown Annealed :62?“ at As-grown Annealed 2:3“! at

550 °K 550 °K
11(9) 1.85x107 2.2xlo10 5.5x105 3x107 1.4:11010 2:1106
13(1)") 9x10’9 9xlo'l3 mo5 5xlO'9 1.3:110'12 1.4x10'10
n 0.7 0.9 0.1 0.7 1 0.8
R8 (Q) 171 66 609 389 28 473
Cg (F) 9x10'” 1:110'll 9x10'12 1.7x10'“ 6x10‘12 mo-12
% Error 13.1 16.5 12.8 14.4 7.9 11.4

 

 

 

 

 

 

 

 

an.

15.;—

 

 

136

the low frequency region, and is very close in value to the dc measured

conductance. Table 6.5 also reveals that the values of Rg after annealing, for both

type of samples, are decreased. This may suggest that the incorporation of
hydrogen in the films affects the grain boundaries not the crystallites themselves,
that is, the diamond crystals in polycrystalline diamond films may not contain any
hydrogen even in the as-grown state. In this study, these results are demonstrated in
two samples, namely SK-62 and SK-72.

To study and analyze the individual contribution of hopping and cross-grain-
boundary paths to the total conduction in thin diamond films, consider Figures 6.22
and 6.23. Part (a) of each figure shows the ratio of the hopping path’s admittance to
the total admittance, and part (b) shows the ratio of the cross-grain-boundary path’s
admittance to the total admittance for the as-grown samples SK-62 and SK-72,
respectively, and according to the data listed in Table 6.5. The Figures clearly show
that hopping conduction is dominating in the low frequency region while cross-

grain-boundary conduction is not as significant. As we move to higher frequencies,

higher than 105 Hz, conduction across the grain boundaries’ potential barriers
becomes more active, and contribute over 20% of the total admittance for sample
SK-72, and close to 60% for the case of sample SK-62, in certain frequency

regions. The hopping admittance to the total admittance ratio shows a sharp

decrease for frequencies higher than 105 Hz, however, still plays a considerable

Hopping to Total Admittance Ratio

Grain Boundary to Total Admittance Ratio

Figure 6.22: Individual path contribution to the total admittace for the as-grown sample SK-62

137

 

 

 

 

 

 

 

 

a I ' ""I ' va""1 I ' ' ""'I i f" I ' ' vvvVVTI ' I I ' '
10° +—++
r— + + + -<
L + + <
+ +
L + _.+
4.. 1
[ d
+ '4
+
1
d
4
1
10" - - 1-----1 - ---1--1 - ------1 1 - ------1 1 1-11-“1 - - ------1 - - - -----1 - -- --
o 1 2 a o s s
10 1O 1O 1O 1O 1O 1O 1O 10
Frequency, Hz
0
1o ' I ffv‘I'T ' ' v""I ' Vi V'I'T 7""'I 'I ' ' "mf ' 'I
. ... ++ .
4+-
++
.4.
+
h 4
+"""f
-1
— d
10 . + 4
r + 4
b 4
p + <
, +
+
> 4
4
10‘? -----1 - - -1----1 - 1---- -1 11 11111-11 1 11- -1 1 1 ---1-11 - -----
2 3 4 5 0 7
1O 1O 1O 1O 1O 1O 1O 10

Frequency, Hz

 

 

 

138

 

v v vvv—rrvT v *7 vvvvvv' V vwvvw—v

10" +++++ +++

+++

   

Hopping to Total Admittance Ratio

 

 

 

1o2 103 10‘ . 105 10° 107 1o

 

 

 

 

 

.2 (b)
H
CB
“ 100 . ' ' ' ' v"'I ' I a 'fiVYI T v ' ' ""I T V ' fvvf'T ' ' ' ' "V'I ' ' ' f‘Vw'
0 r .
U ' 1
:1 > .
H
.-
E 4
13
< + ++
'3 +
4.
ed + +
63 1o”-— +
+

s +

+ 1
E’ 1
“g t + 45". ,
g: +
:1
a? r 1
=1
'5
h 10-2 2 ‘ A ‘A‘A‘Al3 A A AAAAA" A A AAA‘AA'S A A gA‘AAAIG A LLAA—LAA17 A AJALAA .
CD 10 10 1o 10 1o 10 10

Frequency, Hz

Figure 6.23: Individual path contribution to the total admittace for the as— grown sample SK-72

139

role in the total conduction of the as-grown film. These conclusions are
demonstrated with both samples with disregard to the films’ morphologies.
Now, consider the case where the samples are tested at elevated

temperatures higher than room temperature. This case is established in this study

by testing the two annealed samples, SK-62 and SK-72, at 550 0K temperature.
Figure 6.24 shows a comparison between experimental and modeled ac
conductance, based on the numbers shown in Table 6.5, for both thin film samples.
To understand the contribution of each path, the absolute value of the total
simulated admittance, the absolute value of the ac hopping admittance, and the
absolute value of the cross-grain-boundary admittance are plotted as functions of
frequency for both samples. Figures 6.25 and 6.26 display the results for SK-62 and
SK-72 samples, respectively. Part (a) of each Figure displays the results in the
frequency range from 100Hz to 1 MHz, and part (b) displays the results in the
frequency range from 10 MHz to 100 MHz. The Figures indicate that hopping
admittance plays a bigger role at lower frequencies than cross-grain boundary
admittance. However, and in contrast to the results shown for the same samples in
the as-grown state, the contribution of cross-grain boundary conduction to the total
conduction at high frequencies is higher than the contribution of hopping
conduction. These results justify the claim for the need to add both hopping and

cross-grain-boundary paths to the ac circuit model in order to explain the high

 

rd

 

 

 

140

 

1o - -fi-.-, - - ---fiq . v-.-..., - . ---.-., - - ...V.., v -44-

 

 

 

 

 

 

 

 

 

E 4
I 1
d
+ Experimental
10'3 E- o Modeled
1.
>-
p
10":
,. O + +++
O Oct)
CD 0 + .
1r + + +'H'
10—5 1 111111111 1 1 1111111 1 1 1111111 1 1 1 111111 1 11111111 1 11111111
10? 1o8 10‘ 105 10° 10’ 10'
10-2: ' ' ' 'V'V'T I ' i ' ""I ' ' ' ""'I ' ' ' ' ""I
104':-
F
4 + Experimental
10' r:- oModeled
I
I
L
O
10“: :
+4i- 4
1 + d’ '
6 O
10 E- ++4+ 1
I a Q Q 6 00cm 1
.1
4
10"7 - - - -----1 - - - 1111-1 - - ---1--1 1 - ------1 - - ------1 1 1 - -----1 1 1 1-----
1o‘ 102 1o3 10‘ 105 10° 10’ 10'

Figure 6.24: Comparison between experimental and modeled ac conductance for annealed

samples, (a) SK-62, and (b) SK-72 at measurement temperature of 550 °K

 

 

141

 

 

 

 

(a)
‘0". , ~v~mw , vvvvvm v vvvwm + cs,”

5 D D
to“; D

E p I} k 922 + + 6

q} a? 3’ WW 0
10*r

000
O
O

104:—

5 o
'0- F 6) Annealed at 400°C

’ 0 0 Tested at 550 0K

O

10";-

d

i
1O"D 1 ‘ “**~“ 1 --.---1 A 1111A--1 - A”-..

‘02 103 10‘ 105 10°

Frequency, Hz
to" - - , ,
Annealed at 400 °C
Tested at 550 °K

 

 

 

 

 

Frequency, Hz

Figure 6.25: Comparison of ac conductance for sample SK-62 with both hopping and grain
boundary paths of the ac circuit model in two frequency regions: (a) 100 Hz to 1 MHz, and (b)
10 MHz to 100 MHz.

[>Total admittance, o Hopping admittance, and + Grain Boundary admittance

 

 

1‘12

 

 

 

 

 

,3 (a)
10 ' ' '—' "fif ' V ' '_'*"T fii ' ' ' "Y'l ' ' V V ""T ' ' V ' "" V V ' "VY
E D >
4 . D .
10 ? D 1
E 1’
. t> Dy 6 G l
10" D o E
E ,
E D + Egg :
r "' 0
to“ 0
g >1 D- D' D">‘>u> 2, 1
10" r + +‘* 1
- +
: <9
. + O O .
10" =- + o O 1
+ O Annealed at 400 C 3
‘ 0 Tested at 550 OK I
10_0 F o 1:
t 3
_ ’ 1 i
10 K1’0C A A A UHlO‘ A A A 102 L “1‘33 ‘ L““1‘“ A A A AAUAIS k A ‘“T“ ‘
0 10 10
Frequency, Hz
10": . . v , , , , j
’ Annealed at 400 °C

Tested at 550 oK

 

 

 

 

 

10’ 10'

Frequency, Hz

Figure 6.26: Comparison of ac conductance for sample SK-72 with both hopping and grain
boundary paths of the ac circuit model in two frequency regions: (a) 100 Hz to 1 MHz, and (b)
10 MHz to 100 MHz.

[> Total admittance, o Hopping admittance, and + Grain Boundary admittance

3‘94

 

I43

frequency electrical conduction phenomena in polycrystalline diamond films.

 

 

CHAPTER 7

DISCUSSION AND FUTURE WORK

This chapter summarizes the results of the research work which is described
in earlier chapters, and discusses related research issues which need to be further
investigated.

The ac electrical conductivity of polycrystalline thin and thick, free-standing
diamond samples is investigated in the frequency range from dc to 1 GHz. The
impedance spectroscopy results are well modeled over this frequency range by the
developed four path ac circuit model described in chapter 4. The model contains
two frequency dependent conduction paths, one representing hopping and the other
representing transport across grain boundaries, in addition to the basic electrical
model of the sample. The contact resistance, although small enough to produce a
negligible voltage drop at dc, plays a non-trivial role at high frequencies, on the
order of several hundred MHz. The results indicate that both transport across grain
barriers and hopping contribute to the impedance spectroscopy results for both

types of samples. The inclusion of both conduction paths in the IS model is

144

 

 

145
essential and is in better agreement with experiment than either one alone. After

studying the relative role of various contributors, this study concluded that the
frequency dependent current-voltage characteristics for polycrystalline diamond,
beyond those expected as a result of the sample’s geometric capacitance, are
principally associated with grain boundaries, either owing to hopping conduction
within the boundaries or to capacitive effects associated with grain boundary
potential barriers.

The correlation between the dc electrical properties of CVD diamond films
and the growth input and output parameters are also investigated in this study.
Results clearly show that the as-grown dc resistivity of CVD films is related to the
hydrogen flow rate used during the growth process. It is hypothesized that this is
mainly caused by the incorporation of hydrogen atoms within the film’s grains.
This results in the passivation of electrically active defect states in diamond which
leads to a decrease in resistivity. There may also be a suggestion of an increase in
resistivity with increasing grain size and decreasing FWHM.

Investigating the as-grown film’s ac electrical properties using the developed
ac circuit model reveals the individual role of conduction paths within the film, and
helps relate these properties to key film attributes. For example, it is observed that
the ac hopping admittance is inversely proportional to both the diamond to graphite

signal ratio, Id/Ig, and to the average grain size. The second observation indicates

 

146

that hopping is mainly associated with grain boundaries, as noted in chapter 5. It is
also observed that the ac cross-grain-boundary admittance is inversely proportional
to the film’s average grain size.

The temperature and annealing effects on dc electrical resistivity and ac
circuit model parameters were also investigated. The dc resistivity of the films
show sharp increase after annealing. This is believed to be related to the expulsion
of hydrogen atoms from the films. When the IS results of the annealed samples are
fitted to the four path circuit model, the numbers reveal a slight decrease in the

grain boundary resistance, Rg, and a large decrease in hopping conductivity. This

may suggest that the incorporation of hydrogen in the films takes place at the grain
boundaries, and not within the crystallites themselves. This again emphasizes the
important role that grain boundaries play in the total conduction mechanism in
polycrystalline diamond films.

In conclusion, it is demonstrated that the frequency dependent electrical
properties of polycrystalline diamond, beyond those expected as a result of the
samples geometric capacitance, are principally associated with grain boundaries.
Both hopping and cross-grain-boundary conduction paths play important roles in
the total conduction process of both thin and thick, free—standing polycrystalline
diamond films.

To achieve more comprehensive understanding of this subject, future

 

147

research is required in the following areas. (1) Study the importance of the
depositing system’s purity, particularly the role of nitrogen, in producing diamond
films with pre-determined characteristics. (2) Study the correlation between the
films’ electrical properties and plasma diagnostics. (3) Given the apparent
important role of grain boundaries in determining the electrical properties of
polycrystalline diamond, it would be useful to use other techniques such as TEM to
provide additional information that may add to the understanding of their role. (4)
Study the effect of hydrogenation on both dc and ac electrical properties of the
films. (5) Apply the findings of the current research study on a wider variety of
diamond samples grown by different techniques and at different conditions. (6) Use
more advanced temperature measurement equipment to achieve more accurate

results.

 

 

 

 

 

BIBLIOGRAPHY

 

BIBLIOGRAPHY

[1] G. Sokolina, A. Botev, L. Bouilov, S. Bantsekov, O. Lazareva, and A. Belyanin,
Sov. Physincs Semiconductors, 24 (1990) 105.

[2] Y. Muto, T. Sugino, K. Kobashi, and J. Shirafuji, Jpn. J. Physics, 31 (1992) L4.

[3] T. Sugino, Y. Muto, J. Shirafuji, and K. Kobashi, Diamond and Related
Materials, 2 (1993) 797.

[4] O. Ermakova, V. Polyakov, M. Ermakov, P. Perov, O. Lazareva, G. Sokolina,
and B. Spitsyn, Diamond and Related Materials, 2 (1993) 1336.

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