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This is to certify that the
dissertation entitled
CVD DIAMOND PIEZORESISTIVE
MI CROSENSORS

presented by

Izzat Ibrahim Taher

has been accepted towards fulfillment
of the requirements for

Ph. D. degree in Electrical Engineering

 

 

 

Major professor

Date 11/3194

K,
MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

 

LIBRARY
Mlchlgan State
Unlverslty

 

 

 

PLACENRETURN ”Xbmmwmmfimmm
TOAVOIDFINESMImonubdonddoduD.

DATE DUE DATE DUE DATE DUE !
1"?“ 9029‘” OUT—7 20 002

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU loAnMIrmdlvoMloNEqnl Opportunlylm
W1

CVD DIAMOND PIEZORESISTIVE
MICROSENSORS

By

Izzat Ibrahim Taher

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Electrical Engineering

1994

 

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ABSTRACT

CVD DIAMOND PIEZORESISTIVE
MICROSENSORS

By

Izzat Ibrahim Taher

Diamond piezoresistive pressure, acceleration, and strain sensors can be uniquely
suited to chemically harsh, high radiation and high-temperature environments. The
piezoresistive effect in both polycrystalline and homoepitaxial chemical vapor de-
posited (CVD) diamond films was studied. The diamond films were produced by
hot filament CVD system. The piezoresistive gauge factors, measured at 300 °K are
in the ranges of 200 - 550 and 6 - 25 for homoepitaxial and polycrystalline p-type
diamond films, respectively. The gauge factor for polycrystalline films decreases with
decreasing resistivity but increases with increasing temperature.

A multisensor microchip, with a number of diamond test structures and a mini-
mum feature size of 5 pm, was designed and fabricated using a six mask process. The
chip employs diamond both as an electronic and a mechanical material. An array of
cantilever beams of various sizes ranging from 100 to 1500 pm in length, from 20 to
150 pm in width and 3 to 5 pm in thickness were fabricated.

The residual total stress of the diamond films was investigated as a function of

methane fraction in hydrogen with or without addition of carbon monoxide. It was
observed that the magnitude of the total stress for films deposited in the absence of
CO was very high in comparison with the samples deposited in the presence of CO.
This result indicates that by using CO in the gas mixture, it is possible to control

the type and magnitude of the total stress in the diamond films.

To

my parents, my wife, my brothers and sisters
and
to the memory of my grandparents and my father-in-law.

iv

my c
toda

 

ACKNOWLEDGEMENTS

In The Name Of Allah

 

Most Gracious, Most Merciful.

 

All praises be to Allah (soobhanaho wa taalah), the creator and sustainer of this
universe for providing me the strength and the patience to complete this work.

I owe my greatest thanks to my parents. They have always allowed me to make
my own decisions. They have worked hard and sacrificed much so I can be where I am
today. A very special thanks goes to my wife Saida Benromdhane, who helped keep
me going especially when it seemed like this dissertation would never get finished.
My deepest appreciation for her understanding and patience when I had to spend
long nights in the lab. Also—I am grateful for the support of my brothers Raafat, Ali,
Mouhammad and Houssein, my sisters Jomana, Silvana and Amal, my brother—in-law
and best friend Mahmoud Awada, my sister-in-law Souad Benromdhane and all of
my other relatives. I would like also to thank all my high school, undergraduate and
all friends back home in Lebanon for their encouragement.

V

for

Me

COD

Sham

C0111.

Cart

I would like to express my deep gratitude to my advisor, Dr. Mohammad Aslam
for his guidance and encouragement throughout my doctoral program. In addition to
Dr. Aslam, I also had the fortune of having a second excellent adivisor: Dr. Allen H.
Meitzler, from Ford Motor Company. Allen’s inspiration and enthusiasm have been
contagious.

I would also like to thank the members of my orals committee, Dr. Michael
Shanblatt, Dr. Timothy Grotjohn and Dr. Jeffrey Ledford for their time and their
comments. A very special thanks goes to Dr. Michael A. Tamor, Dr. Shaun Mc-
Carthy and Dr. Margherita Zanini for their valuable discussions. I would also like
to thank the members of my research group at Michigan State University for their
helpful discussions in particular, Nayef Abu—Ageel, Sondes Sahli, Dongsung Hong,
Syed Shahzaman and Saeid Khatami.

Many thanks also go to the group at Ford for the technical assistance. In particular
I wish to thank: Mr. George Saloka, Mr. Timothy Potter, Mr. Amer Samman, Mr.
Mark Sulek, Mr. Bill Vassell, Dr. Bruce Artz, Mr. Larry Cathey, Mr. Michael
Parsons, Edith Behringer and Mr. Ron Gilland. I also wish to thank Dr. Chuck
Eagen, Mr. Carlton Avant and Mr. Paul Ohtonen for mask fabrication, Georgianna

Purnell for low temperature oxide deposition, and Ronald Elder for SEM micrographs.

vi

LIS

 

 

 

LIS'.

 

 

TABLE OF CONTENTS

LIST OF TABLES x
LIST OF FIGURES xi
1 Research Motivation and Goal 1
1.1 Introduction ................................ 1
1.2 Objective of this Work .......................... 2
1.3 Organization of Dissertation ....................... 3

2 Background 4
2.1 Introduction ................................ 4
2.2 Sensor Background ............................ 4
2.3 Piezoresistive Sensors ........................... 9
2.3.1 Piezoresistive Coefficients .................... 11

2.3.2 Gauge Factor Expressions .................... 15

2.3.3 Explanation of the Piezoresistive Effect ............. 17

2.4 Diamond Properties ............................ 19
2.5 Diamond Technology ........................... 24
2.5.1 Chemical Vapor Deposition Methods .............. 28

2.5.2 Nucleation ............................. 30

2.5.3 Effect of Substrate Temperature ................. 31

2.5.4 Diamond Film Characterization ................. 32

2.5.5 Doping of Diamond ........................ 34

2.5.6 Patterning ............................. 37

2.5.7 Highly Oriented Films ...................... 39

2.6 Diamond Devices ............................. 41
2.7 Diamond Sensors ............................. 42
2.8 Summary ................................. 47

3 Diamond Film Technology 49
3.1 Introduction ................................ 49

vii

3.2 The HF CVD Deposition System .....................
3.2.1 Description of the System ....................
3.2.2 Operation of the System .....................

3.3 The Nucleation Method .........................

3.4 Diamond Film Patterning ........................

3.5 Effect of Deposition Parameters .....................
3.5.1 Effect of Substrate Temperature .................
3.5.2 Effect of Gas Composition and Flow Rates ...........

3.6 Doping of Diamond Films ........................

3.7 Homoepitaxial Doped Film ........................

3.8 Summary .................................

Design and Fabrication of a Multisensor Microchip

4.1 Introduction ................................

4.2 Microchip Design .............................

4.3 Metalization ................................

4.4 Microchip Fabrication ..........................
4.4.1 Undoped Diamond films .....................
4.4.2 Selectively Doped layer ......................
4.4.3 Metalization Steps ........................
4.4.4 Micromechanical Structures ...................

4.5 Intrinsic Stress in the Diamond Films ..................
4.5.1 Sample Preparation ........................
4.5.2 Results ...............................

4.6 Summary .................................

Measurement Techniques

5.1 Introduction ................................
5.2 Plate Bending System ..........................
5.3 Cantilever Beam Technique .......................

5.4 Summary .................................

Piezoresistive Effect of CVD Diamond Films

6.1 Introduction ................................

6.2 Polycrystalline Diamond Films ......................
6.2.1 Doping Dependence ........................
6.2.2 Temperature Dependence ....................

6.3 Homoepitaxial Diamond Films ......................

viii

49
49
52
53
61
67
67
69
71
77
79

80
80
80
82
90
91
93
93
93
101
102
102
106

107
107
107
108
112

113
113
113
116
116
120

 

 

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6.4 Diamond piezoresistance coefficients ................... 122

6.5 Discussion ................................. 125
6.5.1 Energy Band and Qualitative Model .............. 128

6.6 Summary ................................. 131

7 Summary and Future Research 132
7.1 fixture Work ................................ 133

A Piezoresistive Coefficient 134
B Gauge Factor Derivation 144
C Strain Analysis 148
D Sample Descriptions 154
BIBLIOGRAPHY 158

ix

2.1
2.2
2.3
2.4

3.1
3.2
3.3
3.4
3.5

4.1
5.1

6.1
6.2

D.1
D.2
D.3
D.4

LIST OF TABLES

Signal domains with examples of measurable parameters ........ 5
Physical effects for sensors in semiconductor material .......... 5
gauge factors for various materials in the longitudinal direction. . . . 10
Comparison of diamond properties and some commonly used semicon-

ductor materials. ............................. 23
Sample preparation for nucleation study ................ 54
Optimum processing parameters. .................... 71
Resistance measurements for one boron holder .............. 75
Resistance measurements for two boron holders. ............ 75
Resistance measurements for two samples. ............... 78
Stress dependence on methane concentration and carbon monoxide. . 104
Computed and measured strain ..................... 111
Diamond piezoresistance coefficients. .................. 122
Estimated Piezoresistive coefficients and gauge factors of HPIIT p-type

synthetic diamond. ............................ 124
Sample description after the deposition of the diamond films ...... .154
Sample description after the deposition of the diamond films ...... 155
Sample description after the deposition of the diamond films ...... 156
Sample description after the deposition of the diamond films ...... 157

2.1
2.2
2.3

2.4
2.5
2.6

2.7

2.8

2.9

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12

LIST OF FIGURES

Typical structure of a capacitive silicon pressure sensor .........
Typical structure of a piezoresistive silicon pressure sensor. ......
Layout of piezoresistors on the membrane (a) and Wheatstone bridge
circuit (b) for a typical piezoresistive pressure sensor. .........
Effect of the temperature on p-type silicon strain gauges. .......
Cross-section of constant energy for n-type silicon centered about EC.
A simplified and roughly drawn energy band diagram of p-type silicon
(a) zero stress and (b) with uniaxial stress ................
Thermal expansion coefficients of diamond and silicon as a function of
temperature .................................
Resistivity of poly-diamond film thermistors, measured as a function
of temperature (77 - 1273 K) for three doping levels. .........
Stress dependences of resistance of the semiconducting synthetic di-
amond doped with boron (p-type) in the (a) <100> and (b) <111>
directions (original plots). ........................

Schematic diagram of the deposition system ...............
SEM micrograph for sample G-la .....................
SEM micrograph for sample G-3a .....................
SEM micrograph for sample G-4b .....................
Surface roughness of sample deposited for a) 9 hours and b) 20 hours.
Effect of diamond film thickness on the surface roughness. ......

Schematic diagram of 3 configurations used for double-layer patterning.

SEM micrograph for diamond microchip prepared by Config-l .....
SEM micrograph for diamond microchip prepared by Config-2 .....
SEM micrograph for diamond microchip prepared by Config-3 .....
SEM micrograph for an array of resistors with different dimensions. .
Raman spectra for the samples deposited at different substrate tem-
peratures; a) 825 °C b) 890 °C c) 925 °C .................

xi

12
19

20

22

46

48

51
56
56
57
59
60
63
65
65
66
66

68

3.13 Raman spectra for the samples deposited at different hydrogen flow
rates. CH4 = 0.7 sccm and CO = 12 sccm for all samples. ......
3.14 Raman spectra for the samples deposited with or without CO .....
3.15 Schematic diagram of the boron holder ..................
3.16 Composite layout of the discrete-chip ...................
3.17 a) Boron powder holder b) Cross-section holder placed on silicon.
3.18 Raman spectrum of doped homoepitaxial films deposited on type 2a
diamond substrates (Dubbelldee Harris Corp., Mt. Arlington, NJ).

4.1 Composite layout of the masks. Resistors r; to r15 are used for piezore-

sistive and temperature measurements. .................
4.2 (a) Layout of mask 1 (undoped diamond), (b) Layout of mask 2. . . .

72
74
74
78

79

83
84

4.3 (a) Combined mask 1 and mask 2, (b) Layout of mask 3 (doped diamond). 85

4.4 (a) Layout of mask 4 (metal contacts), (b) Layout of mask 5 (metal
patterns). .................................
4.5 Layout of mask 6 (Sacrificial layer window). ..............
4.6 SEM micrographs for sample during the etch and before striping the
photoresist. Photoresist lines were pulled away from the substrate
surface. ..................................
. 4.7 Major fabrication process steps for the multisensor microchip. . . . .
4.8 SEM micrographs for a resistor (a) top view and (b) close-up view from
the microchip ................................
4.9 SEM micrographs showing doped diamond and SiOz (LTO) mask; (a)
top view, doped diamond (dark areas) and LTO (bright area), and (b)
close-up view, doped diamond (bright areas) and LTO (dark area).
4.10 SEM micrograph showing (a) array of cantileverbeam structures curled
upward ( 600 to 1500 pm in length, 150 pm in width and 4 pm in
thickness) (b) close up view of one of the beam. ............
4.11 SEM micrograph showing (a) array of cantilever beam structures (200
to 1200 pm in length, 20 pm in width and 4 pm in thickness) (b) close
up view of one of the beam. .......................
4.12 SEM micrograph of a bridge (z 8 pm in width, 100 pm in length and
4 pm in thickness); (a) top view and (b) side view (bridge does not
touch the substrate). ...........................
4.13 SEM micrograph showing an overview of the multisensor microchip. .
4.14 Convention showing (a) Compression (b) Tension ............
4.15 Dependence of the total stress on methane concentration. Data points
are for CO = 0.0 sccm (open circle) and for CO = 12 sccm (*).

xii

86
87

92

94

95

96

97

98
99
103

105

5.1

5.2

6.1

6.2

6.3

6.4

6.5

6.6
6.7
6.8

A.1
B.1

C.1

Schematic diagram of arrangement for strain measurements by plate

bending method. ............................. 109
Schematic diagram of arrangement for strain measurements of can-
tilever beam method ............................ 110

Fractional change in resistance (a) and gauge factor (b) as a function
of tensile strain in the longitudinal direction. ............. 115
Doping dependence of piezoresistance; fractional resistance change (a)
and gauge factor (b) as a function of strain, in the longitudinal direction.117
Fractional change in resistance of a polycrystalline p-type diamond
piezoresistor (a) and gauge factor (b) as a function of strain at different

temperatures. ............................... 1 18
Gauge factor as a function of temperature at 500 microstrains in the

longitudinal direction. .......................... 119
Strain dependence of the (a) fractional change in resistance and (b)

gauge factor of a (100)-oriented homoepitaxial diamond film ...... 121
Gauge factor of diamond and silicon as a function of strain ....... 126
Energy band structure of diamond. ................... 129
A simplified band diagram of diamond valance band; (a) zero stress

(b) under uniaxial stress .......................... 130
Euler’s angles used for axis rotation. .................. 140
Thin rectangular resistor .......................... 144

Schematic diagram for strain calculation (a) Cross section view of the
bending beam (b) Side view for element inside the dashed circle (c)

cross-section view front section (y,z) plane ................ 149

xiii

 

 

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CHAPTER 1

Research Motivation and Goal

1 .1 Introduction

Today, many sensors are based on silicon device technology. Many of these sensors
are piezoresistive. In contrast to an integrated circuit (IC), a sensor must be exposed
to its environment in order to function. The use of the piezoresistive silicon sensors
has been limited to dry, uncontaminated environments. In general, silicon devices are
not suitable for use in chemically harsh, high radiation and high temperature environ-
ments. Material technologies superior to silicon are needed for pressure, acceleration
and strain sensors to operate in such environments. A promising material for these
applications is diamond.

The high thermal conductivity, wide energy gap, chemical resistance, high dielec-
tric strength, radiation hardness, and moderately good carrier mobilities of diamond
make it an excellent material for use in sensors. However, natural semiconducting
diamond is generally p-type (type II-b) and is too expensive. Therefore, for the last
three decades a considerable amount of research has focussed on the development of
diamond synthesis methods. The major breakthrough occurred in the early 19808,
when Spitsyn et al. [1] deposited thin diamond films on diamond and non-diamond

substrates using a chemical vapor deposition (CVD) technique. This has attracted the

 

 

 

 

 

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interest of many researchers and has led to the fabrication of low cost, diamond-based
semiconductor devices.

Most present devices are fabricated with p—type diamond formed by introducing
boron either during deposition of the film or by ion implantation after the film is
deposited. However, none of the currently available techniques are suitable for the
introduction of donor impurities with reasonable activation energies to create n-type
semiconducting diamond. Given the tremendous difficulties in developing a com-
pletely new electronic technology, it is not surprising that no crystalline diamond-
based semiconductor devices yet demonstrated even approach the performance of
their conventional silicon equivalents. However, diamond passive devices do not re-
quire crystalline diamond or n—type doping. CVD polycrystalline diamond films can
be used for such devices.

1.2 Objective of this Work

The focus of this work is to study piezoresistive properties of CVD diamond films. In
view of a huge application potential of diamond sensors, design, fabrication and test-
ing of a multisensor diamond microchip is undertaken. The chip contains a pressure
sensor, an accelerometer, a Hall structure, and a variety of other structures.

To overcome the limitation of silicon piezoresistive sensors, there is a definite need
for new sensors based on materials with properties that are superior to silicon. The
attractive and unique properties of diamond make it a viable candidate for sensors for
harsh environment applications. In order to realize the true potential of diamond as
piezoresistive material for strain gauges and micro sensor applications, high quality
doped and undoped diamond films are needed. The development of a technology
compatible with conventional Si fabrication technology, is also important. Therefore,

this work had the following objectives:

 

 

 

 

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ter
of

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in

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(I) Grow device quality poly-diamond films.
(2) Characterize the piezoresistive properties of p-type diamond films.

(3) Design and fabricate a diamond multisensor testchip.

1.3 Organization of Dissertation

A review of silicon-based and diamond-based sensors technologies is presented in
Chapter 2. After an overview of diamond film deposition methods, nucleation, pat-
terning and doping of diamond films are also presented. Mathematical derivation
of the piezoresistive coefficients and gauge factor is also described in this chapter.
Chapter 3 describes the deposition system, sample preparation and characterization.
Nucleation, patterning and doping methods used in this research and their results
are presented in this chapter. The next chapter describes the design and fabrication
of a multisensor diamond microchip. Fabrication of micromechanical structures are
also described in this chapter. Chapter 5 describes the measurement techniques used
in this research. The dependence of gauge factor on doping and temperature depen-
dence is presented in Chapter 6. Finally, Chapter 7 summarizes the results of this

study.

 

 

 

 

 

 

 

 

 

CHAPTER 2

Background

2.1 Introduction

In this chapter, an overview of the silicon and diamond-based sensors is presented.
Mathematical derivation of the piezoresistive coefficients and gauge factor is de-
scribed. Physical explanation of the piezoresistive effect in n-type and p-type silicon
is also discussed. Chemical vapor deposition methods of diamond film are described
in this chapter. Nucleation, patterning and doping of the CVD diamond films are

also presented.

2.2 Sensor Background

A sensor is a device that detects a change in a physical parameter such as temperature,
pressure, acceleration and light intensity and converts it into a signal which can be
measured, usually electrical (see Table 2.1) [2]. The most important effects for sensors
in silicon are shown in Table 2.2.

Solid-state sensors have seen rapid developments in the past two decades. The
key technology for this growth, is silicon micro-machining. Basically, silicon micro—

machining is used to fabricate precise three- dimensional silicon based microstructures

 

 

 

 

 

 

 

 

of
Tl

SU

Table 2.1. Signal domains with examples of measurable parameters.

 

Signal Domains Examples

Radiant signals light intensity, wavelength,
polarization phase etc.

Thermal signals temperature, temperature gradient,
heat, entropy etc.

Mechanical signals force, pressure, acceleration, flow,
vacuum, thickness, displacement etc.
Electrical signals voltage, current, electric field,
resistance, capacitance etc.
Magnetic signals field intensity, flux density,
permeability etc.

Chemical signals concentration, toxicity, pH,
reduction potential etc.

 

 

 

 

 

 

 

 

 

 

of great diversity, including thin diaphragms, microbridges and cantilever beams [3].
These micromachined microstructures combined with electronic circuits, have been
successfully employed to realize a large variety of solid-state sensors for measuring

most of the parameters listed in Table 2.1. The most popular mechanical structure

Table 2.2. Physical effects for sensors in semiconductor material.

I Physical Signals Effect
Radiant signals photovoltaic effect, photoelectric effect,
photoconductivity,

Mechanical signals piezoresistive J'ect, capacitive effect,
piezojunction effect, piezoelectric effect

lateral photoelectric and lateral photovoltaic effect
—Thermal signals Seebeck (fiat , temperature dependence of
conductivity and junctions, Nernst effect
Magnetic signals Hall effect, magneto-resistance

Chemical signals ion-sensitive field effect

 

II.—

 

 

 

 

 

 

 

 

 

 

 

has been
In lht

most suct

 

 

 

basically 1
The typic

schematic

has been the thin diaphragm. The diaphragm is preferred for most applications.

In the present development of various solid-state sensors, pressure sensors are the
most successful and account for a major portion of commercial market. There are
basically two types of monolithic silicon pressure sensors, capacitive and piezoresistive.
The typical structures of a capacitive and a piezoresistive silicon pressure sensors are

schematically illustrated in Fig. 2.1 and Fig. 2.2, respectively. Both types of sensing

Metal FIXBd Plate On-Chip Circuits

 

  
  
 

    
 

Silicon

 

\

Seal (Anodic Bonding)

Diaphragm
Reference Chamber

 

 

External Pressure

Figure 2.1. Typical structure of a capacitive silicon pressure sensor.

structures embody a thin silicon diaphragm formed by wet etching of the silicon wafer.
The silicon wafer is bonded to a glass substrate, normally a 7740 Pyrex glass wafer.

In the capacitive sensors [4], the front surface of the silicon wafer is anodically
bonded to the glass substrate. The thin silicon diaphragm and the metalization layer
on the glass substrate create a parallel plate capacitor. An applied pressure on the
diaphragm deflects it and causes a change in the diaphragm capacitance, which is
then detected by a capacitance readout circuitry and can be converted to a voltage

or frequency output.

Piezoresistors

w \\s
,_Z ‘ \ Silicon \

Glass Seal

 

 

 

 

 

 

 

 

 

External Pressure

Figure 2.2. Typical structure of a piezoresistive silicon pressure sensor.

In the piezoresistive sensors, the sensing elements are p-type diffused or implanted
resistors in the n-type diaphragm material. As the diaphragm is deflected by an ap—
plied pressure, the stresses induced in these resistors cause a change in their electrical
resistance (the piezoresistive effect), which is detected and is usually converted to
a voltage change by Wheatstone bridge circuit [5]. The bridge output voltage is
usually amplified and possibly temperature compensated by circuitry usually fabri-
cated on-chip with the sensor. The layout of piezoresistors on the membrane and the

Wheatstone bridge circuit are shown in Figure 2.3(a) and Figure 2.3(b), respectively.

The capacitive sensors are more sensitive, less vulnerable to temperature changes,
consume less power, but are inherently nonlinear in their pressure response and are
scaled poorly [4]. On the other hand, the piezoresistive sensors are easier to manufac-
ture, can be easily scaled down, have a more linear response and, as a result, require

less signal conditioning and cost less.

 

\\\\\\\\\
O

a)

 

 

 

 

 

b)

Figure 2.3. Layout of piezoresistors on the membrane (a) and Wheatstone bridge
circuit (b) for a typical piezoresistive pressure sensor.

 

 

 

2.3

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effect we.
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2.3 Piezoresistive Sensors

Currently, many micro-mechanical sensors are based on the piezoresistive effect in
silicon [6]. The piezoresistance effect is defined as the change in the electrical resis-
tance of a material due to the application of mechanical stress. The piezoresistance
effect was first discovered in 1856 by Lord Kelvin. In his experiment, he found that
the resistance of copper and iron wires increased when they were loaded in tension;
furthermore, he also noticed that the amount of change depended on the material.
Bridgman also studied the piezoresistive effect in single and polycrystalline metals
in the 1920’s [7, 8]. Additional work on the piezoresistive effect of many metals was
done in the 1930’s by Rolnick [9], Allen [10, 11, 12, 13] and Cookson [14]. These
effects are now used in the well-known, commercially marketed, metal wire and foil
strain gauges [15, 16].

The piezoresistive effect in semiconductors was first studied by C. S. Smith in the
mid 1950’s [17]. Smith measured the piezoresistance coefficients of germanium and
silicon, he found that the semiconductors exhibit piezoresistance coefficients much
higher than those of metals. Smith’s observations stimulated an increased interest
in the investigation of the effects of stress on other semiconductors [18, 19, 20, 21],
organometallic crystals and other materials [22, 23], and in the application of this
effect to micromechanical sensors [24, 25, 26, 27, 28, 29, 30].

A useful measure of piezoresistance is the gauge factor (CF), which is defined
as the fractional change in resistance 9i! per unit strain E. The magnitude of the
piezoresistive effect varies between different materials. Typical gauge factors for var-
ious materials in the longitudinal direction are shown in Table 2.3.

The magnitude of the gauge factor in some organometallic materials is large but,
they are not stable enough to be used in micromechanical sensors [22]. Consequently,

the use of these materials has not been as revolutionary as the use of silicon. How-

 

 

 

" Advanc
l Platinur
Nickel
. Platinu‘

Silver

. Copper
r§
' Semico

 

 

10

Table 2.3. gauge factors for various materials in the longitudinal direction.

 

 

 

 

 

 

 

 

 

 

 

 

‘ Material descriptions Gauge Factor (GF)
metals [16]
Composition, percent
Advance 45 Ni, 55 Cu 2.0 to 2.1
Platinum, Tungsten 92 Pt, 8 W 4.0
Nickel 100 Ni -12.l
Platinum 100 Pt 6.1
Silver 100 Ag 2.9
Copper 100 Cu 2.6
Semiconductors
Types
Single Crystal Silicon [17, 24, 31] p-type +100 to +175
n-type -133
Poly- Silicon [18, 19, 32, 33, 34] p-type 15 to 30
n-type ~30
Germanium [17, 24] p-type +48.7 to +101.5
. n-type -147 to -157
Poly- Germanium [34, 35] p-type +30
n-type -30 to -40
Indium-antimonide [24] -60.5
Silicon Carbide n-type‘ a-SiC (6H)[36] -55 to - 994
n-type B -SiC [37] - 26.6 to -31.8
n-type Poly-SiC [38] +5 to +10
Organometallic Crystals [22]
Strain (p6)
Magnus’Salt 500 500
Ir(CO)2acac 500 100
Thick Film Resistors [39, 40] Inks +8.2 to +123

 

 

 

ever, si
and big
attire a
temper
piezore
and th
These
In the
induce
voltag
and r:
juncti
Tl
mauy
range
COn p
limit
lSOlatj
ternp,
mm C
Howe-

Single

11

ever, silicon strain gauges are not suitable for chemically harsh, high radiation [41]
and high temperature environments [5, 42]. Figure 2.3 shows the effect of the temper-
ature on p-type silicon strain gauges [42]. The gauge factor decreases with increasing
temperature for low doping level. The operating temperature of diffused or implanted
piezoresistive silicon sensors is often limited to 100 or 125 °C. Since the diffused gauges
and the diaphragm have different types of doping impurities, they create p-n diodes.
These diodes must be reversed biased in order to channel the current into the gauges.
In the case of a dramatic increase in reverse current, its flow in the diaphragm may
induce stray voltage that are not easily controlled and may modify the bridge output
voltage. Therefore, silicon-based piezoresistive sensors in addition to the chemical
and radiation environment problems, can not operate over 125 °C due to the p-n
junction effect.

The piezoresistive effect of polycrystalline silicon films was also investigated by
many workers [18, 19, 33]. The gauge factor of the polysilicon films was found to
range from less than 10 to about 25 depending on the resistivity [19]. The polysili-
con piezoresistor offers the advantage of a potentially higher operating temperature
limit than diffused single crystal Si piezoresistor, because p-n junction piezoresistor
isolation is not required. Use of polycrystalline film resistors increases the operating
temperature range of the sensor to 200 °C. This is because the polysilicon piezoresis-
tors can be deposited on insulator layer, this is known as silicon on insulator (SOI).
However, the sensitivity of polycrystalline silicon piezoresistors is lower than that of

single crystal silicon resistors (see Table 2.3).

2.3.1 Piezoresistive Coemcients

The piezoresistive effect is defined as the change in the electrical resistance of a
material due to the application of mechanical stress or strain.

From a mathematical point of view, the effect of homogeneous mechanical stress

 

 

 

Ofll
of;

Hot

brit

Cur:

12

§

LIGHTLY OOPED < to"

3
0

5x0”

8

I
x to"

GAUGE (ACTOR

.‘t
i l

o l
-” ~‘O 0 ‘0 so IZO ISO zoo
TE¥°ERATURE IN DEGREES CENTIGRADE

       

Figure 2.4. Efl'ect of the temperature on p-type silicon strain gauges.

on the electrical resistance of a conducting crystal can be described generally in terms
of a set of constants. These constants are known as the piezoresistance coefficients.
However, in most practical cases the piezoresistive effect is characterized by the gauge
factor. The expressions for the piezoresistive coeficient and the gauge factor are
briefly derived next. More detailed derivations are given in appendix A and appendix
B for piezoresistive coefficients and gauge factor, respectively.

In a material subjected to stress X“, the electric field E,- is a function of the

current density J,- and stress X“ which can be written as [24, 30, 42].
E; = pg,‘ Jj + Wijlcl JJ' X“ i,j,l€,l = 1,2,3 (2.1)

where p;,- is the resistivity, and 1n,“ is the piezoresistive tensor. Equation (2.1) is

 

deriv

xijkl 1

Where
sistive
For lo

Same I

Where .

For

13

derived in appendix A Eq. (A.9). The stress can be written as

f

X; for longitudinal stress

Xkl = t X; for transverse stress (2-2)

 

X. for shear stress

L

In the case of crystals with cubic symmetry, such as diamond and silicon, m,“ is given

by [24]

p0 am if both J and X are in one of the {100} directions
p0 In if J and X are in one of the {100} directions but are perpendicular
to each other

Tim = t

 

\ po 13* for shear stress

(2.3)
where 111, rm, and tr“ are the fundamental longitudinal, transverse and shear piezore-
sistive coeficients, respectively [17]. p0 is the resistivity under zero stress.

For longitudinal case ( the current density and the mechanical stress are all in the

same direction, e.g. [100]), the piezoresistive coefficient is given by
$11 = £— —— (2.4)

where the subscript 1 denotes [100] direction, X1 = Xi.

For transverse case, the piezoresistive coefficient is given by
- 1
In — L—eg — (2.5)

In Eq. (2.5), the current density is assumed in [100] direction whereas the stress is in
[010] direction.

In arbitrary directions, following similar derivation as (2.4) and (2.5) the piezore-

 

 

 

 

sistive c

for uhit

for arbitr

ln arl
of the in

for t

30].

and for

where

F0! ra

EiV’en

l4
sistive coefficients can be written as

- ”1 " ”° 1 (2.6)

 

for arbitrary longitudinal direction and

 

7n ___ Pi - Po _L (27)
P0 X 2
for arbitrary transverse direction. The primed quantities refer to arbitrary direction.
In arbitrary direction, the piezoresistance coefficient can also be expressed in terms
of the fundamental piezoresistance coefficients and the direction cosines.
For the longitudinal case, the piezoresistance coefficient can be written as [24, 42,
30].

I] = In - 2(111 - W12 — 1r“)(lfmf + 1711271124" 1112112) (28)

and for transverse case, the piezoresistive coefficient can be written as
7": = 1r12+(7T11 —1ru—1r«)(lflf +mfmf+flfnf) (29)

where 1;, 1m, and n,- (i = 1,2,3) are the direction cosines of the transformation.
For randomly oriented polycrystalline films the longitudinal piezoresistive coefficient
can be estimated by averaging of 1n in Eq.(A.27) over all possible directions and is

given by [43]
“‘5‘ ""‘l 404
< n > ___ fo=oo=§f¢=o *1 45

0:0 155 we

where 0 and ¢ are the angles between the arbitrary coordinate system and the princi-

(2.10)

 

ple coordinate system aligned with the crystal axes. d denotes l and t for longitudinal

and transverse directions, respectively.

 

 

2.3.2 .

The mc

sistive g

which i

for lor.

15

2.3.2 Gauge Factor Expressions

The most suitable and practical quantity in microsensor applications is the piezore-

sistive gauge factor (CF), which is normally measured, and is defined by

AR 1
which for isotropic materials can be written as [24]
A 1
GR, = -—”— + (1 + 2y) (2.12)
Po 6:
for longitudinal direction (see appendix B equation (3.4)), and
P0 ‘1

for the transverse direction (see appendix B equation (B6)). In above equations V,
e; and p are the Poisson’s ratio, longitudinal strain and resistivity, respectively, and
Ap = p - p0. The subscripts i, l, and t refer to isotropic, longitudinal and transverse,
respectively. pa is the unstrained resistivity.

For an anisotropic homogeneous material, the gauge factor is given in terms of
the compliance coefficients 511, Sn and the longitudinal piezoresistive coefficients an

by [44, 45]

512 TI
GF = l - 2— + ___... 2.14
" 5.. Sn ( )
For diamond 511 = 0.09493 x10“: cmf/dyne, 5'12 = 0.00978 x10‘12 cmz/dyne
(monocrystal diamond), u as 0.07 and Young’ s modulus Y = 11.43 x 1012 dynes/cm2

(polycrystalline diamond) [46, 47, 48] and the equations (2.12),(2.l3) and (2.14) can

16

be written as

CF.) = 931 (2.15)

PO 61
as. = 951 —1 (2.16)

Po 61

GP“, = 1'. (2.17)

311

the anisotropic transverse gauge factor can be written as

GE“ = i (2.18)

511

Now for randomly oriented polycrystalline diamond films the longitudinal piezoresis—
tive coefficient can be determined using Hook’s law and equations (2.6), (2.10) and
(2.15):

1

< W1> = CF“ 7 (2.19)

< tr, > can be determined using Hook’s law and equations (2.7), (2.10) and (2.16):

l

<1r, > = GP}, 37 (2.20)

In the case of monocrystalline diamond films in and an are given by [44, 45]:

in = 5110151,, (2.21)

 

 

 

2.3.

The

sim
Spe
due
“1

lat
r651

wit;

17

Wt = 51] CF," (2.22)

2.3.3 Explanation of the Piezoresistive Effect

The piezoresistive effect in n-type semiconductor materials was explained by the
many-valley model developed by Herring [49]. In silicon the constant energy sur-
faces are ellipsoidal in form. A total of six equivalent energy minima exist along the
<100> directions in n-type silicon (<100> valley model). Because the surfaces are
ellipsoidal the effective mass of an electron in each valley is anisotropic. Hence, the
mobility associated with each valley is anisotropic although the overall mobility is
not.

For a qualitative explanation of the piezoresistive effect in n-type silicon, let us for
simplicity, call the [100], [010] and [001] valleys as k,valley, Icyvalley and lc,valley, re-
spectively. In the absence of strain all the valleys are equally populated with electrons
due to crystal symmetry. The energy minima are all located at the same energy level.
When a uniaxial tensile stress is applied, for example, in [100] direction, the lattice
spacing increases in [100] and [100] directions, whereas in the directions perpendicu-
lar to this direction ([010], [0T0], [001] and [001]) the lattice spacing decreases. As a
result, the two energy minima along the considered direction of the stress are raised
with respect to the other four energy minima. The result is to cause more carriers
to be scattered into the k,valley and lczvalley, than are scattered into the lczvalley.
The ellipses in Figure 2.5 represent cross-sections of constant energy centered about
EC. For simplicity two valleys are only shown in Fig. 2.5. These are ktvalley and
k,valley. In the absence of strain, the two ellipsoids are equal in size. Within each
ellipsoid, there are two groups of electrons with different effective mass. These two
groups of electrons have different mobilities, that is, the mobility of electron 11,, in a

direction perpendicular to the major axis of the valley is larger than the mobility of

18

electron Ila-.1: in a parallel direction.

The effect of .the uniaxial tensile stress applied along the [100] direction, is shown
schematically in Fig. 2.5, by the decrease in the valley size along the [100] direction
and an increase in the [010] valley size. The effect of stress on the valley energies is
indicated by the dotted ellipsoids. An increase in the size of an ellipsoid corresponds
to a lowering of the band edge. Now, if an electric field is applied along the direction
of the mechanical stress (longitudinal direction), the resistivity will decrease. This
is because, the application of the stress has resulted more electrons of high mobility
(small effective mass) and fewer electrons of low mobility (large effective mass) in the
field direction. This has been observed experimentally by the negative piezoresistive
coeficient of n-type silicon [17]

The piezoresistive effect in p-type silicon is still not clear. The constant energy
surfaces in the valence band are much more complicated than the conduction band
due to the degeneracy. A simplified and roughly drawn energy band diagram of p-type
silicon is shown in Fig. 2.6(a) [50, 51, 52]. Because of the degeneracy at k = (000)
the constant energy surfaces of the valence band cannot be described as ellipsoids or
spheres, but they are warped in such a way to retain their cubic symmetry.

The application of uniaxial stresses to the crystal lifts the cubic symmetry and
removes the degeneracy at k = 0 of the valence band which is responsible for the
warping of the surfaces. This causes the subbands to be shifted relative to each other
[50, 51, 52]. This results in transfer of carriers between heavy holes and light holes.
Under uniaxial tensile stress, the heavy hole subband moves up and the light hole
subband moves down (Fig. 2.6(b)), as a result more carriers with low mobility and
less carriers with high mobility. The resistance increases with tensile stress, which has
been observed experimentally by the positive value of the piezoresistive coefficient or

gauge factor [17] .

 

Figur

19

“a

 

l'l'z:
ff”\> 4) 0

V
kx-valley [100]

Figure 2.5. Cross-section of constant energy for n-type silicon centered about EC.

2.4 Diamond Properties

Since the discovery that diamond is a crystalline form of carbon many attempts to
synthesize diamond have been made, but these attempts have met with only limited
success. It was not until the 1955 [53, 54, 55], when scientists at General Electric
(GE) succeeded in producing synthetic diamonds.

Diamond is the densest form of carbon. In the diamond lattice each carbon atom
is tetrahedrally coordinated, making strong , covalent bonds to its neighbors, using
hybrid sp’ atomic orbitals that give it hardness and strength. The lattice can also be
visualized as planes stacked in an ABC ABC ABC sequence along < 111 > directions
so that every third layer is identical. Natural diamonds are most commonly found in
octahedral and dodecahedral shapes with faces parallel to {111} and {110} planes,

respectively. Simple cubic diamonds with faces parallel to {100} faces also exist, but

 

 

 

 

 

 

 

]
Li]

I

l

l

l

I
Fig.

J

20

 

 

 

A 500
Heavy Hole Band
a) ] i /
44 meV
i I y-ot‘f Band
Light Hole Band m
A 155(k)

Heavy Hole Band

//\ /
b) /

Light Hole Band 59W“ Bud

/\

Figure 2.6. A simplified and roughly drawn energy band diagram of p-type silicon
(a) zero stress and (b) with uniaxial stress.

 

21

these are less common [55].

Diamond has long been known to be the strongest and the hardest of all materials.
Its knoop hardness is as 100 GPa [56]. Diamond has the highest Young’s modulus
of any materials. Its Young’s modulus is 10.5x10‘2 dynes/cm2 which is five times
that of the silicon [46, 47, 48]. A potential application of these properties is in
micromechanical transducers which may be made very thin and yet remain rigid
[57, 58, 59, 60, 61, 62]. It also exhibits low friction coefficient of 0.05 in the < 110 >
type I natural diamond, which is similar to that of Teflon [56, 63]. This low coefficient
is believed to result from a hydrogen termination of the surface. The low coefficient
of friction is particularly relevant in extending the tool life of diamond cutting tools
by reducing heat generations.

The thermal conductivity of diamond at room temperature is higher than that of
any other material [64, 65]. It is 5 times greater than that of copper, 13 times that of
silicon, and 43 times that of gallium arsenide. This conductivity derives from phonon
propagation. It is exceptionally efficient when used as a heat spreader.

The thermal expansion coefficient of diamond at room temperature is 0.8 x 10'6
°C"1, lower than that of Invar. This is caused by the very strong binding force of
diamond. The thermal expansion coefficients of diamond and silicon as a function of
temperature is shown in Fig. 2.7. [66, 67, 68].

Diamond is virtually immune to chemical attack by all substances unless they
are energetic (e.g., ion beams)[69] and those which act as oxidizing agents at high
temperature. It has been known that if a diamond is heated to a temperature of
about 600- 700 °C or higher (depending on the initial quality of the diamond) in pure
oxygen or even in air, it will wholly or partially oxidized to CO and 002. If diamond
is heated in the absence of oxygen, preferably in vacuum, to a temperature of about
1400- 1500 °C or higher (again depending on the quality of the diamond), it will
be wholly or partially converted to graphite [70, 71]. Molten potassium and sodium

 

 

A—d—IL—n‘—l——‘——.—-b-‘_‘—

mu mum (mum sermon". I04":

 

 

.L
0
§

Figure 2.7. Thermal expansion coefficients of diamond and silicon as a function of
temperature.

23

Table 2.4. Comparison of diamond properties and some commonly used semiconduc-
tor materials.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Materials
Properties Si GaAs SiC Diamond
Natural CVD
Band Gap (eV) 1.12 1.42 3.0 5.45 5.45
Carrier mobility
Electron (cmz/ V.s) 1450 8500 400 1800 -2000
Hole (cm2/ V.s) 500 400 50 1600 - 2100 (10-1000)I74v 75. 761
Dielectric constant 11.7 10.9 10 5.7 6.5”“
Breakdown
(V/cm) x 10° 0.37 - 0.5 0.6 2 - 3 (4-20)I781
Resistivity (Ohm-cm) .
Intrinsic 1x103 1 x103 1 x1016 (106-10“)!“
fiermal conductivity
(W/cm.°K) 1.5 0.5 5 1020 (lO-20)[80. 81]
Thermal
expansion x 10"/°C 2.6 5.9 4.7 1.1 2.6[801
Lattice constant (A) 5.431 5.653 4.36 3.57 3.57
Melting point (°C) 1412 1240 2540 3827
Emmy (g/cm3) 2.329 5.317 3.216 3.52 3.52
Hardness (G135) 8.5 24.8 100 70 - 100
Young’s
modulus (GPa) 130 - 180 85 700 1050 - 1200 (800-1180)[47' 321
Poisson’s ratio 0.22 - 0.24 0.31 - 0.32 0.10.21 (0.071-0.14s)l47v 321

 

 

 

nitrides are most commonly known to attack the diamond surface at a temperature
in the range 427-827 °C [55, 72, 73].

Electrically, pure diamond is an excellent insulator. The band gap associated with
the indirect transition between the valence and the conduction bands is as large as 5.48
eV. Table 4 [3, 57, 68, 80, 81, 83, 84, 85] provides a comparison of some of the most
important material parameters between most commonly used semiconductors and
diamond. The electrical properties of diamond exceed those of other semiconductors.
Diamond should be a good candidate for high temperature (due to large band gap)
high speed (due to carrier mobility) and high power (due to high thermal conductivity

24

and breakdown voltage) electronic devices.

According to impurity content, optical, and electrical properties, diamond is
grouped into four distinct types: I-a, I-b, II-a, and II-b [55].

(i) Type I-a: These diamonds are often nearly colorless, but they may also
be yellow, brown or gray; they are optically transparent and are believed to be less
perfectly crystalline. Their electrical resistivity is greater than 10160 -- cm.

(ii) Type I—b: These diamonds contain up to 0.2% paramagnetic nitrogen which
is present on isolated substitutional lattice sites. Most of the synthetic diamonds
produced under high pressure are typically type Ib.

(iii) Type II-a: These type of diamonds are very rare in nature, and are generally
believed to be the most perfectly crystalline, practically free of nitrogen, near-colorless
and are transparent in the ranges 220 nm to 2.5 pm and > 6pm. and are absorbed to
IR in the range 2.5 nm to 6 pm. Thermal conductivity at room temperature ranges
up to 26 W/cm-K. Electrical resistivity is in general similar to type Ia diamonds.

(iv) Type II-b: Extremely rare in nature, these diamonds contain boron in small
quantities and are usually blue or gray in color. They are p-type semiconductors with

electrical resistivity of only 10 to 1000 fl-cm.

2.5 Diamond Technology

In 1954 researchers at General Electric succeeded in converting graphite to diamond
under high pressure and high temperature (HPHT) conditions [53]. Typically syn-
thetic diamond is fabricated at temperatures around 4237 K and a pressures near
200 kbar [53]. By the use of a metallic catalyst such as nickel and iron, the conver-
sion rates from graphite to diamond can be increased, and temperature and pressure
can be reduced to around 1500 °C and 50 Kbar respectively [86, 87, 88, 89]. How-
ever, synthetic diamond made by HPHT process has a variety of disadvantages, such

 

 

 

high ;
methi
and 1
creat
have
finer

usei

Der]
denl'
pres

Aug

low

pra
dial
Esta
vtor
sion
CODC
0f dj

that

a“ th.

25

high pressure conversions are costly and require a small growth chamber, so that the
method is only suitable for production of diamond in the form of small pieces, grit,
and powder, but it is not suitable for large area coverage. Using a metal catalyst
creates metal inclusions and small voids in the diamond films. These metal inclusions
have a different thermal expansion coefficient than that of the diamond and cause
internal stresses to develop and weaken the diamond, that make them unsuitable for
use in semiconductor devices.

In the late 19608, two separate groups, one from the Soviet Union led by Boris
Deryaguin and the other from the United States headed by John Angus, indepen-
dently showed that diamonds could be deposited on diamond seed crystals at low
pressure from a vapor of hydrocarbons and hydrocarbon-hydrogen mixtures [87, 90].
Angus and co-workers were the first to report on the preferential etching of graphite
compared to diamond by atomic hydrogen. By the mid 1970s diamond growth at
low pressures had been achieved by several groups [1, 91, 92]. The beneficial role of
hydrogen was known and understood to some extent and growth rates of <01 um
/hour had been achieved. However, the use of diamond as a substrate and the low
growth rates attained were the major reasons for the process being judged to be im-
practical. Nevertheless, the critical role of atomic hydrogen in achieving metastable
diamond growth as a preferential etchant for removing graphite against diamond was
established, and these results provided the experimental foundation for much of the
work that followed. Moreover, this process produces diamond that is free of inclu-
sions. An important breakthrough by Soviet scientists in early 1970’s indicated the
conditions under which gas activation techniques can greatly increase the growth rate
of diamond and suppress the graphite deposition. Soviet scientists also announced
that they had grown crystalline diamond on non-diamond substrates but they re-
leased no details about their method. Finally, in the early 19808 a Japanese group
at the National Institute for Research in Inorganic Materials, under the direction of

 

Nol
rate

diff

byd

{HOE

on '
sub:
1001

user
dep<

p011]

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the I
met}
int—cg
PTOCI
Com};
ble fc
diam]
in t h e
W
Subs”

give a

26

Nobuo Setaka and Seiichiro Matsumoto [93], deposited diamond with high growth
rates by chemical vapor deposition on diamond and non-diamond substrates using
different techniques. These latter disclosures led to worldwide interest.

The most successful growth method has been in the deposition of diamond from
hydrocarbon-hydrogen gas mixtures. Methane (CH4) and acetylene (CgHz) are the
most common carbon-containing gas species which have been used for diamond de-
position . The percentage of the hydrocarbon gas is generally 0.1- 5.0% depending
on the growth technique and the desired film quality versus growth rate. Similar
substrates temperatures are used in most of the low-pressure experiments (~600° to
1000 °C).

Other hydrocarbon gases such as ethane, ethylene and acetylene can also be
used to deposit diamond in the microwave plasma CVD method. For hot filament
deposition, Hirose and his co-workers [94], have shown that various organic com-
pounds including acetone (CH3 — CO — CH3), ethanol (CH3 - CH2 - OH), methanol
(CH30H) and diethyle ether (C2HsOC2H5) can also be used to deposit diamond films.
Growth rate of 8 pm/ h were also reported [94] by using these organic compounds in
the hot filament method, approximately 20 times greater than those obtained when
methane is used in a similar system. Oxygen can be added, either directly or as an
integral part of the carbon carrier, and can have a marked influence on the deposition
process. The variation in growth rate is possibly due to varying efficiency of each
compound in supplying CzHg, CH3, and other radicals thought to be mainly responsi-
ble for diamond growth[95]. Deposits may vary from nanocrystalline to single crystal
diamond with no or little non-diamond C, depending upon proportions of C, H, or O
in the supply of gases, but without reference to type of gas phases activation used.

With a correct set of other important deposition parameters, such as pressure,
substrate temperature or power density in the activation zone, the C-H-O diagram

give a clear picture on where to search for diamond. The vast majority of diamond

CV1
the «
limi
I963

WOL

dia
mo

of

to
w]
at

th

de
Pb
die

We

27

CVD experiments started from less than 5% methane in hydrogen [96]. Depending on
the quality criteria and diamond detection methods applied, the upper concentration
limit for diamond formation from CH4-H2 mixtures is somewhere between 3% and 4%
[96]. For methane concentrations around 3%-5% small additional amounts of oxygen
would shift data points off the GR sideline into the diamond domain.

Atomic hydrogen serves several critical roles in the temperature range of CVD
diamond growth. First, stabilization of diamond surface, that is to prevent the dia-
mond surface from reconstruction into a graphitic like surface containing a mixture
of sp2 and sp bonds and to satisfy the dangling bond of the surface by preserving
the sp3 like bond (diamond). Second, reaction with surface hydrogen to form H2 and
leave a vacant surface site in which a reactive carbon species may attach. Finally,
etchant for graphite which forms simultaneously with diamond.

Oxygen also play an important role in the growth mechanism of CVD diamond.
Various studies [97, 98] have shown that addition of oxygen in HFCVD growth envi-
ronment leads to increase of atomic hydrogen concentration at the surface of diamond
which in turns contribute to the purification of diamond films even at low temper-
ature. Direct oxidation of non-diamond carbon is also enhanced by the presence of
the 03. Oxygen also improves the formation of additional radicals in the gas phase
which is necessary for diamond growth. Oxygen also causes increase in atomic carbon
density by the destruction of gas phase pyrocarbon-forming species. Forming OH gas
phase which attack the non-diamond carbon. The range of total pressure at which
diamond could be obtained was extended by the addition of oxygen. Optimum results
were obtained for gas mixtures of 02:0H42H2 =0.2:0.8:50 SCCM [98].

The precise effect in the growth mechanism of CVD diamond from the hydrogen

and the oxygen is still debated.

 

 

temp.
ckme
°Cl I
hour

Efiven

\Bed
HUCI(
Wan
Cuba
at a I
ConCe:
um p,

were T1

28

2.5.1 Chemical Vapor Deposition Methods

So far, several techniques have been developed for chemical vapor deposition (CVD)
of diamond [87, 93, 99, 100, 101], such as hot filament (HFCVD) [93, 94], radio
frequency (rf) plasma [102, 103], d.c. plasma [104, 105], microwave discharge [99, 106]
and microwave plasma disk reactor [107]. Other deposition method was also reported
[108]. All of these methods have in common that diamond is deposited from a carbon
carrier gas that is decomposed and the formation of non-diamond carbon is prevented
by the presence of a selective etchant such as atomic hydrogen or oxygen. Some of
these diamond CVD methods are capable of producing the desired carbon phase at
linear growth rates of 0.1 to 1 pm per hour while for other methods up to 180 pm
per hour were reported [102].

Hot filament HFCVD system consists of tungsten filament which is heated to a
temperature range of z 2000-2400 °C and a substrate holder which is usually mounted
close to the filament and independently heated to temperatures between 800- 1000
°C. The growth rates in HFCVD reactor is usually in the order of 0.5 to 10 pm per
hour depending on the gases employed. More details on the HFCVD system will be
given in the next section.

Microwave plasma in the high frequency range (2.45 GHz) has been extensively
used for the deposition of diamond films [99, 109]. The reaction chamber in a typical
microwave plasma is composed of a quartz tube which is placed inside a microwave
waveguide and a substrate holder which is positioned inside the tube. Plasma of
carbon carrier gas and hydrogen mixtures are formed and diamond were deposited
at a pressure of 10- 100 torr, a substrate temperature of 800- 1000 8C, and methane
concentrations of 0.2 - 5.0 % in hydrogen. Generally, linear growth rates of 0.5 - 5
pm per hour were achieved. Rates up to 30 pm / hour under atmospheric pressure

were reported using a microwave torch reactor, which was developed by Mitsuda et

 

 

 

a] [110
< 500
substra
A h
plasma
['niver
tuned :
a sing].
into if
proces
Which
steel 5
Chaim}
height
sits o;
(915 1
film 0
IL-
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of 4 }
Conce
diam.
Subst

Was e

29

al [110]. Growth of diamond films on silicon and other substrates at low temperature
< 500 °C were also reported [111, 112]. J. Wei, et a1. deposited diamond films on Al
substrates at 0.1 Torr and 500 °C using magneto-microwave plasma [113].

A high quality diamond film was also achieved in a large area by a Microwave
plasma disk reactor (MPDR) [107]. The MPDR was developed at Michigan State
University by Asmussen et al. [114]. The MPDR system is an electrodeless, internally
tuned reactor design which uses a circular cylindrical cavity which can be adjusted to
a single resonant mode by means of two degrees of tuning. Microwaves are introduced
into the system via a short antenna, which is a coaxial microwave input probe. The
processing vacuum chamber is composed of a quartz disk, a graphite substrate holder
which is held by two quartz tubes, stainless steel baseplate and a perforated stainless
steel sheet which is affixed to the baseplate in the bottom part of the processing
chamber and serves to terminate the cavity and still allow gas to flow through. The
height of the quartz disk is 6 cm and its inner diameter is 9.25 cm. The quartz disk
sits on 3.5 cm thick stainless steel baseplate. The MPDR is scalable with frequency
(915 MHz/ 2.45 GHz) which allows for the possibilities of depositing uniform diamond
film on large area. [115]

Radio frequency plasma technique developed by S. Matsumoto, et al [102] operated
at atmospheric pressure, has also been used to deposit diamond. In this method, rf
of 4 MHz inductive heating and a power of 60 kW were used. Up to 10 % methane
concentrations (much higher than in other techniques) could be used. High quality
diamond films at growth rate up to 180 pm per hour were obtained on molybdenum
substrates. However, the handling of such plasmas is not easy, the plasma temperature

was estimated to be greater than 4000 °C.

30

2.5.2 Nucleation

Generally, the nucleation density for diamond growth on non-diamond substrates is
very low, roughly 104 cm”. Enhancing nucleation on a wafer surface is the require-
ment for the development of a pinhole-free film in a reasonable deposition time. Sev-
eral techniques have been used to enhance the nucleation density for diamond growth
on non-diamond substrates by many investigators. The most commonly known tech-
nique is based on scratching the host substrate manually or via ultrasonic by diamond
powder [106, 116, 117].

In the case of diamond powder the nucleation on the substrate can be achieved
by abrading the surface directly with the powder [116], or by ultrasonic treatment in
a suspension of diamond powder in organic solvents, such as ethyl alcohol, methanol,
etc. [118, 119]. Following the treatment, the substrate is always rinsed by deionized
water or by one or more organic solvents. This method has substantially increased
the nucleation density of diamond growth by several orders of magnitude, up to 1011
cm'2 has been reported [106, 116].

More recently a novel technique was developed at Michigan State University, which
does not require scratching of the substrate [119]. This method is based on spreading
diamond seed crystals, suspended in photoresist, on the substrate surface. During
CVD diamond deposition, the photo-resist evaporates in initial stages and the dia-
mond particles act as nucleation sites for the diamond growth. The nucleation den-
sity of this method is relatively 5-8 times smaller than that of ultrasonic or damaging

treatment [119]. However, this method is compatible with the lithographic process
used in IC technology. The nucleation density and the grain size in the deposited di-
amond film is easily controllable through the size and density of diamond particles to
be suspended in the photo-resist and the spin speed of substrate during photo-resist

coating [119]. A further extension of the method has resulted in nucleation densities

 

 

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31

in the range of 1011 cm‘2 [120].

Transmission electron microscopy (TEM) indicates that scratching leaves very
small plaques of diamond is 50 A in size, which serve as nucleation sites for diamond
growth [121]. It has been also reported that diamond nucleation density was enhanced

by only sand-blasting the silicon wafer without using the diamond powder[103].

2.5.3 Effect of Substrate Temperature

The typical substrate temperature for diamond CVD, growth on a variety of sub-
strates, in almost all the techniques, is in the range of 800-1000°C. Lowering the
substrate temperatures usually results in the formation of the amorphous carbon
films which contain mixed bonding of 3;)3 and sp’. Low temperature growth of pure
diamond films is an important goal for the extension of diamond applicatiOns towards
semiconductor, optical emitting materials as well as optical and mechanical coating
materials or heat sinks. Ramesham et al. [122] used a high pressure microwave
plasma-assisted (HPMA) chemical vapor deposition system to grow low temperature
diamond films. It was observed that deposition at lower temperatures (460-600°C)
requires a higher percentage of methane than at higher temperatures (800—1000°C)
[111, 112, 122]. It was also noted that, as the substrate temperature decreases, depo—
sition rate decreases, smoothness increases, and diamond crystal size decreases [122].
Liou et al. [123] have deposited diamond on different substrates at low temperatures
in a microwave plasma enhanced chemical vapor deposition (MPCVD) system. they
have reported that, diamond could be deposited at less than 300°C via the addition
of oxygen to the gas mixtures. Films deposited without oxygen were white soot coat-
ings and easily scraped off. The deposition rates of films on silicon with 2% methane
drop down quickly with decreasing substrate temperatures. The deposition rate de-
creases as the oxygen concentration increases. However, the quality of the diamond

deposited films was increased with increasing oxygen concentrations[123]. Most of

32

the reported results on the deposition of diamond at low temperatures were achieved
by plasma CVD systems. However, highly crystallized and purified films has never
been reported.

Low temperature diamond deposition by hot filament chemical vapor deposition
system HF CVD has not yet been achieved. Matsumoto et al. [93] in their first
reported experiment, they deposited diamond at a substrates temperatures in the
range of 600-1000°C using HFCVD system. They found that lower temperatures
(600 -700°C) decreased the number and size of the diamond particles formed. In
addition, no continuous film was reported by these authors, this might be due to
that, no special method to enhance nucleation was used.

Kikuchi et al. [124] deposited a continuous film by HFCVD systems, where the
temperature of the surface of the substrate was kept at 750°C with radiation from
the filaments. The silicon substrate was scratched by 3 pm diamond powders before
deposition. High quality and continuous diamond films were achieved after 12 and
16 hours deposition time for 1% and 0.5% methane concentrations in hydrogen, re-
spectively. The efiect of substrate temperature was also studied by A. Masood at
Michigan State University [125] using HFCVD method. It was observed that the
quality of the diamond film improves when the temperature increases from 830°C to
890°C and then the quality shows some deterioration at a temperature greater than
900°C. It was also observed that the growth rate of the diamond films increases with
increasing temperatures from 830°C to 890°C. It is very important to known that,
when the substrate temperature is greater than 1300°C, only graphitic carbon, if any,

is deposited.

2.5.4 Diamond Film Characterization

An extensive range of analytical techniques are currently used to monitor and char-

acterize various stages of CV D process of diamond. Most of them are, however,

33

used either to study in situ gas reaction and substrate surface chemistry or physical
composition of the films. In this research, diamond films will be characterized after
deposition. Raman spectroscopy, scanning electron microscope (SEM) and surface
profilometers will be used in this work. A brief description of each in context with

its specific use in diamond film characterization is given here.

Raman Spectroscopy

Raman spectroscopy is based on the phenomenon of inelastic scattering of radiation by
a medium. In case of diamond, they are dominated by the intramolecular vibrational
transitions corresponding to optical phonons.

Raman spectroscopy is widely used in CVD diamond characterization due to its
high sensitivity not only to crystalline material, but also to the various possible non-
crystalline phases. A factor of 30 for the ratio of graphite to diamond has been
reported [126]. Raman analysis for natural diamond indicate a strong peak at relative
wavenumber of 1332 cm"1 [127]. Well-ordered graphite, similarly, has only one Raman
peak at N1600 cm'1 [128]. The presence of disorder or small crystallite size gives rise
to a peak at 1355 cm’1 [128, 129]. A peak at around 1550 cm'1 has been commonly
attributed to the presence of graphite i.e., sp’ hybridization. This is not an accurate
assignment, since it has been argued to arise from diamond-like carbon (DLC), which
may not be graphitic in nature [130]. In addition, films with nanocrystallites show
a broad peak centered at £81133 cm'1 [131]. Despite some objections, the quality
of deposited diamond is generally judged from the relative intensity of the peaks at
1332 and 1550 cm"1 [130]. Robins et al. has published a comprehensive analysis of

various attributes to the shape of Raman Spectra [132].

34

Scanning Electron Microscope (SEM)

One of the most commonly analytical tool for studying the morphology and visual
analysis of diamond films is scanning electron microscope (SEM). Since the CVD
diamond films generally have micron or sub-micron size grains, optical microscopes
which has an upper limit of magnification of about 2000 times and, at that magnifi-
cation, a small depth of field, cannot resolve them effectively. The high resolution of
SEM, is capable to resolve objects in dimensions down to 100 A. SEM micrographs
of the film surface provides details of the surface morphology, film uniformity, voids,
cracks, selectivity of patterns and crystal orientations, etc. In this work SEM will be
also used to determine the thickness of diamond film by inspecting the film’s cross

section.

2.5.5 Doping of Diamond

Natural semiconducting diamond was discovered in 1952 [133]. This discovery re-
vealed its outstanding electronic properties in addition to its already known physical
properties. Semiconducting type II-b diamond is lightly p-doped. It has been shown
that the acceptor center is substitutional boron. Nitrogen also is a common impurity
in diamond and it has been suggested that nitrogen is present on isolated substitu-
tional lattice sites and is known to be the donor center in semiconducting natural
diamond [55].

Many researchers have attempted to realize semiconductive diamond by doping
impurity atoms such as boron and phosphorus and lithium [134, 135, 136]. The p-type
diamond doped with boron atoms is more easily obtained than the n-type diamond.
Because of the low diffusivity of most impurities (dopants) in natural diamond, the
diffusion doping technique that is commonly used to dope semiconductors can not

be used for diamond. Doping by ion implantation is the only technique to introduce

35

impurities in natural diamond. Ion implantation technique was first investigated
by workers in the Soviet Union [134, 135, 136]. Lithium (Li+), boron (B+) and
phosphorus (P+) ions have been used with varying degrees of success. Li+ and Ft
ions produced n-type layers. However, post-implant annealing of these n-type layers
at 1200 °C resulted in an increase in sheet resistance, but the layer remained n-type.
The alkali metals of smaller atomic size may be good n-type dopants since it is known
from nuclear reaction studies that lithium occupies an interstitial site in the diamond
lattice and can therefore donate an electron to the conduction band [134, 135, 136]. In
1982, Prins [137] produced n-type regions in natural p-type diamond. These n-type
regions were induced by implantation of carbon ions into diamond in order to fabricate
n-p-n transistor[137]. Experiments have shown that the conductivity is dependent on
the ion dose, dose rate, and the temperature during implantation. However, the lack
of large area single crystal semiconducting diamond and the high cost of fabrication
combined with the difficulty in controlling dopants limit the applicability of these
devices in microelectronics.

Synthetic semiconducting diamond was successfully manufactured in 1962 by re-
searchers at General Electric [138, 139]. They reported synthetic p-type semiconduct-
ing diamond from a mixture of graphite and catalyst metals (Ni, Fe, etc.) and small
amounts of B, Be, and Al using high pressure high temperatures process. Electri-
cal transport measurements on B, Al, and Be doped synthetic diamond, [48] showed
p-type conductivity with impurity activation energies of 0.17-0.18, 0.32 and 0.2-0.36
eV, respectively. Similar measurements by Wilson [56] in the temperature range of
88 K to 293 K on B doped specimens yielded nearly 30 discrete activation energies
ranging between 2.9 and 87 meV. These data were interpreted as evidence of impurity
conduction or hopping transport which is commonly observed in heavily doped and
highly compensated semiconductors at low temperatures [58,59,165]. In both natural

and synthetic semiconducting diamonds acceptors are typically compensated by deep

36

nitrogen donors with activation energy of about 4 eV above the valence band. The
acceptor activation energy for boron in natural semiconductor diamonds has been
recognized at 0.37eV [134, 135, 136]. However, HPHT method is costly and is not
suitable for production a thin film diamond. Furthermore, the metal catalyst creates
metal inclusions and small voids. Therefore, synthetic semiconducting diamond is
not suitable in semiconductor devices.

The latest developments in the growth of doped and undoped diamond films on
diamond and non-diamond substrate by chemical vapor deposition CVD has led to
the current interest in the use of diamond for semiconducting devices [1, 93, 99, 140].
This CVD method enhanced the possibility of semiconducting diamond devices with
extraordinary characteristics. Doping during growth (in-situ) from gas phase and
solid sources using the CVD method has been demonstrated. Semiconductive n-type
diamond was produced with phosphorus pentoxide (P305) as the doping sources [141,
142]. The n-type films demonstrated a high resistance. The problem of producing
(in-situ) n-type layer with very low resistance has not been solved at the present
time.

The production of device quality diamond requires techniques for introducing con-
trolled amounts of dopant impurities. So far, boron is the only dopant successfully
used to fabricate thin film diamond based devices [140] using CVD techniques. It has
been known that the boron atoms are present on substitutional sites which creates
acceptor centers with activation energy of 0.37 eV [143]. Typically, 0.1% of the ac-
ceptors are ionized at room temperature. In most of the experiments boron doping
was achieved by admixing relatively toxic diborane 32113 to methane and hydrogen
during film growth process [141]. A nontoxic saturated solution of boron trioxide
8203 powder in CH3OH mixed with acetone was also used [144]. A high purity
boron powder was also used during diamond film growth in CVD deposition chamber
[145]. During the growth process boron is etched away by the hydrogen plasma to

37

form boron hybrids. The boron hybrids enter the plasma and boron is incorporated
in the diamond film during the growth process. Boron doping can also be performed
by lowering a boron rod into the plasma during the growth process. Homoepitaxial
semiconducting diamond films have been grown selectively on natural diamond sub-
strate (type Ia) using sputtered SiOg as a masking layer [69, 145, 146]. Polycrystalline

semiconducting diamond films have been grown on many substrates.

2.5.6 Patterning

Because of diamond’s extreme resistance to chemical attack, it is very difficult to
pattern using chemical etch. The geometry and physical dimensions are some of the
prime parameters in determining the functionality of any electronic and microme-
chanical devices. Dry etching and selective nucleation techniques were studied by
many investigators [59, 61, 119, 147, 148, 149, 150, 151, 152, 153, 154, 155].

Several techniques such as ion beam etching, reactive ion etching, and plasma
assisted etching and electron cyclotron resonance (ECR)-assisted etching for the dry
etching of diamond have been reported [151, 152, 156].

T. J. Whetten, et al. [151] reported that they etched single crystal diamonds by
exposing the (100) face to argon and oxygen ion beams. Etch steps were made in the
diamond surface by masking a region of the diamond with a silicon chip. Ion energy
of 500 eV, 750 eV, and 1000 eV was used. No etch rate was reported [151].

Reactive ion etching (RIE) with oxygen was also investigated by N. N. Efremow,
et al [152]. Etch rates on the order of 20 nm/ min and poor etch selectivity between
the masking material Ni or Cr and the single crystal diamond (type IIa) was reported
[152]. However, in a later experiment, an ion-beam-assisted etching system was used
by the same group. A beam of 2 keV Xe‘l’ ions with a flux density of 1 mA/cm’, and

a reactive gas flux of nitrogen dioxide (N02) were used, etching rate of 200 nm/ min

 

ll

 

 

38

was obtained with an etching rate ratio of 20 between the diamond and an aluminum
mask.

The use of an electron cyclotron resonance plasma source for oxygen etching of
type Ila (100) natural and synthetic diamond was also investigated by Beetz et al
[153]. Etch rates of 290 2.4/min were obtained. The metals used for masking the
diamond were gold (1 pm) and titanium (1000 A).

K. Tankala and T. Debroy investigated the etching of HFCVD diamond films
in air, nitrous oxide and argon using an oxidation method [154]. The weight of the
sample was measured before and after oxidizing the sample in a heated furnace. They
reported that the oxidation of the diamond films starts at 773 °K in air and at 873 °K
in N 20. The etch or oxidation rates for the HFCVD films were 600 A/ min and 280
A/min in air and N20, respectively. Oxidation of natural diamond crystals starts at
about 900 °K in air. Dry etching was also performed at room temperature using argon
plasma etching which was generated by capacitively coupling two electrodes energized
by a 13.56 MHz radio frequency generator inside a vacuum chamber. Etching rate
of 250 A/ min was reported (25 watt radio frequency power and pressure of 3.0 torr
were used).

An alternative approach to etching an existing film is to actually grow a patterned
film through selective nucleation. Different methods of patterning have been reported
on the selective deposition of diamond [61, 119, 147, 148, 157, 158].

In the approach reported by Hirabayashi et al. [157], the selective growth of dia-
mond was achieved by using an Art ion beam with vertical incidence on a pretreated
silicon substrate which was patterned with resist. They explained that, Ar“ beam
was used to remove the pretreated surface layer which was not covered with photore-
sist. Ma et al. [158], in a similar attempt, obtained selective nucleation of diamond

particles by using Ar beam irradiation on a pretreated substrate having small SlOz

dots on silicon.

39

Davidson et al. [147] reported that polycrystalline diamond films were selectively
deposited on a pretreated silicon surface. In their approach, the polish side of silicon
wafer was manually scratched using diamond paste. Silicon nitride was then deposited
after cleaning the wafer. The silicon nitride was then photolithographically patterned
and plasma etched. An oxide layer of 1.2 pm in thickness was then thermally grown
on the exposed area of silicon. The silicon nitride was then completely etched in
boiling phosphoric acid, washed with DI. water, rinsed with acetone, methanol, and
nitrogen dried. The diamond was then deposited on the exposed pretreated areas.

Recently, a novel technique to selectively deposit high quality polycrystalline di-
amond films has been developed at Michigan State University [119]. The selective
nucleation was achieved by patterning photoresist, which was premixed with fine dia-
mond powder (0.1-0.2 pm), using standard photolithographic process. The nucleation
density, uniformity, and smoothness of the resulting diamond films were optimized
by controlling the photoresist thickness through the careful choice of spinning time
and speed. In this method, fine diamond particles acted as seeds for the growth of
diamond only in the patterned areas.

Comparing this technique, to the previously described ones, diamond powder
photoresist is the simplest one. It may be employed on nearly all substrates found in
electronic device manufacturing. This method is easily incorporable in the existing
integrated circuit fabrication technology. It only requires one mask step process, The
method described by Davidson et al. required two or more mask process steps in

addition to scratching the substrates.

2.5.7 Highly Oriented Films

The growth of highly oriented or single crystal diamond films on non-diamond sub-
strates (heteroepitaxy) is a necessity for most practical electronic devices. To date,

most semiconducting diamond films grown on non-diamond substrate are polycrys-

40

talline.
The growth of heteroepitaxy is believed to be dependent on matching the lattice

parameter of diamond and/or the thermal coefficient of expansion to the deposited
substrate. The effects of varying the deposition parameters controlling both the gas
phase chemistry and the surface chemistry are other factors. Substrate orientation
and process conditions are also important factors.

Heteroepitaxy has been accomplished on Ni, C-BN , SiC [159, 160] and most
recently Si single crystals[161]. The epitaxial films grown on c-BN single crystals were
highly oriented although the size and quality of the substrate material has limited
the exploitation and further development of this epitaxial approach [159].

Geis et al. [65] have demonstrated a technique named “artificial epitaxy” or
“MOSAIC”to achieve large area single crystal diamond on silicon substrate. In that
approach, diamond seed crystals were aligned by placing them in inverted pyramid
shaped structures micromachined on a silicon substrate surface. During diamond
deposition, the growth of each diamond particle proceeds laterally as well as vertically,
joining with the other particles in close proximity, forming a continuous layer of
diamond.

As explained by Van der Drift [162], textured growth can be understood as a
result of growth competition between differently oriented grains. The basic parameter
which determines the film texture is the direction of fastest growth. The growth of
polycrystalline film starts from distinct nucleation sites. As individual randomly
oriented nuclei grow larger, their diameters equal the average distance between the
nucleation sites and they begin to form a continuous film. With increasing film
thickness, more and more grains are over grown and buried by adjacent grains. Only
those crystals with the direction of fastest growth perpendicular to the surface will
survive. For an initial distribution of randomly oriented diamond nuclei, the resulting

film-texture will be a function of the relative growth rate parameter (a) which is

41

described as [161]
a = J3 V100 (2.23)

I/lll

where V100 and V111 are the growth rates on the {100} and {111} faces respectively.
In order to obtain < 100 >-textured diamond films, the direction of fastest growth
must be < 100 >, that is 3.0 < a < 2.6 [161].

Most recently, it was demonstrated by Stoner et al. [161] using microwave plasma
enhanced chemical vapor deposition system, that under certain grOwth conditions the
growth competition between differently oriented grains can result in the formation of
strongly < 100 >- textured diamond films with smooth {100}-faceted surfaces. In
that approach, textured films were nucleated by a two step process that involved the
conversion of the silicon surface to an epitaxial SiC layer, followed by bias—enhanced
nucleation (BEN) process.

Boron-doped layers were selectively deposited onto the surface of these oriented
films. Room temperature hole mobilities between 135 and 278 cm2[V-s were mea-
sured, this indicated a 3 to 5 times improvement in hole mobility over polycrystalline

diamond films grown under similar conditions.

2.6 Diamond Devices

From an electronic perspective, diamond should be a good candidate for high tem-
peratures and harsh radiation environments due to its wide band gap, high speed
due to its carrier mobility, and high power due to its high thermal conductivity and
breakdown voltage. Most common semiconductors require reverse biased junctions in
order to avoid leakage current. In contrast, a very high electric field may be applied
across a diamond device without producing significant leakage current.

In 1982, Prins [137] was able to fabricate a bipolar transistor behavior. He pro-

duced n-type regions in natural p-type diamond. These n-type regions were induced

42

by implantation of carbon ions into diamond. However, very low current gain was
obtained and the conductivity disappeared after annealing at 700-800 °C,
Point-contact transistors and Schottky diodes were formed on a synthetic boron
doped diamond [69]. The transistors exhibited power gain at 510 °C, and the Schottky
diodes were operational at 700 °C. Field effect transistors (FET’s) fabricated from
ion-implanted single-crystal diamonds (SCDs) have shown excellent characteristics
exhibiting both current saturation and active channel pinch-off [163, 164]. Also,
F ET’s were fabricated from in-situ doped homoepitaxially grown on synthetic single
crystal substrates [146, 156, 163]. Operation of polycrystalline diamond FET’s at
temperature up to 285 °C and drain-to-source voltage of up to 100 V have been
demonstrated [164, 165]. The operation of diamond-based depletion type MOSFET’s
has been achieved in the 300-400 °C temperature range [166]. Typically, most of the
above mentioned devices were achieved by using homoepitaxy on natural or synthetic
diamond substrates. These devices were not commercially produced, because of high

cost and limited size.

2.7 Diamond Sensors

Diamond as a sensor material has been studied by many investigators, especially for
the application as radiation and high temperature sensors [125, 167, 168, 169, 170].
The intrinsic radiation hardness of a semiconductor relates primarily to its chem-
ical bonding energy and the manner in which radiation induced lattice dislocations
produced energy states within the forbidden band. The chemical bonding energy of
diamond .is the strongest of all semiconductors and therefore the most immune to
radiation damage. Photoconductive UV and ionizing radiation detectors have been
used for over 70 and 50 years, respectively. Due to the large band gap, high resistivity

10“ ohm-cm, high carrier mobility and the large saturated carrier velocity of insu-

43

lating diamond, very high electric field may be applied across diamond film without
producing significant leakage current. The high carrier saturation velocity permits
the high speed and high sensitivity operation of diamond detectors. Any radiation
that generates free carriers in the diamond can be detected. These radiations include
electromagnetic radiation with an energy of greater than 5.5 eV. This incorporates
UV, X-rays and 7 rays. High energy particle radiation such as 0 particles, electrons,
neutrons, and other exotic particles can also be detected.

A diamond radiation detector is a simple two-terminal metal-insulator-metal
(MIM) structure. The generation of free carrier is usually detected by an exter-
nal circuit. The motion of the free charges is driven by an externally applied electric
field. The generation rate is proportional to the intensity of the absorbed radiation
divided by the average ionization energy 6, that forms mobile electron-hole (e-h) pair.
The figure of merit for radiation detectors is the average distance a carrier moves
(distance the electron-hole pairs drift apart). This is expressed as the product of the
carrier mobility 14, the lifetime 1 of the mobile charges, and the applied electric field
E and is given by [168]:

d = p 1' E (2.24)

The lifetime may be limited by material defects or device geometry. For a given
electric field, (I is a measure of the sensitivity of the material to radiation detection.

Kania et al. [168] have studied the radiation detector properties of polycrystalline
CVD diamond films by two methods: (1) UV transient photoconductivity (PC) and
(2) charge collection measurements using ionizing radiation. The collection distance
d was measured between two electrodes on the surface of the sample. They observed
that d increases with thickness. According to their explanation, this might be due to
the reduction in the defect density of the material as it grows thicker. It has been
concluded by the authors that, the current state of the art in CVD diamond films

44

gives (1 z 20 pm, which is equal to that of type-Ila single crystal diamond detectors.

The diamond thermistor is the first application of diamond films in the field of
sensors. The thermistor is a passive device and a very simple one. The thermal prop-
erties of p-type semiconducting diamond have been reported by many investigators
[125, 169, 170, 171].

Thermistors fabricated from single crystal diamond type IIb have been reported
[172]. However, economic considerations have rendered these thermistors unaccept-
able for most applications. The first synthetic diamond thermistors were produced
by General Electric in 1969 [173]. These thermistors were doped by boron during
synthesis. They observed that the p-type synthetic diamond thermistors are superior
to natural diamonds, since they did not exhibit the resistivity increase with temper-
ature between 700 and 800 K. Because, of high production cost and limited shape
and size, none of these thermistors were produced commercially, Thermistors made
of synthetic semiconducting diamonds were also reported by other investigators [169].
These thermistors were used as the level meter for liquids which was corrosive such
as acids or alkalis and were shown to operate at temperatures from -100 to 400 °C
[169].

Thermistor made of CVD diamond films have been reported by [125, 170, 174].
Fujimori and Nakahata [170] have claimed the first fabrication of a polycrystalline
and homoepitaxial CVD diamond thermistors. The diamond films were deposited
by microwave plasma CVD. Undoped and boron-doped resistive elements were de-
posited on silicon nitride substrates. The ohmic metal contacts were fabricated using
Ti / Mo/ Au multilayers. The use of Mo as a barrier layer was introduced to stop al-
loying between the gold and titanium at elevated temperatures. Silicon dioxide was
used as a passivation layer. Nickel wire was used to be the lead wire and brazed to
the electrodes by refractory silver paste. Highest temperature of diamond thermistor

was 600 °C. The device made by non-doped film is the most sensitive to temperature.

45

The sensitivity decreases with increasing B / C ratio. The response time of thermistor
is compared by 63% change of applied temperature difference. Using oil bath, the
response time was measured to be 1.4 sec. For homoepitaxial film the response time
was observed to be 0.15 sec. It was observed that at 500 °C the resistance of one
thermistor increased by 5% after 100 h in air.

P-type CVD polycrystalline diamond thermistors have been also fabricated at
Michigan State University [120, 125]. The diamond films were deposited using
HF CVD reactor. The resistivity of poly-diamond film thermistors, measured as a
function of temperature (77 - 1273 K) for three doping levels, is shown in Fig. 2.8
[125]. All the samples were annealed at temperatures of 600 °C and 1000 °C for 35
and 8 minutes, respectively, at a pressure of 10’7 torr before taking measurements
for temperature response of resistivity. The high sensitivity is achieved at low boron
concentration. All devices exhibit a negative temperature coefficient (NTC) over the
entire temperature range. This is unique to poly-diamond films, because other con-
ventional semiconductors display NTC only in freeze-out and intrinsic regions and

positive temperature coefficient (PTC) in extrinsic region. The sensitivity of a tem-

perature sensor is characterized by its temperature coefficient a = % 36% where p is the
resistivity of the sensor at temperature T. For the samples shown in Fig. 2.8, a is in
the range of 0.005 - 0.02 K'1 over most of the temperature range. The response time
was in the range of 290ns-25ps which is three to four order of magnitude smaller than
previously reported results [170]. In addition to the reduction of the response time,
the temperature range was also extended to 1000 °C comparing to 600 °C reported
earlier [170]. The parameters of these highly sensitive devices are characterized by a
high stability because the diffusion of electrically active impurities in diamond is very
slight in the temperature range. The responsiveness of a thermistor is determined

by the thermal conductivity (high) and the specific heat (low) of diamond. Diamond

thermistor made by CVD technique are superior to that of any other material in

46

 

10"= ' l

 

"4‘ I a.

1035

101%

 

‘JMM- A col

10°g’

to"!

RESIST IVITY (KI-cm)

z.
lO’E

 

10" _r

 

to" '
o 200 400 600 ;800 1000 1200 1400
TEMPERATURE“)

 

Figure 2.8. Resistivity of poly-diamond film thermistors, measured as a function of
temperature (77 - 1273 K) for three doping levels.

47

r cg'rv A'IOfav

 

 

 

 

 

 

 

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0 mu “’00 £000 AIR/U" I [an I“ {M Adi/nus!

 

 

Figure 2.9. Stress dependences of resistance of the semiconducting synthetic diamond
doped with boron (p-type) in the (a) <100> and (b) <111> directions (original plots).

48

terms of temperature range, speed, stability and sensitivity.

The piezoresistive effect in CVD diamond was not investigated before our work.
However, there was some early Russian work done in the piezoresistance of the HPHT
synthetic diamond [175, 176]. The samples were p-type synthetic diamond doped
with boron. The samples were orderly shaped as cubooctahedrals with side facet 0.5-
lmm. Before measurement the samples were subjected to chemical heat treatment
and following annealing in'vacuum at temperature in the range of 800-900 °C for 30
minutes. In their experiment, a uniaxial (compression) stress was applied through
a small sphere with different dimensions. Measurement of the stress was calculated
from the contact area between the surface of the sample and the sphere. Figure 2.9
shows the resistance as a function of stress in (a) <100> direction and (b) <111>
direction. For both directions of stress the resistance decreases drastically within the
range of pressures 0 to 2000 kg.cm". With the increase of pressure the curve slope
decreases and the resistance tends to saturation. It is seen from their results that
semiconducting diamond is extremely sensitive to the change of pressure (uniaxial
stress). Therefore, diamond piezoresistive sensors could be a good candidate for
micromechanical sensor applications in harsh environments. In this work we estimated

their gauge factor from their curves. The results are given in Chapter 6.

2.8 Summary

Silicon-based and diamond-based sensors were discussed in this chapter. Chemical
vapor deposition, nucleation, patterning and doping methods of diamond film were

also presented in this chapter.

CHAPTER 3

Diamond Film Technology

3.1 Introduction

In this chapter, film preparation by the HFCVD deposition system will be explained.
The description of the diamond powder photoresist (DPPR) nucleation method will
be presented. Raman spectroscopic and SEM techniques will be used to characterize
the diamond films. Pure boron powder was used as a doping source for iii-situ doping.
Two new approaches have been developed to improve the doping profile across the

surface of the sample.

3.2 The HFCVD Deposition System

3.2.1 Description of the System

The simplest and most widely used method for growing the diamond films is the
HFCVD technique. This technique was first used by Matsumoto et a1 [93]. In this
research, the diamond films were deposited using the HFCVD technique. The system
was originally designed and built at Ford Scientific Research Lab. The improvements

are mainly in terms of control and stability of growth parameters, doping and flexi-

49

50

bility of operation.

Figure 3.1 shows a schematic diagram of the deposition system. The deposition
chamber is a 6" hollow cube made of stainless steel provided with openings for flanges
on each face. Visual access during deposition to the substrate and various components
inside the chamber has been provided by a glass window. Before the deposition,
the reaction chamber is evacuated by a mechanical pump to reduce residual gases.
Nitrogen is used to purge and backfill the chamber. Pressure measurement within the
vacuum chamber is performed by a baratron pressure transducer. This transducer
supplies suitable signals through a controller to a down stream valve which maintains
the chamber pressure to be within 0.1% of the preset value up to 100 torr. Up to
three different gases may be used simultaneously. The source gases were H2, CO, and
OH. or CgHz. The flow rate of all three gases is precisely adjustable independently
by three mass flow controllers. The flow controller for H2, CO, and CH4 or CgHg has
maximum operating flows of 100, 50 and 1 sccm respectively. The gas output of each
mass flow controller is mixed simultaneously into a single gas channel which feeds the
processing chamber. The gas is uniformly distributed above the filament.

The filament is a horizontal array of seven 2” long parallel Ta wires (0.005” di-
ameter, 99.9% pure) spaced at 8 mm. A sample with surface area of 2.5x6 cm2 can
be uniformly coated with diamond using this arrangement. The temperature of the
filament is monitored by a two wavelength pyrometer and controlled automatically
to within :1: 2 °C by a controller using an SCR based power supply. The filament
typically draws 25-30 A current at 25-35 VAC at nominal temperature of 2400 °C.
The filament is placed within z 1 cm of the substrate surface to minimize thermaliza-
tion and radical recombinations. However, radiation heating can produce excessive
substrate temperatures leading to nonuniformity and even graphitic deposits [177]. In
our system, the substrate temperature caused by the heat radiation from the filament
is about 725 :1:1 °C.

51

 

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Figure 3.1. Schematic diagram of the deposition system.

52

The substrates are placed on a 1%" diameter Boralectric heating plate (made of BN
with graphite heating element embedded inside) below the filament. The temperature
of the substrate, is an extremely important parameter for CVD diamond growth.
The substrate temperature is measured by a type K thermocouple at its top surface.
The t0p surface temperature monitoring is unique in the sense that in almost all
cases reported in the literature, the temperature of the back surface is monitored
which obviously causes an indefinite error in temperature measurement. The heater
typically draws 5-8 A current at about 50-70 Vac to maintain a temperature in the
range 875 to 890 ° C in the presence of filament at 2400 °C.

3.2.2 Operation of the System

Generally, the number of the experimental parameters that affect the quality of the
CVD diamond film is very large. Gas flow rates, chamber pressure, position of the
substrate and filament and substrate temperatures all may contribute to the quality
of the diamond deposition. Therefore, after setting the pretreated substrate, fixing
the thermocouple on the top surface of the substrate and adjusting the filament to
substrate surface spacing to (3/16)", the turning on and shutting of procedure was

performed as follows.
0 The reactor was first evacuated down to less than 10 mtorr.

0 Second, after reaching the pressure range (<10 mtorr), the hydrogen gas was
introduced into the chamber. Then, the filament and heater temperatures were
brought up slowly in hydrogen environment (>20 torr) in the respective order
manually to their desired temperatures. It is important to avoid any damage
to these elements or substrates by heavy in rush current or sudden temperature

changes especially beyond the desired temperature.

53

0 After two or three minutes of reaching the deposition temperature (typically

890 °C), the carbon sources were switched on.

0 Because of the presence of a very thin conducting carboneous layer on the
surface of CVD diamond film, a special procedure to terminate the deposition
process was followed. In that, only carbon containing gases are shut down and
all other parameters are left unchanged including hydrogen gas for 3 minutes
before the termination of the deposition process. In this period hydrogen, being

the preferential etchant, is assumed to etch away the non-diamond layer.

3.3 . The Nucleation Method

Generally, the nucleation density for diamond growth on non-diamond substrates is
10“ cm"2 [119]. Enhancing the number of nucleation sites on the wafer surface is very
important for the development of a pinhole-free film in a reasonable deposition time.
Difl'erent nucleation methods have been developed by many investigators which were
reviewed in chapter 2 [106, 116, 117, 118, 119]. In this research, the diamond powder
photoresist (DPPR) is used to enhance the nucleation density [119]. This method is
highly compatible with standard integrated circuit (IC) processes. In this research

DPPR was prepared according to the following steps.

0 First the diamond powder (particle size 0.1 to 0.2 pm) was initially dried at

temperature of as 60°C for 2 hours on a heating plate.

0 Second, the dried diamond powder was mixed in the photoresist thinner and
stirred magnetically for 15 minutes followed by 15 minutes of ultrasonic agi-
tation. The magnetic stirring and ultrasonic agitation were repeated for three

cycles.

54

0 Finally, the photoresist was added to the suspension and further stirred and
ultrasonically agitated for 15 minutes each. Again the magnetic stirring and

ultrasonic agitation were repeated for three cycles.

Table 3.1. Sample preparation for nucleation study

 

 

 

 

 

Group Diamond powder Spin speed Number of Nucleation
I.D. density in DPPR DPPR density
(mg/ml) (RPM) layers (cm-2)

G-l 1.98 1

G-la 3000 2.7 x 107

G-lb 2000 3.1 x 107
G-2 2.27 1

G-2a 4000 7.5 x 107

G-2b 2000 8.7 x 107
G-3 5.68 1

G-3a 3000 1.56 x 108

G-3b 3000

G-3c 2000 1.62 x 108

TM 2.27 2

G-4a 2000

G-4b 3000 1.75 x 10°

G-4c 3000

 

 

 

 

 

 

 

The substrate is a 4" (100) single-crystalline silicon wafer or thermally oxidized
silicon or deposited SiOg layer on a silicon wafer. Before spreading the DPPR on the
Si wafer, the wafer was cleaned by piranha solution (stO4zH202, 1:1) for 30 minutes,
then rinsed in the DI water and dried with nitrogen gun. After that the wafer was
coated with a photoresist adhesion promoter (HMDS). The HMDS was applied by
evaporation method in a special furnace at 150 °C for 30 minutes. During CVD
diamond deposition, the photoresist evaporates in initial stages and the diamond

particles act as nucleation sites for the diamond growth.

55

Four different groups of samples were prepared. These samples are grouped ac-
cording to the quantity of diamond powder mixed in the photoresist and the number
of DPPR layers used to coat the substrate. The samples and their parameters are
listed in Table 3.1. The spin time for all sample was 20 second. The deposited dia-
mond films were inspected by SEM. SEM micrographs of the diamond films deposited
on the substrates pre-treated by this method are shown in Figs. 3.2, 3.3 and 3.4.

Figure 3.2 shows SEM micrograph for sample G-1a from Group G-1. The film
was not continuous after 6 hours of deposition time. The nucleation density was
calculated by counting the number of diamond particles in a square area in the early
stage of deposition periode. The result is shown in Table 3.1. It was also observed
that the nucleation density increased by decreasing the spin speed of the substrate
during photoresist coating. Approximately, 10 hours of deposition time was needed
to have a continuous film.

In order to obtain a continuous film for less than 10 hours of deposition time
the density of diamond powder was increased from 1.98 mg/ml to 5.68 mg/ ml. The
result of this approach is shown in Figure 3.3. The SEM micrograph is for sample
G-3a (7 hours of deposition time). The nucleation density of this sample is an order
of magnitude higher than sample from groups G-1 and G-2. Slowing the spin speed
to 2000 RPM resulted in a large amount of cluster particles and nonuniformity of the
film with very little increase of nucleation density (see Table 3.1). A continuous film
was obtained for about 7 hours of deposition time.

In Group G-4 samples, two layers of DPPR were spun on the substrate. The
DPPR used for this group of samples, was from the same mixture of group G-2 (2.27
mg/ml). After coating the first layer, the substrate was loaded into the furnace in
order to cure the first layer (Softbake, 90 °C, 20 min). As shown by SEM in Figure

3.4, the film is continuous for 7.5 hour of deposition time.

 

20K U 013 250

 

Figure 3.3. SEM micrograph for sample G-3a.

57

 

Figure 3.4. SEM micrograph for sample G-4b.

58

It is visible from the SEM micrographs, especially Figure 3.3 and Figure 3.4,
that the film has fairly uniform grain size (as 1 to 2 pm). In fact, by utilizing the
pretreatment of the last two approaches (G-3 and G4), it was possible to obtain a
complete surface coverage after roughly seven hours of deposition time with deposition
rate in the range of 0.25 0.30 pm / hour. Raman spectra of the diamond films deposited
on the silicon substrate show a strong peak at 1332 cm“.

In conclusion of this study, the following observations were recorded during SEM

inspection of diamond films.

0 Higher spin rate leads to lower nucleation density but higher uniformity (Group
G-2).

e Spreading the DPPR on the wafer after half hour of preparation has led to more
non-uniformity and clustering. Using DPPR suspension which is rested for two

hours leads to less clusters than a freshly agitated one.

o A larger quantity of diamond powder in a given solution of photoresist and
thinner gives higher nucleation density (Group G-3). Using two layers of DPPR
has also led to higher nucleation density (Group G-4).

This experiment provided an optimum quantities of diamond powder, photoresist
and photo-resist thinner in DPPR suspension which leads to a continuous diamond

films with deposition time for almost 7 hours.

Surface Roughness

In order to quantify film roughness, a Tencor P-2 surface profiler was used. Fig.
3.5(a) shows the surface roughness of sample deposited for 9 hours. The maximum
surface roughness is about 1450 A. The film thickness is about 2.1 pm. Fig. 3.5(b)
shows the surface roughness of sample deposited for 20 hours. The thickness of this

film is 5.8 pm and the maximum surface roughness is about 4000 A.

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Figure 3.6. Effect of diamond film thickness on the surface roughness.

61

Generally, as the film thickness grows (longer deposition time) the surface rough-
ness was also observed to grow. Figure 3.6 shows the effect of diamond film thickness
on the surface roughness. A larger surface roughness of the thicker films results from

the larger grains on the surface.

3.4 Diamond Film Patterning

Many of the potential microelectronic and microsensor applications require patterned
thin films of polycrystalline diamond. Etching of diamond film by dry etching tech-
niques has been investigated [151, 152, 153]. The non-uniformity of the etch, the low
etch rates and poor etch selectivity between mask materials and the diamond have
limited the application of the dry etching techniques [59].

Selective deposition of polycrystalline diamond can be achieved if the two regions
on the substrate have nucleation densities differing by several orders of magnitude.
Many attempts employing varying methods of patterning of diamond films on non-
diamond substrates through selective nucleation have been reported [61, 119, 147,
148, 157, 158]. Many of these techniques were described earlier in section 2.4 chapter
2. Most of these techniques cause surface damage.

Recently, a novel process has been developed to selectively deposit high quality
polycrystalline diamond films [119]. This has been achieved by patterning photore-
sist, which was premixed with fine diamond powder (0.1-0.2 um), using standard
photolithographic process. The preparation of this solution was described in section
3.4 chapter 3. This technique not only preserves the high quality of substrate sur-
face but is also compatible with the existing integrated circuit fabrication technology.
Consequently, this technique will be adopted for this research.

62

Double-Layer Patterning

In this work, as the substrate is a 4” (100) silicon wafer and minimum feature size
is 5 pm, an improvement of this technique was suggested and studied. A double
layer structure was used to enhance the patterning. Three different approaches were
developed during this work. Fig. 3.7 shows the schematic of 3 configurations used
for double-layer patterning. Mask 1 of the microchip was used in this study.

In the first configuration (Config-l), the samples were patterned by first coat the
oxidized wafer with layers of photoresist (PR)(AZ1470) and a double layer of DPPR.
The PR layer helps removes residual diamond particles during the spray-developing.
After patterning the photoresist layers and prior to the diamond deposition, the
sample was treated by BHF for 2 minutes via ultrasonic treatment. Fig. 3.8 shows
SEM micrograph for diamond microchip prepared by Config-l, It is clear that some
scattered diamond particles were grown on the undesired areas. However, These
particles did not form a continuous film as shown in the Figure. The nucleation
density in the undesired area was z 1.1 x105/cm2 which is very small comparing to
the nucleation density in the desired area which was z 1.75 x108/cm2.

In the second configuration (Config-2) a layer of undoped polycrystalline silicon
was deposited on the top of the oxidized wafer. The polycrystalline silicon layer was
deposited in a LPCVD furnace at a SiH‘ pressure of 320 mT and a temperature of
z 600 °C. Polycrystalline silicon layers with different thicknesses (2000 A, 1 pm, 2
pm and 3 pm) were used for this study. Two layers of DPPR were then dispensed
on the poly-Si / 8102 / Si wafers. After patterning the photoresist, the wafer was then
loaded into a plasma reactor to etch the exposed polysilicon areas. The polysilicon
was etched by using SF5 and Freon 115 (Cst) gases. The gas flow rates was 50 sccm
for each gas. The power was 110 watt and the over all pressure in the reactor was 150

torr. The etch rate of the polysilicon was z 700 to 900 A per minutes. After etching

63

DPPR/DPPR

PR(AZI470)

  
  

Conf. 1

PO Y-Si

Conf. 2

    
 

PR(AZI470)

vow..- mm: '

Conf. 3

Figure 3.7. Schematic diagram of 3 configurations used for double-layer patterning.

64

the polysilicon, diamond was then deposited. Figure 3.9 shows SEM micrograph for
diamond microchip prepared by Config-2. It is clear from this micrograph that the
polysilicon layer also helped remove the residual particles. The nucleation density in
the undesired area was a: 3 x10‘/cm2 which is almost one order of magnitude less
than the samples patterned by using Config-l.

The last configuration Config-3 is a combination of Config-l and Config-2. The
result of this configuration is shown in Fig. 3.10. It is clear that the sample is
the cleanest. The nucleation density in the undesired area was z 1 x104/cm2. The
above results show that the polysilicon layer was very successful. However, the most
successful result was achieved by using sample with 1 pm and 2 pm in thickness.
In the case of thin polysilicon layer 2000 A in thickness, the film was stripped away
during diamond deposition and the patterns were destroyed. In the case of thick
polysilicon layer (3 pm), the problem was during etching the polysilicon. The etch of
the thick polysilicon layer required longer time (> 17 minutes). The photo-resist mask
was unable to withstand the etching process for a time longer than z 17 minutes.
Since the DPPR was used as a mask, etching the DPPR layer means loosing the
nucleation sites. Also, using a thick polysilicon layer makes the step of the diamond
patterns too high which is not desired for metalization.

Based on these observations, most of the diamond films used in this study were
patterned using Config-l or Config-3. A 3 to 4 pm of low temperature oxide was
deposited instead of a 2 pm thermally grown oxide in the case of Config-l. In the
case of Config-3 only 1 pm of polysilicon layer was used. Using the double-layer
patterning technique developed in this research we were able to have a microstructure
with minimum feature size of 5 pm in width. Fig. 3.11 shows SEM micrograph for

an array of resistors with different dimensions.

65

li'il'l SDKU 1 ‘3

 

Figure 3.9. SEM micrograph for diamond microchip prepared by Config-2.

 

 

Figure 3.10. SEM micrograph for diamond microchip prepared by Config-3.

 

 

      

 

01

 

BEIK'J

Figure 3.11. SEM micrograph for an array of resistors with different dimensions.

67

3.5 Effect of Deposition Parameters

The structure and the quality of the CVD diamond films strongly depend on the
deposition conditions. The correct selection of experimental parameters, such as
reactant gas composition, filament and substrate temperatures, substrate to filament
spacing, system pressure, and absolute and relative flow rates of gases, and their
stability throughout the growth process is very important to achieve reproducible,
high quality diamond films. Almost all successful diamond growth experiments appear
within a fairly well-defined range of parameters.

In this research the effect of the substrate temperature and the gas composition
and flow rates were studied. The source gases were H2 and OH. or Csz in the
presence or absence of CO. The deposited films were characterized by SEM, Raman

spectrosc0py and surface profiler.

3.5.1 Effect of Substrate Temperature

In this research the substrate temperature was studied at 825 °C, 890 °C and 925 °C.
In all cases, the total pressure was kept at about 50 Torr and the gas flow rates used
were 100 sccm, 0.75 sccm and 12 sccm for H2, Csz and CO, respectively. Raman
spectra for the samples deposited at different substrate temperatures are shown in
Figure 3.12. All spectra show the characterization peak at 1332 cm". The broad
shoulder around 1500 cm‘1 indicates amorphous diamond-like component in the film.

These results show that the quality of the diamond film improves when the sub-
strate temperature increases from 825 °C to 890°C, and then the quality shows some
deterioration at 925°C. As determined by surface profiler, it was also observed that
the growth rate of the diamond film increases with increasing temperatures from 825
°C (#018 pm/hr) to 890 °C (z0.28 um/hr). This observation is consistent with the
results reported by other investigators [122, 123, 125].

68

 

 

 

 

 

 

 

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800 1000 1200 1400 1600 1800 2000
WAVE NUMBERS (11cm)

Figure 3.12. Raman spectra for the samples deposited at different substrate temper-

atures; a) 825 °C b) 890 °C c) 925 °C.

69

3.5.2 Effect of Gas Composition and Flow Rates

Most of the reported results at high substrate temperatures showed that the graphitic
components in the film increased with increasing methane concentration in the hy-
drogen gas mixtures [111, 123]. To investigate this effect, a number of diamond films
were deposited at different hydrogen flow rates while keeping all other deposition
conditions the same.

In Fig. 3.13, the Raman spectra of deposited films on silicon at 890 °C show the
effect of different concentrations of methane in hydrogen. CH4 flow rate was kept at
0.75 sccm and CO flow rate was kept at 12 sccm. The total gas pressure was kept
at 50 Torr during deposition. An inspection of these Raman spectra show that, as
the hydrogen flow rate decreased from 100 sccm to 40 sccm (methane concentration
increased), the graphitic components in the film increased. A degradation in purity of
the diamond is clearly visible from the presence of large graphitic peak especially in
spectrum 95L (40 sccm of H2), 93L (50 sccm of H2) and in spectrum 96L (55 sccm of
H2). The diamond peak was relatively small in these samples. The best quality was
for sample 92L (100 sccm for H2, 0.700 sccm for CH4, 12 sccm for CO). The effect
of methane concentration on the internal stress of the diamond film will be described
in chapter 4 (section 4.5).

Effect of CO

Various studies have shown that oxygen plays an important role in the growth
mechanism of CVD diamond [97, 98]. These studies have shown that addition of
oxygen improves CVD diamond purity and growth rate. However, adding even small
amounts of oxygen resulted in failure of filament. Therefore, an alternative way
was adopted and CO instead of pure oxygen was used. The effectiveness of CO in
supplying oxygen or modifying the character of the film was observed by Raman

Spectra. Raman Spectra for two samples deposited with and without C0 are shown

70

 

 

 

 

 

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800 1000 1200 1400 1600 1000 2000
WAVE NUMBERS (11cm)

 

Figure 3.13. Raman spectra for the samples deposited at different hydrogen flow
rates. CH4 = 0.7 sccm and CO = 12 sccm for all samples.

71

in F ig.3.14. A degradation in purity in the absence of CO was clearly visible from the
presence of large graphitic peak (spectrum a). However, an SEM inspection of the
film without CO did not reveal any significant difference. In addition to the above
mentioned effect, another eflect was also observed for the first time which is related
to the internal stress of the diamond film. This effect will be described in chapter 4
(section 4.5).

In summary of this study, the correct selection of deposition parameters for best
quality diamond film was optimized and given in Table 3.2. some of the value indi-
vidually or in combination are reactor dependent. Therefore, this formulation should

be considered more specific to the present deposition system than a general one.

Table 3.2. Optimum processing parameters.

 

 

Substrate to Gas Flow (SCCM) F il.Temp. Sub. Temp. Pressure
filament spacing H; CH4 CO (°C) (°C) (Torr)
(3/16)” 100 0.7 12 2400 890 50

 

 

 

 

 

 

 

 

 

3.6 Doping of Diamond Films

Since gaseous doping sources are highly poisonous, only solid sources (boron powder)
were considered in this research. Pure boron powder was introduced directly into
the chamber. The powder is placed on the substrate holder (heating plate) using a
specially designed holder. Fig. 3.15 shows a schematic diagram of the boron holder.
The holder consists of Mo plate (1 mm thick) with a number of 1 mm diameter holes
drilled in it. The plate is inserted in a clip which covers its one face and a selected

number of holes are filled with boron powder. One hole takes an average 0.2 mg of

72

 

CO = 12 sccm

 

INTENSITY (Arbitrary Units)
1

 

 

 

'- CO = 0.0 sccm

lrl

INTENSITY (Arbitrary Units)

1411lnlnlnl-l
800 1000 1200 1400 1600 1800 2000

WAVE NUMBER (1/cm)

 

 

 

Figure 3.14. Raman spectra for the samples deposited with or without CO.

73

boron powder to fill. The boron powder was introduced into the chamber in two
different approaches. In the first approach only one boron holder was used. The
boron holder is placed very close to the substrate (within 0.5 cm) at a fixed place on
the substrate holder. In the second approach two boron holders were used and were
placed one at each side of the substrate.

In order to see the effect of each approach, a test chip was designed and fabricated.
The size of the chip is 1.1 inch x 1.1 inch. It employs two masks. The masks
were designed using CAD software and fabricated on 2 inch x 2 inch high resolution
photographic glass plates at Ford’s photographic facility. The first mask is used to
define the desired diamond growth area. The second mask is for metalization. In most
cases, the metal pattern was generated by shadow mask. The mask was fabricated
on thin Cu plate at the Ford’s photographic facility.

The test chip consists of a rectangular shaped diamond resistors of various size,
500 to 1000 pm wide and 1500 to 4000 pm long structures. Figure 3.16 shows a com-
posite layout of this test chip. Since the test chip contains only diamond resistors, the
chip will be refered to as discrete-chip. The resistors are grouped into four identical
groups (G-l, G-2, G-3 and G-4). Each group contains five different resistors which
are labeled as R4, R3, Rc, RD and RE as shown in Fig.3.16 and illustrated further
in Table 3.3. The discrete-chip was fabricated in three steps. Using the first mask,
an undOped diamond film was deposited on the top of an oxidized silicon substrate.
After the deposition of the undoped diamond films, the substrate was loaded back
into the chamber to be doped with boron powder using one of the two approaches
described earlier. After the deposition of the doped layer, the metal was then evap-
orated using the shadow mask. The resistance of each resistor was measured using a
multimeter(HP 3468A).

Table 3.3 shows the result of the resistance measurement using the first approach

(one boron holder). The boron holder was placed in the right side of the undoped

74

 

Figure 3.15. Schematic diagram of the boron holder.

 

Figure 3.16. Composite layout of the discrete-chip.

75

Table 3.3. Resistance measurements for one boron holder.

 

 

 

 

Resistance (k0) Change %
G-l G-2
R4 = 1100 RA = 267 +312
R3 = 821 R3 = 186 +341
RC = 630 RC = 157 +301
R0 = 297 R3 = 61 +386
R3 = 476 R3 = 163 +192
G-3 G-4
R3 = 1400 R4 = 393 +256
R3 = 970 R3 = 237 +309
RC = 798 Rc = 206 +287
R0 = 405 R3 = 97 +317
R3 = 563 R3 = 209 +169

 

 

 

Table 3.4. Resistance measurements for two boron holders.

 

 

 

 

Resistance (k9) Change %
G-l G-2
RA = 83 R4 = 189 +127
R3 = 101 R3 = 119 +18
Rc = 97 R0 = 64 +51
R0 = 114 R3 = 39 +192
R3 = 75 R3 = 127 +69
(ii-3 G-4
R3 = 149 R4 = 271 +82
R3 = 147 R3 = 165 +12
RC = 131 RC = 95 +38
R3 = 174 R0 = 76 +128
R3 = 113 R3 = 89 +27

 

 

 

 

 

76

substrate (closer to resistor R3 (Cu-2) and RD (G-4)). The result shows that the
resistor closest to the boron holder has the lowest value of resistance. The percentage
change in resistance was in the range of 170 to 486 ‘70.

By using two boron holders (second approach), one at each side of the substrate,
the percentage change of resistance for most resistors was in the range of 12 to 82
% less than 100 % except for resistor R3 and RA which was over 100 % . This is
because one resistor was located next to the boron holder and the other was located
in the center of the sample (see Figure 3.16 and Table 3.4).

Based on this observation, a new boron holder was designed and fabricated. The
schematic diagram of the new design is shown in Figure 3.17. In the new design, two
different size of holes were drilled in the Mo plate from the top to the bottom. The
large hole (six large holes were drilled in each Mo plate) with 1.2 cm in diameter is
surrounded by 8 small holes 1 mm in diameter. The small holes are used to carry the
boron powder as was done in the old design. Each one of the large holes encloses a
different diamond chip. The doped layer of diamond was deposited thru the opening
of the large hole. This new boron holder was especially designed to be used for the
microsensor microchip. The fabrication process of the microchip will be described in
chapter 4 section 4.3. The size of the microchip is 1 cm x 1 cm. Each sample contains
six chips. Table 3.4 shows the result of resistance for an identical resistor from each
chip. Six chips were fabricated at the same time. Since in the new design, the holes
filled with boron surrounded each chip, as expected, the change in resistance at any
position on any chip was very small. Table 3.4 shows that the maximum percentage
change was z 16 %, depending on the number of holes filled with boron. Therefore,
for better reproducibility of temperature and hence, of doping concentration and
distribution of boron everywhere on the surface of the chip, the new design is the
most successful and reliable approach to dope diamond chips. The vapor pressure

of boron at growth temperature appears to be sufficient to evolve boron vapor for

77

controlled daping of the diamond films. The temperature of the boron powder is
assumed to be equal to the substrate temperature as measured by thermocouple and
is not measured independently.

All the films display typical Raman spectra of diamond with a strong peak at
1332 cm“. Although there is some scatter in the data (resistance measurements),
the controlling of doping through the quantity of boron powder appears to hold
sufficiently. As a result of these observations, all the films for the piezoresistive
measurements were deposited on an undoped buffer layer of diamond using the second

or third approach.

3.7 Homoepitaxial Doped Film

In this research a thin doped diamond film was grown on a synthetic diamond sub-
strate. The diameter of the diamond substrate was 3 mm and the thickness was
400 pm. The boron holder was placed next to the diamond substrate. The Raman
spectrum of doped homoepitaxial film deposited on thin diamond sample is shown in
Fig. 3.9. The spectrum shows strong peak at 1332 cm”. The intensity of Raman
signal for homoepitaxial films is much larger than polycrystalline films (see Fig. 3.13).
The full width at half maxima (FWHM) of diamond peak is relatively much smaller
for homoepitaxial films (3 cm"1 for homoepitaxial, 7 to 9 cm”1 for polycrystalline
film). An important observation to note is that a peak corresponding to Diamond-like
Carbon (DLC) or disordered carbon at 1355 cm'1 is totally absent which is another

evidence of the superior purity of the homoepitaxial diamond films.

78

Hole for Diamond 30'0"
Deposition POWdel'

 

 

(0.2mm) Mo (1mm)

Figure 3.17. a) Boron powder holder b) Cross-section holder placed on silicon.

Table 3.5. Resistance measurements for two samples.

 

 

 

Sample ID. Resistance (k9) Change %
3550 Chip-1, R = 385.1 C1332, R = 410 +6
(35133, R = 302.4 Chip-4, R = 310.25 +3
Chip-5, R = 130.15 Chip-6, R = 128 +2
353D Chip-1, R = 20.4 Chip—2,
Chip-3, R = 18.3 Chip-4, R = 21.25 +16
Chip-5, R = 19.5 Chip-6, R = 22.3 +14

 

 

 

 

 

 

79

 

 

 

Homoepitaxial (100)

La? ..

'E

:1

b

e —

E

S,

<73

2

w _

H k

E
1.1.121.1.1.1

 

 

 

Figure 3.18. Raman spectrum of doped homoepitaxial films deposited on type 2a
diamond substrates (Dubbelldee Harris Corp., Mt. Arlington, NJ )

3.8 Summary

In this chapter, the study to synthesize and characterize semiconducting diamond film
for device fabrication has been presented. The DPPR seeding method to enhance the
low intrinsic nucleation density of diamond on non-diamond substrates was described
and was improved by using two layers of DPPR instead of one layer. Experimental
parameters such as substrate temperature and relative flow rate of gases were studied
and Optimized. Three different approaches to load the boron powder into the chamber

were studied.

CHAPTER 4

Design and Fabrication of a

Multisensor Microchip

4.1 Introduction

This chapter deals with the design and fabrication of a multipurpose test microchip.
Fabrication details of micromechanical structures such as cantilever beams, bridges,
and membranes with different dimensions and shapes are described. Boron doped
layers were selectively deposited on undoped diamond films using boron powder as
doping source and low temperature oxide as doping mask. For metalization of dia-
mond devices, a double layer of Pt / Ti is used. An appropriate process for patterning
of the Pt / Ti layers with wet chemical etching solution was developed. The total stress
in the diamond film was also measured. All the patterning methods presented in this

chapter are adopted from 10 fabrication technology.

4.2 Microchip Design

A multisensor test microchip is designed to demonstrate the feasibility of diamond

film for sensor applications. The sensor test chip contains a series of resistors of

80

81

varying sizes, shapes and orientation. It also contains cantilever beams, bridges,
membranes, a MOSFET, Hall structure, a pressure sensor and an accelerometer.
Each device is designed for a specific purpose. The resistors are designed for thermal
and piezoresistive measurements. The size of the chip is 1 cm x 1 cm. The smallest
feature size is about 5 pm in width. It employs a six mask fabrication process.

Fig 4.1 shows a composite layout of the masks whereas the individual mask layouts
are shown in Figs. 4.2, 4.3, 4.4 and 4.5. The masks were 5 inch x 5 inch with chrome

patterns which were designed and fabricated at Ford Scientific Research Laboratory.

Mask 1 : Mask 1 is used to define the desired diamond growth area (first undoped

diamond layer). The layout of Mask 1 is shown in Fig. 4.2(a).

Mask 2 : Mask 2 is used to define holes on the back side of the wafer for membrane
(pressure sensor). The layout of Mask 2 is shown in Fig. 4.2(b). Two sided
mask aligner and infrared microscope are used for simultaneous mask alignment
using masks 1 and 2. The design of the back etch mask is based on the following
equation [178].

I = M — Via—h) (4.1)

where I is the diaphragm size, M is the mask opening and T is the wafer
thickness. In case of silicon membrane h is the membrane thickness. However, in
this work the wafer is etched to the back side of the diamond film. KOH is used
to etch silicon. Since KOH does not etch diamond, thus h = 0. Figure 4.3(a)
shows Mask 1 and Mask2 aligned simultaneous and the expected membrane size

(light area) in the middle.

Mask 3 : The third mask is used to selectively deposit doped diamond on the previ-
ously deposited undoped diamond films. Selective growth of boron-doped poly-

crystalline diamond films is achieved using low-temperature 8102 as a masking

82

layer. 8102 is removed selectively using mask 3. Fig. 4.3(b) shows the layout

of this mask.

Mask 4 : The fourth mask is designed to define the metal contacts in the passivation

layer. The layout of this mask is shown in Fig. 4.4(a).

Mask 5 : The metal mask is designed to define the metal interconnection lines and
pads. The width of all the interconnection lines is 50 pm. The size of bonding
pads is 500 pm x 500 pm, except for the Hall structure for which the size of
bonding pads is 700 mm x 700 pm . Fig. 4.4(b) shows the layout of this mask.

Mask 6 : The layout of mask 6 is shown in Fig. 4.5. This is designed to define
window for sacrificial layer etching in order to fabricate microstructures such as
cantilever beams and bridges. This also can be used to fabricate the accelerom-

eter sensor.

4.3 Metalization

Since the diamond devices are intended to operate at high temperatures in chemically
and physically harsh environment, the choice of the metal is important.

In case of test chip, diamond film is deposited on SiOz or undoped polycrystalline
silicon. Therefore, in addition to a good ohmic contact of metal with diamond, an
additional requirements of a good metalization scheme may include planarization and
good mechanical bonding with both diamond and the insulated layers.

A double-layer Pt / Ti structure was used for ohmic contacts in this research. This
is because, the carbide of titanium is easily formed at 400 °C [145] (good adhesion).
This is also because of the high melting point of Pt and its high resistance to oxidation

and to KOH etchant.

83

MOSFET

 

Figure 4.1. Composite layout of the masks. Resistors r1 to r15 are used for piezore-
sistive and temperature measurements.

 

 

84

a)

 

r—_—______—_——_____

b)

 

Figure 4.2. (a) Layout of mask 1 (undoped diamond). (b) Layout of mask 2.

oo
0‘

I
l
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
.1

3)

 

r—————————————————.—1

I
l
I
|
I
I
I
I
l
I
I
I
I
I
I
I
|
I
I.

b)

 

Figure 4.3. (a) Combined mask 1 and mask 2, (b) Layout of mask 3 (doped diamond).

86

 

3)

 

 

 

.0

(metal

Figure 4.4. (a) Layout of mask 4 (metal contacts), (b) Layout of mask 5

pat terns

87

 

Figure 4.5. Layout of mask 6 (Sacrificial layer window).

88

In earlier work [125] on the double-layer Pt / Ti structure, the metal pattern was
generated by shadow mask. However, in the case of the microchip it is necessary
to develop a process which is compatible with the IC fabrication technology. A wet
chemical etch process which was developed in this research is described next.

As a first experiment, the thickness of the Ti layer was 200 A and the thickness
of the Pt layer was 0.5 pm. Both metals were deposited using E-Beam evaporation
system. In order to avoid oxidation of the Ti layer, the Pt was evaporated immediately
after the Ti without breaking the vacuum in the system. Pressure during evaporation
process was as 1 x 10‘7 torr.

After evaporation of the metals, the sample was coated with photoresist. Next
the photoresist was patterned using the metal mask of the microchip (Mask 5). The
Pt/ Ti layer was then etched in a saturated solution of H20:HN03:HC1/ 4:4:1 at 90°C
for 2 min, followed by a rinse in deionized water. Figure 4.6 shows SEM micrographs
for sample during the etch and before striping the photoresist. It is clear that the
photoresist was etched by the chemical etchant and the photoresist lines were pulled
away from the substrate surface.

From these observations following deductions were drawn.

0 The photoresist film as a mask by itself was not sufficient. Other or additional

mask is required.
0 The diamond film step coverage was not good. A thicker Pt film is required.

0 After testing the devices by a multimeter, it was observed that the devices were
not electrically isolated from each other. This might be due to the base layer
(Ti) forming its oxide during the inspection and before ending the etch process.
A thinner Ti layer is suggested and the etching should be done in one step

without removing the sample from the etch solution.

89

 

 

 

 

EIIIOPI'I 2 DK U 42

 

Figure 4.6. SEM micrographs for sample during the etch and before striping the
photoresist. Photoresist lines were pulled away from the substrate surface.

90

On the basis of the above observations, the metalization scheme was changed as

follows:

0 (1) Decrease of Ti layer thickness from 20024 to 125221.
0 (2) Increase of Pt layer thickness from 0.5 pm to a: 1.0 pm.

0 (3) Cover the Pt/Ti layer with plasma nitride or oxide before coating with

photoresist.

The above metalization scheme was successful and was used for the fabrication of
the microchip. The fabrication of the microchip will be described in the next section.
In most of the fabricated microchips the cross sectional step coverage is still not good
enough on some of the devices. This might be due to mishandling or misalignment
of the sample with the mask. Since the mask was 5 inch x 5 inch and the sample
was 1 inch x 3 inch it was not easy to align both together. The samples were heat
treated in vacuum chamber at a: 500 °C in order to improve the adhesion and stabilize
the contacts. Furthermore, to verify the compatibility with IC technology, gold wire
bonding was made on the metal bonding pads before and after heat treatment. The

gold wire adhesion was stronger after the heat treatment.

4.4 Microchip Fabrication

In order to demonstrate the feasibility of diamond for microsensor applications in
harsh environments, it is important to test the use of diamond piezoresistive and
micromechanical structures on the same chip. This can be achieved by selectively de—
posited two polycrystalline diamond layers. The first layer is undoped polycrystalline
diamond layer which can be used as micromechanical structures such as cantilever
beams, bridges and membranes. The second layer is for piezoresistor which can be

achieved by selectively deposited p-type doped layers.

91

4.4.1 Undoped Diamond films

The major fabrication sequence of the multisensor microchip is shown in Fig. 4.7.

Starting substrates were 4-inch p-type (100) silicon wafers.

Mask 1 and Mask 2

First, the wafer was cleaned by piranha solution (H2304zH202, 1:1) for 20 minutes.
Second, two layers of LPCVD silicon nitride and of low temperature oxide (LTO),
with thicknesses of 100 nm and 3 pm, respectively, were deposited on both sides of a
Si wafer Fig. 4.7(a). Wafer was then coated with positive resist on the backside and
front side. The front side was coated after baking the wafer at 100 °C for 45 seconds
on a hot plate. Wafer was then heat treated (softbake at 90 ° for 15 minutes). Two
diamond powder photoresist DPPR layers were then dispensed on the front side of
the wafer. The wafer was again heat treated (softbake at 90 ° for 15 minutes).
Using a double-sided mask aligner, both resists were patterned as shown in Fig.
4.7(b). Mask 1 and Mask 2 were used in this step. The LTO and Si3N4 layers were
then dry-etched from the backside Fig. 4.7(c). The wafer was then cut into 1 inch x 3
inch piece and loaded into the diamond deposition system. An undoped diamond film
was grown at 890 °C in the HFCVD reactor. The photoresist evaporates in the reactor
and the remaining diamond particles act as seeds for the growth of polycrystalline
diamond film only on the front side. A part of the LTO layer is removed by the
atmosphere of diamond deposition process (Fig. 4.7(d)). Figure 4.8 shows SEM

micrographs for a structure from the microchip fabricated at this level.

(a)

ill.|llnéiilli+illl.f;illl.1.14..i 11', '

Hi‘L011H$HkJilz+hlimH.“L1m n~ ‘,
‘ ( , 1 ; 1 ‘ ‘ ‘ 1 ‘1 , + .
'11 HI: I l r _ 1' i V 1‘

min“ nm‘lrl‘lnt I< ' NH-‘IH'HH'r‘lilinIi‘II:

 

(c)

 

 

(e)

 

(g)

 

 

(1) t J \/ i
3 /

 

 

 

DPPR 1

 

PRAZ1512

 

 

    

 

z 111.11';1;, J 11,1111' : .11 .1
., 1.11111 11111

     

 

llfitlf'il‘. 1" 13‘ ‘i’x ,."1 n

  
 

 
     

   

(b) i >

111 |‘ ‘v: 1'1““
lanmmwMWMLWVI'r ”1

23%;; 111':
11»: 11:11 :11;1_

 

(d)

 

    

  
 
 

 
 
  

111111131.111.Llnlillilhlkumn‘111 ‘
‘1 1.1 ‘11 i“ ‘l; I} “ 1‘

 

 

   

(k)

       

il

Diamond (undopped) -

Plasma (oxide/nitride)

“Uri. . ‘,..-11 :1-14 “til" 11.31,
{1}. 11 .11 1.11 1+ 11 1‘1‘11 .1 1 .-.l

 

 

Diamond (dopped)
PtlT i (contacts)

 

Figure 4.7. Major fabrication process steps for the multisensor microchip.

93

4.4.2 Selectively Doped layer
Mask 3

A new layer of Low temperature oxide was then deposited over the entire sample and
patterned using Mask 3 (standard photolithography was used). The diamond was
then exposed by removing the oxide from the desired areas by using buffered oxide
etchant. The sample was again loaded in HFCVD reactor to grow p-type diamond
which can only grow in exposed areas as shown in Fig. 4.7(f). Boron holder which
was designed and fabricated in this research was used to carry the boron for in-situ
doping. The effectiveness of this technique was described in chapter 3. An SEM

micrograph taken after the deposition of the doped diamond is shown in Fig. 4.9.

4.4.3 Metalization Steps

Mask 4 and Mask 5

Plasma oxide and plasma nitride were then deposited over the entire sample (Fig.
4.7(g)). Then plasma oxide and plasma nitride were dry etched in order to define
holes for metal contacts. Titanium and platinum layers were evaporated on the
entire sample using E—beam system. The metal were then patterned as described in

the metalization section.

4.4.4 Micromechanical Structures
Mask 2 and Mask 6

A process has been developed in this work for fabricating micromechanical struc-
tures, particularly cantilever beams, bridges (doubly supported beams) and mem-
branes. Surface and bulk micromachining techniques are used to fabricate the can-

tilever beams, bridges and membranes. The sacrificial layers were low temperature

 

Figure 4.8. SEM micrographs for a resistor (a) top view and (b) close-up view from
the microchip.

 

 

95

a)

 

 

IDOPM

b)

10PM 31:11.11

 

Figure 4.9. SEM micrographs showing doped diamond and Si02 (LTO) mask; (a)
top view, doped diamond (dark areas) and LTO (bright area), and (b) close-up view,
doped diamond (bright areas) and LTO (dark area).

a)

4' U I} ' I‘l £1:1I<".,.|

 

Figure 4.10. SEM micrograph showing (a) array of cantilever beam structures curled
upward ( 600 to 1500 pm in length, 150 pm in width and 4 pm in thickness) (b) close
up view of one of the beam.

 

 

97

b)

_2+'1-1 20+: 1.1 1:1 1

 

Figure 4.11. SEM micrograph showing (a) array of cantilever beam structures (200
to 1200 am in length, 20 pm in width and 4 pm in thickness) (b) close up view of
one of the beam.

98

a)

.Z'IIIKU 44

 

want-“1

11)

 

 

Figure 4.12. SEM micrograph of a bridge (3 8 pm in width, 100 pm in length and 4
pm in thickness); (a) top view and (b) side view (bridge does not touch the substrate).

99

 

Figure 4.13. SEM micrograph showing an overview of the multisensor microchip.

100

oxide (LTO) or undoped polycrystalline silicon. An array of cantilever beams of var-
ious sizes ranging from 100 to 1500 pm in length, from 20 to 150 pm in width and 3
to 5 pm in thickness were fabricated on the microchip. An array of bridges of various
sizes ranging from 100 to 200 pm in length, from 5 to 50 pm in width and 3 to 5 pm
in thickness were also fabricated on the microchip. These micromechanical structures
were fabricated as follows:

After patterning the metal (Fig. 4.7(h)), the sample was loaded in a KOH bath
(30 % at 80 °C) for anisotropic etching of silicon (Fig. 4.7(i)). Prior to the loading
into the KOH bath, the sample was heated to 500 °C to improve the adhesion of the
metal to the substrate. After heating the sample, a thin layer of plasma nitride 3000
to 4000 A was then deposited on the sample. This layer was used to protect the edge
of the titanium layer and other structures from KOH, since the etch of the silicon
usually takes more than 12 hours.

After silicon etch, two layers of photoresist AZl470 (in order to have a thick layer
of photoresist) were then spun on the sample and then softbake (30 min at 90 °C).
The photoresist was then exposed and developed using Mask 6 of the test chip. The
photoresist thickness after patterning was z 2.5 pm. The plasma nitride which was
deposited earlier, was then dry etched to expose the sacrificial layer.

The sacrificial layer LTO was etched by buffered hydrofluoric acid (BHF 7:1) to
form the free standing structures as shown in Figures 4.10, 4.11 and 4.12. During
this step, the sample was removed from the etching solution every three hours. The
sample was inspected under the microscope and then loaded in a furnace to hardbake
the photoresist and again loaded back into the etchant bath.

Fig. 4.10(a) shows that the diamond cantilever beams are curled upward indicat-
ing an intrinsic stress in diamond films. The intrinsic stress in the diamond film will
be explained in the next section. Different micromechanical structures are shown in

Fig. 4.11 and in Fig. 4.12. An SEM micrograph shown in Fig. 4.13 gives an overview

101

of the multisensor microchip. The light areas are Pt/ Ti interconnects and bonding
pads. The test-chip contains a number of structures, including piezoresistors, ther-
mistors, a Hall structure, a MOSFET, a pressure sensor, an accelerometer, cantilever
beams, bridges and membranes. The fabrication technology of pressure sensor and

accelerometer was demonstrated in this chip. However, these sensor were not tested.

4.5 Intrinsic Stress in the Diamond Films

Generally, most deposited diamond thin films on silicon or other substrates used in
microsensors are in a state of internal stress, either compressive or tensile [179, 180,
181]. The internal stress has an effect on the deflection of beams (accelerometer) and
diaphragms (pressure) and thus influences the response parameters of sensors which
use them. Tensile stress exceeding the strength of the film may break the film, and
large compressive stress can cause films to buckle. Therefore, knowing the properties
of internal stress of the diamond film is very important in controlling the flatness of
films and in predicting the response parameters of sensors that utilize diamond films.

It is known that a layer of one material grown on another material with different
mechanical properties is often in a state of stress. The stress may be due to thermal
expansion mismatch between the film and substrate (thermal stress) or due to the
difference in crystal structure between the bottom and top of the film or may be due
to impurities or dislocations in the film.

The deformation of the thin film can be accommodated by the bending and com-
pressing or expanding (depends on the curvature) of the substrate. The internal stress
is compressive if the film tends to expand parallel to the surface (substrate bent up-
ward) as shown in Fig. 4.14(a). The internal stress is tensile if the film tends to
contract parallel to the surface (substrate bent downward) as shown in Fig. 4.14(b)

The type and magnitude of the intrinsic stress in the film usually depend on the

102

method of deposition and on the growing conditions of the films. In this work the
stress is investigated as a function of methane fraction in a hydrogen environment with
or without addition of carbon monoxide. Films with both tensile and compressive
total (thermal and intrinsic) stress were produced depending on deposition conditions.

The preparation of the sample and the measurement technique used to measure the

stress is described next.

4.5.1 Sample Preparation

Starting material was a 4—inch p-type (100) silicon wafer. No oxide or nitride layers
were deposited on the silicon wafer used for this study. After cleaning the wafer with
piranha solution, two layers of DPPR were dispensed on the polish side of the wafer,
using the coating procedure described in chapter 3. After coating the wafer with the
DPPR layers, the wafer was heat treated (softbake) at 120 °C for 1 hour.

After this step the wafer was cut into pieces 1 inch x 1 inch each. The sample
curvature was measured by determining the surface profile using Tencor P-2 instru-
ment. The sample curvature was measured before and after the deposition of the
diamond films. The total (thermal and intrinsic) stress was calculated from a radius-

of-curvature measurement. The equation for the stress is [180, 181]

Y 1.2
X " 5(1 — u) Rt, (4'2)

 

where (1%,; is the substrate biaxial Young’s modulus, which for (100) silicon is 180
GPa. R is the net change in radius of curvature of the substrate, t, and t I are the

substrate and film thickness.

4.5.2 Results

The result of this study is shown in Table 4.1.

103

Diamond Film

/
A

a)
Diamond Film
b) /
Silicon

 

Figure 4.14. Convention showing (a) Compression (b) Tension.

104

Table 4.1. Stress dependence on methane concentration and carbon monoxide.

 

 

 

Sample Gas Flow (SCCM) Methane Total Stress
S3H92 100 0.7 12 0.621 - 80
531193 50 0.7 12 1.116 + 81.4
S3H94 70 0.7 12 0.962 - 87.4
S3H95 40 0.7 12 1.328 + 38
S3H96 55 0.7 12 1.034 + 83.6
S3H97 50 0.7 12 1.116 + 90.2
S4H00 50 0.7 0.0 1.38 + 126
S4H01 60 0.7 0.0 1.15 +340
S4H02 70 0.7 0.0 0.99 + 260
S4H05 100 0.5 0.0 0.497 - 149

 

 

 

 

 

 

 

 

Figure 4.15 shows the dependence of the total stress on methane concentration
with or without carbon monoxide. In the present of carbon monoxide and for methane
concentrations below 1 % the total stress in the film is compressive. For methane
concentrations above 1 % the total stress in the film is tensile. The maximum stress
was z 90 MPa for 1.1 % of methane concentration. However, in the absence of CO
the total stress is compressive for methane concentration of z 0.5 % and is tensile for
methane concentration above 1 %. It was also observed that the magnitude of the
total stress was very high in comparison with the samples deposited in the presence of
CO. The maximum tensile stress was 340 MPa which is more than 3 times higher than
the sample deposited in the presence of CO. This result indicates that by using CO in
the gas mixture, it is possible to control the type and magnitude of the total stress in
the diamond films. This is very important for micromechanical sensor applications.
To our knowledge, no study has been made or reported on the effect of CO on the total
stress in the diamond films. Windischmann et al [181] have studied the dependence
of the total stress on methane concentration. Their diamond films were deposited

by microwave plasma CVD. They reported that the total stress was tensile with a

105

 

400 _ ' I ' 1 f I I ' T ' I ' I
. TENS'LE o 0 CO = O sccm .
300 - as CO =12 sccm}

d

200 E. .j

 

 

. o I
g 100 _. g 1‘ .:
2 I ll! 1
m 0 :- ...................................................................................... .1
U) - 4
g -100: " a 3
U) 1' ‘1
3‘3 : ° :
o -200 - -
I- : j
-300 L _
E COMPRESSIVE 3

-400 A 4

 

0407503 101212 L1i6 ‘ 1.8
CH4%

Figure 4.15. Dependence of the total stress on methane concentration. Data points
are for CO = 0.0 sccm (open circle) and for CO = 12 sccm (*).

106

maximum value of 460 MPa at 0.2 % methane, and decreases with increasing methane
concentration. They have also observed that the total stress converts from tensile to
compressive at about 1.5 % and remains compressive up to 3 % methane.

The inconsistency between our result and their result may be due to the method

of deposition, the deposition temperature and the film structure.

4.6 Summary

The feasibility of fabricating diamond-based sensors has been demonstrated. Fabri-
cation details of micromechanical structures such as cantilever beams, bridges, and
membranes with different dimensions and shapes were described. The selectivity of
deposited boron doping layers on undoped diamond films using low temperature oxide
as doping mask was presented. For metalization of diamond devices, wet chemical
etching solution was developed to pattern Pt / Ti double structure. Total stress in the

diamond film was measured and presented.

CHAPTER 5

Measurement Techniques

5.1 Introduction

The experimental apparatus and techniques used to characterize the piezoresistive
effect of p-type polycrystalline CVD diamond thin films are described in this chapter.
Two systems for gauge factor measurements were used, one using a simple plate
bending system and another using cantilever bending system. The difference between

the two techniques is explained in this chapter.

5.2 Plate Bending System

This system was used previously to characterize the piezoresistive effect for ion-
implanted p-type layer in silicon [31]. Fig. 5.1 shows a schematic diagram for the
plate bending system. The sample was cut from the wafer in a rectangular shape (1
cm x 1.5 cm) and mounted to a stainless steel plate (2.5 cm x 7.5 cm), using epoxy
(cured for 2 h at 150 °C). A wire strain gauge (R=350 Ohms, GF=2.07) was mounted
on the top of the silicon sample next to and parallel to the diamond piezoresistor using
special glue (3M610, cured for l h at 150 °C). The purpose of the wire strain gauge

is to calculate directly the strain induced on the silicon surface, by measuring the

107

108

resistance changes using a digital multimeter (HP 3468A Multimeter). The stainless
steel plate is bent in flexure over a pivoting cylindrical surface. As illustrated in
Figure 5.1, the stress was applied by two parallel forces. Thus inducing tensile strain
at the surface of the plate.

Only preliminary measurement was done using this technique. The result of this
measurement is described in chapter 6. In this method, only the tensile strain was
measured. It was not easy to apply a compressive strain (the silicon sample touched
the pivot by flipping the plate up side down). Also, it was not easy to apply a
uniform and uniaxial strain (the application of two equal forces at both ends of
the plate was not easy). Therefore, a new technique was developed in this work to
measure and characterize the piezoresistive effect of CVD diamond which can be used
for measurements of compressive and tensile strain. This technique is described in

the following section.

5.3 Cantilever Beam Technique

For measurements of the piezoresistive effect, it is necessary to apply uniaxial me-
chanical strain to the piezoresistors. In order to apply a uniaxial strain (tension
or compression) our experiment involved using a silicon sample with dimensions of
7.5x2.5x0.045 cm3 as a cantilever beam. The beam is clamped in a fixture at one end
and a mechanical strain is produced in the beam by applying force at its free end.
Fig. 5.2(a) shows a schematic diagram of the cantilever beam method. The strain
at a point on the beam can be calculated by a knowledge of the beam geometry and
displacement at the free end. The displacement is measured with a micrometer head.
The strain was calculated using an expression which is developed in appendix C. The

expression for the strain (C22) is given by

109

Diamond
Piezoresistor

Wire Strain Gauge
(GF = 2.07, R = 350 Ohms )

GOId Wire Force

 

Silicon Substrate
Stainless Steel

Figure 5.1. Schematic diagram of arrangement for strain measurements by plate
bending method.

110

 

 

 

 

  
  

8102 / Si

2 m / 500 m
Diamond chip ll Ll

 

 

 

 

 

Figure 5.2. Schematic diagram of arrangement for strain measurements of cantilever
beam method.

 

 

where
beam
the CT

'1
tech:
resist
calcu
was 1
usnn
actu

than

$0”:

111

I:

I3 [I _ $40 + b)l y? (5.1)

.—§
"2

where y is the deflection of the beam at the free end, h is the beam thickness, I is the
beam length and a and b are the distance of the two terminals of the piezoresistor to
the clamped edge of the beam.

The majority of gauge factor measurements were made using the cantilever beam
technique. The displacement is measured with a micrometer. By monitoring the
resistance of the piezoresistor with a digital multimeter, the gauge factor can be
calculated by dividing the relative resistance change by the applied strain. The strain
was calculated using equation (5.1). The validity of this method was first checked by
using a calibrated metal foil strain gauge (R=350 Ohms, GF=2.07) to determine the
actual applied strain. The computed and measured strain were found to differ by less

than (10-15)%. Table 5.1 shows the predicted strain and the measured strain.

Table 5.1. Computed and measured strain

 

 

Computed Strain Measured Strain Variation
(pstrain) (pstrain) ‘70
75 68 9.3
155 136 12.2
227 204 10.1
316 272 13.9
403 340 15.6

 

 

 

 

 

Comparing the two measurement techniques, the cantilever beam method has
some advantage over the plate bending method. In the case of cantilever beam method
it was easy to measure strain for both cases of strain (compressive and tensile). The

strain was induced uniformly, since only the force that create the stress/ strain was

slowl)
meth'
strait
two 1
bend
temr
']
ther

rfiez

rner
hit
the
bet

ofl

112

slowly applied by the micrometer head. However, in the case of the plate bending
method two forces were applied at the same time at both ends of the plates. The
strain induced by the two forces might be nonuniform, due to difficulty of applying
two equal forces. In addition to the above mention problems in the case of plate
bending method it was not easy to apply force when measuring the gauge factor at
temperatures higher than room temperature.

The temperature dependence of the gauge factor was measured in a chamber
thermally controlled, to prevent any effect on the detected change in resistance of the
piezoresistor except the desired change. A 1.5 cm x 1.5 cm sample was used. This
sample was mounted on the top of stainless steel beam (2 cm x 6 cm x 0.08 cm) in di-
mension using epoxy. The measurement was done using the cantilever beam method.
In this case the beam was placed horizontally instead of being placed vertically as was
the case for room temperature measurement. Unfortunately due to adhesive problem
between the sample and the beam our measurement was limited to 75 °C. The result

of this measurement is described in chapter 6.

5.4 Summary

Two experimental techniques used to measure the gauge factor were presented. The

advantages of one technique over the other were also discussed in this chapter.

CHAPTER 6

Piezoresistive Effect of CVD

Diamond Films

6.1 Introduction

The piezoresistive effect in CVD diamond was studied for the first time in this work.
The results of the piezoresistive effect of CVD diamond films are presented in this
chapter. All piezoresistors, used in this study consisted of ptype polycrystalline or
homoepitaxial diamond films. Two groups of samples were used for the poly-diamond
films measurements. The first group consists of rectangular shaped discrete diamond
resistors 500 pm wide and 3 mm long and the second group of piezoresistors were

included in a sensor test chip.

6.2 Polycrystalline Diamond Films

As a preliminary experiment, discrete polycrystalline piezoresistors were used. The
plate bending method described in section 5.1 of chapter 5 was used to produce strain.
Evaporated Al was used for the Ohmic contact to diamond. The sample was cut from

the silicon wafer containing the diamond piezoresistors after the metalization step.

113

The s
and t
in Fl.
polyc
relati
for it
over

adhe

6.1(t
of In
four

usin;

tileV
diar.
Wen
size
the
The
hea

dev

114

The sample was then mounted in a test fixture (stainless steel plate) using epoxy,
and then was deflected as described in chapter 5. The result of this study is shown
in Figure 6.1. Figure 6.1(a) shows the fractional change in resistance for p-type
polycrystalline diamond film as a function of tensile strain at room temperature. The
relative change in resistance of the resistor was nearly linear and reproducible both
for increasing and decreasing values of strain. A small hysteresis efiect was observed
over the range of strains investigated (0-1000 pstrain). This might be due to the
adhesive which was used to mount the sample on the stainless steel plate.

The longitudinal gauge factor, computed from these results, is plotted in Fig.
6.1(b). The gauge factor is in the range of 6 to 8. Compared with the majority
of metals, the gauge factor of p-type polycrystalline diamond film is about three to
four times higher. Following these results more samples were prepared and measured
using the cantilever beam technique.

Three groups of samples were used for piezoresistive measurements using the can-
tilever beam technique. The first group consists of rectangular shaped discrete poly-
diamond resistors 500 pm wide and 3 mm long. The second group of piezoresistors
were included in an earlier test chip, with a chip area of 1 cm2 and a minimum feature
size of 160 pm, which was used for temperature sensors [120]. Beams were cut from
the silicon wafers containing the diamond piezoresistors after the metalization step.
The sample was then mounted in a test fixture and deflected using a micrometer
head. The strain on the surface of the bending beam was calculated using Eq. (5.1)
developed in chapter 5. This equation is rewritten here for convenience.

6 = §_25(1_a2b)
(3

 

. 6 (6.1)

The third group of samples were boron—doped homoepitaxial diamond films grown on

a synthetic diamond substrate.

115

 

 

 

1-O 1 j 1 I I I r I r I
:_TChm-cml
E
% _ // ‘
:\3
1.: /‘/
0
E O ‘/A
z -5 / A
a) ‘U P /A
LU a
o /
Z A
:5 /
m 1' / .
a /‘
3 /./
/ Tension
0 x‘. 1 . 1 1 1 . 1 1

 

0 200 400 600 80011000
STRAIN (Microstrains)

 

 

 

 

10 l ' I r I ' I ' I ' I .1
9 [ (TOhmocm) .
F d
8 : AAA” ka :
7 .. /‘ -
c: _ f .
E 6 - “A’k‘A -
b) E 5 L .‘
LIJ .. .1
g 4 .. -
< P :1
o 3 1" _
2 I. ..
1 L , L
Tensno .

O I 1 I m l 1 1 l 1 I
O 200 400 600 800 1000

STRAIN (Microstrains)

Figure 6.1. Fractional change in resistance (a) and gauge factor (b) as a function of
tensile strain in the longitudinal direction.

6.2.1

Sampl
is give

Fig
amon<
at. r00
pressil
resisti
repr01
Figur
sive s
negat
the Ir
betW1
gaug1

hex

6.2.

The

first

at hi

Piezc

the S

samp

116

6.2.1 Doping Dependence

Samples with different resistivities were studied. The result of the doping dependence
is given in Figure 6.2.

Figure 6.2(a) shows the fractional change in resistance for the polycrystalline di-
amond film as a function of tensile and compressive strain for different resistivities
at room temperature. The resistance increases with tension and decreases with com-
pression. The slope of the fractional change in resistance increases with increasing
resistivity. The fractional change in resistance of the piezoresistors was nearly linear,
reproducible and no hysteresis was observed over the range of strains investigated.
Figure 6.2(b) shows the longitudinal gauge factor as a function of tensile and compres-
sive strain. The gauge factor was found to be positive in the case of tensile strain and
negative in the case of compressive strain. As expected for a typical semiconductor,
the magnitude of the gauge factor increases with increasing resistivity. Gauge factors
between 7 and 20 were observed, depending on doping concentration. The transverse
gauge factor was also measured for some samples. For the 20 Q-cm, it was found to

be z-2.5.

6.2.2 Temperature Dependence

The dependence of the piezoresistance on the temperature was also studied for the
first time in this work. Since the diamond sample was epoxied on a stainless steel
cantilever beam, the temperature range was limited to #60 °C. Epoxy became soft
at higher temperatures, thus strain did not transfer to the sample.

Figure 6.3 shows the fractional change in resistance of a polycrystalline diamond
piezoresistor as a function of strain at four different temperatures. The resistivity of
the sample is 5 fl—cm. The fractional change in resistance and the gauge factor of this

sample at room temperature are shown in Fig. 6.2(a) and Fig. 6.2(b), respectively.

 

FigL
and

1.0

a- (1.2 Ohm-cm) d
E1? 'b-- [5 Ohm-cm)
E c- 20 Ohm-cm)
1: ' d- (30 Ohm-cm) C.
i 0.5 1. J
a) g 0.0 ' ' ‘ a
UJ . f5" ..
‘2’
g -O.5 — ..
9
(D ' a
DJ
0‘ -1.0 . .
Compression Tensnoln
-600 -400 -200 O 200 400 600

30
25
20
15
10
5

0
-5
-10
-15
-20
-25

b)

GAUGE FACTOR

-30 .
-600 -4

Figure 6.2. Doping dependence of piezoresistance; fractional resistance change (a)
and gauge factor (b) as a function of strain, in the longitudinal direction.

117

 

 

 

 

 

 

 

STRAIN (Microstrains)

 

' a- (1.2 Ohm-cm)
'_'b- (5 Ohm-cm)

_. c— (20 Ohm-cm)

- d- (30 Ohm-cm)

H-I-O-I-I-H
a

Z
lllll

O

A-a-a-A-a-A-a b

.1

 

' a
— W
.. b A-L-A—A-H-A

:‘c M
:‘d

:' Compression

 

I 1 I

 

llllJllllln

Tension
1 . 1

 

 

00 -200 0 200 400.600

STRAIN (Microstrains)

A

 

Figur
pleZOl
tWES.

118

0.06 T

5 C i

0.05 -1 J
1 v 4

0.04 4 / I

 

RESISTANCE CHANGE (dR/RO)

 

 

 

 

0 260 H 400 ' 600 ' 800 ' 10'00
STRAIN (Microstrains)

 

 

 

 

 

 

200 ' I I I T I I
180- -
160- . ..
140 - 52 C .
5 1 1
I- 120 . -
o ‘ . 1
< 100 . ..
b) :J- 1
(D 80.. ..
D 1 <
< 60‘ 45 c ‘
o ‘ V\'
40- -
. ‘_ 30 c
20 d A ‘1‘- -1
1 21 C
0 T I ' I - I — ' I -' _I
O 200 400 600 800 1000

STRAIN (Microstrains)

Figure 6.3. Fractional change in resistance of a polycrystalline p-type diamond
piezoresistor (a) and gauge factor (b) as a function of strain at different tempera-
tures.

rig.
lOng

119

120

 

100-

80-

604

401

GAUGE FACTOR

O

20- /

0 1 T fir W fi v 5 Y I

20 25 3'0 35 4'0 45 50 ' 55
TEMPERATURE (C)

 

 

 

Figure 6.4. Gauge factor as a function of temperature at 500 microstrains in the
longitudinal direction.

 

Ther

apph

unde

func

vet)
tha‘
inc1
hig
by

f0

28

120

The measurement was done in the longitudinal direction. Positive tensile strain was
applied on this sample.

The temperature dependence of the longitudinal gauge factor for the same sample
under tensile strain is shown in Figure 6.4. Figure 6.4(a) shows the gauge factor as a
function of strain at different temperatures. Figure 6.4(b) shows the gauge factor as
a function of temperature at 500 microstrains. As shown, the gauge factor shows a
very strong increase with temperature, and exceeds that of poly-Si above 30 °C and
that of single—crystal Si above 50 °C. In contrast, the gauge factor of Si decreases with
increasing temperature [42]. No measurement was done on sample with a resistivity
higher than 5 II—cm. The temperature dependence of the gauge factor was confirmed

by other investigators [182].

6.3 Homoepitaxial Diamond Films

For the study of the piezoresistive effect of single-crystal diamond, boron-doped ho-
moepitaxial films were grown by microwave CVD on commercially available type
2a diamond substrates (Dubbelldee Harris Corp., Mt. Arlington, NJ). The diamond
samples were epoxied on a stainless-steel cantilever beam. A metal strain gauge could
not be mounted on the surface of diamond due to the small size of the samples (4-mm
disk or 3-mm squares). Instead, the strain was measured on the surface of the beam.
The tensile strain on the diamond surface was estimated using the known elastic prop-
erties of the diamond and steel, and the ABAQUS finite-element modeling program
(Hibbit, Karlsson and Sorenson, Inc., Providence, RI). For the 4—mm x0.25-mm disk
used for this study, the strain in the surface of the diamond was found to be 31% of
that in the top of the steel cantilever at the location of the strain gauge. The epoxy
was assumed to be a perfect adhesive.

Figure 6.5 (a) shows the fractional change in resistance of the homoepitaxial film

F1
fa<

121

 

0.03

Homoepitaxial diamond film <100>

0.02 .

0.013

GD
V
RESISTANCE CHANGE (dR/RO)

 

 

0.00 - . - . - I - I .
0 20 40 60 80 100

STRAIN (Microstrains)

 

500
4501
4001
350:
3001
250i
200i
150;
100i
503

0 , . I . r . , -
20 40 60 80 100

STRAIN (Microstrains)

 

   

Homoepitaxial diamond film <100>

b0

GAUGE FACTOR

 

 

 

Figure 6.5. Strain dependence of the (a) fractional change in resistance and (b) gauge
factor of a (100)-oriented homoepitaxial diamond film.

Table 6.1. Diamond piezoresistance coefficients.

122

 

 

 

 

 

Units in 10’12 ch/dyne
Diamond p (II-cm) 7r; <1r1> <7r¢>
Synthetic
Stress in <100> N/ A 92- 206
Stress in <111> N/A 114- 319
Homoepitaxial <100> 0.03 20- 45
Polycrystalline l .2 0.38
5 0.58
7 0.65
20 0.90 - 0.22
30 1.60

 

 

 

 

 

 

 

as a function of tensile strain. Figure 6.6 (b) shows the measured gauge factor as
a function of strain. The gauge factor decreases with strain, suggesting that not all
the strain is transmitted through the epoxy layer. To partially correct for this, we
take the gauge factor to be the value obtained by extrapolating back to zero strain.
Even this corrected value should be taken as a lower limit to the actual gauge factor.
With these uncertainties, the gauge factor measured in the [100] direction in a (100)-

oriented homoepitaxial p-type diamond film is at least 550 at room temperature.

6.4 Diamond piezoresistance coefficients

The average longitudinal piezoresistive coefficient < an > for the polycrystalline film

was calculated using equation (2.19) which was derived in Chapter 2, and is given by

1

CF“ 7 (6-2)

<1n> =

123

The results are shown in Table 6.1. As shown < 1n > is in the range of (0.38 - 1.6)
x10‘12 cmz/dyne depending on the resistivity. The average transverse piezoresistive
coefficient was also calculated using equation (2.20) derived in Chapter 2 and is given

It is found to be a: - 0.22 x10’12 cmz/dyne.

The longitudinal piezoresistive coefficient 71’; of the homoepitaxial diamond film

was calculated using Eq. (2.21).
7r, = Sn CF“: (6.4)

It was found to be m 45 x10"12 cmz/dyne and 20 x10'12 cmz/dyne for low strain (28
pstrain) and high strain (140 pstrain) regions, respectively. Table 6.1 present the re-
sult of the longitudinal piezoresistive coefficient for polycrystalline and homoepitaxial
diamond films.

The effect of pressure on the HPHT p-type synthetic diamond doped with boron
was previously investigated by Russian workers [175, 176]. Their work was described
in Chapter 2. The original plots were also shown in Chapter 2. In their paper, they
reported neither the gauge factors nor the piezoresistance coefficients. However, in
this work we estimated the piezoresistive coefficients and gauge factors from their
curves.

The plot was enlarged first then printed out on scale paper. Ten data points
were read from each curve. The fractional resistance change 9373 was calculated. The
piezoresistive coefficients were then calculated. The stress was then converted to

strain. In the computation of strain from their results, we used a Young’s modulus

Table 6.2. Estimated Piezoresistive coefficients and gauge factors of HPHT p-type

synthetic diamond.

124

 

 

 

 

 

 

 

 

 

 

 

Stress Resistance Stress Stress in Strain Gauge
Direction x(105 Q) (Kg/cm”) x108 A3? x 10’12 pstrain Factor
(dyne/cm’) (cmz/dyne)
< 100>
9 0 0 0 0
7.178 1000 9.8067 0.20244 206 82 2472
6.045 1500 14.710 0.32833 223 123 2678
5.335 2000 19.6134 0.40722 207 163 2491
4.400 3000 29.4201 0.51111 I73 245 2086
3.67 4000 39.2268 0.5922 151 326 1816
3.335 5000 49.0335 0.62944 128 408 1540
2.933 6000 58.8402 0.67411 114 490 1375
2.665 7000 68.6469 0.70388 102 I 572 1230
2.5025 8000 78.4536 0.72194 92 653 1105
<111>
2.8934 0 0 0 0
1.9866 1000 9.8067 0.3134 319 81.7 3836
1.56 1500 14.71 0.4608 313 122.58 3777
1.26 2000 19.6134 0.56452 287 163.445 3453
0.8773 3000 29.4201 0.69679 237 245.16 2844
0.706 4000 39.2268 0.75599 193 326.89 2319
0.546 5000 49.0335 0.81129 165 408.613 1985
0.4396 6000 58.8402 0.84806 144 490.335 1730
0.3653 7000 68.6469 0.8737 127 572.05 1527
0.3066 8000 78.4536 0.8940 114 653.78 1369

 

 

125

value of 12 x lO”dynes.cm‘2. Table 6.2 shows the estimated piezoresistive coefficients

and gauge factors.

6.5 Discussion

The results of studies of piezoresistivity in monocrystalline and polycrystalline p-
type diamond are summarized in Fig. 6.6. With the exception of synthetic diamond,
all the strain values are tensile. The data for monocrystalline (homoepitaxial) and
polycrystalline CVD diamond are from our measurements. The results for Si [33] are
provided for comparison. It may be pointed out that the curves for synthetic diamond
were estimated from the reported pressure dependence of resistivity measured by
Latsa et al. [176] who did not provide any information about the degree of accuracy
of their results, the doping level of diamond and the gauge factor.

The gauge factor of homoepitaxial diamond, is a factor of 4 higher than the highest
value for Si and is an order of magnitude lower than the values shown for synthetic
diamond. The lower values of gauge factor for homoepitaxial diamond as compared
to synthetic diamond are believed to be due to very low resistivity, defects in the film
and due to the measurement problems related to the epoxy used between a 3 mm2
diamond sample and a cantilever beam [62].

At 300 K, the gauge factor for the polycrystalline diamond film is shown in Figure
6.2(b), is in the ranges of 5 - 20 [183]. Values up to 40 or higher have been found
for some doping levels in our recent experiments and up to 100 are reported by other
researchers [184]. It was also reported that the gauge factor increases with increasing
of the grain size [184]. These relatively low values of gauge factor may be related to
grain sizes, grain boundaries and high densities of defects which have been observed in

the grain boundaries and within the grains [177]. For polycrystalline semiconductor

material, the resistivity of the film can be described by contributions from both the

i

 

GAUGE FACTOR

1o2

10‘

10°

126

 

 

- SYNTHETIC [111]
M§~\~—
SYNTHETIC [1001
\HOMOEPITAXIAL [1 001 0.03 omcu

x—u——x—*—x—-x5| 0-001 OHM-CM
H—fi—W POLY-SI 20 OHM-cu

W

POLYCRYSTALLINE 20 OHM-CM

 

0 200 400 600

STRAIN (x 10-6)

Figure 6.6. Gauge factor of diamond and silicon as a function of strain.

 

127

grain and the grain boundary and is given by [44]

= L—(2w+6) + (2w+6)

L pg L pb (6'5)

 

where p, p9 and p5 are the resistivities of the film, grain and grain boundary, respec-
tively, and 6 is the grain boundary thickness. L and w are the lengths of the grain
and depletion region, respectively.

From Eq. (6.5) the fractional change in resistivity per unit strain (gauge factor)
can be given by:

L—(2w+6)Apgl + (2w+6)Apb_1_

L P9 5 L Pb 5 (6.6)

 

 

fl 1 =
p c

It was observed that for high doping levels, the electrical properties of polycrys-
talline silicon approach those of single-crystalline silicon [185]. This is because the
effect of the grain boundary is very small (to decreased). This is also true when the
grain size of the crystallite is large as compared to the thickness of the grain boundary.

From the temperature dependence of Hall concentration of p-type (B-dopant)
polycrystalline diamond film, it was observed that the Hall concentration increases
with temperature [125]. The Hall concentration measured at 50 °C, was found to
be three times higher than the Hall concentration measured at room temperature.
This is because at room temperature < 1% impurities are ionized. Thus, the effect of
crystallites on the conductivity of the diamond film is increased and the effect of the
grain boundary on the conductivity of the polycrystalline diamond film is decreased
or could be negligible. Equation (6.6) can now be given by

 

£1 _ L—(2w+6)Ap,_l_
p c

L p, c (6.7)

Therefore, the increase of the gauge factor with temperature might be mainly due to

128

the bulk crystallites.

6.5.1 Energy Band and Qualitative Model

Due to difficulties in producing n-type CVD diamond films piezoresistive data for
n-type diamond is not available. Consequently, our qualitative discussion of the
piezoresistive effect is limited only to p-type diamond. The qualitative model is
based on studies of the energy band structure of diamond [140, 186].

The energy band structure of diamond [140] is shown in Fig. 6.7. A simplified
band diagram of diamond valence band is shown in Fig. 6.8(a) for zero stress. The
heavy hole band with an effective mass of m1; = 2.18 mo and light hole band with
an effective mass m}; = 0.7 mo [186] are degenerate at lc = 0, where mo is the free
electron mass. The split-off band with an effective mass m}, = 1.06 mo is separated
from the degenerate bands only by 6 :1: 1 meV due to spin-orbit interaction. Since the
separation is small, the valence band is nearly tripled degenerate in energy. Since,
the valence band structures of p-type silicon and diamond are similar to a certain
degree, the discussion of the former can be extended carefully to the later.

In the case of Si, the energy separation between the degenerate bands and the
split-off is z 44 meV and is usually neglected in the discussion of stress -induced
changes in the valence band. Following a similar discussion for diamond it is assumed
that, for a qualitative discussion, only the changes in the heavy and light hole bands
play a dominant role in the stress -induced change of resistivity of diamond. When
a uniaxial positive stress (tension) is applied in the longitudinal direction, the heavy
hole band Ev“. moves up relative to the light hole band Ev". (Fig. 6.8(b)). This
results in an increase in the number of the heavy holes and a decrease in the number
of the light holes. Consequently, the resistivity increases. The compressive stress
(negative) causes the light hole band to move up w.r.t the heavy hole band resulting

a decrease in resistivity.

129

 

 

 

 

Elecuon energy. eV

 

 

 

 

 

 

Figure 6.7. Energy band structure of diamond.

130

 

 

  

’ k
'\ Heavy Hole

.) ~X/\ a...

- _ Light Hole
@3233 Band

 

b) /
Figure 6.8. A simplified band diagram of diamond valance band; (a) zero stress (h)
under uniaxial stress.

 

131

In the above discussion, only the relative shifting of subbands is considered. The
direct changes in effective mass may also occur if the stress causes a change in the
curvature of the subbands. The stress-induced changes in the band gap, as suggested
Latsa et al. [176], seem less likely because of large band gap (5.5 eV) of diamond.
Since in the case of diamond A is z 6 :1: 1 meV, and the effective mass is not small,

the effect of uniaxial stress on split-off subband may be appreciable.

6.6 Summary

The piezoresistive effect in both polycrystalline and homoepitaxial CVD diamond
films was studied and presented in this chapter. The piezoresistive gauge factors,
measured at 300 °K are in the ranges of 200 - 550 and 6 - 25 for homoepitaxial and
polycrystalline p-type diamond films, respectively. The gauge factor for polycrys-
talline films decreases with decreasing resistivity but increases with increasing tem-
perature. Although the piezoresistivity in diamond is not well understood, the high
gauge factor of diamond films demonstrates superiority of diamond sensors over Si or
SiC counterparts. The diamond piezoresistive sensors are appropriate for applications

in chemically / radiation harsh environments, especially at elevated temperatures.

CHAPTER 7

Summary and Future Research

The aim of this thesis has been to investigate the piezoresistive effect in CVD dia-
mond film deposited by chemical vapor deposition method and to demonstrate the
feasibility of CVD diamond for piezoresistive sensor applications. To our knowledge,
the piezoresistive effect of diamond film was not investigated at all before this work.
Owing to the originality of this work a full characterization was required. The effects
of processing parameters on the quality of the diamond film was first investigated and
the results were presented in chapter 3.

A multisensor microchip was designed and fabricated. The feasibility of diamond
as piezoresistive sensor material was demonstrated by fabricating a very small mi-
cromechanical structures. The minimum feature size was 5 pm.

The piezoresistive effect was characterized by measuring the gauge factor as a
function of resistivity and temperature. Gauge factor was found to be in the range of
6 to 20 depending on the resistivity of the polycrystalline diamond film. The gauge
factor was found to increase with increasing resistivity. The temperature dependence
for piezoresistive diamond film was investigated between room temperature and 52
°C. An increase of the gauge factor with temperature was observed. The gauge factor
of homoepitaxial diamond film was also measured in this work.

The piezoresistive coefficients of polycrystalline diamond film and homoepitaxial

132

133

diamond film were calculated and presented for the first time in this research.

7 .1 Future Work

It was mentioned in chapter 6 that the attempt to investigate the piezoresistive effect
at high temperature was limited due to epoxy problem. It is very important to in-
vestigate the piezoresistive effect at a wider temperature range before the application
of this effect in pressure sensor. It was also reported that the gauge factor increases
with increasing grain size. Thus, the effect of grain size on the piezoresistive effect
need also to be investigated. It was also demonstrated in chapter 4 that a very small

micromechanical sensor (pressure and accelerometer) can be fabricated.

APPENDICES

APPENDIX A

 

Piezoresistive Coefficient

From a mathematical point of view, the effect of homogeneous mechanical stress on
the electrical resistance of a conducting crystal can be described generally in terms
of a set of constants. These constants are known as the piezoresistance coefficients,
the number of which is equal to the number of elastic moduli. The piezoresistance
coefficients connect the resistance with stress by equations very much like the equa-
tions connecting strain with stress, except for the difference of a factor of 2 in some
of the terms. These piezoresistance coefficients have to be determined completely in
order to characterize the piezoresistance effect in a conducting crystal.

In order to determine the piezoresistance coefficients in a cubic crystal materi-
als, let us consider first a rectangular coordinate system, with its axes x1, x2, and
x3 aligned along the crystallographic axes {100} of the crystal. Fortunately, these
coefficients can be determined by the general form of Ohm s’s Law.

According to Ohm’s Law the relationship between the electric field intensity E,‘,

the current density J,- and the electrical resistivity pg,- is given by

3 3

E.- = 221’qu (Al)

i=1 j=l

Since E.- and J,- are vector quantities, the resistivity components form a second rank

134

135

tensor with nine components which is symmetric, that is p;,- = pjg. Eq. (A.1) can be

written in matrix form as:

r 1 - 1 r- a

El P11 P12 P13 J1
E2 = P12 P22 P23 ' J2 (A2)

 

 

 

 

 

 

_Es _P13 P23 P33] _Jsd

d

In an unstressed symmetrical cubic crystal, the electrical resistivity tensor pg,- is

isotropic, that has only the diagonal components,

Pa = Po 5:5 (A-3)
where 6.3 is the Kronecker delta given by:

0 ifz'yéj

1 ifi=j

.3—

In order to determine the piezoresistance coefficient, it is necessary to assume that
the electric field components E.- is a function of the current density Jj, as well as the
stress, X H [24]:

E; = E,(J,-,Xk,) i,j, k,l = 1,2,3 (AA)

where X k; is described earlier, Expanding E.- as a Taylor series about the state of zero

current density J50 = 0, and zero stress XHO, Eq. (A.4) will be written as follows:

6E5 313;
(IE; -- 6—.I,- de-l- +6—-sz —kal
62E 62E.-
+ 21-—! 6.7"— 6.1m de dJm + mix—n: kal an0 (A5)
2
+ 3 E de kal] +

2,-3——_J 8X“

136

This expression can be reduced by considering that a cubic crystal has a center of
symmetry, that is the components of an odd rank tensor vanish [187]. Therefore, the
second, third, and fourth terms are identically zero. Eliminating these terms reduces

the expression to:

6E; 62E.“
i = _ d . __ . d .
dE M J, + a.1,-ax,., dJ, X... (A 6)
where
6E.- - p~ - resistivity components
'51: - .. -
and
62E.- . .
m = in,“ = p1ezoresnstance components
1

Eq. ( A.6) can now be written as:
(1E; = pgj de + ”51'“ de dXH (A.7)

The integration of Eq. (A.7) is expressed as:

Xu)

3‘ dE 1’ dJ (1" dJ dX A 8
o , —/0 p., , + [(0,0) «.11.: 1 Id ( -)

Using Eq. (A.3) and considering that all components of 1mm tensor are constants,

Eq. (A.8) gives
E; = P0 5.3 J,‘ + We,“ Jj Xkl (A-9)

In general, the 1.3-u term in equation (A.9) forms a fourth-rank tensor with eighty-
one components. Since, the resistivity pg,- and the stress X H tensors are symmetric,
that is the subscripts corresponding to the electric field and current density directions

i and j can be interchanged with each other, and the subscripts corresponding to the

137

stress directions k and I can be interchanged with each other resulting,

Wijkz = 7511.: = Fun. = Wjiuc

Therefore, these number can be reduced to a thirty-six independent components. It

can be shown that the i and j as a pair can be interchanged with the k and I as a

pair resulting in only 21 components

77in = "we

Now, like the stiffness tensor, by using matrix notation and by the use of crystal sym-
metry, only three independent coefficients are required to determine the piezoresistive
property of cubic crystal[l7].

Further reduction also can be done by factoring out the zero stress resistivity p0,
and to introduce a factor 2 only to those coefficients whose second subscript is a 4,
5, or 6, which are those associated with shear stresses (because each single subscript
shear stress is twice the corresponding tensor components), these are denoted as

follows [17]:

P07? 11 = Wm;
P0" 12 = Fiijj
P07?“ = 277.5.)

Thus the piezoresistive coefficients can be written as a 6 x 6 matrix which has three

independent components for crystals of the diamond structures such as silicon, ger-

138

manium and diamond [17].

P Q P

 

 

 

1r1111 1r1122 7"1122 0 0 0 7'11 1r12 7'12 0 0 0
1r1122 “1111 171122 0 0 0 7r12 7711 1r12 0 0 0
71122 1r1122 771111 0 0 0 _ W12 7r]: 7r“ 0 0 0
0 0 0 2 «2323 0 0 — po 0 0 0 1r“ 0 0
0 0 0 0 2 W23” 0 0 0 0 0 1r“ 0

o 0 0 o 0 2 «2323 J _ 0 0 0 o 0 7r... ]
(A.10)

where the 1r“, 1r”, andw“ are the fundamental piezoresistance coefficients of the crys-
tals.

Finally, after the substitution the right-hand side of Eq. (A.10) into Eq. (A.9), the
three piezoresistance equations specialized to materials of diamond crystal structures

can be written as

E

El = J1[1+ «1in + «12(X2 + X3)l + “44(J2X6 + J3X5)

E

z? = J2[1+ 711X2 + 712(X1 + X3)] ‘f’ 7744(J1X6 'l' J3X4) (All)
E

p—: = J3[l + W11X3 + 7712(X1 + X2” + "44(J1X5 + JQX“)

When stress and current density are both in the x1 direction, X.- = 0 for 1' 7E 1, and

E2 = E3 = 0. Eq. (A.ll) reduced to

E
:5 = J1[1+ “11 X1] (AJ2)

which yields

 

P - P0 = 7T1] X1 (A.13)
P0

 

139

with
E1

= , A.14
J1 p ( )
In an arbitrary coordinate system where the coordinate axes x'l , x1», and x3 do not

coincide with the crystallographic axes x1, x2, x3 of the cubic crystal, the piezore-

sistance equations (A.11) will be derived according to the following transformation

[30,188]
[ ' 2 r
x} 11 m1 711 X1
X2 = I: m, n, ' X2 (A-15)
LX231 _I: m, "ad _X3J

 

 

 

 

 

 

where 1;, mg, and n.- (i = 1,2,3) are the direction cosines of the primed axes at. with
respect to the crystal axes xi, that is, cosines of the angle between the axes of the
arbitrary coordinate system with the crystallographic axes [25]. Also, Eq. (A.15)
can be used to transform from the new coordinate system back to the old coordinate

system, which can be written as:

 

 

 

 

 

P d F H P 'l
X1 I] lg 13 X3
X2 = m1 m: m: X2 (A'IG)
X3 72, 12, n3 X's

b d b d b J

 

The general matrix of direction cosines can be expressed in terms of Euler’s angles

(0 , c3 and :12) (See Fig. A.1) as follows:

 

 

 

P I. m. n. ' mom/z - s¢s¢ swap + c¢s¢ -soc¢ '
12 m: n, = —C¢0081/) — 343a]; -s¢c03¢v + c¢c¢ 3031p (A.17)
. I, m, n: 4 C¢80 84580 09

 

where (:43 5 cos d), 80 5 sin 9, etc.

140

 

 

Figure A.1. Euler’s angles used for axis rotation.

All the components of equations (A.11) in the crystallographic system need to be
transformed to the rectangular coordinate system.
The current density components in the crystallographic coordinate system in terms

of the primed coordinate system become:

J] = I] j; + Igjg + l3'j3
J2 = m, j} + mzjz + m3j3 (A.18)

J3 = n1j1+ngj2+n3j3

The old components of the normal stress Xi, (i=1,2.3) in terms of the new can be

written as [187]

X1 = zfx’, +15X’, +1526, + 20.1.21”, +1,1,X’5 +1,1.X’.)
X2 = me1+ mszlz + mgX’g + 2(m2m3X" + m1m3.’(5 + m1m2.\;5) (A.19)

X3 = an1+ 11ng + nng + 9(n2n3.X" + n,n3X.s + n, nng)

141

The old shear stress components Xi, (i=4,5,6) in terms of the new, can be written as

[187]

X4:

X5:

X6:

mint X1 + mznzxz + mansX: + ("12713 + mane)!“

(m, n, + mamlxls + (m, "2 + mzn,)X’4

11 n1 XI: + lzan’z + 1: n3X’3 + (12713 + Isnzlx’s

(I; n, + 13111)X5 +(11 n, + 1212,)X’4 (A.20)

11 m, X1 +127":ng + I: max: + (Isms + Ism2)X’s

(11m: +13m1)X5 +01 m, + Izm1)X4

Substitution equations (A.18), (A.19) and (A20) into (A.11) gives

E1
P0J 1
E2
Poji
Ea
PoJ 1

 

II [1 + X1 [W111]2 + (7’12 + "44)("112 + "12)”

m1[1 + X! [771177112 + (7n: + 7m)(1f+ "12)” (A-21)

"111 + X, [7711":2 + (7'12 +1I’u)(mf +112)”

The electric field components in the prime coordinate system are given by:

El:
12.:

E3:

11E] + mlE2 + “IE3
lel + ngz + fl2E3 (A.22)

13E] + m3E2 + ”3E3

Now, in the case where the electric field, the current density, and the stress are all in

the same direction for example X}, which is the longitudinal direction we will obtain

142

 

E 1
‘. = ——.(I, E, + m, E. + n, E3) (A.23)
PoJi PoJi

substitution Eq. (A.21) into Eq. (A.23) gives

E.

p j (112+ mi '1' nf) +X1[1r11(l}‘ + m,‘ + "f)
o 1

 

4' 2(7le + Fulafmf +112": + mfnfll (A24)
Since (If + mf + 111’: 1), and
(If + mf + nf) = (If + m,2 + nf)2 — 2(lfmf + lfnf + mfnf) (A.25)

Equation (A.24) becomes

E1

'7' = 1+ Xllvru + 2(7r4. + m — «11)(Ifmf + If nf + "11‘an (A-26)
P0 1

= 1 + Wilxl
where xil is given by [25]
1"i1 = 7"11 — 2(“11 — 7'12 — W44)(Ifmf + mfnf + 11,2112) (A27)

Since 52‘- is the resistivity component p} in the :r’l under the uniaxial stress X1, equa-

tion (A.26) can be written as

— = «3,221 (A.28)
P0

The derivation of the transverse piezoresistance coefficient «12 (the current and field

143

are perpendicular to the stress) is analogous to that of 2'11 and is given by [25]

77i2 = 7712 +(7r11- 7712 - W44)(l,21§ '1' "1,2771; + fling) (A29)

APPENDIX B

Gauge Factor Derivation

The most useful measure of piezoresistive effect is the gauge factor (CF), which is

defined as the fractional change in resistance ATE per unit strain 6. The resistance R

 

Figure 3.1. Thin rectangular resistor.

of a long and thin film made from an isotropic or polycrystalline material with length

144

145

L, width w, and thickness t as shown in Fig. 3.1, is given by

L
12: p.11; (13.1)

The fractional change in resistance can be found by differentiating the logarithm of

Eq. (3.1) and the result is

+——-———— (R?)

Aww

The term ALL 18 the longitudinal strain 6) and the terms , and— are the transverse

strains Cg. Thus equation (3.2) can be written as

AB A
'12— =7£+.,_.._.. (B.3)

Now, from Eq. (B.3) the gauge factor in the longitudinal direction (strain parallel to

the length) will be written as

(GF). = (9511

AR
= p )1— +1 — 2— (3.4)
AP :1

(— 1—+(1+2 )

where V is the Poisson’s ratio, relating to the reduction in the thickness of the film
due to strain, which is defined as the ratio of the transverse strain to the longitudinal
strain resulting from the simple tension. As we can see in Eq.(B.4), the change in
resistance due to the strain produced by uniaxial stress consists of three terms: The
first term represents the change in resistivity due to the strain while the second two
terms represent the change in resistance due to dimensional changes caused by the

strain.

146

For the transverse direction where the strain is parallel to the width of the resistor
w, 951 becomes the longitudinal strain 6; and 951’- and % are the transverse strains 6,.

Eq. (B.3) can be written as

M
(p

= (__P ¢- 61 (B.5)

(LR):

1+61-Cl—Ct

R)

and the gauge factor in the transverse direction can be written as

(G1). = (9511

= 91)}— —1 (B.6)

P 61

Since the Poisson’s ratio V of polycrystalline diamond is less than 0.07 [47, 48] the
contribution of the dimensional term is less than 1.14. Therefore, the gauge factor of
semiconductor polycrystalline diamond film depends mainly on the resistivity of the

material and will be written as

GF = 9.1"}. (13.7)
p 6:

Now, from Hook’s law and equation (A.28) the gauge factor can be written in terms

of Young’s modulus Y and piezoresistance coefficient 1rd

.921
P 61
= WJY (3.8)

GF=

where the subscript d = I in the longitudinal direction and d = t in the transverse

direction.

147

In the general case, within an anisotropic homogeneous material, it is often de—
sirable to define elastic modulus as is common in isotropic media [189]. For uniaxial

stress X1 in the 1' direction, the Young’ .3 modulus Y is given by

1

Y = — B.
82'; ( 9)
and the Poisson’s ratio is given by
. 3";
ng - -13.;
3:3
= —— 3.1
81'; ( 0)

where, s}.- are the compliance coefficients.

Now, the gauge factor can be described by [44, 45]

GF=1—2§(1—6fi)+"—f‘ (13.11)
i=1 811 511

In the longitudinal direction (d=I), when the current and field are both in the same

direction of the stress, (e.g. i = 1), the gauge factor can be shown as

GF = 1 — 2533 + 1}—
Sll 511
= 1 + 2.4, + 1}— (3.12)
511

Again, in equation (3.12) the contribution of the dimensional term 1 + 214; is
approximately between 1.02 and 1.22 for monocrystalline diamond [48]. Therefore

equation (3.12) can be rewritten as

GF = I; (3.13)
811

APPENDIX C

Strain Analysis

The objective of this analysis is to derive an expression for the calculation of the strain
on the top surface of our specimen which is needed in the gauge factor calculations.

Figure C.1(a) shows a simple cantilever beam in bending. The beam has a fixed
length I, and is deflected by a force F using a micrometer head. After loading, the
axis is bent into a curve that is known as the deflection curve of the beam. Figure
C.1(b) shows a cross section of the bending beam. This figure is greatly exaggerated
to illustrate the analysis. It is clear that the top surface of the beam is extended
(under tension) and the bottom surface is contracted (under compression). It is clear
that the middle plane indicated by the dotted line in the figure is unaltered in length.
This plane is known as the neutral surface.

The radius of curvature, p, is defined as the distance from the neutral surface to
the center of curvature Figs. 5.2(b) and (c). It is known from the calculus that the
curvature of a plane curve is given by

dzy

Z=Iifi

(C.1)

where y(x) is a function of x.

148

149

 

 

 

 

b)

 

radius of
center of curvature

curvature

 

 

 

Figure C.1. Schematic diagram for strain calculation (a) Cross section view of the
bending beam (b) Side view for element inside the dashed circle (c) cross-section view
front section (y,z) plane.

150

Now, assuming small deflection, then from the geometry of the figure, we obtain
dzo = pdfl (C.2)

and

d:t = (p + y)d9 (0.3)

where d9 is the deflection angle, dz the length of a small element (PQ) located on
a surface (ds) above the neutral surface and y is the distance between this element
and the neutral surface. dzo is the initial length of the small element.

Using geometry, and by similar triangles, the longitudinal strain on the surface ds
is given by

dz - dzo

£3,- —
(1.120

(0.4)

‘bl‘d

where (dz - dzo) is the elongation.

Now, this strain can be thought to be produced by a longitudinal stress X,” which

from Hook’s law can be written as
X, = Y 6, (C5)

where Y is the Young’s modulus.

The distribution of stress in any section perpendicular to the x direction can be given

by substituting Eq. (0.4) into Eq. (C5)
1’
x, = Y - 0.6
p ( )

Consider an element of area dA in the cross-section (y,z) at a distance y from the

151

neutral axis as shown in Fig. 5.2(d). The force acting on this element is normal to
the crossosection and has a magnitude X, dA.

The moment about the z-axis is given by

M, = lyX3dA
= /Y%ydA

_ Y 2
3: 1

where I, is the moment of inertia of the cross-sectional area with respect to z axis,

Which in this case is equal to
1: "' ' (C 8)
12 . .

where b is the width of the beam and h is its thickness. Equation (0.7) can be written

 

as
1 M,
P — Y1, (C.9)
Now, substituting Eq. (C.9) into Eq. (CA), the strain can be written as
M
£3 _ fig (C.10)
and the stress is written by
X..- = 9% (C.11)

The bending moment M at a point A, a distance x from the fixed end of the beam
(Fig. 5.2(b)) is given by
M = F(I—z) (C.12)

152

now from (C.9) and (C.1) and (C.12) we can get

 

 

£1 ._ M
dz2 — Y],
F I—z
= ___—(Y1 ) (C.13)
Integration Eq. (C.13) gives,
dy_ F 1 2
E—YLUJ-gt +01] ((3:14)

where 01 is a constant. Considering boundary condition at the fixed end of the beam
(z = 0), 5‘1 = 0 giving C1 = 0. Replacing Cl by zero and integrating a second time

produces

F 1 1
Y] ['5 1:2 — .6- 133 + C2] (0.15)

 

y:

where 02 is a constant. Again, considering boundary condition y = 0 at z = 0 gives
02 = 0. Now, replacing C: by zero, results in the final equation for the deflecting

beamas
_ F 1 2 1 3
y-YI,[2x 6z]. (C.16)

 

The maximum deflection of the beam occurs at its free end (2: = I) and is given by,

 

 

F I3
Eq. (C.17) can be rewritten as,
F 3],
7 = I3 3] (0.18)

The bending moment M1 at point A1 (center of the sample), a distance x; from

the free end is given by
M1 2 F131 (0.19)

153

Now from Eq.(C.10) and (C.19) the strain at point A1 is given by

F$1_h_.
YI2

 

(0.20)

e, =
Looking at Eq. (C.20), it can be seen that two variables, namely the force F and the
Young’s modulus Y are needed to calculate the strain. However, these two variables
can be eliminated by substituting Eq. (C.18) into Eq. (C.20) and the expression for
strain is given by

3 h
e, = 2F“ y (C.2l)

In our experiment Fig. 5.2(a) and (b), where z, = (I — %(a + b)), the final expres-

sion for strain is
h

1
(3 [I — §(a + b)] y (C.22)

”a
"2

APPENDIX D

Sample Descriptions

Table D1. Sample description after the deposition of the diamond films.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I.D. Gas Flow (SCCM) Sub. Temp. Dep. Time
H2 CH4 CO (°C) (1113.)
H3ST25/DP19 100.0 0.7511210“ 825 8.5
H3ST43/PE22 100.0 0.75 12.0 890 14
H3ST69/T-2 100.0 0.75 12.0 925 8
H3ST71/T-3 100.0 0.75 12.0 925 8
H3ST74/T-2 100.0 0.75 12.0 825 9
H3ST75 100.0 0.75 12.0 825 4
HssT77/H3fi67 100.0 0.75 12.0 825 8
H3ST20/NL08 100.0 0.75 12.0 890 14
H3ST73/T-1 100.0 0.75 12.0 890 11
H3GF91/TS-l 100.0 0.75 12.0 825 10
H2GF80 100.0 1 12.0 825 10
HBGF92 100.0 0.75 12.0 825 12.5
H3GF93/PE20-S 50.0 0.75 12.0 890 9.5
H3GF94/PE20-S 70.0 0.75 12.0 890 8
H3GF95/PE20 40.0 0.75 12.0 890 12
H3GF96/PE20 55.0 0.75 12.0 890 12
H3GF97/PE20 50.0 0.75 12.0 890 11
H3GF98/DP16 70.0 0.75 12.0 890 13.5
H3GF99/DP16 60.0 0.75 12.0 890 12.5
H4GF00/fi‘1 50.0 0.75 0.0 890 16

 

 

 

 

 

 

154

 

155

Table D.2. Sample description after the deposition of the diamond films.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I.D. Gas Flow (SCCM) Sub. Temp. Dep. Time
112 CH. co (°C) (hrs.)

H4GF01/IT1 60.0 0.75 0.0 890 13
H4GF02/IT4 70.0 0.75 0.0 890 12.5
H4GF03/T51 70.0 0.75 0.0 890 20.5
H4GF05/IT-1 100.0 0.5 0.0 890

H280/H279 100.0 0.5 12.0 890 4.5
H281/H280 100.0 0.753 12.0 890 8
H282/2P20-4 100.0 0.753 12.0 890 8
H283/MA161 100.0 0.753 12.0 890 9
H284/PE16-2 100.0 0.753 12.0 890 5

H285/ 100.0 0.753 12.0 890 7
lP3LTO-5
H286/PE14-16 100.0 0.753 12.0 890 6
PE14-16

H287/DP13 100.0 0.753 12.0 890 7
H288/I42 100.0 0.753 12.0 890 4+5
H294/H288 100.0 0.753 12.0 890 +10
H289/NLO-6 100.0 0.753 12.0 890 4.5+4.5
H302D/H289 100.0 0.753 12.0 890 +3.5
H290/LTO-l2 100.0 0.753 12.0 890 8+7
H296/H290 100.0 0.753 12.0 890 +5
H291/NLO-l 100.0 0.753 12.0 890 6
H292/DP14-1 100.0 0.753 12.0 890 3.5
H297/H292 100.0 0.753 12.0 890 +5.5

H293/ 100.0 0.753 12.0 890 7.5
2P3LTO-8

H293/ 100.0 0.753 12.0 890 7.5
2P3LTO-8

H295/H8-11 100.0 0.753 12.0 890 7.5
H298/SC461 100.0 0.753 12.0 890 7
H299/SC47-2 100.0 0.753 12.0? 890 3.5
H300/SC47-3 100.0 0.753 12.0 890 8

 

 

156

Table D.3. Sample description after the deposition of the diamond films.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I.D. Gas Flow (SCCM) Sub. Temp. Dep. Time
H: CH. CO (°C) (hrs.)

H301/NLO-7 100.0 0.753 12.0 890 8
100.0 0.753 12.0 890 +6
H303D / H282 100.0 0.753 12.0 890 4
H304D/ H300 100.0 0.753 0.0 890 3
H306D / H295 100.0 0.753 12.0 890 4
H307/ H299 100.0 0.753 12.0 890 5.5
H308 / SC46 100.0 0.753 12.0 890 8
H310/ H308 100.0 0.753 12.0 890 8
H314D / H310 100.0 0.753 12.0 890 3.5
H309/ N L01 100.0 0.753 12.0 890 12
H311 / H309 100.0 0.753 12.0 890 4
H312/ H813 100.0 0.753 12.0 890 8
H317/H312 100.0 0.753 12.0 890 6
H313a/NLO5 100.0 0.753 12.0 890 8
H315/ NLO5 100.0 0.753 12.0 890 7
H318/H315 100.0 0.753 12.0 890 10
H316D/H304D 100.0 0.753 12.0 890 3
H319/HSl3 100.0 0.753 12.0 890 12
H320/ N L08 100.0 0.753 12.0 890 14
H321/HSl4 100.0 0.753 12.0 890 9
H322/H815 100.0 0.753 12.0 890 7.5
H323/HSl4 100.0 0.753 12.0 890 4.5
H324 / LTO3 100.0 0.753 12.0 890 7
H325 / DP19 100.0 0.753 12.0 890 8
H328/157 100.0 0.753 12.0 890 7
H389/ H328 100.0 0.700 12.0 850 1

H329/2P205 100.0 0.753 12.0 890 7+3
H330/l60 100.0 0.753 12.0 890 15
H331 /1P-1 100.0 0.753 12.0 890 12
H333 / PNHl 100.0 0.753 12.0 890 10
H334/ 157 100.0 0.753 12.0 890 12

 

 

157

Table D.4. Sample description after the deposition of the diamond films.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I.D. Gas Flow (SCCM) Sub. Temp. Dep. Time
H; CH4 CO (°C) (hrs.)
H335/2P205 100.0 0.753 12.0 890 10
H336/160 100.0 0.753 12.0 890 12
H336D 100.0 .7 0.0 800 +2.3
H337/1P-1 100.0 0.753 12.0 890 .5
H338/NY-1 100.0 0.753 12.0 890 .5
H341/H338 100.0 0.753 12.0 890 2.5
H339/L'1‘O-2 100.0 0.753 12.0 890 8
H342/PE21 100.0 0.753 12.0 890 12.5
H343/PE22 100.0 0.753 12.0 890 14
H344/PE21 100.0 0.753 12.0 890 20.5
H345/H819 100.0 0.753 12.0 890 16
H346/H818 100.0 0.753 12.0 890 17
H347/HSI9 100.0 0.753 12.0 890 13
H348/MA-1 100.0 0.753 12.0 890 12
H349 / N LO-9 100.0 0.753 12.0 890 8
H350/PNH1 100.0 0.753 12.0 890 10.5
H350D 100.0 0.700 0.0 800 1.3
H351D/H322 100.0 0.753 12.0 890 3
H352D/H329 100.0 0.753 12.0 890 4.5
H354D/H342 100.0 0.753 12.0 890 3
H355D/H343 100.0 0.753 12.0 890 3.5
H356D/ H346 100.0 0.753 12.0 890 4
H357D/H347 100.0 0.753 12.0 890 3.5
H359/MA1 100.0 0.5 12.0 890 10.5
H361/PNH3 100.0 0.5 12.0 890 9.5
H362/PNH3 100.0 0.7 12.0 890 10.5
H364/PNH2 100.0 0.7 12.0 890 10
H366/PNH3 100.0 0.7 12.0 890 1
H367/T-1 100.0 0.7 12.0 890 8
H368/T-1 100.0 0.7 12.0 890 8.5
H373/H368 100.0 0.7 12.0 890 3

 

 

 

 

 

 

 

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