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This is to certify that the
dissertation entitled

ELECTRICAL CONDUCTIVITY OF HETEROEPITAXIAL
DIAMOND

presented by
MAHDOKHT BEHRAVAN

has been accepted towards fulfillment
of the requirements for the

PHD degree in Physics

 

Kai/3r Professor’s Signature
‘ q (9&2 d LUV 7.2005,

Date

MSU is an Affirmative Action/Equal Opportunity Institution

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PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

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2/05 p:/ClRC/DateDue.indd-p.1

ELECTRICAL CONDUCT IVITY OF HETEROEPIT AXIAL DIAMOND

By

Mahdokht Behravan

A DISSERTATION
Submitted to
Michigan State University

in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

2005

Abstract

ELECTRICAL CONDUCTIVITY OF HETEROEPITAXIAL DIAMOND

By

Mahdokht Behravan

The purpose of this research is to understand the electrical conduction
mechanisms of heteroepitaxial diamond by performing direct current (DC) electrical
measurements. Of particular interest is the temperature dependence of the DC
conductivity. The project takes advantage of recent advances at Michigan State
University in the growth of diamond by chemical vapor deposition on lattice-matched
substrates, i.e., by heteroepitaxy. This investigation represents the first detailed study of
an electrical transport property of heteroepitaxial diamond. The characterization of the
electrical properties of a wide bandgap, high resistivity material such as diamond requires
low current, high temperature measurements. A number of new techniques were
developed to perform reliable electronic measurements at elevated temperatures. The
magnitude of the DC conductivity of heteroepitaxial diamond was found to be
remarkably similar to that of high-purity, Type Ila natural diamond. Heteroepitaxial
diamond exhibits thermally activated conductivity, with a single activation energy of
1.401003 eV from 250 °C to 550 °C. This result is similar to previous measurements by
other workers on Type IIa natural diamond, suggesting the presence of electronic states at

comparable concentrations in materials of completely different origin.

ACKNOWLEDGMENTS

I would like to thank my advisor, Professor Brage Golding, for showing me how
to think as a scientist, and particularly, for his questions that forced me to challenge
myself more.

I cannot thank enough my wonderful friend, David Story, for helping me to
understand my true potential, for his patience and support, and his father, Martin Story,
for his depth of experience and physical intuition.

Also, this project would not have come to fruition without the technical help and
consultation of the following: Reza Loloee, Peter Tobias, Nathan Verhanowitz, Baokang
Bi, Barry Tigner, Tom Palazzolo, Tom Hudson, Ryan Kruse, Murari Regmi.
Additionally, Ann Kirchmeier, Darla Conley, Debbie Simmons, Sandy Teague, and
Laura Winterbottom were always helpful and supportive.

Finally, my heartfelt appreciation goes to my mother and father for their support

and encouragement.

iii

Table of Contents

List of Tables ......................................................................................................... vi
List of Figures ....................................................................................................... vii
Chapter 1 Introduction ......................................................................................... 1
Chapter 2 Properties of Group IV Semiconductors ............................................. 4
2. 1 Structure .................................................................................................. 4
2. 2 Electronic Structure ................................................................................ 5

2. 3 Impurities and Defects ............................................................................ 8

2. 4 Conduction Mechanisms ....................................................................... 16
2.4.1 Effective Mass .................................................................................. 16
2.4.2 Carrier Density .................................................................................. 20
2.4.3 Mobility ............................................................................................. 23

2. 5 DC Conductivity ................................................................................... 24
2.5.1 Intrinsic Behavior .............................................................................. 24
2.5.2 Extrinsic Behavior ............................................................................ 25
2.5.3 Variable Range HOpping Conduction ............................................... 28

2. 6 AC Conductivity ................................................................................... 29

2. 7 Diamond Transport ............................................................................... 30
2.7.1 Surface Properties ............................................................................. 30
2.7.2 Surface Conduction ........................................................................... 34
2.7.3 Metallization ..................................................................................... 38
2.7.4 Bulk Conduction of Diamond ........................................................... 47
Chapter 3 Heteroepitaxial Diamond Growth ..................................................... 55
3. l The Epitaxial Process ............................................................................ 55

3. 2 CVD Diamond Growth ......................................................................... 57

3. 3 Characterization .................................................................................... 60
Chapter 4 Experimental Methods ...................................................................... 69
4. 1 Contact Geometry ................................................................................. 69
4. 2 Electrode Fabrication ............................................................................ 70
4.2.1 Chemical Cleaning ............................................................................ 70
4.2.2 Electrode Deposition ......................................................................... 71
4.2.3 Thermal Annealing ........................................................................... 74
4.2.4 Oxygen Plasma Treatment ................................................................ 74

4. 3 High Temperature Measurement and Thermal Isolation ...................... 75
4.3.1 Vacuum System ................................................................................ 75
4.3.2 Sample Holder .................................................................................. 77
4.3.3 Thermal Isolation .............................................................................. 82
4.3.4 Temperature Measurement ............................................................... 84
4.3.5 Heaters .............................................................................................. 84

iv

4.3.6 Thermal Time Constant .................................................................... 85
4. 4 High Resistance Measurement Considerations and Electrical Isolation87

4.4.1 Current Leakage ................................................................................ 87
4.4.2 Noise ................................................................................................. 89
4.4.3 Voltmeter Input Resistance ............................................................... 90
4.4.4 Time Constant ........................................................................ ' ........... 90

4. 5 DC Measurement .................................................................................. 91
4.5.1 Probe Station Circuit ......................................................................... 91
4.5.2 Measurement Setup ........................................................................... 93
Chapter 5 Results ............................................................................................... 98
5. 1 DC results .............................................................................................. 98
5.1.1 Surface Conductance ........................................................................ 98
5.1.2 Estimate of Surface Conductance ................................................... 100
5.1.3 I-V Characteristics .......................................................................... 104
5.1.4 Temperature Dependent Conductivity of Heteroepitaxial Diamond

1 12

Chapter 6 Discussion of Results/Analysis ....................................................... 115
6. 1 Comparisons with other measurements .............................................. 115

6. 2 Origin of activated behavior ............................................................... 116

6. 3 Outlook ............................................................................................... 121
Appendix A Metallization Repair and Removal .............................................. 122
Appendix B Setup Procedure ........................................................................... 130
Appendix C LabView Code ............................................................................. 132
References ........................................................................................................... 144

List of Tables

Table 1 Comparison of mobility, electric field break down, and band gap of diamond. 2

Table 2 Comparison of interatomic distance, lattice parameter, and bonding energy of
diamond, Si, and Ge. ................................................................................................... 5

Table 3 Light and heavy hole masses. .............................................................................. 19

Table 4 Dependence of the type of the contact metal on the work function and electro-
negativity and surface treatment. Treatment A is CrO3 in H2804, and treatment C is
02 plasma. GM and XM are metal work function and electro-negativity [l4] ........... 39

Table 5 Parameters for biasing and growth of thick diamond used for electrical

measurement. ............................................................................................................ 59
Table 6 Data from linear fits to I-V for Run-2 ................................................................ 105
Table 7 Fit results of run 1 and 2. ................................................................................... 113

vi

List of Figures

Figure 1 Cubic unit cell of diamond. .................................................................................. 4
Figure 2 fcc first Brillouin zone. ......................................................................................... 5
Figure 3 Energy band structure of: (a) diamond, (b) silicon and (c) germanium. .............. 8

Figure 4 (a) substitutional impurity (b) interstitial impurity, (c) vacancy, and (d) Frenkel

defect. ........................................................................................................................ 10
Figure 5 Various types of point defects in diamond [9]. .................................................. 11
Figure 6 (a) Edge and (b) screw dislocation. .................................................................... 12
Figure 7 Screw dislocation in diamond [9] ....................................................................... 13
Figure 8 (a) Intrinsic and (b) extrinsic stacking fault (generic). ....................................... 14
Figure 9 Intrinsic (a) and extrinsic (b) stacking fault in diamond [9] ............................... 15
Figure 10 (a) Free electron band structure (b) First derivative (c) Effective mass. .......... 18
Figure 11 Schematic band diagram and Fermi-Dirac function F(E) for T>0. .................. 20
Figure 12 Density of electron and holes vs. energy. ......................................................... 21
Figure 13 Conduction electron density vs. temperature at low doping. ........................... 23
Figure 14 Temperature variation of the electron and hole mobilities ............................... 24
Figure 15 Typical conductivity behavior of a semiconductor with T]. ........................... 26
Figure 16 Conductivity of high and low doped semiconductor with temperature. .......... 27
Figure 17 Dangling bonds on the interrupted surface of a crystal. ................................... 30
Figure 18 (a) Truncated bulk and (b) dimerized (100) surface [13]. ................................ 31

Figure 19 Top and side views of two models for hydrogen terminated (100) surface, (a)
lxlz2H, (b) lxl:H and :2H [13]. .............................................................................. 32

Figure 20 Two models for oxygen terminated (100) surface, bridging and double bonded
structures [13]. .......................................................................................................... 33

vii

Figure 21 I-V relation of the as-grown, hydrogen and oxygen plasma treated undoped
homoepitaxial diamond surfaces. Note reversible behavior with alternate plasma
exposures [18]. .......................................................................................................... 34

Figure 22 Energy diagram of the hydrogenated/oxygenated diamond surface [18] ......... 35
Figure 23 Surface conductance of different diamond samples [16]. ................................ 36

Figure 24 Band bending model of the hydrogenated surface (below); hydrogen extracted

from the diamond by catalytic effect of water on the surface (above) [16]. ............. 37
Figure 25 Schottky barrier height for various metals on clean and oxygen-terminated
surfaces; UPS: UV photoemission spectroscopy. [48] ............................................. 40
Figure 26 Dependence of specific contact resistivity of Ti and Mo versus annealing
temperature [26]. ....................................................................................................... 42
Figure 27 I-V behavior with temperature for titanium on boron doped polycrystalline
diamond [56]. ............................................................................................................ 43
Figure 28 Band diagram of Ti contact on diamond; (a) as deposited , (b) narrowed
depletion layer by defects, (c) decreased banier height by defects [49] ................... 45
Figure 29 Electrical conductivity of natural diamond Ha and two CVD diamond vs. UT
[55]. ........................................................................................................................... 49
Figure 30 Electrical conductivity versus l/T for two Crystallume, Norton diamond,
Raytheon, and Type Ila natural diamond [59]. ......................................................... 50
Figure 31 Electrical resisitivity of diamond type IIa, Ib HPHT, and two undoped
homoepitaxial diamond grown on type Hb and boron doped substrates [60] ........... 52
Figure 32 Log conductivity vs. l/T for Type Ila natural diamond and Norton diamond
(before and after cleaning for both heating and cooling) [59]. ................................. 54
Figure 33 Growth of heteroepitaxial diamond [66]. ......................................................... 55
Figure 34 Surface and structure of SrTi03 [67] ................................................................ 56
Figure 35 SEM image after 20 minutes biasing (20-Ju1-02) [68]. .................................... 58
Figure 36 SEM image after 60 minutes biasing (18-Jul-02) [68]. .................................... 58
Figure 37 SEM image after (a) 20 and (b) 180 minutes growth on (17-Jul-00) and (23-
Jun—Ol) [67]. .............................................................................................................. 59
Figure 38 AFM of epitaxially grown iridium [67] ............................................................ 60
Figure 39 XRD of diamond grown on Ir/SrTiO3 after 180 minutes [67]. ........................ 61

viii

Figure 40 Raman spectrum of a free standing 25 pm (001) diamond [67]. ..................... 62
Figure 41 AFM of a 12 hour diamond growth [67]. ......................................................... 63

Figure 42 (a) diamond sample at 5X, (b) dark spots at 20X, and (c) spiral type defect
detected by optical microscope at 20X (diamond grown by Z. Dai on 04-May-04). 64

Figure 43 SEM images of (a) the center of the diamond surface, and (b) a magnified
inclusion. (04-May-04) ............................................................................................. 65

Figure 44 (a) and (b) SEM images of the area near the edge of the sample at two
magnifications (O4-May-04). .................................................................................... 66

Figure 45 SEM image of (a) the tilted sample showing the surface and cross section
simultaneously, (b) and ( c) cross section. The iridium side in (a) and (b) is on the

top side of the images. .............................................................................................. 67
Figure 46 Optical microscope images of the cross section of the diamond with the iridium
side up at 20X (a) 0.5 mm far from the edge, and (b) near the edge. ....................... 68
Figure 47 Free standing transparent heteroepitaxial diamond, Diameter: 3.5 mm,
Thickness: 35 um [68]. ............................................................................................. 68
Figure 48 Schematic of the sample electrode geometry. .................................................. 70
Figure 49 Drawing of the stainless steel holder, side view and top view. ........................ 72
Figure 50 Stainless steel holder with the mask on the right. ............................................ 72
Figure 51 Optical microscope image of a loaded sample, with iridium side up, in the
holder pocket held with the clip. ............................................................................... 73
Figure 52 Optical microscope images of diamond sample (04-May-04) and top Ti/Au
electrode. Electrode diameter is approximately 0.5 mm .......................................... 74
Figure 53 QF flange design; for feed-through BNC connectors ....................................... 76

Figure 54 Bell jar showing QC flange, coaxial cables, and aluminum minibox inside... 77

Figure 55 Side view of the sample holder assembly (not to scale) ................................... 78
Figure 56 Detail of the electrical connections to the diamond sample. ............................ 79
Figure 59 Heater power versus temperature. .................................................................... 83
Figure 60 Platinum micro-heater (Heraeus, dimension in mm). ...................................... 85

Figure 61 Thermocouple voltage, corresponding to temperature, versus time between: (a)
496 and 508 °C, and (b) 265 and 300 °C. .................................................................. 86

ix

Figure 62 Schematic of the probe-station circuit. ............................................................. 92

Figure 63 Diamond sample on the Au-pad of the silicon substrate. ................................. 93
Figure 64 Sample setup at the probe-station. .................................................................... 93
Figure 65 DC circuit diagram of the measurement system ............................................... 94
Figure 66 Schematic of the DC measurement system. ..................................................... 95

Figure 67 Circuit diagram: measurement circuit, microheater circuit, thermocouple

circuit, diffusion pump circuit, and DC-Source (voltage divider). ........................... 96
Figure 68 I—V before exposure to oxygen plasma for two top electrodes ......................... 99
Figure 69 I-V after exposure to oxygen plasma for two top electrodes .......................... 100

Figure 70 Heteroepitaxial diamond with two Ti/Au electrodes- with diameter of ~0.38
mm- on the top surface and iridium on the back ..................................................... 101

Figure 71 Circuit for measurement with two top electrodes; the bottom electrode can be
switched between a floating and grounded state ..................................................... 102

Figure 72 Total current I vs. time at :5 V bias with floating back contact (above) and

with grounded back contact (below). ...................................................................... 102
Figure 73 I-V at 300 °C, 350 °C, and 400 °C. ................................................................. 104
Figure 74 I-V at 265 °C: Run-2 ....................................................................................... 106
Figure 75 I-V at 301 °C; Run-2 ....................................................................................... 107
Figure 76 I-V at 350 °C; Run-2 ....................................................................................... 107
Figure 77 I-V at 399 °C; Run-2 ....................................................................................... 108
Figure 78 I-V at 428 °C; Run-2 ....................................................................................... 108
Figure 79 I-V at 425 °C; Run-2 ....................................................................................... 109
Figure 80 I-V at 495 °C; Run-2 ....................................................................................... 109
Figure 81 I-V at 545 °C; Run-2 ....................................................................................... 110
Figure 82 Resistance versus temperature for Run-l (Heatingl) and Run-2 (Heating2 and

Cooling2). ............................................................................................................... 111
Figure 83 I-V at 300 °C for voltages between -12 and 12 volts ...................................... 112

Figure 84 Conductivity of heteroepitaxial diamond versus inverse temperature; Run-1.
................................................................................................................................. 113

Figure 85 Conductivity of heteroepitaxial diamond vs. 1/T; Run-2. .............................. 114

Figure 86 Comparison of conductivity vs. l/T between heteroepitaxial 0, natural type 113
A [55], type Ha E] and type Ib diamond I [60] ........................................................ 116

Figure 87 Optical microscope images of (a) a broken Ti/Au electrode, and (b) The
circular pad is a Au electrode- with diameter of 0.015 inches- on the diamond

surface, a bubbled electrode. ................................................................................... 122
Figure 88 SEM image of overlapped electrodes residue; electrode diameter: 0.015 inches.
................................................................................................................................. 123
Figure 89 SEM images of (a) partially etched electrode after 70 minutes exposing to
ammonium solution, and (b) and (c) particles that came off the electrode. ............ 125
Figure 90 SEM image of partially etched electrode after 100 minutes HF etching. ...... 126

Figure 91 SEM images of electrode after (a) 100 minutes, and (b) 170 minutes HF
etching. .................................................................................................................... 126

Figure 92 SEM images of electrode residue after ~5 hours of HF etching (a) and (b). . 127

Figure 93 SEM image of metal carbide islands on boron doped polycrystalline diamond
surfaces after etching aluminum contacts from the silicon [58]. ............................ 128

Figure 94 Optical microscope images of cleaned diamond surface before electrode
deposition at 20X (a), and after electrode deposition at 50X showing no electrode
deformation (b). ...................................................................................................... 129

xi

Chapter 1 Introduction

Single crystal diamond is a wide band-gap semiconductor, E8 = 5.5 eV, that has
shown outstanding electrical properties, such as very high carrier mobilities and a large
dielectric breakdown field, coupled with unsurpassed room temperature thermal
conductivity and mechanical hardness. These unique properties make diamond an
excellent material for electronic devices such as transistors, high-voltage capacitors and
radiation detectors.

It was found recently that homoepitaxial diamond (diamond grown on a diamond
substrate) has larger mobilities for electrons and holes than Type IIa natural diamond
(high purity natural diamond with only trace nitrogen impurities present) [1]. This has
raised questions about the fundamental electronic properties of diamond. Some electrical
properties of diamond and other'semiconductors are compared in Table l [2]. It can be
seen that diamond has the largest bandgap and dielectric breakdown field. The room
temperature electron mobility of homoepitaxial diamond is exceeded only by GaAs.

The major problem with growing homoepitaxial diamond is the lack of large
diamond substrates at reasonable cost. This limitation opens up an area of research for
heteroepitaxial diamond (diamond grown on non-diamond substrates). The potential
advantage of heteroepitaxial diamond over homoepitaxial diamond is substrate scale and

cost, provided suitable hi gh-quality, lattice-matched substrates can be found.

Table 1 Comparison of mobility, electric field break down, and band gap of diamond.

PROPERTIES OF DIAMOND
AND OTHER SEMICONDUCTORS

 

 

 

 

 

 

 

 

Semiconductor Mobility Maximum Band-
Electrlc field gap
cm’v‘s" v cm" (E...) eV (5,)
Natural Diamond Ila ggwmmn) 107 5.5
1 800-21 00 (hole)
Homoepitaxial Diamond 4500 (electron) 107 5.5
3800 (hole)
Silicon carbide (SiC) 700 (electron) 3.0 x 106 3.26
Gallium nitride (GaN) 2000 (electron) 2.0 x 106 3.0
Gallium arsenide (GaAs) 8500 (electron) 4.0 x 105 1.42
Silicon (Si) 1500 (electron) 3.7 x 105 1.12
450 (hole)
Ge 3900 (electron) 2.0 x 105 0.66
1900 (hole)

Only a few investigations of the transport properties of natural diamond have
occurred, and no research to date has been done on the transport properties of
heteroepitaxial diamond. The mobilities of heteroepitaxial diamond have yet to be

reported. Heteroepitaxial diamond with areas of 10 mm2 and thicknesses up to 50 um has

been grown on Ir/SrTiO3 substrates by the Golding group.

Using this newly available material, this dissertation will address the issues of

performing electrical measurements on heteroepitaxial diamond, describing research

methods that have led to the following results:

Current-voltage (I-V) characteristics of heteroepitaxial diamond at high
temperatures.
Temperature dependence of the DC conductivity.

Activation energy of the DC conductivity.

Chapter 2 Properties of Group IV Semiconductors

2. 1 Structure

The group IV elements of the periodic table, C (in diamond form), Si, and Ge are
important due to their semiconducting properties. Their lattice structure is fcc with basis
(0, 0, 0), (1/4, 1/4, 1/4) [3]. There are eight atoms per cubic cell with each carbon bonded
to four nearest neighbors that form a tetrahedron. The cubic cell is shown in Figure l.

The neighboring atoms form hybridized sp3 covalent bonds.

 

Figure 1 Cubic unit cell of diamond.

The interatomic distances, lattice parameters and bond energies of diamond,
silicon and germanium are compared in Table 2 [4]. It can be seen that diamond has the

shortest interatomic distance, lattice parameter, and the largest bonding energy.

Table 2 Comparison of interatomic distance, lattice parameter, and bonding energy of diamond,

 

 

 

 

Si, and Ge.
Material Interatomic Distance Lattice Parameter Bond Energy
. (nm) (nm) (KJ/mol)
Diamond 0.153 0.357 347
Silicon 0.235 0.543 196
Germanium 0.245 0.565 163

 

 

 

 

 

 

2. 2 Electronic Structure

The first Brillouin zone of the fcc structure is shown in Figure 2 [5].

kz

x 4 . ..

\'”

Figure 2 fcc first Brillouin zone.

The energy gaps of diamond, Si, and Ge are 5.5 eV, 1.1 eV, and 0.66 eV,
respectively. Their energy band structures are shown in Figure 3 [6, 7]. They all are
indirect bandgap materials, and have four valence bands. Three p bands and one 5 band
form sp3 hybrids. Diamond has a larger band gap due to its shorter atomic distances and

larger bonding energy (Table 2).

 

 

 

 

 

 

 

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Figure 3 Energy band structure of: (a) diamond, (b) silicon and (c) germanium.

2. 3 Impurities and Defects

In general, even nominally pure materials have defects and unintentional dopants.
These defects and dopants can act as donors, acceptors or trap centers with energy levels
that lie between the conduction and valence bands, i.e., within the bandgap. Since these
states may affect the transport properties, understanding the electrical properties of
crystals requires a good understanding of their defects. Here, general forms of defects in

semiconductors are reviewed. Four different types of defects are described: point defects,

line defects, area defects, and volume defects.

General forms of point defects are shown in Figure 4 [8]. A point defect may be:
(a) incorporation of a different type of atom or impurity into a substitutional site, or (b)
interstitial site, (c) a vacancy in the lattice caused by a missing atom, or (d) a lattice
vacancy and an interstitial host atom (Frenkel defect). Vacancies are classified according
to their charge states: Vo (neutral vacancy), V' (acceptor vacancy), VZ' (double-charged
acceptor vacancy), V+ (donor vacancy), and so on.

The various types of point defects, i.e., vacancy (V), self-interstitial (I), and

foreign interstitial and substitutional atom, that may form in diamond are shown in Figure

5 [9].

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ty, (c) vacanc

ty (b) interstitial impuri

Figure 4 (a) Substitutional impuri

10

Foreign Interstitial Atoms
9.9., H, U

:oroze >:+°+:+:~:o:

0.0.0.e@o.:.'.9.020

 

 

Figure 5 Various types of point defects in diamond [9].

Line defects, i.e. dislocations, may occur in a crystal as edge or screw types.
These defects are shown in Figure 6 [8]. The edge dislocation is visualized as the
insertion of an extra plane of atoms AB into a section of the lattice (a). This insertion
causes compression of the atoms in that section and extension of the atoms in the nearby
section. The screw dislocation is the sliding of one half-plane of the crystal over a lower
plane (b). Impurities may be trapped at line defects and may alter the electrical

conductivity of the crystal.

ll

 

 

(a) (b)

Figure 6 (a) Edge and (b) screw dislocation.

Dislocations, both edge and screw type, can also occur in diamond. The screw
type is most prominent and is shown in Figure 7 [9]. The screw dislocation structure (13—
12-11-10—9-8—7) can be distinguished from the normal hexagon form (1-6-5-4-3-2-1).

Dislocation densities of 108 cm’2 have been found in Type 11a natural diamond [9].

 

Figure 7 Screw dislocation in diamond [9].

Area defects can occur either on the surface or inside a crystal. Typical forms of
area defects are twins and stacking faults. Formation of an oriented plane of a lattice with
respect to the un-deformed plane is twinning. Twinning can form between the grain
boundaries and on the surface of a single crystal. A stacking fault can be either intrinsic
or extrinsic (Figure 8) [8]; a missing layer section is intrinsic (a), and an inserted layer is

extrinsic (b).

13

 

 

 

 

 

 

 

 

 

 

 

 

 

,1 V .-1 ( ——/’ \——t
t. —- -——( A

ii A H B ——\ /—— ii
-\ —-——-/\ .\ .1 f— 1
(‘ l: (j (
B ii ii B
\ .1 A \

(a) (b)

Figure 8 (a) Intrinsic and (b) extrinsic stacking fault (generic).

Twins and stacking faults in diamond originate at dislocations and impurity atoms
and they often appear together. The coexistence of monolayer twins and <11 l> stacking

faults in the diamond structure is shown in Figure 9 [9].

l4

 

[111]

 

 

 

 

Figure 9 Intrinsic (a) and extrinsic (b) stacking fault in diamond [9].

Dislocations and vacancies may coexist. Point defects can interact with other
types of defects. A vacancy may combine with another defect and form a larger vacancy.
Dislocations can trap point defects and impurities. These dislocations can be sources of
dangling bonds, and form charged regions. They can scatter phonons and electrons,
affecting mobilities, and trap carriers and recombine with them, influencing the lifetime

of carriers.

2. 4 Conduction Mechanisms

2.4.1 Effective Mass

The electron mass in a solid may appear to deviate from the free electron mass.
This deviation is caused by the interaction between accelerated electrons in an electric
field and the crystal lattice. Scattering between electrons and ions can slow down the
electrons resulting in a larger effective mass. The velocity of an electron moving in an
energy band can be written as [5]:
,g z d_w = 121.2:
dk h dk
where, vg is the group velocity of a wave packet from which the acceleration can

be found:

_dvg _ 1 d2E dk

___———, 2
dt h dkz dt

Taking the first derivative of pzhk with respect to time will give dk/dt:

£=hfl 3
dt dt

Acceleration of the electron is found by combining Equations 2 and 3:

1 dzEdp__l_d2E

a — ———— — — 4
ii2 rik2 dt hz dir2
where, F can be considered the classical force causing the electron to accelerate:
F
a = —
m

Equating Equations 4 and 5 gives an expression for the effective mass:

16

d2E “I
m* =h2 — 6
rik2

This shows that the effective mass is proportional to the inverse of the second
derivative of the energy with respect to the wave number, i.e., the curvature of a band.
The effective mass is small for large curvatures and large for small curvatures.

A simple band structure (a), the first derivative (b), and inverse of the second
derivative of E-kx (c) within the first Brillouin zone for an electron are shown in Figure
10. The effective mass is small and positive near F, the center of the Brillouin zone, and
increases with kx. The effective mass can be negative or diverge to infinity for kx far from

the energy band minimum. Generally, the effective mass depends on direction and has a

tensor form.

17

 

 

 

 

 

 

I
I
I
I
I
I
:g——r—"‘L‘i I ‘17, ‘9

 

 

Figure 10 (a) Free electron band structure (b) First derivative (c) Effective mass.

The concept of the effective mass is useful in understanding the shape of energy
versus k bands. The light and heavy hole masses (relative to the electronic mass m) for
diamond, silicon and germanium are compared in Table 3 [10]. Light and heavy hole

masses of diamond are larger than for silicon and germanium.

18

Table 3 Light and heavy hole masses.

 

 

 

 

Material Light Heavy
hole mass hole mass
Diamond 0.7 2.12
Silicon 0.16 0.52
Germanium 0.043 0.34

 

 

 

 

 

The conduction band has a minimum between F and X. As the energy surface in

proximity to the minimum is not perfectly spherical, effective mass is different along two

a o e a e * *
directions, defining a longitudinal mass m; and transverse mass m [5].

19

2.4.2 Carrier Density

The number of carriers depends on the band gap, Eg, and temperature. For an

intrinsic semiconductor at T>O K the number of carriers in the conduction band and
valence band are equal. Therefore, the Fermi energy lies midway in the band gap

assuming me*= mh* (Figure 11) [5].

%
/

    

 

 

 

 

 

 

 

0 V; _ >F(E)

Figure 11 Schematic band diagram and Fermi-Dirac function F(E) for T>0.

The density of electrons, or holes, in the conduction band, or valence band, of an
intrinsic semiconductor increases exponentially with temperature. Figure 12 shows
density of electrons in the conduction and holes in the valence band for an intrinsic

semiconductor [5].

20

 

 

Figure 12 Density of electron and holes vs. energy.

The carrier concentration N, in cm'3, for either electrons or holes is a function of

the effective mass and temperature, and is given by the following equation [5]:

3/2

* E
N,=4.84x1015 ”'— T3/2 exp - —g— 7
mo ZkBT

The exponential term dominates the temperature dependence of N).

If a semiconductor is doped (extrinsic semiconductor), the Fermi level is not in
the middle of the band gap, and depending on the impurity type and level it shifts toward
either the conduction or valence band. The impurity atoms contribute to the carrier
concentration. For an n-type semiconductor, the relationship between the density of
donors ND, ionized donors N+D, donor energy relative to the conduction band minimum

ED is given by [6]:

21

l
1.1,,{MJ
L 8 kBT _

For p-type material with acceptor density N A, ionized acceptors N}, and acceptor

 

 

 

energy relative to the valence band EA one has:

" 1

NA

E -E
kBT -

where g is the ground state degeneracy of the impurity level.

 

 

 

b

At 0 K, impurities cannot contribute to the electrical conduction. For T finite but
small, the impurities ionize and provide extra charge carriers. At higher temperature, all
the impurities are ionized and do not provide additional charges. At still higher
temperature, the intrinsic carriers add to the number of carriers. This behavior for

electron density for a specific doped semiconductor can be seen in Figure 13 [5].

22

N. 10‘“ -
[o__l___:::;u]1 017

10“
' 10“
1o“'
10‘3

1012
0 I00 ZOO 300 400 TIKI

 

 

 

Figure 13 Conduction electron density vs. temperature at low doping.

2.4.3 Mobility

Mobility is the drift velocity, v, of the carriers in unit electric field, E,

,u = v/ E 10

and is related to the carrier relaxation time, I, by:

,u = 76/ m 11

The mobility of the electron, ,ue, differs from the mobility of the hole, ,uh. In cases

of interest here, mobilities of electrons and holes generally decrease with increasing

temperature due to phonon scattering. This behavior is shown in Figure 14 [5].

23

 

T

 

Figure 14 Temperature variation of the electron and hole mobilities.

In a doped semiconductor, the mobility may also depend on the dopant
concentration. Experimentally, the mobility of a lightly doped semiconductor varies with
temperature as T3’2 at low temperature, due to scattering of the carriers by impurities. At
high temperatures the mobility of the lightly doped semiconductor will vary with

temperature as T3”, due to scattering of the carriers by phonons. [3].

2. 5 DC Conductivity

2.5.1 Intrinsic Behavior
In an intrinsic semiconductor, the conduction mechanism is controlled by the
properties of the pure crystal, and is given by [3]:
0': Neeye +Nhe,uh 12
where e and h stand for electron and hole, respectively, and:
0 = conductivity

N ,- = density of charge carriers of type i

24

,ui = mobility of carrier type i

e = electron charge.
The temperature-dependent intrinsic conductivity can be obtained by combining

Equations 7 and 12 [5]:

 

* 3/2
E
a = 4.84x1015 "'— T3/2e(fle + flh)exp — g 13
mo ZkBT

The mobility and the number of charge carriers depend on temperature. The

dominant temperature factor in Equation 13 is the density of charge carriers, as the
exponential term varies faster than 7‘”. Therefore, the conductrvrty variation wrth

temperature mainly follows the change in the carrier concentration. Thus the temperature

dependence of the intrinsic conductivity varies as:

a = 0, exp(— Eg /2kBT) 14

and is governed by the bandgap energy.

2.5.2 Extrinsic Behavior

A semiconductor may have sources of carriers other than the intrinsic carriers,
such as dopant impurities and defects. The impurities and defects can produce states in
the band gap and affect the electrical conductivity. The conductivity generally increases
with temperature provided there is a dominant single carrier type. Figure 15 shows a
typical variation of conductivity with temperature [3]. At very low temperatures (D), the

conductivity arises from electrons hopping between states within the band gap. Hopping

25

is triggered by the exchange of energy of an electron with a phonon, and requires the
presence of both occupied and empty states. In this range of temperature, hopping
conduction is very small because the electrons can only hop from one site to the next,
limited by the weak overlap of their wave functions. At higher temperatures, the electron
concentration increases rapidly (C). Electrons at the dopant level absorb enough energy
to reach the conduction band, dramatically increasing conductivity. This effect saturates
with temperature when nearly all of the electrons at the dopant level become ionized. At
this point, the carrier concentrations become largely independent of temperature, and the
mobility determines the conductivity (B). At temperatures above this region, the

conduction corresponds to the intrinsic behavior of the material (A).

Ina

 

 

 

0 T7I (14")

Figure 15 Typical conductivity behavior of a semiconductor with T".

26

The magnitude and variation of the extrinsic conductivity with the temperature
depends on the dopant concentration. Figure 16 is an example of the variation of the
conductivity for high and low dopant concentrations. For low dopant concentration, 1012
cm'3, the conductivity decreases with temperature for T<300 K (decreased mobility), and
increases with temperature for T>300 K (increased number of carrier). For high dopant

concentration, 1016 cm'3, the conductivity is mostly controlled by the higher carrier

 

 

concentration.
- lo 0’0...“
O 103 ._ a Nd-10 [ 0:11,]
1 _.
[oTn-I 1°”
10' ""
1 ...
10" - .
' I I ‘- l . I I

 

 

100 200 300 400. 500 mg

Figure 16 Conductivity of high and low doped semiconductor with temperature.

An empirical expression for the conductivity of a highly doped semiconductor can
be expressed as [11]:

0' = 0'1 exp(— El/kBT)+ 0'2 exp(— Ez/kBT)+ 0'3 exp(— E3/kBT) 15

where E) > E2 > E 3, and E), E2, E3 are activation energies arising from different
conduction mechanisms. The first term is related to the activation from the impurity level
to the valence or conduction band. The second term corresponds to conduction in an

impurity band. This mechanism occurs when the impurity concentration is high enough

27

that conduction occurs through a narrow band of singly filled neutral donor states within

the band gap. The third term corresponds to nearest neighbor hopping.

2.5.3 Variable Range Hopping Conduction

According to the Davis-Mott model [12], another form of hopping conduction
may occur in semiconductors. At lower temperatures, carriers may hop to larger distances
to find unoccupied localized states with energies equivalent to or lower than nearest
neighbors. Localized states in the band gap considered in this model may correspond to
localized impurity or vacancy states in semiconductors. At very low temperatures,

conduction can occur by thermally assisted tunneling between states at the Fermi level. This

is called variable range hopping (VRH) conduction, and for a 3-dimensional system is given

by [12]:
0 = o,(T)cxp(— AT‘1/4) 16
where;
2 N E 1/2
00(T):_e_T/z_vphl:_(—F)] l7
2(87r) 043T

A=2.1Lz3/kBN(EF)Il/4 18
where;

N (E F ) = Density of states at the Fermi energy
e = Electron charge

Vph = Phonon frequency

28

k B = Boltzmann constant

T = Temperature

a = Inverse range of the wave function

2. 6 AC Conductivity

AC conductivity provides more information about the conduction mechanism in a
material. The frequency dependent conductivity is different for charge transfer in
extended states than for hopping in the localized states. Conductivity due to charge
excitation into the extended states is generally frequency independent below a few GHz.
Hopping conduction between localized states, on the other hand, requires electrons to

interact with phonons, and is expected to vary with frequency as [12]:

0(a)) = C0)” 19

where C is a constant.

Hopping near the Fermi energy can be distinguished from hopping between the
band tails of localized states by studying the temperature behavior of the conductivity.
Band tail conduction depends exponentially on the temperature because the charge carrier
density increases exponentially with temperature, exp(— l/T). For this mechanism, AC
conduction is similar to DC conduction in terms of temperature dependence. For hopping
at the Fermi energy level, the AC conductivity varies linearly with temperature, as the

number of carriers remains relatively constant. This can be compared with the

aforementioned variation of the DC conductivity with temperature, exp(— T‘“ 4 ).

29

2. 7 Diamond Transport

2.7.1 Surface Properties

The lattice is discontinuous at a surface and is thus not periodic in the
perpendicular direction to the plane of the surface. The surface discontinuity may
produce dangling bonds with localized energy states (Figure 17) [8]. Such a surface has a
large surface energy and is very reactive. Some materials, including silicon, germanium
and diamond, reconstruct their surface by re-bonding, as a way to lower their surface
energy. The surface termination of diamond is very important as it affects both the

surface electrical and contact properties.

Dangling bonds
/l\

 

 

Figure 17 Dangling bonds on the interrupted surface of a crystal.

Surface sensitive techniques like photoelectron spectroscopy (PES), Auger

electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), low energy

30

electron diffraction (LEED), high resolution electron energy loss spectroscopy
(HREELS) have been used for studying the surface of materials including diamond.

Initially, it was thought that diamond reconstructs its surface to graphite, as
graphite is the stable phase of carbon. However it was found that the clean surface of
diamond is different from graphite and is more closely related to reconstructions that
occur in germanium and silicon [13].

Different diamond planes at the surface undergo different reconstructions. Figure
18 shows a clean diamond (100) surface before and after surface reconstruction. The
neighboring carbon atoms form carbon dimers (C=C) to reconstruct to 2x1 symmetry

[13].

 
         
       
   

    

' cu
\\ \\ \\
In .” 09’0”
‘ ‘ '60 in ‘i
n on

(a) Truncated-Bulk C(100) 1111 (b) C(100)2xl
Figure 18 (a) Truncated bulk and (b) dimerized (100) surface [13].

The surface of diamond can be terminated by foreign atoms as well. Two
important diamond surface impurities are hydrogen (Figure 19) and oxygen (Figure 20),
as they may appear in various stages of the diamond growth process. However, very little
oxygen has been found on as-grown CVD diamond using XPS even when a COM; gas
mixture was used [14]. A single hydrogen bonded to carbon, C(100) 2xle, was found

by the HREELS technique [15].

31

Hydrogen temrination of the (100) diamond surface can be by found in two
forms: (a) two hydrogen atoms bonded to one carbon, C(100) 1x1:2H or (b) a disordered
form, where two hydrogens bond to a carbon and one hydrogen bonds to one carbon
atom, a combination of C(100) 1x1:2H and C(100) 2x1:H (Figure 19). The latter is

found on (100) surfaces of germanium and silicon as well [13].

 

Figure 19 Top and side views of two models for hydrogen terminated (100) surface, (a) 1x1:2H,

(b) lxl:H and :2H [13].

Oxygen can form CO with the diamond surface in two ordered structures of
C(100) 1x120, bridging between two carbon atoms and bonding to only one carbon atom

(Figure 20) [13].

32

 

Diamond (100) 1x1:O Bridging structure Diamond (100) lxl:O Double-bonded structure

Figure 20 Two models for oxygen terminated (100) surface, bridging and double bonded

structures [13].

Hydrogen and oxygen can be removed from the diamond surface by annealing.
Annealing at 1300 K is reported to be sufficient for a C(100) surface to free oxygen and
hydrogen and to obtain a clean C(100) 2x1 surface [13]. Hydrogen desorption is reported
to commence at 1000 K [16]. Oxygen on the diamond surface is stable up to 1173 K [14].
It is interesting to note that the surface of clean diamond can be exposed to a hydrogen or
oxygen plasma, and recover the hydrogen [17] or oxygen terminated diamond surfaces
(Figure 21) [18-20]. This can be used to change the surface properties of diamond. It can
be seen that the surface of as-grown diamond has a low resistance which is increased by
three orders of magnitude after oxygen plasma treatment. The low resistance state is
partially recovered after hydrogen plasma treatment. A band bending model explains the

surface conduction in the next section.

33

as-grown

H2 Plasma

0; Plasma

CURRENT (A)

 

VOLTAGE (V)

Figure 21 I-V relation of the as—grown, hydrogen and oxygen plasma treated undoped

homoepitaxial diamond surfaces. Note reversible behavior with alternate plasma exposures [18].

2.7.2 Surface Conduction

The electrical conductivity of the diamond surface depends on its termination and
adsorbants. The presence of the adsorbates causes band bending near the surface. The
band bending direction, upward or downward, depends on the surface termination.

Surfaces terminated with hydrogen and oxygen have shown conductive and non-
conductive behavior, respectively. This shows that hydrogen and oxygen on the diamond
surface introduces surface states. A band bending model for the diamond surface shows
that the hydrogen termination has low resistivity due to upward band bending caused by
hole accumulation (Figure 22) [18]. According to this model, a high density of acceptor

type surface states below the bulk Fermi level produces the hole accumulation on the

34

diamond surface with the Fermi level at Ev+0.9 eV. This model relates the high
resistivity of oxygen terminated surfaces to downward bending produced by hole

depletion. The depletion layer is produced by donor type surface states around E.+1.7 eV.

 

 

 

 

 

 

E
acceptor- - »- ------------ F donor. . a, ............. .F
type < \ 1.0 9 9V type 0.9 eV
< Ev I .7 8V , EV
FULLY PARTIALLY OXYGENATED
HYDROGENATED HYDROGENATED

Figure 22 Energy diagram of the hydrogenated/oxygenated diamond surface [18].

Ristein et al. [16] have shown how the diamond surface conductance varies with
surface treatment. It can be seen from Figure 23 that the as-grown surfaces and surfaces
exposed to hydrogen plasma have a surface conductance greater than 1x10‘6 S. But
annealed surfaces in vacuum, acid treated surfaces, and air heated surfaces at 500 K have
surface conductance of less than 1x10'll S. It was also shown that hydrogen surfaces are

less stable in air than in a vacuum.

35

(100), Ila ,

(111), llb
(100)116

(100). llb ..
Homoepitaxial .
Homoepitaxial 7

CVD on Si
CVD on Si

Homoepitaxial :T
Homoepitaxial .,
(100), Ila _

(111),llb

(100), llb :
Homoepitaxial ‘

Homoepitaxial
CVD on Si

CVD on Si :
CVD on Si .
CVD on Si _.

 

1E-9

 

Conductance (S)

Figure 23 Surface conductance of different diamond samples [16].

HNOJ+HZSO,
1000 K (vac.)
CnstO‘
1000 K (UHV)
1000 K (UHV)
500 K (air)

~ 500 K (air)

500 K (air)

H-tenn, UHV. no ads.
H-term. reeexp. to air
H-Piasma

H-Plasma

H-Plasma

as-grown

asgrown

as-grown

H-Plasma

as-grown

H-Plasma

The hydrogen terminated diamond surface shows p-type surface conductivity. A

proposed model [16], suggests that an aqueous phase on the top of the diamond extracts

an electron from the valence band of the diamond, and forms 1/2 H2 by reacting with H30+

and leaving HC03' on the surface. This would leave holes accumulating in the diamond

near the surface--and negative charges of HCO3' on the diamond surface--resulting in

band bending near the surface and thus a finite surface conductivity (Figure 24).

Hydrogen-terminated diamond is surface conductive in air because it is invariably

exposed to water vapor, but is not conductive after the surface water layer is removed by

vacuum evaporation.

36

Diamond Molecuar Air
Water-Layer

 

 

 

 

 

accumulation layer
in
semiconductor

 

 

 

 

Figure 24 Band bending model of the hydrogenated surface (below); hydrogen extracted from the

diamond by catalytic effect of water on the surface (above) [16].

The origin of the surface states may also be related to surface structural defects,
which are not necessarily due to the type of surface termination. The surface of diamond
may go through more surface constructions than silicon because diamond can change to
spl, sp2, and sp3 while silicon generally forms only sp3 bonds.

The surface conductivity can be removed or changed by various surface

treatments; chemical cleaning of the surface with acids such as HF, HNO3, HCI, H2804,
37

CrO3, HCIO4 [14, 21-41], electrochemical cleaning [42], oxygen annealing [20], heating
in ultra-high vacuum at 950 °C [43], heating in air 700 °C [44], oxygen plasma cleaning

[14, 24, 36], Nz-Ar plasma [37], and He-Oz plasma [34].

2.7.3 Metallization

The metal-semiconductor contact may be rectifying or Ohmic. To find the bulk
electronic properties of a material, Ohmic contacts are advantageous. A good Ohmic
contact should have good adhesion, low contact resistance, and high thermal stability.
Poor Ohmic contacts can be a substantial source of noise, with errors introduced if a
significant voltage drop occurs across the contact. Fabrication of Ohmic contacts to
diamond can be problematic, since a potential barrier usually forms at the metal-diamond
interface. This is presumed to be due to the differing work function of the two materials
or the high density of states at the interface caused by diamond covalent bonds.

A high density of surface states can produce a surface barrier on the surface even
before metallization. The surface states are affected by the surface termination, either
hydrogen or oxygen. These surface states may trap charge carriers. For example, in an n-
type semiconductor, the surface states can extract some electrons from the donors in the
bulk of the semiconductor, and become negatively charged resulting in ionization of
donor atoms. The region near this negatively charged area will be positive to maintain the
charge neutrality. Therefore, the ionized donor atoms produce a charge density and
potential barrier. This potential barrier makes the contact rectifying [45].

If there are a lot of surface states, ~10'2 cm'z, the Fermi level cannot change
substantially and is said to be pinned. As the density of dangling bonds may be two

orders of magnitude larger than this value [18], dangling bonds can also pin the Fermi

38

level. When the Fermi level is pinned, the barrier height does not depend on the metal
and its work function [46, 47].

Much research has been performed on metal-diamond interfaces. Different kinds
of metals have been deposited on diamond to investigate the effect of surface treatments
and the role of the metal work function on the type of contact and I-V behavior. Mori has
studied characteristics for eleven kinds of metals (Table 4). It was found that if the
surface is oxygen-free, the I—V behavior depends on the metal work function and its
electronegativity. If oxygen is on the surface, this dependence vanishes [14].

Table 4 Dependence of the type of the contact metal on the work function and electro-negativity

and surface treatment. Treatment A is GO; in H2804, and treatment C is 0; plasma. (0).). and XM are metal

work function and electro-negativity [l4].

 

 

 

(0” XM After After
Metal (eV) (cV) As-grown treatment A treatment C
Pt 5.65 2.2 Ohmic Schottky Schortky
Ni 5.15 1.8 Schottky Schottky Schottky
Au 5.10 2.4 Ohmic Schottky Schottky
Cu 4.65 1.9 Ohmic Schottky Schottky
Sn 4.42 1.8 Schottky Schottky Schottky
Zn 4.33 l.6 Schottky Schottky Schottky
Ti 4.33 l.5 Schottky Schottky Schottky
Al 4.28 1.5 Schottky Schottky Schottky
Ag 4.26 1.9 Ohmic Schottky Schottky
Ta 4.25 I.S Schottky Schottky Schottky
In 4.12 1.7 Schottky Schottky Schottky

 

 

This is in agreement with Baumann, who found that the metal-diamond interfaces,
where diamond is hydrogen-terminated with negative electron affinity, lower the

Schottky barrier heights (SBH) [42]. The SBH is highest for positive electron affinity,

39

oxygen terminated, and is the lowest for a clean surface [42, 48]. This is shown for

various metals in Figure 25.

 

2 I i I II I ii
Zr Al Ti WCu Co NiAu

 

Mead and Spitzer rule

  
 

Oxygen terminated I:

I.

 

 

 

 

 

 

 

clean
+ UPS
+ UPS
1‘ Electrical meas.
0
f I . I .
4.0 4.5 5.0 5.5
MetalworkfimctionieV)

Figure 25 Schottky barrier height for various metals on clean and oxygen-terminated surfaces;

UPS: UV photoemission spectroscopy. [48]

A variety of methods have been used to fabricate Ohmic contacts on diamond,
including damaging the diamond surface by mechanical roughening, sputtering, and
exposure to uv laser radiation. A contact made by these methods is Ohmic for metals

40

such as W probes, Ag paint, and evaporated Al [49, 50] but is mechanically fragile and
electrically noisy. Also, laser damage may produce graphite on the surface, leading to
poor metal adhesion.

Doping during growth or doping the region under the contact to make a p-type
layer is another technique used to make Ohmic contacts to diamond. Boron is commonly
used to dope the region under the contact to reduce the width of Schottky barrier. The
advantage of this method is that it is easy to control the concentration and depth of the
dopant

Using the chemical reaction between diamond and carbide-forming metals by
annealing also produces Ohmic contacts. This method gives a contact with good adhesion
with small contact resistivity. A low specific contact resistivity of 10'5 Ohm-cm2 for

single crystal diamond with a carrier concentration of 1016 cm'3

was achieved [49]. A plot
of the reduction of specific contact resistance versus annealing temperature for Mo and Ti
is shown in Figure 26 [26]. The samples were polycrystalline diamond, boron-doped at
1018-1020 cm’3. The specific contact resistance of the Ti contact decreases near 300 C, and
remains close to the same value at higher temperatures. The specific contact resistance of

the sample with larger dopant levels changes less with temperature compared to samples

with lower dopant levels.

41

 

  

seecrnc comer RESISTANCE (Dana)

 

10" W
335 o 0

ANNEALING TEMPERAWREI‘C) FOR 5 mln

Figure 26 Dependence of specific contact resistivity of Ti and Mo versus annealing temperature

[26].

Different kinds of metals have been used for making Ohmic contacts using
chemical reactions. Titanium has been used on polycrystalline, doped polycrystalline, and
boron-doped homoepitaxial diamond [14, 21, 24-26, 30-33, 35-37, 43, 51-54]. Ta was
used on B-doped polycrystalline diamond to obtain an Ohmic contact [27]. Nb was used
to make an Ohmic contact on natural diamond [55].

Titanium is most often used as a carbide-forming metal. TiC forms at

temperatures above 430 °C, and changes the contact from Schottky to Ohmic [21, 30-33,

42

35-39, 51, 52, 54, 56]. Figure 27 shows the effect of annealing on the I-V behavior of

boron doped polycrystalline diamond, becoming nearly Ohmic after a 430 °C anneal.

 

‘__A AA“

--- as do osited
------ . 140° .30 min ‘
280°C, 30 min

480°C, 30 rnin -

2 4
Voltage (V)

 

  
 

 

Current (ILA)

 

 

 

 

Figure 27 I-V behavior with temperature for titanium on boron doped polycrystalline diamond

[56].

The chemical reaction between the metal and diamond can be explained using the
Gibbs free energy (AG) of carbide formation. AG is negative at 430 0C, which forces the
reaction to form titanium carbide. The carbide can form in solid reactions by annealing
because the free energy of the carbonizing reaction is minimized for Na metals (Ti, Zr,
Hf) and Va metals (V, Nb, Ta) [21].

It appears that carbide acts as a defect layer which lowers the barrier height or
enhances tunneling, or both. It is possible that annealing may increase the local disorder

by introducing point defects. The model to explain the Ohmic contact resulting from

43

carbide formation is shown in Figure 28. There is a barrier at the metal and diamond
interface before annealing (a).The carbide formation produces point defects at the surface
of the diamond. These defects can either decrease the width of the depletion layer, and
therefore enhance the probability of tunneling for the carriers (b), or reduce the effective

barrier height (c).

44

metal diamond

 

 

 

 

 

 

 

(a)
c .
f as deposited metal
. on diamond
EF - — — — EF erectiiylng
1:1 r—Ev
l
I l
(b) , 5.0
I l high cone. of defects
. . at diamond surface
EF , 1 - - - - EF ->narrower depletion region
Ev -> more tunneling current
| ' “Inn."ng _’ "ORMIC"
carbide < I) detect layer
I I £0
((3) I U -C
r 1 high cone. of defects
' j , , at diamond surface
EF ' I - _ .. ._ 5,: ->lower effective barrier
W" ,_ Ev height I rib-ell)
i ' -.-) ”ohmic”
l 1 l '

 

Figure 28 Band diagram of Ti contact on diamond; (a) as deposited , (b) narrowed depletion layer

by defects, (c) decreased barrier height by defects [49].

The role of the annealing temperature to make Ti contacts Ohmic has been
investigated: 400 °C by Shiomi and Nakanishi and Chen and Craciun [21, 26, 32, 33, 43],

430 °C by Tachibana [38, 39, 56], 450 °C by Conte [35, 52], 500 °C by Nebel and

45

Alexander [36, 51], 700 °C by Chen [32, 33], 800 °C Waytena and Hoff and Landstrass
[30, 53, 57]. However, Tareji did not find the Ti-diamond contact Ohmic for P-doped n-
type diamond annealed at 600 °C, and TiC formation did not make the contact Ohmic
[29]. Yokoba obtained non-Ohmic behavior for Ti on p-type polycrystalline diamond
annealed at 600 °C [25]. Gonon found identical I-V behavior for both Au and Ti on
polycrystalline diamond, with some of the contact area doped with boron, but did not
relate the Ohmic behavior to carbide formation under the metal [37]. He suggested a
conductive layer between diamond and the metal makes the contact Ohmic.

These results are in contradiction to another group that found Ohmic contacts for
Ti. An interesting finding for the annealed contact is that when carbide-forming metals
are removed from the surface, small carbide islands are identified at the surface. These
islands may cause an inhomogeneous current density [48, 58].

Most of the research on Ohmic contacting has been performed on doped diamond
or polycrystalline materials. Vandersande and Zoltan have used sputtered Nb [55], Pt,
and Ir foil (pressure contact) [59] to make Ohmic contacts to natural diamond at high

temperatures.

46

None of the research cited has fully explained different contact behaviors. If there
is a high density of states at the surface, then the contact may not be Ohmic, and other
forms of voltage-dependent conduction may be observed. Therefore, it is reasonable to
think that annealing changes the interface density of states by forming TiC. Since no
study to date has been conducted on Ohmic contacts to heteroepitaxial diamond, one of
the intermediate goals of this research is the fabrication of Ohmic contacts to this

material.

2.7.4 Bulk Conduction of Diamond

Research has been carried out previously on the electrical properties and
conduction mechanisms of doped and undoped CVD diamond and Type Ib natural
diamond (with nitrogen concentrations of 50-150 ppm) [60] and Type Hb (with boron
concentration of 5x1016 cm'3) [31]. Only a little research has been performed on the
electrical conductivity of Type IIa natural diamond and CVD-grown homoepitaxial
diamond. This may be due to difficulties in performing DC electrical measurements on
material with very small conductivity.

Type IIa natural diamond has a very low conductivity, believed to be lower than
10'16 (Q-cm)’l at room temperature. Two common dopants found in natural diamond are
boron and nitrogen. Boron acts as an acceptor, with a level 0.37 eV above the valence
band. Nitrogen is a donor, with a level 1.7 eV below the conduction band. As 1.7 eV is
fairly deep, even a high concentration of nitrogen does not cause significant conductivity
at room temperature [61]. A conductivity of 10'6 to 10‘12 (Q-cm)’l has been found at

room temperature for polycrystalline CVD diamond, 4 to 8 orders of magnitudes larger

47

than the conductivity of the best natural diamond. The larger conductivity of
polycrystalline diamond is related to the dangling bonds at grain boundaries.

Variation of the conductivity of Type IIa natural diamond and two other CVD
polycrystalline diamond films grown by Applied Sciences and by Crystallume was
reported by Vandersande (Figure 29) [55]. It can be seen from Figure 29 that the
conductivity of the polycrystalline diamond films is larger than that of natural diamond
by a few orders of magnitudes below 500 0C, and less than natural diamond at
temperatures >800 °C. An activation energy of 1.4 eV was found for Type Ila natural
diamond between 300 and 1200 °C, and activation energies of 0.9 eV and 1.8 eV were
found for CVD diamond films between 200 and 800 °C and between 600 and 1200 °C ,

respectively.

48

 

10'2 l'Il‘l'I‘l'l‘Il'Tl T'l I

A NATURAL TYPE IIA DIAMOND
A CRYSTALLUME 611m FILM __4
O APPLIED SCIENCE 50 um FILM

 

ELECTRICAL CONDUCTIVITY. 0(1/S2. cm)

 
   

IOOO‘C

 

1200°C

  :.

l

10'15_L 11 1 l I 1 I'IL L
.4 .5 .a 1.0 12 1.4 1.6 1.8 2.0 2.2 2.4 as 16 3.03.2

lo‘Ir (K)

l——

)-

 

r-SOO‘C
~200°C

Moore

Figure 29 Electrical conductivity of natural diamond Ila and two CVD diamond vs. UT [55].

An activation energy of 0.9, 1.8, or 1.4 eV cannot be due to intrinsic conduction.
Vandersande and Zoltan suggested that the lower activation energies could be due to

donor levels from interstitial carbon or acceptor levels caused by isolated vacancies.

49

Activation energies in Type Ila natural diamond and polycrystalline diamond
were also found to be between 1.5-1.6 eV in another report by Vandersande and Zoltan
[59]. The conductivity of five diamond samples vs. HT is shown in Figure 30, with four
polycrystalline CVD and one Ha sample [59]. Two samples are from Crystallume (one 6
pm thick on silicon and one free standing 300 pm thick), one sample from Norton (free

standing 1.1 mm thick), one sample from Raytheon (free standing 660 um), and one Type

IIa natural diamond (1mm).

10'2
10’3
10"4
m*
10"6
10‘7 .
10"8
10'9
10-10’
10.11
1o..12
'0.13
10'14

10'15
'0-16
10'17

If“ w , — - —
64in LZI£ UJZAIM $235

TEMPERATURE lo’/r(l<)

 

“v V

O

I

I

: «0 o. 0.... 0

Natural Diamond 1

   
   
  
     

Crystallume-1

Crystallume-2
Norton

Rayteon

 

 

oboe.

 

 

. . poo-1b’o—PO

 

who.” -

 

 

 

 

ELECTRICAL cououcrlvmr a (onm"cm")

 

 

 

 

 

 

Figure 30 Electrical conductivity versus l/T for two Crystallume, Norton diamond, Raytheon, and

Type Ila natural diamond [59].

50

As it can be seen from Figure 30, the conductivities of the Raytheon and one of
the Crystallume samples are smaller than that of natural diamond, in the range of 300 °C
to 1000 °C. Vandersande and Zoltan suggested that CVD samples are less defective and
more pure than Type Ila natural diamond, and the conductivity in all of those samples
was governed by the same type of conduction mechanism with the activation energies in
the range of 1.5-1.6 eV. This activation energy was related to the isolated substitutional
nitrogen with the activation energy of 1.7 eV [59, 62].

The activation energies of 1.4 eV and 1.5-1.6 eV can indicate that point defects
are the source of the thermally activated conductivity in those diamonds. But, the
discrepancy between the measured activation energy of 1.5-1.6 eV and the expected
value of 1.7 eV for nitrogen impurity is not explained.

The activation energy of 1.5-1.6 eV might be a result of a combination of
different conduction mechanisms. One could be due to vacancies with activation energy
~l.3 eV and one due to nitrogen centers with activation energy 1.7 eV. Measurements at
higher temperature should result in an activation energy of 1.7 eV and possibly dominate
the 1.3 eV energy if the conductivity is caused only by the nitrogen.

Activation energies of 1.3 and 1.0 eV were observed for homoepitaxial diamond
grown on B-doped homoepitaxial and HPHT Type Ilb substrates, respectively (Figure
31) [36, 60]. The origin of those activation energies was not certain. The activation
energies of 1 and 1.1 eV are related to the polycrystalline diamond [31, 36] as grain
boundaries are believed to give activation energies in this range. It should be pointed out
that the activation energy for both natural diamonds, Types 11a and lb (with nitrogen

~5x1018 cm'3) are found to be 1.7 eV. This indicates that although the substitutional

51

nitrogen impurity density is small in diamond Ha, it may influence the conductivity, and
look similar to Ib.

It is reasonable to believe that the smaller conductivities of the Raytheon and the
Crystallume samples may be due to lower nitrogen levels. But, as those samples are
polycrystalline, it is unlikely that they are less defective than single crystalline diamond.
Grain boundaries scatter carriers and lower the mobility, another possible reason for the
lower conductivities of the polycrystalline diamond samples.

TEMPERATURE (’C)

.016 360 300— 250 200 150
on HPHT - type Ilb Substrate
.0 ~exp(1 .OeWkT)

5 cvo - LAYERS

 

    
  
 

V‘ 'V

101 5

14
10
00

VI.“

 

 

5 .013! on B-doped layer on °
4 i ’ D~exp(1.YeVikT) . ‘
t 1012I' ’ x A
.. i , SUBSTRATES
'- : Ila
g), min
in I
In : o ~exp(1.3eVikT)
0‘ “’gi lb HPHT
3'
w I . . . . . - . E . 1
0.0015 0.0020 0.0025

RECIPROCAL TEMPERATURE (K")

Figure 31 Electrical resisitivity of diamond type Ila, lb HPHT, and two undoped homoepitaxial

diamond grown on type Ilb and boron doped substrates [60].

Another source of carriers in CVD diamond could be hydrogen. Hydrogen is
incorporated during growth at structural defects such as dislocations at high

concentrations, and is distributed homogenously in CVD diamond. Hydrogen-related

52

defects in the bulk are more stable against thermal treatments compared with surface
hydrogen, which desorbs at 900-1000 °C [63]. The activation energy for CVD diamond
with hydrogen incorporation is stated to be 1.8 eV below the conduction band [64, 65].
Diamond surface properties change with heat treatment leading to experimental
difficulties. As an example, heating and cooling curves are shown for Norton diamond
sample in Figure 32 [59]. This plot shows the effect of cleaning on conductivity and the
change in conductivity for heating and for cooling, which do not overlap. This is related
to the leakage through the surface of the sample according to Vandersande and Zoltan. It
is thought that the surface of the sample is reconstructed- to either non-diamond or
graphitic carbon when heating above 900 °C. However, after cleaning the sample, the
same heating conductivity curve was obtained again. This could also be due to changes in

the metallic contacts.

53

10‘2
10‘3

10—4
-5

-1)

Natural Diamond

I
cm

i 0

to“6

10‘7

10'8

10‘9

1 0‘10 -..

_11 Pre-Clean
A Heating

-12 ,

10 V Cooling

10—13

10
1o-‘IS
10
10'17
—18

10 '-
0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6

TEMPERATURE 103/T(K)

10

~14

1:] Heating
I Cooling

~16

ELECTRICAL CONDUCTIVITY 0 (ohm

 

Figure 32 Log conductivity vs. 1/T for Type Ila natural diamond and Norton diamond (before and

after cleaning for both heating and cooling) [59].

54

Chapter 3 Heteroepitaxial Diamond Growth

3. 1 The Epitaxial Process

Heteroepitaxial diamond is presently grown on Ir/ Sr’I‘iO3 or (Ir/sapphire) in the
laboratories of the Golding group. This requires a series of steps from substrate
preparation to CVD diamond growth. The lattice parameter for iridium is only 7.5%
greater than that of diamond, making the iridium (001) surface suitable for epitaxial
growth of diamond. The process steps are shown schematically in Figure 33 [66]. First,
(001) Ir is grown on (001) SrTi03. Then, diamond is grown on Ir. Finally, the substrate

can be removed to make a free standing diamond wafer.

    
 

Srrtoa

7 Diamond Wafer ;

Figure 33 Growth of heteroepitaxial diamond [66].

The Ir substrate is grown epitaxially as a thin film on (5x5x0.5 mm3) SrTiO; with
orientation (001)1,||(001)s,1~io3 and [1101],” [110]s,1~io3 prior to diamond deposition. This
means that the interface of iridium and SrTi03 is in the (001) plane and that all cubic axes

are aligned in that plane. The SrTiO3 structure is shown in Figure 34. The lattice

mismatch between this surface and iridium is small (1.7%).

 

Figure 34 Surface and structure of SrTiO; [67].

The iridium deposition process begins with etching of the SrTi03 in buffered HF.
Iridium is grown by electron beam evaporation at a substrate temperature of 900-950 °C
in an initial vacuum <10'9 Torr. The SrTi03 is heated for 20-120 minutes at 900 °C before
iridium is deposited at a rate of 2.4 nm/min. The thickness of the iridium film is typically
150 nm.

Diamond is grown by chemical vapor deposition (CVD). Prior to the CVD

growth, a biasing process induces nucleation of diamond on the Ir surface. Biasing leads

56

to an enhanced nucleation density of diamond near 1012 cm'2 [67]. This high nucleation

density provides the sites for deposition of carbon radicals during the growth step.

3. 2 CVD Diamond Growth

To initiate the process, CH4 (99.999%) and H2 (99.9995%) gases are introduced
into the reaction chamber following a vacuum state <10‘7 Torr. When the gas pressure
reaches the desired level, microwave power at 2.45 GHz is applied to the chamber to
create a plasma that forms just above the Ir/SrTiO3 substrate. The microwave power
dissociates and ionizes the gas into positive ions and electrons. For the biasing process, a
voltage between -150 and -200 V is applied to the stage containing the substrate. Positive
ions in the plasma are accelerated toward the substrate surface. After approximately 60
minutes, the bias is turned off, nucleation occurs, and diamond growth proceeds by
deposition of the plasma species. The substrate temperature is between 600-700 °C during
biasing and growth.

During biasing, a high-density carbon layer forms on the iridium, which provides
the precursor for diamond nuclei. The layer is believed to be an amorphous or
nanocrystalline sp3 carbon. Nuclei appear on the surface as small carbon clusters, and
lead to arrays of diamond nanocrystallites that cover the iridium surface. Scanning
electron microscope (SEM) images show sp3 carbon with high contrast at 20 minutes and
at 60-80 minutes biasing (Figure 35 and Figure 36). The dark areas are Ir. When biasing
is interrupted before complete surface coverage, the crystallites form a pattern that is
oriented predominantly along Ir [110] directions. The lengths of the blocks are 100-200
nm. As can be seen in Figure 36, the dark area is significantly covered after 60 minutes

biasing; from 75% coverage after 20 minutes to 89 % coverage after 60 minutes.

57

 

-02) [68].

Figure 35 SEM image after 20 minutes biasing (20-Jul

 

 

Jul-02) [68].

Figure 36 SEM image after 60 minutes biasing (18

After biasing the parameters are set for the Growth I step as shown in Table 5.

Parameters given in Table 5 for the Growth 11 stage are applied when thicker films are

58

desired. The parameters given in Table 5 were applied to grow the sample (04-May-04)

used for the electrical measurements in this research.

Table 5 Parameters for biasing and growth of thick diamond used for electrical measurement.

current

Temperature

 

Figure 37 is an SEM image of the diamond grth after (a) 20 and (b) 180
minutes. The dark area is reduced for longer periods of the growth, as the film becomes
thicker when coalescence is complete. A thickness of 0.54 t 0.02 pm was found for 180

minutes of growth (23-Jun-01) [67].

    

__ (a)

Figure 37 SEM image after (a) 20 and (b) 180 minutes growth on (17-Jul-00) and (23-Jun-01)

[67].

59

3. 3 Characterization

The diamond sample and the substrate are characterized by different techniques
such as optical microscopy, SEM, atomic force microscopy (AFM), Raman, and X-ray
diffraction (XRD).

AFM of the epitaxially grown iridium (thickness ~300 nm) is used to study the
morphology of the iridium (Figure 38). The dark circular areas represent voids in the
iridium film. The AFM measurement confirms a mean iridium surface roughness of only

a few nanometers.

9nm

   

Figure 38 AFM of epitaxially grown iridium [67].

XRD is used to identify crystallographic phases in the sample and the substrate,
and to obtain information on the atomic arrangements at the interface. A {111}-¢ scan of
a diamond sample grown for three hours confirms the epitaxial growth of iridium on

SrTiO; and diamond on iridium (Figure 39); that is, (100)dia<110>di,,l||(100)1,<110>[r

60

II(100)SrTiO3<llo>SrTi03. The rotation angle of the sample ((1)) is with respect to <001>
direction.

It can be seen that the four peaks of diamond, iridium, and SrTi03 appear at the

same angles, which shows epitaxial alignment.

 

 

 

 

 

 

 

 
 

 

 

 

107 . . . . . .
1o“ - (111) (ill) (1_11) (iii) .
‘05 ’ :i ‘
10‘ +01) L? 7i 7i S'T'O3 7: -
10a ' v '
10?
10'
E 106 h " I : I
E ." "
=_ 105 -(b) ,; , ." 1
co 3 :. y ,,
I—l 1 cl
a 0,
g 10 i
2 1
E 10 g -_I .1. ..
1o5 - p -
4 (C) i g g
10 ' Diamond
103 ' iii: '
102 In} L
1 l J 1 A l A
10 ‘ *
0 90 180 270 360
Phi [degrees]

Figure 39 XRD of diamond grown on Ir/SrTiO; after 180 minutes [67].

61

Raman spectroscopy was also used on free standing (001) crystal 25 pm thick to
characterize the diamond (Figure 40). The expected peak for diamond is at 1332 cm"; a
peak at 1331 cm'1 with a linewidth of 8 cm'1 is found. The shift of the diamond peak is
due to the stress in the diamond, caused by the lattice mismatch between the iridium and
diamond. The small set of peaks at about 1500 cm'1 may be due to the presence of a small

amount of graphite.

 

iasicm"

Intensity (arbitrary units)

 

 

 

500 I 1000 v 1500 v 2000
Wavenumber shift (cm'1)

Figure 40 Raman spectrum of a free standing 25 pm (001) diamond [67].

AFM was used to reveal the surface topography of a diamond sample grown for
12 hours on Ir/SrTi03 (Figure 41). Some steps, with the average height of 20 nm, can be

seen on the surface.

62

113nm

   

Figure 41 AFM of a 12 hour diamond growth [67].

Figure 42 shows optical microscope images of the 20 pm thick sample used in our
experiments. The sample area is 3x22 mmz. The dark spots are areas with macroscopic
defects. A piece of this sample was used for the present electrical measurements.

SEM images of this sample are shown in Figure 43 and 44. Figure 43 (a) and (b)
are taken from the central region. The size of the inclusions ranges from 1 pm to 10 pm.
One of the inclusions with a size of 2-10 pm with different facets can be seen in (b).
Figure 44 (a) and (b) are taken from the areas near the edge of the diamond film. These
images show a different texture —macrosteps— with fewer defects.

Figure 45 shows SEM images of the cross section of the diamond sample. Figure
45 (a) is with a sample tilt of 5 deg around the y axis (taking 2 as the normal to the
surface and x pointing down in the image plane). This allowed imaging of the surface and
cross section simultaneously. The lower portion of (a) is the surface with macrosteps, and

the upper portion is the cross section with the growth side on the top of the image.

63

The thickness of the diamond sample was found by SEM in Figure 45 (b) and (c)
and optical microscopy in Figure 46 (a) and (b). The thickness varies from 18 um near
the edge to 24 um at center. An average thickness of 20:1 um was found for the diamond
piece used for the electrical measurement. Smaller thickness of the edge can be seen in

(b) and larger thickness can be seen in (a), which is about 0.5 mm far from the edge.

 

   

(b) C)
Figure 42 (a) diamond sample at 5X, (b) dark spots at 20X, and (c) spiral type defect detected by

optical microscope at 20X (diamond grown by Z. Dai on 04-May-04).

 

and (b) a magnified inclusion.

Figure 43 SEM images of (a) the center of the diamond surface,

(04-May-04)

65

 

 
   
  
 

 

ll
ii
Ill.

'11.
ll

ll

illl ll

    

Figure 44 (a) and (b) SEM images of the area near the edge of the sample at two magnifications

(04-May-04).

66

 

Figure 45 SEM image of (a) the tilted sample showing the surface and cross section
simultaneously. (b) and ( c) cross section. The iridium side in (a) and (b) is on the top side of the images.

67

   

(a)

Figure 46 Optical microscope images of the cross section of the diamond with the iridium side up

at 20X (a) 0.5 mm far from the edge. and (b) near the edge.

The optical microscope image of the free standing heteroepitaxial diamond grown
with a 35 um thickness 3.5 mm diameter is shown in Figure 47 [68]. The image shows

that the diamond film is transparent.

i

 

 

Figure 47 Free standing transparent heteroepitaxial diamond, Diameter: 3.5 mm, Thickness: 35

pm [68].

68

Chapter 4 Experimental Methods

The goal of the electrical measurements is the determination of the bulk DC
electrical conductivity of CVD heteroepitaxial diamond. The sample is highly resistive,
p>10 ‘4 Q-cm at room temperature, with lateral dimensions of a few mm. To facilitate
measurements, a geometry was chosen that takes advantage of the much smaller diamond
thickness, approximately 20 um. With metal contacts on the lateral faces, the current
flow is perpendicular to the faces, provided surface currents can be made negligible. The
contact to diamond from the metallic electrodes should be highly Ohmic.

At room temperature, the conductance of the sample is too low for accurate
measurement. Therefore, it was necessary to heat the sample well above room
temperature where the conductance is sufficiently high. This requirement led to the
design of a novel sample holder and sample mounts that enabled thermal control with
sufficient stability for accurate electrical measurements. These points are discussed in the

following sections.

4. 1 Contact Geometry

A “sandwich” geometry was developed for the electrical contacts, Figure 48.
Since the sample was grown on a 250 nm 1r substrate, it seemed useful to leave lr in
place, serving as a lower electrode, provided the Ir-diamond contact proved Ohmic. For
the top electrode, Au was deposited on top of a thin Ti adhesive layer. A similar
deposition was carried out on the Ir layer, initially to facilitate wire-bonding. The top

electrode was as large as possible to increase the contact area.

69

Ti/Au top electrode

Diamond

\

Iridium

\

TilAubottom electrodeV/>

Figure 48 Schematic of the sample electrode geometry.

 

 

 

 

 

 

 

An estimate of the minimum measurable conductivity is readily made for this
geometry. The conductivity of the diamond is given by 0' = (GXr/ A), where G is the
transverse conductance, t is the sample thickness, and A is the area of the top electrode.
With an electrode diameter of 0.5 mm and t = 0.02 mm, the geometrical factor is
approximately 1 cm". By Ohm’s Law, G = I / V , at a bias voltage V =1 volt, and with

an accuracy of 10 fA for pA range, we require 0 > 10'14 (Q-cm)‘l for a measurement to be

meaningful.

4. 2 Electrode Fabrication

It is necessary to prepare metallic contacts to diamond that are Ohmic, with low
specific contact resistance, and that exhibit strong adhesion, even at elevated
temperatures. This requires that a number of processing steps be taken that involve
sample cleaning, multi-step thermal evaporation of metals, thermal annealing, and a final

oxygen plasma treatment, as described below.

4.2.1 Chemical Cleaning

CVD diamond growth leaves the surface of the crystal covered with graphitic

surface residues and carbon particulates. The residues prevent good adhesion between the

70

diamond surface and evaporated metal films and may contribute to electrical surface

leakage. Chemical cleaning removes graphite, loose particles, and oxidizes the surface of

the diamond. The procedure is:

1.

2.

Rinse diamond sample with acetone and methanol.

Clean and rinse with Alconox and DI water.

Let stand in 1H20221H2SO4 solution for 30 minutes (30% H202 with 95%-
98% H2804) to remove non-diamond phases and organics.

Let stand in 3HCI: II‘INO3 solution for 10 minutes (CMOS grade HCl with
68%-70% I'INO3) to remove specific ionic and some metal surface
contaminants.

Let stand in 24.5%HF:75.5%H20 solution for 10 minutes (48% HF) to
remove some metallic particles which cannot be removed with other acids.
1NH40Hz5H202 for 1h at 65 °C with NI-I40H 28%-30%, H202 30% to remove

organic material causing surface contamination.

The sample is rinsed with deionized water (DI) water thoroughly after each

chemical treatment.

4.2.2 Electrode Deposition

To define the deposition area, a mask and sample holder were designed for

loading the sample and depositing the electrodes. A shop drawing is shown in Figure 49,

a photograph in Figure 50. A stainless steel mask, 0.25 in square and 0.005 in thick, with

a 0.02 in diameter aperture, fit into a recess in the center of the mask holder. A phosphor

bronze clip secured the sample against the mask from its back surface, Figure 51.

71

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

<——’
‘————>
0.25"
4 1.24" _
- - For 2-56
/
0090.. l”) 0.08" . ’
0.35" -: i '0 .1415 ’
l: i i/
we? 17 renew-8°
: ,-/"”/
l I
10.62" I
I 1'" |

Figure 49 Drawing of the stainless steel holder, side view and top view.

 

Figure 50 Stainless steel holder with the mask on the right.

72

 

Figure 51 Optical microscope image of a loaded sample, with iridium side up, in the holder

pocket held with the clip.

The mask was first placed in the recess of the holder, the sample positioned over
the mask aperture, and the clip placed against the sample. The openings for 2-56 screws
on the holder allow it to be mounted on the Edwards evaporator in the KMF cleanroom.
This holder design allows for electrode deposition on irregular sample shapes and various
sample sizes.

The Edwards Auto 306 thermal evaporator, a turbo pumped system with base
pressure 10’7 Torr, was used for Ti and Au deposition. The Au was deposited
immediately after the Ti deposition with care taken to maintain a good vacuum in the
system. The top electrode on the diamond growth surface consisted of Ti (13 nm) and
Au (250 nm). The Ir electrode was Ti (10 nm) and Au (300 nm). The diameter of the
evaporated electrodes was measured by optical microscope to be 495:10 urn. Figure 52
shows an optical microscope image of diamond sample (04-May-04) and top electrode.
The dark horizontal line above the electrode is a partial cleavage fracture that occurred

when the sample was accidentally broken into a few pieces.

73

 

Figure 52 Optical microscope images of diamond sample (04-May-04) and top Ti/Au electrode.

Electrode diameter is approximately 0.5 mm.

4.2.3 Thermal Annealing

Following metal deposition, the sample was annealed at 650 °C for 20 minutes
with an initial pressure of 2x10‘8 Torr. The system (APX Multigun Sputtering Facility) is
turbopumped and features a programmable SiC heater. The sample was mounted in its
evaporation mask holder as the temperature was ramped up and down over a period of a

few hr. The sample was cooled to room temperature in vacuum before exposing it to air.

4.2.4 Oxygen Plasma Treatment

Although an acid treatment is generally effective in oxidizing the diamond surface
and destroying its surface conductivity, it is possible that the annealing procedure could
alter surface termination. Therefore, the sample was subsequently exposed to an oxygen
plasma. Exposure of the sample to an oxygen plasma for 30 seconds removes the surface
conduction. A 30 s oxygen rf plasma treatment in a March Instruments PX-250 reactive
ion etcher in the KMF was carried out. Conditions were: 02 gas flow at 40 sccm and at
135 W power.

74

4. 3 High Temperature Measurement and Thermal Isolation

A system was designed to allow heating of the diamond to at least 550 °C. Since
diamond reacts with air above 500 °C, measurements were performed in a vacuum
chamber. In a good vacuum, heat transfer by gaseous conduction and convection is
negligible. Thus, small resistive heaters attached to a small sample holder, allowed
heating to the desired temperatures with only modest power.

Other design considerations were: small sample holder size to minimize thermal
time constants and weak thermal coupling to the sample holder environment to minimize
heat leaks. The assembly was mounted in a small metal box with coaxial feedthroughs
for the conductance measurement that also provided isolation from external electrical

interference.

4.3.1 Vacuum System

An existing bell jar system was used to perform the experiments. It was equipped
with an liquid nitrogen trapped, oil-based diffusion pump capable of 2x107 Torr. Coaxial
cables were brought into the bell jar via a QF flange with 3 BNC coaxial feedthroughs.
The feedthroughs were supplied with hermetic seals between the center conductor and
insulator. Vacuum seals between the connectors and flange were made with Stycast-
1266 epoxy. A shop drawing of the modified QF flange and connectors is shown in
Figure 53.

Inside the bell jar, two standard RG-58 coaxial cables, with outer jacket removed,
ran between the flange and an aluminum minibox with dimensions 4.3 x 3.2 x 1.6 inches.
The bell jar, with box inside, is shown in Figure 54. To connect the thermocouple wires

and heaters another QF flange with pin connectors on the bell jar system was used.

75

Blank Qf50 flange + 3 holes for BNC connectors

(0.225 ‘. 0.39 ‘1

Hole Dia.=0.51 ‘
for BNC connector

Hex nut of the
bulkhead BNC Dlo.=l .77 “

 
   
 

Figure 53 QF flange design; for feed-through BNC connectors.

76

 

Figure 54 Bell jar showing QC flange, coaxial cables. and aluminum minibox inside.

4.3.2 Sample Holder

A schematic drawing of the sample holder is shown in Figure 55. The diamond
sample sits on a 10 mm x10 mm x0.5 mm single crystal sapphire substrate. The sapphire
not only provides a platform for the sample but also serves as a contacting surface for
electrical leads. The low electrical conductivity of sapphire below 600 C, <10'15 (SI-cm)"l
[69], allows electrical isolation between Au contact pads at several places on the

substrate. Its nominal resistivity at room temperature is quoted as >10]8 (SI-cm) [70]. Its

77

high thermal conductivity implies a homogeneous temperature distribution and short
thermal time constants. Heaters were attached to the sapphire from below. The
components were held together with stainless steel spring clips since it was found that
conductive adhesives, such as silver paint, were unsuitable owing to their high vapor

pressure at high temperatures (T>400 °C).
C

< K/
h \F

A: Diamond (thickness=20 micron)

 

 

 

B: Ti(10 nm)lAu(250 nm) Top Electrode

C: Au Wire (0.002 “)

D: Ti(100 nm)lAu(320 nm) pad on Sapphire
E: Sapphire (thickness=0.5 mm)

F: Heater (thickness=0.15 mm)

Figure 55 Side view of the sample holder assembly (not to scale).

Electrical connections to the diamond electrodes are shown in Figure 56. The
diamond was placed on a 3 mm diameter gold pad, deposited in the center of the
sapphire, which served as an electrical contact to the back electrode of the diamond. A

total of three Ti(10 nm)lAu(320 nm) pads were deposited. To contact the top electrode, a

78

50 um Au wire was held against the electrode with a small stainless steel spring clip. A
sapphire chip between the sample and the clip prevented damage to the Au electrode.
Owing to the small size of the diamond crystal, it was not possible to mount a
thermocouple directly on the sample. Instead, a spotwelded thermocouple junction of 5
mil (1 mil = 0.001 in = 25 um) Alumel and Chromel wires (thermocouple type-K) was

clipped to the sapphire substrate, see Figure 57.

SS CIIp3

  
 
 

 

 

 

 

 

 

 

 

Sapphire
Au-Wire__/
TilAu top
/Electnode
Diamond
Iridium Ear- .. , xxx-:3. .----3...- - ~-T-l:7-1:LI-'-?.-._.. .- .1...__,- —'--'! 1:2. -_;-.-.:.:x-..ti

Figure 56 Detail of the electrical connections to the diamond sample.

79

Thermocouple

\

 

li—

Sapphire
Diamond\
Ti/Au Top
Au-pad\ Electrode

/

Au-wire

  

 

.h‘

[1119111
{41111195,
i‘

ll"

 

- l'IIIII

ii“

1')

Hill

C
E...

l
l

 

 

llillllll
Illll

ll

Heater/

Spot Weld
Heaters' Lead

Figure 57 Top view of the sample on the sapphire substrate.

Figure 57 also shows the thermocouple position on the substrate, the two leads to
the diamond sample, and the three Pt miniheaters protruding from beneath the sapphire
substrate. A 50 um Au wire, clipped to the central Au pad in contact with the Ir side of

the diamond sample, ran directly to the center conductor of a BNC connector in the

minibox. The Au contact from the top diamond electrode was run directly to the center

conductor of the BNC connector on the opposite side of the minibox.

 

Figure 58 Photograph of assembled sample holder with all connections in place. The top

of the minibox has been removed for clarity. The sample holder is suspended by Chromel wires
that run from substrate clips to the minibox. Gold electrical leads run from the diamond to BNCs
(one is visible on the right). Thermocouple and heater leads pass through small holes in the

sidewalls of the box. A radiation shield is mounted above the floor of the box.

A stainless steel clip (Clip 1) was used to hold the heaters, stainless steel radiation
shield, Cu—sheet, the sapphire substrate, and the sample together. The assembly was
suspended with wires of Chromel, a low thermal conductivity metallic alloy, inside an

Al-shielded box (Figure 58).

81

4.3.3 Thermal Isolation

The two major contributors to heat transfer from the sample holder assembly to its
environment are by conduction through leads and by radiation. To minimize radiative
losses, the size of the sapphire substrate was made as small as practicable. An estimate of

heat transfer by radiation between the sample holder at 600 °C and the minibox at 25 °C

was made using Q = 08A(T4 -T61 ) [71], where o, s, A, T, and T0 are Stefan’s constant

(5.67x10'8 W/m2K4), emissivity, area, and system temperature and room temperature,
respectively. Surface areas of the high temperature components are: sapphire substrate
(10x10x0.5 mm3), stainless steel clip (Clip 1, 4 mmx24 mmx0.004 in), and a sapphire
disk (9mmx0.005 in) at the bottom of the assembly. Radiated powers of 1.8, 1.3, and
0.8 Watts at 600 °C, respectively, were calculated, totaling 3.9 W. Experimental data
showed that 4.3 W was needed to reach 600 0C, in remarkably good agreement with the
estimate considering that emissivities are probably known only to 20-30%. A plot of

heater power vs. temperature is shown in Figure 59.

82

 

 

 

 

T

I ' l ' l ' I ' r
350 400 450 500 550
T (C)

I ' I
250 300

Figure 59 Heater power versus temperature.

To minimize conductive losses, the sample assembly was suspended by wires
connected to the minibox. Conductive heat transfer resulted from: (1) two Chromel wires
(10 mil dia, 5 in long) holding the setup, (2) two Au wires (2 mil dia, 2 in long) used for
wiring the contacts, (3) two Cu wires (5 mil dia, 8 in long) spot welded to the heater

leads, and (4) two 5 mil, 7 in long thermocouple wires (Chromel-Alumel). Estimates of
heat transfer using Q = K (A/ L)AT [71] was made, where K, A, L, and AT are the thermal

conductivity, area, length, and temperature difference. Using KChmmeI=19 W/m-K,

KAu=320 W/m-K, Kcu=400 W/m-K, and KAlumd=32 W/m-K, the thermal losses through

Chromel, Au, Cu, and thermocouple wires were estimated at 0.01, 0.02, 0.04, and 0.003

W, respectively. Thus conductive losses through all wires were virtually negligible

83

relative to radiative losses throughout the temperature region explored. These losses

were less than <1% of the applied power, 4.3 W, required to heat the setup to 600 °C.

4.3.4 Temperature Measurement

Temperature of the sample was measured with a K—type (Chromel-Alumel,
diameter 5 mil) thermocouple in contact with the surface of the sapphire substrate. This
thermocouple was mounted at one of the comers of the sapphire with a stainless steel clip
(Clip-2). The temperature of the Al-box was measured with another K-type (Chromel-
Alumel, diameter of 10 mil) thermocouple. This thermocouple was held at one of the
comers on the top of the Al-box under a screw head. In one of the runs, the temperature

of the Al-box was measured as 40 °C when the temperature of the sapphire was at 400 °C.

4.3.5 Heaters

Platinum micro-heaters (Heraeus, Pt-100) were used to heat the sample. A
drawing of the heater is shown in Figure 60. These are thin-film Pt heating elements
encapsulated in a ceramic alumina casing. Three heaters, wired in series, were attached to
the underside of the sapphire substrate with clips. Here, it was possible to make
connections between heaters by spot-welding their leads. A Cu-sheet (10mmx8 mmx
0.125 mm) was sandwiched between the heaters and the sapphire substrate to improve
thermal contact. A stainless steel sheet (8mmx10 mm x0.2 mm) placed on the other side

of the heaters served as a radiation shield.

84

0.3

 

 

6'1

 

 

 

Figure 60 Platinum micro-heater (Heraeus, dimension in mm).

Heater resistance was nominally 7 Q at room temperature, increasing to 21 Q at
600 °C. The heaters are specified for use up to 500 °C and a maximum current of 2 A.
Nevertheless, it was found that three heaters, wired in series, can heat the sapphire
substrate to 600 °C. Series connection yields lower current for a given power, so that the
Cu lead wires of the heaters do not exceed their bum-out rating. An initial experiment,

using only a single heater, found that the heater burned out at 3.7 W.

4.3.6 Thermal Time Constant

The thermal relaxation time 1: between an object of heat capacity C at a given
temperature, connected to its environment at a different temperature by a thermal
resistance R, is given byr = RC . The internal time constant I of the sample assembly is
determined by properties of sapphire and the interfacial thermal resistance between
sapphire and diamond. The time constant between the sample assembly and its
environment 1,. was found by introducing an abrupt change in the heater power and
measuring the thermocouple voltage as a function of time. An exponential function was
fit to thermocouple voltage vs. time data at different temperatures (Figure 61). The time

85

constant is strongly temperature-dependent. At 283 0C, 1: = 81 s; at 502 °C 1: = 45 3.
Since the thermal resistance of the leads is essentially temperature independent, or
increases slightly with temperature, it cannot be responsible for the relaxation time. On
the other hand, radiative losses increase strongly with temperature, leading to a shortened

thermal relaxation time.

 

 

 

 

 

 

 

 

 

 

 

 

12.4 . . . . . - r . , . . . . 305
12.2- - 300
12.0- .. 295
11.8- - 290
g 11.64 - 285 Q
0
> 1 a P
g 11.4- - 280
> 11.2- 4 275
11.0- -1 270
10.8: - Thermocouple Voltage I 265
. Fit of Data .
10-6 r ' r ' r ' r ' r ' I ' r 260
0 200 400 600 800 1000 1200
t(S)
(a)
21.0 f r 510
20.9“ 508
l 506
20.8-
504
g 1
E 20 7- 502 6
V 500 I-
> 20.6- .
. 498
20.5 - - Thermocouple Voltage ‘
. / Fit of Data 496
20.4 - J L A . , . , A , 494
0 50 100 150 200 250
t(S)
(b)

Figure 61 Thermocouple voltage, corresponding to temperature, versus time between: (a) 496 and
508 °C, and (b) 265 and 300 °C.

86

4. 4 High Resistance Measurement Considerations and
Electrical Isolation

4.4.1 Current Leakage

Low current measurements require that current paths other than those through the
sample be eliminated or minimized. Current leakage may occur in various forms: (1)
Current may leak at the instrument input due to internal instrument circuitry when
voltage biased. This is called input bias current. Its value is very small, less than 3 fA for
the electrometer (Keithley 6514) used for current measurement. (2) Current may leak
through the electrometer’s internal circuitry, through the insulator and devices inside the
instrument, even when it is open. This can be partially nulled by zero check of the
instrument.

Another source of error in current could be voltage burden, which is caused by a
small voltage drop at the input terminals of the instrument. Voltage burden values are
given in the manual of the electrometer for various current ranges. The voltage burden
introduces an error of (VB/Vs)100%, where VB and V5 are voltage burden and source
voltage, respectively. The maximum voltage burden of <100 uV is given for 200 pA
range. The minimum voltage source for the measurements was 0.1 V. Using these
voltages, the voltage burden error was estimated to be <0.1% of the measured current.
This did not affect our measurements.

The current leakage problem in our measurement circuit was mainly eliminated
by placing the electrometer at the low side of the measurement circuit. Therefore, only
the current passing through the sample went to the electrometer, without the addition of

any leakage current. This can be seen in the circuit diagram in Figure 65. Also, the top

87

electrode was wired directly. This assured that the current went to the sample and that the
measured current was not leakage current from other components.

Testing the circuit with 10 GO, 100 G0, and IT!) standard resistors showed that
the leakage currents did not interfere with the measurements. The circuit was tested by
performing I-V measurements on these standard resistors. The given tolerances of the
standard resistors were 1%, 1%, and 5%, respectively. The measured resistance for the 10
GO resistor was found to be 997100] G9. The measured resistance for the 100 GO
resistor was found to be 99.7101 GQ. The measured resistance for the 1 T0 resistor was
found to be 1.14:0.01 TO. The 9.97 and 99.7 GQ measured values differ from the 10 and
100 60 values by <0.3%, within the specified 1% tolerance of these standard resistors.
The error of the measured value of the 1 T0 resistor is 14%. This is not due to the
inaccuracy of the measurement, which is 1% of the reading for the electrometer pA

range. This error was not due to Johnson noise, as the peak-to-peak Johnson noise for a 1
T0 resistance is estimated at 10'” A using I ,h- Noise = 5 4k BTB/ R , where I,;,_N0,-se, k3,
T, B, and R are peak to peak thermal noise current, Boltzmann’s constant (1.38x10'23
J/K), the absolute temperature (K), the band width (Hz), and the resistance (Q),
respectively [70]. The bandwidth was estimated using B = 7r/ 416,-, = 7t/(4x 260) = 0.003
H2, where Ta). is the circuit time constant. This is much smaller than the electrometer

reading error for pA range current, 1% of reading. Since this error is systematic, it is most

likely that the error is due to a miscalibrated resistor.

88

4.4.2 Noise

Noise can be internal or external to the measurement system. The origin of the
internal noise is in the measurement system such as thermal noise (Johnson noise), shot
noise, and flicker noise. The external noise is mostly 60 Hz pickup, atmospheric noise,
and cosmic ray noise. Reducing the noise level is very important in low current
measurement. The major source of external noise is background noise (60 Hz radiation).
This is reduced by placing the sample setup in an aluminum box, using coaxial cables and
connectors in the circuit, and grounding the low end of the circuit.

The most common form of the internal noise in a resistor is thermal noise, which

is temperature dependent. The thermal noise for the diamond sample was estimated from:
I ,h_N0,-S€ = 5M . The bandwidth, B, was estimated using B = ”/41“, [70] to
be 0.1 Hz with estimated circuit time constant, 10,, of 10 seconds at 300 °C. The
bandwidth at higher temperature was determined by the longer time constant of the
integration time, rim = 6(power line cycle) x (l/60Hz) = 0.1 s. The bandwidth was
estimated using B = 0314/23nt [70] to be 3 Hz at 550 °C. Using these bandwidths, the

thermal noise for 300 and 550 °C was found to be approximately 1x10” A and 2x10’l3
A, respectively. The thermal noise at 300 °C and 550 °C is not significant compared with
the accuracy of the current at those temperatures, 10‘” A and 10'll A, respectively.

Shot noise arises from fluctuations in the number of carriers due to charge
quantization. The shot noise was estimated from: I sh- Noise = ,/2qIB [72], where q and I

are the charge of the electron, and current, respectively. The shot noise for 300 and 550

°C was found to be 2x10'16 A anle'13 A, respectively. The shot noise at 300 °C is about

89

at the detection limit of the electrometer, 10'16 A, but is much smaller than the error in
current reading, ~0.01%. The thermal noise at 550 °C is above the detection limit, but is

not significant compared with the measured current, ~0.001 %.

4.4.3 Voltmeter Input Resistance

The input resistances of the voltmeter in parallel with the sample can introduce an
error to the current reading of high resistance materials. The size of this error depends on
the input resistance of the voltmeter and the sample. To reduce this error the input
resistance of the meter must be much larger than that of the sample. For example, for an
error less than 1% the input resistance must be 100 times larger than the impedance of the

sample.

Rin
s Rin + Rs

1", = I
where 1,", I s , Rm, and Rs are the measured current, the applied current, the

input resistance, and the resistance of the sample, respectively.

Many voltmeters or multimeters have input resistance of 10 GS). This value can
cause significant errors for our sample with resistance > 100 T9 at room temperature.
This error is eliminated in our measurements by placing the voltmeter-—with an input
resistance of 10 G!) for--in parallel with the electrometer and sample (Figure 65, circuit
diagram). This eliminates the current error, and there will be no voltmeter error because

the electrometer has approximately zero resistance.

4.4.4 Time Constant

Another important concern in high resistance measurements is the electrical

circuit time constant, T = RC , where t, R and, C are the time constant, total resistance,

90

and capacitance of the circuit, respectively. Reducing the error in the current reading to
<1% requires waiting five time constants. The main source of the capacitance in the
circuit is the capacitance of the coaxial cables. The capacitance of the sample was

estimated to be C = k8,, A/l ~l pF, where C, k, 8° , A: 0.5 mm , and l = 0.02 mm are the

capacitance, diamond dielectric constant (6-7), space permittivity (9x10'12 F/m), area of
the electrode, and the sample thickness, respectively. This was insignificant compared
with the capacitance of the coaxial cables, a few hundreds of pF. The capacitance in the
coaxial cables (~30 pF/ft) couples with the large resistance of the sample (>1014 (2) at
room temperature, resulting in a very long time constant at room temperature. Therefore,
minimizing the coaxial cable lengths of the circuit reduces the time constant.

The capacitance of the measurement circuit is reduced by grounding the center
conductor at the low side of the circuit. The length of the cable without grounding was 14
ft, which was reduced to 5-6 ft resulting in a shorter time constant. Even so, a 5-6 ft cable
length (150-180 pF) was estimated to give a very large time constant ~4 hours making a
measurement difficult. This problem is alleviated at high temperatures as the sample
resistance decreases. The time constant decreases significantly, for example, to less than

one second at 300 °C.

4. 5 DC Measurement

4.5.1 Probe Station Circuit

To test the surface conduction before and after the oxygen plasma treatment, I-V
measurements were performed on the sample in air at a probe-station, which was
equipped with a Keithley 236 measurement system. Using this unit, the voltage was
sourced and swept across the desired voltage range and the current was measured with

91

the same unit simultaneously. A schematic of the circuit is shown in Figure 62. The data
was recorded by a computer.

For these measurements, the sample was cleaned in acetone and methanol. Then
four electrodes (Ti/Au) were deposited on the sample. A silicon substrate with Au-pad
was placed on the metal base inside the metal box (shield box) of the probe-station for
both the purpose of electrical isolation and to contact the iridium, if needed. Then, the
sample was placed on the Au-pad/silicon substrate. For the measurements, two probes
were placed on either of two electrodes on the top surface or one on the top and the other
on the Au-pad on the silicon (iridium contact) (Figure 63 and 64). These measurements

were performed in air.

Output HI

 

 

 

 

 

 

admos-u
W
99846le

 

 

 

 

 

 

 

 

 

 

 

Ouipui LO

 

Figure 62 Schematic of the probe-station circuit.

92

 

 

 

Si-subslroie

 

 

 

Figure 63 Diamond sample on the Au-pad of the silicon substrate.

Probe

 

 

ll/AU EleClTOde

 

Diamond

 

 

 

Au-pod

 

 

 

Silicon

 

Figure 64 Sample setup at the probe-station.

4.5.2 Measurement Setup

The components in the high temperature circuit are: (1) a variable DC voltage
source providing voltages between -12 and +12 Volts, which is made with 7 1.5 Volt Li

batteries in series, a potentiometer, and a three-position switch, (2) a multimeter (HP-

93

3457A) with 10 uV resolution and 0.002% accuracy of 53 V, (3) an electrometer
(Keithley 6514) with 0.1 fA resolution and 1% accuracy, and (4) an aluminum box (4.3
x3.2 xl.6 in3) that contains and shields the sample setup. The circuit diagram can be
seen in Figure 65. The electrometer is placed at the low side of the circuit in series with
the sample and the battery allowing current measurement independently. This avoids
current leakage from the cables into the electrometer. The multimeter is placed in parallel
with the sample and electrometer; this configuration eliminates the multimeter as an
alternate current path around the sample under test. The input resistance of the multimeter
is in parallel, and is shown as R-input. The resistance and capacitance due to coaxial

cables, Rleakage and Cleakage , are in parallel as well. The DC source is a voltage divider

that has a potentiometer and battery, which allows setting the voltage. The DC source has
a three positions switch by which the polarity can be reversed or set to zero. The variable
DC source is shown with the arrow on the battery in the circuit diagram. A more detailed
schematic of the measurement system is shown in Figure 66. All the cables are coaxial,

with lengths shown in feet.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

R-sample
WW
.< Ci.) E :0
A 9" ill 8 —_' 8 E 5 (v)
S.
P a Z-L E A E E.
“ co ‘— (D
’77 /'77

Figure 65 DC circuit diagram of the measurement system.

94

Bell-jar Vacuum

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4ft

 

 

 

 

 

System
Al-box
1 ft , Sample 1 fl
W
4 ft g
1 fl V ltmet
—D Hi 0 er
11 o HP-3457A
_— DC voltage
—_ Source Tri-axial to
—l [— Coaxial Adaptor\
Input
Common \‘
Uii 23 ©/
‘1
3 ft /77
Electrometer
keithley-6514

Figure 66 Schematic of the DC measurement system.

Another circuit diagram is shown in Figure 67 that includes all the electronics.
The upper part shows the thermocouple circuit including the resistance of the
thermocouple and the voltage created by the thermoelectric effect. The switch on the

upper left side of the diagram belongs to the two-channel multimeter, which allows

reading the voltage corresponding to the temperature and the bias voltage to the sample.

95

 

V-Thermoccnple
Q
\J

R-Therrn ooouple

———vwv——

 

 

 

0 Voltm eter
V

 

0
n7

Voltm eter
R—inp ut

R-leak age
—\NW‘-

 

 

 

 

DC Source (V-divider) circuit
I I

l K "
C—leakage
DC-Source ‘ 2) ______ ,6

l I
+ l

 

 

 

 

 

 

 

 

 

 

 

Eledrom eter

 

R-sample
/'77
1;...

 

 

 

 

 

 

 

 

 

 

 

 

 

 

’WW

1‘
H” R
A
Moro-H eaters 4”
Diffusion pump
Heater
—@

 

 

 

Figure 67 Circuit diagram: measurement circuit, microheater circuit, thermocouple circuit,

diffusion pump circuit, and DC-Source (voltage divider).

96

The lower part is the rnicroheater circuit in series with a DC power supply and a digital
voltmeter for current reading, and in parallel with a digital voltmeter for voltage reading.
The lower right side is the diffusion pump heater in series with its ac source. The details
of the DC source (voltage divider) is shown on the mid-right hand side of the Figure 67.

The measurements were performed as follows: after reaching a base pressure of
10'6 Torr, the heater was gradually heated to 300 °C in 2 hours. When the temperature
settled, data were taken. The data were acquired by pc running LabView code. The code
records the time, the temperature, the voltage, and the current. The number of current
readings can be entered as required. The code is shown in Appendix C.

The current readings were taken for each temperature after setting the voltage
manually. The voltage was first set to zero, and increased to higher values for positive
polarity, and was lowered back to zero. Similarly, negative voltage was applied, and the
current readings were taken. After taking data at 300 °C, the temperature was increased to
350 °C, and I (V) measurements were similarly performed. This was continued up to 550
°C. Then, the temperature was lowered and data were taken while cooling the sample

down for comparison with the heating data.

97

Chapter 5 Results

In this chapter, measurements of the temperature-dependent conductivity of
heteroepitaxial diamond are presented. The current—voltage (I-V) characteristics show a
linear (Ohmic) relationship for voltages |V| < 1 volt at temperatures above 250 °C. After
extracting the conductance from these data, the bulk conductivity of diamond is
calculated. At temperatures above 300 °C, the conductivity exhibits a thermally activated

behavior with a single activation energy.

5. 1 DC results

In this section, it is demonstrated that the conductance of CVD diamond measured
perpendicular to the surface using front and back contacts can be ascribed to current
transport in the bulk diamond. Surface conductance is shown to be largely eliminated by
sample processing. In certain temperature and bias regions, Ir and Ti/Au contacts are

shown to be Ohmic.

5.1.1 Surface Conductance

I-V measurements at room temperature, in the probe station, taken between top
and bottom contacts before and after oxygen plasma exposure for two top electrodes (RT
and RB electrodes in Figure 63- probe station system) are shown in Figure 68 and 69.
With bias in the range of :3 V, the current is in the range of uA prior to oxygen treatment
but is reduced to the noise level, 0.1 pA, following treatment. This is interpreted as
elimination of surface conduction, a result of transforming the hydrogen-terminated

diamond surface to an oxygen-terminated surface. However, no conclusions about the

98

actual conductance of the sample at room temperature could be drawn, other than it is
less than or of order 10'13 (0"). This indicates that bulk conduction could not be

measured at room temperature with this system.

 

 

 

 

 

 

 

 

r r T r r r r r r ' T ' r
20‘ 0 RBandlr 0 -
‘ A RTandlr G
15- 00 -
. Ge .
10- 6 -
0
. 00 -
5- 0 -
0
A o
< 3°
<9 0'1 Go -
93 nn°
_ '51 nan -‘
-10- a” -
a
. an
-15- a” -
‘ E
-204 —4
I T T I r I I r I
-3 -2 -1 0 1 2 3
V(Volt)

Figure 68 I-V before exposure to oxygen plasma for two top electrodes.

99

 

 

 

 

 

 

 

 

0-4 r ' r ' r fi r ' r f 1 ' r
‘ 0 RT and Ir
0.3 J o 0 RB and Ir -
4 q
0.2 - o o o o -
0.1 - o -

2? 0.0 - o o -

o.

: 1 *
-0,1 -l O O O -‘
-0.2 - o o ..
-0.3 - o -
'0-4 r T T f r r r r r r r 1 r

-3 -2 -1 0 1 2 3

V (Volt)

Figure 69 I-V after exposure to oxygen plasma for two top electrodes.

5.1.2 Estimate of Surface Conductance

To estimate the magnitude of any remaining surface leakage following the oxygen
plasma treatment, additional measurements in vacuum were made using combinations of
the two top electrodes and the back electrode. Test measurements were performed near
220 °C. First, the current was measured with :5 V bias between the two top electrodes
(Figure 70) with the back contact floating. Then, the measurement was repeated with the
back contact grounded (low side). In both cases, the left electrode was connected directly
to the electrometer, see Figure 71.

Currents at 5 V (-5 V) were approximately 0.3 pA (-0.4 pA), with a floating back

contact (Figure 72). With the back contact grounded, the current fell below the

100

electrometer noise level for pA range, approximately 0.01 pA. The small offset current in
Figure 72 is a result of a thermoelectric effect.

It is now argued that the observed current is not from surface conductance but it
represent transport through the bulk. The circular contacts are separated by a distance of
0.4 mm, measured from the closest electrode edges. The shortest distance between top
and back contacts is 20 um. Let us assume first that a substantial surface conductance
exists. The shortest path connecting the two top electrodes is not solely on the surface,
but to the closest edge of the sample, across the edge, through the low resistance back
contact, and then via a similar path to the other top electrode. This surface path on the
diamond has a total length of about 0.2 mm. If there were surface leakage by this path, by
connecting the iridium contact to the low (ground) potential, the current registered would
be about one third the value measured with a floating back contact, approximately 0.1
pA. Instead, it was found that the current remained at the noise level of the electrometer,
even with :12 V bias applied when the back contact was grounded. It was concluded that
the surface leakage at this temperature is below the detectable level of the measurement
circuit under these conditions. The conclusion is that the measured current was due to
bulk conduction, and the bulk conductance is much larger in the perpendicular direction

than the lateral direction.

 

Figure 70 Heteroepitaxial diamond with two Ti/Au electrodes- with diameter of ~0.38 mm- on the

top surface and iridium on the back.

101

 

 

 

 

. Li:
E‘s r:—

Diamond

 

 

.. fit— uv

 

 

.2. _.-.- -

A —_:_— ®

 

 

 

 

 

 

Figure 71 Circuit for measurement with two top electrodes; the bottom electrode can be switched

between a floating and grounded state.

 

 

 

 

 

 

 

 

 

 

o 6 if T V I V I I I I I I' l V I V
‘ +5 V“
0.5 - — -5 V
d d
0.4 4 -
0.3-l w V -
1 -l
0 2 1 4
5% ° 1 if :5
0.02 - _
0.00 - ..
-0.02 - -l
-0.04 - -
I I I ' I ' I I f I ' I '
-10 0 10 20 3O 40 50 60 70
i (5)

Figure 72 Total current I vs. time at :5 V bias with floating back contact (above) and with

grounded back contact (below).

102

Evidence for surface contamination by silver paint

In a preliminary set of I-V measurements, using the back contact and one of the
top electrodes, the effective conductance was observed to increase abruptly from 7x10’lo
(52") at 350 °C to 6x10'7 (52") at 400 °C, three orders of magnitude increase for a
temperature change of 50 °C. This is surprising inasmuch as the conductance increased
from 3x10'll (9") at 300 °C to 70x10'11 (52") at 350 °C , a factor of 25 for the same
temperature difference, see Figure 73. Having increased the temperature to 400 °C,
measurements at lower temperature did not yield significantly lower conductances. After
cooling to room temperature and following chemical cleaning of the sample, the low
conductance was restored, yielding currents at the noise level, about 10 fA. The near
irreversible increase in the conductivity is thought to be due to surface contamination
caused by silver paint. It is suggested that components in the Ag paint can evaporate, or
the Ag may sublime, leading to a thin conductive layer on the diamond surface. As a
result of this finding, it was decided that all high temperature contacts should be made

without adhesives, using only highly temperature stable components.

103

 

 

 

 

 

 

 

 

1 I I I ' I r I I I J

‘ I'- u'. o 3000
15-71 . I A 350C 1
§ In I 4000 §
15-81 1
1E9- A ‘ ‘ A ..
g ' 1 A A I

1E-101 D
5 D 0 ‘A U j
[:1 U ‘
15-111 1.

1 DD
T ' I ' r ' I ' I I T
-3 -2 -1 0 1 2 3
V(Volt)

Figure 73 I-V at 300 °C, 350 °C, and 400 °C.

5.1.3 I-V Characteristics

The next section describes successful experiments at temperatures above 250 °C
that were used to obtain the diamond conductivity. Two sets of I-V measurements were
performed. In Run-l (25-Jan-05), the sample was heated from room temperature to 450
°C, and in Run-2 (30-Jan-05) a similar procedure was followed with a maximum
temperature of 545 °C. The I-V characteristics showed that the bottom and top contacts
were Ohmic between 250 and 550 °C for voltages between -0.5 and 0.5 volt. The I-V
plots from Run-2 are shown in Figure 74-81 for heating cycle. The conductance at

different temperatures was found from a linear fit of I vs. V using y = A+ Bx (Origin
program) with voltages between +5 V and -5 V, where B, the conductance G, and A, the

104

zero-offset, are the fit parameters. The results are shown in Table 6 for Run-2.
Conductivity is found using electrode diameter of d = 49514 um (AA/A=2%) and
thickness of t = 1911 um (At/t = 5%). Conductivity is found using 0' = G(t/ A), where G,
t, and A are the slope of the I-V plot, the thickness of the sample, and the area of the

electrode, respectively.

Table 6 Data from linear fits to I~V for Run-2.

 

 

 

 

 

 

 

 

 

Temperature B=Conductance A=Zero-Offset Conductivity Duration
(°C) (9") (A) mm)" (min)
265:2 1.5x10“:<5x10‘l3 2x10“ 15x1012 35
301:2 6.80x10'”:3x10'” 2x10“ 6.80x10'12 40
350:2 5.09x10°”:2x10'13 2x10” 5.09x10‘” 30
399:2 3.14x10"°:1x10'12 4x10“ 3.14x10‘"’ 40
428:2 8.58x10'wi1x10'” 1x1013 8.58x10°'° 20
452:2 1.946x10‘°:2x10'12 3x1013 1.95x10'9 30
495:3 7.724x10'9:6x10'12 1x10"2 7.72x10'9 20
545:2 3.197x10'3:2x10'” 5x1012 3.20x10'8 35

 

 

 

 

 

 

 

The error bars in the I—V plots are found as the sum of the standard deviation in

current over 10 readings and the instrument error. The measurement errors and the

 

instrument errors are used to find the total error, AI, using AI = J 0' ,2 + 0M 2 , where GM

is the measurement noise standard deviation (noise from environment) and a, is the

instrument noise standard deviation.

105

The instrument noise is calculated from table values given in the electrometer
manual. These values are dependent on the measurement range. As an example, for 1 pA
operating in the 20 pA range, the table values for percentage of current reading, count,
and resolution are given as 1%, 30 counts, and 100 aA, respectively. This yields an
instrumental noise standard deviation of 0.013 pA, as shown in the following equation:

0', = (%rdg) X I ave + count X resolution

a, = %1x(10‘12)+30x(100x10'18)=0.013 pA
The error bars are larger for larger current values in the same range of the

electrometer. The total current error readings were calculated as < 1 % in all experiments.

 

.0
a.
l .
1

| (PA)
0
E

J:
l l A l J 1 A J 1

 

 

 

I ' I ' I

. , .
-0.6 04 02 0.0 0.2 0.4 0.6
V(Volt)

Figure 74 I-V at 265 °C: Run-2

106

 

I (9A)
‘?

 

 

r I ' I ' I

I
0.4 02 0.0 0.2 0.4 0.6
V(Volt)

Figure 75 I-V at 301 °C; Run-2.

30

 

20-

10—

| (PA)
‘3

 

 

r I V I T

' I
-0.4 -0.2 0.0 0.2 0.4
v (Volt)

.1

.0
a:

Figure 76 I-V at 350 °C; Run-2.

107

 

 

 

200
150-
100-

50-

I (DA)

-50 ..

4004

-150-/

 

 

-200

Figure 77 I-V at 399 °C; Run-2.

I ' I

0.2 0.4

0.6

 

600

400-

 

 

Figure 78 I-V at 428 °C; Run-2

I f I

0.2 0.4

108

0.6

 

 

 

 

 

 

' I j I I I I I j
1.0 J
0.5 -
.1
2‘ 0 0 ~

5

-0.5 ~
-1 .0 -

' I ' I ' I ' I ' I I I

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
V (Volt)

Figure 79 I-V at 425 °C; Run-2.

 

 

 

 

I I I ‘ I I I I
4 ..
.1
2 -
if 0 4
5
-2 _
.1
-4 _ /
r r ' r ' r ' I T r ' r
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
v (Volt)

Figure 80 I-V at 495 °C; Run-2.

109

 

l (nA)

 

 

 

 

-20 f I v I v I v I v I v I

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
v (Volt)

Figure 81 I-V at 545 °C; Run-2.

Resistance versus temperature is plotted in Figure 82 for the heating cycle in Run-
1, and for heating and cooling cycles in Run-2. The two heating Runs are in good
agreement for T>350 °C over much of the temperature range although for T<300 °C a
larger discrepancy is evident. It can be seen that there is a difference in the resistance
between cooling and heating in Run-2. However, since the circuit time constants
increase at lower temperatures it may be that data at 300 °C and 265 °C in Run-2 were
taken before settling. It is also possible that the lower resistance during the cooling cycle
may be due to changes in the diamond surface at high temperatures that increase surface
conductance relative to the bulk conductance. The annealing that occurs at the highest

temperatures might alter the interface by increased formation of TiC.

110

 

 

   

 

 

‘ r ' r ' r ' r ' T ' I ' T ‘
1 E12 .5 o A Heatingz
5 ‘ 0 Heating1
. x A 00011” 2 :
1511-: 1
: A g .
g 1 a
d A 1
a: 1591 ‘ 1
a 2 5
1 1
158-, ‘A 3
i x i
.. d
1E7 :

 

 

 

I I I ' T ' I
250 300 350 400 450 500 550

T(C)

Figure 82 Resistance versus temperature for Run-l (Heatingl) and Run-2 (Heating2 and

Cooling2).

The I-V characteristic does not show Ohmic behavior at 300 °C for voltages >1 V
(Figure 83). However, it is anti-symmetric with respect to the current axis. This behavior
is a field effect. No convincing explanation for this non-Ohmic behavior has been
advanced for highly resistive diamond. The scale at which nonlinearity sets is close to
that expected for potential barriers at interfaces, a few eV. As the diamond band gap is

5.5 eV, voltages above 5 V would also lead to strong nonlinearities.

111

 

 

 

 

1.2 . , . , . . . r - , .
1.03 l
0.84 " l
0.6: I -
0.43 . -'

A 02-: I . 1

g 0.0- I," 4

:02; ‘ . " 3
-0.4: I :4
0.61 . l
0.33 J
4.0; ' .

15 T 10 r 6 0 6 I 10 j 15
V(Volt)

Figure 83 I-V at 300 °C for voltages between -12 and 12 volts.

5.1.4 Temperature Dependent Conductivity of Heteroepitaxial

Diamond

The natural logarithm of 0 versus HT is plotted for the two sets (Figures 84 and

85). If 0 is thermally activated, then we expect it to follow the functional form,

0' = Cexp(- E/kBT)

where E is the activation energy, k3 is the Boltzmann constant and T is
temperature in K. Since ln0' = lnC— E/kBT, we expect a straight line in a plot of ln 0

vs. I/I‘ . An unweighted linear fit was used to find the slope, where B = Mg and A = lnC

are the fit parameters. For both Runs, the fits yield E = 1.40 i 0.03 eV .

112

The details of the fits are shown in Table 7. Data in Run-2 at 265 °C are excluded
from the fit as the data at that temperature were taken before current settling. The ranges
of the fits are from 300 to 453 °C and 300 to 545 °C in Run-1 and Run-2, respectively.
Conductivity of heteroepitaxial diamond changes from 5x10'12 (Q-cm)’l at 300 °C to
2x10’9 (Q-cm)‘l at 453 °C, by three orders of magnitude, in the first run, and from 7><10'l2
(Q-cm)’l at 300 °C to 3x10'8 (0cm)l at 545 0C, by four orders of magnitude, in the

second run.

Table 7 Fit results of run 1 and 2.

 

 

 

 

Run no. Tmm(°C) Tm, (°C) No. of Points A=ln C B=E/K (T) E (eV)
1 301 453 4 2 161821297 1.401003
2 301 545 7 3 162691328 1.401003

 

 

 

 

 

 

 

 

 

‘ Y I V V V
1

113-91 -,
: I
: :

1E-11-5 1

A \

E . '\

0.

e 15104, \ 4
5 a 3
g

.2

*5

3

'O

8

0

1E-12-5 \K'il

I ' I I r I

1.3 1.4 1.5 1.6 1.7 1.8 1.9
1000/T(1/K)

 

 

 

Figure 84 Conductivity of heteroepitaxial diamond versus inverse temperature; Run-1.

113

 

 

 

: I ' I ‘ I ' I ' I ' I ' I r I
3\ a
1E8? ‘ 1‘
E 1 ‘
q a
E 159% 1
Q i
3? 112-101: 1:
23 ‘ 2
3 .
E 15.11' \\
4 . 4
1E-121
I ' r 1 I ' I ' I 1 I 1 I ' I
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

1000fT(1/K)

Figure 85 Conductivity of heteroepitaxial diamond vs. 1/T; Run-2.

114

 

Chapter 6 Discussion of Results/Analysis

6. 1 Comparisons with other measurements

The temperature-dependent conductivity of heteroepitaxial diamond is compared
here with natural diamond: two Type IIa crystals (containing only trace amounts of
nitrogen) and one Type Ib crystal (with 50-100 ppm nitrogen) diamond. Two different
groups obtained results for the DC conductivity as shown in Figure 86. A single slope in
the lno vs l/T plot is observed for each sample, indicating an activated process with a
single activation energy. Three of the samples, the heteroepitaxial crystal and two Type
IIa crystals, show conductivities within one order of magnitude of each other at the same
temperature. The conductivity of the Type Ib diamond crystal is larger by four orders of
magnitude. Although detailed information on impurity content is not available, the
difference is most likely due to its higher nitrogen concentration.

Although all four samples show activated behavior of the conductivity, the
activation energies differ and the measurement temperature regions are somewhat
different. For heteroepitaxial diamond, we found an activation energy of 1.4 10.03 eV
between 300 and 550 °C. Vandersande [55]found 1.4 eV for Type IIa diamond between
300 and 1200 °C. Borst [60]quoted an activation energy of 1.7 eV for Type IIa diamond
between 180 to 350 °C and the same for Type Ib diamond between 100 to 280 °C.

To see if some of the differences had occurred in the data analyses, we performed
a least squares fit to the data taken by the other groups in the temperature region shown in
Figure 86. For Type IIa diamond, activation energies of 1.461002 eV and 1.671001 eV

were found for the data of Vandersande and Borst, respectively, and 1.81-0.04 eV for

115

Borst’s Type Ib diamond. Possible origins of these activation energies are discussed in

the next section.

 

1E'7 Tfi r r ' r r 1 r r T r r T I on
O I 4
15-8'! A . 1
i A . .
1E-91 . r!
E 1 A O D .
0' 115-10‘
g a. A . a . 1
O 1
\
'- 1E-11 A
v o Cl .1
'2 1512' A ’
r‘ U
8 1: 3.
‘o - .
8 E131 0 ‘
o 1 ‘ 1 1
3 D
1E-141 1
c1
1E‘15 I I I I I I I T

 

 

 

U I r U I U I U ' U l I
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
1000/T(1/K)

Figure 86 Comparison of conductivity vs. l/T between heteroepitaxial 0, natural type Ila A [55],

type Ila C] and type Ib diamond I [60].

6. 2 Origin of activated behavior

In general, the temperature-dependent electrical conductivity of diamond might be
the result of several different sources that introduce carriers into current-carrying states.
As noted in Chapter 2, even a small concentration of defects or impurities can strongly
influence electrical transport in semiconductors. In the case of diamond, there are
relatively few impurities that can be incorporated into the lattice owing to the small C-C

interatomic distance. These are generally light atoms, such as H, B, N, O, P, Si, etc. In

116

addition, there are native defects that may exist alone, in clusters, or in combination with
impurities. Examples are carbon interstitials and carbon vacancies. These may be located
randomly or may be associated with structural defects, particularly dislocations.

Information about impurity and defect states is obtained from a number of
sources: from measurements such as those described in this thesis, from optical
spectroscopy (including cathodoluminescence, photoluminescence, and photothermal
absorption) and from electron spin resonance (ESR), to mention some of the most useful.
These methods are often complementary inasmuch as some centers may be invisible to
certain probes. For example, electron spin resonance is only sensitive to defects that have
unpaired electron spins. Furthermore, a defect may exist in more than one charge state.
That state could be controlled by interactions with other defects.

Thermally activated conductivity by intrinsic carriers, with an activation energy
of Eg/2 = 2.7 eV, is not observed. The activation energies that are observed, in the range

of 1.4 to 1.7 eV, must have other origins, presumably from localized impurity states
and/or defects whose energy levels lie within the bandgap of diamond. As noted
previously, an activation energy of 1.7 eV has been related to the substitutional nitrogen
donor. This activation energy was found by Borst [60] for Type Ib diamond (50-100 ppm
nitrogen) and it is reasonable to suppose that nitrogen could be contributing electrons to
the conduction band, although there is no independent knowledge of the carrier density.
It is somewhat surprising that the Borst result for Type IIa diamond also indicates an
activation energy near 1.7 eV inasmuch as there should be < 1 ppm nitrogen in this
crystal. Since there is about two orders of magnitude difference in nitrogen concentration

between the two Borst crystals, the observed conductivity difference of four orders of

117

magnitude would appear to be inconsistent with a single type of dopant or defect. This is
especially true if the carrier mobility increases significantly in the purer Type IIa crystal,
owing to the lower probability of scattering by neutral or charged N impurity states.

The result for Type IIa by Vandersande[55], 1.4 eV, does not agree with the
Borst result, 1.7 eV, on Type IIa diamond. Since detailed impurity analyses are not
available for these crystals, it is entirely possible that different concentrations of trace
impurities are responsible for the different activation energies. It should be noted that the
Borst crystal has a conductivity at least an order of magnitude greater than the
Vandersande crystal. Also, the temperature ranges of the two measurements do not
overlap appreciably.

If we accept that the Vandersande crystal is appreciably purer than the other
natural diamond crystals measured, its comparison with the heteroepitaxial crystal is the
most appropriate. Our finding of an activation energy of 1.4 eV for heteroepitaxial
diamond, in close agreement with the Vandersande result for Type IIa diamond, is
therefore striking. Since the heteroepitaxial process used here does not intentionally
introduce nitrogen into the growth process, the crystal is expected to exhibit nitrogen
concentrations below 1 ppm, as does the clean Type IIa diamond. Note that the statistical
error bars on the fits are sufficiently small to rule out overlap with the Borst results.

One impurity that is introduced into all CVD diamond is hydrogen.
Measurements of the hydrogen concentration in a heteroepitaxial sample grown three
years earlier by the same process in the same reactor exist. The concentration was
estimated from the absorption strength of the infrared-active CH2 vibrational doublet in

the vicinity of 2900 cm]. The result of 360 ppm hydrogen is within a factor of 2-3 of the

118

typical residual hydrogen content of CVD diamond and thus appears reasonable. There
may be more hydrogen present that is not detected since it may not contribute to
vibrational modes in this spectral region. Natural diamond may also contain high
concentrations of hydrogen.

The role of hydrogen in diamond is particularly intriguing as it is known to
complex with donors and acceptors. In the case of B-doped diamond, hydrogen can
effectively passivate the boron acceptor. More relevant to the present situation is the case
of the hydrogen-vacancy center. Unlike Si:H [73], the hydrogen in diamond does not
form in a bond-centered configuration, i.e., in a position midway between two carbons.
Instead, it appears that a more favorable situation occurs when a carbon vacancy occurs.
Here, the hydrogen bonds to a single carbon, leaving two bonded carbons and carbon
dangling bond. The electron on the dangling bond renders the defect paramagnetic
allowing ESR to determine the symmetry properties and geometry of the state. This has
been facilitated by the observation of weak sidebands to the main Am = 0 transition
brought about by hyperfine coupling between the electron and the nuclear spin of the
hydrogen. [74]

This defect, referred to as the H1 hydrogen-vacancy center, is remarkably stable:
it does not show signs of annealing out at temperatures up to 1500°C. Although it was
first investigated[74] in polycrystalline diamond leading to the suggestion that the center
is associated with distorted bonds at grain boundaries, it has more recently been
studied[75] in CVD heteroepitaxial diamond similar to the material studied in the present
investigation. It was found from ESR that the hydrogen concentration is about 200 ppm,

representing only hydrogen associated with the H1 center.

119

The formation of a paramagnetic state by introducing hydrogen into a
semiconductor appears to be contrary to conventional practice, in which hydrogen is used
to passivate dangling bond states in materials such as Si or $02. In diamond, it would
appear that the environment in the vicinity of the carbon vacancy is somewhat distorted,
yielding a single site most favorable to forming a C-H bond. Two of the remaining
carbons bond to each other leaving a dangling bond state at the other carbon. Apparently,
there is not enough space for a second hydrogen to passivate the dangling bond. Thus,
the net effect of hydrogen is to create a paramagnetic center in diamond.

In the situation in which both hydrogen and nitrogen are present in diamond, it
was found [74]that increased hydrogen concentrations causes a decrease of the neutral
nitrogen donor. At H concentrations above 10 ppm, the nitrogen donor is reduced by
over an order of magnitude, suggesting that hydrogen may directly passivate the nitrogen
or that H1 may act as a compensating center for the nitrogen. Despite considerable effort
using density functional theory to calculate defect energy levels, including H1 in
diamond, the methods are not sufficiently accurate to warrant serious comparison with
substantiated experimental data. At this point, there is no evidence, experimental or
theoretical, that can be used to confirm the assignment of an H1 state approximately 1.4
eV from a band extremum.

Native defects, those that are independent of impurities, appear to be electrically
active in diamond. For example, the single vacancy has an acceptor level that lies near
midgap. Single and double interstitial defects appear in various configurations but all

appear to be quite deep, making assignment to the 1.4 eV state improbable. It would be

120

helpful if information were available on the sign of the charge carriers as well as the
concentrations of impurities known to produce shallow levels [60, 64].

In conclusion, the single activation energy of 1.4 eV found in heteroepitaxial and
natural diamond argues for a single type of electrically-active defect that is responsible

for the thermally activated conductivity in these materials.

6. 3 Outlook

There are a number of questions that remain to be answered if the origin of the
thermally activated conductivity of heteroepitaxial diamond is to be understood. For
example, what is the carrier type, the carrier mobility, and the origin of the defects or
impurities that contribute the carriers?

Further experiments are suggested to answer these questions. The carrier type can
be determined with Hall effect measurements. Using the van der Pauw method, the Hall
mobility and carrier sign can be found in a quasi-2D geometry using four edge mounted
electrodes. A perpendicular magnetic field will need to imposed. The impurity and its
concentration can be determined by secondary ion mass spectroscopy (SIMS). With this
technique, hydrogen, nitrogen, and oxygen concentrations with the detection limits of
5x1018 cm'3, 10l7 cm'3, 1018 cm'3, respectively, can be detected in the diamond sample.

Finally, it is suggested that future measurements employ a guard ring that
surrounds the top electrode in the sandwich geometry structure. This will insure that
surface leakage currents can be shunted away from the current-measuring device and will

not contribute to the conductivity.

121

Appendix A Metallization Repair and Removal

Since one often encounters poor adhesion of the electrode to the diamond surface,
it may be necessary to remove part of the thin film. Since the diamond sample was not
cleaned with ultrasound owing to the possibility of damage, it was initially cleaned with
Alconox solution, acetone and methanol. Four Ti/Au electrodes were deposited on the
sample. Then the sample was heated in air to 250 °C for surface leakage tests. The
electrodes came off the surface due to poor adhesion after heating. Another set of the
electrodes was deposited and annealed in vacuum, but failed by peeling off partially or
fully, and by bubble formation. The optical microscope images of a broken electrode
indicating poor adhesion, and a bubbled electrode are shown in Figure 87. The reasons
for peeling and bubbling were thought to be either gas trapped or formed during
annealing (for example, oxidation of titanium when heating in air) or the presence of

loose particles on the surface not removed by the limited cleaning process.

 

Figure 87 Optical microscope images of (a) a broken Ti/Au electrode, and (b) The circular pad is

a Au electrode- with diameter of 0.015 inches- on the diamond surface, a bubbled electrode.

122

The bad electrodes peeled off completely in a methanol spray. After the
electrodes came off, the sample was cleaned only with aqua regia. It appeared that the
electrodes were removed from the surface when viewed by optical microscope. However,
SEM imaging revealed electrode material still on the surface (Figure 88). Four circular
electrodes, each with three overlapped electrodes from three individual sets of electrode
depositions were identified in Figure 88. The electrode residue is most likely Ti, T102 or
TiC. Titanium oxide was possibly formed as the sample was heated in air after electrode
deposition in the first sets of measurements at the probe-station before annealing the

electrodes in a vacuum.

 

Figure 88 SEM image of overlapped electrodes residue; electrode diameter: 0.015 inches.

To remove the electrode residue, wet chemical etching was used. Initially, the
sample was placed in 1NH40H:5H202 for 70 minutes. This solution can attack both Ti
and TiC. Figure 89 (a) shows SEM images after 70 min etching. Figure (a) shows the

upper right electrode of Figure 88 is partially etched. The small particles spread around

123

the electrode following etching- seen in Figure 89 (b) and (c)- show definite crystal
structures.

To remove Ti more aggressively, and possibly TiC formed deep in the electrodes,
HF was used. The SEM image in Figure 90 shows the lower right electrode of Figure 88
is partially etched after 100 minutes exposure to HF. Figure 91 (a) and (b) compare the
SEM images of the upper right electrode of Figure 88 after 100 minutes and 170 minutes
HF etching, respectively. It can be seen from these images that most of the electrode is

etched.

124

lltllilllll
1.00

 

LI '3" r r o rfrr
’ '500nm

Figure 89 SEM images of (a) partially etched electrode after 70 minutes exposing to ammonium

solution, and (b) and (c) particles that came off the electrode.

125

 

Figure 90 SEM image of partially etched electrode after 100 minutes HF etching.

Irrrrltllrl

15 cw 1'} 1mm x200 SElU) 6124420111 21 4: 2000.11

0))

llIlIIIIIIi

15.0141 12 0mm x200 5500111252001 13 48 ZOOum

 

Figure 91 SEM images of electrode after (a) 100 minutes, and (b) 170 minutes HF etching.

126

There was an important observation made while researching and establishing the
chemical recipe for electrode removal. The SEM images of the sample showed bright
electrodes pads remained on the surface even after hours (~5 hours) of HF etching. The
bright area can be seen in the SEM images of Figure 92 (a) and (b). These bright areas
indicate different surface texture than diamond, possibly TiC formed on the surface after
annealing. These areas may be similar to the metal carbide islands that Werner observed
on boron doped polycrystalline diamond surfaces after etching aluminum contacts from

the silicon surface by phosphoric acid (Figure 93).

 

Figure 92 SEM images of electrode residue after ~5 hours of HF etching (a) and (b).

127

. TU
iEtERLIN

 

Figure 93 SEM image of metal carbide islands on boron doped polycrystalline diamond surfaces

after etching aluminum contacts from the silicon [58].

After chemical cleaning, a very good adhesion between the electrode and the
diamond surface was obtained. A primary test for adhesion- spraying alcohol to the
electrode- did not cause electrode peeling. The optical microscope inspection of the
electrode did not show any bubbling or electrode deformation after annealing (Figure
94b). Figure 94 shows: (a) a portion of the diamond sample after chemical cleaning and
before one of the successful electrode depositions (20X), and (b) a portion of the Ti/Au

electrode on the diamond surface after electrode deposition and annealing (50X).

128

 

Figure 94 Optical microscope images of cleaned diamond surface before electrode deposition at

20X (a), and after electrode deposition at 50X showing no electrode deformation (b).

The following procedure was established for removing the Ti/Au electrode:

1) 3HCl: lI-INO3 for 10 minutes. This removes Au.

2) 1H20221 H2804 for 30 minutes. This can attack TiOz in addition to non-diamond
phases and organics.

3) 24.5%HF:75.5%H20 for 3h. HF can attack both Ti and TiOz.

4) 1NH40H25H202 for 3h at 65 °C. This can attack TiC in addition to organic
materials.

The sample is rinsed with DI water after each treatment. Each chemical solution is
composed of the same concentration as given in the cleaning procedure. The first step is
to etch the Au, and the follow steps are to etch Ti, and possible TiC; and TiC formed
after annealing in air and vacuum. In addition to PE, other acids such as HCl, I-INO3, and
H2804 can attack Ti. The treatment time can be varied depending on the thickness of the

Ti and Au electrode.

129

Appendix B Setup Procedure

1- The big stainless steel clip (clip-1) was made. Chromel wire with diameter of
0.010” was passed through the two holes on each side of the clip.

2- Thermocouple junction was made by welding 0.005 inch alumel and chromel
wires (thermocouple type-K).

3- A small stainless-steel clip (clip-2) with the thickness of 0.004 inch was made
to hold the thermocouple near one of the comers in contact with the top side of the
sapphire substrate, Au-pad side.

4- The three micro-Pt-heaters were welded in series. A Cu-wire (d=0.005 in, L=7
in) was welded to each free end of the three heaters.

5- The sapphire substrate was placed inside clip-l.

6- The three heaters were placed between the Cu-sheet and stainless steel sheet,
radiation shield, like a sandwich, and this sandwich is inserted between the bottom of the
sapphire substrate and clip-l, keeping the Cu-sheet in contact with the back of the
sapphire substrate and the stainless steel sheet in contact with clip-l.

7- To make contact with the Ir, one Au-wire (0.002 in) was placed on the Au-pad
of the sapphire substrate. Then, clip-4 was pushed, while lifted slightly with tweezers,
from one side of the sapphire substrate- opposite to the heaters’ leads side- and released
on the top of the Au-wire. Then, the sample was placed on the Au-pad of the sapphire
substrate. Another piece of Au-wire (0.002 in) was used to make contact with the top
electrode. One end of the Au-wire and a small piece of sapphire are placed on the top

electrode, respectively, and clip-3 is positioned on the top of small sapphire, with the

130

same technique as clip-4, to hold the small sapphire /Au-wire/electrode-sample. This was
all done under the light microscope.

8- The lead of the Al-box was removed, and the setup was held with tweezers
with one hand on the top of Al-box. While holding the setup, tweezers were used to pass
the thermocouple wires through the two the hole on one side of the Al-box. Then, Cu-
leads of the heaters are passed through the hole on the opposite side of the Al-box.

9- The free ends of chromel wires (four free ends) coming from clip-l was
wrapped a couple of turns around the screws that are holding the BNC panel.

10- Ag-paint was used to connect the free ends of the two Au-wires, coming from
the two electrodes of the sample, terminating at the core of the two BNCs on the Al-box.

11- The Al-lead was placed back on the Al-box.

12- Each heater lead was passed through a piece of Refrasil (a flexible woven
glass insulating jacket) (L=10 mm). The Refrasil prevented the leads from contacting the
minibox. Each of the heaters’ lead was welded to a pin connector.

13- Each of the thermocouples’ lead was passed through a piece of refrasil (L=10
mm). The refrasil piece was pushed toward the Al-box, and placed in the hole on the A]-
box. Thermocouple wires were connected to a connector; alumel to the negative pin and

chrome] to the positive pin.

131

Appendix C LabView Code

22:11.

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