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This is to certify that the
dissertation entitled
FREQUENCY DEPENDENT RESPONSE OF

DIAMOND SCHOTTKY BARRIER DIODE T0
LARGE AND SMALL ELECTRICAL SIGNALS

presented by
Boonchoat Paosawatyanyong

has been accepted towards fulﬁllment
of the requirements for

Ph.D. degree in Electrical Eng

 

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Date II!’3[?X

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ma COMM“

 

Frequency Dependent Response of
Diamond Schottky Barrier diode to Large and
Small Electrical Signals

By

Boonchoat Paosawatyanyong

A DISSERTATION

Submitted to
Michigan State University
In partial fulﬁllment of the requirements
For the degree of

DOCTOR OF PHILOSOPHY
Department of Electrical Engineering

1998

Abstract

Frequency Dependent Response of
Diamond Schottky Barrier diode to Large and
Small Electrical Signals

By
Boonchoat Paosawatyanyong

The response of diamond Schottky barrier diodes to time varying signals has been
studied as a function of frequency and bias voltage. Both small signal waveforms
superimposed upon a dc bias, as well as large signal sinusoidal waveforms which drive
the diode between reverse and forward bias have been studied. The diodes are formed on
thin polycrystalline diamond ﬁlms deposited by a microwave plasma assisted deposition
process. The Schottky metal is typically aluminum. The ohmic contact is generally a
back-contact p-type silicon wafer on which the diamond is deposited, although tungsten
contact overlaid with protective a layer of gold has also been successfully used. Coaxial
microprobes contact the test wafers which are placed on a temperature controlled
substrate holder. Measurements are performed over a temperature range of 27 ° C to 127
° C. Films synthesized under various growth conditions have been tested in this study.

The experimental results of small signal test are compared to three computer
models, which are: (I) a simple model that includes as input parameters the bulk series
resistance, the capacitance associated with the bulk material between the space-charge
layer and the ohmic contact, the space-charge layer capacitance, and the diode dynamic

resistance; (H) a model with additional of a contact resistance; and (III) a model which

includes the effect of trap states represented by frequency-dependent capacitance and
resistance.

The experimental results of the large switching signal test are compared to
computer (SPICE) simulations which include as input parameters the bulk series
resistance, the ideality factor, and diode saturation current, obtained from dc
measurements. Also included are the space-charge layer capacitance, and the capacitance
associated with bulk material between the space-charge layer and the ohmic contact
obtained from curve-ﬁtting. Good agreement is obtained between experimental switching
observations and model predictions. For the diodes in this study, the best large signal
switching frequency between forward and reverse bias is approximately 10 KHz, and the
highest small signal varistors frequency performance is approximately 200 KHz.

For many operating conditions, the speed response of the diode is limited by the
high bulk resistivity of the undoped diamond ﬁlms. The simulation study indicates that
doping the diamond ﬁlm and constructing diodes with a lower bulk resistance while
maintaining the space-charge layer properties would signiﬁcantly improve the diode

switching speed performance.

Acknowledgements

I would like to express my sincere gratitude to my advisor Dr. Donnie K.
Reinhard for his guidance, support, encouragement, and patience. He has been an
excellent mentor throughout the years. Great appreciation goes to Dr. Brage Golding who
always gives the best suggestion throughout my academic career and life at Michigan
State University. I also would like to thank my committee members, Dr. Timothy
Grotjohn and Dr. J es Asmussen for their valuable discussions and comments.

Many thanks go to Dr. Michael Ulzynski, Dr. Saeid Khatami, and Dr. Mohannad
Bataineh, who were always willing to help and give suggestions in the laboratory, Dr.
Michale Jaeger, Dr. Lowell McCann and Dr. Amy Engebretson who spent many hours
helping me with sample preparation. Dr. Ulczynski and Dr. Khathami are particularly
thanked for providing some of the samples used in this study.

My greatest appreciation goes out to my parents in Thailand. Their patience,
unconditional support, and love gave me strength to ﬁnish this work. A special thanks to
Sudawan for her love and patience over the last ten years. She was always there for me
and helped in more ways than she knows.

I thank the MSU Center for Fundamental Materials Research, the Department of
Electrical Engineering, the Physics and Astronomy Department, and The Graduate
School for support throughout this research. The research also was supported in part

through equipment received from NSF grant no. 9413727.

iv

Table of contents

List of tables

List of ﬁgures

1.

Introduction

1.1 Research motivation

 

1.2 Research objective

 

1.3 Dissertation organization

 

Background

2.1 Chapter overview

 

2.2 Schottky barrier diodes

 

2.3 Schottky barrier diodes current-voltage equation

 

2.4 Small signal response of Schottky barrier diodes

 

2.5 Large signal response of Schottky barrier diodes

 

2.6 Electrical properties of diamond

 

2.7 Diamond Schottky barrier diodes

 

2.8 Time varying signal response of diamond Schottky barrier diodes
Experimental Methods

3.1 Overview

 

3 .2 Substrate preparation for diamond growth

 

3.2.1 Nucleation by the diamond photo-resist

 

3.2.2 Nucleation by diamond powder abrasion seeding

 

viii

ix

11

17

25

29

33

37

44

44

44

45

46

3.3

3.4

3.5

3.6

3.7

3.8

3.9

Diamond growth

 

Diamond ﬁlm characterization with Raman Spectroscopy

 

Metalization

 

Probe station setup

 

DC characteristics measurement setup

 

Small signal response measurement setup

 

Large signal response measurement setup

 

DC characteristics of diamond Schottky barrier diode

4.1

4.2

4.3

4.4

4.5

4.6

4.7

Chapter overview

 

General characteristics

 

Temperature dependence of device parameters

 

Inﬂuence of deposition chemistry on diode characteristics

 

Effects of contact area and ﬁlm thickness on I-V characteristics

Variation with time and sample history

 

SPICE modeling and simulation for diode dc characteristics

Small signal response of diamond Schottky barrier diodes

5.1

5.2

5.3

5.4

Chapter overview

 

Experimental results and their basic interpretation

 

Small signal model ﬁtting results

 

Application implications of the small signal results

 

Large signal response of diamond Schottky barrier diodes

6.1

6.2

Chapter overview

 

Measurement circuit considerations

 

vi

48

52

54

56

57

58

63

66

66

67

76

81

92

97

103

108

108

109

116

136

137

137

I37

6.3 Effects of connecting cables and load resistance in the measurement

Circuit

 

6.4 Experimental results and SPICE model comparison

 

6.5 Sensitivity of SPICE model to changes in transit time parameter TT _
6.6 Area scaling effect on switching signal response of diamond

Schottky diode

 

6.7 Anticipated doping effects on the switching performance

 

7. Summary and future work

References

vii

142

146

153

156

165

172

175

List of tables

Table 2.1 Comparison of semiconductor properties for Si, GaAs, SiC, natural diamond

and polycrystalline diamond [2] [9] [22] [45] [46] 31

 

Table 3.1 Typical deposition parameters used in the diamond ﬁlm deposition

process 52

 

Table 4.1 Experimentally determined saturation current, 10, and ideality factor, n and

bulk resistance R3 of BC4 at different temperature. 77

 

Table 4.2 Deposition parameters and other properties of diamond Schottky barrier diodes
in set A. 82
Table 4.3 Deposition parameters and other properties of diamond Schottky barrier diodes

in set E. 82

 

Table 4.4 Deposition parameters and other properties of diamond Schottky barrier diodes
in set C. 83
Table 4.5 Deposition parameters and other properties of diamond Schottky barrier diodes

with different ﬁlm thickness. 95

 

Table 4.6 PSPICE diode model parameters for dc simulation 103

 

Table 5.1 The parameter values used in model ﬁtting of the diode SK7-B in
Figure 5.4. 120
Table 5.2 The parameter values used in model ﬁtting of the diode BC4 in

Figure 5.7. 130

 

Table 6.1 Additional SPICE diode model parameters for ac simulation 146

viii

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

Figure 2.8

Figure 2.9

List of ﬁgures

 

 

Schematic band diagram for metal to p-type semiconductor contact when
tbs > ¢m showing band bending in the semiconductor [22] [23] __ 7
Schematic band diagram for metal to n-type semiconductor contact when
(1)“, > dis showing band bending in the semiconductor [22] [23] + 9
CUrrent-voltage characteristics for an ideal Schottky barrier

diode [25] 10
Deviation from ideal diode characteristic straight line when series resistance
R3 is presented [29]. AV is the bulk voltage IRE. 13
Minority carrier injection results in bulk conductivity modulation __ 16

(a) Schottky barrier diode is modeled by a combination of Cj, Rj, CB and RB.
(b) The measurement circuit can then be represented by parallel or series

equivalent model 17

 

Variation of (I/Cj)2 with reverse bias VJ for Schottky barrier
diode [27] 19
Anticipated log-log plots of Cp versus frequency from Equation 2.12 under

forward and reverse bias 23

 

Anticipated log-log plots of Rp versus frequency from equation 2.12 under

forward and reverse bias 23

 

Figure 2.10 Anticipated log-log plots of Cs versus frequency from equation 2.13 under

forward and reverse bias 24

 

ix

Figure 2.11 Anticipated log-log plots of Rs versus frequency from equation 2.13 under

 

forward and reverse bias 24
Figure 2.12 Idealized Schottky barrier diode switching waveform [33] 26
Figure 2.13 Reverse-recovery waveform involving minority-carrier discharge _ 27

Figure 2.14 SPICE simulation results for the current through a diode excited by a
sinusoidal signal when minority carrier storage is not present [29] _ 28
Figure 2.15 SPICE simulation results for the current through a diode excited by a
sinusoidal signal when minority carrier storage in diode is signiﬁcant_28
Figure 2.16 Current-voltage characteristics of an Au/diamond Schottky diode—36
Figure 2.17 Glover’s Schottky barrier diode model is represented by combination of Cj,

Cf, Rf and RB 37

 

Figure 2.18 Model plot from Glover’s publication [19] 39

 

Figure 2.19 Frequency dependence of the capacitance of Au/CVD diamond contact for
different reverse biases giving an equivalent circuit as in the insert;

Gildenblat [18] 4O

 

Figure 2.20 Frequency dependence of the capacitance of Al/natural diamond contact for
different reverse biases giving an equivalent circuit as in the insert;

Venkatesan [17] 42

 

Figure 3.1 The simpliﬁed schematic diagram of the microwave plasma—assisted

chemical vapor deposition (MPACVD) 49

 

Figure 3.2 Raman spectrum of a polycrystalline diamond ﬁlm on Si substrate, BC4

observed by 532 nm Nd:YAG laser 53

 

Figure 3.3

Figure 3.5
Figure 3.6
Figure 3.7

Figure 3.8

Figure 3.9

Drawing show cross—section view of one example of a diamond Schottky

 

 

 

diode structure 54
A simpliﬁed circuit diagram of a SMU unit of I-[P414SB 57
Schematic diagram of dc measurement setup 58
Schematic diagram of the small signal measurement setup 60

A simpliﬁed circuit model of four-terminal pair conﬁguration

of HP4192A 61

 

A simpliﬁed circuit model of four-terminal pair conﬁguration of

HP4284A 62

 

Figure 3.10 Schematic diagram of large signal switching response measurement

Figure 4.1.

Figure 4.2.

Figure 4.3.

Figure 4.4.

Figure 4.5

setup 65

 

The I-V characteristic of the Ti/Au-diamond ﬁlm-Si-Al samples show ohmic

behavior. The above results are at room temperature 69

 

The I-V characteristics of Al-diamond ﬁlm— Si-Al samples show Schottky
barrier diode behavior. The above results are at room temperature _ 70

The I-V characteristics of samples with coplanar Ti/Au surface contacts show
ohmic behavior. Curve (a) corresponds to 1.5 mm between two contacts and

(b) 4.5 mm between the Ti/Au contacts 71

 

The Schottky barrier diode characteristics of a diode with coplanar surface
contacts. One contact is Al and the other is Ti/Au contact 72

Semi-log plot of forward I-V characteristic of sample BC4. The solid

xi

lines represent the least square ﬁt of the linear portion of log (I) versus the
applied voltage (VF). The value Io=1.82e-012 and n=2.43 result from the

curve ﬁt. 74

 

Figure 4.6 A plot of forward current versus bulk voltage of sample BC4. The solid line
represents the linear least square ﬁt at high bias portion of the bulk voltage
(VB). RB ml .13 M9 results from the inverse value of the slope. __ 75

Figure 4.7 Forward I-V characteristics of BC4 in the temperature range from 27 °C to

127 °C. 77

 

Figure 4.8 Richardson plot of BC4 over the temperature range of 27 to 127 °C _ 78
Figure 4.9 Plot of ln(RB) versus 1/T for sample BC4 over the temperature range of 27 °c

to 127 °C 80

 

Figure 4.10 The plot shows absolute value of current versus bias voltage on sample BC17
(l.5%—CH4), BC15 (1.5%-CH4), BC14 (1.5%-CH4), and BC13 (l.5%-CH4).
A signiﬁcant noise level showed under reverse bias is possibly due to

equipment limit of I-IP4145B. 85

 

Figure 4.11 Effect of CH4 concentration in grth process to the bulk resistivity of

diodes in sample set A. (see Table 4.2) 86

 

Figure 4.12 Effect of CH4 concentration in growth process to the bulk resistivity of

diodes in sample set B. (see Table 4.3) 87

 

Figure 4.13 SEM photos of diamond sample S83, S84, and S78. Courtesy of Ulzcynski

[76] 88

 

Figure 4.14 Effect of CH. concentration in growth process to the bulk resistivity of

 

diodes in sample set B. (see Table 4.4) 90

xii

Figure 4.15 SEM photos of diamond sample S89, S92, and S100. Courtesy of Ulzcynski

[76] 91

 

Figure 4.16I-V characteristics of sample SK7 with top surface contact area of 4.91x10’4
cm'z, 4.45x10'2 cm'z, 7.9lx10'2 cm'2 labeled on the plot as SK7-Y, SK7-C,

and SK7-D respectively. 93

 

Figure 4.17 The forward current at +10V forward bias (triangle marks) and reverse
leakage current at —10V reverse bias (circle marks) versus diamond ﬁlm
thickness. 96
Figure 4.18 Change of I-V characteristics in sample S100. The solid-curve shows
characteristics before and the dot-curve shows characteristic 5 minutes after
sample was exposed briefly to bright light. Here 10 and 11 remain the same
but RB decreases. 100
Figure 4.19 Change of I-V characteristics in sample BC4. The solid-curve shows
characteristics before and the dot-curve shows characteristic after 1 hour of
large signal test (see chapter 6). Here 10 and 11 remain constant but RB
increases. 10]
Figure 4.20 Change of I-V characteristics in BC7. The solid-curve shows characteristics
immediately after a small signal test. The dot-curve shows characteristic 2
hour thereafter. Here R3 is constant but 10 and 11 change. 102
Figure 4.21 An exaggerated display of regions in SPICE diode modeling 105
Figure 4.22 Comparison between the experimental I-V data (cross mark) and SPICE

simulation result (solid line) on BC4 106

xiii

Figure 4.23 Comparison between the experimental I-V data (cross mark) and SPICE

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 6.1

simulation result (solid line) on SK7-C 107

 

Plots of Cp, Rp, Cs, and Rs versus bias voltage at different frequencies of
diamond Schottky barrier diode BC4. Negative voltage values indicate
reverse biases. l 10

Plot of Cs and Cp in form of C'z-V of sample BC4. The C0 is the capacitance
value at zero bias at each test frequency. Negative voltage represents the

reverse bias value. 1 15

 

Experimental results of Cp, Rp, Cs and Rs measurement on sample

SK7-B l 17

 

Fitting between the Cp, Rp, Cs, and Rs experimental and the simple model
results. Solid lines represent model calculation at each bias. 121
Fitting between the Cp, Rp, Cs, and Rs experimental results of SK7-B and the

model which include the contact resistance effect. 125

 

Fitting between the Cp, Rp, Cs, and Rs experimental results of SK7-B and the

model which include Glover’s element Cf and Rf. 128

 

Fitting between the Cp, Rp, Cs, and Rs experimental results and the simple

circuit model of sample BC4. 131

 

Fitting between the Cp, Rp, Cs, and Rs experimental results of BC4 and the
model which include Glover’s element Cf and Rf. Here B = 2.7x10-7

F/(cm2.secm). 134

 

Measurement circuit for large switching signal response experiments _138

xiv

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

Figure 6.9

Responses of BC4 to a 20-Vpp lO-KHz sine wave with (a) no load resistance,
(b) 200 K!) load resistance, (c) 51 KO load resistance, (d) 10 K0 load

resistance, and (e) 2.01 K!) load resistance. 140

 

Coaxial cable circuit 142
Circuit interpretation of the two coaxial cables used in the large signal
response measurement. 144
Measurement and simulation circuit for diamond diode switching
experiments. 149
Switching responses of sample BC4 at (a) l KHz, (b) 4 KHz, (c) 10 KHz,
and (d) 20 KHz. Thick solid lines represent experimental results. Thin lines

with circle marks represent SPICE simulation results. 151

 

SPICE simulation results of sample BC4 at (a) 4 KHz and (b) 20 KHz. The
values of parameter TT are varied between 0 to 10'4 second while all other
parameters are kept constant as the following: IS = 1.8 pA, N = 2.40, RB =
1.2M (2, 1K =12 nA, ISR = 4.3 pA, NR = 3.06, VI = 0.8 V, CJO = 10.86 pF

and CB = 7.01 pF. 154

 

Switching signal responses of diode SK7-Y with contact area of 4.91x10'4

cm2 at (a) 4 KHz, (b) 10 KHz, and (c) 20 KHz. 157

 

Switching signal responses of diode SK7-C with contact area of 4.45x10'2

cm2 at (a) 4 KHz, (b) 10 KHz, and (c) 20 KHz. 158

 

Figure 6.10 Switching responses of sample SK7-C with contact area of 4.45x10'2 cm2 at

(a) 1 KHz, (b) 4 KHz, (c) 10 KHz, and (d) 20 KHz. Thick solid lines

XV

represent experimental results. Thin lines with circle marks represent SPICE

simulation results. 160

 

Figure 6.11 SPICE simulation results at 4 KHz based on the properties of diode SK7-C
when diode areas are (a) 4.45x10’4 cm2, and (b) 4.45x10'2 cmz. 162
Figure 6.12 SPICE simulation results at 10 KHz of diode SK7 with diode area of (a)

4.45x10‘4 cm2, and (b) 4.45x10'2 cmz. 163

 

Figure 6.13 A SPICE simulation result of diode SK7-C with a diode area of 4.45x10‘2
cmz. The input signal for the simulation is a lO-Vpp 20-KHz sinusoidal
waveform. The 1-MQ /14-pF oscilloscope is in parallel with 10 K0 load

resistance. 166

 

Figure 6.14 SPICE simulation results of two hypothetical diodes based on properties of
SK7-C but with the difference in (a) CB = 1/ 100 of that of SK7-C, and (b)
RB = 1/ 100 of that of SK7-C .The input signal for the simulation is a lO-Vpp

20-KHz sine wave. The load resistance RL is 10 KO. 168

 

Figure 6.15 SPICE simulation results of (a) SK7-C, and (b) a hypothetical doped diode
with RB = 1/ 100 of that of SK7-C.The input signal for the simulation is a 10-
Vpp ZOO-KHz sine wave. The load resistance RL is 50 Q. 169

Figure 6.16 SPICE simulation results of (a) SK7-C, and (b) a hypothetical doped diode

with RB = 1/ 100 of that of SK7-C.The input signal for the simulation is a 10-

Vpp SOD-KHz sine wave. The load resistance RL is 50 Q. 170

xvi

CHAPTER 1

Introduction

1.1 Research motivation

The utilization of semiconducting diamond for high performance electronic
devices has been of interest to researchers for many years. For example, the electronic
properties of diamond have been investigated since the 1930's and attempts to fabricate
diamond semiconductor devices started in the 1950’s [1]. Some of the initial interest in
semiconducting diamond was mainly for high temperature and corrosion resistant
semiconductor application, based on diamond’s high energy gap and chemical stability.
However, as the material parameters became better known, it became evident that
diamond possesses a combination of material properties that, in many respects, make it
ideal for various electronic applications. To date diamond has been proposed for use as
power and microwave devices (bipolar and ﬁeld-effect [2] [3] transistors), therrnistors
[4], switching devices, display array (ﬁeld-emission diodes [5]) and various types of
detectors (radiation [6], X-ray [7], and ultraviolet photo-detectors [8]).

The early attempts to utilize diamond were delayed by technological problems
related to crystal growth, purity and doping, and also to the development of suitable

ohmic and rectifying contacts [9]. Moreover, the high cost of even small diamond

samples has been an inhibiting factor in diamond device progress. Lately, a less
expensive, low-pressure diamond synthesis technique, which uses chemical vapor
deposition (CVD), has been developed. The economical deposition of diamond over
relatively large substrates (210 cm in diameter) is now possible. The resulting CVD
diamond is polycrystalline, unless the underlying substrate is single crystal diamond.
Although the properties of CVD diamond n'val those of natural diamond [10] [11], device
physics of CVD diamond is still primitive compared to Si and GaAs.

Most, if not all, devices rely on rectifying contacts or rectifying junctions for their
operation. Because of fabrication simplicity, diamond Schottky barrier diodes have been
studied by many researchers. However, most previous reports are based on dc
characteristics and have investigated the current transport mechanism through the
metal/diamond contact by means of thermionic emission theory [12][l3][14][15][16]
while ac properties of metal/diamond contact have received much less attention.

There are several questions regarding frequency dependent electrical properties of
the diamond Schottky diode which need to be answered if diamond-based technology is
to be developed to the point where high performance devices can be realized. For
example, it is not currently clear whether the observed frequency dependencies of
diamond Schottky diodes are primary due to barrier dynamic or bulk resistivity effects.
Identiﬁcation of the appropriate equivalent circuit to represent the electrical properties of

diamond Schottky diodes is also another question to be resolved.

1.2 Research objective

The main objective of this study is to add to the current understanding of the
frequency-related performance under both large signal switching and small signal
responses of diamond Schottky barrier diodes. To the investigator's knowledge,
information on the experimental switching large-signal responses of diamond Schottky
barriers were not been previously published prior to the investigator's paper at the
Diamond 1997 Conference, 3-8 August 1997, Edinburgh, Scotland.

The small signal responses of diamond Schottky barrier diodes have been
previously studied [15][17][18][19], however, these studies only emphasized the
capacitance versus reverse bias voltage characteristics. As a result, the more general issue
of complex admittance versus frequency still remains to be studied. There are currently
two interpretations on capacitance-voltage-frequency relation on diamond Schottky
barrier diode. One includes the effect of deep state traps in diamond [15] [18] [19] [20],
the other explains the relation only by the combination of junction, bulk, and contact
properties of the diode without a trap role in diamond [17] [21]. This research explores
further the possibility of both interpretations by investigating the entire small signal

admittance, not only the capacitance, at both reverse and forward bias.

1.3 Dissertation organization

This dissertation is divided into seven chapters. After an introduction in this
current ﬁrst chapter, the dissertation is organized and covered in the following order.

Chapter 2 provides background and previous studies of electrical characteristics
of Schottky barrier diode, particularly in diamond. Also included is the review of
electrical models of diamond Schottky diode proposed by other researchers.

Chapter 3 described the sample preparation process, the experiment setup and
equipment used in this research.

Chapter 4 presents the experimental results and discussion on dc characteristics of
diamond Schottky barrier diodes. The dc model simulations are created based on the
experimental data.

Chapter 5 presents the results of the small signal responses of the diamond
Schottky diodes. The results are compared with three types of circuit simulations; basic
model, basic model with contact resistance effects, and model which include trap state
effects.

Chapter 6 presents the results of the large switching signal responses of the
diamond Schottky diodes. The model simulations are generated to match the
experimental results. Methods for possible improvement in diode speed are also
discussed.

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

discussion of the open research issues and suggestions for future work.

CHAPTER 2

Background

2.1 Chapter overview

This chapter reviews the background necessary for discussing the electrical
characteristics and responses of diamond Schottky barrier diodes under dc and time
varying signals. It begins with a discussion of Schottky barrier diodes in general followed
by a description of the basic equations used to describe the dc voltage-current
characteristic of the diode. Next, the response of a general Schottky diode to ac signals is
considered. Models, equations and possible expectations are given for small and large
signal excitation. The electrical properties of diamond as a semiconductor are then brieﬂy
discussed. Finally, the focus falls on diamond Schottky barrier diodes in particular, in

terms of both do and ac responses reported by others.

2.2 Schottky barrier diodes

Metal contacts to semiconductor can be ohmic, rectifying or in between. When a
metal is placed in contact with a semiconductor, charge transfer occurs until the Fermi
levels align at equilibrium. This process alters the potential level in both materials. In a

metal the Fermi level is essentially at the highest occupied state in the conduction band.

Actually the Fermi level corresponds to 50% occupancy probability for a given state,
however the Fermi-Dirac distribution falls off rapidly above the Fermi energy. An energy
required to remove an electron at Fermi level of the metal to the vacuum level is deﬁned
as the metal’s work function rbm. Also, the work function for the semiconductor (I)S is
deﬁned as the distance from the semiconductor Fermi level to the vacuum level [22].

Let us ﬁrst consider a metal contact with p-type semiconductor. For a p-type
material, the Fermi level lies closer to the valence band than to the conduction band at
equilibrium. In the case (1), > d)", as in Figure 2.1(a), the metal’ 8 Fermi level is initially
higher than that of semiconductor. When a metal is placed in contact with such a p-type
semiconductor under zero applied voltage, holes; majority carriers vacate from the
semiconductor to the metal and create a negative charge region of width W in the
semiconductor near the junction interface. This interface region which is vacated by holes
is called a “depletion region” or “space charge region”. The change in potential caused
by uncompensated ionized acceptors bend the bands in semiconductor as shown in Figure
2.1(b), creating a contact or built-in potential Vbi, which prevents ﬁrrther net hole
diffusion from the semiconductor into the metal. This contact potential V1,, retarding hole
diffusion at equilibrium is given by (11S — chm. The potential barrier height (113,, for hole
injection from metal into the semiconductor valence band is Eg — (rt)s — x), where x
(called electron affinity) is measured from the vacuum level to the semiconductor
conduction band edge, and Eg is the band gap energy of the semiconductor [23] [24]. The.
equilibrium potential difference Vbi can be decreased or increased by the application of
either forward or reverse bias voltage. Note that band bending in metal is negligible

because of its much higher carrier density.

 

 

 

 

 

1i—_ —_lﬁ1'

1 C"

(a) metal / p-type q m 11 Ec
semiconductor
__y (11’s

I777]; _l_________r-:,..
Ev

metal p-type

 

 

 

(b) zero bias

 

 

 

 

(0) forward bias

 

 

 

 

(d) reverse bias

 

 

 

Figure 2.1. Schematic band diagram for metal to p-type semiconductor

contact when d), > (1)", showing band bending in the semiconductor [22] [23]

A similar description can be given for a metal and n-type semiconductor contact.
However, in n-type material, the Fermi level is lying closer to the conduction band at
equilibrium. Figure 2.2(a) illustrates a metal contact on a n-type semiconductor, with
¢m > (1),. In this case aligning the Fermi levels at equilibrium requires a negative charge on
the metal side and a positive charge on the semiconductor side of the junction. The
positive charge is accommodated by a depletion region W in which ionized donors are
left uncompensated by electrons. The potential barrier V1,] retarding electron diffusion
from the semiconductor to the metal is (hm - (1),, and as before this barrier can be raised or
lowered by the application of voltage across the junction. The limiting value of the
barrier height (ban, is given by (bm — x.

At zero applied voltage, the system is at equilibrium. The negative charges (p-
type) or positive charges (n-type) due to uncompensated carriers within W match the
opposite charges on the metal and the net current will be zero across the junction. If a
forward (VF) or reverse (VR) bias is applied across the junction, the semiconductor bands
will shift down or up in energy relative to the metal as shown in Figure 2.1(c) and Figure
2.1(d) in p-type and Figure 22(0) and Figure 2.2(d) in n-type semiconductor,
respectively.

In equilibrium the net current flow across the Schottky junction is zero since the
carrier ﬂow from metal to semiconductor and from semiconductor to metal are equal, but
in opposite directions, hence they cancel. A metal-to-p-type junction is forward biased
when the semiconductor is positively biased relative to the metal. When forward biased
as in Figure 2.1(c), the barrier for p-region holes is decreased by the value of bias

voltage, and the semiconductor to metal current flow across the junction increase sharply.

(a) metal / n-type q¢m

semiconductor

 

 

 

 

 

metal

(b) zero bias

(0) forward bias

(d) reverse bias

 

qX
Ec
l- -....__. _. - EF
E3v
n-type

 

 

 

 

 

 

 

 

 

Figure 2.2 Schematic band diagram for metal to n-type semiconductor

contact when (bm > (1), showing band bending in the semiconductor [22] [23]

Hence the net current in the diode increases. When reverse biased as in Figure 2.1(d), the
barrier for semiconductor holes is increased, reducing the semiconductor to metal current
ﬂow to essentially zero. However, the metal to semiconductor carrier ﬂow remains the
same since the metal to semiconductor barrier height is unchanged by bias. Under this
condition, a small reverse current ﬂows.

Contacts that behave as described above are called Schottky barrier diodes and
exhibit non-linear I-V characteristics as shown in Figure 2.3 for an ideal diode, where

positive voltage represents forward bias.

Forward
direction

 

Current

Contact voltage

 

 

Reverse direction

Figure 2.3 Current-voltage characteristics for an ideal Schottky

barrier diode [25]

10

2.3 Schottky barrier diodes current-voltage equation

One difference between Schottky barrier diodes and p-n junction diodes is that
Schottky barrier diodes operate as a majority-carrier device under low-level injection
conditions [26]. As a consequence, storage delay time (due to storage of minority
carriers) on switching from forward to reverse bias is eliminated and fast response is
obtained.

The forward current-voltage (l-V) characteristics of a Schottky barrier diode
obeying the thermionic emission theory is given by the following Shockley equation [22]

[23] [27] [28]

I=Io[exp(qu/kT)—l] (2.1)

where q is the electronic charge, V; the voltage applied across the diode, k is the
Boltzmann constant, and T is the absolute temperature. The value 10 can be determined

from the equation

1., = AeA **. T2 exp(—q¢,, NJ) (2.2)

where AC is the effective area of the diode, A** is the effective Richardson’s constant and
rim is the Schottky barrier height of the diode.
A complication of the current-voltage relationship in practical diodes is that, for

large forward currents, the voltage drop across the diode series resistance RB associated

11

with the neutral region of the semiconductor (between the depletion region and the ohmic
contact) causes the actual voltage developed across the barrier region (V1) to be less than
the voltage applied to the terminals of the diode (V). The voltage V; across the diode can
then be expressed in terms of the total voltage drop V across the series combination of the

diode and the resistor. Thus, V; = V — R3, and for V] 2 3kT/q, 1 becomes

1 E I,,[exp(q(V—IRB)/k7)]

where I is the current through the diode. Figure 2.4 shows the diversion from the straight
line of I-V plot of a diode, which indicates the effect of series resistance at high forward
voltages.

Furthermore, most Schottky diodes show deviations from ideal behavior. It is a
common practice to approximately account for many of the effects by which the diode
characteristics deviate from the above equation (i.e. non-ideal effects) by a empirically

determined dimensionless parameter called the ideality factor n such that.

I Elo[exp(q(V—IRB)/17kT)] (2'3)

Low forward bias non-ideal effects include barrier height lowering, quantum
mechanical tunneling of carriers through the junction, and recombination of the carriers
in the depletion region. On the other hand, the effects of drift and diffusion of carriers in
the space charge layer and minority carrier injection are signiﬁcant at very high bias

corresponding to high ﬁeld and large current density [27]

12

In!

 

 

 

Figure 2.4 Deviation from ideal diode characteristic straight line when series

resistance RB is presented [29]. AV is the bulk voltage IRB.

With the proper choice of 10, n, and RB, Equation 2.3 can be generally used to
approximately describe the behavior of a given diode. However, when using current-
voltage data to provide diagnostic information about the barrier, it is necessary to treat
this equation with caution because different barrier structures can result in the same value
of 11 over a given range of current [30].

A method to extract the series resistance R3 of ideal Schottky diodes (i.e., n = 1)
was proposed by Norde [31]. For the n > 1 cases, Sato and Yasumura [32] modiﬁed
Norde' s approach to extract the values of n, rim, and RB from the forward I-V data of a

Schottky diode. For a given Schottky diode, their approach requires two or more
experimental I-V measurements conducted at different temperatures and the

determination of the corresponding minima of the modiﬁed Norde’s function. This

13

research, however, did not use their method since most I—V measurements were
conducted at room temperature.

The barrier height of a Schottky diode is also an important parameter in the
simulation of the device. From Equation 2.2, if the value of the effective Richardson’s
constant A** is known then the barrier height (113 can be obtained from

«5 =—1n(A—A——**T2> (2.4)
10
Generally, A** is not known. However, the value of (193 is not very sensitive to the choice
of A**, since at room temperature, a 100% rise in A** will only cause the increase of
0.018 Volt in (is.
Another traditional method for evaluating the barrier height from the I-V data is

the activation energy method. Equation 2.2 may be rewritten as

1, _ *4 “w. 1
ln(—7—Q—)—ln(AeA ) k (T) (2.5)

One can experimentally obtain the saturation current 10 at several temperatures,
consequently, the slope of a semi-log plot of (Io/T2) versus (1/T ) yields the value of
effective barrier height and the intercept on the axis gives the logarithm value of effective
Richardson’s constant. The advantage offered by this method is that prior knowledge of
either the Richardson’s constant A** or the diode’s effective area Ac is not necessary.
Analysis of the I-V characteristic at different temperatures could also yield the

value of another parameter, the activation energy EA. The temperature dependence of the

14

bulk resistance R3 of the semiconductor is inversely related to bulk conductivity 0, which
can often be described by the equation [15][18][23]

—1— 0C 0' = const - exp(——E") (2.6)

R3 kT

Thus, a semi-log plot of RB versus (l/T) should be linear and the slope would correspond
to the activation energy of the semiconductor.

As mentioned above, Schottky barrier diodes operate with majority carriers,
however at sufﬁciently high current densities, minority-carrier effects can become
signiﬁcant. Injection of minority carriers leads to excess carrier storage in the bulk of the
devices. The stored excess carriers, in turn, change Schottky barrier diodes I-V
characteristics as shown in Figure 2.5. Under forward bias, minority carriers are injected
into the bulk of the semiconductor and travel for an average distance of the diffusion
length before they recombine with majority carriers. For semiconductors with large
diffusion lengths compared to the semiconductor thickness, such as Si [33], most of the
minority carriers reach the contact before being recombined. Hence, minority carrier
injection leads to the presence of excess minority carriers throughout the bulk part of the
devices. The excess minority carrier concentration can be considerably higher than the
material’s equilibrium concentration. These excess minority carriers, in addition to the
excess majority carriers stored in the bulk to maintain quasi charge neutrality, give rise to

an increase in the bulk conductivity, 0. The increase in conductivity, or conductivity

modulation, A0, is given by [29]

15

A0 = q(#,,An+#,,Ap)

Where An and Ap are excess electron and hole concentration and 11., and up are electron
and hole mobilities. Conductivity modulation results in a decrease of the resistance of the

epitaxial layer, consequently, the diode conducts a larger value of current for a given

voltage compared to without modulation.

ln(l)

 

 

 

Figure 2.5 Minority carrier injection results in bulk conductivity modulation

l6

2.4 Small signal response of Schottky barrier diodes

In the last section, the response of Schottky barriers to a dc voltage has been
described. However, most of the important applications of the Schottky barrier diode
involve time varying signals, either small signal or large signal. The responses of the
diode to a small signal (sine wave) voltage superimposed upon the dc voltage is therefore
one issue we wish to study. The term “small signal” implies that the peak value of the ac
signal current and voltage are much smaller than the dc values.

Usually the signal responses are studied in term of small signal admittance (Y), of
which the real part is related to resistance and the imaginary part is primarily related to
capacitance in the equivalent circuit models. A simple approach to model the Schottky
barrier diode for small signal purposes is by parameters Rj, Cj, RB, and CB as illustrated in
Figure 2.6(a) [34][35][36][37]. The device admittance can be represented either by a

parallel or series equivalent circuit as shown in Figure 2.6(b).

RP

RI RB '—
m <§ CP
|
C1 C8
_MA—l1—
F"s Cs

 

(a) (b)

Figure 2.6 (a) Schottky barrier diode is modeled by a combination of C], Rj, CB and RB. (b)

The measurement circuit can then be represented by parallel or series equivalent models.

17

As in the last section, the bulk resistance of the diode is labeled as RB. However,
under time varying signals, we also need to consider the capacitive effect from the
geometry of the bulk part. R3 is then modeled in parallel with capacitance CB. This
combination is in series with the depletion region, which modeled by the parallel
combination of a small-signal resistance Rj, and capacitance C].

The capacitance Cj of a Schottky barrier is associated with its depletion region,
which in some respects resembles a parallel-plate capacitor with a separation between the
plates that increases when reverse bias is applied and decreases with forward bias [27].
Such phenomenon is caused by a change in the depletion layer width. Consider the
depletion region at some ﬁxed value of reverse bias voltage V]. For a Schottky barrier

diode, the depletion width is given by [32]

1:2
W : [EEG/b, —V, 15)] (2.7)
(W q

Where Vb, is the difference between the work ﬁinction of metal and semiconductor and N
is the semiconductor dopant concentration, assumed to be uniform. With a small signal
superimposed, VJ is replaced by (V j+Vj) and W changes by an increment AW. The

depletion-region capacitance Cj is obtained from the parallel plate capacitance formula as

64.
C}. = W (2.8)

 

where 8 is the dielectric constant of material and AC is area of the diode. The above
equation, however, is valid provided W is essentially ﬁxed; that is, AW must be small

compared to W [83]. For a small signal le| << IVJ', then AW << W gives

18

 

, quN I":
C , :

The above equation is often generalized and written in term of the zero-biased junction

capacitance Cjo. At V] = 0; then the deﬁnition of Cjo is as follows

This gives

Figure 2.7

 

1.42
(r = C1,. 0: We” (29)
J” j ’" 2(Vm — kT/q)

C. =___L_ (2.10)

 

.' v
f ' >
'(Vbi ' kT/Q) reverse bias

 

Variation of (I/Cj)2 with reverse bias V] for Schottky barrier diode [27]

19

If N is constant throughout the depletion region, a plot of (I/Cj)2 versus VJ should give a
straight line with an intercept of — (Vbi—kT/q) on the voltage axis as shown in Figure 2.7.
The depletion region resistance R,- of Schottky barrier diode is derived under the
assumption that the carriers are able to response to the signal quasi-statically; that is the
carriers return to near steady state in much less time than the period of the signal. Thus,
the diode reacts instantaneously to a small signal (Vj) superimposed on the dc value (VJ)
and the time-dependent response can be treated as a series of dc solutions at incremental

step [24][3 8]. The diode Equation 2.1 with the perturbed small signal is then becomes
1(V1 + Vj) = Io[exp(q (V; + Vj) / kT) — 1]

And the small signal current i is deﬁned as i = I(VJ+Vj) — 1(VJ). By Taylor series

expansion, keeping only ﬁrst two terms, i can be written as

U d1
12v.
J[dVJ]

The small signal conductance of the junction is deﬁned from above equation as

 

 

By differentiating the ideal diode equation, 1(Vj) = Io[exp(q V] lkT) — 1], we obtain the

small signal conductance as

20

 

d1 q W <1
G: =I —-ex —’ =—1+I
dv, OkT p(kT) kT( 0)

Then the junction or “dynamic resistance” Rj can be obtained from the reciprocal of G

 

= ~—-— (2.11)

As can be derived, according to circuit in Figure 2.6, the Schottky barrier diode can be

represented in either parallel or series equivalent circuit model with the following

 

 

 

parameters
. : (7'in + C811; + w’RngCjCB (C1. + C8)
P (R.].+RB)2+w2RfR§(Cj+CB)2
(2.12)
_ (Rj+RB)2+a)2RfR§(Cj+CB)3
P '" (R, + RB) +w2RjRB (C312,. +C§R,)
and
ZRZC 2 2 —1
C=[ a) 1'7 + wRBCB]
’5 2 2 42 2 2
1+0) RjC.J. 1+a) R§CB
(2.13)

 

R
Rs: ale "1+ I382 a
‘ 1+w‘RJTC} 1+0) REC;

Here to is the frequency of the small signal, Cj and Rj are the depletion region capacitance

and dynamic resistance respectively, R3 is the bulk series resistance associated with the

21

neutral region of the semiconductor as described in section 2.3, and CB represents the
capacitance of this bulk part of the diode (between the depletion region and the ohmic

contact). IfL is the total length of the diode, C B can be calculated from

 

CE = (2.14)

Let us examine the two limiting cases.

(I) At low frequency ((11 —> O), Cp in Equation 2.12 beComes

Cij.z + GER;
(Rj + RB)2

 

CP (0) =

The value of Cp(0) depends whether the diode is under forward or reverse bias. Under
reverse bias, Rj is very large due to small reverse bias current; Rj >> RB. As a result,
Cp(0) —> Cj. However, if the diode is under forward bias, Rj is small (Rj << RB). Then
Cp(0) ——> C3.

(H) At high frequency ((1) —> oo), Cp in Equation 2.12 instead becomes

 

 

cc Willie): .4

CLUE) : 4"]. "3‘ Z _
(.1. + C, B “[1 + 1 L
W L — W
This means Cp(00) approaches the geometrical capacity of the whole diode regardless of

the bias condition. Figure 2.8 shows the typical Cp responses one would expect from the

model of Figure 2.6(a) and the above limiting cases [3 9].

22

 

  
    

forward bias

eA/L ‘

 

C C.
EA——~,L
t reverse bias

 

 

1 LLlllll 1 1 111111 1 1111111 1 1 144111

 

Freq (to)

Figure 2.8 Anticipated log—log plots of Cp versus frequency from

Equation 2.12 under forward and reverse bias

 

 

 

 

 

 

. R.
1. __|____ .1
f \
i: \ .
E \ reverse bias
: \ :
.. \‘ 2 4
t \ R (C.+C ) ,
E \ —l——8 2 B s
D. ..
m : _____ ‘31-“;
E E
1- RB 2
. R. C.+C
forward bias ( B) ,
c2 i
13
Freq (m)

Figure 2.9 Anticipated log-log plots of Rp versus frequency from

equation 2.12 under forward and reverse bias

23

 

 

\ , -
reverse bias 8 AIL :

g

-_—_—-———_

 

 

11414111 L 1_1_11lll l 1 111111 1 1 11111] 1 1 111111

 

Freq (m)

Figure 2.10 Anticipated log-log plots of Cs versus frequency from

equation 2.13 under forward and reverse bias

 

 

    

forward bias

 

 

 

Freq (m)
Figure 2.11 Anticipated log-log plots of Rs versus frequency from

equation 2.13 under forward and reverse bias

24

We can also explore the two limiting cases of Rp.

(I) At low frequency (w —> O), Rp in Equation 2.12 becomes just (R,-+RB). The value of
Rp(0) again depends on the bias condition of diode. Under reverse bias, Rj >> RB. Thus,
Rp(0) —-> Rj. Under forward bias, Rj- << RB then Rp(0) —> RB.

(11) At high frequency ((1) —> oo), Rp in Equation 2.12 now becomes

_ RjRB(Cj + C3)2

 

 

 

Rp(w) — CZR '2
( .J. J. +QBRB)
R C. +C 2
—-) B( 2 B) ; reverse bias R}. >> R8
-1.
RJ.(C,. + C8)2 ,
—> ' , ; forward b1as R. << RB
Q; 1

Typical Rp responses one would expect from the model of Figure 2.6(a) and above
limiting cases are illustrated in Figure 2.9. By same consideration, we can reach the

limiting cases result for Cs and Rs shown in Figure 2.10 and 2.11 respectively.

2.5 Large signal response of Schottky barrier diodes

In circuit applications, Schottky barrier diodes are also often used as a switch
which is “ON” when the diode is conducting in forward direction and “OFF” or non-
conducting when a reverse potential is applied to the devices. Consider a forward bias
voltage Vf applied to the circuit so that the Schottky barrier diode is the ON state carrying
a current If z Vp’RL, where the current is limited by a circuit load resistance RL much

greater than the diode junction and series resistance. Now consider that the potential is

25

suddenly reversed in an attempt to place the diode into the non-conducting OFF state. At
low forward bias, the minority carrier injection level in a Schottky barrier diode is
negligible [33] and the entire switching current is due to discharge of the junction and
parasitic capacitance. Figure 2.12 gives an idealized plot of the reverse-recovery current

through the load resistor R1, as a function of time [24].

Current

 

Time

 

 

Figure 2.12 Idealized Schottky barrier diode switching waveform [33]

Again at high forward bias voltage, minority-carrier effects have been reported to
become signiﬁcant in Si Schottky diodes. Injection of minority carriers leads to excess
carrier storage in the bulk of the diodes. Consequently, upon rapid switching from
forward to reverse bias, a reverse current flows while the excess carriers stored in the
quasi-neutral regions are being swept out [38]. This removal process of the excess
minority carriers induces a switching delay time. Integration of the reverse-recovery

current yields the total charge associated with excess minority carriers stored in the diode

26

prior to switching. Figure 2.13 shows the switching current of a high-injection recovery

involving minority carrier discharge.

Current

 

'1?

Time

 

 

Figure 2.13 Reverse-recovery waveform involving minority-carrier discharge [33]

Krakauer [65] developed a measurement method to observe the response of the
diode to large-signal sinusoidal inputs. Figures 2.14 and 2.15 show SPICE [26]
simulation results of the response of a diode to sinusoidal excitation. Figure 2.14 shows
the response of a device with purely capacitive charge storage corresponding to a linear
reverse-recovery current. Figure 2.15 shows the response of a device in which some
minority carrier storage is present. As shown in this ﬁgure, the reverse-recovery current
due to excess minority carriers can easily be distinguished from the linear capacitive
current. Krakauer developed an expression for a ﬁgure of merit concerning the excess
minority carrier storage in the device, which is related to the exciting frequency, the
source voltage, the impedance involved in the test circuit and the ratio of If to Ir as shown

in Figure 2.15.

27

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l-
20'
E
ml- / \ /
.5 - / .
:5 r
P
E E \\"'Fare1y Capacitive
'5 - Discharge
Q 1.
-10
-20'
,
lLll 1L11111111|11111 LJIL
O 5 10 15
Time (ns)

Figure 2.14 SPICE simulation results for the current through a diode excited by a

sinusoidal signal when minority carrier storage is not present [29].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10 \\ 7
E; :, /// If ~;'—iﬂ//4 ‘\\\
: 0b 11 \
E - - Capacitive
I)
E I Ir Discharge
“’ -10 _ Minorit,
. Carrier
; Removal
-20 _
114111111111111J 11111111
0 5 10 15
Time (ns)

Figure 2.15 SPICE simulation results for the current through a diode excited by a

sinusoidal signal when minority carrier storage in diode is signiﬁcant [29].

28

2.6 Electrical properties of diamond

For years diamond has been known as a promising material for several types of
semiconductor devices. In the past decade, a renewed interest in electronic applications of
semiconducting diamond has stemmed from the development of the chemical vapor
deposition (CVD) processes for the growth of thin diamond ﬁlm.

Diamond, when considered as a semiconductor material, possesses a unique
combination of desirable electrical and physical properties (see Table 2.1). Two distinct
advantages of diamond over other semiconductors are its high thermal conductivity and
high electric ﬁeld breakdown. The higher the thermal conductivity, the more power a
device can dissipate for the same temperature rise. The wide energy gap of diamond (Eg =
5.45eV at 300K) is responsible for the high breakdown ﬁeld [20]. This combined with the
surface stability of diamond at high temperatures (500-600 °C in air) [40] makes it an
ideal candidate for high temperature device applications. In this respect, it is notable that
diamond also has higher carrier mobilities than other wide band gap semiconductors (i.e.
SiC, GaP, AlAs) at both room and higher temperature [20]. Other advantages of diamond
include a high saturation velocity, i.e. the velocity at which electrons move in a high
electric ﬁeld, which is nearly 3 times of Si and GaAs,

The intrinsic material limits to electronic performance are usually compared in
term of ﬁgures of merit. Two commonly used ﬁgures of merit are Johnson’s ﬁgure of

merit and Keyes’s ﬁgure of merit. Johnson’s ﬁgure of merit (IF M) is deﬁned as [40]

JFM = E—V— (2.15)

29

where Ec is the breakdown ﬁeld and vS is the charge carriers saturation velocity. The
JFM for diamond is roughly about 90 times higher than the corresponding value for Si.
Note that in some publications IF M is deﬁned as (Ech/Zit)2 so that a ratio of (JFM)diamond
to (IFM)S; of 8206 is often quoted. The JFM is useful for predicting the suitability of a
semiconductor for operating with large internal electric ﬁelds, such as in power devices
[41]. JFM comparisons for other semiconductors are listed in Table 2.1.

Keyes’s ﬁgure of merit 0(FM) is used to estimate a material's potential for digital
or high-speed circuits. As deﬁned by Keyes,

l/
M)

KFM = 43—) b (2.16)
47mr
Where )1. is the thermal conductivity, c is the velocity of light in vacuum, and e, is the
dielectric constant of the material. The ratio of (KFM)dgam.md to (KFM)Si comes out to be
32.2 [40]. Compared to other materials, as shown in Table 2.1, the KFM indicates that
diamond has the potential of being one of the best materials for digital or high-speed
devices.

Intrinsic diamond, that is, diamond in its pure form with no impurities, is
electrically insulating at room temperature. This is because the energy gap is sufﬁciently
large that hole and electron concentrations are negligible. Resistivities of highly pure
diamond have been measured in the 10l2 Q-cm range and above. However, band
conduction can occur if impurities or defects act in such a way so as to introduce either

holes in the valence band or electrons in the conduction band.

30

 

Natural

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Properties Si GaAs SiC diamon Polycrystallr
d ne diamond
Band gap, Eg (eV) 1.11 1.43 2.3 5.45
Intnnsrc resrstrvrty, 2. 5x105 4x108 1 0'“ 1 016
p (Qcm)
Dielectric constant, a, 1 1.8 13.2 10.2 5.5 6.7 [42]
Electron mobility u"
’ 5 850 0
(cm2/V.s) 13 0 0 100 2200
Hole mobility up
’ 480 400 50 1600 .8- 0
(cm2/V.s) 2 1 [21]
Break down ﬁeld, E3
(105 V/cm) 3 60 40 100 1 - 10 [43]
Saturated electron
velocity 1.0 2.0 (peak) 2.5 2.7
(107 cm/s)
Thermal conductivity, )1.
(w/cm.K) 1.45 0.5 5 20 4 21.8 [44]
Thermal expansion
coefﬁcient, 2.6 5.9 4.7 1. 1
1c (106/°c)
Lattice constant, a (A) 5.43 5.65 4.36 3.57
Density (g/cm") 2.33 5.31 3.21 3.52
Subl lmes Eight];
' ' ° 14 0 1238 “hm a ove
Melting pomt ( c) 2 1800 1b20()
JOhi‘SO" .S.ﬁg“’e Ofmem 1.0 6.9 1137.8 8206.0
(ratlo to Silicon)
Keyes s ﬁgure ofmerrt 1.0 0.5 5.8 32.2

(ratio to silicon)

 

 

 

 

 

 

Table 2.]

diamond and polycrystalline diamond [2][9][22][45][46]

31

Comparison of semiconductor properties for Si, GaAs, SiC, natural

 

For example p-type diamond results if boron, from column-III of the periodic
table, is introduced as an impurity which substrates for carbon atoms in the diamond
lattice. Boron doped diamond is found in nature (although rarely). Boron can also be
introduced into natural or synthetic diamond by ion implantation [3] [17] [21] or can be
incorporated into diamond ﬁlms by adding boron during the CVD process. The resistivity
of boron doped diamond can be on the order of l Q—cm or less.

Interestingly, many CVD diamond ﬁlms are found to be p-type even without the
introduction of column-HI impurities such as boron. The resistivity of such ﬁlms is
substantially lower than insulating diamond, but not as low as diamond which has been
heavily doped with boron. The origin of this p-type behavior has been the subject of
speculation. One view is that it is associated with the role of hydrogen in the ﬁlms. The
effects of atomic hydrogen in passivating inter-band states in various semiconductors,
such as amorphous silicon and polycrystalline silicon, have been well established. In case
of natural diamond crystals and CVD diamond ﬁlms, Landstrass and Ravi [47] postulate
that the resistivity of hydrogenated diamond is governed by shallow acceptor levels,
whereas removal of the hydrogen activates deep donors, pinning the Fermi level and
giving rise to high resistivity.

In contrast to the situation for p-type diamond, creation of n-type diamond has
been extremely difﬁcult. Column-V dopants are generally not effective as n-type dopants
in diamond because the donor levels that they introduce are far removed from the
conduction band edge. Although some researchers have reported the achievement of n-

type diamond, the quality of the doping is at best much less than for p-type diamond.

32

Therefore, bipolar devices that require both n and p-type doping would be
difﬁcult to achieve at this time entirely in diamond. Most device work has focused on
uni-polar or majority carrier devices including Schottky diodes or Field Effect Transistors
(FET's). This dissertation focuses on the former. A brief review of previous works on

diamond Schottky barrier diodes follows.

2.7 Diamond Schottky barrier diodes

Both ohmic and rectifying contacts are required in Schottky barrier diode
fabrication. The electrical properties of metal-to-diamond ﬁlm contacts depend strongly
on the properties of the diamond ﬁlm and surface treatment (such as heat treatment, and
chemical cleaning). For example, Grot et a1. [48] have shown that surface preparation
plays an important role in determining the characteristics of metal contacts on diamond
surface. They reported that exposure of boron-doped diamond CVD ﬁlm surface to a
hydrogen plasma resulted in ohmic I-V characteristics of the Au/diamond contacts
regardless of the doping level.

In many reports, silver paint or a damaged surface have been used for establishing
ohmic contacts on semiconducting diamond. In some cases, the contacts were annealed to
reduce contact resistance. Moazed et al.[45] [49] studied the formation of Ti, Ta, Mo,
and Mo/Ni contact on natural boron-doped diamond. A layer of 100-150 A of the metal
followed by a 1500 A layer of protective Au was employed. An ohmic contact was
obtained following an anneal at 885 °C for 8-16 minutes in a hydrogen ambient. Geis [2]

found that In forms ohmic contacts to diamond without high-temperature processing or

33

ion implantation. However, the low melting temperature (156 0C) of In makes it
impractical for high-temperature devices. In the case of polycrystalline CVD diamond
deposited on silicon wafers, there are reports by Grot et.al [50], Gildenblat et al. [40] and
Huang and Reinhard [43] that the silicon wafer also acts as an ohmic back contact to the
polycrystalline CVD diamond.

For ﬁlms with high doping [2] or high defect densities [43], contacts are basically
ohmic because any depletion layers at the contact are sufﬁciently thin to allow adequate
tunneling current. Geis [51] observed that ohmic contacts can be obtained on heavily
boron-doped (1021 cm") natural diamond with several metals. Similar results have also
been reported for polycrystalline diamond ﬁlms. For ﬁlms of higher purity, however, the
depletion layer is larger allowing the formation of electrical samples with rectifying
characteristics.

Rectifying contacts have been reported forming on naturally occurring
semiconducting diamond crystals [17], on synthetic boron doped crystal [19], on CVD
grown homoepitaxial ﬁlms [40][48][52], and on CVD grown polycrystalline ﬁlms
[40][50][53]. These contacts have been formed by using point contacts [95] or by
evaporation of ﬁlms of various metals, eg. Pt[17], Al [13][53][54], and Au [50][52],
provided the contact area is small (typically less than 1 mmz). The defective nature of
typical CVD diamond ﬁlms is thought to lead to excessive leakage across Schottky
barriers when contact areas are signiﬁcantly larger than this, giving rise to (poor) ohmic
characteristics [52][55].

Varying reports exist for diamond-metal barrier height values. Hicks [56] and

Gildenblat [20] have measured barrier heights of 1.13 eV for Al contacts on

34

polycrystalline undoped diamond ﬁlms using internal photoemission spectroscopy. Other
groups also reported a similar result on Au [20][50][57]. Trew [9], however, noted that
the height of the potential barrier is essentially independent of the metal due to surface
pinning and has value in the range of 1.3-1.7 eV. It should be pointed out that barrier
heights are difﬁcult to determine from current-voltage (I-V) or capacitance-voltage (C-V)
measurement on undoped CVD diamond ﬁlms since the contacts deviate widely from
ideal behavior as a result of high bulk resistivity [15][58]. To reduce the high series
resistivity, Ebert et al. [59] successfully used a p+-doped diamond substrate for the
homoepitaxial growth of the p-doped active layer. The structure of metal/undoped
diamond/p-doped diamond has also been reported by Kang etal [15].

Diamond Schottky barrier diode dc characteristics have been studied by several
researchers. These tests have demonstrated diamond Schottky diode to be capable of
operating under very high temperature up to 1000 °C [52][60][61]. A high breakdown
voltage of 400 V has been reported by Jeng and Tuan [13] for Al/polycrystalline CVD
ﬁlms. Gildenblat et al. reported that the breakdown voltage exceeded 200 V at 300 K on
Au/CVD ﬁlms. An example of do I-V characteristic of an Au/ polycrystalline CVD
diamond is shown in Figure 2.16.

By using the thermionic emission / diffusion model, Hicks [56] and Jeng [13]
reported an ideality factor of 1.8 and 1.85 at room temperature for Al/CVD diamond
respectively. However, at an elevated temperature of 1000°C, Vescan et al. [61] reported
an ideality factor close to unity (11:10]) on Au / CVD diamond ﬁlm, clearly showing
thermal emission dominated the forward I-V characteristics. This has been conﬁrmed by

the reduction of ideality factor from 1.8 to 1.1 while the temperature was elevated from

35

100 to 500 °C reported by Ebert et al. [16] on Au / p-doped CVD diamond. Kang et al.
[15] also reported the reduction of ideality factor from 2.4 to 1.1 while the temperature

increased from 25 to 300 0c on Au / undoped diamond/ p-doped diamond structures.

 

 

CURRENT. PA
§

 

 

 

 

em
.80 g
-100 0 1w 200

VOLTAGE. V

Figure 2.16 Current-voltage characteristics of an Au/CVD

diamond Schottky diode [20]

36

2.8 Time varying signal response of diamond Schottky barrier diodes

When a small-signal voltage is applied to an electrical sample such as a diamond
Schottky barrier diode, the resulting current is characterized by both an amplitude and by
a phase relative to the applied voltage. The results may be expressed mathematically by a
complex admittance (ratio of current to voltage) where the real part corresponds
effectively to a measured small-signal sample conductance and the imaginary part
corresponds effectively to a measured small-signal sample capacitance.

Small-signal capacitance versus voltage (C-V) methods have been used by several
groups to study the small-signal responses in semiconducting diamond [15][17][18][19]
[20][21][62][63]. Glover [19] did a thorough analysis of the reverse-biased C-V behavior
of Schottky diode form on natural, single-crystal type IIb diamond. He found an
anomalous frequency dependence of the capacitance versus voltage and derived a model,
which included both deep level traps and bulk resistivity effects, to explain the
phenomenon. He found that the results could be represented by a series circuit consisting

of two capacitors Cj and Cr and two resistances Rf and RB as shown in Figure 2.17.

—H—-i|—’Wtr—’Wv—
Cj Cf Rf RB

Figure 2.17 Glover’s Schottky barrier diode model is represented by

combination of C], Cf, Rf and RB.

37

Comparing this model to the simple model of Figure 2.6, CB is now missing
because for Glover’s bulk samples, CB is negligible. Also Rj is not included by Glover
because for his reverse biased samples it is very large. Thus CB and Rj are replaced by
open circuits in Glover’s model. The elements Cj and R3 in Glover’s model are the
depletion layer capacitance and bulk diamond resistance as in Figure 2.6. In addition to
these, Glover added Cr and Rf as additional elements. Cf and Rf were included to model
hole emission from slowly responding deep levels.

From a theoretically analysis, Glover found that Cf is proportional to of”. He

expressed his measured capacitance, Cm, as

(31‘
1+ (nR,C,)2
1 1 1

= +
C-r C.<V) C.~(m.T>

 

Cm(V,(1),T)=

 

(217)

RT : R119), T) + RB(T)

The simulation result of his work is shown in Figure 2.18. According to his model
it could be seen that at low frequency, measurement capacitance Cm approaches Cj.
However, at high frequency two cases could be distinguished depending on the value of
RB. When R3 is small, the term mRTCT —> 1, so that Cm = Cf/2, therefore the

~l/2

measurement Cm falls off with frequencies as a) . When R3 is large, however, the

second term of Cm in Equation 2.17 dominates, so Cm depends on frequency as (11412.

38

 

   
 

EFFECTIVE CAPACITANCE. “171:1

10f—
’ c. . 500 vs

Cf. =TOOPF
coin-150111:
L 1.41, ISOO‘I

 

 

1 l 1 L l 1 I 1
l 10 100 10”

49150061161 11 H11

 

Figure 2.18 Model plot from Glover’s publication [19]

Kang et a1. [15] applied Glover’s equations to their experiment on metal/undoped

diamond/p-doped polycrystalline diamond structures with a modiﬁed term in

1 I I

=i+ +
CT Cl C,(V) C,.(6,T)

 

where C; was needed to account for the contribution of the capacitance by the undoped
diamond layer. No ﬁtting comparison between model and experimental results have been

“2 and (11"!2 fall off were conﬁrmed by their experimental results. They

made but the co’
also concluded that the fall off in capacitance at high frequency was due to the high series
resistance of the diode.

Gildenblat et al. [18][20] obtained a very similar frequency dependence to that

obtained on single crystal diamond by Glover for their Schottky diodes fabricated using

39

Au and Al contacts on thin CVD polycrystalline diamond ﬁlms. A model for the
equivalent circuit was proposed by the authors (see Figure 2.19), very similar to that of
Glover, which agreed qualitatively with their experimental results. Because of the thin
ﬁlm nature of their samples, it was necessary to add the component Cg due to the
contribution of geometric capacitance from the bulk part of the sample. Note that in
Gildenblat’s model, Co and Cg correspond to Cj and CB in Figure 2.6.

C-V characteristics of Schottky diodes, fabricated using sputter-deposited Ag
contacts on boron doped polycrystalline diamond thin ﬁlms grown by hot ﬁlament CVD,
were studied by Zhao et al. [64]. The results obtained for these diodes were very similar

to those of Schottky diodes fabricated using a single-crystal diamond substrate by Glover.

 

 

 

 

 

‘°° 05711
.0 _ C0 of Rf Cg
E:
9
m
g 00
E
g 40
20
o l l l
103 10‘ 105 10° 107 10'
FREQUENCY (Hz)

Figure 2.19 Frequency dependence of the capacitance of Au/CVD
diamond contact for different reverse biases giving an equivalent circuit as in

the insert; Gildenblat [18]

40

The frequency dependence in the C—V measurements of both type Hb naturally
boron-doped crystals and polycrystalline diamonds were investigated by von Windheim
et al. [21] using good ohmic back contacts, achieved by B ion implantation followed by
an Ag paste contact. The authors observed that the frequency dependence signiﬁcantly
reduces after back contact implantation. From the analysis of their experimental results
they concluded that a poor back contact has a strong effect on high frequency
measurements and may be at least partially responsible for the frequency dependence
observed on diamond by Glover [19] as opposed to trapping effects. This view argues
against the use of Rf and Cf in a circuit model.

Differential C-V measurements as a function of frequency were also performed
on Al and Pt rectifying contacts on natural type [lb diamonds by Venkatesan et al. [17].
The sample preparation was very similar to that of Glover. However, in some samples,
the backsides of the diamond are exposed to B ion implantation. Again, the effects of
back contact capacitance and resistance, the size and shape of the Schottky contact, and
the bulk resistance of diamond on the frequency dependence of the measured capacitance
of rectifying contacts were reported. The authors observed a frequency-dependent
capacitance that decreased signiﬁcantly after reducing the back contact impedance. A
circuit model without deep level traps was proposed by the authors to explain the
phenomenon as in Figure 2.20.

In the circuit of Figure 2.20, Cs is the speciﬁc capacitance of the Schottky barrier,
RB is the series bulk resistance of the diamond. The effects of the ohmic contact were

represented as a parallel combination of CC and RC. However, the Cc-RC combination was,

41

according to authors, negligible and only Cs and RB were used to model the sample with

reduced back contact impedance.

 

 

 

 

 

 
  
  
 
 
 
   
 

 

 

 

 

 

 

3511110“2
C3 ﬂ. Cc
q
6 '°

35:11: o soon:
C 25 - “1 . 0 Him
a: it“ A sum

. 0 room:
0 4-.
z 100qu “‘—"‘e-- a 250 11H:
,3 20 250 qu—. x 500qu
a L . + comm:
g , -— oanm
‘ 5‘ .
U 15 P" "'-’__‘:., .
50011112“? '
to — WW
“WW-1W
eoomz\//——
5 1 1 1 1 1 1
-2 -1 o 1 2 :1 4 s
REVERSE BIAS (V)

Figure 2.20 Frequency dependence of the capacitance of Al/natural diamond
contact for different reverse biases giving an equivalent circuit as in the insert;

Venkatesan [1 7]

To summarize the small signal C-V studies on diamond Schottky barrier diodes,
some studies (eg. Glover’s) indicate that traps play an important role in understanding
the experimental results, requiring the addition of Rf and Cf to the circuit model. Other
results (eg. Venkatesan) indicate that such elements are not necessary and indicate that
the model of Figure 2.6 should apply. In this study the issue is explored further by

investigating the entire small signal admittance, not just capacitance, at both reverse and

forward bias.

42

Finally, in terms of large signal ac response, the author is not aware of previous
studies. The results of this investigation on large signal (switching) responses of diamond

Schottky barrier diodes are described later in this dissertation.

43

CHAPTER 3

Experimental Methods

3.1 Chapter overview

This chapter presents the details of how samples were grown, electrically
contacted and characterized. It starts by describing the substrate preparation prior to the
diamond ﬁlm deposition. The microwave plasma—assisted chemical vapor deposition
system and process is brieﬂy described and typical process parameters for the diamond
growth are given. The formation of ohmic and rectifying contacts on the samples is then
discussed followed by the probe system setup description. The last three section of this
chapter give details on equipments, measurement setup and processes for electrical dc
characteristics measurement, small signal response and large signal response of diamond

Schottky barrier diodes.
3.2 Substrate preparation for diamond growth
Diamond has been reported to be successfully grown on several substrates such as

diamond (homoepitaxy), Si, nickel and sapphire (polycrystalline) [40] [66] by other

researchers. Consequently, there are a number of candidate substrates for a study of this

44

type. Ready availability, the ability to form a back ohmic contact with the diamond
polycrystalline ﬁlm, and adequate mechanical support for the thin ﬁlm diamond made
silicon (Si) a good choice of substrate for this study. Due to the low nucleation density on
non-diamond substrate (~104 cm’z), the silicon substrate was treated to enhance
nucleation density. There are several techniques to enhance and control nucleation
density on Si wafers described in the literature such as diamond photo-resist coating [67],
abrasion seeding [68], ultrasonic agitation technique [69], and bias enhanced nucleation
[70]. However, only ﬁrst two methods have been utilized to nucleate the Si substrate in
this study.

Before Si substrates were seeded for the diamond deposition, they were ﬁrst
cleaned and weighed. The Si substrates were cleaned by rinsing the substrates with
acetone followed by methane and ﬁnally with de—ionized water. Each rinsing step took
approximately 2 -—3 minutes to ensure the thoroughness. The substrates were then dried
with a nitrogen blowgun. The weight gain of the substrates after the deposition compared
to before the deposition was used to approximate the average thickness of the deposited
diamond ﬁlms. The Si wafers were either 2-inch or 3-inch diameter and were p-type,

(100) orientation, and with resistivities in the range of 0.01 — 20 Q-cm

3.2.1 Nucleation by the diamond photo-resist

Diamond photo-resist seeding was developed at Michigan State University by

Masood et.al. [67] [71] as a method of patterning or selectively seeding desired areas of

the substrate with diamond powder. The process basically consists of the following steps:

45

(1) diamond powder is mixed in the photo-resist solution, (2) the solution is spun on the
substrate using wafer spinner, and (3) the substrate is baked in an oven. If needed, the
photo-resist can be patterned by lithographic processing to selectively remove diamond
seed from the substrate afterward.

In this study, ultra virgin natural diamond 0-1/10 um powder from Amplex Corp.
was utilized with Shipley 1813 photo-resist and type-P Shipley photo-resist thinner in
order to seed a few of the earlier samples by the author and Khatami [72]. However, all

of the later samples were prepared by abrasion seeding described in next section.

3.2.2 Nucleation by diamond powder abrasion seeding

The general technique of abrasion seeding or “scratch-treatment” on Si substrates
to control nucleation density involves abrading the substrate with micron-sized diamond
particles and following a debris removal process. Sufficient nucleation density to produce
ﬁne-grain continuous diamond ﬁlms has been reported by H. Windischmann [68]. In
Windischmann’s process, a small amount of 1 um diamond powder was sprinkled on the
substrate. The substrate was then polished by hand with a laboratory paper tissue
(KimwipeTM). The excess diamond powder was rinsed away with methanol.

One possible reason why diamond nucleates on the diamond scratched surface is
that during the scratch-treatment, small amounts of diamond particles are left on the
surface. Work by S. Iijima etal [73] showed that tiny (less than several tens of
nanometers) clumps of sp3 carbon may remain after the debris removal. However, it has

been demonstrated that diamond nucleation is also possible on substrate that are

46

scratched with non-diamond powders [74]. Another study by P. A. Dennig [75]
concluded that diamond nucleation can be linked to the modiﬁcation of the silicon
surface.

In this study, adequate nucleation density to yield continuous diamond ﬁlms were
successfully obtained on Si substrates by scratching with ultra virgin natural diamond 0-
1/4 um powder from Amplex Corp. The scratching process was accomplished by the
author and Ulczynski [76] by rubbing the substrates, which are sprinkled with diamond
powder, with KimwipeTM tissue. After approximately 2-3 minute of thoroughly rubbing
in a circular motion on the substrate surface, the remaining diamond powder was wiped
away and blown clean with a nitrogen gun. The seeded substrates were then rinsed with
acetone followed by methane and ﬁnally with de—ionized water. Each rinsing step took
approximately 2 -3 minutes to ensure thoroughness. Finally the rinsed substrates were
blown dry with a nitrogen blow gun.

As mentioned earlier, only a few earlier samples were seeded by the photo-resist
process, all later samples were fabricated using scratch-treatment since the scratch-
treatment is somewhat simpler for nucleating our un-patterned Si wafers. Another
advantage of scratch-treatment is that nucleation occurs from structures created on the
silicon substrate [74] [75] or from very small sp3 fragments rather than from relatively
large diamond particles which could themselves be defective from the start. Scratch-
treatment nucleation can also avoid question of the contamination effects from
photoresist etch during diamond deposition. It was also noted that the scratched seeding

give ﬁner-grain ﬁlms than that of photo-resist seeding ﬁlms.

47

3.3 Diamond growth

All diamond ﬁlms used in present research were prepared by the microwave
plasma—assisted chemical vapor deposition (MPACVD) process. Details of the
MPACVD process for the diamond deposition in the microwave cavity plasma reactor
(MCPR) have been described by Huang [46], Zhang [77], Kuo [78], Khatami [72], and
Ulczynski [76]. The MCPR acronym is commonly applied to a particular variation of
Asmussen [79] reactors. This research used samples grown by Khatami, by Ulczynski,
and by the author. The main features of the deposition system and process used by the
author are brieﬂy described here.

Figure 3.1 shows the simpliﬁed schematic diagram of the deposition system
constructed by Ulczynski [76]. The body of the MCPR’s cavity is a brass cylinder with
water cooling on the base plate. The upper end of the cylinder is terminated by a movable
sliding short with the end-feed microwave-coupling probe. Microwave energy is
introduced into the system via this probe. The length of the probe inside the cavity is
adjustable. The length of cavity can also be varied by the sliding short. These features
make it possible to match the impedance of the cavity to the microwave power source. A
perforated stainless steel screen is afﬁxed to the base plate in the bottom part of the cavity
to terminate the cavity and still allow gas to ﬂow through.

The plasma is contained inside a quartz bell jar, which is vacuum sealed to the
base plate. The stainless steel sample holder is placed on top of two cylinder quartz tubes

with an insert stainless steel disk between the tubes.

48

 

 

microwave source

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t J waveguide l
1,.
i .I’
sliding sho probe
H2 .* L—r’ . *— . L—‘F —*~ -——1 quartz bell jar
C02 :2 ﬂow _—‘—. f. i ' plasma
controller l /’
CH4 —1 —'~; 7» I sample
j
quartz tubes
inf—Fm ‘
"——* ———~ perforated screen
pressure gauges vacuum chamber
/:
N2 :11-
V2753)
1‘ pressure
It vacuum __ 1 controller
pump
, 6 exhaust
N2 :3, - r .
to arr
i ure . e sim i re so a ic ia a microwave —
Fg 31 Th lfd hemt d gr mofthe lasma

assisted chemical vapor deposition (MPACVD)

49

The mixture of H2, CH4 and optional C02 is uniformly distributed to the system
through a common gas inlet in the base plate. The ﬂow rate of all gases is precisely
adjustable by a computerized mass ﬂow controller. The sample can be accessed to be
loaded/unloaded from the large stainless steel vacuum chamber below the base plate and
the quartz bell jar. The pressure measurement within the vacuum system is performed
through a system of four vacuum gauges. Each gauge is set to measure pressure in
different range, ranging from mTorr vacuum to above an atmosphere.

The pressure level in the system is adjusted by a computerized throttle valve
controller which is connected to a mechanical pump. The pump is ﬁlled with Acatel 200
oil, which is safe for pumping hydrogen and methane gases. Due to the explosive nature
of H2 and CH4, nitrogen gas is mixed into the exhausted gases before releasing them to
the atmosphere. Nitrogen is also used to purge and backﬁll the vacuum chamber after the
deposition process.

It should be noted that a leak/outgas check was not performed for every
deposition run in this research. However at various times, the leak/outgas rate of the
entire system (approximately 70 liters in volume) was between 0.1 to 1 mTorr/min. To
ﬁnd the effective ﬂow rate of leak/outgas in the system, let us consider the following

ﬂow unit conversion [80] [8]]

seem = 1 cm3/min at standard pressure 760 Torr and standard
temperature 300 K (STP)

soc/sec = 1 cm3/sec at STP

mTorr = 0.001 Torr = l p. Hg (or u) (very nearly)

50

u liter/sec — liter/sec at a pressure of l 11

Thus, 1 sec/sec 760 p. liter/sec.
For a leak rate of 1 mTorr/min in a 70 liter chamber, the flow rate of leak in the

system becomes

 

 

 

 

lmTorr X 70 liter : 1;: x 7011ter _ 1.17 ,ulrter
min 60 sec sec
,uliter
1.17 sec -3 scc -2
—_—ﬁt_r = 1.54X10 — : 9.2X10 SCCIn
760 ,u e sec
sec

or roughly 0.1 sccm. Thus, leak rate 0.1 to 1 mTorr/min corresponds to effective leakage
of approximately 0.01 to 0.1 sccm. As a result a non-negligible amount of gases such as
N2 and O2 in the atmosphere are also incorporated into at least some of the samples used
in this research.

Throughout this research, the range and typical values of deposition parameters
used by the author were varied or ﬁxed as in table 3.1 to explore variation in electronic
quality of the diamond ﬁlms. In addition, some higher temperature samples grown by
other investigators were also used in this study. The thickness of diamond ﬁlms used in

this research was from 0.3 pm to 8 pm. I

51

 

Gas composition CH41H2 = 1.5 — 5 %

CO2:H2 = 4% (optional)

 

Gas ﬂow rate H2 = 200 sccm

CH4=3 — 10 sccm

 

 

 

 

 

 

 

CO2 = 0, 8 sccm
Operation pressure 7 -— 25 Torr
Microwave power 1000 W
Substrate temperature 470 — 520 °C
Table 3.1 Typical deposition parameters used in the diamond

ﬁlm deposition process.

3.4 Diamond ﬁlm characterization with Raman Spectroscopy

Raman Spectroscopy has been widely used to characterize diamond quality. A
sharp narrow peak at 1332 cm'1 is characteristic of diamond and often interpreted as an
indication of high quality diamond ﬁlm. Graphitic carbon produces a broad band Raman
signal centered around 1580 cm". However, it should be noted that the ratio of intensities
of the diamond peak to the graphitic carbon centered is not proportional to the ratio of the
diamond to non-diamond components in the ﬁlms. This is because the Raman scattering
efﬁciency is typically 50 times greater for sp2 bond (graphitic carbon) than sp3

(diamond).

52

The Raman analysis system in this study most often used an Argon laser with a
wavelength of 514 nm. The conﬁguration and operation of this Raman system is well
documented by J. Mossbrucker [82]. In some samples, the Raman spectroscopies were
also obtained using a Kaiser Optical System Inc. Raman system. This second system uses
the 532 nm doubled Nd:YAG laser. The Raman spectrum of a polycrystalline ﬁlm is
shown in Figure 3.2. The spectrum shows a distinct peak around 1332 cm", which is the
signature of crystalline diamond. The broad characteristic arch between 1350 and 1580
cm'1 of graphitic carbon is almost absent from the spectrum. This indicated a good

quality diamond thin ﬁlm on the Si substrate.

 

I I I I T TII I I I I I I I l I I I I

1332

 

 

 

 

1 1 1 1 1 l 1 1 1 1 1 l

1200 1300 1400 1500 1600

 

Raman Shiﬂ (Cm")

Figure 3.2 Raman spectrum of a polycrystalline diamond ﬁlm on Si

substrate, BC4 observed by 532 nm Nd:YAG laser.

53

3.5 Metalization

Metalization on diamond surfaces has been studied by many researchers due to its
importance in electrical characterization of diamond ﬁlms. As mentioned in chapter 2,
two general categories of metals have been used by researchers in this area, namely
carbide and non-carbide forming metals. Carbide forming metals such as Ti, Ta and M0
were shown to give ohmic contacts while non-carbide forming metals tend to give
rectifying contacts on diamond surface.

Schottky barrier diodes require one ohmic contact and one rectifying contact. In
this research, Schottky diodes are generally fabricated in a sandwich structure with the

diamond ﬁlm between a back ohmic contact and a top rectifying contact (see Figure 3.3).

A] electrode
Ti/Au electrode

 

 

 

 

A1 back contact

Figure 3.3 Drawing show cross-section view of one example of a

diamond Schottky diode structure

54

The silicon wafer acts as an ohmic back contact [83] [50] as well as giving the
mechanical support to the diamond thin ﬁlms. After diamond deposition was performed
on the Si wafers surfaces, aluminum was thermally evaporated onto the whole bottom
side of the substrates as a conduction path. This allowed electrical measurements to be
made in the direction perpendicular to the diamond surface.

The top rectifying contacts were formed by thermally evaporated aluminum [13]
[17] [18] [20] [50] [52] [84] electrodes (1200 - 1800 A thick) on the diamond ﬁlm
surface through a shadow mask. The rectifying contact area evaporated on diamond
surfaces were between 4x10'4 to 2x10’3 cmz.

Alternatively, in some samples, 100 - 200 A of titanium followed by 1200 — 1600
A of gold as a protective layer are deposited through a shadow mask forming the ohmic
contacts [45] [49] [52] [58] on the top diamond surface with contact areas of 4x10’4 -
5x10'2 cmz. All evaporation in current study was done under 10'6 torr vacuum. The metal
deposition rates on the sample were controlled to be 12 - 18 A/sec for Al and Au and 5 -
8 A/sec for Ti. The samples were hold in the water-cooled substrate holder to prevent
sample heating during the evaporation.

Although research suggests that annealing processes can improve the quality of
diamond as observed by Raman spectroscopy [40] [85], there was no annealing
performed before or after the metalization process in this study in fear of increasing the
resistivity of diamond ﬁlms. Landstrass [47], Vandersande [11] and Sugino et.al. [85]
[86] showed that annealing process could cause a several order increase in resistivity of
polycrystalline diamond ﬁlm. The study of McKeag et.al. [55] also showed a reduction in

rectiﬁcation ratio on diamond Schottky barrier diode aﬁer 400 °C heat treatment in air.

55

3.6 Probe station setup

All of the electrical measurements on diamond Schottky barrier diodes in this
study were performed on a Signatone S-116O station. The S-1160 is a general-purpose
analytical probe station designed for probing various geometries down to 1 pm in size.
To protect the measurements from any photo-conductive noise signal, the probe station
was shielded within a Signatone light-tight box model PSDB-1160. Eight feed through
BNC connectors were attached on the side of the light-tight box to provide high
frequency electrical access from the test equipment outside.

In order to test devices under different temperature, the probe station was
equipped with a Signatone QuieTemp temperature-controlled chuck model S-1060 and a
NESLAB re-circulating chiller model CTF-33. A measurement temperature from 10 to
350 °C can be achieved with this setup. Under the normal measurement process, a
circular quartz disk, 3 mm thick, was placed on the top surface of the temperature-
controlled chuck. This allowed heat transfer between chuck and samples placed atop,
while the samples were isolated from the electrical circuit and noise of the chuck below.

Special high-speed microprobes, GGB model 10, were used with this probe
station to conduct measurements up to approximately 1 MHz. The limitation range of

operation for these microprobes is do to 3.5GHz.

56

3.7 DC characteristics measurement setup

A Hewlett Packard model 4145B semiconductor parameter analyzer was used to
measure the dc current-voltage characteristic of the diamond Schottky diodes. It is
equipped with four programmable Source/Monitor units (SMU's). Each SMU can be set
up to ﬁlnction as a voltage source/monitor, current source/monitor, or source common. A
simpliﬁed circuit diagram of a SMU is illustrated in the Figure 3.5. By setting one SMU
as a variable voltage source and another SMU as a common current source; the dc
current-voltage characteristic of the diodes can be obtained by two-point probe
measurement. The HP4145B can monitor current resolution as low as 0.05 pA with the
maximum range of i105 mA.

In this study, all dc measurements are conducted in the light-tight box. Figure 3.6
shows a schematic diagram of the measurement setup. SMU3 is used as a variable

voltage source, and SMU] is used as a common current return path.

Current Monitor

Voltage

 

 

Common V ‘
o \ Source (SMU
{ Monito out

Current Source I
Common -

 

 

 

 

Voltage Monitor

Figure 3.5 A simpliﬁed circuit diagram of a SMU unit of I-[P4l4SB

57

 

HP4145B

SMUl S/lYLUZ SMU3 SMU4
‘1

(g) L!) <\_ p

 

 

 

 

Inside of the

 

 

light-ﬁght box

A1, Ti/Au electrode
microprobe CVD diamond
Silicon wafer

microprobe

 

 

 

 

 

     

Al plate Al back contact _

 

 

Figure 3.6 Schematic diagram of dc measurement setup

58

3.8 Small signal response measurement setup

The ac small signal responses of the Schottky barrier are measured by a HP4192A
LF impedance analyzer and a HP4284A precision LCR meter; both controlled by a
computer. Again all measurements are conducted in the light-tight box. Figure 3.7 shows
the schematic diagram of the measurement setup.

The Hewlett Packard model 4192A LF impedance analyzer was primarily used
earlier in this research to measure the small-signal response in terms of capacitance, C
and the resistance, R of diamond Schottky diodes at various frequencies and bias
voltages. The internal frequency synthesizer of HP4192A provides a sinusoidal wave test
signal that can be set to a measuring frequency which may range from 5 Hz to 13 MHz
with 1 mHz maximum resolution. The sine wave amplitude level can be varied from 5
mV to 1.1 V,ms with 1 mV resolution. The internal dc bias voltage source could provide
up to $35 V in 10 mV increments.

The HP4192A provides measurement , in two equivalent circuit models, the
parallel or the series modes. The instrument has four terminals, two current terminals:
HCUR, and Leon, and two potential terminals: Hpm, and LPO'I‘ The test signal is output
from the HCUR terminal as shown in the Figure 3.8. The purpose of the current terminals
is to cause a measurement signal to flow through the sample, and the potential terminals

are used to detect the voltage drop across the sample.

59

 

 

 

 

 

 

 

 

HP4192A / HP4284A
L_CUR % HPoT HCUR
"E Q
(\5‘ J \l/ [kl/J
4| inside of the
light-tight box
Al, Ti/Au electrode
microprobe CVD diamond
Silicon wafer
microprobe

  
 
 

 

 

 

 

quartz plate
“x \‘\

    
 
   

Al back contact

 

Al plate

 

Figure 3.7 Schematic diagram of the small signal measurement setup

60

In this research, to compose a measurement circuit loop in a four-terminal pair
conﬁguration, the Ham and HPOT , me and LCUR terminals were connected together
respectively and, in addition, the shields of all conductors were also connected together
as shown in Figure 3.8. This four-terminal method provided the shielding required for
high-impedance, high-frequency measurements. Since the same current ﬂow through
both the center conductors and the outer shield conductors (in opposite directions, hence
canceling each other), no external magnetic ﬁelds are generated around the conductors.

As mention above, the HP 4192A LF impedance analyzer was used earlier in this
research. Later measurement were performed by the HP4284A precision LCR meter due
to convenience of use and simpler computer controlled capability. However, in selected

measurements HP4192A were also used to verify and cross-check the experimental data.

Vector
Ammeter

Lcur
I ,ll ,

W

 

OSC ‘ Hm

 

 

Hpot Vector Voltmeter Lpot

_._.

Figure 3.8 A simpliﬁed circuit model of four-terminal pair

 

 

conﬁguration of HP4192A

61

The Hewlett Packard model 4284A performs similar to the HP4192A. It measures
the capacitance, C and the resistance, R of diamond Schottky diodes over a wide range of
frequencies (20 Hz to 1 MHz) and test signal level (5 mV to 20 Vmg, 50 uA to 100
mAms). The HP4284A offers C-R measurement with a basic accuracy of 120.05% at all
test frequencies. The measurement ranges of C and R for this instrument are 0.01fF to
9.99999 F and 0.01 m!) to 99.99MQ respectively. Similar to the HP4192A LF
Impedance Analyzer, the I-IP4284A offers two measurement modes, the parallel and
series equivalent circuit models. Also, this instrument employs the four-terminal pair

conﬁguration : the He , Hp , Lp and LC as shown in Figure 3.9.

Virtual Ground

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Output '. = O V Lc
Resistor HO 1 -.—* I '- _
’l A
I
I
|
I
1
‘ I
System .‘ J
Ground VX \ ________ /

 

Auto Balance Bridge

Figure 3.9 A simpliﬁed circuit model of four-terminal pair

conﬁguration of HP4284A

62

In this research, the instrument test frequency was increased systematically from
100 Hz to 1 MHz in each test. The center dc bias was also varied within —1 0 V to + 10 V,
while the oscillation level was ﬁxed at 0.1 mV. The values of resistance and capacitance
of the Schottky diodes under test were measured and stored into data ﬁles. Both
instruments operate so as to measure the resistance and capacitance versus frequency in

both parallel (Cp, Rp) and series (Cs, Rs) equivalent circuit models.

3.9 Large signal response measurement setup

To study the diode responses to a large switching signal, a Hewlett-Packard
model 8116A programmable pulse/function generator was used to generate 20 V peak-to-
peak input sine waves for the test. The input signals passed through a coaxial microprobe
to the test wafer. The responses of diamond Schottky diodes were then probed by the
HP54200D and/or Tek11401 oscilloscopes in parallel with load resistance. The schematic
diagram of the measurement setup is shown in Figure 3.10.

The speciﬁcation of The Tektronix model 11401 is the following. Its main unit
has a vertical accuracy of 1.0% of the volts/division setting and a time-base accuracy of
0.01% of the time/division setting. Combined with the 11A32 plug-in unit, this system
provides 200 MHz bandwidth with a risetime of 1.8 ns. The 0.9% amplitude accuracy as
well as 100 ps i 0.002% horizontal time-base accuracy can be achieved at all test ranges
(lmV to 10V full-scale, 20 ns to 1000 s full-interval). However, since the 1 1A32 plug-in
unit only has input channels with 50 Q impedance (shunted by approximately 15 pF), it is

difﬁcult to probe weak output signal from the high resistance diamond diodes.

63

Therefore, the Hewlett-Packard model 54200D digitizing oscilloscope was also
used to investigate the large-signal switching response. This oscilloscope has two input
channels with input impedance of 1 M0 21:2%, shunted by approximately 14 pF. This
much higher impedance makes it easier to detect signal from the high resistance samples.
The instrument is a dedicated, multi-channel, simultaneous, waveform acquiring digital
storage oscilloscope with full GPIB programmability. It has digital storage bandwidth of
50 MHz (200 megasamples/second sampling rate) with i2% full-scale gain accuracy.
The horizontal time-base measurement accuracy of the instrument is :1:2 ns.

Note that a load resistance is introduced into the measurement setup to adjust the
input impedance of the oscilloscope to the suitable value. It has been found that the 1 M52
(shunted 14 pF) input impedance of the HP 54200D gave too large an RC time constant
to detect the weak signal from the diamond Schottky barrier diode without distortion. The
load resistance used in this research was varied between 10 K!) to 50 KO. The effects of

load resistance will be further described in detail in chapter 6.

64

 

 

 

 

 

 

 

 

 

HP54200D / Tekl 1401
(P HP8116A
load resistor
Al, Ti/Au electrode inside of the
microprobe CVD diamond light-tight box
Silicon wafer

 

micrpprobe

  

::1 : v rm

 

 

 

Al plate Al back contact

Figure 3.10 Schematic diagram of large signal switching response

measurement setup

65

 

CHAPTER 4

DC characteristics of diamond Schottky barrier diodes

4.1 Chapter overview

During the course of this research, Schottky diodes were formed on over 30
different diamond substrates that were deposited under a variety of CVD conditions. On
each substrate, approximately 34 diodes were formed. At least 10 diodes on each
substrate were electrically tested to some extent. On selected diodes, extensive
measurements were made. This chapter describes the results of dc measurement on these
diodes.

This chapter begins with the general current-voltage (I-V) characteristics
observed for contacts formed with two different type of metals; Ti/Au and Al contacts.
Next, the diode parameters, which are ideality factor 11, saturation current 10, and bulk
resistance R3, are extracted from the dc characteristics at room temperature. The dc
characteristics obtained at different temperatures are then used to yield two additional
parameters; barrier height (b3, and activation energy EA. The following sections explore
the roles of methane concentration in the CVD growth process, and the effects of diode
area and ﬁlm thickness on the dc characteristics of diamond Schottky diodes. Finally, the

experimental I-V characteristics are compared with computer simulation (SPICE) results.

66

4.2 General Characteristics

As described in detail in chapter 3, the dc device current-voltage (I-V)
characteristics are obtained by using the HP4145B semiconductor parameter analyzer.
All measurements are conducted in a light-tight box. Typical I-V characteristics of the
Ti/Au-diamond ﬁlm-Si-Al and Al-diamond ﬁlm-Si-Al structures at room temperature are
shown in Figure 4.1 and Figure 4.2 respectively.

For low voltages less than 8 V, the I-V characteristics of Ti/Au are nearly linear
and symmetric, as shown in Figure 4.1, as would be expected for top and bottom ohmic
contacts. This shows that both the Si substrate and the Ti/Au metalization provide ohmic
contacts to the diamond. For a ﬁlm thickness of 0.91 pm (based on weight gain), 8 V
corresponds to an electric ﬁeld of 8.8x104 v/cm. This indicates that for electric ﬁelds
below about 105 V/cm, the sample exhibited predominantly ohmic behavior with a
resistivity that is independent of the applied voltage. Taking a ﬁlm thickness of 0.91 pm
and a contact area of 4.9lx10“4 cm2 into account, the resistivity of the diamond sample is
then determined to be 72x106 (2 — cm.

On the other hand, for the Al-diamond structures. the results show a rectifying
characteristic, indicating that the rectifying property is a result of the Al-diamond
interface. This is consistent with earlier work which attributed the rectifying property to
the band bending at the top contact-diamond interface [18] [46].

When two coplanar Ti/Au contacts are used to contact the diamond ﬁlm, almost
identical I-V characteristics are obtained regardless of the distances between the Ti/Au
contacts as shown in Figure 4.3. This indicates that the current passes via the ﬁrst Ti/Au-

diamond ohmic contact through the diamond ﬁlm to the silicon ohmic contact, through

67

the silicon and back up through the diamond ﬁlm to the second Ti/Au ohmic contact. The
resistance of the doped silicon path is negligible compared to that of diamond path. The
current is, as expected, approximately half that of ﬁgure 4.1 because the path length
through diamond is twice as long. This also indicates a lack of appreciable surface
conduction between contacts to the diamond ﬁlm.

Figure 4.4 shows the I-V characteristic between two coplanar contacts with one
contact being the evaporated Al circle and the other being the Au circle. In this case,
Schottky barrier diode characteristics with less forward current than the one in Figure 4.2
are observed because of the longer (essentially double) path length through the diamond
ﬁlm.

However, it should also be noted here that not all Al or Ti/Au contacts on the
sample give exactly the same I-V data (comparing the same type of metal), despite the
fact that all contacts for a given sample are fabricated under identical processing
conditions. This is probably due to variation in ﬁlm thickness, and in some cases,

variation in the diamond quality across the wafer.

68

Current (A)

1.0x10’5

0.5x10'6-

-o.5x1o“5

-1.0x1o4s
-10

Figure 4.1.

 

 

 

 

 

 

 

 

Voltage (V)

The I—V characteristic of the Ti/Au-diamond ﬁlm-Si-Al samples show

ohmic behavior. The above results are at room temperature.

69

Current (A)

 

2.0x10'7’ f

 

 

 

 

 

 

 

 

 

 

1.5x10'7y ’ , j J ————
1 .0x10'7 :7 J A I J
' l ‘ ' L . l '
; 7 i l
0.5x10'7er J ..
’ l
0 l
. l
,V J I . . 1
-0.5x10' . . k .
-1o -5 o 5 1o
Voltage(V)

Figure 4.2. The I-V characteristics of Al-diamond ﬁlm-Si-Al samples show

Schottky barrier diode behavior. The above results are at room temperature.

70

Current (A)

 

4x10‘7

 

 

 

 

 

 

2x10‘7- ———% ﬂ - (bl- 11
l ‘ ‘ . J
0—‘—7 1
and7 J
.4x10'7 1 4
-1o -5 0 5 10
Voltage (V)

Figure 4.3. The I-V characteristics of samples with coplanar Ti/Au surface contacts
show ohmic behavior. Curve (a) corresponds to 1.5 mm between two contacts and (b)

4.5 mm between the Ti/Au contacts.

71

 

2.0x1o‘7 .

 

 

 

 

 

 

 

 

 

 

 

1-5x10‘7;.} 4 if ' J .. i - 7
g 1.0x10'7*——_ ‘ ~—
E . I
e .. L
8 0.5x10‘77 J
o I J
, J I 777777777
-o.5x10'7i J I I i J
-1o -5 0 5 1°
Voltage(V)

Figure 4.4. The Schottky barrier diode characteristics of a diode with coplanar

surface contacts. One contact is Al and the other is Ti/Au contact.

72

The rectiﬁcation ratio of the diode samples fabricated in this study at i10 volt, 27
°C is found to be between 104 to 1.8x105. This range of values is comparable to the best
results previous reported [13] [83] [84], although recently Al/diamond Schottky diodes
with rectiﬁcation ratios greater than 106 have been reported [16] [87].

The current-voltage results of each diode can be analyzed by considering the
device current as a function of both the voltage across the depletion-layer region, and the
voltage across the bulk region. From the diode equation (Equation 2.1) in forward bias

I z [0 exp (qu/nkT) (4.1)
Here VJ- is the junction voltage across the depletion-layer region (junction region), 1] is
the diode ideality factor, T is temperature, k is Boltzmann’s constant, and 10 is the
saturation current [22] [27]. For a given forward current, I, the junction voltage is
therefore found to be

Vj = (nkT/q) 1n (1/10) (4.2)
And the bulk voltage VB is subsequently found from

VB = V - V,-
where V is the applied voltage. In Equation 2.3, VB is expressed as IRB. The value of Io
and n can be determined from the linear portion of a plot of log I versus applied voltage
as shown in Figure 4.5 for a particular representative Al-diamond ﬁlm-Si-Al sample
BC4. At 27 °C, the ideality factor n and the saturation current 10 of sample BC4 are
found to be 2.43 and 1.82 pA respectively. n values in a range from 2.4 to 4.6 were
obtained for all other diamond diode samples in this study. The literature has reported a
wide range of n values for diamond Schottky barrier diodes [13][15][16][56][88]. The

resistivity of the bulk diamond, obtained from the plot between bulk voltage VB and

73

current I of sample BC4, as shown Figure 4.6, is approximately 1.13 MQ. Note that the
value of R3 in Figure 4.6 is obtained at high bias voltage, at which the current should
only be limited by the bulk resistance. RB values in a range from 1.1x106 to 5x1010 Q-cm
were obtained for all other diamond diodes in this study. This range of values is also
comparable to the values in as-grown diamond reported by several others [47] [50] [85]
[86] [89] [90] [91] [93] but substantially less than values of 1015 to 10'6 reported by

Vandersande and Zoltan [1 1].

 

 

 

     
  

WV?'5’TeXP(IE/<0-0.26*nl),

. . ‘_ ‘ }
// IO—1.82e-”012, J

J ~n=2-43 i: J

 

|F (Amp)

 

 

 

 

 

 

VF (Volt)
Figure 4.5 Semi-log plot of forward I-V characteristic of sample BC4. The solid
line represent the least square ﬁt of the linear portion of log (1) versus the applied

voltage (VF). The value Io=l .82e-012 and n=2.43 result from the curve ﬁt.

74

 

6X10-6 ' 1 f
J

  

 

slope +8. 85E- 7,
4x10“6 »————R— = 1/slope - 1.130E+6

 

 

 

 

 

 

 

 

 

a
E
s .......
2x106
0
-2 10

vE3 (Volt)

Figure 4.6 A plot of forward current versus bulk voltage of sample BC4. The
solid line represents the linear least square ﬁt at high bias portion of the bulk

voltage (V3). The value RB z1.13 MQ results from the inverse value of the slope.

According to Equation 2.4, the barrier height of the Schottky diode can be
determined if the value of effective Richardson’s constant is known. Actually if we
account only for thermionic emission, for a p-type Schottky diode

A**: 120 m*lh +m*lrlr
m

0

75

where m, is the free electron mass and mm, and m*;,;, are the effective masses for light
and heavy holes, respectively. To the extent that diffusion effects in the space charge
layer are important, the A** theoretical values is further modiﬁed to account for an
effective diffusion velocity.

However, since ()3 is not very sensitive to the choice of A** (see section 2.3), one
can, as a ﬁrst approximation, assume the theoretical value of A** based on thermionic
emission theory with an effective mass of unity, that is 120 A em'2 K'2 [15] [23]. The
barrier height on BC4, using Equation 2.4, is then calculated to be 0.926 eV. The barrier
height of all the samples in this research, assuming the ideal value of A**, are calculated
to be between about 0.72 to 1.08 eV. Reported values in the literature for barrier height
range from approximately 0.85 to 2 eV. As a point of reference, if surface states were
negligible and the diamond electron afﬁnity were zero, then the theoretical barrier height
would be about 1.4 eV. However, surface states in diamond are reported to play an

important role.

4.3 Temperature dependence of device parameters

The experimental current-voltage characteristics of BC4 were obtained at ﬁve
temperatures for the Al-diamond ﬁlm-Si-Al structure. These temperature dependent I-V
characteristics of BC4 are shown in Figure 4.7. Table 4.1 contains the extrapolated
saturation current axis intercept Io, ideality factor n, and bulk resistance RB obtained

from each I-V curve (each temperature) in Figure 4.7.

76

 

 

 

 

 

 

 

 

VF (Volt)

Figure 4.7 Forward I-V characteristics of BC4 in the temperature

range from 27 °C to 127 °C.

 

 

 

 

 

 

 

 

Temperature (°C) 10 (A) 11 RB (Q)
27 1.80 x 10''2 2.43 1.13 x106
52 2.58 x 10'” 2.16 624 x 103
77 6.16x10'll 2.20 356x 103
102 8.14x10'9 2.16 218x103
127 1.48 x 10'8 2.06 168 x 103
Table 4.1 Experimentally determined saturation current, 10, and ideality factor,

n and bulk resistance RB of BC4 at different temperature.

77

As can be seen in Table 4.1, the reduction of ideality factor at increased
temperature reported by Ebert [16] and Kang [15] is also observed in the course of this
study. As established earlier, the potential barrier height based on the theoretical A**
calculation of BC4 is 0.926 eV. As described in chapter 2, the barrier height can also be

determined from a Richardson plot of ln(IO/TZ) versus (1/T). According to Equation 2.5

ln(L’j—j = ln( AcA * *) — m(l)
T“ k T

The slope of the plot yields the value of barrier height and the intercept on the axis gives
the value of the effective Richardson’s constant. Figure 4.8 shows the Richardson plot for

sample BC4.

 

 

 

 

 

 

In (IO/T2)
do
.b

I. ”2-..

 

 

 

 

 

 

 

 

 

 

0.00250 0.00275 0.00300 0.00325 0.00350

1/T

Figure 4.8 Richardson plot of BC4 over the temperature range of 27 °C to 127 °C.

78

The barrier height determined from the slope of best-ﬁtted straight line is 0.923
eV. This value is close to the estimate of 0.926 eV established earlier. Given the diode
area of 4.91x10'4 cmz, the extrapolated interception of the plot on the vertical axis yields
an A** value of 92. In comparison, H.Kiyota et.al. [28] observed an A** value of 84 for
a diamond Schottky barrier diode which corresponds to a combined effective hole mass
value of 0.7. It is interesting that, based on cyclotron resonance experiments [93], m*.h =
0.7 m0 and m*hh =2.1 m0 which would predict a larger value of A** than obtained either
in this research or by Kiyota.

As described in section 2.3, a plot of ln(RB) versus (1/T)should be linear and the
slope would correspond to the activation energy (EA) of the semiconductor. Such a plot
for sample BC4 is shown in Figure 4.9. The activation energy of sample BC4 obtained
from the slope of plot in Figure 4.9 is approximately 0.21 eV (above the valence band)
which implies the presence of acceptor-like impurities or defects. EA values between 0.17
to 0.24 were also obtained in other samples in this research.

For boron doped CVD diamond, the activation energy has been reported to be a
strong function of the deposition conditions and the doping levels, varying between 0.013
eV, in the case of extremely heavy doping (boron concentration about 1020 cm'3), to 0.41
eV for very lightly doped ﬁlms [15] [18] [20] [92] [94] [95] [96]. The reported EA for
undoped polycrystalline diamond can range from 0.2 to 1 eV or higher depending on
deposition conditions [21] [90] [96] [97]. Although the diamond ﬁlms in this research
were not intentionally doped, the activation energy EA of the tested samples are at the

lower end of the undoped diamond range and were in the range of doped CVD diamond.

79

In (RB)

 

15

 

 

 

 

 

 

 

 

 

 

 

0.00250 0.00275 0.00300 0.00325 0.00350

1/T

Figure 4.9 Plot of ln(RB) versus l/T for sample BC4 over the temperature

range of 27 °C to 127 °C.

80

4.4 Influence of deposition chemistry on diode characteristic

Although a number of studies have been carried out to investigate the correlation
between deposition parameters and morphology/quality/growth-rate of CVD diamond
ﬁlm [72] [78] [98], the effects of deposition parameters, such as CH4 concentration, on
diamond Schottky diode I-V characteristics have not been studied to the knowledge of
the author.

For the reason that will become clear later in chapter 5, the bulk resistance of the
diamond diode is preferred to be as small as possible in this research. There appear to be
few reports on CH4 concentration effect on CVD diamond resistivity. It was shown by
AT. Collins [99] that the concentration of defects increases as the concentration of
methane (CH4) increases, therefore, increasing CH4 concentration in the CVD process
should reduce ﬁlm resistivity. However, ﬁlm grown with CH4 concentration higher than
5% is usually lower quality diamond based on Raman analysis [72] [78], or cauliﬂower-
like. Such material does not produce good Schottky barriers. This research studied the
role of CH; concentration for undoped diamond Schottky barrier diode fabrication.

For this purpose, 10 diamond ﬁlms grown on silicon substrates were studied. The
10 diamond ﬁlms were organized into three sets. Each set included ﬁlms grown at the
same H2 ﬂow rate, pressure, microwave input power and substrate temperature. The
CH4/Hz concentration in each set was varied between 1.5 to 5 %. Tables 4.2 through 4.4
show the deposition parameters and some other key properties of the samples. All ﬁlms
were prepared for measurement in a similar way as describe earlier in chapter 3. Al is
used to form the top surface contacts (contact area = 4.91x104 cmZ). Al is also thermally

evaporated on to the whole backside of the sample, the silicon wafer side, to form the

81

ohmic contact. The l-V measurements were performed on random Al contacts of each

sample in the direction perpendicular to the surface of the ﬁlm.

 

 

 

 

 

 

 

 

 

 

 

Sample Seeding H2 CO2 CH4 Substrate Film
Method ﬂow rate ﬂow rate Flow rate temp thickness

(sccm) (sccm) (sccm) (°C) (um)

BC 1 7 Scratched 200 0 3 518 1.432
BC 1 5 Scratched 200 0 5 514 1.501
BC 14 Scratched 200 0 8 514 l .446
BC 13 Scratched 200 0 10 518 1.474

Table 4.2 Deposition parameters and other properties of diamond Schottky

barrier diodes in set A.

 

 

 

 

 

 

 

 

 

 

Sample Seeding H2 CO2 CH4 Substrate Film
Method ﬂow rate ﬂow rate ﬂow rate temp thickness

(sccm) (sccm) (sccm) (°C) (pm)

883 Photoresist 200 0 5 471 2.372

S84 Photoresist 200 0 8 470 2.498

S78 Photoresist 200 0 10 473 2.428

Table 4.3 Deposition parameters and other properties of diamond Schottky

barrier diodes in set B.

82

 

 

 

 

 

 

 

 

 

 

 

 

Sample Seeding H2 CO2 CH4 Substrate Film
method ﬂow rate ﬂow rate ﬂow rate temp thickness
(sccm) (sccm) (sccm) (°C) (pm)
S89 scratched 200 8 3 476 0.814
S92 scratched 200 8 5 470 0.912
S 1 00 scratched 200 8 8 470 1 . 1 80
Table 4.4 Deposition parameters and other properties of diamond Schottky

barrier diodes in set C.

In contrast to the Fujimori [42] result on B-doped ﬁlm, which reported poor diode
characteristics in low CH4 ﬁlms and good diode characteristics in high CH4 ﬁlms, it is
found in this study that all measured contacts on each as-grown undoped ﬁlm of every
sample sets showed fairly good Schottky diode characteristics. For instant, Figure 4.10
shows I-V characteristics of one contact from each sample; BC17, BC15, BC14, and
BC13 in set A. The bulk resistances of the diodes were extracted from the I-V data of
each contact as describe in section 4.2. Figure 4.11 shows the graph of the bulk resistivity
of the diodes in set A for the CH4 ﬂow rates ranging between 3 seem and 10 sccm (1.5 —
5% CH4/H2 concentrations) while the H2 flow rate, the gas pressure and the substrate
temperature were held constant. The graph shows that for CH4 ﬂow rates below 2.5% the
measured bulk resistivity of diamond Schottky diodes appear to decrease as the CH4

concentration increase as one might expect. However, for percentages of CH4 higher than

83

2.5%, the bulk resistivity of diamond Schottky diodes seems to increase as the CH4
concentration increase. This phenomenon of increasing values of resistivity was
unanticipated since higher CH4 concentration was expected to give a higher graphitic
concentration and lower ﬁlm resistivity. An alternate hypothesis is that increasing CH4
gave more defects and more scattering, increasing resistivity.

Similar result of decreasing then increasing values of resistivity are also observed
in sample set B and C as shown in Figure 4.12. However the differences in bulk
resistivity of sample set B are less than in sample set A. It should be note that higher
resistivity of CVD diamond ﬁlm grown with higher CH4 concentration (6%) than that of
ﬁlm grown with lower CH4 concentration (0.5%) was also observed by Fujimori [42].
However, it is an opinion of the author of this research that the different in resistivity of
Fujimori’ 5 ﬁlms may result from the much different morphology of his diamond ﬁlms.
In Fujimori’s experiment, ﬁlm grown with higher CH4 concentration has ﬂat smoother
surface while sample grown with lower CH4 concentration exhibited rougher surface and
bigger grain size. Interestingly, contrary to one’s expectations, Fujimori’s ﬁlm with
smoother surface demonstrates higher ﬁlm resistance than a ﬁlm with a rough surface.

In this regard, the SEM (Scanning Electron Microscopy) photos of the ﬁlms in set
B from M. Ulczynski [76] are shown in Figure 4.13. Although, there appears to be
somewhat more twinning in the ﬁlm grown with higher CH4 concentration, the photos
generally show that all ﬁlms consist of polycrystalline diamond with very similar
morphology. Also there is not much different in resistivity of the ﬁlms in this set. It
appeared that the different diode bulk resistivity in this sample set B should not result

from the different ﬁlm morphology.

84

Current (A)

 

 

 

 

 

 

 

 

1 - - 2
10's: x—x BC13
’ v—v BC15
D—D BC17

0—0 BC14 ,

10-16 1

10-12;<
-10 -5 0 5 10
Voltage (V)

Figure 4.10 The plot shows absolute value of current versus bias voltage on
sample BC17 (1.5%-CH4), BC15 (1.5%-CH4), BC14 (1.5%-CH4), and BC13

(1.5%-CH4). A signiﬁcant noise level showed under reverse bias is possibly due to

equipment limit of HP4145B.

85

 

 

 

 

11
10 g
E : 0
°- 10- 3 o
g 10 J 8 g 0
.4? i e 6
.2 r (9,
4—1
1’ 109,r "‘0
U) :
(D : g 0
[r .
8
10 g
7
10 ‘
0 1 2 3 4 5 6

% CH4/H2

Figure 4.11 Effect of CH4 concentration in growth process to the bulk resistivity

of diodes in sample set A. (see Table 4.2)

86

Resistivity (9.0m)

 

A

O
.1.
O

 

 

 

o 3
8
é a
109:  ° E
108 A A A A A . A A A A A
o 1 2 3 4 5 6

% CH4/H2

Figure 4.12 Effect of CH; concentration in growth process to the bulk resistivity

of diodes in sample set B. (see Table 4.3)

87

S83

SS4

S78

 

Figure 4.13 SEM photos of diamond sample S83, S84, and S78. Copyright

by Ulzcynski [76], used with permission.

88

In sample set C, CO2 was added during the CVD process. The ﬂow rate of CO2,
as the O2 source, in sample set C was maintained at 8 seem. Again, as shown in Figure
4.14, the bulk resistivity of diodes decreases as the CH4 concentration increase from 1.5%
to 2.5% then increases as the CH4 concentration increase from 2.5 to 4%. When the SEM
photos of samples in set C, as in Figure 4.14(b), are examined, it shows that, under the
present of CO2, ﬁlm grown with higher CH4 concentration give much smaller grain than
ﬁlm grown with lower CH4 concentration. In contrast with one might expect, the
resistivity of ﬁlm with smallest grain and smoothest surface, S100, is highest among the 3
ﬁlms in sample set C. This observation is in agreement with F ujimori’s result mentioned
earlier. It is still inconclusive whether the different diode bulk resistivity in this sample
set C result from the difference in ﬁlm morphology.

H. Lux [100] reported that without O2 in the growth process, volume resistivity of
CVD diamond ﬁlms grown with 1.25 % CH4 is approximately an order of magnitude
lower than that of ﬁlms grown with 0.63 % CH4. However, with O2 addition in the
growth process (0.25-0.63%), he found an increasing in volume resistivity of CVD
diamond ﬁlm with increasing CH4 concentration (1 25-31 3%). According to Lux, adding
O2 to the reactive gas is a key to yields high volume resistivity of the CVD diamond.

In summary, undoped ﬁlms grown with CH4 concentration between 1.5 to 5%
yielded fairly good Schottky diode characteristics. However, increased CH4 concentration
in the ﬁlm growth process does not necessarliy reduce the bulk resistivity of diamond
diode as one might expect, in fact, CH4 concentration higher than 2.5 — 4% in the growth
process increased the bulk resistivity of the diode. The reason for this is not yet

understood.

89

Resistivity (0cm)

 

1012;

v ff Y—Vﬁ"

 

 

 

Figure 4.14

% CH4/H2

Effect of CH4 concentration in growth process to the bulk resistivity

of diodes in sample set B. (see Table 4.4)

90

S89

S92

8100

 

Figure 4.15 SEM photos of diamond sample S89, S92, and 8100. Copyright

by Ulzcynski [76], used with permission.

91

4.5 Effects of contact area and ﬁlm thickness on I-V characteristic

From the fact that the bulk resistance of the semiconductor material can be
reduced simply by making the metal contact area larger or by making the diamond ﬁlm
thinner, the effects of contact area and ﬁlm thickness on diamond ﬁlm were also studied.
Diamond Schottky diode samples were prepared on silicon wafers as described in chapter
3. Aluminum was thermally evaporated to cover the whole backside of silicon wafer
forming the ohmic contact. Aluminum was also used to form the top diamond surface
contacts with different contact areas on the same sample.

Figure 4.16 shows the I-V characteristics of sample SK7 with top surface contact
areas of 4.912410“ cm'z, 4.45x10'2 cm'z, and 7.91x10'2 em'2 denoted as SK7-Y, SK7-C,
and SK7-D respectively. As can be seen in Figure 4.16, the forward bias current of the
diodes improves as the Al contact area become larger. However, the reverse leakage
current also becomes much more signiﬁcant with larger contact area. In fact, the reverse
leakage current rises at a higher proportion to the diode area than forward current. This
substantially reduces the rectiﬁcation ratio of large area diode. For SK7-Y, the
rectiﬁcation ratio at 10 V is approximately 5x104, which is reduced to approximately 292
in SK7-C, and ﬁnally to only about 18 in SK7-D.

Similar results were obtained with other diamond Schottky diodes. Therefore, the
smaller contact area of 4.91x104 cm'2 was utilized regularly on all other measurements to
ensure good rectifying characteristics. McKeag [55] suggests that metal contact areas of

2

less than ~1x10'2 cm' are typically required to provide good rectifying characteristics.

92

1 0'2

 

Current (A)

 

 

 

 

-10 -5 0 5

10

Voltage (V)

Figure 4.16 I-V characteristics of sample SK7 with top surface contact area of

4.9lx10“1 cmz, 4.45x10'2 cmz, 7.91x10'2 cm2 labeled on the plot as SK7-Y, SK7-C,
and SK7-D respectively.

93

The defective nature of as-grown CVD diamond ﬁlms is thought to lead to excessive
leakage across the barrier when signiﬁcantly larger than this, giving rise to poor reverse
current characteristics.

The question of ﬁlm thickness is linked to the space charge layer thickness. As
described previously in chapter 2, a region of space charge (or depletion layer) exists in a
semiconductor just inside of a metal-semiconductor interface when the potential barrier is
non-negligible. To calculate this space charge width associated with the Al/diamond
contacts in this study, we start with Equation 2.7 for the dependence of the space charge
width on the applied voltage. As a rough estimation, we use the middle range value of
10'4-1018 cm'3 reported hole concentration on natural type IIb diamond [21] [101], which
is 10'6 cm'3, a dielectric constant for diamond of 5.5, and use the Schottky barrier height
as an upper bound for the built-in potential Vb]. Reported Schottky barrier diode height
for most metals on diamond range from approximately 0.85 to 2.0 [56] [97] [102] [103]
[104] [105] [106] and is believed to be relatively independent of non-carbide forming
metal type or metal work ftmction due to the pinning of Fermi level by surface states. The
barrier heights of all the samples in this research are between 0.72 to 1.08 eV (see section
4.2), therefore, a value of 1.08 eV will suit as an upper limit for the built-in potential.

For those values given above, the space charge region width in the diamond is
approximately 0.25 pm at room temperature. This means that space charge region may
extend a considerable distance into the diamond ﬁlm which is of special concern if diode
samples are fabricated on a very thin diamond ﬁlm. To avoid running into the question of
space-charge-limited current or a punch-through effect, our diodes were usually

fabricated on ﬁlm with thickness of 0.4 pm or higher.

94

However, one set of samples, which were prepared for measurement in a similar
way as described earlier in chapter 3, was used to study the effect of ﬁlm thickness on the
l-V characteristics. Al was used to form both the top surface contacts (contact area =
4.91x10'4 cm2) and the whole backside ohmic contact. Tables 4.5 shows the deposition

parameters and some other key properties of this set of samples.

 

 

 

 

 

 

 

 

 

 

 

Sample Seeding H2 CO2 CH4 Substrate Average
method ﬂow rate ﬂow rate ﬂow rate temp thickness
(sccm) (sccm) (sccm) (°C) (pm)
BC5 Scratched 200 0 5 476 0.309
8106 Scratched 200 0 5 439 0.604
BC 12 Scratched 200 0 5 502 1.081
BC 1 5 Scratched 200 0 5 514 1.501
S83 Photoresist 200 0 5 470 2.372
Table 4.5 Deposition parameters and other properties of diamond

Schottky barrier diodes with different ﬁlm thickness.

Again, the I-V measurements were performed on random Al contacts of each
sample in the direction perpendicular to the surface of the ﬁlm. All contacts of each
sample yield fairly good rectifying characteristic except sample BC5 which have very
high reverse leakage current. Figure 4.17 shows the values of forward and reverse current

of each sample at i 10V. As expected, the plot indicates that although the bulk resistance

95

of the diode can be reduced by making the diamond ﬁlm thinner, thereby increasing the
forward current, the reverse leakage of the device became large for the two thinnest
samples. In fact, the I-V characteristic of the very thin diamond ﬁlm sample BC5

resembles poor ohmic contacts with non-linear effects.

 

 

 

 

 

 

 

 

BC5 S106 BC12 BC15 883
1.504 Q A
1.1505 . - 4W W .M___.. M
@1567 ,- -~ 1L2 A—e—ﬁ—A
51.5094- ~ M- *WW . ,__ ~---._--____-
1.E-10—-——— __M W M- M_
1.E-11 ‘ ,M- ~- . a _M, M-
1.E-12— . :2
0 0.5 1 1.5 2 2.5
ﬁlmthickressmm)

Figure 4.17 The forward current at +10V forward bias (triangle marks) and

reverse leakage current at —10V reverse bias (circle marks) versus diamond

ﬁlm thickness.

96

4.6 Variation with time and sample history

It has been observed that the dc I-V characteristics of the many diamond Schottky
barrier diodes investigated in this study often exhibited some variation from one test to
another. Two types of change were observed in the experiments: ( 1) a change in bulk
resistance of the ﬁlm (shown in Figure 4.18 and 4.19), and (2) a change of ideality factor
n and saturated current 10 of the junction (shown in Figure 4.20).

Changes such as shown in Figs. 4.18, 4.19 and 4.20 were observed under a variety
of test conditions. These include (1) exposure to light, (2) electrical testing at high
temperatures (greater than 100 °C), and (3) prolonged (several hour) testing involving dc
biases. The literature [89] [107] [108] [109] [110] indicates that the electrical
conductivity of CVD polycrystalline diamond is strongly affected by states fairly deep in
the gap (an eV or more from the valence band edge). These states include both acceptor
type and donor type states. The acceptor-like states dominate, causing the CVD diamond
material to be p-type in nature. However, the donor states are also important because they
act to compensate the acceptor states. Changes in population of either can cause
substantial changes in the valence band hole concentration and, because the states are
deep lying, non-equilibrium population of these states can persist for long periods of
time, including several days.

Changes in the population of deep lying states can therefore cause an increase or
decrease in the bulk resistivity. Changes in the barrier height and space-charge layer, on
the other hand, are also strongly affected by changes in the population of interface states,
and near-interface states. Both bulk states and interface state populations can be changed

by the three device test conditions described above.

97

Considering the case of exposure to light in Figure 4.18, the result of 8100 shows
that light exposure causes little or no change in the space charge layer properties (10 and
11 remain essentially the same), however a signiﬁcant decrease in the bulk resistance RB.
This is consistent with observations of Ashok et.al. [108] and Gonnon et.al. [110]. Ashok
reported that change in I-V characteristic of their thin CVD diamond ﬁlms, which were
very sensitivity to illumination, resulted from the presence of exponential distributed
traps in diamond. Gonnon et.al. observed a persistent photoconductivity in
polycrystalline diamond after illumination. They explained the phenomena as follows.
The illumination created electron-hole pairs. After illumination, electrons raised in the
conduction band were trapped in deep-lying states below the conduction band. The
population of free holes left in the valence band was believed to give rise to the persistent
photoconductivity.

However prolonged exposure to an electrical bias has been observed in this study
to sometimes cause an increase in bulk resistivity, as seen in Figure 4.19 for sample BC4
after a series of large signal switching experiments, indicating a decrease in the hole
population. One possibility is that a portion of the donor-type levels are emptied (and
therefore activated) by the bias, causing increased acceptor compensation. Alternatively,
if injected electrons are trapped by deep-lying acceptors, the effective population of
acceptors would be reduced, also increasing the bulk resistance. Our experimental
observations do not distinguish between these possibilities.

It should be noted that observation of temperature induced long-term variations in
bulk resistance as in Figure 4.19 were also reported by other researchers and were

attributed to dissociation of hydrogen from the diamond surface which cause anomalous

98

or unstable conduction [47]. Hydrogen is believed to exist and passivate the deep traps in
CVD diamond ﬁlms [89] [111]. High temperature can cause hydrogen to out-diffuse
resulting in an increase of trapping density leading to increased capture of holes,
therefore, reduction in free carrier concentration and increasing resistivity of the ﬁlm.
However, the idea of increased bulk resistance in our sample caused by the out-diffused
hydrogen is doubtful, since the lowest reported temperature, which may cause hydrogen
dissociation, of 300 °C [85] [86] is much higher than our test temperature (27 — 127 °C).
We did not anneal our samples because an increase in bulk resistance is contrary to good
diode characteristics.

Finally, it was noted that long term electrical bias could also cause different test
condition induced variations. For example, as shown in Figure 4.18, under prolonged dc
bias conditions associated with small signal testing (chapter 5), BC7 showed changes in
IQ and 1] but not RB, indicating the changes involved interface states and band-bending,

but not bulk properties. In contrast, BC4 showed only changes in R3.

99

 

 

 

 

 

 

E 000°0000000000000000000001
00°
-8
10 3
A
<
v 1
_'-L 3
-10
10 3
1
-12
10 ““‘*“““‘*4“‘*
0 0.5 1.0 1.5 2.0

VF (V)

Figure 4.18 Change of l-V characteristics in sample 8100. The solid-curve shows

characteristics before and the dot-curve shows characteristic 5 minutes after sample

was exposed brieﬂy to bright light. Here 10 and 11 remain the same but RB decreases.

100

 

 

 

 

 

vF (V)

Figure 4.19 Change of I-V characteristics in sample BC4. The solid-curve shows
characteristics before and the dot-curve shows characteristic after 1 hour of large signal

test (see chapter 6). Here 10 and n remain constant but RB increases.

101

 

106:

108,

 

 

 

 

vF (V)

Figure 4.20 Change of I-V characteristics in sample BC7. The solid-curve shows
characteristics immediately after a small signal test. The dot-curve shows characteristic

2 hour thereafter. Here RB is constant but 10 and 11 change.

102

4.7 SPICE modeling and simulation for diode dc characteristics

The acronym SPICE stands for Simulation Program with Integrated Circuit
Emphasis. It was developed originally at the University of California Berkeley, and has
since effectively become an industry standard for device and circuit simulation [112].
The simulation tool PSPICE-6.3 [113] used in this research is a commercial version of
SPICE. The PSPICE diode model allows for the input of up to 29 parameters to describe
the device. Many of these parameters, however, are not relevant to the dc I-V

characteristics modeling for the diode. Table 4.6 shows the PSPICE diode model

parameters for dc simulation [26] [113].

 

 

 

 

 

 

SPICE Compared Parameter description
parameter notation
IS 10 Saturation current
RS RB Parasitic bulk resistance
N ‘1 Ideality factor, emission coefﬁcient
[K High-injection “knee” current
EG Eg Energy gap = 5.45 eV for diamond
ISR Recombination saturation current
NR Recombination current emission coefﬁcient
Table 4.6 PSPICE diode model parameters for dc simulation

103

 

In SPICE, the dc characteristic of the diode under low-injection condition is
modeled by a nonlinear current source that follows the Shockley equation (see section

2.2), rewritten for convenience in the SPICE implemented form

V
IzlS-EXP ——
JN-VtJ (4'3)

where V is the voltage across the diode and Vt is the thermal voltage (=kT/q). However,
the above equation is based on the assumption that the carriers are constant throughout
the space charge layer. In reality some carriers may be lost in this region by the
generation-recombination process. SPICE thus uses a different set of parameters to model

this region as

 

I=ISR~EXP[ V ]
NR-Vt

Under high-injection/high current condition, it can be shown [26] that the observed diode

current stops follow the Shockley form and approaches a modiﬁed form

 

I=IS~EXP[ V ]
2-N-Vt

For practical reasons, SPICE includes this effect by using the parameter 1K to determine
the onset of high-injection. Figure 4.21 shows each region in SPICE simulation.

By using the values of IO, 11, and RB determined from section 4.2, and adjusting
the remaining parameters to give the best ﬁt to the experimental result, we can obtain the
SPICE characteristic parameters for each diode. These parameters will be used as a basis

for other parts of this study including time varying waveforms.

104

I 1S(e(V—I.RS)/2N.Vt _

   
 
   

1K Is(eV/2N.Vt _1)

 

ISR(eV/NR.VI _1)

 

Figure 4.21 An exaggerated display of regions in SPICE diode modeling

Figure 4.22 shows the ﬁtting between the experimental result and SPICE
simulation for sample BC4. We obtain a very good ﬁt between experimental data and
SPICE simulation with IS = 1.8 pA, N = 2.40, RS = 1.2 MO, IK = 1.2 nA, ISR = 4.3 pA
and NR = 3.06. However, in some samples especially those with high leakage current, a
discrepancy between experimental data and SPICE simulation remains. Figure 4.23
shows the ﬁtting of sample SK7-C. Good ﬁt is obtained in forward bias part while
reverse bias part shows appreciable difference. The best-ﬁt SPICE parameters used in
Figure 4.23 are IS = 48 nA, N = 447, RS = 17.95 k9, IK = 400 nA, ISR = 351 nA, and

NR '= 19.98.

105

1 (Amp)

 

 

 

 

10 t - 1
l
.6J 1
10 r
-3' J ‘
10 r """ A; ~ 1
E l
-10’ ‘
10 '" " 1
-12’ ._ V. ‘
1° : x i
-14 i '
10 L ‘
-10 -5 0
V(Volt)

10

Figure 4.22 Comparison between the experimental l-V data (cross mark) and

SPICE simulation result (solid line) on BC4

106

1 (Amp)

 

1 0'3

 

 

 

r 5 ....
oos“‘.‘
[I"...
-5
10 3 '—
m. ....... .
[ ......................
-7 J '
10 t _ AA x
x
E .
-9
1 0 L I . - . - - . M 1 1 . . - . 1 -
-1 0 -5 0 5 1 0
V (Volt)
Figure 4.23 Comparison between the experimental I-V data (cross mark) and

SPICE simulation result (solid line) on SK7-C

107

CHAPTER 5
Small signal response of diamond

Schottky barrier diodes

5.1 Chapter Overview

This chapter presents the results of the investigation on the small ac signal
responses of diamond Schottky barrier diodes. Immediately following this chapter’s
introduction section, the admittance results in both parallel (Cp, Rp) and series (Cs, Rs)
equivalent circuit modes versus bias voltage and frequency are presented. The qualitative
interpretation of the results is given. In the next section, Cp, Rp, Cs, and Rs experimental
results are compared to three different models. These three models are: (I) a simple
model that only includes the combination of junction capacitance-resistance and bulk
capacitance-resistance as shown in Figure 2.6(a); (II) a simple model with an addition of
a series contact resistance RC; and (III) a model which includes the effect of trap states
represented by a frequency dependent capacitance (Cf) and a frequency dependent
resistance (Rf). The last section discusses the application implications of diamond

Schottky diode in this study under small ac signal.

108

5.2 Experimental results and their basic interpretation

In this study, before each small signal test, the dc current-voltage characteristic
measurement was performed on each diode at 27 OC. The diode parameters such as 10, r],
and RB were then extracted from the dc current-voltage result as described in section 4.2.
The values of these diode parameters were used in model calculation to compare with the
experimental results.

As described in detail in section 3.8, the diode responses to a small signal were
studied by using a HP4284A precision LCR meter. A HP4192A LF impedance analyzer
was sometime used to verify and cross check the experimental data. All measurements
were conducted at 27 °C in the light-tight box. The experimental results at difference ac
frequencies and dc bias will be presented in this section along with some remarks. Under
normal test conditions, the instrument (HP4284A/HP4192A) test frequency was
increased systematically from 100 Hz to 1 MHz in each test. The center dc bias was
varied between —5 V to + 5 V, while the oscillation level were kept ﬁxed at 100 mV. The
small signal resistance and capacitance values of the Schottky diodes were measured and
stored into data ﬁles. Both instruments operate so as to measure the resistance and
capacitance versus frequency in both parallel (Cp, Rp) and series (Cs, Rs) equivalent
circuit models.

Figure 5.1 shows the frequency and bias dependence of capacitance and
resistance in both parallel (Cp, Rp) and series (Cs, Rs) equivalent circuit modes for a

diamond Schottky barrier diode (sample BC4).

109

 

 

 

 

 

 

10:112/4
104°: /
/
/
A > / 11(14er
LL, / ”My
0. .n
0 /./‘“ 10KHz
10-11, 4/ raw-"'4 "
//A"" 100KHz
v, ),..—»-‘-
’ ‘- _K I—I-J ‘J"'-."‘ 5“.
1MHz
-6 -4 -2 0 2 4
BiasVoItage(V)
101°, . - - -
766112 _.._ \
109: H-.-_.W.-.\ \
. 1KHz \ \
K
A 8 \Fﬁw-‘V‘WW \‘\\
g 10’ 10KHz '\ \\
O O—o_.._._‘_.H \ \R\
6% 107t 100m ‘\\ ‘«\
. \ \a\
J ”I'd-“I "“‘ \ ‘\\\.
: 1Ml-lz ‘\\ \M «mt—A
6 ‘1‘ “q“
10 J \ \T‘kgﬁﬂ
‘\. —o
105 AAA I“- 7""
-6 -4 -2 0 2 4
BiasVoItage(V)

Figure 5.1 Plots of Cp, Rp, Cs, and Rs versus bias voltage at different

frequencies of diamond Schottky barrier diode BC4. Negative voltage values

indicate reverse biases.

110

 

 

Cs (F)

Rs (Ohm)

 

10.9;
10.10 _

10-11

 

 

10-12

 

 

ﬁ“

1OKHz ,W_W..+_.._.M_.

./.._.._.A——&--O—.——D—Q—O—O
/
Y
100KHz /
I—O—ﬁ—hﬁ—O—‘—.’
’0‘..- "".- -—‘ h..-
1MHz ,5
I

 

Bias Voltage (V)

Figure 5.1 Continued

111

 

 

It is of interest to make a comparison of these experimental results with the small
signal simple model discussion of section 2.4.Consider ﬁrst the capacitance results. In
both the C3 and Cp measurements, it is observed that at high frequencies (eg.lMHz) the
results approach a saturation value for both forward and reverse bias. In comparison with
Figure 2.8, this saturation value should be equal to eA/L. Taking diode area of A =
4.91x10'4 cm‘z, the experimental results for Cp and CS at high frequency indicate an L
value of 0.54 pm. This compares to an L value of 0.56 um based on average weight gain
measurements. At reverse bias, the expectation (as illustrated in Figure 2.8) is that the Cp
value remains at eA/L. This is also in agreement with the experimental results. However,
for CS in reverse bias, the experimental results show that the C3 value remains constant as
frequency increased. Figure 2.10 indicates that at sufﬁciently low frequency, Cs should
begin to increase. This increase was not observed experimentally for BC4. Now,
considering capacitance results at forward bias, Cs is observed experimentally to increase
as frequency decreases. This agrees qualitatively with the prediction of Figure 2.8. Cp
also remain with decreasing frequency, however the experimental results do not show the
eventually saturation in Cp that is predicted by the simple model.

Next, considering the resistance results, comparing Figure 5.1 with the prediction
of Figure 2.9 and 2.11, at low frequencies, the reverse bias value of Rp is very large as
expected, also at low frequencies, the forward bias value of Rp is in the order of RB, again
as expected qualitatively. At high frequencies, Rp decreases for both forward and reverse
bias, again as expected from the simple model. For Rs again for the low frequencies, RS

is on the order of RB for forward bias and much larger for reverse bias. At high

112

frequencies, Rs decreases for both forward and reverse biases, more rapidly for the later
than the former as expected from Figure 2.12.

Therefore, from a qualitative point of view the results for Cp, Cs, Rp, and Rs as a
function of frequency and bias seem to agree with expectation with two exceptions,
namely, (1) Cp does not saturate in forward bias at low frequency, and (II) the increase in
Cs with decreasing frequency in reverse bias is not seen.

It is also observed that in both capacitance and resistance measurement results for
BC4, the responses monotonically change between forward bias values and reverse bias
values for every test frequency. In contrast, Liu et al. [114][115], and Fox et al. [116]
have observed a peak of capacitance and conductance versus voltage which moved with
increasing frequencies in CVD diamond. They indicated that the interface states in
diamond were the source for the peak. However, no peak of capacitance, resistance or
conductance versus applied voltage is observed for any test frequency for BC4. It is
suggested by Viktorovitch [36] that the absence of peak should indicate either that the
density of surface/interface states is negligible or that their occupancy is controlled by the
metal Fermi-level in such a way that they do not contribute to capacitance. Some of our
samples show monotonic behavior as BC4, others do not.

Finally as stated by Rhoderick in his book [27] on Schottky diodes, the
capacitance of a Schottky barrier structure under reverse bias obeys the relation as given
in Equation (2.9) and (2.10). Thus, a linear relation can be obtained between C'2 and bias
voltage. From the linear relation, the carrier (acceptor) concentration in the semi-

conductor can be obtained.

113

For our experiment on diamond Schottky barrier diode BC4, both Cp and Cs
spectroscopy at various frequencies are plotted in Figure 5.2 in the form of C’2 versus
reverse bias voltage. However, no linear relationships were found in the plots. Kiyota
et.al. [28] concluded in their study that a non-linear relation between C'2 versus bias
voltage (C'Z-V) indicated that acceptor concentration, and therefore ionized states, were
not uniform in their as-grown ﬁlm. A non-uniform effective-acceptor concentration
would, in fact, be expected if, as suggested by Hayashi et.al., Looi et.al. [117], and
Gluche et.al.[84], the p-type nature is associated with near-surface hydrogenation.

With traditional silicon electronics, it is generally met in practice that a C'z-V plot
has a linear characteristic However, a non-linear relation between C'2 and bias voltage are
often found in Schottky barrier diodes fabricated on other type of materials eg. GaAs, and
ZnO even when the materials have uniform doping. These phenomena are currently not
fully understood [118] and have been attributed to interface state [119], minority carrier
injection [120], or non-zero free-carrier transit time in the space charge region [121].

For diamond Schottky barrier diodes, there are only a few articles which address
the non-linear relation between C'2 and reverse bias voltage. One was by Kiyota on un-
doped as-grown diamond Schottky diode as noted earlier. Liu et.al. [114][115] also
observed such non-linear relations in their boron-doped diamond Schottky diodes. Since
the doping conditions were kept unchanged in the sample growth, they concluded that the
non-linear characteristic of C'z-V in their boron-doped diodes should not come from non-
uniform doping proﬁle but rather from the interface states, deep level centers, and the

series resistance in the diamond sample.

114

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1001-12.
3’ a
a1KHz
g 2’ ’ 10Ksz
0
8 J //
, +
1. . 100KHz
O - .
1 0 -1 -2
8 BiasVoItage(V)
7* 100 1
6J ..
N 5*
7:? J 1
O IKHZ/MWE-y—ﬁ
o 4* 5
8 > O,
3, 10KHz _ J
2t '
, . 190K112 .
1” - _ H
O - E - I M M - M1 - -
1 0 -1 -2
BiasVoItage(V)

Figure 5.2 Plot of Cs and Cp in form of C'z-V of sample BC4. The C0
is the capacitance value at zero bias at each test frequency. Negative

voltage represents the reverse bias value.

115

5.3 Small signal model ﬁtting results

This section describes the results of ﬁtting the small signal experimental results
with the models in chapter 2. In this section, models are applied to two diodes SK7-B,
and BC4. Sample SK7-B is ﬁtted to the models ﬁrst. Later, sample BC4, which we
already gave some results qualitative interpretations in the last section are considered.

Figure 5.3 shows Cp, Rp, Cs and R5 of diode SK7-B at different center bias
voltage. As can be seen from the ﬁgure, the response of SK7-B is more complex than that
of BC4. The non-monotonic behaviors i.e. peak of capacitance Cp and resistance Rp are
observed. Such peak possibly indicates the presence of interface states in diamond
[114][115][116]. However, compare Figure 5.3 to Figure 2.8 - 2.11, the responses of
SK7-B qualitatively agree with most of the simple model predictions. Saturation of both
Cp and Cs at high frequency regardless of bias is observed. At low frequency forward
bias, Cp approaches saturation while C3 increases with decreasing frequency. The values
of both Rp and R5 approach saturation under low frequency. At higher frequency Rp
decreases and seems to approach a saturation value while R3 continue to decrease with
the increasing frequency.

According to the equivalent circuit model in Figure 2.6(a), the impedance and the

admittance of the circuit can be written as

_ R. + RB
1+i-w-RJCJ 1+i-co-RBCB

 

 

1
, and Y=E (51)

116

Cp (Farad)

 

1.3x10’10 -

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Jr... x -5.0v
-10J0 ﬁ*“‘ A '2.5V
1.1x10 : ”Xx v 0v
ngvv ex 0 +2.5V
’ vV Ax 0 +5.0V
-10 0 v Ax
0.9X10 5 0 V x 1
t 0 V A
013 00 v x
J ouuﬂnﬁﬁagnaoooo
J D: x0
-10 V 11 °
0.7x10 . v 6..
AD 0
V A5 0
v a
VV AAgnuooo
vv Ax an o .
10 vvol"99§9lllillllll
O-5X10- 2 ‘ ‘ A3 L4 ‘5 #4 6
10 10 10 10 10
Freq(Hz)
7JAA‘A X -5.0V
10 IXXXXX A ”2.5V
I x )1: v 0V
J 92* U +2.5V
’vvvav x O +5.0V
vvv K
V
A > vv:
8
g zvaVVVVvv
Q. 6! Q“A Vvvvv
m 10 ;DUDUUDDDDDDDD xxAAAAAAAAAA vv
. Dana xxx AA XX
1 an XXxxXXxx X
0000 Dan xxx ‘
0000000000000 DDDDDDDD Xx J
0 0° 0000 g
0000 D 8
000000000 001
5 00°?”
2 3 4 5 6
10 10 10 10 10
Freq(Hz)
Figure 5.3 Experimental results of Cp, Rp, C5 and RS measurement

on sample SK7-B

117

Cs (Farad)

Rs (Q)

 

1cr6. -- - AAA 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

J x -5.0V J
. A -2.5V .
'7, v CV
10 J° a +2.5V
10°C 0 +5.0V
-8JD 0
10 g “a 00
J D
t D o
J an 0o
-9 o
10 va no 0
Ex vvi7 no 000
104°Jhxﬁx“‘*“*:r°§;°°°oo 1
J 6V8338iiiﬁiiauuuueuuo.u..1
l
-11
10 ‘ ”A “ ‘ ‘
102 103 1o4 105 1o6
Freq(Hz)
107, ~ ., 2- ~
J“;
,v ”in,
IUDDDDEIEEBIB
’ 0000 3:32:22
10st '83
eggoo
V2900
VAR o
: VAE o J
t vAgno 1
1 Veﬁnoo l
3 X '5.0V vﬁguo J
10 f A -25\/ Vergzo «
J V 0V ‘7 1:10o ,
u -+25V 655°ao
t o 5 D1
, +50v 11,,]
1
10 w ‘ * ‘
102 103 104 1o5 106
Freq(Hz)

Figure 5.3 Continued

118

All the variables have the usual meaning as in section 2.4. The value of Cp, Rp, Cs and Re,

can then be calculated from

c, :11“?- , 1773118 , €527.11]sz ,and 12,: Re(Z) (5.2)

which will give the ﬁnal expressions as in written in Equation 2.12 and 2.13.

In equation 5.1, there are four parameters - C J, CB, R) and R3. The value of C j and
CB can be obtained from the sample thickness, L, and depletion layer width, w, as from
the expressions in Equations (2.8) and (2.14). However, in both the Cs and Cp
measurement, it is observed that at high frequency, the capacitance of the diode
approaches a saturation value of 51 pF regardless of bias. According to the analysis in
section 2.4, this value should equal to the geometrical capacity of the whole ﬁlm, sA/L.
Taking the area of the diode 1.99x10'2 cm2 into account, the thickness of the diode, L, is
found to be 1.90 pm which is close to 2.02 pm based on weight gain. Also, the dc
current-voltage characteristic measurement of this diode yields the value of R3 of 198
KQ. However, since the thickness of the depletion layer is not constant but rather
depends on the bias voltage, the value of RB can be adjusted to reﬂect the change in
depletion layer thickness. Under forward bias, value of the dynamic resistance R; can be
calculated from nkT/I, where I is the dc current at that speciﬁc bias voltage. From dc
measurement, the ideality factor of SK7-B is 14.1 and saturation current is 58 nA. Under
reverse bias, ideally R) is very large (inﬁnite), practically R) can be obtained from dI/dV

at speciﬁc reverse bias voltage of the dc measurement.

119

From the above discussion, one should be able to ﬁnd a ﬁt to all the Cp, Rp, C3
and Rs results at each different bias voltage by only adjusting the value of two variables,
namely depletion layer width, w, and the bulk resistance. RB. Figure 5.4 shows the results
of the ﬁtting between experimental data and simple circuit model. To obtain a ﬁt to all

bias voltage, the value of depletion layer width, w, was varied between 0.81 pm at 5 V

forward bias to 0.94 pm at 5 V reverse bias. The value of bulk resistance, R3, was also
varied from 180 K!) to 330 K!) as shown in table 5.1.

From Figure 5.4, it can be seen that, although we can obtain a qualitatively
acceptable ﬁt between experimental and model results, discrepancies between
experimental and model are remained in all plots, for example Rp and Rs at high

frequency, and Cp at low frequency

 

 

 

 

 

 

 

 

Bias voltage w (um) RB (ohm) R; (ohm)
+ 5.0 V 0.81 330 K 48 K
+ 2.5 V 0.83 325 K 250 K
0.0 V 0.88 320 K 15 M
- 2.5 V 0.91 250 K 48 M
- 5.0 V 0.94 180 K 42 M
Table 5.1 The parameter values used in model ﬁtting of the

diode SK7-B in Figure 5.4.

120

Cp (Farad)

 

1.3x10"° -- -. - -- -
“‘ BiasVoItage

-10
. 1 x -5.0V
1 1x 0 1 )3 -2.5V

 

        

v 0V
1:1 +2.5V
o

0.9x10'10 . + 5.0 V

 

 

 

 

 

0.7x10'1o -

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-10 .
0.5x10 2 3 4 5 6
10 10 10 10 10
Freq (Hz)
‘ - . \.\ Bias Voltage
7 ‘f ‘5‘ \‘\ 1
1° {XXXxxXX \ x -5.ov :
-2.5V 3
IVVVVVV ; V 0V 1
’5 ‘7va ‘5 1:1 +2.5V .
V Vv, o + 5.0V «
@- . :. v V V V V v v v
6 ks». VVV
10 JDDUDDDDDDDDDDDD 'X ‘zezeffi tidﬁk/LZEIVV ,
DU XXX J “J1: at)?
UD xxxxxxxx ~m j
.OOOOOOOOOOOW
48%)., DD 95.
DD
0 OOOOODD
5 0 ll
10 M . . -- . - - . 1 MA - O-
2 3 4 5 6
10 10 10 10 10

Freq (Hz)

Figure 5.4 Fitting between the Cp, Rp, C3, and R5 experimental and the

simple model results. Solid lines represent model calculation at each bias.

121

Cs (Farad)

Rs ((2)

1015. . A - A .2. A

 

 

 

 

 

 

 

 

J BiasVoItage
-7 x -5.0V
10 I. -2.5V
I .0 V 0V
_8 6 °o e +2.5V
10 g “E, o o +5.0v
. u 0
J 0 0
l ”D °o
10.9va DD 00
Exxvvvv 000000
-10 WEI. va. ' A 0.00,
10 J "m '.':=_-_‘..__
-11J
10 ‘ ‘ “
102 103 104 105

 

 

 

 

 

 

 

 

 

 

5 Bias Voltage ' A.\ j .
3 x -5.0V ”*7. ~; ,
10 g -2.5v ~~ ._,
. 0 v
0 + 2.5 V
f o + 5.0 V
1
10 AAA~A A AAA-~A A A - -
102 103 1o4 105
Freq (Hz)

Figure 5.4 Continued.

122

Snell [37] observed a rapid rise in conductance (drop off in resistance) in the
capacitance-conductance spectroscopy measurement on Au/Si Schottky barrier diodes at
test frequencies higher than 10 KHz. He attributed such a rapid rise to a 40 (2 contact
resistance. This may be expected since all metal-semiconductor contacts have a ﬁnite,
non-zero, contact resistance. After taking the contact resistance effect into his model
calculation, Snell observed perfect ﬁt between his model and experimental results.

A study by Bataineh [122] on CVD diamond impedance spectroscopy suggested
that although contact resistance is small it plays an important role at high frequencies and
needed to be included into the equivalent circuit model. Studies by Venkatesan, and von
Windheim et.al. [17] [21] on diamond Schottky barrier diodes also conclude that the
frequency dependent capacitance of the sample is the results of the combination of
junction capacitance, bulk resistance and back contact resistance. The authors observed
that the frequency dependence signiﬁcantly reduced after the back contact resistance was
reduced.

In order to accommodate the contact resistance into our model calculation,

Equation 5.1 is modiﬁed to include RC as

: RJ RB
1+i-a2-RJCJr 1+i-w-RBCB

 

+RC, and Y=% (5.3)

Where RC is the contact resistance. The value of Cp, Rp, Cs and Rs can then be calculated

from Equation 5.2.

123

Figure 5.5 shows the ﬁtting between experimental results and the model in
Equation 5.3. Note that all the value of C j, R), CB and RB were maintained at the same
value as used in previous ﬁtting between experimental results and model in Equation 5.1
(without RC). With the addition of Rc=52 Q in our model, the fall of at high frequencies
of the resistances are observed in the model calculation. Now, a better ﬁt in Rp and Rs
than those in Figure 5.4 can be obtained.

As mentioned in section 2.8, there are two major interpretations of small signal C-
V studies on diamond Schottky barrier diode. Some studies, e.g. Venkatesan’s, indicate
that the frequency dependent of capacitance can be simply model by the combination of
the junction, the bulk, and the contact elements. Others, e.g. Glover, indicate that deep
trap states in diamond play an important role in the interpretation of C-V results. It is
important that we try to adapt Glover’s model into our result interpretation.

Glover[19] models the effects of deep trap states with the combination of Cf and
Rf as shown in Figure 2.17. Based on earlier work by Schibli [123], the values of Cf and

Rf can be calculated from

 

 

 

B 1
C =——- ,and R =
I 40) f 60C,
2
Where B=J2e JNaJlfszCCAPJPI

N = acceptor concentration

(I

Cm, = capture probability

2 KT

N R = valence band density of states

 

124

Cp (Farad)

 

1.3x10*°

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

  

 

 

t x Bias Voltage
J‘Stxx,
~10 ° .....'_-?“x
1.1X10 . ”Noggx >< -5.0V .
V° J‘ 4 -2.5V 1
7 Vvvv \\\ V 0v 4
-10J 0 vv 0 +2.5V
0.9X10 é o v 0 +5.0V
J
cr7x1040A
J
10 J '
0.5x10' AAAA . M- -
102 1o3 104 105 106
Freq (Hz)
\ J
- - Bias Voltage
7 .
10 FXXXXX ‘ \ J
Xx .\ x -5.0V
-\ -2.5V
A JV‘JJVVVVV‘7 J V 0V
9, 'vv ..\ a +2.5v
é}. o +5.0V
106FDDDDDDUUDDDDD J\xx‘ 2222 Az2gAvav 3
DDDDDXXXXX xAAAAJ‘ ‘
XXX x ‘, ‘
lO°oOoooooooo°°°o Du UDDUJXXXXX 1
I .. DU §JJ 1
5 .
10 ‘ ‘ ‘ ‘ ‘
102 103 104 1o5 106
Freq (Hz)
Figure 5.5 Fitting between the Cp, Rp, Cs, and Rs experimental results

of SK7-B and the model which include the contact resistance effect.

125

Cs (Farad)

Rs (9)

 

10'6

 

 

 

 

 

 

 

 

 

r a f v V I 3
£ Bias Voltage 3
-7 x - 5.0 V ‘
10 ;. -2.5v
g . O O V
-8 ’ u o + 2.5 V
10 l a D o + 5.0 V
. c1 0
I u 0
O
10'9 iv 0 D o o
D
E V v D 0 o
l D
x x v v v U 0 o o
)5 X V V D .
-10 -~‘-....._._. l D D ~
10 ’ ' "i”. 'MT':.:;_ _' “5:...
1
-11
10 ~ ~ - -
2 3 4 5 6
10 10 10 1O 10
Freq (Hz)
\\\\ v v 4
106 I U D D \ v v7 8 E :

    

 

 

 

 

 

 

 

 

4
10 : Bias Voltage
E x .5.0 v
2 r. - 2.5 V
10 l v o v
’ D + 2.5 V
E o + 5.0 V
o
10 ‘ ‘ “ “ ‘ *
1o2 103 1o4 105 1o6
Freq (Hz)
Figure 5.5 Continued

126

To obtain results which include Glover’s Cf and Rf elements, our model Equation 5.1
must be re-written as
R, RB 1

1+i-w-RJCJ 1+i-w-RBCB i-w-C,

 

 

./ (5.4)
The value of Cp, Rp, Cs and Rs can then be calculated from Equation 5.2.

In order to obtain the value of B, one must have the values of Na, CCAp, and NR.
However, for the ﬁrst approximation, we use the middle value of 1014-1018 cm'3 reported
acceptor concentration on natural type IIb diamond [21] [101], which is Na = 1016 cm'3, a
dielectric constant for diamond of 5.5, a valence band density of states Nr = 1015 cm'3
[124], and use the activation energy of 0.21 eV obtained in section 4.3. Glover also
reported the CCAp value in the order of 10'10 cm3/s for natural type IIb diamond.

For those values given above, the approximated value of B is in the order of 10'6

1/2). Figure 5.6 shows the ﬁtting between experimental results and the model in

F/(cmzsec
Equation 5.4. Note that all the value of C1, R1, CB and RB were maintained at the same
value as used in previous ﬁtting between experimental results and model in Equation 5.1
(without RC). With B = 7x 10'6 F/(cm2.sec”2) in our model, an improved ﬁt in Cp, Rp, Cs
and Rs can be obtained than that of simple model in Figure 5.4.

Let us now turn our attention to the admittance results of BC4 given in the last
section. We also apply the models described above to BC4 results with the similar

process. In both the Cs and Cp measurement, it is observed that at high frequency, the

capacitances of diode BC4 approach a saturation value of 4.41 pF regardless of the bias.

127

Cp (Farad)

1.3x10"°

 

 

 

 

 

 

 

 

 

  
  

 

l Bias Voltage
’ X it a 3 r:
1.1x1o"° '*~ x x - 5-0 V
v v N X X "- ' 2.5 V
: v v v \‘\ O V
_10 v 5. + 2.5 V
0.9x10 v v + 5.0 v
0 0 V «\t
000 Bﬁaonnox o
O
0.7x10'10 » v c. o o
v \ °
V
V
V
V V V
-10
0.5x10 - - w
102 103 1o4 105 1o6
Freq (Hz)
’ " Bias Voltage ‘
107 x - 5.0 v ,
. - 2.5 v 3
I v 0 V <

RP (Q)

   

 

 

 

 

+2.5V

 

 

 

 

106

V V
106’000000000050000 Xi” 3
i°°°°ooOo000000°n j
r
10:02 i U 153 A A104 105
Freq (Hz)
Figure 5.6 Fitting between the Cp, Rp, CS, and R5 experimental results

of SK7-B and the model which include Glover’s element Cr and Rf.

128

Cs (Farad)

Rs ((2)

 

 

 

 

 

 

 

 

; Bias Voltage
-7’ x -5.ov
10 » -2.5V
a 0 0V
8 r :1 ° 0 + 2.5V
10' : 0,, o +5.0v
C] O
D O
. D 0
-g' 0 °
10 "7 D °o
: Vvv DU 00
Q3 v"'v Dun ' '
'10 ~~—---- X V : » D I . ' ~
1 O E ‘F‘ﬂﬁg’g-g}- -—._‘.m:-~. i
l ' ' " ‘ .
—11
10 * r “ rm ‘ r *
102 103 1o4 105

 

 

 

 

 

 

  

 

 

Bias Voltage
3 ’ x -5.0 v
10 r - 2.5 v
L v 0 V
CI + 2.5 V
, o + 5.0 v
1
10 r e * ‘ A ‘
1o2 103 10“ 1o5
Freq (Hz)
Figure 5.6 Continued.

129

According to the analysis in section 2.4, this value equals to the sample geometrical
capacity, 8A/L. Taking the area of the diode 4.91x10'4 cm2 into account, the thickness of
the diode, L, is found to be 0.54 pm. Also, the dc current-voltage measurement of this
diode yields the value of RB of 1.2 MQ.

Under forward bias, value of the dynamic resistance R; can be calculated from
nkT/I. From dc measurement, the ideality factor of BC4 is 2.4 and saturation current is
1.8 pA. Under reverse bias, ideally R; is very large (inﬁnite), in practice R] can be
obtained from dI/dV at a speciﬁc reverse bias voltage of the dc measurement. Again, by
adjusting the value of two variables, w and RB, we can ﬁnd the ﬁt for the simple model.
Figure 5.7 shows the results of the ﬁtting between experimental data and simple circuit
model results at three different bias voltages. Table 5.2 shows parameters used in the ﬁt.
From the plot in Figure 5.7, it is shown that the simple model does not explain the
characteristic of the responses of BC4. Furthermore, by adding contact resistance effect
as in equation 5.3, we found that with the contact resistance up to 1 KS), there is no

signiﬁcant change in model calculation results.

 

 

 

 

 

 

 

 

Bias voltage w (um) . R3 (ohm) R1 (ohm)
+ 5.0 V 0.81 330 K 48 K
0.0 V 0.88 320 K 15 M
- 5.0 V 0.94 180 K 42 M
Table 5.2 The parameter values used in model ﬁtting of the

diode BC4 in Figure 5.7.

130

Cp (Farad)

RP (Q)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10-9i " ' ' ' " ' ' v~
f —— model+5.0V
. ---- modelOV
, model-5.0V
* v -5.0V
10-10; 0 0 0V
: ° 00 o +5.0V
3 o
i D
U at: o
D 0
1ww:::::::;.__ ___ 1
i ‘3 a :7 v v ;\“‘--S- g \O—j
-12
1O ‘ “4 ‘
102 1o3 10“ 105 106
v - H *1
---- modelOV :
— model-5.0V
—— model+5.0V l
v —5.0V «
:1 0V 1
8 ° +5.0V
10 : \ v
I a \
D an \\ v ‘
7 D \
10 ' D\\\ 1
l——g———————_£.‘:_“_- —————————————
o 00 \\\ v
0 U
106 ° 0 n \ .
o o \D t
5’ €
10 r -
1o2 103 1o4 105 1o6
Freq (Hz)

Figure 5.7 Fitting between the Cp, Rp, Cs, and Rs experimental results

and the simple circuit model of sample BC4.

131

Cs (Farad)

r2s(cn

 

10*ﬁ

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E \ — model-5.0V
; \ ---- modeIOV j
_9 o \ —— model+5.0V
10 s \ v -5.ov 1
o a CV
c,\ o +5.0v
°\\
-10:
10 D \
. \ °
an a \ 0
-11 _______________ o ,
1O E‘¥:T*r*———~i
’ 7 7 :7 7 v v ‘T‘v‘“$ H
r .
-12
10 ‘ ‘ * “ *
102 1o3 104 105 1o6
Freq (Hz)
108, - ﬁfe
’ v
r V
I D vV
: a l
t on V :
lV\—O'— _—~a—\
\ ------- 0‘- \
1065 ”5“§-\ a
. v \x\ .
\\s
E \\\ 3 ‘
; — model-5.0V \\\
4 —--- modelOV " v\\ o
105 —-— model+5.0V \\““-°-\,‘
’ V -5.0V \ v I
:1 0V \\ 1
f 0 +5.0V \
. \
2
10 “ ”w ‘ ‘ ‘ ‘
1o2 103 1o4 105 1o6
Freq (Hz)
Figure 5.7 Continued.

132

Finally, the experimental results of BC4 are ﬁtted with model that includes trap
state effect. As can be seen from Figure 5.8, although there are some ﬁtting improvement
in the plot at high frequency over that of simple circuit model in Figure 5.7, the model
still can not explain the admittance characteristics of BC4.

In conclusion, we have compared the experimental results with three types of
models — (I) a basic model which only involves junction (C), R;) and bulk (CB, RB)
components, (II) a model which adds the effect of contact resistance RC, and (III) a model
which instead of RC includes deep trap state effects. Some of our sample’s small signal
responses can be generally represented by models given above (e.g. SK7-B). However,
the responses of other such as BC4 could not be explain by those three models. The
comparison between those models and the experimental results of SK7-B show that the
model with trap state effects give the best ﬁt to Cp, Rp, Cs and Rs among the three
models. However, it has been observed that the simulation results of model with contact
resistance (RC) and the model with trap state components (Cf ,Rf) gave a very similar
results in Rp, Cs, and R5 simulations. The difference between those two models is in the
results of Cp, which will not be observed if the experimental data are only taken in series
mode (Cs, Rs). This has in fact often been the case in the literature. Furthermore, since
the characteristics of both models are very similar, the real response of the diamond
Schottky barrier diode is possibly affected by both the contact resistance and the deep

trap state effects.

133

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10-9: f
’ — model - 5.0 V
- - - - model 0 V
’ — — model + 5.0 V
r V ' 5.0 V
-10 p 0 a O V ‘
q; 10 g o o o + 5.0 v g
s » ° .
(U l o .
E; i o ‘
0. r\ D an O l
0 -11 _ _ _ ° °
WE' —::::£\o 3
l —-~ :: T: — It’d—- —g- —— _~ \ \ ‘
’ ‘7 :- v': ? ‘v‘ 7 ‘ ‘¢--¢— ——-ﬁ--—-(
1
-12
1O ‘ ‘ “ ‘ ‘
1o2 103 1o4 105 1o6
Freq (Hz)
1010 5 ﬁ frﬁ T - - v".
"\ — model-5.0V i
K ---- modelOV 1
109{ \v — — model 4' 5.0 V
:5,
o.
o:
Freq (Hz)
Figure 5.8 Fitting between the Cp, Rp, Cs, and Rs experimental results

of BC4 and the model which include Glover’s element Cr and Rf. Here B

= 2.7x10'7 F/(cm2.secm).

134

Cs (Farad)

Rs (Q)

10‘8

 

 

 

 

 

 

 

 

 

E\
: \ .
t \ — model-5.0V
: o \ ---- modelOV .
g \ —— mode|+5.0V
I o v -5.0V
: oo\ :1 0V
I \o o +5.0V
.. \
: a a \\ 0
° 0 \

r---—-——-------2-:u.. ;

: c 77 = r v ““-—--3 3.:
o2 103 104 1o5 106

Freq (Hz)

 

 

 

 

model - 5.0 V
model 0 V
model + 5.0 V
- 5.0 V

 

 

 

 

 

 

 

Freq (Hz)

Figure 5.8 Continued.

135

5.4 Application implications of the small signal results

In the previous sections of this chapter, the focus has been primarily on the
implications of the small signal results on diode models. However, diodes are also used
for small-signal electronic applications. When reverse biased, they are used as small-
signal, voltage-variable capacitors, or varactors. When forward biased, diodes may be
used as small-signal, voltage-variable resistors, or varistors.

In terms of using the diamond Schottky barrier diodes as forward-biased varistors,
Figure 5.3 which represents the results for a sample on ﬁlm SK7, one of the faster diodes
in the study, shows a signiﬁcant bias dependence of the small signal resistance Rp well
beyond 100 KHz. For example, at 200 KHz, the small signal resistance is approximately

700 KQ at zero volt bias, 350 K!) at 2.5 volt bias, and 200 KQ at 5 volt bias, decreasing

with forward bias as expected. By 1 MHz, however, the varistor action is largely lost.

As for the use of diamond diodes in this study as varactors, Figure 5.2 shows that
sample BC4 shows appreciable reverse bias variation, decreasing with increasing reverse
bias, for frequencies up to about 10 KHz. For sample SK7, the capacitance variation is
more complex, as previously discussed, with non-monotonic variations of capacitance

with voltage. Speed limitations are discussed in more detail in the next chapter.

136

CHAPTER 6
Large signal response of diamond

Schottky barrier diodes

6.1 Chapter overview

This chapter presents the results of investigations on the large switching signal
response of the diodes. The ﬁrst two sections of this chapter discuss the effects of load
resistances and the coaxial connecting cables which give rise to a signiﬁcant parasitic
capacitance in the measurement setup. These parasitic capacitances are incorporated into
the SPICE model. The experimental results are then presented and compared to the
SPICE simulation results. Next, the sensitivity of the SPICE simulation results to changes
in transit time parameter of the diode are considered. The ﬁnal two section in this chapter
discusses possibilities for improving the rectiﬁcation frequency limit or “speed” of the

diamond Schottky diode by mean of area scaling and material doping.
6.2 Measurement circuit considerations

To study diode responses to a large switching signal, basically, we can pass

switching signals between forward and reverse bias from a function generator to the

137

Schottky barrier diode, then, probe the output responses by an oscilloscope. However,
there are some circuit considerations needed before the data be presented. Figure 6.1
illustrates the measurement circuit used to obtain the measurement results from the setup

in Figure 3.10.

 

 

 

 

 

 

 

 

 

 

diode coaxial coaxial
under test cable-2 cable-1
detecting
probe
:21 m, R R __C
“iglbteI resistance L OSC —" OSC
function p
generator
oscilloscope
Figure 6.1 Measurement circuit for large switching signal

responses experiments.

In Figure 6.1, RL represents the load resistance used in the setup to adjust the
effective input impedance of the oscilloscope. To appreciate the effect of this RL, let us
ﬁrst consider the HP 54200D oscilloscope without any load resistance RL. The
oscilloscope is connected to the detecting probe via a SO-Q coaxial cable. The
oscilloscope speciﬁcation indicates its input impedance as a 1 M Q resistance in parallel
with a 14 pF capacitance. However, the effect of the coaxial cable-l , as will be described

in the next section, is to cause the effective value of input impedance at 10 KHz to be a 1

138

MQ resistance in parallel with a 112 pF capacitance. The RC time constant of these input
components is then approximately 112 us which is even larger than a 100 us full period
of a 10 KHz signal. Figure 6.2 (a) shows the effect of this large time constant for a 10
KHz input, in which the diode plus the RC components basically act as an ac to do
converter, with a ripple voltage. This precludes observation of diode switching action.

By introducing an appropriate load resistance, RL, into the measurement circuit,
this large RC time constant can be reduced to give less effect on the circuit responses.
Figures 6.2 (b) to 6.2 (e) show the experimental results when RL values of 200 KQ, 51
K9, lOKQ, and 2.01KQ were used with sample BC4. It can be seen in Figure 6.2(b) to
6.2 (d) that as expected, the lower the value of load resistance RL, the less effects of the
input RC are noticed. However, the response while using a 2.01KQ load resistance in
Figure 6.2 (e) does not show signiﬁcant differences in shape characteristics from the
response while using 10K!) load resistance in Figure 6.2 (d). At this point, another issue
needs to be addressed, which is the lower the value of RL, the weaker the response signals
detected by the oscilloscope. This is simply due to the voltage division resulting from
high bulk resistance of the diamond samples. Although similarity in shape of response is
observed when using lOKQ and 2.01KQ load resistance values, the response is much
weaker and exhibits much higher noise when using the 2.01KQ load resistance.
Therefore, a load resistance of 10 KS2 was used in sample BC4 experiment.

By using the same consideration as above, an appropriate value of RL could be
established for other samples. The suitable RL for other samples used in this research was

found to be between 10 K0 and 50 KO.

139

588 mV/dlv 28.8 us/dlv
'f—;—.= 2 5,.-:—““¥§

 

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

 

 

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

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

 

 

 

 

 

.............................................................................................................. .
(a)
288 mV/dtv 28.8 us/div
...................... f.*_hv-'.~_—:-"
: ,r‘ : ‘1, : 1..“ ”L :
3.“ ' i‘ 5.." ‘1 i
..................... ux_1‘.'i‘..
if I ."E \S
..' : ‘ : J." ' ‘1
............. _..r.*.._.."1
_—‘ t 1.. : .1."- "‘_~_
_£—‘ ; -1%}r- 5 =
8.88 V I ‘
l. .............................................................................................................
........--.......................~...........s...-. .u..‘. .p.:...--hu........-.......-.u.: ..................... 4

 

 

 

Figure 6.2 Responses of BC4 to a 2O-Vpp lO-KHz sine wave with (a) no load

resistance, (b) 200 K!) load resistance, (c) 51 KO load resistance, ((1) 10 KS)

load resistance, and (e) 2.01 KQ load resistance.

140

188 mV/div ‘ 28.8 us/dlv

.-'“—.
.

 

38.8 mV/dlv 28.8 1v

 

(d)

7.58 mV/dlv

 

(0)

Figure 6.2 continued

141

6.3 Effects of connecting cables and load resistance in the measurement circuit

In dc or low frequency testing, normal laboratory practice usually neglects the
effects of connecting cables between probes and the measurement equipment. As the
frequency of operation is increased, however, connecting cables can have marked effect
on the sample under test. In the large signal test part of this research, two coaxial cables
were utilized; one to connect from the detecting probe to the load resistance and another
from the load resistance to the oscilloscope as shown in Figure 6.1.

To account for the effects of these cables, we begin by considering the simple
cable system shown in Figure 6.3. At dc and very low frequencies, the input impedance
Z, would be equal to load resistance 2,. This is simply the expected behavior of a pair of

wires from a circuit point of View [125].

 

 

 

 

 

 

 

l
——————————— ’\
lo,-
Zi—> ___________ '3’
C - Zr
Ci
21 —>
Rin ﬁtCm

 

 

 

Figure 6.3 Coaxial cable circuit.

142

However, as frequency is increased, the coaxial cable in Figure 6.3 should be
viewed as a transmission line terminated with load 2,. For the case of a lossless cable
under sinusoidal excitation the relationship between Zr and Z, for a cable of length I is

given by [125] [126]

z, =z.,[Z'+j.Z"ta“‘”"’] (6.1)
Z() + JZr tanCBl)
where Z0 is the characteristic impedance of the cable, and ,6 is the propagation constant.
If vP is deﬁned as the speed at which an electromagnetic wave propagates along the

cable, and f is the frequency, the value of ,6 can be found from

 

ﬂ = — = (6.2)

If vc is the velocity of light, the coaxial cable vP value can be calculated from its

dielectric value of polyethylene medium a: 2.25 80 and ,u = ,uo as [125] [127]

1
\/2'25 ' Emuo

 

= 0.68-v(. (6.3)

v,,

For a l-meter SO-Q coaxial cable connect to a IMQ (shunted by 14 pF) oscilloscope, at
10 KHz measurement frequency, B = 1.54x10'5 m". The effective input resistance Rin and

capacitance Cin can be calculated from

143

 

I

Z _509 (mm/14m?)+SOo.jtan(1.54,10—s)
i 500+(1MQ//14PF)-jtan(1,54.10-5)

to be 1060 and 112 pF respectively.

Let us consider our measurement circuit interpretation shown in Figure 6.4. As
can be seen from the circuit, the impedance Zosc of the oscilloscope can be calculated
from the parallel circuit of oscilloscope load value Rose and oscilloscope shunt
capacitance Cosc- Equation 6.1 then can be applied to give the input impedance Z. as

observed “looking in” form the ﬁrst coaxial cable

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l l
-—--——,\ / ------ i
'r H
22 _+ ————— 4] z1 _, ————— —\ J
C . ' RL - . Rosc :Cosc
coaxral coaxral T
cable-2 cable-1
of
22 —->
Rin ::Cln

 

 

 

Figure 6.4 Circuit interpretation of the two coaxial cables used in

the large signal response measurement.

144

 

Zl = 20(2051' +120 tan(;81)] (6.4)
Zn + IZusr' tan(ﬂ ' 1)

Equation 6.1 can also be applied to give the input impedance 22 as “looking in” from the

second coaxial cable

22 = 20(21, +./:Z() tan(ﬂl)] (6.5)
Zn +JZL tamﬂ")

Here, the value of Z2 is calculated from the parallel combination of the additional load
resistance RL and input impedance Z. from the ﬁrst cable. To utilize the result of 22 in
our later simulation process, the equivalent circuit resistance Rin and capacitance Cm can
be obtained from real and imaginary part of Z; respectively.

For our measurement setup, the HP54200D oscilloscope Rose and Cosc are, as
noted, given as IMO and 14pF respectively. Two 1.0-meter RG-58/U coaxial cables are
used. These cables have a nominal characteristic impedance of 53.5 ohms [127]. With a

load resistance RL of 10 KO, at a test frequency of 10 KHz, the effective input resistance

Rin and capacitance Cm are calculated to be 9.901 KS2 and 197.2pF respectively. This
result shows that the combination of coaxial cables and load resistance will introduce 3
Significant amount of capacitance, which appears in parallel with the input of the

oscilloscope and must be included into our simulation model.

145

6.4 Experimental results and SPICE model comparison

As described in detail in section 3.9, the diode responses to a large switching
signal were studied by passing a 20 Vpp sine wave from a ﬁrnction generator to the
Schottky barrier diode. The output responses were then probed by an oscilloscope with
load resistance RL as in the circuit model of Figure 6.1. All measurements were

conducted in the light-tight box. The experimental results at difference input frequency

will be presented in this section in comparison to SPICE simulation results.

In SPICE simulation, the response of the diode under an ac signal is modeled not
only by the nonlinear current source described earlier in section 4.7, but also by diode
capacitances, which are voltage-dependent and represent the charge storage effects of the

junction. Table 6.1 shows the addition SPICE diode model parameters for the ac

 

 

 

 

 

 

simulation.
SPICE Compared Parameter description
parameter notation

CJO C10 Zero-bias junction capacitance

VJ Vb, Barrier potential or “built-in” potential
M Grading coefﬁcient

TT I'D Transit time

F C Coefﬁcient for forward bias depletion

capacrtance formula
Table 6.1 Additional SPICE diode model parameters for ac simulation.

146

 

SPICE models charge storage in diode with two distinct capacitive mechanisms
[26], which are (1) capacitive effect of the depletion region and (2) capacitive effect from
mobile carriers (diffusion capacitance). The depletion region capacitance follows the
simple approximation that the depletion region serves as the gap between “plates” of a
capacitor. The depletion region varies in thickness, and therefore the capacitance varies
with applied voltage. The approximation of depletion region capacitance in SPICE

implementation is given by
CJO

(FLY (6.1)
VJ

where CJO is the zero-bias junction capacitance value, V is the applied voltage, VJ is the

CJ=

junction barrier potential and M is the grading coefﬁcient. M varies between 1/2 for step
junction to 1/3 for linearly graded junction. The above equation is actually the same as
equation 2.10 with M equal to 1/2 for Schottky barrier diode.

Inspection of the capacitance equation 2.10 and/or 6.1 reveals that it predicts
inﬁnite capacitance for a forward bias, which is not the case for a real junction. For
practical reasons, SPICE uses a simple approach: for forward bias beyond some fraction
(set by parameter PC which by default = 0.5) of the value of VJ, the capacitance is
determined as the linear extrapolation of the capacitance at the departure.

In diodes with both majority and minority carriers, the charge storage due to
excess minority carriers injected across the junction under forward bias gives rise to
another capacitive effect in SPICE simulation, diffusion capacitance. This charge, and

therefore capacitance, is proportional to the total current injected across the junction. The

147

proportionality constant (SPICE parameter TT) between the current and the charge is a
time constant which represents the minimum time required to either store or remove the
charge. It is called the transit time of the diode [26]. The total charge Q in the region is

therefore
Q = device current x transit time

SPICE calculates the diffusion capacitance from the derivative of the above equation with

respect to bias as the following (see also equation 4.3)

diffusion capacitance = TT--——IS——EXP[—V——] (6-2)
N oVT N -VT

Figure 6.5 shows the circuit used to perform the SPICE simulation. It should be
noted that one disadvantage of the SPICE diode model is that SPICE neglects the effect
of the capacitance due to the bulk part of the thin-ﬁlm diode and does not include it into
its model parameters. Therefore, the element CB representing the bulk capacitance is
placed in parallel with the bulk resistance RB. Actually the bulk resistance of the diode
may be provided as one of the SPICE diode parameters, namely RS (see section 4.7).
However, to simulate both the resistive and capacitive effects of the bulk part, the value
of RS in the diode parameters is set to zero and the bulk resistance value is instead placed
into RB. Again, CB is calculated from the simple approximation of parallel plate

capacitance as in equation 2.14.

148

 

 

 

 

 

 

 

 

 

18. N. IK. ISR. NR
w, TT. CJO W
iii-l s
CB ~_ 3
CIN F“ : RIN
1 ‘
Figure 6.5 Measurement and simulation circuit for diamond

diode switching experiments.

In Figure 6.5 the elements RIN and CIN represent the combination of the load
resistance, coaxial cables and the oscilloscope input impedance as described in detail
earlier in section 6.3. The values of diode parameters - IS, N, RS (now RB), IK, ISR and
NR are obtained from dc current-voltage measurement as described in section 4.7. The
rest of parameters, which are VJ, TT, CJO and CB, are obtained by adjusting the
parameters to ﬁt the SPICE modeled results to the experimental results.

There are some considerations for what range of value of VJ, TT, CJO and CB
should be used in the simulation. As discussed in section 4.5, the barrier height value of
diode ((1)3) obtained from section 4.3 can be used as an upper bound limit and guide line

for the built-in potential VJ value. And since Schottky barrier diode operates as a

149

majority carrier device under low-level injection, small values (between 10'18 - 10'9
second) were ﬁrst be used for TT in the SPICE simulation. Also because the value of
both CJO and CB are only dependent on the depletion width W as in equation 2.8 and
2.14, one only needs to vary the value of W in the simulation to obtain both CJO and CB.
A limitation of the SPICE simulation is that CB is constant for a given simulation ren. In
fact, W changes with bias. This is accounted for in SPICE for CI but not CB. However,
as will be shown later in this chapter (section 6.7), CB does not play a dominant role in
the switching properties of the diode.

For the switching waveform of sample BC4 in Figure 6.6, the oscilloscope input
resistance and capacitance were 1 MO and 14 pF respectively. The load resistance was
10 KS), so the values of RIN and CIN within the test frequency of l KHz to 10 KHz are

approximately 9.901 K!) and 197 pF respectively. The dc current-voltage measurements
in chapter 4 on the diode indicated a bulk resistance RB value of 1.2 M0. The parameters
IS = 1.8 pA, N = 2.40, IK = 1.2 nA, ISR = 4.3 pA and NR = 3.06 were obtained from the
ﬁtting between the dc current-voltage experimental result and the dc SPICE simulation as
described in section 4.7.

When the values of VJ = 0.8 V, TT S 1 us, CJO = 10.86 pF and CB = 7.01 pF
were used in the SPICE simulation, a good ﬁt to the measured data was obtained within 1
to 20 KHz frequency range as shown in Figure 6.6. Given the ﬁlm thickness of 0.56 pm,
the values of CJO and CB given above correspond to the depletion width of 0.22 mm at
zero bias. Note that varying values of TT parameter from O to 1 us did not give

signiﬁcant difference in the SPICE simulation. This will be discussed in the next section.

150

 

0.12

Volt

 

 

 

 

 

 

 

 

boa—a ~~~ »——~:— ———'———
j I
0.12 . . .
0.0010 0.0015 0.0020 0.0025
Time (see)
(b)
0.12 f
l
0.08» e e 4— _ f A .-. 1—~
0.04, _— + ~ ' ___.“ - ' _- a
3: \ g.” ‘ .5: .
e 0...- a -. — x.
0.’ w" ."
0.044 e + ﬁe” e ——+—m—a
ooe~~~ ~ ~ — e L e—«
0.12 l .
0.0011 0.0013 0.0015 0.0017
Time (sec)
Figure 6.6 Switching responses of sample BC4 at (a) 1 KHz, (b) 4 KHz, (c) 10

KHz, and (d) 20 KHz. Thick solid lines represent experimental results. Thin lines

with circle marks represent SPICE simulation results.

151

 

0.12

 

 

 

 

0,03r.——w-_-m " _..: _L __. "fl. , A _~ _,
0.04-+ __,__ . .- .f‘ l L-
E 0+ .4. ~m" ‘3 - ._..,"-.L
0.04. g e W _ i 1?... g A
0.08»—-—- e a +-- av —--~- e —v T" ———.
40700055 000065 0.0(i075

 

0.12' -

0.08’ ;

 

0.04»

Volt

 

0 --*
-0.04‘

 

 

 

 

-0.08>— ,

 

 

 

0.12ﬁ -- J ,_,__-__[___r

5.75x10“ 6.00x104 6.25x10“ 6.503(10“ 6.75x10“
Time (sec)

 

Figure 6.6 Continued

152

6.5 Sensitivity of SPICE model to changes in transit time parameter TT

As previously mentioned in section 2.5, if an appreciable fraction of the forward
bias current in the Schottky barrier diode is due to minority carriers, then upon switching
to reverse bias, a reverse current flows while the excess carriers stored in the depletion
region are being swept out. This removal process of the excess minority carriers induces
a transit time and effects the response of the diode to the excitation.

Minority carrier storage is common in P-N junction diodes and is the cause of the
diode’s diffusion capacitance, which is added to the ordinary depletion region
capacitance when the junction is forward biased. Generally, in Schottky barrier diode,
one can assume no minority carrier storage, hence, no diffusion capacitance. In this case,
the capacitance of the Schottky barrier should simply due to that of space charge in the
depletion region. However, there are reports of minority carrier effects especially at high
forward current levels in some Si Schottky barrier. Also the response of few samples
under large switching signal in this study, such as BC4 in Figure 6.6, qualitatively
resemble that of minority storage effected to the sinusoidal excitation as previously
shown in Figure 2.15.

SPICE analysis can provide insight into whether the similarity between responses
of diodes in this study such as in Figure 6.6 to that of Figure 2.15 is the evidence of
minority carrier storage effect in diamond Schottky barrier diode. In SPICE analysis of
the switching responses of sample BC4 at 4 KHz as shown in Figure 6.7, the parameter

TT representing transit time in the diode is varied while all other parameters are ﬁxed.

153

Figure 6.7

Volt

Volt

0.12

 

 

 

 

 

 

 

 

 

 

0.08
0.04
or
I
004' o 7‘ .
\
\ I
-0.08 ‘08"
- .12 A
0.0011 0.0013 0.0015 0.0017
Time (sec)
(3)
0.15 e
o/
0.10 ' I
0.05»
0 ‘II 101'
. ,-/° 1T 5 1E-6 / , .)
-0.05’. ,d; d4 TT-1E5 m
I dIdi’l E“ Fiﬁ/[V - - dF-i //
0.101: / TT=1E-4 \f’ ,I i\ ,9
\j \OMJ/ bvo/
- .15 A A A A e
5.75x10" 6.00x10‘ 6.25x10‘4 6.50x10“ 6.75x10“
Time (see)
(b)

SPICE simulation results of sample BC4 at (a) 4 KHz and (b) 20 KHz.

The values of parameter TT are varied between 0 to 10'4 second while all other

parameters are kept constant as the following: IS = 1.8 pA. N = 2.40, RB = 1.2M Q, IK =

1.2 nA, ISR = 4.3 pA, NR = 3.06, VJ = 0.8 V, CJO =10.86 pF and CB = 7.0] pF

154

From the SPICE analysis in Figure 6.7, it is observed that with the values of TT
less than 1 us, there is no signiﬁcant different in the results of the simulation. This means
that even if the minority carrier storage exists in the diamond Schottky barrier diode, the
effects of its diffusion capacitance will not be observed in our KHz experiment unless the
storage time of the actual Schottky barrier diode is larger than 1 us. Compared to Si
Schottky barrier diode in which the storage time in range of ns are reported, it is unlikely
that diamond Schottky barrier diode will have storage time larger than 1 us.

Therefore, the similarity between our experimental results and that of Figure 2.15
should not be because of the effects of diffusion capacitance and is not an evidence of
minority carrier storage. In fact, the switching response characteristic appearance of BC4
was also found in other samples in this research. To measure the minority carrier storage
in Schottky barrier diode, one usually needs to perform the reverse-recovery experiment
[29][65][128][131][132][133] on the diode at much higher frequency than KHz range.
However, such experiments were not investigated further in this research since at
frequencies higher than KHz range, most of our sample no longer yield a good rectifying

capability as in Figure 6.6 (c) and (d) for sample BC4.

155

6.6 Area scaling effect on switching signal response of diamond Schottky diode

From the experimental results in Figure 6.6, sample BC4 shows good rectiﬁcation
at 1 KHz (or less) but does not at appreciably higher frequencies. This section explores
the role of diode area on switching performance. The area scaling effect on the switching
signal response of the diamond Schottky diode was studied as shown in Figure 6.8 and
6.9. The diodes in Figure 6.8 and 6.9 were fabricated on the same diamond ﬁlm under
identical process but one with the contact area of 4.91x10'4 cm2 (SK7-Y) and the other
with contact area of 4.45x10'2 cm2 (SK7-C).

For the switching waveform of diodes in Figure 6.8 and 6.9, the oscilloscope
input resistance and capacitance were 1 M0 and 14 pF respectively. The load resistance
of 10 KS) was used in the measurements. From the result in Figure 6.8, diode SK7-Y
with contact area of 4.91x10'4 cm2 shows good rectiﬁcation up until 4 KHz but does not
at higher frequencies of 10 and 20 KHz. Interestingly, the same rectiﬁcation frequency
limit was also obtained from diode SK7-C with larger contact area of 4.45x10'2 cm2 as in
Figure 6.9. The response results of Figure 6.9 are very similar to those of Figure 6.8. The
different is the amplitude of the responses in Figure 6.9 is in the order of hundred times
larger than that of Figure 6.8. From the above results, it is shown experimentally that we
do not successfully improve the rectiﬁcation limit or “speed” of the diode by making the
contact area larger or smaller.

To study the area scaling effect on switching signal response of diamond Schottky
diode by SPICE, we ﬁrst ﬁt the SPICE simulation results to the responses of SK7-C with

contact area of 4.45x10‘2 cm2 at various frequencies as shown in Figure 6.10.

156

18.88 mV/dlv 58.8

18.88 mV/dlv

 

(b)

18.88 mV/div 18.8

 

(C)

Figure 6.8 Switching signal responses of diode SK7-Y with contact

area of4.91x10“‘ cm2 at (a) 4 KHz, (b) 10 KHz, and (c) 20 KHz.

157

1.25 V/dlv 58.8

 

1.25 V/dlv 28.8

 

(b)

1.25 V/dtv 18.8

 

(C)

Figure 6.9 Switching signal responses of diode SK7-C with contact

area of 4.45x10'2 cm2 at (a) 4 KHz, (b) 10 KHz, and (c) 20 KHz.

158

For the switching waveform of sample SK7-C in Figure 6.10, the oscilloscope
input resistance and capacitance were 1 M9 and 14 pF respectively. The 10 KS) load
resistance was used in the measurement. The values of RIN and CIN within the range of
test frequency are again calculated to be 9.901 K!) and 197 pF respectively. The dc
current-voltage measurements on the diode (with an area of 4.91x10‘2 cmz) indicated a
bulk resistance RB value of 17.95 KQ. The parameters IS = 48 nA, N = 4.47, IK = 400
nA, ISR = 351 pA and NR = 19.98 were also obtained from the dc current-voltage
experiment. Although, there was some discrepancy between experimental and SPICE dc
results (see Figure 4.21), when the values of VI = 1.8 V, TT 5 1 us, CB = 270 pF and
CJO = 177 pF were used in the SPICE switching signal simulation, a good ﬁt to the
measured data was obtained within 1 — 20 KHz frequency range as shown in Figure 6.10.

The values of above parameters are then used as a basis for SPICE simulation on
area scaling effect on large switching signal responses of diamond Schottky diode.
Assume that we decrease the diode area by factor of 100. For smaller diode areas, the
values of N, NR, VJ and TT are assumed unchanged. For smaller area diode, values of
IS, IK, ISR, CJO and CB are reduced by factor of. The values of RB are also increased by
factor of 100 for small area diode. The simulation results of the diode responses under 4

KHZ and 20 KHz are shown in Figure 6.11 and 6.12.

159

 

 

 

 

 

(b)

 

5.0

 

-2_5.— a a. a- A .L. Lam. L

 

 

 

__,
l

50 l

0.00015 0.00030 0.00045 0.00060 0.00075

Time (see)

Figure 6.10 Switching responses of sample SK7-C with contact area of 4.45x10'2
cm2 at (a) 1 KHz, (b) 4 KHz, (c) 10 KHz, and (d) 20 KHz. Thick solid lines represent

experimental results. Thin lines with circle marks represent SPICE simulation results.

160

(C)

5.0

 

 

 

 

 

_252 A e A v A AM”— —
l
-5.0 . 1
0.0001 0.0002 0.0003
Time (sec)
(d)
5.0

 

 

 

 

 

_5_0 l l .
0.00003 0.00006 0.00009 0.00012 0.00015

Time (see)

Figure 6.10 continued

161

 

0.06 ’

0.03

 

Volt
0

-0.03 ’

-0.06 *

 

 

 

0.00015 0.00030 0.00045 0.00060 0.00075

Time (sec)

(8)

 

5.0 -

 

Volt

 

 

 

-2.5
-5.0 ‘ * *
0.00015 0.00030 0.00045 0.00060 0.00075
Time (sec)
(b)

Figure 6.11 SPICE simulation results at 4 KHz based on the
properties of diode SK7-C when diode areas are (a) 4.45x10'4 cm2, and

(b) 4.45x10'2 cmz.

162

 

0.061

003*

 

Volt
0

-0.03‘

-0.06’

 

 

 

0.00003 0.00006 0.00009 0.00012 0.00015

Time (see)

(a)

 

Volt

 

 

 

 

-2.5
-5.0 ‘ ‘ ‘
0.00003 0.00006 0.00009 0.00012 0.00015
Time (sec)
(b)

Figure 6.12 SPICE simulation results at 10 KHz of diode SK7 with

diode area of (a) 4.45x10'4 cm2, and (b) 4.45x10'2 cmz.

163

The results of SPICE analysis in Figure 6.11 and 6.12 verify that changing the
diode bulk resistance by scaling the diode area do not signiﬁcantly improve the speed
response of the diode. The results of plot (a) and (b) in both Figures 6.11 and 6.12 are
very similar in term of frequencies limitation even thought the area of diode in plot (b) is
100 times larger than that of plot (a).

The experimental and SPICE simulation results on area scaling suggest that speed
response of the diode is limited by RC time constant consideration, where R decreases
with area and C increases with area. Considering the bulk material, RB = pL/A and CB =
eA/L such that the RC time constant is p3, the dielectric time constant. Here, all of the
parameters have usual meanings; p is the resistivity, and a is the dielectric constant of the
diamond material. This dielectric time constant can only be reduced by reducing p, i.e. by
doping the diamond. The next section of this chapter will explore the possibility of
improving the rectiﬁcation frequency limit or “speed” of the diamond Schottky diode by

means of doping.

164

6.7 Anticipated doping effects on the switching performance

The effect of doping on diode frequency response was not studied experimentally.
However, as described in this section, simulation studies were used to assess potential
improvements in diode switching response that could be achieved by doping. Such
doping should ideally be only in the bulk part of the device, since it is desired to keep the
space charge layer unchanged. If the entire ﬁlm were doped, than the space charge layer
would become thinner, increasing the junction capacitance and eventually also the
leakage current due to tunneling. The best diamond Schottky diodes reported so far were
achieved by multi-layer growth of CVD diamond thin ﬁlm [16][59][124].

Considering the simulation model for the diode, there are two potential beneﬁts
for doping the bulk portion of the ﬁlm. One is that for a given ﬁlm thickness, RB would
be reduced. Another is that by increasing the ﬁlm thickness, CB could be reduced for a
given RB. This section explores the two possibilities. In both cases, it is assumed that the
bulk portion of the ﬁlm has been doped such that the resistivity is decreased by two
orders of magnitude. In the ﬁrst case, the bulk portion of the ﬁlm is increased in thickness
such that R3 is the same as for the undoped case, but CB is reduced essentially by a factor
of 100. In the second case, the ﬁlm thickness is kept the same such that R3 is reduced by
two orders of magnitude, but C3 remains the same.

For this study, we ran SPICE simulation based on properties of sample SK7-C
with a contact area of 4.45x10'2 cmz. From section 6.6, the best-ﬁt values for each
parameter are then the following; IS = 48 nA, N = 4.47, IK = 400 nA, ISR = 351 pA, NR

= 19.98, RB = 17.95 KQ, VJ = 1.8 v, CB = 270 pF and CJO = 177 pF. Figure 6.13

165

shows the SPICE simulation response of SK7-C to a lO-Vpp 20-KHz signal while using
TT = 1 ps and the load resistance of 10 K0.

Now, assume that we dope the bulk portion of the diode such that the resistivity is
decreased by two orders of magnitude but we also increased in thickness of the bulk part
by two orders. Let us call this sample - hypothetical diode-A. For this diode-A, the value
of RB is still maintained at 17.95 KQ, while CB is reduced essentially by a factor of 100
to 2.70 pF. Also, the values of all other parameters are still the same as in previous
paragraph. The response of such diode to a 10-Vpp 20-KHz signal is shown in Figure

6.14(a).

 

Volt

 

 

 

 

030003 0.00006 0.00009 0.00012 0.0001 5
Time (see)
Figure 6.13 A SPICE simulation result of diode SK7-C with a diode area
of 4.45x10'2 cmz. The input signal for the simulation is a 10-Vpp 20-KHz
sinusoidal waveform. The l-MQ /14-pF oscilloscope is in parallel with 10

KO load resistance.

166

Next, suppose we fabricate another diode, hypothetical diode-B, without changing
thickness of bulk portion of the diode. In this second case, the value of RB would reduce
to 179.5 (2 while the value of CB would maintain at 270 pF. The 179.5 Q bulk resistance
in our diode would correspond to a resistivity in order of 104 Q-cm, which is very
achievable in d0ped CVD diamond. The lowest resistivity for doped diamond reported so
far is between 10'2 -10'3 Q-cm [12] [49] [95]. The response of the second diode to the
same lO-Vpp 20-KH2 signal is shown in Figure 6.14(b).

It is shown by the simulation in Figure 6.14(a) that reducing CB while
maintaining RB (diode-A) does not signiﬁcantly change the speed response of the diode.
In fact, the response in Figure 6.14(a) is similar to the response of the undoped diamond
ﬁlm SK7-C in Figure 6.13. On the other hand, the response of diode-B in Figure 6.14(b)
shows both amplitude and speed improvement over that of undoped diode SK7-C.
Therefore, the potential advantages of doping are primarily in reducing RB not CB.

As noted earlier, diode SK7-C showed good rectiﬁcation up until 4 KHz but does
not at higher frequencies. Figures 6.15 and 6.16 show how the doped diode-B response
to higher frequency signals, compared to SK7-C. In order to see the performance
advantage more clearly, the load resistances in Figure 6.15 and 6.16 were reduced to 50
0. This mainly to reduce the time constant associated with the measuring setup (Rm-Cm,

see section 6.2).

167

 

 

 

 

 

.4 a . P
0.00003 0.00006 0.00009 0.00012 0.00015

 

Time(sec)
(a)
10 A A . A A A A A5 . A

1

1

5L 1
r
l
E 0
-5.

 

 

 

-10 e e A
0.00003 0.00005 0.00009 0.00012 0.00015

Time (sec)

0?)

Figure 6.14 SPICE simulation results of two hypothetical diodes based on

properties of SK7-C but with the difference in (a) CB = 1/ 100 of that of SK7-

C, and (b) RB = 1/100 of that of SK7-C .The input signal for the simulation is

a 10-Vpp 20-KHz sine wave. The load resistance RL is 10 K0.

168

 

0.1'

 

 

 

§ 0
-0.1 .
l
0.8x10'5 1.2x10‘5 1.6x10‘5 2.0x10'5
Time (sec)
(2!)
2

 

 

Volt

1 1

 

 

 

-2 A A A A
0.8x10'5 1.2x10‘5 1.6x10'5 2.0x10'5

Time (see)

(b)

Figure 6.15 SPICE simulation results of (a) SK7—C, and (b) a hypothetical
dOped diode with RB = 1/100 of that of SK7-C.The input signal for the

simulation is a 10-Vpp ZOO-KHZ sine wave. The load resistance RL is 50 Q.

169

 

0.2 - - - - -

 

 

 

 

 

§
1
-0.2 AAA A AAAA AeAA-A
0.9x10‘5 1.0x10’5 1.1x10'5 1.2x105 1.3x10'5 1.4x10‘5
Time (see)
(a)
2 a ﬁ a 2 ﬂ f a
’5
>

 

 

 

 

-1 r
l
'2 15‘ ‘ i 2-55 ‘ i 815‘ A I 154 ‘ ITlst T -5
0.9x10 1.0x10 1.1x10 1.2x10 1.3x10 1.4x10
Time (see)
(b)

Figure 6.16 SPICE simulation results of (a) SK7-C, and (b) a hypothetical
doped diode with RB = 1/ 100 of that of SK7-C.The input signal for the

simulation is a 10-Vpp 500-KHz sine wave. The load resistance RL is 50 Q.

170

Figures 6.15 and 6.16 show the responses of diode SK7-C and diode-B to the 10-
Vpp ZOO-KHZ and the lO-Vpp SOO-KHz sine wave, respectively. With load resistance of
50 Q in both cases, the value of Rm and Cm were found to be 49.99 Qand 92 pF,
respectively. Also, the diode parameters in the simulations were set at IS = 48 nA, N =
4.47, IK = 400 nA, ISR = 351pA, NR =19.98, VJ =1.8 V, TT = 1 ps, CB = 270 pF and
CJO = 177 pF. However, the value of RB was 17.95 K!) for diode SK7-C and 179.5 for
diode-B.

In Figure 6.15(a), diode SK7-C does not show good rectiﬁcation performance to
the 200 KHz signal. Compare to SK7-C, diode—B in Figure 6.15(b) shows signiﬁcant
improvement in the signal rectiﬁcation. Similar result is found as shown in Figure 6.16
for 500 MHz input signal. At several MHz, however, even the doped diode—B does not
rectify well. Further simulation showed that this is the case even if the doping is reduced
ﬁrrther. The reason for this is that the switching speed is now substantially effected by Rt"
and Cm of the measurement circuit, also, the relatively large junction capacitance
associated with these diodes becomes an issue. For higher speeds a low resistance, low
capacitance measurement circuit combined with small area diode would be desired.

In summary, the speed limitation of diamond Schottky barrier diodes in this study
is the result of high bulk resistance of the undoped diamond ﬁlm. As shown by the
simulation in this study, doping the diamond ﬁlm and constructing diodes with a lower

RB would signiﬁcantly improve the switching performance or “speed” of the diode.

171

CHAPTER 7

Summary and future work

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

In this research, ohmic and rectifying contacts, and consequently Schottky barrier
diodes, were successfully formed on undoped polycrystalline CVD diamond ﬁlms
deposited by microwave plasma-assisted deposition. It was found that increasing the CH4
concentration in the diamond ﬁlm grth process does not reduce the resistance of the
diode beyond a CH; concentration of 2.5 - 4 %. The results of do current-voltage
measurements are well modeled by SPICE analysis. The diode parameters extracted from
the dc analysis were used in the frequency-related part of the research.

The small signal responses in term of capacitance and resistance of diamond
Schottky barrier diodes were investigated in the frequency range from 100 Hz to 1 MHz
at various voltages under both forward and reverse biases. The capacitance and resistance
results were modeled over the above frequency range by three types of equivalent circuits
model. The frequency-independent elements from simple geometric considerations were
developed as the ﬁrst model. The contact resistance, although small enough to produce a

negligible voltage drop under dc or large switching signal measurements and claimed to

172

have marked effect under small signal measurement by few authors, was included into
the second model. The third model accommodated the effect of deep trap states as a
series combination of frequency-dependent capacitance and resistance into the simple
model.

It was demonstrated by model simulations that the frequency dependent properties
of diamond Schottky barrier diode under small signal measurement, beyond those
expected as a result of the samples geometric consideration, can be associated with
contact effects and/or deep trap states inside the diamond. Although the responses could
possibly be the combination of both effects, at this time, the results indicated that the
response is an effect of trap states in diamond.

Recent work by Liu [114][129] indicates an effect of surface states in boron-
doped CVD diamond Schottky diodes on the C-V results. They suggest that Glover [l9]
overlooked the effect of these surface states which gives a very strong inﬂuence at low ac
frequency. Although diamond samples in this study are not doped, it is a good idea to
give some attention to the effect of surface states and possibly incorporate into the diode
model.

The results from the large switching response measurements in this study are
believed to be the ﬁrst large signal data reported on polycrystalline CVD diamond
Schottky barrier diode. The responses of diamond Schottky barrier diodes to the test
frequency range up to 20 KHz are reported and well ﬁtted to the SPICE model analysis.
The experimental and SPICE analysis suggest that speed response of the diamond
Schottky barrier diode is primarily limited by the large bulk resistance of the diode. The

reduction of bilk resistance of the diode by changing the contact area in order to improve

173

speed response of the diode proved to be unsuccessful. The results shown by the
simulation in this study indicate that doping the diamond ﬁlm and constructing diodes
with a lower RB would signiﬁcantly improve the speed responses of the diode.

The next logical step would be to experimentally test diamond diodes fabricated
on doped diamond ﬁlms. However, an undoped diamond layer is crucial to high-quality
diamond Schottky barrier diode [130] apparently because a doped diamond layer has
sufﬁcient defects to reduce the space charge layer to the point where tunneling
contributions are non-negligible. The solution may be to grow a base layer of low
resistivity doped diamond, followed by undoped diamond, possibly in a quarter of a
micron thickness range. Such work would ideally be coupled with SIMS (secondary ion

mass spectroscopy) analysis to document the dopant proﬁle in the diamond ﬁlms.

174

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