DIAMOND HETEROEPITAXIAL LATERAL OVERGROWTH
By
Yung-Hsiu Tang

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Physics-Doctor of Philosophy
2015

ABSTRACT
DIAMOND HETEROEPITAXIAL LATERAL OVERGROWTH
By
Yung-Hsiu Tang
This dissertation describes improvements in the growth of single crystal diamond by
microwave plasma-assisted chemical vapor deposition (CVD). Heteroepitaxial (001) diamond
was grown on 1 cm2 a-plane sapphire substrates using an epitaxial (001) Ir thin-film as a buffer
layer. Low-energy ion bombardment of the Ir layer, a process known as bias-enhanced
nucleation, is a key step in achieving a high density of diamond nuclei. Bias conditions were
optimized to form uniformly-high nucleation densities across the substrates, which led to wellcoalesced diamond thin films after short growth times.
Epitaxial lateral overgrowth (ELO) was used as a means of decreasing diamond internal
stress by impeding the propagation of threading dislocations into the growing material. Its use in
diamond growth requires adaptation to the aggressive chemical and thermal environment of the
hydrogen plasma in a CVD reactor. Three ELO variants were developed. The most successful
utilized a gold (Au) mask prepared by vacuum evaporation onto the surface of a thin
heteroepitaxial diamond layer. The Au mask pattern, a series of parallel stripes on the
micrometer scale, was produced by standard lift-off photolithography. When diamond overgrows
the mask, dislocations are largely confined to the substrate. Differing degrees of confinement
were studied by varying the stripe geometry and orientation. Significant improvement in
diamond quality was found in the overgrown regions, as evidenced by reduction of the Raman
scattering linewidth. The Au layer was found to remain intact during diamond overgrowth and

did not chemically bond with the diamond surface. Besides impeding the propagation of
threading dislocations, it was discovered that the thermally-induced stress in the CVD diamond
was significantly reduced as a result of the ductile Au layer. Cracking and delamination of the
diamond from the substrate was mostly eliminated. When diamond was grown to thicknesses
above 0.1 mm it was found that crystallographic perfection continuously improved, leading to a
diamond surface nearly free of stress.

Copyright by
YUNG-HSIU TANG
2015

For my dear mom

v

ACKNOWLEDGMENTS
During the past five years, I immersed myself in the lab and tried to figure out the clues
from the results. Most of time, I was completely in the dark and missed the puzzles. My advisor,
Dr. Golding, was always there with me to look for the clues and put the puzzles together. In the
beginning of the research, I often felt anxious and discouraged from uncontrolled experiments.
My advisor told me that doing real research is living with high uncertainty. It takes more than
anyone can imagine to accomplish this goal. Then, I started to learn how to adjust myself to
mold into this lifestyle. I gratefully appreciate his guidance. He always encourages me and is
always there with suggestions. Without his support, in every respect, in the first place, I would
not be able to finish this degree. His patience and enthusiasm for scientific research will always
be my model in the future.
I also greatly thank Dr. Baokang Bi, not only for his technical support in the KMF facilities,
but also for valuable ideas for experimental designs. He always patiently answers my questions
of any kind. The encouragement from Dr. Bi and Dr. Reza Loloee strongly motivated me to
focus on the project. Thanks my committee members: Dr. Chih-Wei Lai, Dr. Carlo Piermarocchi,
Dr. Megan Donahue, and Dr. Wade Fisher for their encouragement and suggestions.
The experiments would not be improved without help from the machining experts: Thomas
Palazzolo, James Muns and Thomas Hudson from the Physics machine shop and Scott Bankroff
from the Chemistry glassblowing facility. I always submitted complicated and difficult works. I
really appreciate that they always finished the jobs on time with perfect parts. Finally, I would
like to thank my dear mother who always supports my decisions, so I can endeavor to

vi

accomplish the PhD degree. My husband, Tung-Wu, always accompanies me, sharing my
happiness and tears in every moment.
I also thank the DOE for support of this research under grant DE-FG52-08NA28767.

vii

TABLE OF CONTENTS
LIST OF TABLES ....................................................................................................................... xi 
LIST OF FIGURES .................................................................................................................... xii 
1. 

Chapter 1 Introduction .................................................................................................. 1 

2. 
2.1 
2.2 
2.3 
2.4 
2.5 

Chapter 2 Diamond: structure and physical properties ............................................. 4 
Diamond crystal structure ......................................................................................... 4 
Electronic properties ................................................................................................. 5 
Optical properties ...................................................................................................... 8 
The synthesis of diamond ....................................................................................... 10 
Diamond types: Impurities ...................................................................................... 11 

3. 

Chapter 3 Characterization methods ......................................................................... 12 
3.1 
Scanning electron microscopy ................................................................................ 12 
3.2 
Atomic force microscopy ........................................................................................ 14 
3.3 
X-ray diffraction (XRD) ......................................................................................... 16 
3.3.1 
Rocking curve .................................................................................................. 18 
3.4 
Raman spectroscopy ............................................................................................... 19 
3.4.1 
Theory of Raman scattering ............................................................................ 19 
3.4.1.1 
Polarized Raman spectroscopy ................................................................... 21 
3.4.1.2 
Stress measurements by polarized Raman spectroscopy ............................ 23 
3.4.2 
Micro-Raman spectral method ........................................................................ 27 
3.4.2.1 
Spectrum analysis ....................................................................................... 28 
3.4.2.2 
Spatial Raman scanning .............................................................................. 29 

4 

Chapter 4 Plasma-assisted heteroepitaxial growth ................................................... 30 
4.1 
Properties of plasma ................................................................................................ 30 
4.1.1 
Glow discharge ................................................................................................ 30 
4.2 
DC magnetron sputtering ........................................................................................ 32 
4.2.1 
Configurations of AJA sputtering system ....................................................... 33 
4.2.1.1 
Oxidation issue in AJA ............................................................................... 35 
4.3 
Chemical vapor deposition (CVD) ......................................................................... 35 
4.3.1 
Configurations of the CVD reactor ................................................................. 36 
4.3.1.1 
Energy source of CVD reactor .................................................................... 36 
4.3.1.2 
Gas handling of CVD reactor...................................................................... 38 
4.3.1.3 
Biasing set up and circuit ............................................................................ 38 
4.3.1.4 
Computer controlling/monitoring system ................................................... 40 
4.3.1.5 
Substrate loading in CVD reactor ............................................................... 40 
4.3.2 
Configurations of AsTex reactor ..................................................................... 40 
4.3.2.1 
Energy source of AsTex reactor.................................................................. 41 
4.3.2.2 
Gas handling of AsTex reactor ................................................................... 41 
4.3.2.3 
Temperature measurement .......................................................................... 43 

viii

4.3.2.4 
4.3.3 
4.3.3.1 
4.3.3.2 

Substrate loading in AsTex reactor ............................................................. 43 
Diamond CVD methods .................................................................................. 44 
Effects of growth parameters ...................................................................... 47 
Growth anisotropy: the α parameter ........................................................... 49 

5 

Chapter 5 Diamond nucleation and heteroepitaxy ................................................... 51 
5.1 
Nucleation ............................................................................................................... 51 
5.2 
Crystal growth modes ............................................................................................. 53 
5.3 
Heteroepitaxial diamond growth............................................................................. 54 
5.3.1 
Epitaxy ............................................................................................................. 54 
5.3.2 
Definition of diamond heteroepitaxy ............................................................... 55 
5.3.3 
Substrate criteria for diamond heteroepitaxy................................................... 56 
5.3.3.1 
Heteroepitaxial diamond growth on bulk substrates ................................... 59 
5.3.3.2 
Heteroepitaxial diamond growth on Ir ........................................................ 60 
5.4 
Enhancement of diamond nucleation ...................................................................... 61 
5.4.1 
Bias enhanced nucleation (BEN) ..................................................................... 62 
5.4.1.1 
Proposed mechanism of BEN ..................................................................... 62 
5.4.1.2 
Bias and plasma chemistry .......................................................................... 65 
5.4.1.3 
Bias enhanced nucleation on iridium .......................................................... 70 

6. 

Chapter 6 Epitaxial lateral overgrowth (ELO) ......................................................... 79 
6.1 
Dislocations............................................................................................................. 79 
6.2 
ELO method ............................................................................................................ 82 
6.3 
Types of ELO on GaN ............................................................................................ 83 
6.3.1 
Facet-initiated ELO (FIELO) .......................................................................... 83 
6.3.2 
Different masking materials ............................................................................ 83 
6.3.3 
PENDEO epitaxy............................................................................................. 84 
6.3.4 
Air-bridged ELO.............................................................................................. 86 
6.3.5 
Cantilever epitaxy ............................................................................................ 87 
6.3.6 
Direct lateral epitaxy ....................................................................................... 88 
6.4 
Types of ELO on diamond ...................................................................................... 89 

7. 

Chapter 7 Epitaxial Ir growth on a-plane sapphire .................................................. 92 
7.1 
A-plane sapphire (a-ALO) ...................................................................................... 92 
7.1.1 
Epitaxial relation between Ir and a-ALO ........................................................ 93 
7.2 
Ir sputtering procedure ............................................................................................ 94 
7.2.1 
Sapphire preparation ........................................................................................ 95 
7.2.2 
Sample mounting and loading ......................................................................... 97 
7.2.3 
Ir DC sputtering ............................................................................................... 97 
7.2.3.1 
Bias cleaning on a-ALO .............................................................................. 99 
7.2.3.2 
Ir DC sputtering rate ................................................................................. 102 
7.3 
Results for Ir (001) epilayers ................................................................................ 103 
7.3.1 
Ir x-ray diffraction (XRD) ............................................................................. 103 
7.3.2 
Ir surface topography on a-ALO ................................................................... 106 
7.4 
Ir-ALO wafer processing ...................................................................................... 109 

ix

8. 
8.1 
8.2 
8.3 
8.4 
8.5 
8.6 
9. 

Chapter 8 Heteroepitaxial growth of diamond........................................................ 111 
Fixtures for biasing ............................................................................................... 111 
Procedure for diamond growth ............................................................................. 112 
Result of BEN on Ir .............................................................................................. 115 
Heteroepitaxial CVD diamond thin film growth .................................................. 116 
Procedure of thick diamond growth in AsTex ...................................................... 120 
Heteroepitaxial CVD diamond thick film growth ................................................ 120 

Chapter 9 Diamond heteroepitaxial lateral overgrowth ........................................ 126 
9.1 
Au-masked Diamond ELO ................................................................................... 126 
9.1.1 
Photolithography on diamond ....................................................................... 127 
9.1.2 
Diamond regrowth ......................................................................................... 131 
9.1.2.1 
Early stage of coalescence ........................................................................ 133 
9.1.2.2 
Intermediate thickness diamond films ...................................................... 138 
9.1.2.3 
Thick diamond growth .............................................................................. 139 
9.2 
PENDEO for Diamond ELO ................................................................................ 144 
9.2.1 
Substrate preparation ..................................................................................... 145 
9.2.2 
Diamond plasma etching ............................................................................... 147 
9.2.3 
Regrowth of protected diamond stripes ......................................................... 150 
9.3 
Diamond ELO with SiO2 mask ............................................................................. 152 
9.3.1 
Substrate preparation ..................................................................................... 153 
9.3.2 
BEN on patterned SiO2/Ir (001)/a-ALO substrates ....................................... 154 

10. 

Chapter 10 Conclusions and outlook........................................................................ 158 

APPENDIX ................................................................................................................................ 162 
BIBLIOGRAPHY ..................................................................................................................... 167

x

LIST OF TABLES
Table 2.1 Bandgaps, Eg, of some common semiconductors. .......................................................... 6 
Table 2.2 Diamond types according to impurities and corresponding concentrations.28 ............. 11 
Table 3.1 Raman selection rules for backscattering from a (001) surface, with ′|| 110 ,
′|| 110 , and ′|| 001 .35 ......................................................................................................... 25 
Table 3.2 Raman selection rules for backscattering from a (110) surface, with ′|| 110 ,
′|| 110 , and ′|| 001 .35 ......................................................................................................... 26 
Table 5.1 Thermal expansion coefficients of some substrates used in diamond heteroepitaxy (at
300 K).73,74,75,76,77,78 ....................................................................................................................... 58 
Table 5.2 Comparison of growth conditions for samples shown in Figure 5.16. ......................... 78 
Table 5.3 Bias conditions for groups studying diamond heteroepitaxy on Ir. .............................. 78 
Table 7.1 Typical steps for Ir sputtering. The pressure is set at 30 mTorr in the first step to ignite
the RF plasma prior to substrate cleaning. .................................................................................... 98 
Table 8.1 Detailed conditions for CVD diamond thin film growth, with temperature measured on
the Mo cap by a single-color pyrometer. .................................................................................... 113 
Table 8.2 Standard bias conditions. ............................................................................................ 115 
Table 8.3 Detailed growth parameters of thick heteroepitaxial diamond. Row lists the
corresponding growth conditions. Multiple growth steps were used for samples A and B. The
listed temperature is the reading from a single color pyrometer focused on diamond top surface.
..................................................................................................................................................... 121 
Table 9.1 Growth conditions of ELO diamond with different initial thicknesses. Growth with two
steps is indicated by x/y. ............................................................................................................. 132 
Table 9.2 Conditions of diamond plasma etch in pure H2. ......................................................... 147 
Table 9.3 Regrowth conditions of sample 13-3 after H2 plasma etch. ....................................... 150 
Table A.1 Temperature dependent thermal expansion coefficients of diamond and sapphire.173
..................................................................................................................................................... 164 

xi

LIST OF FIGURES
Figure 2.1 Diamond crystal structure which belongs to the space group Fd3m.14 The red balls
represent the basis from (0,0,0) to ( , , ) and the blue balls are the neighboring carbon atoms
connected by the nearest neighbor bonds, the orange sticks. ......................................................... 4 
Figure 2.2 Diamond electronic band structure calculated by linearized augmented plane wave
method (LAPW) 15, where the conduction band minimum occurs at 0.73
, and the valence
band maximum is at the center of the Brillouin zone. Therefore, the diamond bandgap is indirect
and 5.5 eV. ...................................................................................................................................... 5 
Figure 2.3 Brillouin zone of diamond.15 ......................................................................................... 6 
Figure 2.4 Schematic diagram of energy levels in materials with (a) positive electron affinity,
such as silicon and (b) negative electron affinity, such as diamond. EC is the energy minimum of
the conduction band, EV is the energy maximum of the valence band, EF is the Fermi energy, and
EVac represents the vacuum level. ................................................................................................... 7 
Figure 2.5 Transmission spectrum of diamond.19 ........................................................................... 8 
Figure 2.6 Raman-active vibrational mode of diamond. The arrows represent the relative
displacement of a near-zero wavevector optical mode.19 ............................................................... 9 
Figure 2.7 Pressure-temperature diagram of carbon.27 ................................................................. 10 
Figure 3.1 Schematic of a scanning electron microscope (SEM).29 ............................................. 12 
Figure 3.2 Interaction between primary beam and sample, where the range R depends on the
primary beam energy and the specimen.29 .................................................................................... 13 
Figure 3.3 Schematic of Digital Instruments DI 3100 AFM in tapping mode.31.......................... 15 
Figure 3.4 Schematic of XRD geometry....................................................................................... 16 
Figure 3.5 Illustration of Bragg condition. The solid circles represent a 2-D projection of the
ordered atoms with lattice spacing d. Solid arrows are the incident and scattered x-ray beams
with diffraction angle θ respect to the lattice plane. The path difference between ray (1) and (2) is
2dsinθ. If it equals an integer multiple of the x-ray wavelength, ray (1) and (2) will
constructively interfere. ................................................................................................................ 17 
Figure 3.6 Schematic of Bruker AXS D8 x-ray diffractometer.31 ................................................ 18 
Figure 3.7 Raman spectrum of CCl4 (488 nm excitation), showing Stokes and anti-Stokes spectra
and the central Rayleigh scattering.32 ........................................................................................... 21 

xii

Figure 3.8 Raman spectra of Type IIa natural diamond in [001] backscattering geometry. (a) For
ei || [110], only polarization of incident light parallel to the polarization of scattered light, es ||
[110], is allowed. (b) For ei || [010], the polarization of the scattered light must be perpendicular
to the polarization of the incident light, es || [100]. Due to a polarization “leak”, the measured
intensity is non-zero for forbidden polarizations. ......................................................................... 28 
Figure 4.1 ne vs. Te for different plasmas.43 .................................................................................. 31 
Figure 4.2 A glow discharge tube and its major characteristics.44................................................ 32 
Figure 4.3 Schematic of AJA sputtering system. .......................................................................... 34 
Figure 4.4 Schematic of the microwave plasma-assisted CVD (MPCVD) system for heteroepitaxial diamond growth.47.................................................................................................................. 37 
Figure 4.5 Illustration of the TM013 electromagnetic mode inside a cavity.48 Solid lines represent
electric fields; dashed lines the magnetic fields. ........................................................................... 37 
Figure 4.6 Schematic of bias set up in CVD reactor with: (1) Mo cap (2) Ir/a-ALO substrate (3)
Mo post (4) bias lead (5) Mo shield (6) Mo base plate (7) ceramic spacer (8) tungsten bias ring (9)
ceramic spacer (10) grounded stainless steel spacer (11) cooling stage. ...................................... 39 
Figure 4.7 Illustration of bias circuit.47 ......................................................................................... 39 
Figure 4.8 Schematic of AsTex system.31 ..................................................................................... 42 
Figure 4.9 Illustration of the water-cooled sample stage in AsTex system.31 .............................. 44 
Figure 4.10 Illustration of model of diamond nucleation and growth on a substrate.45 ............... 45 
Figure 4.11 Diamond growth rate vs. growth temperature in 4% methane.59 The growth rate
follows the Arrhenius relation but saturates above 1000 °C. ....................................................... 48 
Figure 4.12 Diamond growth rate vs. methane concentration at 770 °C (upper two points) and
800 °C (lower two points).31 ......................................................................................................... 48 
Figure 4.13 Shapes of diamond crystals for different values of α, the growth parameter. The
arrow indicates the fastest growth direction for each case.63 ........................................................ 50 
Figure 4.14 α vs. methane concentration at different temperatures.63 .......................................... 50 
Figure 5.1 Change of free energy (∆ ) vs. radius of nucleus according to CNT, where r* is the
radius of the critical nucleus. The first order phase transition becomes energetically favorable
when the nucleus radius is beyond .69 ....................................................................................... 52 
Figure 5.2 Illustrations of three thin film epitaxial growth modes as a function of surface coverage θ in terms of monolayers (ML): (a) island growth, or Volmer-Weber mode, (b) layer-plusisland growth or Stranski-Krastanov mode, and (c) layer-by-layer growth or Frank-van der
Merwe mode.70.............................................................................................................................. 53 
xiii

Figure 5.3 Illustration of BEN mechanism.103 .............................................................................. 63 
Figure 5.4 Optical emission spectrum of a CH4-H2 plasma at 30 Torr and 2% CH4. Ar was used
as an actinometer to estimate the concentration of atomic hydrogen. The wavelengths of
emission lines of C1 and C2 type species are indicated.114 ............................................................ 66 
Figure 5.5 Intensity of Hα emission vs. methane and oxygen flow rates, representing the
relationships between atomic hydrogen, methane, and oxygen concentrations. The methane
concentration is 9% with a hydrogen flow rate of 100 sccm and methane flow rate of 10 sccm.115
....................................................................................................................................................... 66 
Figure 5.6 Concentrations of (a) atomic hydrogen (b) two types of hydrocarbons (c) Hß/Hα and (d)
ratios of C2/H and CH/Hα vs. bias voltage at 15 Torr and 2% CH4.121 ......................................... 68 
Figure 5.7 Concentrations of (a) atomic hydrogen (b) Hß/Hα and (c) ratios of C2/CH vs. position
relative to substrate surface in vertical direction, where the solid triangles and hollow
rhombohedra represent the data points without and with bias voltage under conditions of 30 Torr
and 2% CH4.114.............................................................................................................................. 69 
Figure 5.8 Plan-view SEM images of BEN-treated Ir surfaces with increasing methane
content.127 ...................................................................................................................................... 70 
Figure 5.9 Plan-view SEM image of BEN-treated Ir surface showing Ir furrows, Ir balls, bright
spots and the domains, where the scale of the images inside the circles is 100 nm.129 ................ 71 
Figure 5.10 Low-resolution SEM image of BEN-treated Ir surface showing the bright areas referred to as domains.128 .................................................................................................................... 71 
Figure 5.11 Plan-view SEM images of (a) domain formation on Ir after 30 min BEN and (b) 15
min diamond growth in the domain.129 ......................................................................................... 72 
Figure 5.12 Plan-view SEM image of Ir surface after 20 min bias.9 ............................................ 73 
Figure 5.13 (a) Plan-view SEM image and (b) HRTEM cross-sectional image of BEN treated Ir
surface after 60 min.31 ................................................................................................................... 74 
Figure 5.14 (a) Plan-view SEM image and (b) HRTEM cross-sectional image of 90s diamond
growth on a 60-min biased Ir surface. In (b) each white line is the (111) plane of Ir (bottom) and
diamond (surrounded by blue dashed line) crystals.31 .................................................................. 75 
Figure 5.15 Plan-view SEM image of diamond surface after 10 min growth following 60 min
biasing. .......................................................................................................................................... 76 
Figure 5.16 Heteroepitaxial diamond surface after 20 min growth (a)47 and (b)127. Diamond
surface after 60 min growth (c)47 and (d)127.................................................................................. 77 

xiv

Figure 6.1 Illustration of dislocation geometry: (a) a perfect single cubic lattice as reference;
distorted crystal lattices with a dislocation line DC which is a positive edge type in (b); a lefthanded screw type in (c); and a right-handed screw type in (d).138 .............................................. 80 
Figure 6.2 HRTEM image at the interface between diamond and Ir. The circled area by the blue
dashed line is the diamond grain. The blue and white lines represent the diamond (111) and Ir
(111) lattice planes, respectively. A misfit dislocation formed at the interface, indicated by .31
....................................................................................................................................................... 81 

T

Figure 6.3 Illustration of an ELO process. (a) A thin epi layer serves as a substrate, where the
solid lines generated from the substrate represent the threading dislocations. (b) A mask, e.g.
SiO2, is deposited and patterned by lithography. (c) Material overgrows the mask which blocks
the threading dislocations during regrowth. The threading dislocation density is greatly reduced
in the overgrown regions. ............................................................................................................. 82 
Figure 6.4 Illustration of PENDEO epitaxy. (a) A GaN epitaxial layer grown on a 6H-SiC
substrate with AlN buffer layer serves as a substrate for the PENDEO process. (b) The GaN
epilayer is plasma-etched to form alternating columns and trenches. (c) Regrowth of GaN
columns has a large lateral-to-vertical growth rate ratio.150 ......................................................... 85 
Figure 6.5 Illustration of air-bridged ELO: (a) a GaN/sapphire substrate; (b) GaN layer partly
plasma etched to form ridges; (c) regrowth of GaN and (d) coalesced GaN overgrown layer in
the center of masked region. In (b), except for the top surfaces of GaN ridges, other areas are
covered by the Si3N4 mask.151....................................................................................................... 86 
Figure 6.6 Illustration of cantilever epitaxy. (a) Substrates 6H-SiC, Si and Al2O3, are plasma
etched to form trenches (etched area) and terrace (unetched). (b) GaN layers grow on substrate
terraces. ......................................................................................................................................... 88 
Figure 6.7 Steps of the diamond ELO process by Ando et al. and Washiyama et al.12 ............... 90 
Figure 7.1 Hexagonal crystallographic unit cell of sapphire. The a-plane is shaded. .................. 93 
Figure 7.2 Illustration of proposed epitaxial relationship of Ir and a-ALO, where the small and
large spheres represent the O and Ir atoms, respectively. ............................................................. 94 
Figure 7.3 AFM images of annealed surfaces of (a) 0-a-ALO (b) 1C-a-ALO (b) 1M-a-ALO and
(d) 0.7M-a-ALO wafers. ............................................................................................................... 95 
Figure 7.4 AFM images of 1C-a-ALO surface annealed at (a) 1300 °C and (b) 1500 °C for 24h.
....................................................................................................................................................... 96 
Figure 7.5 XRD diffraction patterns of 24-nm Ir on 1C-a-ALO substrates sputtered at 3 mTorr,
100W and 850 °C: (a) with plasma cleaning at 3 mTorr, 30W and 850 °C for 5 min and (b)
without cleaning prior to the Ir sputtering. ................................................................................. 100 

xv

Figure 7.6 AFM images of a-ALO (a) before plasma cleaning and (b) after plasma cleaning at 3
mTorr, 30W and 850 °C for 5 min. The sparse bright spots in (a) are nanoparticles which cannot
be removed by standard solvent cleaning. .................................................................................. 100 
Figure 7.7 Linewidth of (002)Ir XRD rocking curve vs. (a) bias duration and (b) bias power. .. 101 
Figure 7.8 AFM image of 300-nm Ir on a-ALO plasma cleaned at 3 mTorr, 30W and 850 °C for
10 min. ........................................................................................................................................ 102 
Figure 7.9 Ir sputtering rate vs. (a) sputtering gun power and (b) Ar pressure in the AJA system
measured at room temperature. ................................................................................................... 103 
Figure 7.10 XRD diffraction pattern of 300-nm Ir on highly-oriented a-ALO. Small peaks
originate from the small fraction of Cu Kβ radiation in the incident x-ray beam. ...................... 104 
Figure 7.11 X-ray rocking curve of Ir (200) with Gaussian fit. .................................................. 104 
Figure 7.12 Ir (200) rocking-curve linewidth vs. substrate deposition temperature. .................. 105 
Figure 7.13 AFM images of 300-nm Ir sputtered by the process in Table 7.1 on a (a) 0-a-ALO (b)
1C-a-ALO (c) 1M-a-ALO and (d) 0.7M- a-ALO. ...................................................................... 106 
Figure 7.14 High-resolution AFM images of 300-nm Ir on a (a) 0-a-ALO (b) 1C-a-ALO (c) 1Ma-ALO and (d) 0.7M-a-ALO....................................................................................................... 107 
Figure 7.15 AFM images of 24-nm thick Ir on unannealed (a) 0-a-ALO and (b) 1M-a-ALO. .. 108 
Figure 7.16 AFM image of 150-nm Ir sputtered at 10 mTorr, 100W and 850 °C...................... 109 
Figure 7.17 Illustration of sample holder for substrate side coating........................................... 110 
Figure 8.1 Fixturing for the CVD reactor: (1) Mo cap (2) Ir/a-ALO substrate (3) Mo post (4) bias
lead (5) Mo shield plate (6) Mo base plate (7) ceramic spacer (8) tungsten bias ring (9) ceramic
spacer (10) stainless steel plate (11) grounded cooling stage. .................................................... 112 
Figure 8.2 Time plot of the standard procedure of heteroepitaxial CVD diamond growth. ....... 113 
Figure 8.3 Plan-view SEM images of biased Ir surface: (a) the featureless amorphous carbon
layer covering the Ir surface and (b) Ir nanopillars buried in the carbon layer. ......................... 116 
Figure 8.4 Four selected optical images of 550 nm diamond thin films, grown in a sequence. The
burn marks on edges are caused by the Mo cap. (b) Film is about 100 nm thicker than other
samples at its center. ................................................................................................................... 117 
Figure 8.5 Plan-view SEM image of 3h-grown diamond thin film showing a well-coalesced
diamond (001) surface. Bright dots are small height fluctuations on the diamond surface........ 118 
Figure 8.6 XRD diffraction pattern of 550-nm diamond on a Ir/a-ALO substrate. Small peaks
originate from the small fraction of Cu Kβ radiation in the incident x-ray beam. ...................... 119 
xvi

Figure 8.7 XRD ϕ-scan of 550-nm diamond on a Ir/a-ALO substrate. ...................................... 119 
Figure 8.8 Cross-sectional tilted SEM image of a 70-μm delaminated diamond (001) piece
showing a (111) cleavage. At bottom is the Ir layer. .................................................................. 122 
Figure 8.9 XRD diffraction pattern of a piece of 85-μm delaminated diamond......................... 123 
Figure 8.10 X-ray rocking curve of diamond (004) reflection with Gaussian fit. ...................... 123 
Figure 8.11 Raman spectra of IIa natural diamond and thick heteroepitaxial diamonds. The peak
center and linewidth of natural diamond are at 1332 cm-1 and 1.65 cm-1, respectively. ............ 124 
Figure 8.12 Raman linewidth and frequency vs. thickness of a 85-μm diamond sample. The
linewidth decreases with thickness and the stress is largely relaxed after 30 μm. ..................... 125 
Figure 9.1 Illustration of Au-masked diamond ELO (not to scale). The vertical wavy lines depict
threading dislocations which are partially restricted in the diamond overlayer. ........................ 127 
Figure 9.2 Schematic of sample preparation for Au-masked diamond ELO: (a) patterned
diamond substrate after PR exposure and development; (b) substrate after Au evaporation; and (c)
completed substrate after Au lift-off. .......................................................................................... 128 
Figure 9.3 Optical images of patterned diamond substrates with (a) 4-μm wide Au stripes with 16
μm gaps and (b) 8-μm wide Au stripes with 4 μm gaps. In both cases, the stripes are parallel to
the diamond <110> direction. ..................................................................................................... 130 
Figure 9.4 Plan-view SEM images of (a) 10-μm thick ELO diamond with 8-μm wide Au stripes
centered on the non-overgrown region. The pits are the terminations of dislocations at the top
surface. (b) 2-μm thick ELO diamond with 4-μm wide Au stripes, just prior to diamond
coalescence. The white arrows indicate the position of the Au stripes. ..................................... 133 
Figure 9.5 Spatial variations of the Raman linewidth and intensity for a (a) 2-μm thick ELO
diamond with 4-μm wide Au stripes and (b) 10-μm thick ELO diamond with 8-μm wide Au
stripes. In both cases the diamond has not detached from the substrate. The linewidth is
minimized at the overgrown region above the Au stripe. ........................................................... 135 
Figure 9.6 (a) Photograph of diamond (001) surface with both delaminated and non-delaminated
regions and (b) comparison of the adherent and delaminated regions on 2-μm thick ELO
diamond with 4-μm wide Au stripes. The delaminated film has the unstressed diamond Raman
frequency whereas the strongly attached film shows large compressive stress. The red dashed
line represents the unstressed diamond frequency at 1332.4 cm-1. The polarizations of incident
and scattered laser beams were parallel to <110>. ..................................................................... 137 
Figure 9.7 SEM images of a 30-μm thick ELO diamond grown with 4-μm wide Au stripes. (a)
Tilted image, the top surface is the (001) face and the sides are {110} fracture surfaces. The Au
stripes are visible in the lower part of the crystal. (b) Expanded {110} fracture surface at the
region near the Au stripe. The diamond only weakly contacts the Au stripe during overgrowth
and forms a void at the top surface of the gold. .......................................................................... 139 
xvii

Figure 9.8 Optical image of Au stripes taken through a 190-μm thick ELO diamond overlayer.
The 8-μm wide stripes are oriented parallel to the <110> diamond direction. ........................... 140 
Figure 9.9 Plan-view SEM images of (a) 75-μm thick ELO diamond with 4-μm wide Au stripes
and (b) 190-μm thick ELO diamond with 8-μm wide Au stripes. .............................................. 141 
Figure 9.10 Raman center frequency of 190-μm thick ELO diamond with 8-μm wide Au stripes.
The scan covers 8 mm, the diameter of the entire diamond crystal. Very low stress is apparent
from the small Raman shift, 1332.4±0.26 cm-1. ......................................................................... 142 
Figure 9.11 (a) Raman linewidth and (b) Raman frequency vs. thickness of a 75-μm thick ELO
diamond with 4-μm wide Au stripes. The linewidth decreases with thickness and the stress is
mostly relaxed on the top surface. (c) Photograph of diamond {110} surface. The arrow indicates
the scan direction, along [001]dia. ............................................................................................... 143 
Figure 9.12 Schematic of PENDEO process during diamond growth........................................ 144 
Figure 9.13 Illustration of sample preparation for PENDEO diamond ELO: (a) a 550-nm thick
diamond substrate patterned with stripes of PR layer by standard photolithography; (b) Au (100
nm) mask layer thermally evaporated on a diamond substrate; and (c) diamond substrate covered
by the Au stripes along the <110> direction. See Figure 9.12 for the two last steps of the process.
..................................................................................................................................................... 146 
Figure 9.14 (a) Plan-view SEM image of a diamond stripe after etching with Au mask remaining
(center). The Au mask shows damage, with holes visible. (b) 45° tilt SEM image at the boundary
of a diamond stripe and the etched trench. The Au masked diamond stripe is on right side; the
area on the left has been etched. Note the steep sidewalls of the diamond and the cone-like
features in the etched area. .......................................................................................................... 148 
Figure 9.15 Plan-view SEM image of etched area showing the bare Ir surface. Small structures
may be Ir coalescence boundaries. No trace of diamond residues is seen. ................................. 149 
Figure 9.16 Plan-view SEM images of the plasma-etched diamond substrate after regrowth. (a) A
diamond stripe, showing the formation of {111} facets on the side walls. (b) Diamond stripes
and etched areas shown at lower magnification. The diamond grew in the etched areas and
formed oriented crystallites after 3h. .......................................................................................... 151 
Figure 9.17 Illustration of diamond ELO with SiO2 mask. ........................................................ 152 
Figure 9.18 Steps followed in ELO with the SiO2 mask process. (a) 500-nm thick SiO2, the
masking layer, was sputtered onto a Ir (001) surface, where the lines represent the dislocations
lines in the Ir layer. (b) The SiO2 surface was covered with a layer of PR, patterned by
photolithography. (c) SiO2 in the channels was etched by BOE, forming trenches. .................. 154 
Figure 9.19 SEM image of exposed Ir surface after biased, showing nanoparticles randomly
deposited on the surface. ............................................................................................................. 155 

xviii

Figure 9.20 DIC optical image of damaged SiO2 pattern on Ir (001)/a-ALO substrate. After 30
min of -200V bias, the SiO2 and Ir surfaces were eroded by arcing. .......................................... 155 
Figure 9.21 SEM images of diamond growth near a SiO2 boundary. The SiO2 layer is the dark
region in the images. (a) Plan-view and (b) 5° tilt SEM image showing diamond growth adjacent
to SiO2. ........................................................................................................................................ 157 

xix

1. Chapter 1 Introduction
Diamond, a wide bandgap semiconductor, is known for its unique physical properties. Its
large band gap, high carrier mobility, unsurpassed dielectric breakdown field, and resistance to
radiation damage make diamond a good detector for energetic particles, especially fission
neutrons. In the 1 MeV energy region of fission neutrons, diamond has the largest linear
attenuation coefficient of any known material, 4% per mm. In this region, energy transfer is by
elastic collisions, leading to a maximum energy transfer of 28% between a carbon atom and a
neutron. Diamond, with atomic number Z=6, has a small photoelectric cross-section, so it is
fairly insensitive to gamma rays. As a consequence, diamond is a superior alternative for the Si
detector, provided that it can be fabricated as a large area single crystal of high quality. However,
very few natural diamonds are suitable for detector applications, owing to their substantial
concentration of chemical impurities. Although the chemical vapor deposition (CVD) method
has produced wafer-size polycrystalline diamond, the presence of grain boundaries introduces
carrier traps. The traps decrease the carrier mobilities and reduce the charge collection
efficiency.1 Therefore, high-purity single crystal CVD diamond grown by epitaxial methods is
the most promising choice for particle detectors.
Heteroepitaxial growth of diamond, where diamond is deposited on a non-diamond substrate,
is a potential method for expanding the size of single crystal diamond to the wafer scale. Si
substrates were first used for CVD diamond heteroepitaxial growth, but due to the large lattice
mismatch between diamond and Si, only textured growth, with highly-oriented diamond grains,
was achieved.2,3 The demonstration of diamond heteroepitaxy on oxide substrates such as MgO,

1

with an Ir buffer layer between the substrate and the diamond, was the first indication that true
diamond heteroepitaxy was feasible.4,5 Later, the use of SrTiO36,7,8,9 as a substrate showed
improvement in the reproducibility and quality of heteroepitaxial diamond. Ir epitaxy on a-plane
sapphire (a-ALO)10, a very high-quality and mechanically stable substrate, suggested that
heteroepitaxial diamond growth on wafers up to 5-10 cm in diameter should be possible.
Somewhat later it was found that the use of multiple buffer layers, Ir and YSZ, on Si11 was an
effective system for low-stress growth.
The major concern in heteroepitaxy is the presence of dislocations, which can act to relieve
the stress introduced by lattice mismatch, but can also introduce internal stresses. In III-V
semiconductors, restricted growth methods, particularly the development of epitaxial lateral
overgrowth (ELO), have been shown to reduce threading dislocation densities by 2 to 3 orders of
magnitude. However, ELO methods require considerable adaptation to be effective under the
conditions used for CVD diamond growth. The first attempts in patterned diamond growth
showed that it could lead to a significant reduction of internal stress.12,13
This dissertation describes experiments on diamond heteroepitaxy that utilize lateral
overgrowth methods. Growth is conducted with iridium buffer layers on a-plane sapphire
substrates. Appreciable effort has been placed on developing reproducible methods for growth of
epitaxial Ir on sapphire by sputtering and subsequent microwave plasma CVD diamond
nucleation and growth on one centimeter square substrates. A novel and particularly effective
method for lateral overgrowth that uses a thin metal mask has been discovered. The Au-masked
ELO method successfully prevents dislocations from propagating into the growing crystal, thus
reducing internal stress in the diamond layer. This method also appears to reduce significantly

2

the stresses that occur between diamond and its substrate. The net result is high-quality, single
crystal diamond of nearly 1 cm diameter and arbitrary thickness.
This dissertation contains ten chapters. Chapter 2 describes the physical properties of
diamond and some historical information. Chapter 3 covers the analytical tools used for diamond
characterization. Chapter 4 describes the instrumentation used for a variety of thin-film
depositions, namely, sputtering systems for Ir epitaxy and CVD reactors for diamond growth.
Factors affecting CVD diamond growth are discussed here as well. Chapter 5 provides
background for diamond heteroepitaxy on various substrates and the method of bias-enhanced
nucleation. Chapter 6 summarizes a number of previous lateral overgrowth methods used for
other semiconductors as well as previous studies on diamond. Chapter 7 describes Ir epitaxy by
sputtering and characterization of sputtered films. Chapter 8 introduces the presently used
methods for heteroepitaxial thin- and thick-film CVD diamond growth. Chapter 9 discusses three
variants of ELO that have been devised to improve diamond heteroepitaxy and subsequent
characterization of the crystal quality of the materials. Finally, Chapter 10 summarizes the
accomplishments of this project and provides suggestions for future work.

3

2. Chapter 2 Diamond: structure and physical properties
2.1 Diamond crystal structure
The diamond structure is a face-centered cubic (FCC) lattice with a basis. It can be viewed
as two superimposed FCC lattices, one displaced relative to the other along a body diagonal by
one quarter of the lattice parameter a0, (0,0,0) to

, ,

from the origin, where a0 = 0.375 nm,

Figure 2.1 The four valence electrons of each carbon atom hybridize to form tetrahedral sp3
bonds with four other carbon neighbors. The nearest-neighbor bond length is 0.154 nm which is
the shortest of any three-dimensional crystal, leading to a highly compact structure and the
hardest known material.

Figure 2.1 Diamond crystal structure which belongs to the space group Fd m.14 The red balls
represent the basis from (0,0,0) to ( , , ) and the blue balls are the neighboring carbon atoms
connected by the nearest neighbor bonds, the orange sticks.

4

2.2 Electronic properties
The electronic band structure of diamond, similar to silicon, has an indirect band gap of 5.5
eV, shown in Figure 2.2 The conduction band minimum occurs at a distance 0.73

, which is

the unit vector in the [100] direction, Figure 2.3, and valence band maximum is located at the Γ
point. The strong sp3 bonding and short bond length of diamond give rise to the largest bandgap
among the semiconductors, about 5 times larger than silicon. The bandgaps of common
semiconductors are shown in Table 2.1 for comparison.

Figure 2.2 Diamond electronic band structure calculated by linearized augmented plane wave
method (LAPW)15, where the conduction band minimum occurs at 0.73

, and the valence

band maximum is at the center of the Brillouin zone. Therefore, the diamond bandgap is indirect
and 5.5 eV.

5

Figure 2.3 Brillouin zone of diamond.15

Table 2.1 Bandgaps, Eg, of some common semiconductors.
Semiconductor

Symbol

Eg
(eV)

Silicon

Si

1.1

Gallium Arsenide

GaAs

1.4

Silicon carbide

SiC

3.3

Gallium Nitride

GaN

3.4

Zinc oxide

ZnO

3.4

Diamond

C

5.5

Owing to the large bandgap of diamond, only a very small fraction of carriers are excited to
the conduction band, even at temperatures of 600 oC. In Si, electric field-induced migration
occurs at these temperatures, leading to device failure. Diamond also has a very high thermal
conductivity, 2000

⁄

∙ , which is nearly 5 times larger than copper at room temperature, a

high dielectric strength, 107 V/cm-1 and high electron and hole mobilities, 4500 and 3800

6

cm2/V∙s16, respectively. Combining the advantages mentioned above, diamond is a promising
material for high temperature and high frequency devices.
The hydrogen-terminated surface of CVD diamond exhibits negative electron affinity (NEA)
because of the growth environment of a hydrocarbon plasma.17 NEA indicates that the energy of
the vacuum level, i.e., the continuum of unbound electron states outside the semiconductor, lies
below the conduction band minimum, Figure 2.4. Consequently, surface electrons can escape
from the diamond, which makes diamond an attractive electron emitter.18

(a)

(b)
EC

Evac

EC

EF

EF

EV

EV

Evac

Figure 2.4 Schematic diagram of energy levels in materials with (a) positive electron affinity,
such as silicon and (b) negative electron affinity, such as diamond. EC is the energy minimum of
the conduction band, EV is the energy maximum of the valence band, EF is the Fermi energy, and
EVac represents the vacuum level.

7

2.3 Optical properties
Diamond is clear and colorless because of its large band gap and the lack of first-order
infrared absorption. In addition, it has a refractive index of 2.42 at 532 nm. Figure 2.5 is the
transmission spectrum of diamond, where the measurement shows little absorption except in the
ultraviolet (UV) and infrared (IR) regions. The UV absorption below 227 nm, corresponding to
5.47 eV, represents the onset of inter-band transitions. The indirect bandgap prohibits electronic
excitations without the creation of phonons. Hence, strong band to band luminescence is
quenched.

Figure 2.5 Transmission spectrum of diamond.19
The IR absorption, at 2.6-6.2 μm, arises from vibrational multiphonon absorption. In Figure
2.5, the two-, and three-phonon absorption peaks are located at 2.6 and 3.75 μm, respectively,
which correspond to integer multiples of the highest phonon frequencies, 2665 and 3997 cm-1.

8

The diamond Raman vibrational mode is the relative movement of two interpenetrating FCC
lattices which comprise the diamond C-C bond, shown in Figure 2.6. This Raman mode is triply
degenerate. The longitudinal and the two transverse vibrational branches converge at a single
point in their phonon dispersion curves20. The Raman linewidth is measured as 1.6 cm-1 at room
temperature, measured on differing samples.21,22,23,24

Figure 2.6 Raman-active vibrational mode of diamond. The arrows represent the relative
displacement of a near-zero wavevector optical mode.19

9

2.4 The synthesis of diamond
The phase diagram of carbon, Figure 2.7, shows that, at ambient conditions, graphite is the
ground state of carbon, whereas diamond is a metastable phase. Thus, the formation of natural
diamond occurs in a high temperature and high pressure environment. In 1955, Bundy et al.
invented the high pressure, high temperature (HPHT) method to mimic the conditions of natural
diamond genesis.25,26 In this method, a pressure cell containing graphite powders with a catalyst,
such as Fe, Co or Ni, is compressed to thousands of atmospheres and heated to over 2000 K,
creating bulk diamond crystals. The size of HPHT diamond is limited by the cell, typically 1-3
mm2 on each face. On the other hand, diamond deposition on a substrate was found to be feasible
in its metastable region by chemical vapor deposition (CVD) methods. This synthesis method
operates at sub-atmospheric pressures, 101-102 Torr, and growth temperatures near 1100 K. CVD
diamond size can, in principle, be enlarged to the wafer scale, but has not yet been possible.

Figure 2.7 Pressure-temperature diagram of carbon.27

10

2.5 Diamond types: Impurities
Because of its small lattice parameter, diamond can incorporate only few impurity species.
The most common ones are boron and nitrogen. According to the included impurity types and
their corresponding concentrations, diamonds can be classified into four types, listed in Table 2.2:
Types Ia, Ib, IIa, and IIb. Most natural diamonds, 98%, are Type Ia. Diamond grown by the
HPHT method belongs to Type Ib, which is yellow due to substitutional nitrogen. Type IIa
diamonds are the cleanest, almost or entirely devoid of impurities. Hence, they are colorless.
Table 2.2 Diamond types according to impurities and corresponding concentrations.28
Diamond type

Boron (ppm)

Nitrogen (ppm)

Color

Ia

-

2000

Clear to yellow

Ib

-

10-103

IIa

-

~1

Green, brown,
yellow
Colorless clear

IIb

~100

~

Blue

11

3. Chapter 3 Characterization methods
3.1 Scanning electron microscopy
The scanning electron microscope (SEM) is in some ways similar to an optical microscope,
replacing light with an electron beam to achieve nanoscale resolution. It uses a focused electron
beam, with wavelength 10 pm, which is rastered across a small area, forming an image of the
sample surface (Figure 3.1).

Figure 3.1 Schematic of a scanning electron microscope (SEM).29

12

In a field emission SEM, the gun is composed of a sharp tungsten tip, with radius smaller
than 100 nm which serves as cathode, and an anode plate. A large electric potential difference
applied across the electrodes creates a very high electric field at the tip, typically above 107 V/cm.
As a result, the electrons at the Fermi level tunnel through the potential barrier into vacuum.
Typically, the beam crossover diameter for cold cathode emission is about 10 nm rather than 10
µm for the thermionic gun of a conventional SEM. The electron beam then passes through pairs
of magnetic condenser lenses to be collimated, followed by magnetic objective lenses which
determine the area for the electron-beam raster scan. FESEM requires fewer magnetoptics to
focus the electron beam, yielding higher resolution and brightness, than thermionic SEMs.

Figure 3.2 Interaction between primary beam and sample, where the range R depends on the
primary beam energy and the specimen.29
The electron beam impinging on the sample surface is called the primary beam. When the
primary beam, with energy between 10-30 keV, strikes the sample surface, the electron-solid
interaction produces a large number of scattered electrons and photons. Figure 3.2 illustrates the

13

interaction between the primary beam and the sample. Secondary electrons and backscattered
electrons are the most important signals for SEM. The secondary electrons, in particular, are
important in forming SEM images. They arise from weakly-bonded electrons close to the sample
surface scattered by inelastic collisions, and typically have low energy, less than 50 eV. The
detector, usually an Everhart-Thomley (E-T) type, accelerates the scattered electrons into a
scintillator by applying positive bias on a collector grid. Photons are emitted and detected by a
photomultiplier. The number of secondary electrons depends on the topographical features of the
surface. Small particles, steep surfaces and edges enhance the emission. Therefore, the secondary
electrons produce a higher resolution SEM image, relative to backscattered electrons, due to the
large volume of interaction. SEM images described below have been acquired with a Hitachi
4700 II FESEM with a cold cathode field emission source.

3.2 Atomic force microscopy
An atomic force microscope is one of the scanning probe microscopies with very high
resolution, on the order of 0.1 nm, used mainly to map surface topography. Instead of using light
(optical microscope) or a focused electron beam (SEM), the probe is a sharp tip, with radius of
10 nm, attached to one end of a cantilever with a spring constant of order 1N/m. The scanning
area, which depends on the instrument design, is typically a few 100 nm to a few 10 μm.
According to the tip motion, the imaging modes of AFM can be classified as: contact, tapping
and non-contact modes.
In this work, the Digital Instruments DI 3100 is used in tapping mode to image the sample
topography. A Si tip is driven at the resonant frequency of the Si cantilever in air using a
piezoelectric crystal.30 The oscillating tip is then brought to near the sample surface. As the tip

14

scans the sample surface, the changes in topography cause damping of its oscillations. A
photodetector captures the reflected light from a laser focused on the back side of the cantilever
to track the tip movement. The amplitude of cantilever oscillation is maintained constant by a
feedback loop in the system. Consequently, the surface topography is interpreted as a change of
feedback signal amplitude. Figure 3.3 shows a schematic of the AFM system.

Figure 3.3 Schematic of Digital Instruments DI 3100 AFM in tapping mode.31

15

3.3 X-ray diffraction (XRD)
X-ray scattering enables scientists to probe crystalline structures at the atomic level,
determining atomic arrangements and interatomic distances. For single crystal x-ray diffraction,
the lattice planes of a crystalline specimen elastically scatter a monochromatic x-ray beam at a
diffraction angle θ relative to the sample surface. A detector, which can be rotated in the
scattering plane, records the intensity of the x-ray interferences while the incident beam rotates
with respect to the sample. A typical XRD pattern plots the intensity of x-ray interferences as a
function of 2θ, the angle between the incident and scattered beam. Figure 3.4 shows the
schematic geometry of x-ray diffraction.

x-ray
source

x-ray
detector
θ

2θ
crystal
sample

Figure 3.4 Schematic of XRD geometry.
In a diffraction pattern, strong peaks, which are constructive x-ray interferences, occur only
at certain diffraction angles. By examining the path differences of the x-rays, the relation
between wavelength λ, lattice spacing d, and the diffraction angle θ is found which is known as
the Bragg condition:

2

,	where the integer n refers to the order of the diffraction. See

Figure 3.5.

16

(1)
(2)
2θ

d

dsinθ

dsinθ

Figure 3.5 Illustration of Bragg condition. The solid circles represent a 2-D projection of the
ordered atoms with lattice spacing d. Solid arrows are the incident and scattered x-ray beams
with diffraction angle θ respect to the lattice plane. The path difference between ray (1) and (2) is
2dsinθ. If it equals an integer multiple of the x-ray wavelength, ray (1) and (2) will
constructively interfere.
The Bruker AXS D8 instrument, Figure 3.6, with a 4-circle Eulerian cradle, is used for XRD
measurements in this project. A Cu target serves as the x-ray source, producing Cu Kα and Kß
radiation, the latter blocked by a Ni filter. For this diffractometer, the position of the incident
beam is fixed, so the sample stage rotates to vary the diffraction angle. The stage has a vacuum
chuck to hold the sample. The plane containing the incident and scattered beams is defined as the
z plane or scattering plane. By moving the stage in the z direction, the converging beam can be
focused at the sample surface; x and y translations position the beam on the sample. The stage
rotates around three mutually perpendicular axes for precise alignment and rotational scans. ω-2θ
scans and rocking curves involve rotations about the x-axis, χ-scans rotate about the y-axis, and
the ϕ-scan rotates about the z-axis.

17

χ
ϕ

θ

2θ

or
Figure 3.6 Schematic of Bruker AXS D8 x-ray diffractometer.31

3.3.1

Rocking curve

In single crystal XRD, the rocking curve can be used to determine crystal quality. It is a θor ω-scan with the detector fixed at the Bragg 2θ angle. For an imperfect crystal, it is a Gaussian
peak whose full-width at half-maximum (FWHM) is a measure of the mosaic spread. Defects,
such as dislocations and impurities, will broaden the linewidth. A small linewidth and a
symmetric Gaussian peak are indications of crystal quality.

18

3.4 Raman spectroscopy
When an incident light beam with frequency υ0, usually in the UV-visible region, impinges
on a specimen, a small fraction of photons, typically 10-5, is scattered inelastically, i.e., with a
small frequency shift. This phenomenon was first discovered by C. V. Raman in 1928. The
frequency differences, called Raman shifts, were found to be consistent with the vibrational
modes of the molecule. In a Raman spectrometer, the scattered light is dispersed by a grating and
is sent to a multichannel analyzer. The output of the analyzer is the inelastic spectrum, i.e., the
number of photon counts per time interval, or intensity, as a function of photon energy, usually
expressed in wave numbers, cm-1, shifted from the laser frequency.
3.4.1

Theory of Raman scattering

Assume a sample is irradiated by a monochromatic incident light beam with an electric field
E given by Eq. 3.1. If the electric susceptibility of the sample is χ, the local polarization P in the
sample can be described by Eq. 3.2

,
,

cos

,

∙
,

cos

∙

3.1

, ,

,

, ,

,

cos

∙
3.2

where k and ω are the wave vector and frequency of the incident light, respectively. Q is a lattice
displacement which can be expressed by the phonon wave vector q and its frequency ωo, in Eq.
3.3.

,

,

cos

19

∙

3.3

, ,

We further expand the

as a Taylor series,

, ,

⁄

,

,

⋯.

3.4

replacing χ in Eq. 3.2 with Eq. 3.4, and find that the polarization has a quasi-elastic part, the
Rayleigh scattering, and an induced term caused by phonons, which is the Raman term.

,

, ,

, ,

3.5

where Pind is

, ,

⁄

,

cos

∙

,

cos

∙

3.6

Eq. 3.6 can be further expressed as

, ,

⁄
cos

,

,

cos

∙

3.7

∙

The first cosine term is called the Stokes process, corresponding to 1-phonon creation. The
second cosine term, the anti-Stokes process, corresponds to 1-phonon annihilation. If the system
is in thermal equilibrium, the vibrational state populations are given by the Planck factor, so that
the anti-Stokes line is weaker than the Stokes line. Figure 3.7 shows the scattered spectrum for
three vibrational frequencies.

20

Figure 3.7 Raman spectrum of CCl4 (488 nm excitation), showing Stokes and anti-Stokes
spectra and the central Rayleigh scattering.32

3.4.1.1

Polarized Raman spectroscopy

The term

⁄

,

in Eq. 3.7 is known as the Raman tensor R. The intensity of

Raman scattering can be written as

∑|

∙

∙

|

3.8

where C is a constant, and ei and es are unit polarization vectors of incident and scattered light,
respectively. If this term is non-zero, it indicates that a phonon is “Raman-active” and will
appear in the spectrum. This can be viewed as a Raman selection rule.

21

The triply degenerate zone-center,

0, optical phonons of diamond have F2g symmetry33:

One longitudinal phonon (LO) and two transverse phonons (TO) propagate along q = ki-ks,
where ki and ks are the propagation direction of incident and scattered light, respectively. For
these phonons, the Raman tensors Rj34,35, referred to the cubic axes x||[100], y||[010], and z||[001],
are

0
0
0

0
0

0
0

0
0
0

0
0

0
0

0
0
0

0
0

0
for TO1
0
for TO2

for LO

where the matrix element d is a characteristic of the material. Specifically,

is the

change in the polarizability, α, with displacement of the two sublattices along q. For a diamond
single crystal, the Raman intensity in the backscattered direction normal to a (100) crystal
surface is a function of the angles of the incident and scattered light polarizations ei and es.
According to the selection rules, only two intensities, I||	 and I 	 can be observed when ei || es || [110]
or ei || [010] and es|| [100], respectively.

22

3.4.1.2

Stress measurements by polarized Raman spectroscopy

The triple degeneracy of optical phonons in diamond will be lifted by stresses which lower
the cubic symmetry. The sources of stress in diamond will be discussed in Chapter 9. The new
phonon frequencies are given by solutions of the secular equation, Eq. 3.9, which derives from
the lattice dynamical equations.36,37

2

2
2

2
2
with λ

ω

0 3.9

2
,

~ ⁄2

1, 2, 3, and ∆

, the stress-dependent Raman shift.

The ϵ are elements of the strain tensor referred to the cubic crystal axes, x || [100], y || [010], z
|| [100], and p, q, r are the deformation potential constants, related to the change in the spring
constant due to the stress. To simplify the solutions, we only consider the cases with high
symmetry: biaxial stress in (001), (110), and (111) planes and uniaxial stress along [100], [110],
and [111] directions.
The in-plane biaxial stress σ can be expressed as a matrix in Eq. 3.10,
1
∙ 0
0

0
1
0

0
0
0

3.10

where τis the stress amplitude. The strain tensor can be found by using Hooke’s law
where the
independent

,

are elements of the elastic compliance tensor. Inserting the numbers of the three
elements38 for cubic symmetry and those of p, q, and r

23

39

in Eq. 3.9, the Raman

shift of each stress-shifted phonon mode can be calculated, Appendix.

35,39,40

In addition, the

corresponding intensities can be calculated from Eq. 3.8, the Raman selection rules.
Therefore, using polarized Raman spectroscopy, the stress-shifted contribution to the Raman
tensor can be found. In other words, by measuring the Raman peak shift, the stress state in a
sample can be calculated. The results for different combinations of incident and scattered
polarizations for backscattering geometry, ki || ks || [001], are summarized in Table 3.1 and Table
3.2 from (001) and (110) surfaces, respectively. The Porto four-letter notation is used41: the first
two letters indicate the direction and the polarization of the incident light, and the last two give
the polarization and direction of the analyzed scattered light.

24

Table 3.1 Raman selection rules for backscattering from a (001) surface, with
||

, and

||

||

.35

Biaxial stress in a (001) plane or uniaxial stress along [001]
Measurement
geometry

TO1 (doublet || [100])

TO2 (doublet || [010])

LO (singlet || [001])

0

0

d2

0

0

0

0

0

d2

Biaxial stress in a (110) plane or uniaxial stress along [110]
Measurement
geometry

TO1 (doublet || [100])

TO2 (doublet || [010])

LO (singlet || [001])

d2

0

0

0

0

0

d2

0

0

For the case of biaxial stress in a (111) plane or of uniaxial stress along [111]
Measurement
geometry

TO1 (doublet || [100])

TO2 (doublet || [010])

LO (singlet || [001])

(1/3)∙d2

0

(2/3)∙d2

0

0

0

(1/3)∙d2

0

(2/3)∙d2

25

,

Table 3.2 Raman selection rules for backscattering from a (110) surface, with
||

, and

||

||

.35

Biaxial stress in a (001) plane or uniaxial stress along [001]
Measurement
geometry

TO1 (doublet || [100])

TO2 (doublet || [010])

LO (singlet || [001])

0

0

d2

0

0

0

0

0

d2

Biaxial stress in a (110) plane or uniaxial stress along [110]
Measurement
geometry

TO1 (doublet || [100])

TO2 (doublet || [010])

LO (singlet || [001])

d2

0

0

0

0

0

d2

0

0

Biaxial stress in a (111) plane or uniaxial stress along [111]
Measurement
geometry

TO1 (doublet || [100])

TO2 (doublet || [010])

LO (singlet || [001])

(1/3)∙d2

0

(2/3)∙d2

0

0

0

(1/3)∙d2

0

(2/3)∙d2

26

,

3.4.2

Micro-Raman spectral method

The Raman spectra presented later were measured by a Kaiser Optical Systems HoloProbe
Raman spectrograph, coupled to an Olympus BX-60 optical microscope with 100X objective and
532 nm laser excitation. The polarized Raman measurements used a fixed polarization for the
incident beam and a λ/2 plate to rotate the polarization of the scattered beam. Spatial resolution
was approximately 1.5 µm. The system has two interchangeable gratings: a low-resolution
grating with spectral range 0 to 4000 cm-1, and a high-resolution grating with range 1000 to 1600
cm-1. The instrumental resolutions for high- and low-resolution gratings are 2 and 5 cm-1,
respectively. The Raman spectrum from a nearly-perfect Type IIa natural diamond was used as a
reference, with peak position at 1332.4 cm-1 and a linewidth of 1.65 cm-1. Figure 3.8 shows the
background-subtracted polarized Raman spectra of the reference, taken with the high-resolution
grating. The apparent breakdown of the selection rules is a result of imperfect polarizers.

27

Type IIa diamond

Type IIa diamond
ki||ks||[001]

Intensity (arb. unit)

ei||es||[110]
ei||[110], es[-110]
xc =1332.4 cm-1
 = 1.65 cm-1

1310

1320

1330

1340

1350

Raman shift (cm-1)

ki||ks||[001]

(b)

1360

Intensity (arb. unit)

(a)

1310

ei||[010], es||[100]
ei||es[010]
xc =1332.4 cm-1
 = 1.65 cm-1

1320

1330

1340

1350

Raman shift (cm-1)

1360

Figure 3.8 Raman spectra of Type IIa natural diamond in [001] backscattering geometry. (a) For
ei || [110], only polarization of incident light parallel to the polarization of scattered light, es ||
[110], is allowed. (b) For ei || [010], the polarization of the scattered light must be perpendicular
to the polarization of the incident light, es || [100]. Due to a polarization “leak”, the measured
intensity is non-zero for forbidden polarizations.

3.4.2.1

Spectrum analysis

Analysis of the Raman scattering peak in diamond used the following process: (1) a fairly
large region about the peak is identified, (2) the background is subtracted and (3) the peak is
fitted, using a non-linear least squares method. The ranges analyzed are 1250-1410 cm-1 and
1310-1350 cm-1 for low- and high-resolution Raman spectra, respectively. In the range of interest,
it is sufficient to take a linear background, found by interpolation from the intensities at the two
ends of the range. The Raman linewidth contains a contribution from instrumental resolution.
The instrumental contribution is taken to be a Gaussian function whereas the Raman spectrum of
28

diamond is a Lorentzian function. The instrumental resolution function was found by measuring
the Raman spectra of a high-quality single crystal Si substrate and a Type IIa natural diamond,
which have well-established linewidths at room temperature. After deconvolution, the
instrumental Gaussian FWHM was found to be 2 and 5 cm-1, for high- and low-resolution
gratings, respectively. Accordingly, the background-subtracted modified spectra were fitted by a
Voigt function, a convolution of a Gaussian and a Lorentzian function.
3.4.2.2

Spatial Raman scanning

Lateral scans of the incident beam across a sample are performed with a motorized sample
stage, with spatial resolution 1.5 µm. Data were taken point-by-point, making sure that the
incident beam focal point was at the sample surface. Spectra were acquired with counting times
of approximately 10 sec. Scans were performed on diamond {100} and {110} surfaces in
backscattering geometry. For spectra taken from (001) planes, the incident laser beam is parallel
to the [001]dia axis, and only the scattered light propagating parallel to [001 ]dia direction is
collected, i.e, ki || ks || <100>dia. According to selection rules, Eq. 3.8, there are two ways to
arrange the input and output polarization: input and output polarizations are parallel to [110], ei ||
es || [110] or are perpendicular to each other, ei || [010] and es || [100], as shown in Figure 3.8. For
spectra collected from a (110) surface, ei || es || [110] or ei || [110] and es || [001]. For the CVD
diamond grown with the epitaxial lateral overgrowth (ELO) method, Raman lateral scans were
used to compare the Raman linewidth and frequency of non-overgrown and overgrown regions.

29

4 Chapter 4 Plasma-assisted heteroepitaxial growth
4.1 Properties of plasma
Plasma is a collection of ionized gas species, with coexistence of positive and negative
charges, created when sufficient energy is provided. It shows charge neutrality on a macroscopic
scale, preserved by the rearrangement of charges in the plasma to shield external and internal
electrostatic fields. Within the Debye length,	

, significant departures from charge neutrality

can occur,

743

⁄

⁄

4.142

(cm)

where Te is the electron temperature, expressed in electron volts eV (1eV=11600K) and ne is the
electron density (cm-3). For a typical microwave plasma discharge,
10 	

resulting in

0.02	

5	

and

. Figure 4.1 shows the relation between electron number

density and temperature.
4.1.1 Glow discharge
A glow discharge, a kind of plasma, is created at a reduced pressure when an electric
potential, DC or AC, applied across two metal electrodes exceeds a threshold, weakly ionizing a
low-pressure gas. In a glow discharge, the electrons, having much higher energy than ions,
≫

, are colliding with gas molecules and ionize them at lower temperature.

30

Figure 4.1 ne vs. Te for different plasmas.43
Figure 4.2 illustrates a DC glow discharge in a tube where the features are characterized by
luminosity, potential, field strength, space charge density and current density. The cathode region
comprises the Aston dark space, the cathode glow and the cathode dark space in the middle. The
negative glow is next to the cathode region. It has the highest current density, thus the highest
brightness. The Faraday dark space and the positive column are next to the glow on the anode
side. The latter is considered to be the main discharge because it generally extends to the anode
side, occupying most of the entire glow volume. In the anode region, there consists the anode
dark space and anode glow.
31

Figure 4.2 A glow discharge tube and its major characteristics.44

4.2 DC magnetron sputtering
Sputtering deposition, one of the physical plasma depositions which only involves a phase
transition at the substrate surface, is a process in which the positive ions, extracted from a
discharge, are accelerated by an electric potential, ranging from a few hundred to a few thousand
volts, toward to a neutral or negatively biased electrode, i.e. the target. Atoms are ejected after
the ions strike the target surface and the ejected atoms condense on the substrate. In magnetron
sputtering deposition, electrons in plasma are trapped near the target with a closed magnetic field
and the substrate is placed in proximity to the magnetron sputtering cathode. It consequently,
results in an enhancement of the initial ionization which allows plasma formation at rather low
32

pressure, several mTorr. At low pressure, voids incorporated into the growing layer are reduced.
For a conductive material a DC electric field is applied; otherwise, a RF (typically 13.56 MHz)
power supply is used. In this dissertation, two sputtering systems were used for sputtering
processes—the AJA and APX instruments. The AJA system was used exclusively for Ir epitaxy
to avoid contamination and the APX system was used for back and side coatings of Ir on a-ALO
substrate, described in Chapter 7.4.
4.2.1

Configurations of AJA sputtering system

The AJA sputtering system was acquired from AJA international. The system body contains
two chambers separated by an exchange valve (VAT), Figure 4.3, a load-lock chamber for
sample loading, and the main chamber where the sputtering takes place. Each chamber is
connected to a dedicated Pfeiffer turbomolecular pump (TMP), each of which is backed by a dry
roughing pump. The lowest base pressure in the main chamber is 2×10-8 Torr. A transfer arm
moves the sample holder from load lock to main chamber, allowing the main chamber to always
remain at low pressure.
This system is designed for upward sputtering, which tends to suppress particulate
contamination. The system is equipped with two DC and one RF sputtering guns located at the
bottom of the main chamber. The maximum powers of the DC and RF guns are 750W and 300W,
respectively. The sample plate is mounted on a shaft extending from the top plate and faces
downwards toward the sputtering guns. A variable speed rotating “propeller” engages the sample
plate or “puck”, allowing for substrate rotation during sputtering improving deposition
homogeneity. A motorized gate valve shutter is at the inlet of the TMP to the main chamber so
that the process pressure can be controlled. The sputtering gas used is ultrapure Ar (99.999%)
33

from a pressurized cylinder. The stainless steel gas line from the tank is always pressurized to
eliminate external contamination. Two quartz lamps behind the sample holder serve as a heater
with a maximum temperature at the sample plate of 850 °C. A thermocouple near the sample
plate monitors its temperature. Additional details are given in Chapter 7.2.

Figure 4.3 Schematic of AJA sputtering system.

34

4.2.1.1

Oxidation issue in AJA

A uniform discoloration of the Inconel sample plate was observed after sputtering. To
identify the material, Raman spectra were collected from the plate surfaces which suggested
transition metal oxides. Suspecting an air leak, a mass spectrometer helium leak detector was
connected to the outlet of turbo pump. A few extremely small leaks were identified and fixed.
The discoloration on the sample plate, however, was still present after heating to 850 °C in
several mTorr Ar; it did not appear after the plate was heated in a vacuum near 10-8 Torr. The
problem has not been fully solved, but it appears that impurities in the Ar may the source. The
discoloration did not appear to affect Ir epitaxy.

4.3 Chemical vapor deposition (CVD)
Chemical vapor deposition proceeds by a chemical reaction, or a set of reactions, near a
substrate surface. The CVD processes can be categorized into two types: thermal and activated.45
In thermal CVD, near thermal equilibrium, the chemical reaction of the gas flow is initiated on a
hot substrate surface. In activated CVD, far from thermal equilibrium, the reactions are
kinetically controlled. Thus, an external energy source, such as a hot filament or plasma, is
required to ionize the gas species. For plasma-assisted CVD (PCVD), the types of chemical
reactions on the substrate depend strongly on the properties of the plasma. CVD makes the
deposition possible, at relatively low temperatures, of a large variety of elements and compounds
in the form of both amorphous and crystalline layers.

35

4.3.1

Configurations of the CVD reactor

Figure 4.4 shows a schematic diagram of the microwave plasma assisted CVD reactor used
for heteroepitaxial diamond thin film growth. This reactor will be referred to as “the CVD
system “.46 The CVD system comprises four sections: (1) energy source (2) gas handling system
(3) water-cooled sample stage, and (4) computer automation.
4.3.1.1

Energy source of CVD reactor

The energy source is a 2.45 GHz microwave generator whose magnetron is capable of
outputting a maximum power of 7 kW (Cober SF6). A rectangular waveguide and coaxial
transition direct the microwaves to a cylindrical brass cavity. The cavity can be tuned to the
microwave frequency by a movable end plate and coupling can be varied with an electrostatic
probe. The cavity is operated in its TM013 mode, which creates a plasma above the substrate
surface in a hemispherical quartz dome, as shown in Figure 4.5.

36

Water 
chiller 

Figure 4.4 Schematic of the microwave plasma-assisted CVD (MPCVD) system for heteroepitaxial diamond growth.47

Excitation
probe

Figure 4.5 Illustration of the TM013 electromagnetic mode inside a cavity.48 Solid lines represent
electric fields; dashed lines the magnetic fields.
37

4.3.1.2

Gas handling of CVD reactor

The gas sources for the CVD system are ultrahigh purity hydrogen (99.9995%) and methane
(99.99%). Prior to starting a growth process, the reaction chamber, the quartz dome and the
stainless steel vacuum chamber are pumped down by a water-cooled Pfeiffer TMP through a
VAT gate valve. An Alcatel, Fomblin filled, oil pump serves as backing for the TMP and as a
process pump during growth. The reaction gases are mixed in a stainless steel manifold before
flowing into the main chamber; flow rates are controlled by individual MKS mass flow
controllers. A MKS type 635 throttle control valve interfaced to a pressure controller (MKS
651C) maintains the process pressure between 0-100 Torr. For safety, exhaust gases are purged
with compressed N2 gas at the outlet of the roughing pump before being exhausted.
4.3.1.3

Biasing set up and circuit

A water-cooled stainless steel sample stage keeps the substrate cool so that high microwave
powers can be used. The bias set up fixturing is shown in Figure 4.6. During biasing, an external
DC power supply (Kepco, 0-300V/0-200 mA) applies a voltage to the substrate. A grounded
tungsten ring immersed in the plasma serves as a return path for the bias current. Figure 4.7
shows the circuit for biasing. Two 50 Ω resistors are serially connected in the bias circuit to
suppress arcing and to monitor the current.

38

Figure 4.6 Schematic of bias set up in CVD reactor with: (1) Mo cap (2) Ir/a-ALO substrate (3)
Mo post (4) bias lead (5) Mo shield (6) Mo base plate (7) ceramic spacer (8) tungsten bias ring (9)
ceramic spacer (10) grounded stainless steel spacer (11) cooling stage.

Figure 4.7 Illustration of bias circuit.47

39

4.3.1.4

Computer controlling/monitoring system

All CVD processing is controlled by a PC running Labview, which also records the process
parameters in a data file at short time intervals. Prior to a growth run, a stage file is prepared with
input parameters: gas flow rates, process pressure, and stage duration. The typical growth
parameters monitored are given in Table 8.1. Temperature is measured by an optical pyrometer
through a window of the microwave cavity. The pyrometer is usually focused on the top surface
of Mo cap, with emissivity ε=0.35.
4.3.1.5

Substrate loading in CVD reactor

The substrate is first placed on the Mo sample post which is then screwed into the Mo base
plate attached to the bias lead; a Mo cap is placed on the substrate. The Mo plate rests on ceramic
spacers for isolation. The assembly is placed onto the cooling stage. A stand, which resides in the
bell jar below the microwave cavity, supports the cooling stage for easy access. Finally, the
entire fixture, including the cooling stage, is slid vertically and is bolted to the bottom of the
cavity. Since the system is not equipped with a load lock, sample loading is always performed in
air. Pump down from 1 atmosphere takes four hours to reach a pressure of 5×10-7 Torr.
Overnight pumping allows the system to reach a base pressure of 2×10-7 Torr.
4.3.2

Configurations of AsTex reactor

The AsTex CVD system, henceforth “the AsTex system”, was acquired from Seki
Technotron (Japan), Figure 4.8. Only the reactor body and microwave source were supplied; the
gas handling, vacuum system, and sample cooling stage were designed and constructed at MSU.

40

4.3.2.1

Energy source of AsTex reactor

The energy source is a 2.45 GHz microwave generator with a maximum output power of 1.5
kW. A triple-stub tuner impedance matches the source to the cylindrical cavity operated in its
TM013 mode. The plasma is confined to the region just above the substrate, which is mounted on
a variable-height stage. A quartz plate forms a window for the microwaves and provides a
vacuum-tight seal to the main reactor chamber.
4.3.2.2

Gas handling of AsTex reactor

An air-cooled Pfeiffer TMP pump is backed by an oil roughing pump (Oerlikon Leybold)
that exhausts the main chamber to a base pressure of 2×10-7 Torr. Mass flow controllers
(MKS1249) control the gas flow. Pressure is controlled by a pressure controller (MKS type 653),
with an interface (MKS type 651C), backed by the roughing pump. Exhaust gases are mixed
with compressed N2 before venting.

41

Figure 4.8 Schematic of AsTex system.31

42

4.3.2.3

Temperature measurement

The AsTex system is equipped with two types of optical pyrometers, located in different
positions, to monitor the sample temperature. A two-color pyrometer (Williamson), which is
sensitive to 2.2 and 2.4 µm IR radiation, is located above the substrate with a view of the
substrate through a quartz plate. Optical fibers are used to transmit the IR radiation to a detector;
a red-light laser beam is used to center the fibers on the substrate. The other pyrometer is a single
color type (Ircon) that views the substrate through a side port window.
4.3.2.4

Substrate loading in AsTex reactor

Access to the growth chamber is through a small rectangular door. Figure 4.9 shows the
reactor components relevant to diamond growth. A Mo sample post is threaded into the cooled
stage, a substrate placed on the post, and the Mo cap placed over the substrate and post. A Mo
shield resides above the cooling plate to protect it from the plasma. A corona ring placed over the
edge of the shield suppresses microwave leakage below the stage. The entire stage is translated
vertically to the growth position.

43

Figure 4.9 Illustration of the water-cooled sample stage in AsTex system.31

4.3.3

Diamond CVD methods
As mentioned in Chapter 2.4, CVD opens the possibility for diamond crystallization in a

thermodynamically metastable region. In early studies, formation of graphite and diamond were
found to simultaneously occur during CVD growth. It was realized that suppressing graphite
deposition was needed to improve diamond quality, which was achieved by preferential etching
of graphite by atomic hydrogen.49,50,51 Therefore, CVD diamond growth has subsequently been
conducted in a hydrogen-rich hydrocarbon gas mixture.
44

The model of CVD diamond growth considers the major reactants to be hydrogenated
carbon radicals and atomic and molecular hydrogen. Hydrogen molecules are dissociated to
atomic hydrogen by an external energy source, which also forms hydrocarbon radicals. The
hydrocarbon radicals attach to the carburized hydrogen-terminated substrate surface by forming
sp2 or sp3 chemical bonds, accompanied with the detachment of hydrogen molecules. The
formation of a diamond film takes place owing to the higher etching rate of sp2 carbon relative to
sp3 carbon by hydrogen. The primary chemical reactions are summarized in Eq. 4.2-4.4 and the
illustration in Figure 4.10, where methane is an example of a hydrocarbon molecule:
→2
→C

C
C H+	C

→

C

C

Figure 4.10 Illustration of model of diamond nucleation and growth on a substrate.45

45

4.2
4.3
4.4

Prior to diamond growth, the treatment of the substrate surface differs for two epitaxial
processes. A diamond substrate for homoepitaxy is prepared by acid cleaning and by plasma
etching in an O2/H2 mixture to remove impurities and surface damage. The treatment of a nondiamond substrate surface for heteroepitaxy is quite different and will be discussed in detail in
Chapter 5.4.
The first studies of diamond crystallization on non-diamond substrates, Si, Mo, and W
(carbide-forming) and Cu, Au (non-carbide forming), were performed52 in a thermal CVD
system. Later, diamond growth on hetero-substrates by microwave plasma-assisted CVD
(MPCVD) and hot filament CVD (HFCVD) was demonstrated.53,54 MPCVD is advantageous for
large-area deposition and high growth rates. In this dissertation, all diamond films were grown
by MPCVD.

46

4.3.3.1

Effects of growth parameters

The variables for CVD diamond growth are: substrate temperature, methane concentration,
process pressure, and microwave power density. To achieve high quality diamond epitaxial films,
all the parameters have to be optimized. We summarize below how these growth conditions
influence the outcome of a diamond film.
Substrate temperature depends mainly on plasma density which is controlled by absorbed
microwave power and process pressure. In some CVD systems, an external heater may also be
used. For homoepitaxial CVD diamond growth, the typical growth temperature is in a range of
700-1200 °C. In this temperature range, diamond growth is controlled by chemical kinetics
rather than by surface diffusion. Figure 4.11 shows that the growth rate Rg, below 1000 °C obeys
an Arrhenius relation,

⁄

, where

is the growth temperature and Ea is a

facet-dependent activation energy. Generally, {100} planes have the highest Ea, leading to the
slowest growth rate compared to other crystal planes.55,56,57 At temperatures below 700 °C58, the
growth rate is low, resulting in highly pitted or non-epitaxial diamond. High quality CVD
diamond growth exists only for a small range of growth parameters.
Hydrocarbon, e.g. methane, concentration is another major factor. It is usually denoted by
the flow rate ratio of methane to hydrogen. The diamond growth rate is proportional to methane
concentration over a significant range, Figure 4.12.

47

Figure 4.11 Diamond growth rate vs. growth temperature in 4% methane.59 The growth rate
follows the Arrhenius relation but saturates above 1000 °C.

Figure 4.12 Diamond growth rate vs. methane concentration at 770 °C (upper two points) and
800 °C (lower two points).31

48

As the total gas pressure increases, the plasma volume shrinks, accompanied by a shorter
mean free path. The plasma temperature increases owing to the higher possibility of particle
collisions. In MPCVD the electrons are accelerated by the microwave electric field but the heavy
ions cannot follow the frequency at pressures in the 1 to 101 Torr range. Thus, the plasma
temperature in this regime is represented by the electron temperature. As pressure increases
towards 102 Torr, both electron and ion temperatures increase, the plasma becomes hotter as
electrons and ions thermalize. Due to the low density of excited radicals, the growth rate is low
at low pressure. In the high pressure regime, the growth rate increases because of the higher
densities of ionized species. In a pressure regime between 150-200 Torr, homoepitaxial diamond
rates up to 40 µm were observed.60
The plasma volume is also microwave power dependent; it expands as microwave power
increases. Growth rate generally increases with higher microwave plasma density. It was
observed that increasing the plasma density from 65 to 125 W/cm3 led to a growth rate increase
for diamond homoepitaxy from 3 to 8.5 µm/hr.59 Later work extended power densities from 300
to 1000 W/cm3, with growth rates of 20 to75 µm/h.61

4.3.3.2

Growth anisotropy: the α parameter

Diamond growth textures can be parameterized by the diamond growth parameter,α, defined
as62

α

⁄

√3

49

4.5

where V100 and V111 are the growth rates in the [100] and [111] directions. Figure 4.13 shows the
shapes of diamond crystals for different α values. It is clear that, for α=1, the fastest growth is
along [111] direction. Thus, the (111) plane will eventually vanish. For α=3, on the other hand,
the growth rate along [100] direction becomes the fastest. Then, a diamond octahedron forms.

Figure 4.13 Shapes of diamond crystals for different values of α, the growth parameter. The
arrow indicates the fastest growth direction for each case.63
The dependence of α on temperature and methane concentration has been studied, Figure
4.14. However, the actual diamond growth mode is much more complicated, requiring other
growth parameters to understand fully facet formation.64

Figure 4.14 α vs. methane concentration at different temperatures.63

50

5 Chapter 5 Diamond nucleation and heteroepitaxy
5.1 Nucleation
Nucleation is a prerequisite to crystal growth. It is a process whereby a substance undergoes
a phase transition initiated by forming a small ensemble of atoms or molecules of the new phase,
called a nucleus, within the parent phase. For example, in water, small nuclei, the ice phase, form
in the liquid phase as the temperature approaches 0 °C from above. To understand the
transformation, classical nucleation theory (CNT)65,66,67,68 considers the free energy G of the
system, treating the nucleus as a bulk core surrounded by an interface. When nucleation takes
place, the change in Gibbs free energy, shown in Eq. 5.1, is the sum of a bulk term (first term)
and a surface term (second term);

∆

∙

∙

5.1

where n is associated with the number of atoms in a cluster, ϕ (=ΔG/Δn) is the affinity of the
transformation associated with the change of chemical potential, σ is the surface energy and A is
the surface area. Figure 5.1 shows a plot of free energy change ΔG vs nucleus radius r, where r*
is the radius of the critical nucleus. In the first regime (r < r*), the nucleus formation from the
free atoms or molecules is not thermodynamically stable, so the small nuclei in the parent phase
appear and decay continuously. Once some nuclei exceed the critical nucleus size, the growth of
nuclei leads to a decrease in ∆ . After the radii of nuclei are larger than
phase transition now is energetically favorable, i.e., a spontaneous process.

51

,∆

0; that is, the

Figure 5.1 Change of free energy (∆ ) vs. radius of nucleus according to CNT, where r* is the
radius of the critical nucleus. The first order phase transition becomes energetically favorable
when the nucleus radius is beyond

.69

Since the creation of a nucleus implies the formation of an interface at the boundary of a
new phase in a uniform substance, homogeneous nucleation may be difficult. However,
heterogeneous nucleation, which is considered as a surface catalyzed process starting at
preferential sites such as surfaces or impurities, is more common. In terms of free energy change,
the free energy barrier is lowered more than that of homogenous nucleation owing to wetting,
shown in Eq. 5.2.

∆

where

2

3

∆

∙

5.2

⁄4, and θ is the contact angle of the nucleus with respect to

the core surface for the case of a liquid. Heterogeneous nucleation is essential for heteroepitaxial
thin film growth as described in Chapter 5.3.

52

5.2 Crystal growth modes
If there is no interdiffusion between the substrate and the deposited material, thin film
epitaxial growth is classified into three modes, according to the morphology of the first few
monolayers: island, layer by layer, and layer plus island growth.70 The modes are shown in
Figure 5.2.

Figure 5.2 Illustrations of three thin film epitaxial growth modes as a function of surface coverage θ in terms of monolayers (ML): (a) island growth, or Volmer-Weber mode, (b) layer-plusisland growth or Stranski-Krastanov mode, and (c) layer-by-layer growth or Frank-van der
Merwe mode.70
In island growth, also known as Volmer-Weber (VW) mode, adatom cohesive force is
higher than surface adhesive force. Hence, the growing material prefers to form islands on the
substrate surface which then coalesce in a lateral direction. In terms of surface energy, this mode
can be expressed as

∗

, where

,

and

∗

are the surface energies of deposited

layer, substrate, and interface, respectively. On the other hand, when the adatom cohesive force

53

is lower than the surface adhesive force, the material tends to wet the substrate surface
completely with the first few monolayers. This is the Frank-van der Merwe (FM) mode or layer∗

by-layer growth, where the relation of surface energies is

. The layer plus island

growth, or Stranski-Krastanov (SK) mode, is a combination of VM and FM modes. The growth
of first few monolayers proceeds by the FM mode until it reaches a critical thickness, which
depends on the strain and the chemical potential in the film. Then, the VW mode becomes
energetically favorable. The initial expression of surface energies, therefore, starts as
, and eventually turns into

∗

(VW mode) as

∗

∗

increases with the deposition

thickness due to the stress.

5.3 Heteroepitaxial diamond growth
5.3.1

Epitaxy

Epitaxy is the process of single crystal layers depositing on a single crystal substrate of
which one crystal plane serves as a template for the crystal structure of the deposit. This can be
described in terms of Miller indices of the crystal planes and directions. For example,
(001)d<001>d || (001)s<001>s means that a (001) plane of the deposit resides on a (001) plane of
the substrate where the <001> direction of deposited crystal is parallel to the <001> substrate
direction. In many cases, the coincident growth planes are identical and of low index, such as
(001) and (111) for cubic systems and (0001) for the hexagonal system. For cubic systems,
twinning in particular may easily occur on (111) planes due to the geometric symmetry, reducing
the crystal perfection in epitaxial films. As a consequence, (100) epitaxy is preferred for many
materials including diamond.

54

When the deposited layer and the substrate are the same material, this process is specifically
called homoepitaxy. In contrast, heteroepitaxy describes the process where the deposited layer
and substrate are different materials. Because of the different lattice constants of epitaxial layer
and substrate in heteroepitaxy, the lattice mismatch f is an important parameter for choosing
suitable substrates. It is defined by

⁄ , where

and

are the lattice constants

for deposited layer and substrate, respectively. If the crystal structures of deposited material and
substrate differ, the mismatch is calculated from the atomic spacing of the contacting planes of
deposited layer and substrate, instead of lattice constants. Lattice mismatch is one of the most
important criteria for choosing a suitable substrate in heteroepitaxial growth.
Although homoepitaxy is prevalent in single crystal diamond growth, the lateral areas of
CVD crystals have been limited by small, high-cost HPHT diamond substrates. Recently, a
method of making tiled clones was developed to enlarge diamond crystal areas.71 The alternative
to homoepitaxy is diamond heteroepitaxy, which represents another approach for overcoming the
substrate size limitation by depositing diamond on wafer-size non-diamond substrates. A number
of substrates have been used to achieve relatively large-area and high quality diamond growth.
Substrate criteria for heteroepitaxial diamond growth will be discussed in Chapter 5.3.3.
5.3.2

Definition of diamond heteroepitaxy

To make a distinction from the sparsely faceted diamond grains that may appear on nondiamond substrates, we adopt the following criteria as a working definition of diamond
heteroepitaxy:
(1) Area of a single-facet continuous diamond film to be at least 1 mm2;

55

(2) Crystal structure and the epitaxial alignment of diamond with the substrate confirmed by xray diffraction with XRD linewidths less than 1°; and
(3) sp3 bonding confirmed by polarized Raman scattering, resulting in a single frequency peak
at 1332.4

10 cm-1.

This definition distinguishes a heteroepitaxial film from highly-oriented diamond (HOD),
usually produced by deposition on Si wafers. HOD occurs by coalescence of µm-sized grains
followed by a process of selective growth, in which certain grain orientations overgrow others.
The best HOD films have an XRD mosaic spread generally greater than 1o.
5.3.3

Substrate criteria for diamond heteroepitaxy

Due to the stringent conditions for heteroepitaxial growth, the choice of a suitable substrate
is an important consideration. The important factors for substrate selection are listed below:
(1) Crystal structure. Since the single crystal substrate serves as a template for the deposited
layer in heteroepitaxy, a crystal structure similar to the deposited material is advantageous,
but not absolutely necessary. Substrates with cubic structure, such as Si and cubic oxides,
have been commonly used
(2) Lattice parameter. A small lattice mismatch f, typically less than 10%, is desired. The
lattice mismatch induces strains at the interface which can be accommodated by the
formation of misfit dislocations. A larger lattice mismatch gives rise to greater strain at the
interface and a higher density of misfit dislocations. The misfit dislocations at the interface
can evolve into different kinds of dislocations. A discussion of dislocation types will be
presented in Chapter 6.1. Because of the short C-C sp3 bond in diamond, all substrates have
larger lattice constants than diamond.
56

(3) Surface energy. To form a flat and continuous film in epitaxial growth, the FM growth
mode is preferred, which requires similar surface energies of deposited layer and substrate.
A large difference in surface energy inhibits nucleus formation. For a moderate difference
of surface energy, the VW mode, with a higher density of coalescence boundaries, is
energetically favorable. This opens opportunities for dislocation generation at coalescence
boundaries. Diamond has a rather high surface energy, 5.3 J/m2 for the (111) plane and 9.2
J/m2 for the (100) plane.38 For comparison, Si has surface energy 1.23 J/m2 for the (111)
plane and 2.13 J/m2 for the (100) plane.72 Consequently, creating uniform diamond
nucleation on a non-diamond substrate is a challenge for diamond heteroepitaxy.
(4) Thermal expansion coefficient α. For CVD diamond growth, the growth temperature is
well above room temperature. Cooling from the growth temperature to room temperature
results in stress arising from the differential thermal contraction between film and substrate.
The large thermally-induced stress can lead to fracture of epitaxial film and substrate. To
minimize this thermal stress, a substrate with thermal expansion coefficient matching the
deposited material is advantageous. This is non-trivial, owing to the small thermal
expansivity of diamond. The thermal expansion coefficients of popular substrates are
shown in Table 5.1.

57

Table 5.1 Thermal expansion coefficients of some substrates used in diamond heteroepitaxy (at
300 K).73,74,75,76,77,78
Material

Diamond

Silicon

Iridium

SrTiO3

MgO

Sapphire

α (10-6/K)

1

2.56

6.4

9.4

10.4

5.3

(5) Physical and chemical stability. A substrate should have a melting point much greater than
diamond growth temperatures (700-1200oC) with a single, stable structure. High stress
fracture strength is an advantage. For diamond heteroepitaxy the substrate should have low
carbon solubility to avoid the formation of carbide phases which may impede epitaxial
alignment79,80. The substrate can, however, make a substantial chemical bond with carbon.
(6) Substrate area and finish. Areas greater than 1 mm2 with smooth, epi-polished surfaces are
advisable. In some cases, one or more thin epitaxial buffer layers can be used to make a
transition between the bulk substrate and the heteroepitaxial material.
Due to the unique properties of diamond and the aggressive CVD growth environment, no
ideal non-diamond substrate exists. It is useful to divide diamond heteroepitaxy into two
categories: (1) deposition onto a bulk single crystal substrate and (2) deposition onto a substrate
with one or more epitaxial buffer layers. The latter is more complicated due to the requirement of
multiple epitaxial processes. As a practical matter, large-area and high-quality diamond
heteroepitaxy has only been realized on substrates with an epitaxial Ir buffer layer.

58

5.3.3.1

Heteroepitaxial diamond growth on bulk substrates

Silicon substrates were initially used for diamond growth and diamond (001) heteroepitaxy
was attempted early. However, true heteroepitaxial diamond on Si was not observed. Rather,
highly oriented (HOD) material was obtained, as mentioned in Chapter 5.3.2. Due to the small
lattice constant of diamond, 0.357 nm, the lattice mismatch between silicon and diamond is 52%.
It was suggested that diamond nucleation on silicon substrates involved a ß-SiC transfer layer,
with lattice mismatch of 22%.81,82,83 By carefully controlling the growth conditions, others
observed the direct deposition of diamond on Si.83,84,85 Despite many attempts, an XRD
linewidth less than 1o was never observed.
The properties of cubic boron nitride (c-BN) are similar to diamond. It has a similar crystal
structure, 1.3% lattice mismatch, and similar surface energy, 4.8 J/m2 for the (111) plane. Single
crystal c-BN is itself difficult to produce, so (111) oriented particles embedded in a tantalum disk
or a platinum plate have been tried as a substrate for diamond (111) heteroepitaxy.86,87 Although
deposition of a well-coalesced diamond epitaxial film was observed, the lack of c-BN substrates
makes its use for diamond heteroepitaxy impractical.88
The use of metal substrates with small lattice mismatch to diamond such as nickel and
platinum has been studied. Ni, with misfit 1.3%, is known as an effective solvent-catalyst metal
for HPHT diamond crystallization.89 However, its high carbon solubility and strong catalytic
activity lead to the appearance of a graphite interlayer which forms immediately in a CVD
environment, destroying diamond orientation. The formation of a nickel carbide interlayer forms
under some growth conditions, leading to textured diamond deposition. Certain processing

59

methods led to orientation improvement, but only HOD was observed with its orientation derived
from the carbide layer, not the metal surface.79,80
Pt, with lattice misfit of 11% to diamond, is not expected to form a carbide. Small diamond
crystals have been reported on Pt at an early stage of growth leading to HOD deposition on the Pt
(111) surface.90
5.3.3.2

Heteroepitaxial diamond growth on Ir

Since the first demonstration of diamond (001) epitaxial growth on its (001) surface4,
iridium has emerged as the best buffer layer for diamond heteroepitaxy. The crystal structure of
Ir is FCC with a lattice constant of 0.384 nm, resulting in a 7% lattice mismatch to diamond.
Iridium has a very high melting point, 2450 °C, no crystal phase transitions or carbide formation,
and the lowest carbon solubility (by weight) in the platinum group.91
In the first use of Ir for heteroepitaxy, Ohtsuka et al.4,5 sputtered a 500 nm Ir (001) epitaxial
layer on 10 10 mm2 (001) MgO substrates at 750 °C. Prior to diamond growth, the Ir surface
was treated by bias enhanced nucleation (BEN). As a result, highly-oriented pyramidal diamond
crystals were formed on the BEN exposed area which coalesced to a film of thickness 1.5 μm.
This result stimulated a great deal of subsequent research on diamond heteroepitaxy.
To ensure the reproducibility of surface preparation and to enlarge the substrate area,
commercial epi-polished strontium titanate (STO) was used for Ir deposition, principally by two
groups.6,7,8,9 The lattice constant of STO is 0.391 nm, with lattice mismatch to Ir of 1.8%. The Ir
layer was deposited by electron beam (e-beam) evaporation at temperatures above 800 °C. The
XRD rocking curve linewidth of Ir (002) was 0.17°.6 XRD pole figures showed an epitaxial

60

relation (001)Ir[100]Ir || (001)STO[001]STO. STO substrates are reduced at high temperatures and
blacken; they have low mechanical fracture strength. Sapphire, Al2O3, henceforth ALO, on the
other hand, has good chemical stability at high temperatures and is available in large-area wafers
with excellent crystallographic quality. Electron-beam evaporated Ir on a-plane sapphire (a-ALO)
was studied by Dai et al.8,10 Although ALO is hexagonal, its atomic spacing along [0001]
direction is a good match to the Ir lattice in the [011] direction, with lattice mismatch 1.1%. The
epitaxial relation is (001)Ir || (1120)ALO with [011]Ir || [1100]ALO and [011]Ir || [0001]ALO. The Ir
(002) rocking curve width was comparable with Ir/STO, 0.21°. In this dissertation, we have used
Ir/a-ALO as the substrate of choice for diamond heteroepitaxy.
Ir, with additional buffer layers on silicon, has been explored as another alternative for
diamond heteroepitaxy, principally because of the low thermal expansivity of silicon. For
example, a calcium fluoride (CaF2) interlayer was deposited on a silicon substrate followed by an
epitaxial Ir layer92,93, but CaF2 was not a practical choice due to its high thermal expansion
coefficient and low thermal stability. Later CaF2 was replaced with an yttria-stabilized zirconia
(YSZ) buffer layer and the crystallographic relationship (001)[110]Ir || (001)[001]YSZ ||
(001)[110]Si reported.11

5.4 Enhancement of diamond nucleation
Due to high surface energy, diamond nucleates sparsely on a non-diamond substrate, with
nucleation density 103-105 cm-2, mostly at defects.52 A surface pretreatment prior to diamond
deposition is always necessary to enhance nucleation density. Scratching94, seeding94, electrical
biasing95, covering96, coating97, ion implantation98, pulsed laser irradiation99 and carburization100
are methods used to realize nucleation enhancement. Various enhancement mechanisms
61

proposed were: (1) seeding effect; (2) minimization of surface energy on sharp convex surfaces;
(3) breaking of surface bonds or dangling bonds at edges; (4) strain; (5) carbon saturation at
edges; (6) surface cleaning by removal of oxides; and (7) formation of non-volatile graphitic
clusters.101 Initially, the first two methods were the most efficient in nucleating diamond on
silicon with nucleation density limited to 106-108 cm-2. An improvement, known as bias
enhanced nucleation (BEN)95, increased nucleation densities up to 1010 cm-2.
5.4.1

Bias enhanced nucleation (BEN)

Substrate pretreatment by BEN is a process of ion bombardment. It is implemented on a
substrate surface held at a negative potential in a hydrogen/methane plasma. The accelerating
electric field and presence of methane lead to the bombardment of the substrate with positively
charged hydrocarbon radicals. The diamond nucleation density was found to increase with the
bias current density, the ion flux on the substrate surface.47,102 The major variables in BEN are
the substrate temperature, methane concentration, bias voltage, and the bias duration. The first
few BEN experiments were performed on a Si substrate biased at –60 to -100V in 15 Torr
hydrogen plasma with 2 to 40% CH4 with a substrate temperature of 850 to 900 °C. After 5 min
growth in 0.5% CH4, polycrystalline diamond growth was observed.95,103,104
5.4.1.1

Proposed mechanism of BEN

For BEN on Si, the ion bombardment leads to: (1) ion subplantation, (2) deposition of an
amorphous carbon layer, (3) surface diffusion, and (4) formation of a SiC interlayer. Figure 5.3
shows a proposed BEN mechanism appropriate to Si. Hydrocarbon radicals are formed in the
plasma above the substrate surface which then impinge on the substrate surface and diffuse to
stable sites105,106,107 resulting in the deposition of an amorphous carbon layer.108,109 The energetic
62

Figure 5.3 Illustration of BEN mechanism.103
bombardment also roughens the substrate surface. The hyperthermal (1-103 eV) hydrocarbon
species are implanted110,111,112 just below the substrate surface, a process called subplantation.
Owing to preferential etching of sp2 bonds by energetic atomic hydrogen, sp2 graphitic surface
carbon is eliminated or transformed to sp3-rich clusters.113 Hydrogen-terminated surfaces prevent
63

the formation of further sp2 bonds. The remaining sp3-rich clusters are believed to be the
precursors of diamond nuclei. Excessive methane concentration leads to the formation of sp2-rich
structures while excessive acceleration of ions destroys sp3 structures. As a consequence,
obtaining optimal nucleation density requires striking a balance between methane concentration
and bias voltage.
BEN on Si does not fully explain the BEN process on Ir. The bias conditions for Ir and its
surface modification are significantly different from Si. The most important distinction is that no
diamond nuclei or diamond growth have been observed on Ir immediately after BEN. The
mechanism of BEN on Ir is, in fact, not fully understood. We discuss experimental results for Ir
BEN and the ensuing diamond growth in Chapter 5.4.1.3.

64

5.4.1.2

Bias and plasma chemistry

A typical optical emission spectrum of a CH4-H2 plasma is shown in Figure 5.4 which
reveals the main active species are atomic hydrogen, with emission wavelengths for Hα (656 nm)
and Hß (486 nm), and many hydrocarbon signals. The simple hydrocarbons can be classified into
two categories by their bonding types: C1 (431nm) containing σ bonds, such as CH3, CH2 and
CH, and C2 (516 nm), composed of π bonds, such as C2H2, C2H and C2. The concentration of
each active species near the substrate is a function of hydrogen plasma pressure and methane
concentration. At moderate pressure, 100 to 102 Torr, the concentration of atomic hydrogen, and
Hα and Hß emissions, increases with pressure. The Hß /Hα ratio, representative of the plasma
electron temperature, however, decreases with pressure due to reduction of the mean free path of
gases. On the other hand, the concentration of atomic hydrogen decreases with increasing
methane concentration114,115, Figure 5.5, resulting in a slower etching rate of sp2 carbon.
Therefore, a low methane concentration was initially used for high quality CVD diamond epitaxy.
In BEN, owing to the acceleration of electrons in the plasma sheath, the degree of ionization
near the substrate surface increases, giving rise to the ignition of a bright DC glow discharge
above the substrate surface, the secondary plasma.116,117,118,119 The DC glow indicates a change
of plasma chemistry and the concentrations of active species near the substrate surface. It was
discovered that highly oriented diamond nucleation on Si requires a glow discharge that covers
the entire substrate surface. Figure 5.6 shows that all concentrations of active species increase
with bias and eventually saturate at a high voltage. The ratios of Hß /Hα and C2/CH behave
similarly as well.116,120,121 It was found that diamond crystal quality could be correlated with the
emission intensities of CH and C2.122 Diamond grown under conditions with a strong CH signal
had good crystal quality whereas poorer diamond formed under conditions giving a maximized
65

Figure 5.4 Optical emission spectrum of a CH4-H2 plasma at 30 Torr and 2% CH4. Ar was used
as an actinometer to estimate the concentration of atomic hydrogen. The wavelengths of
emission lines of C1 and C2 type species are indicated.114

Figure 5.5 Intensity of Hα emission vs. methane and oxygen flow rates, representing the
relationships between atomic hydrogen, methane, and oxygen concentrations. The methane
concentration is 9% with a hydrogen flow rate of 100 sccm and methane flow rate of 10 sccm.115
66

C2 signal.122 Despite preferential formation of sp2 bonds at high C2 content, the increased atomic
hydrogen concentration near the substrate surface etched sp2 bonds more rapidly.121 Thus, there
is a competition between the deposition of a sp3-rich layer and substrate surface etching.120 On
the other hand, as methane concentration increases during BEN, the electron temperature
increases and the C2/CH ratio decreases. Then, saturation of Hß /Hα and C2/CH occur at higher
voltage or higher pressure. Plasma chemistry also varies with vertical position above the
substrate during BEN. From the plasma edge to the substrate surface, the concentration of atomic
hydrogen decreases and becomes constant. In contrast, the electron temperature and the ratio of
C2/CH increase and saturate as the substrate is approached.114
In summary, BEN modifies the production of C2 components and atomic hydrogen near a
substrate surface. In addition, the high electron temperature further enhances C2 formation. As a
result, the carbon-saturated clusters with both sp2 and sp3 bonds easily form at the stable sites on
substrate surface. Then, by preferential etching by atomic hydrogen, the weak sp2 bonds will be
removed. The remaining stable sp3-rich carbon clusters are the precursors for the formation of
diamond nuclei.

67

(a)

(b)

(c)

(d)

Figure 5.6 Concentrations of (a) atomic hydrogen (b) two types of hydrocarbons (c) Hß/Hα and
(d) ratios of C2/H and CH/Hα vs. bias voltage at 15 Torr and 2% CH4.121

68

Figure 5.7 Concentrations of (a) atomic hydrogen (b) Hß/Hα and (c) ratios of C2/CH vs. position
relative to substrate surface in vertical direction, where the solid triangles and hollow
rhombohedra represent the data points without and with bias voltage under conditions of 30 Torr
and 2% CH4.114

69

5.4.1.3

Bias enhanced nucleation on iridium

BEN on Ir is typically carried out with a negative bias of 150 to 350 V applied to the
substrate, and 2-5% methane in hydrogen. The duration of BEN depends on the bias voltage and
the methane concentration. Bias times more than 30 min are often used to achieve nucleation
densities on diamond of order 1011 cm-2.
BEN on Ir leads to Ir surface modification and deposition of a thin amorphous carbon
layer.9,31,123,124,125,126,127 It was discovered that the Ir surface was etched into furrows during
BEN126 and that the orientation of the furrows changes from <110>Ir to <100>Ir with increasing

Figure 5.8 Plan-view SEM images of BEN-treated Ir surfaces with increasing methane
content.127
70

methane content127, Figure 5.8. The Ir furrows were partly covered by a layer which appears
bright in SEM images, Figure 5.9. The bright areas occur in clusters named “domains”. 128

Figure 5.9 Plan-view SEM image of BEN-treated Ir surface showing Ir furrows, Ir balls, bright
spots and the domains, where the scale of the images inside the circles is 100 nm.129

Figure 5.10 Low-resolution SEM image of BEN-treated Ir surface showing the bright areas referred to as domains.128

71

The Auger spectrum of the bright layer is similar to amorphous carbon.129 According to xray photoelectron spectroscopy (XPS) measurements, this layer contains partially disordered sp2
carbon, C-H bonds formed in hydrogen-rich plasma and sp3 bonding in an amorphous tetrahedral
carbon structure, like diamond.130,131,132 The depths of Ir furrows were reported as 2-3 nm126,129
and dependent on bias conditions. Conflicting reports of domains heights were given: in one
account, domains were 8.4 nm higher than its vicinity129; others

133

found that domains resided

in 1 nm depressions.
Domains were confirmed to be the precursor region for diamond growth128,129,132,134 as
shown in Figure 5.11. Domain coverage increases with bias duration to a point:128,129 however,
100% coverage by domains has not been achieved. The mechanism of domain expansion during
bias has not been explained.

Figure 5.11 Plan-view SEM images of (a) domain formation on Ir after 30 min BEN and (b) 15
min diamond growth in the domain.129
Qualitatively different Ir surface modification after BEN has been extensively studied.
These studies8,9,31 used a low bias voltage, -150 V, and low methane concentration, 2%. For
72

short-term bias, 20 min, furrows along <110> and dots were observed. The biased Ir surface was
also highly covered by the carbon layer, showing bright SEM regions covering 75% of the
surface. Unlike the irregular domains, the carbon patches in Figure 5.12 are rectangular with
edges along <110>.

1 m
Figure 5.12 Plan-view SEM image of Ir surface after 20 min bias.9
After 60 min bias, Ir dots forming a nearly hexagonal array were observed with a density
1011-1012 cm-2, Figure 15.13(a). The lateral size of an Ir dot is 5 nm with a mean dot to dot
spacing of 15 nm. The coverage of the carbon layer was about 90%. The corresponding highresolution transmission electron microscopy (HRTEM) cross-sectional image, Figure 5.13(b),
shows faceted Ir pillars with a mean spacing 14.6±0.5 nm covered by a bright amorphous carbon
layer. In these images, the mean lateral size and height of Ir pillar is 8 and 4.5 nm, respectively.

73

(a)

(b)

Figure 5.13 (a) Plan-view SEM image and (b) HRTEM cross-sectional image of BEN treated Ir
surface after 60 min.31
Unlike diamond growth on Si, no Ir-C interfacial layer and no crystalline diamond
crystallites on Ir immediately after bias were observed with HRTEM.123,124,135 A diamond
signature was, however, clearly seen by x-ray photoelectron diffraction analysis.135,136 This
suggests that the size of diamond nuclei must be very small, possibly sub-nanometer. Short
interrupted growth experiments, following biasing, showed very early stage emergence of
diamond. After 90s of growth, diamond was observable but crystal facets had not fully
developed, Figure 5.14(a). The HRTEM image in Figure 5.14(b) clearly shows the diamond
crystallites emerging from the Ir interface, indicating that the diamond nucleated on the sides of
the Ir nanopillars.

74

(a)

(b)

Figure 5.14 (a) Plan-view SEM image and (b) HRTEM cross-sectional image of 90s diamond
growth on a 60-min biased Ir surface. In (b) each white line is the (111) plane of Ir (bottom) and
diamond (surrounded by blue dashed line) crystals.31
As a result of high coverage of carbon following biasing, coalescence of individual grains
began soon after growth commenced, leading to the formation of a partially connected film with
a flat top surface, as shown in Figure 5.15 after 10 min growth. Figure 5.16 shows a comparison
of diamond surfaces of two groups after short growth periods. In the present work, after 1h
growth, diamond thin films were well-coalesced, forming a flat and continuous film, with few
visible boundaries. Other groups, as shown in Figure 5.16(c, d), found cubic or rectangular

75

Figure 5.15 Plan-view SEM image of diamond surface after 10 min growth following 60 min
biasing.
diamond crystallites with (001) top surfaces. Given similar growth conditions, listed in Table 5.2,
the coalescence rate will mainly depend on carbon surface coverage and the resulting diamond
nucleation density. Higher diamond nucleation density leads to an earlier continuous thin film.
Table 5.3 lists the bias conditions used by different groups for comparison.

76

(a)

(b))

(c)

(d)

Figure 5.16 Heteroepitaxial diamond surface after 20 min growth (a)47 and (b)127. Diamond
surface after 60 min growth (c)47 and (d)127.

77

Table 5.2 Comparison of growth conditions for samples shown in Figure 5.16.
Pressure
(Torr)

CH4 (%)

N2 (ppm)

Substrate
temperature (°C)

Reactor type

Bauer et al.127

22.5

1

30-50

650

MPCVD

Golding et al.47

18

1

--

670

MPCVD

Table 5.3 Bias conditions for groups studying diamond heteroepitaxy on Ir.
Pressure
(Torr)

CH4 (%)

Bias voltage
(-V)

Substrate
temperature (°C)

Duration
(min)

Reactor type

Bauer et al.127

22.5

0.5-10

250-320

700

45

MPCVD

Chavanne et al.132

15

4

300

700±50

60

MPCVD

Washiyama et al.13

115

2

--

940

90

DC CVD

Stehl et al.137

--

3

300

850

--

MPCVD

Golding et al.8,9,47,31,

18

2

150

710

60

MPCVD

78

6. Chapter 6 Epitaxial lateral overgrowth (ELO)
6.1 Dislocations
A real crystal contains imperfections due to impurities and other defects. The latter can be
categorized into four groups according to their dimensionality: vacancies or self-interstitial
atoms are point defects (0-D), dislocation lines are linear defects (1-D), grain boundaries and
stacking faults are planar defects (2-D) and voids and precipitates are considered as volume
defects (3-D). Dislocations are the most important issue in epitaxial growth. Crystalline quality is
usually compromised by dislocation propagation into the growing layer from the interface.
Especially for heteroepitaxy, the dislocation density typically is 1010 cm-2, due to the lattice
mismatch and the different chemical properties of the substrate and deposited material. Moreover,
although some interfacial dislocations are generated to release stress, a high density of
propagating dislocations usually leads to a high intrinsic stress state, which can cause film
cracking.
Dislocations are classified into two types: edge and screw. They can be visualized as follows.
Consider an extra half-plane of atoms (ABCD) inserted into a perfect crystal, Figure 6.1(b). The
adjacent atoms then are displaced to each side by one lattice spacing. The line DC, thus, is a
positive edge dislocation, noted as . If the half plane is inserted into the lower part of crystal,
the line DC is a negative edge dislocation,

. If the ABCD half-plane is inserted in the same

place but with neighboring atoms displaced to one side of the half plane relative to the other side,
the AB direction, the line DC is a screw dislocation. The helicity of such a dislocation can be
identified by drawing a circle around the dislocation line DC, looking along DC. If the helix

79

advances one plane, it is a right-handed screw dislocation, as shown in Figure 6.1(d). Most of the
dislocations in crystals are of mixed type with the coexistence of edge and screw displacements.

Figure 6.1 Illustration of dislocation geometry: (a) a perfect single cubic lattice as reference;
distorted crystal lattices with a dislocation line DC which is a positive edge type in (b); a lefthanded screw type in (c); and a right-handed screw type in (d).138
In a heteroepitaxial system, with lattice mismatch between growth material and substrate,
coherent growth only survives in the first few layers of deposition due to the enormous stress in
the film. As the thickness reaches a critical thickness, edge dislocations, called misfit
dislocations, form at the interface to release the stress. The critical thickness depends on elastic
strength and is typically 2-3 nm. Because of the rigid diamond lattice, misfit dislocations form
80

directly at the diamond-substrate interface, Figure 6.2. Because dislocations can move along
glide planes, they may propagate upward into the epitaxial layer, forming threading dislocations.
A positive dislocation can be annihilated only by interacting with its negative counterpart, or
may terminate in a closed loop.

diamond

Ir

2 nm
Figure 6.2 HRTEM image at the interface between diamond and Ir. The circled area by the blue
dashed line is the diamond grain. The blue and white lines represent the diamond (111) and Ir

81

T

(111) lattice planes, respectively. A misfit dislocation formed at the interface, indicated by

.31

6.2 ELO method
In the ELO process, a substrate patterned by a mask layer is used. The epitaxial layer, then,
grows vertically from the seed area and laterally over the mask layer. This selective area growth
was invented in the 1960’s for GaAs homoepitaxy in small areas.139,140,141 It was discovered in
1988 that dislocations were blocked in ELO in GaAs homoepitaxy.142 This resulted in a nearly
dislocation-free lateral overgrown GaAs layer. Since then, various ELO methods have been
widely studied for III-V semiconductors, principally GaAs and GaN. In 1997, Usui et al.143
developed an ELO process for GaN heteroepitaxy and reduced the dislocation density by three
orders of magnitude. Figure 6.3 shows the concept of ELO for blocking threading dislocations.

Figure 6.3 Illustration of an ELO process. (a) A thin epi layer serves as a substrate, where the
solid lines generated from the substrate represent the threading dislocations. (b) A mask, e.g.
SiO2, is deposited and patterned by lithography. (c) Material overgrows the mask which blocks
the threading dislocations during regrowth. The threading dislocation density is greatly reduced
in the overgrown regions.
82

6.3 Types of ELO on GaN
6.3.1

Facet-initiated ELO (FIELO)

Usui et al.143 developed the FIELO method for hydride vapor phase epitaxy method, shown
in Figure 6.3. A thick GaN film, 26 μm, was grown on a 2-in diameter sapphire substrate. The
window stripes lie along <1120> of the GaN layer with a period of 7 µm and 1-4 µm wide SiO2
stripes serve as the mask. {1101} facets formed on the side of the GaN stripes at the beginning
of the growth, and the facets gradually coalesced above the SiO2 mask. This method lowered the
dislocation density by 3 orders of magnitude compared to the conventional GaN layer.
6.3.2

Different masking materials

SiO2 was first used as a mask for a GaN ELO process.143 However, the threading
dislocations, especially around the mask, propagated laterally into the overgrown GaN, and
merged at the center of the mask which was the coalescence region.144 In the center of the mask,
the c-axis directions of 2 adjacent GaN lattice planes were found to tilt toward the boundary by
2°, but they tilted ~1° away from boundary at the edges of the mask.145 Kawaguchi et al. chose
tungsten as the masking material.146 They studied the growth rates of different axes for <1120>
and <1100> GaN stripes.
Sone et al., later, discovered the ELO GaN layer did not contact the W layer. Instead, a
triangular void formed above the mask.147 Besides, the rocking curve widths of (0004) planes
were ϕ-independent for ELO GaN with a W mask and were smaller than the corresponding
widths of ELO GaN with a SiO2 mask, where ϕ is the azimuthal angle between the stripe and
rotation axis in an ω-scan. The c-axis tilting contributed to broadening when the stripes were
83

aligned parallel to the rotation axis with a SiO2 mask. It was inferred that the large interfacial
tension between the SiO2 layer and GaN caused c-axis tilting. Transmission electron diffraction
supported the argument that the void between the W mask and GaN prevented interfacial tension,
suppressing c-axis tilting.148
Tomiya et al. found that, with a SiO2 mask, c-axis tilting could be suppressed in GaN ELO
with plasma-enhanced CVD grown SiO2 vs. e-beam evaporated SiO2. In addition, they
discovered less interfacial tension between ELO GaN using a SiNx mask.149
6.3.3

PENDEO epitaxy

Zheleva et al.150 invented the method of PENDEO, a method without a contacting mask. As
shown in Figure 6.4(b), the GaN/AlN/substrate was etched to form alternating columns and
trenches along the <1101> direction with widths of 3-5 µm and 3-40 µm, respectively. The freestanding laterally grown GaN layers coalesced above the trenches of the substrate with a large
horizontal-to-vertical growth rate ratio, Figure 6.4(c). The resulting dislocation density was 4-5
orders of magnitude lower than in the GaN/AlN/substrate.

84

Figure 6.4 Illustration of PENDEO epitaxy. (a) A GaN epitaxial layer grown on a 6H-SiC
substrate with AlN buffer layer serves as a substrate for the PENDEO process. (b) The GaN
epilayer is plasma-etched to form alternating columns and trenches. (c) Regrowth of GaN
columns has a large lateral-to-vertical growth rate ratio.150

85

6.3.4

Air-bridged ELO

As shown in Figure 6.5, GaN was dry etched into a ridge-stripe pattern along <1100>. The
bottoms of the trenches and the sidewalls of the GaN ridges were covered with a thin Si3N4 mask.
In the initial stage, the GaN stripes grew vertically and then extended laterally over the mask
from the newly formed {1120} facets. A c-axis tilting was seen in a split XRD rocking curve,
but the tilt angle was about an order of magnitude lower than that of ELO GaN with a SiO2 mask.

Figure 6.5 Illustration of air-bridged ELO: (a) a GaN/sapphire substrate; (b) GaN layer partly
plasma etched to form ridges; (c) regrowth of GaN and (d) coalesced GaN overgrown layer in
the center of masked region. In (b), except for the top surfaces of GaN ridges, other areas are
covered by the Si3N4 mask.151

86

The reduced c-axis tilting was attributed to the air gap which removes the interfacial tension
between the Si3N4 layer and ELO GaN.151
6.3.5

Cantilever epitaxy

To avoid impurity contamination from masking materials, i.e. SiO2, and reduce the residual
stress caused by thermal and lattice mismatch between GaN layer and substrate, Si (111), 6HSiC (0001)Si, and basal-plane sapphire substrates were fabricated via photolithography and
reactive ion etching techniques to form a grooved structure prior to GaN growth152, Figure 6.6(a).
GaN was then deposited on the exposed substrate surfaces. Owing to the high lateral-to-vertical
growth rate ratio, the GaN layers on two adjacent terraces shielded the trenches. Therefore, they
coalesced laterally before the GaN overgrew the trenches. Flat GaN layers were achieved on the
sapphire and 6H-SiC patterned substrates, but a very low lateral-to-vertical growth rate ratio was
observed in GaN ELO on Si. The rocking curve linewidths of overgrown GaN on different
substrates were comparable to those of GaN grown on the corresponding non-patterned
substrates. The c-axis tilt was found to be in the direction perpendicular to the groove orientation.
For sapphire and 6H-SiC substrates, dislocation densities in the GaN layer on the substrate
terrace were three orders of magnitude lower than a typical GaN layer, and it was one order of
magnitude further lower in the ELO GaN.

87

Figure 6.6 Illustration of cantilever epitaxy. (a) Substrates 6H-SiC, Si and Al2O3, are plasma
etched to form trenches (etched area) and terrace (unetched). (b) GaN layers grow on substrate
terraces.

6.3.6

Direct lateral epitaxy

A low nucleation density, 4 104 cm-2, of GaN in the non-masked region was obtained by a
low temperature buffer treatment on a patterned sapphire substrate with a SiO2 mask.153 With the
high growth temperature and high pressure ratio of V/III content, the lateral-to-vertical growth
rate ratio was increased to 2. The sparse GaN grains coalesced and formed a GaN stripe with a
flat (0001) surface. The GaN layer further extended laterally over the mask region because of the
high lateral growth rate. This method was called direct lateral epitaxy. In the overgrown region,
the rms roughness of the GaN (0001) surface was as low as 0.3 nm indicating the absence of
threading dislocations.

88

6.4 Types of ELO on diamond
Due to the aggressive chemical and thermal growth environment, ELO on heteroepitaxial
diamond has not been widely explored. Ando et al. first demonstrated the ELO idea in
heteroepitaxial diamond without a growth mask.12 The (001)-oriented heteroepitaxial Ir was first
deposited on a MgO substrate and treated by bias enhanced nucleation followed by e-beam
lithography to pattern the surface. The patterned Ir surface was then ion beam etched by Ar to
damage the non-masked region. Diamond (001) selectively grew from the prepared Ir layer, and
overgrew the damaged Ir area. They established a minimum diamond nucleation density needed
to grow specific areas.
Washiyama et al.13 further showed the results of coalesced diamond stripes along <100> and
<110> directions. Owing to the facet-dependent growth rate, the spacing for <100> and <110>
stripes were 20 and 10 μm, respectively. The Raman linewidth of overgrown diamond gradually
decreased to a minimum at the coalescence boundary, indicating a lower defect density.
Compared to the diamond nucleation region, with a Raman linewidth of 10-12 cm-1, the
linewidth of the overgrown diamond was reduced to 5 cm-1. However, tensile strain was
observed both in the overgrown and non-overgrown diamond.

89

Figure 6.7 Steps of the diamond ELO process by Ando et al. and Washiyama et al.12
Bauer et al.154 deposited a very thin, 10-20 nm, Ir heteroepitaxial layer as a percolating mask
layer on a (001)-oriented CVD diamond layer on a Si substrate and a (001)-oriented HPHT Ib
diamond substrate. The porous Ir layer formed a mesh with 10-200 nm holes. For a 13 nm Ir
layer, the coverage was about 70%. Diamond islands penetrated the Ir layer and coalesced into a
(001) facet for the 2 types of substrates. However, overgrown diamond showed larger rocking

90

curve widths and Raman widths relative to those of non-overgrown diamond, indicating a high
level of microstrain attributed to an increased dislocation density. Furthermore, a macroscopic
tilt between the crystal lattice of Ib HPHT diamond substrate and overgrown CVD diamond layer
in the off-axial direction was found.

91

7. Chapter 7 Epitaxial Ir growth on a-plane sapphire
This chapter describes the Ir DC sputtering process and the characterization of epitaxial Ir
(001) growth on a-plane (1120) sapphire (a-ALO). Owing to its cubic structure, its relatively
small mismatch to diamond and its special chemical properties, the epitaxial Ir (001) buffer layer
on various substrates serves as the best template for heteroepitaxial CVD diamond (001) growth,
cf. Chapter 5.3.3.2. The crystallographic quality, as indicated by the mosaic spread of the Ir layer,
is minimized by optimizing growth conditions. The primary characterization method is singlecrystal x-ray diffraction (XRD), Chapter 3.3. The Ir surface topography is revealed by atomic
force microscopy (AFM) scans, Chapter 3.2.

7.1 A-plane sapphire (a-ALO)
We focus mainly on iridium deposition on a-ALO substrates with different miscuts, i.e.,
surfaces at small angles to the a-plane. Commercial a-ALO 2 inch (5 cm diameter) wafers with
high crystallographic quality are available at relatively low cost. Table 5.1 shows that the thermal
expansion coefficients of sapphire are a reasonable match to diamond, better than MgO and STO,
an advantage in decreasing the thermally-induced stress in the diamond film. In contrast to other
materials with a cubic structure used for diamond substrates, sapphire has a hexagonal crystal
structure with lattice constants: a=0.476 nm and c=1.299 nm, shown in Figure 7.1. Sapphire is
thermally stable, with a high melting point at 2040 °C. No crystallographic phase transitions
occur between room temperature and temperatures used for diamond growth, generally below
1200 °C.

92

Figure 7.1 Hexagonal crystallographic unit cell of sapphire. The a-plane is shaded.

7.1.1

Epitaxial relation between Ir and a-ALO

For Ir heteroepitaxy on a-ALO, the lattice mismatch between Ir and sapphire is best
understood by their atomic spacings, rather than by their lattice constants. Figure 7.2 is an aplane projection of oxygen arrangements in a sapphire unit cell, showing the epitaxial relation of
Ir atoms to an oxygen-terminated ALO surface. The spacing of O atoms in the [1100] direction,
or m-axis direction, is 0.275 nm which matches well the Ir spacing in its [110] direction, 0.272
nm. Along the [0001] direction, or c-axis of sapphire, the O spacing is 0.433 nm, giving rise to a
atomic registration ratio of 3:2.

93

Figure 7.2 Illustration of proposed epitaxial relationship of Ir and a-ALO, where the small and
large spheres represent the O and Ir atoms, respectively.

7.2 Ir sputtering procedure
a-ALO 2 inch diameter wafers with 4 different miscut angles were used as substrates: (1)
nominally no miscut angle, denoted as 0-a-ALO (2) miscut angle of 1° rotated about c-axis (1Ca-ALO) (3) miscut angle of 1° rotated about m-axis (1M-a-ALO) and (4) miscut angle of 0.7°
rotated about m-axis (0.7M-a-ALO). All wafers were specified to be one-side epi-polished and
0.5-mm thick. A flat on one side was oriented with its normal to the c-axis. Type (1) was
obtained from Jiaozuo City Crystal; others were supplied by Substrates Technology. Type (1)
substrates were found to have finite miscut angles, generally less than 0.3°, with random axis
rotations.

94

7.2.1

Sapphire preparation

Prior to the Ir deposition, as-received wafers were processed in the KMF cleanroom.
Macroscopic residues, such as dust particles, were removed by solvent cleaning in IPA with
ultrasonic agitation, followed by blow-drying in N2 to avoid any surface stains. This was
followed by a high-temperature air anneal in an alumina tube furnace at 1300 °C for 24 hours for
surface reconstruction. Temperatures were ramped up and down at 2.7 °C/min. The annealed
wafers had strongly adhering particulates requiring another round of solvent cleaning. Figure 7.3
shows the surface topography, after annealing, of the four types of miscut a-ALO wafers studied.

3.00 nm

6.00 nm

(a)

(b)

0.00 nm
4.00 nm

(c)

0.00 nm
4.00 nm

(d)

<1100>
0.00 nm

0.00 nm

<0001>

Figure 7.3 AFM images of annealed surfaces of (a) 0-a-ALO (b) 1C-a-ALO (b) 1M-a-ALO and
(d) 0.7M-a-ALO wafers.
95

The surface reconstruction of a-ALO led to the development of surface terraces. They were
generally irregular, with height differences of 4-6 unit cells in 1C-a-ALO wafers but with height
differences of 2-3 unit cells for the others. The spacing and heights of terraces agreed with the
miscut angle obtained by XRD orientation. Moreover, in Figure 7.3, the surface topography of
annealed a-ALO is strongly dependent on the miscut angle and its rotation axis, as noted in
previous studies.31,47 The 1C-a-ALO shows a tooth-like surface with a largest mean surface
roughness, 0.87 nm. 1M-a-ALO and 0.7M-a-ALO show stripe-like features after annealing. The
mean roughness increases with miscut angle: 0.41, 0.60, and 0.48 nm for a 0-a-ALO, 1M-a-ALO
and 0.7M-a-ALO, respectively. The topography of a reconstructed surface also depends on
annealing temperature and its duration.10,155 Figure 7.4, for example, compares the surface
structures of 1C-a-ALO annealed at different temperatures. The tooth-like features are more
distinct if the a-ALO surface is annealed at higher temperatures, in Figure 7.4(b).
(a)

6.00 nm

(b)

<1100>

0.00 nm

<0001>

Figure 7.4 AFM images of 1C-a-ALO surface annealed at (a) 1300 °C and (b) 1500 °C for 24h.

96

7.2.2

Sample mounting and loading

Prior to Ir sputtering, a cleaned sapphire wafer was mounted in a sandwich structure
composed of a 3.5 inch dia Inconel sample base plate or “puck” and a top 3.5 inch dia Mo
capture ring. The capture ring had a 1.8 inch aperture and a 2-inch-dia recess that pressed the
sapphire wafer against the puck. The structure was secured with stainless steel screws and lock
washers. The substrate and mount were assembled in the cleanroom and transported to the AJA
sputtering system with the protection of clean Al foil. The assembly was inserted into the loadlock of the sputtering system, pumped down to the mid-10-7 Torr range, and transferred to the
main chamber whose minimum pressure was 2-3 10-8 Torr.
7.2.3

Ir DC sputtering

Before beginning sputtering, the Ar gas line was flushed for 15 min to reduce residual
oxygen remaining in the gas lines. During this time, power supplies for the instrumentation were
turned on and allowed to stabilize. The AJA system provides a computer interface for executing
a sequence of operations and it allows the generation of a “stage” file. The stage file is created
before each sputtering run; it can be saved as a record and reused for future runs. The steps for a
typical Ir sputtering run are shown in Table 7.1. and were generated by the PHASEIIJ program
which then executes the sequence.

97

Table 7.1 Typical steps for Ir sputtering. The pressure is set at 30 mTorr in the first step to ignite
the RF plasma prior to substrate cleaning.

Step

Pressure
(mT)

Power
(W)

Ar flow
rate
(sccm)

Temperature
(°C)

Deposition
Duration
rate
(min)
(nm/min)

Ramping substrate
temperature

30

0

15

25-850

6

RF bias cleaning on
sapphire wafer

3

20

15

850

2.5

DC Ir sputtering (1)

3

20

15

850

1.2

10

DC Ir sputtering (2)

3

50

15

850

2.4

10

DC Ir sputtering (3)

3

75

15

850

3.6

10

DC Ir sputtering (4)

3

100

15

850

4.8

47.5

After the system was slowly cooled to room temperature, the sample puck was transferred to
the load-lock. The load-lock was then vented with N2 gas, the puck removed, and wrapped in
aluminum foil for transfer to the cleanroom. The Ir surface must be protected as even a small
scratch will generate lines of defects when diamond is overgrown. Finally, the wafer was
characterized by XRD to confirm Ir structural quality.
An important attribute of the AJA system is its ability to rapidly heat a substrate, only 6 min
to reach 850 °C from room temperature. This suppresses contamination from outgassing by
allowing the walls of the main chamber to remain cool. During heating, the Ar pressure was kept

98

at 30 mTorr, rather than under vacuum, for rapid RF plasma ignition and to allow the puck to
equilibrate with the surrounding gas.
7.2.3.1

Bias cleaning on a-ALO

Despite careful cleaning, sapphire substrates invariably have surface chemical residues,
adsorbates, and very small particulates. The AJA system is equipped with a cleaning system that
surrounds the electrically-isolated substrate with an RF plasma for an in-situ plasma cleaning just
prior to sputtering. The plasma cleaning was found be essential for good Ir (001) heteroepitaxy
on a-ALO. Without the plasma cleaning, sputtering under the same conditions led to Ir (111)
growth. Figure 7.5 shows the dramatic difference between Ir grown on (a) high-temperature
plasma-cleaned sapphire surface and (b) no cleaning. Note the complete absence of Ir (111) in
(a). Figure 7.6 shows AFM images of the a-ALO surface before and after plasma cleaning.
Sparse nanoparticles can be seen in (a) which cannot be removed by standard solvent cleaning
whereas they are absent in (b).

99

10

1

10

10

10

7

10

4

Ir (400)

4

(with bias cleaning)

(b)

(without bias cleaning)

Ir (222)

10

24-nm Ir on
1C-a-ALO

ALO (220)

7

Ir (200)

10

(a)

ALO (110)

10

Ir (111)

Intensity (conts)

10

1

10
20

40

60

80

2 (degree)

100

120

140

Figure 7.5 XRD diffraction patterns of 24-nm Ir on 1C-a-ALO substrates sputtered at 3 mTorr,
100W and 850 °C: (a) with plasma cleaning at 3 mTorr, 30W and 850 °C for 5 min and (b)
without cleaning prior to the Ir sputtering.
5.00 nm

(a)

(b)

0.00 nm

5.00 nm

0.00 nm

Figure 7.6 AFM images of a-ALO (a) before plasma cleaning and (b) after plasma cleaning at 3
mTorr, 30W and 850 °C for 5 min. The sparse bright spots in (a) are nanoparticles which cannot
be removed by standard solvent cleaning.
100

Excessive plasma cleaning can damage the substrate surface and cause deterioration of the
crystal quality of the Ir epitaxial layer. As shown in Figure 7.7, the (002)Ir XRD rocking curve
linewidth has a strong positive correlation with cleaning duration, but only slightly changes with
bias power, having a minimum at 20W. Figure 7.8 shows the Ir surface topography after
deposition on an excessively cleaned (10 min) substrate resulting in a discontinuous Ir film. As a
consequence, only a short exposure to the plasma is sufficient. Therefore, the substrate surface

0.36

0.60
0.55

(a)

(002)Ir linewidth (degree)

(002)Ir linewidth (degree)

was cleaned at 30W for 2.5 min in a standard process.

3 mT
30 W

3 mT
2.5 min

10

15

0.34

0.50

0.32

0.45

0.30

0.40

0.28

0.35
0

(b)

5

10

15

20

25

20

25

30

Bias power (w)

Bias duration (min)

Figure 7.7 Linewidth of (002)Ir XRD rocking curve vs. (a) bias duration and (b) bias power.

101

27.00 nm

0.00 nm

Figure 7.8 AFM image of 300-nm Ir on a-ALO plasma cleaned at 3 mTorr, 30W and 850 °C for
10 min.

7.2.3.2

Ir DC sputtering rate

The sputtering rate is generally a function of process pressure and power as shown in Figure
7.9 for Ir sputtering in the AJA system. The rate monotonically increases with power, but
surprisingly, is independent of pressure at fairly low Ar pressures. At higher pressures, arcing
due to the small gap between the sputtering gun’s ground shield and Ir target occurred above 20
mTorr. There is a relatively short distance (about 10 cm) between the 2 inch diameter sputtering
target and the 2 inch substrate, so the deposition is highly directional.
For the Ir sputtering process described in Table 7.1, the initial sputtering rate was relatively
slow, 1.2 nm/min, to suppress the formation of non-epitaxial grains, and then it was ramped up
gradually to 4.8 nm/min to shorten the processing time.

102

(b) 6
5
4

Ir sputtering rate (nm/min)

Ir sputtering rate (nm/min)

(a)

3 mT
25 C

3
2
1
0
0

20

40

60

Power (W)

80

100 W
25 C
5

4

0

100

5

10

15

Pressure (mT)

20

25

Figure 7.9 Ir sputtering rate vs. (a) sputtering gun power and (b) Ar pressure in the AJA system
measured at room temperature.

7.3 Results for Ir (001) epilayers
7.3.1

Ir x-ray diffraction (XRD)

A typical XRD ω-2θ scan is shown in Figure 7.10. Only diffraction peaks from Ir (200) and
the underlying a-ALO (1120) are visible. Traces such as these were independent of the sapphire
miscut angle. Epitaxial alignment was confirmed by ϕ-scans of the (111) Ir reflections. It was
found previously that small amounts of Ir (111) were present when electron-beam evaporated Ir
or sputtered Ir without plasma cleaning was deposited. Sensitivity to miscut angle was also seen
previously. Thus the reproducible Ir growth can be attributed to plasma cleaning and the rapid
heating provided by the AJA system. A typical XRD rocking curve is shown in Figure 7.11. In
over 20 Ir sputtering runs, the Ir (200) linewidth for films prepared under the conditions shown

103

7

10

6

10

5

10

4

10

3

10

2

holder

10

Ir (400)

8

ALO (220)

10

Ir (200)

9

ALO (110)

Intensity (conts)

10

20

40

60

80

100

2 (degree)

120

140

Figure 7.10 XRD diffraction pattern of 300-nm Ir on highly-oriented a-ALO. Small peaks
originate from the small fraction of Cu Kβ radiation in the incident x-ray beam.

7

Ir (200)

5
Gaussian
fit

4

6

Intensity (10 counts)

6

3
2
Width: 0.35

1
0
22

23

24

(degree)

25

Figure 7.11 X-ray rocking curve of Ir (200) with Gaussian fit.
104

26

in Table 7.1 was 0.35 0.04°. This is somewhat larger than the best films prepared previously by
electron-beam evaporation, which were as low as 0.21°. Figure 7.12 shows that the linewidth of
the Ir (200) reflection for a 150 nm Ir film decreases with increasing growth temperature. Due to
limitations of the AJA quartz heaters, the maximum substrate temperature was limited to 850 °C.

Linewidth(degree)

0.55

Linewidth
of Ir (200)

0.50
0.45
0.40
0.35
0.30
700

750

800

850

Temperature (C)

Figure 7.12 Ir (200) rocking-curve linewidth vs. substrate deposition temperature.

105

7.3.2

Ir surface topography on a-ALO

The surface topography of 300-nm Ir films sputtered at 850 °C substrate temperature
depends on the sapphire miscut angle. The topography of the substrate is not necessarily
transferred to the Ir at this thickness, as can be seen in Figure 7.13. This sensitivity differs from
earlier studies with Ir sputtered in a different deposition system.47 Ir on highly-oriented a-ALO
shows cross-like features, whereas Ir on substrates with larger vicinal angles has star-like
aggregations. Note that the highest mean surface roughness, 1.1 nm, occurs on the 1C-a-ALO.
2.50 nm

(a)

6.30 nm

(b)

0.00 nm

0.00 nm

5.50 nm

4.00 nm

(c)

(d)

<1100>

0.00 nm

0.00 nm

<0001>

Figure 7.13 AFM images of 300-nm Ir sputtered by the process in Table 7.1 on a (a) 0-a-ALO (b)
1C-a-ALO (c) 1M-a-ALO and (d) 0.7M- a-ALO.

106

3.50 nm

(a)

4.30 nm

(b)

0.00 nm
5.00 nm

0.00 nm

(c)

3.60 nm

(d)

<1100>

<0001>
0.00 nm

0.00 nm

Figure 7.14 High-resolution AFM images of 300-nm Ir on a (a) 0-a-ALO (b) 1C-a-ALO (c) 1Ma-ALO and (d) 0.7M-a-ALO.
The mean surface roughness of Ir on a 0-a-ALO, 1C-a-ALO and 1M-a-ALO substrates is
0.49, 1.03, and 0.78 nm, respectively. Compared to the bare a-ALO surface, the Ir surface
roughness increases by 0.3-0.4 nm on a-ALO substrates with the larger vicinal angles, but it does
not change for Ir on a highly-aligned a-ALO substrate. The formation of star-like features
enhances surface roughness. Figure 7.14 shows AFM images of Ir surfaces at higher resolution.
It appears that there is a competition between c-axis and m-axis directional growth; when they
exist in nearly equal amounts star-like features are more likely to be formed, as seen in Fig. 7.14
(b).

107

Experiments were also carried out on unannealed a-ALO substrates with Ir sputtered to a 24
nm thickness. As seen in Figure 7.15 (a), Ir developed textures parallel to the m- and c-axes of aALO with a small mean roughness of 0.2 nm on highly-oriented sapphire. The textures aligned
with the c-axis in (b) the 1M miscut, and then coalesced laterally, with a roughness of 0.52 nm.
The star-like features, meanwhile, started to develop on both substrates as high steps in AFM
images.
1.20 nm

(a)

(a)

(b)

3.00 nm

(b)

0.00 nm

0.00 nm

Figure 7.15 AFM images of 24-nm thick Ir on unannealed (a) 0-a-ALO and (b) 1M-a-ALO.
As a result of strong Ir-Ir bonding, the surface diffusion of Ir atoms is very low, leading to
textured, rough surfaces. The diffusion rate of Ir changes with sputtering parameters such as
pressure, power and substrate temperature, and is the origin of the different surface features. In Ir
films prepared in the AJA system, the Ir surface topography is, somewhat surprisingly,
independent of growth temperature in the range studied but more dependent on the sputtering
pressure. At 10 mTorr Ar pressure, Ir prefers to aggregate on the a-ALO surface. The surface, as
a result, was composed of spherical Ir nanograins with large mean surface roughness near 2 nm,
Figure 7.16. Despite the granular appearance, the Ir grew epitaxially at this pressure, with a
108

rocking curve linewidth comparable to results for films grown below 3 mTorr. There is clearly a
need for more careful investigation of the relationships between sputtering parameters, XRD
linewidths, and Ir topography.
10.00 nm

0.00 nm

Figure 7.16 AFM image of 150-nm Ir sputtered at 10 mTorr, 100W and 850 °C.

7.4 Ir-ALO wafer processing
Following Ir deposition, the 2 inch wafer was inspected under a high-power optical
microscope for growth defects and particulates. The entire wafer was coated with a layer of
photoresist to protect the Ir surface and then exposed to UV light through a specially-designed
low-resolution transparency film mask for reasons noted below. Prior to PR developing, the
wafer was diced with a diamond cut-off wheel under low-light conditions. Dicing resulted in 9
nominally 10 10 mm2 substrates per wafer. To identify ALO orientation, the chips had actual
dimension 9.8 10.0 mm2, with the long dimension along the c axis. Since the wafer was
mounted on the vacuum chuck of the dicer, the sapphire was not completely cut through. It was
subsequently easily broken into individual chips with slightly roughened edges. After developing
109

the PR, the chips were cleaned and ultrasonicated in a dilute Alconox detergent solution and
rinsed in DI water.
Sapphire substrates are highly insulating even at temperatures where the BEN process is
used. During BEN, a continuous current must flow from the top of the Ir surface to the Mo post
below the substrate. Therefore, continuity between top and bottom substrate surfaces was
produced by depositing a continuous Ir coating that connected the substrate’s major surfaces by
conducting edges. A thin 60 nm film of Ir was sputtered in the APX sputtering system with the
substrates at room temperature. Three separate Ir depositions were needed, one that coated the
back surfaces of the ALO chips, and two more that connected the front and back surfaces via two
edges. For back coating, the substrates simply faced down on the sample holder followed by two
rounds of side coating, where a special aluminum holder was used as shown in Figure 7.17. The
reason for the special PR mask was to protect the epitaxial Ir on the front surface except for a
small contact channel to one of the Ir-covered edges. Since the APX system was highly
contaminated, it was necessary to increase the Ar flow rate to a few tens sccm to avoid a highly
resistive film. Tests with an ohmmeter gave a few ohms DC resistance across 1 cm. Finally, the
protective PR layer was removed in solvent.

Figure 7.17 Illustration of sample holder for substrate side coating.

110

8. Chapter 8 Heteroepitaxial growth of diamond
In this chapter we describe a robust procedure for growing heteroepitaxial diamond films on
Ir epilayers by CVD. A method for achieving highly efficient bias enhanced nucleation (BEN)
on 1 cm2 substrates is the most crucial step in the overall process. To achieve high nucleation
density of diamond on Ir, a multitude of issues associated with BEN were addressed, many of
which are influenced by small details of plasma and system geometry. Growth of thick diamond
is discussed along with the physical characterization of the resulting diamond single crystal films.
Topics include structural perfection, surface morphology, and stress state.

8.1 Fixtures for biasing
Figure 8.1 shows the bias set up including cooling stage, sample holder and the bias ring.
Growth is carried out under the same geometry. The bias ring, which is supported by Mo posts,
and the cooling stage are grounded. The bias lead is electrically isolated by a fused quartz tube.
During bias, a negative voltage is applied by a DC power supply to the bias lead. The Mo sample
post, the base plate, Ir/a-ALO substrate and cap are maintained at bias potential. The Mo base
plate is isolated from the cooling stage by ceramic spacers. The shield plate is electrically
isolated by ceramic spacers and is at a floating potential. With microwave plasma present,
application of a bias voltage, typically between -150 and -250 V, forms a DC glow above the cap
and substrate surface.

111

plasma

Figure 8.1 Fixturing for the CVD reactor: (1) Mo cap (2) Ir/a-ALO substrate (3) Mo post (4)
bias lead (5) Mo shield plate (6) Mo base plate (7) ceramic spacer (8) tungsten bias ring (9)
ceramic spacer (10) stainless steel plate (11) grounded cooling stage.

8.2 Procedure for diamond growth
In Figure 8.2, a typical procedure for CVD diamond growth is shown. It consists of a short
hydrogen plasma cleaning, a carburization step where methane in introduced into the system, the
BEN step, and the growth step. Table 8.1 gives the parameters used to produce 550 nm diamond
substrates on an epitaxial Ir layer on sapphire. The reactor was modified from its previous
configuration by the introduction of a water-cooled stage to allow higher microwave power
during biasing and growth while maintaining a low substrate temperature. The detailed
configuration of the CVD reactor was described in Chapter. 4.3.1.

112

Growth

BEN

Hydrogen cleaning
Carburization

Temperature

Bias voltage
Methane concentration
Pressure
0

20

80

260

Time (min)

Figure 8.2 Time plot of the standard procedure of heteroepitaxial CVD diamond growth.

Table 8.1 Detailed conditions for CVD diamond thin film growth, with temperature measured on
the Mo cap by a single-color pyrometer.
H2 plasma
cleaning

Carburization

Bias

Growth

Pressure (Torr)

18

18

18

18

H2 (sccm)

300

300

300

300

CH4 (sccm)

0

6

6

3

Temperature
(°C)

670

680-670

710-730

670

Duration (min)

10

10

60

180

113

The diamond growth carried out previously in this reactor was restricted to 5 mm square
SrTiO3 (STO) substrates, with a growth region 3.5 mm diameter. Scaling the process to 10 mm
square sapphire substrates had not been successful. A major problem was the inability to provide
uniform nucleation with the larger substrates over a diamond growth area 8 mm in diameter. The
larger area requires a higher bias current to maintain the same current density. Two ways to
accomplish this are by (1) better confinement of current paths and (2) increased negative bias
potential. Higher potentials lead to plasma instabilities, breakdown, and arcing. These issues
were addressed by small changes in the fixture geometry and by additional shielding. The
changes were subject to constraints such that the substrate temperature and plasma composition
at the substrate be maintained at the conditions for optimal diamond growth.
Sapphire substrates are superior to STO in a number of ways. They are mechanically
stronger, have better crystallographic quality, are available as very large wafers, and are
generally less costly. STO has one advantage however: it develops a low electrical conductivity
when processed at high temperatures due to oxygen loss. This is not the case for ALO which is
not easily chemically reduced and maintains its insulating ability to temperatures well above
diamond growth conditions. Whereas STO readily conducts a bias current from its Ir-covered top
surface to its bottom surface, ALO does not. Using the fixturing illustrated in Figure. 8.1, it
appears that a continuous path exists between the Ir surface, through the Mo top cap and post, to
the bias lead. However, the cap only rests on the Ir substrate surface and may not make good
electrical contact if it contains insulating deposits or if cap-post contact is poor. This was
identified as a major source of variability in the bias processing. The best solution was to deposit
Ir on the sides and bottom surface of the ALO substrate, as detailed in Chapter 7.4. With this,

114

and other adjustments, the reproducibility of growing diamond films was improved so that good
quality films could be grown consecutively as illustrated in Figure 8.4.

8.3 Result of BEN on Ir
A high nucleation density of diamond on Ir/a-ALO (10

10 mm2) was obtained by

optimizing the geometry and the growth parameters. Table 8.2 lists the bias parameters for the
geometry described above. Figure 8.3 shows the surface morphology of a well-biased Ir surface.
After of 60 min, the bias voltage was turned off with the microwave plasma on. To study the
results just after bias, microwave power and bias voltage were simultaneously reduced to zero. A
thin layer of amorphous carbon covered the biased Ir, showing bright contrast in an SEM image,
Figure 8.3(a). The Ir has a surface covered with Ir nanopillars formed by the ion bombardment,
Figure 8.3(b), where the mean lateral size of an Ir pillar is 11.3±2.3 nm. A similar Ir morphology
is shown in Figure 5.13 where the size and height of an Ir pillar is 8±0.5 and 4.5±0.5 nm,
respectively. As shown in Figure 5.14(b), diamond is most likely to nucleate between the Ir
nanopillars. The density of Ir dots, thus, represents a lower bound on the nucleation density. In
Figure 8.3(b), the density of Ir dots is 1012 cm-2.
Table 8.2 Standard bias conditions.
Pressure Power
(Torr)
(W)
18

1550

Bias voltage
(-V)

Bias current
(-mA)

Bias temperature
(°C)

Duration
(min)

170-180

90-70

710-730

60

115

(a)

(b)

Figure 8.3 Plan-view SEM images of biased Ir surface: (a) the featureless amorphous carbon
layer covering the Ir surface and (b) Ir nanopillars buried in the carbon layer.

8.4 Heteroepitaxial CVD diamond thin film growth
With the high nucleation density, a diamond thin film was able to coalesce in 30 min or less.
The optical images of selected diamond thin films with good coalescence are shown in Figure
8.4 where four samples were grown in a sequence and the growth region is 8 mm in diameter,
limited by the aperture of the Mo cap. Figure 8.5 shows a typical SEM image of a 3h-grown
diamond thin film which is well-coalesced with a flat top surface. Boundaries between coalesced
regions are not observed in good films. Since the growth was done at relatively low pressure, 18
Torr and 670 °C (measured on the Mo cap by a single color pyrometer), the growth rate was 160180 nm/h. Thus, after a typical 3h growth, the thickness of the diamond film was about 550 nm.
The film in Figure 8.4 is transparent and interference fringes are observed from light reflected
between the diamond and Ir surfaces due to the radial thickness variation.

116

(a)

(b)

(c)

(d)

Figure 8.4 Four selected optical images of 550 nm diamond thin films, grown in a sequence. The
burn marks on edges are caused by the Mo cap. (b) Film is about 100 nm thicker than other
samples at its center.

117

Figure 8.5 Plan-view SEM image of 3h-grown diamond thin film showing a well-coalesced
diamond (001) surface. Bright dots are small height fluctuations on the diamond surface.
Figure 8.6 is a typical ω-2θ XRD pattern of a 550 nm heteroepitaxial diamond thin film on a
Ir (001)/a-ALO substrate. Diffraction peaks from a-ALO, Ir, and diamond are observed owing to
the long x-ray absorption length in diamond and Ir, nearly 700 and 2.45 µm respectively. Only
the diamond (400) reflection is observed, consistent with {001} diamond planes. Since the
pattern could arise from a polycrystalline film with (001) texture, it is necessary to carry out a ϕscan, Figure 8.7, to confirm the film is single crystal. Observation of the 4 (111) reflections
during a 360° rotation about the (001) axis confirms this. A rocking-curve gives a 1° linewidth,
indicating a significant mosaic spread at this thickness.

118

10

6

10

5

10

4

10

3

10

2

20

40

60

80

100

2 (degree)

120

holder

7

Dia(400)

10

#20-7
Ir (400)

8

ALO (220)

10

Ir (200)

9

ALO (110)

Intensity (counts)

10

140

Figure 8.6 XRD diffraction pattern of 550-nm diamond on a Ir/a-ALO substrate. Small peaks
originate from the small fraction of Cu Kβ radiation in the incident x-ray beam.

Intenisty (103 counts)

7

Diamond (111)

6

=54.7

5
4
3
2
1
0
0

50

100 150 200
 (degree)

250

Figure 8.7 XRD ϕ-scan of 550-nm diamond on a Ir/a-ALO substrate.

119

300

8.5 Procedure of thick diamond growth in AsTex
Starting with 550 nm diamond substrates, growth of thicker films was carried out in the
AsTex reactor. The fixturing around the sample was shown in Figure 4.9, generally similar to
that in the CVD reactor. After pumping overnight with a turbo-molecular pump, the pressure in
the main chamber reached 10-7 Torr. During growth, the hydrogen flow rate was set at 300 sccm.
Other input parameters, such as pressure, microwave power, and the methane concentration, are
variables. Hydrogen is introduced and a microwave plasma discharge is started. Power is
adjusted until the appropriate substrate temperature, measured with a single-color pyrometer, is
reached. After stabilization, methane is introduced into the chamber, initiating growth. After
growth, system is cooled slowly to room temperature to avoid thermal shock.

8.6 Heteroepitaxial CVD diamond thick film growth
A diamond sample with a thickness greater than 20 μm is referred to a thick film. Three
thick diamond films grown on diamond substrates are now described, labelled A, B, and C. The
growth conditions for each sample are listed in Table 8.3. All were covered with a Mo cap
during growth. The Mo cap, identical to the ones used in the CVD system, surrounded the
substrate with an 8 mm diameter aperture. For the growth of sample C, a cylindrical rounded Mo
dome surrounded the cap. All diamond films and their substrates exhibited cracking after cooldown to room temperature after the last growth step.

120

Table 8.3 Detailed growth parameters of thick heteroepitaxial diamond. Row lists the corresponding growth conditions. Multiple
growth steps were used for samples A and B. The listed temperature is the reading from a single color pyrometer focused on diamond
top surface.
Thickness
(μm)

Sample #

Pressure (Torr)

Power (W)

CH4 (%)

Temperature (°C)

Duration (h)

A

30

650

1

660-670

0.75

30-60

650-700

1-4

830

4

60

700

4

830-840

85.25

60

600-700

5

800-810

4.3

60

700

5

810

23

60-90

700-750

5

880

1.7

90

750

5

930

46

70

90

1100

5

690-665

49

60

B

C

121

85

Due to the thermal stress resulting from the thermal mismatch between substrate and
diamond, all of the thick diamond films peeled from the a-ALO substrate, denoted as
“delaminated”, during cooling. Moreover, in the diamond growth area, the BEN-treated Ir layer
always adhered to the diamond whereas the untreated Ir surface stayed on the a-ALO substrate,
implying the improvement of Ir adhesion to diamond by BEN. Figure 8.8 presents the diamond
(111) cleavage plane of (001) single crystal diamond.

<100>dia

<111>dia

Ir
Figure 8.8 Cross-sectional tilted SEM image of a 70-μm delaminated diamond (001) piece
showing a (111) cleavage. At bottom is the Ir layer.
In Figure 8.9, diffraction peaks from a delaminated diamond/Ir film are shown.
Compared to Figure 8.6, the intensity of the diamond (004) peak has increased significantly, 30
times, relative to the initial diamond film intensity, a result of its greater thickness and the long

122

4

10

3

10

2

20

40

60

80

100

holder

10

Dia (400)

5

Ir (400)

10

holder

6

Ir (200)

Intensity (counts)

10

120

140

2 (degree)
Figure 8.9 XRD diffraction pattern of a piece of 85-μm delaminated diamond.

Dia (004)

2.0

Gaussian Fit

1.5

5

Intensity (10 counts)

2.5

1.0
0.5

Width:0.480.00

0.0
58

59

60

(degree)

61

62

Figure 8.10 X-ray rocking curve of diamond (004) reflection with Gaussian fit.

123

x-ray absorption lengths in diamond, mentioned in Chapter 8.4. As diamond is grown even
thicker, it is found that the XRD linewidth continues to decrease. For 85-μm thick diamond, the
linewidth of XRD rocking curve FWHM is reduced to 0.48°, Figure 8.10.
Raman spectra of thick diamond samples were collected in a micro-Raman spectrometer
operated in backscattering geometry as described in Chapter 3.4.2. Spectra taken from (001) and
(110) faces obeyed selection rules, Chapter 3.4.1. With the high-resolution spectrometer grating,
the instrumental resolution is 2 cm-1. Therefore all spectra shown here should be deconvolved
with the instrumental resolution function. Figure 8.11 compares the Raman spectra of all thick
diamond samples with a Type IIa natural diamond. All of the Raman frequencies of delaminated
thick samples appear near 1332.4 cm-1, indicative of a relatively small internal stress in each
thick diamond sample. Assuming a biaxial stress in (001), it is estimated at 0.1-0.4 GPa.35

Intensity (103 count)

25
20

Type IIa diamond
85 m diamond
70 m diamond
60 m diamond

ki||ks<001>
ei||es<110>

15
10
5
0
1320

1330
1340
Raman shift (cm-1)

1350

Figure 8.11 Raman spectra of IIa natural diamond and thick heteroepitaxial diamonds. The peak
center and linewidth of natural diamond are at 1332 cm-1 and 1.65 cm-1, respectively.

124

Since the thermally-induced stress is removed when the diamond film delaminates from the
substrate, the intrinsic stress in the thick diamond film should be negligible. The Raman
linewidth of 85-μm diamond is only 1 cm-1 larger than that of natural diamond, but for 70-μm
and 60-μm diamond it is larger by 2-3 cm-1.
Raman spectra were also collected from a diamond (110) surface of the 85-μm delaminated
diamond with scans in the [001] direction. Figure 8.12 clearly shows that the stress starts to relax
at a 20 μm thickness. Below 20 μm thickness, the intrinsic stress is compressive, approximately
0.6 GPa. The Raman linewidth of the initial layer was greater than 9 cm-1, but decreases rapidly
as the film thickens. Therefore, a diamond film thicker than 30 μm is essentially unstressed.

Linewidth (cm-1)

Linewidth
Peak center

8

ki||ks||<110>
6

1334
1333
1332

4
1331
2

0

20

40

60

Peak center (cm-1)

1335

10

80

Depth (m)
Figure 8.12 Raman linewidth and frequency vs. thickness of a 85-μm diamond sample. The
linewidth decreases with thickness and the stress is largely relaxed after 30 μm.

125

9. Chapter 9 Diamond heteroepitaxial lateral overgrowth
Three different methods of diamond ELO were attempted with the goal of improving the
structural quality of heteroepitaxial CVD diamond. The two methods described in Chapters 9.1
and 9.2 both start from a thin heteroepitaxially grown diamond film on an Ir substrate and use a
Au masking layer. In the first process, the Au mask functions as a growth mask whereas in the
second process it acts as an etch mask. In the third method, described in Chapter 9.3, the starting
point is the epitaxial Ir (001) surface. A layer of SiO2 is overlaid as a biasing and growth mask.
Most of the present results were obtained with the first process, which has proven quite effective
in producing high-quality single crystal films of (001) diamond up to 0.2 mm thickness and 8
mm in diameter. With further effort, the other two methods could also prove to be feasible routes
to realize improved diamond.

9.1 Au-masked Diamond ELO
The basic ELO idea is shown in Figure 9.1 as applied to diamond. A coalesced
heteroepitaxial diamond (001) thin film, as described in Chapter 8.5, serves as the starting point.
Standard photolithography is used to pattern Au stripes on the diamond surface. Diamond then is
grown through the stripe apertures, eventually overgrowing the masked areas laterally. Gold was
chosen as the masking material for several reasons: (1) a relatively high melting temperature,
1064 °C, (2) compatibility with photolithographic processes, (3) ease of chemical etching, (4)
deposition by thermal evaporation at room temperature, and (5) resistance to carbide formation.

126

ELO diamond
Au
diamond
Ir
                     
Figure 9.1 Illustration of Au-masked diamond ELO (not to scale). The vertical wavy lines depict
threading dislocations which are partially restricted in the diamond overlayer.

9.1.1

Photolithography on diamond

The photolithographic process is illustrated in Figure 9.2. The substrate surface is a 550 nm
thick heteroepitaxial diamond film, grown on a 10 10 mm2 Ir (001)/a-ALO substrate. Growth
conditions are described in Chapter 8.5. The heteroepitaxial diamond covers an 8 mm diameter
circular region in the center of the substrate. Lithography proceeded as follows:
(1) A 300-nm thick lift-off resist (Microchem LOR 5B) was spin-coated at 3000 rpm for 35 sec
directly onto the diamond substrate, then baked at 185 °C on a hot plate for 15 min.
(2) A 1.3 μm-thick positive photoresist (PR) layer (Microposit S1813) was spin-coated onto
the LOR surface at 5000 rpm for 35 sec, then baked in an oven at 95 °C for 40 min.
(3) The PR was exposed to the UV light in an AB-M mask aligner through a photomask for 9
sec.
(4) The exposed PR was developed with Microposit MF-319 for 28 sec followed by rinsing in
flowing DI water and N2 gas drying. The profile of the diamond substrate at this stage is
shown in Figure 9.2(a).

127

(5) To remove any PR residues remaining in open channels, the substrate was lightly cleaned
in an oxygen plasma etcher at 500 mTorr and 100W for 3 min.
(6) A 85-nm thick Au layer, or Au (85 nm)/Ti (3 nm) bilayer, was thermally evaporated onto
the PR patterned diamond substrate, Figure 9.2(b). It was found that the first Ti layer
improved the adhesion of Au to diamond. During evaporation, a Cu foil mask with an
aperture of 7 mm diameter covered the diamond substrate to confine Au to the central
diamond region.
(7) To lift off the Au (or Au/Ti) on the remaining PR bilayer, the substrate was bathed in PG
remover (Microchem). The lift-off process was initiated in a beaker at 80 °C for 1-2h, then

PR
diamond
Ir

(a)

Au
diamond
Ir

(b)

(c)

Figure 9.2 Schematic of sample preparation for Au-masked diamond ELO: (a) patterned
diamond substrate after PR exposure and development; (b) substrate after Au evaporation; and (c)
completed substrate after Au lift-off.

128

the beaker was left overnight at room temperature. The Au layer then easily floated off the
diamond surface with a gentle shaking of the beaker the following morning. Figure 9.2(c)
illustrates the diamond substrate after Au lift-off.
(8) The sample was cleaned again to remove PR and Au residues. To remove LOR residues,
the sample was heated at 80 °C again for 20 min in PG remover. To dissolve the PG
remover on the surface, the sample was transferred to acetone and heated at 80 °C for
another 20 min, followed by an IPA bath at the same temperature and duration. At the
beginning of each step, the sample was gently ultrasonicated for 30 sec to improve the
homogeneous dissolution. The sample was then rinsed in flowing DI water to remove any
residual Au particles, then blown dry.
(9) Finally, the Au-patterned diamond substrate was plasma-etched in oxygen at 500 mTorr
and 300W for 9 min to prepare the diamond surface for regrowth.
Two types of photomasks were used in step (3): a 5-inch and a 4-inch diameter chrome
mask. Both were supplied by Photo Sciences Inc. (PSI). The 5-inch mask consisted of a single
stripe pattern with periodicity 20 μm and 3.5 μm apertures. The 4-inch mask had two separate
sections of stripes: one section with periodicity 12 μm and 8 μm apertures and the other section
with periodicity 16 μm and 12 μm apertures. The apertures are the transparent regions of the
mask that exposes the PR; they ultimately become the Au stripes that mask the diamond.
Due to the radial thickness variation of the diamond film, the photomask did not uniformly
contact the PR surface. The central high point resulted in a series of circular fringes on the PR
surface when viewed in the mask aligner. The stripe direction of the photomask was aligned
parallel to an edge of the a-ALO substrate, corresponding to a <110> diamond direction, or at
45° to an edge, corresponding to a <100> diamond direction. After developing, the PR stripe
129

edges were usually rounded due to the partial contact between photomask and PR. A rounded
profile makes lift-off difficult because the Au layer covers the PR flats and edges. It is then
difficult for the Au layer to break off evenly at the PR edges when the PR is dissolved during
lift-off. For improved lift-off success, it is advantageous to form an undercut edge; this is the
function of the LOR underlay. As a result the PG remover was able to easily dissolve LOR
stripes from the bottom. Examples of diamond surfaces patterned by 4-μm or 8-μm wide Au
stripes are shown in Figure 9.3.

(a)

(b)

100 μm

100 μm

Figure 9.3 Optical images of patterned diamond substrates with (a) 4-μm wide Au stripes with
16 μm gaps and (b) 8-μm wide Au stripes with 4 μm gaps. In both cases, the stripes are parallel
to the diamond <110> direction.

130

9.1.2

Diamond regrowth

The initial experiments on regrowth were performed in the CVD reactor. Those substrates
were patterned with 4 μm wide Au stripes with 16 μm gaps using a mask designed for a different
purpose. Since better dislocation masking is performed with small gaps, a photomask with 8 μm
stripes separated by 4 μm apertures was designed later. Lateral overgrowth with the wider Au
stripes was carried out in the AsTex reactor. During regrowth, the following issues are of
concern: (1) whether the Au mask remains intact until overgrown by diamond; (2) whether
diamond nucleates and grows on the Au surface; and (3) whether there is carbide formation on
the Au. Regrowth conditions for a number of trials are listed in Table 9.1.

131

Table 9.1 Growth conditions of ELO diamond with different initial thicknesses. Growth with two steps is indicated by x/y.
Stripe width/
periodicity
(µm)

Pressure
(Torr)

Power
(kW)

CH4
(%)

Growth
temperature
(°C)

Vertical
growth rate
(μm/h)

Stripe direction
(diamond axes)

Final
thickness
(µm)

4/20

26

1.5

3

750†

0.4

<100>

2

8/12

58

0.51/0.53

2

740/750*

0.7/0.8

<110>

10

4/20

24

1.94

3

750†

0.4

<110>

30

4/20

45/60

0.7

4

710/800*

0.25/1

<110>

75

8/12

58/60

0.50/0.55

2/3

730/750*

1/1.5

<110>

190

†

Growth in CVD reactor, temperature measured on the Mo cap. (cf. Chapter 4.3.1)

*

Growth in AsTex rector, temperature measured on the Ir surface. (cf. Chapter 4.3.2)

132

9.1.2.1

Early stage of coalescence

Diamond regrowth conditions with the Au mask did not differ significantly from nonmasked diamond growth with one exception. Growth temperatures were generally 50 to 60 °C
lower initially to inhibit Au delamination and sputtering in the microwave plasma. Excessive Au
sputtering is believed to enhance twin formation on the growing diamond stripe sidewalls.
(a)

(b)

Figure 9.4 Plan-view SEM images of (a) 10-μm thick ELO diamond with 8-μm wide Au stripes
centered on the non-overgrown region. The pits are the terminations of dislocations at the top
surface. (b) 2-μm thick ELO diamond with 4-μm wide Au stripes, just prior to diamond
coalescence. The white arrows indicate the position of the Au stripes.

133

During regrowth, the lateral diamond growth rate was only weakly dependent on growth
direction. The time for coalescence to occur is proportional to the Au stripe width. Thus, the film
thickness at coalescence will scale roughly with the stripe width. Substrates with 4 μm Au stripes
were observed to coalesce at 2 μm thickness, but for 8 μm Au stripes they coalesced at about 10
μm thickness. The qualitative success of lateral overgrowth can easily be seen by inspection of
Figure 9.4(a) which is an SEM image of a 10 μm thick film at coalescence. The central region is
above the mask aperture where diamond grows unimpeded from the substrate. The dark region
indicates surface roughness, brought about by the high density of dislocations that terminate at
the top surface. The adjacent regions are much smoother and have few visible dislocation
terminations. These are the Au-masked regions where lateral overgrowth has occurred.
In Figure 9.4(b) with 4 μm Au stripes, coalescence has just occurred at a diamond regrowth
thickness of 2 µm. Here the thin film does not allow much SEM contrast between masked and
non-masked regions. More quantitative methods to analyze diamond structural perfection must
therefore be used. More specifically, the use of spatially-resolved micro-Raman scattering to
probe the lateral variation of the regrown diamond is now described.
Figure 9.5 shows Raman linewidths and corresponding Raman intensities for the two
aforementioned overgrown diamond samples. Oscillations of these quantities occur with the
same periodicity as the Au stripes. The minimum Raman linewidths and maximum intensities
occur just above the Au stripes in the laterally overgrown regions. The linewidth oscillated with
amplitude of 30% for the 2-μm thick ELO diamond with 4 μm Au stripes. For the 10-μm thick
ELO diamond with 8-μm wide Au stripes, the oscillation amplitude increased to 60%. More
significantly, the value of the linewidth above the Au stripes was reduced by a factor of two for
the thicker overgrown diamond. These results are consistent with dislocation confinement to the
134

non-overgrown regions. Here the dislocations produce random internal strains that broaden the
distribution of the diamond vibrational frequencies detected by the Raman experiments.
(a)

Linewidth
Intensity

20

Intensity (arb. unit)

Linewidth (cm-1)

25

15
10
-20

0

20

40

60

80

100

Position from reference (m)
(b)

35

Linewidth (cm-1)

Intensity (arb. unit)

Linewidth
Intensity

30
25
20
15
10
5
0

10

20

30

40

50

60

Position from reference (m)

Figure 9.5 Spatial variations of the Raman linewidth and intensity for a (a) 2-μm thick ELO
diamond with 4-μm wide Au stripes and (b) 10-μm thick ELO diamond with 8-μm wide Au
stripes. In both cases the diamond has not detached from the substrate. The linewidth is
minimized at the overgrown region above the Au stripe.

135

Useful information about the mean stress in the diamond film is contained in the Raman line
center position. Since the Raman frequency is stress-sensitive, Appendix, it can be used to
measure the static stress in the film. Two independent types of stress exist in the diamond film,
designated as internal stress and thermally-induced stress. The film itself contains internal stress
as a result of deviations from crystalline perfection, e.g., dislocations, vacancies, and impurities.
Thermally-induced stress arises when the film and substrate have mismatched thermal
expansivities and are cooled from growth temperature. It will be primarily a biaxial stress, with
equal components in the plane of the film. Sapphire has a larger thermal expansivity than
diamond (see Appendix) so that cooling from the growth temperature at 750 oC introduces a
biaxial compressive stress in the diamond. Provided the film is much thinner than the substrate
and that there is no slip at the interface, the theoretical thermal stress in diamond can be
calculated from elasticity theory by

9.1156

/ 1

where σ is the biaxial stress, Δε the thermal strain, E is Young’s modulus and ν is Poisson’s ratio.
The thermal strain is given by

∝

∝

9.2

where α is the thermal expansivity of diamond (d) and substrate (s), T2 is the growth temperature
and T1 is usually room temperature. Evaluation of Eq. 9.1 gives σd = -4.55 GPa for diamond on aplane sapphire.
This prediction can be tested by using the Raman data in Figure 9.6 for the 2-μm thick
diamond film at coalescence. The film was grown at 750 °C and cooled to 25 °C at which time it
136

was found that the diamond film had cracked into large pieces that partially delaminated from
the substrate. The thin Ir film always adhered to the diamond, not to the ALO. However, some
parts of the film remained attached to the substrate, referred to as “non-delaminated”. Figure 9.6
shows that the Raman center frequency is independent of lateral position but undergoes a large
positive shift of +3 cm-1 in the non-delaminated diamond. The delaminated film was essentially
unchanged from the reference Raman peak position of unstressed Type IIa natural diamond at
1332.4 cm-1, indicating the near-absence of thermal and internal stress. The shift for the adhering
film corresponds to a biaxial compressive stress of -1.8 GPa. This is only 40% of the calculated
value for the thermal stress. The low value leads us to infer that the interfaces are not rigidly
connected, violating a validity condition for Eq. 9.1.

Non‐delaminated

Delaminated

(b) 1338

Peak center (cm-1)

(a)

Non-delaminated
Delaminated

1336
1334
1332
1330
0

20

40

60

80

100

Position from reference (m)

Figure 9.6 (a) Photograph of diamond (001) surface with both delaminated and non-delaminated
regions and (b) comparison of the adherent and delaminated regions on 2-μm thick ELO
diamond with 4-μm wide Au stripes. The delaminated film has the unstressed diamond Raman
frequency whereas the strongly attached film shows large compressive stress. The red dashed
line represents the unstressed diamond frequency at 1332.4 cm-1. The polarizations of incident
and scattered laser beams were parallel to <110>.
137

The low stress is most likely a consequence of the Au masking stripes, since Au is very
ductile and easily deformed. It allows the overgrown diamond to slip with respect to its substrate.
As we discuss below for a thicker diamond film, it appears that the Au does not adhere well to
the diamond after growth and cool-down. Therefore, this Au ELO process not only improves
diamond structural quality but acts to relieve thermal stress build-up.
9.1.2.2

Intermediate thickness diamond films

Figure 9.7 shows SEM images of a slab of 30 μm thick ELO diamond grown with 4 μm
wide Au stripes. Figure 9.7(a) was taken at a tilt angle to demonstrate the flat and smooth (001)
diamond top surface and two rough {110} fracture surfaces. Note that the Au stripe edges are
visible at the lower edge of the crystal. Figure 9.7(b), at higher magnification, was taken without
tilt near a Au stripe buried under the ELO diamond layer. The Au stripe appears to be intact
following diamond growth but there is some evidence for deformation. Just above the center of
the stripe is a triangular void. This is the coalescence region of the diamond film, i.e., the point at
which diamond overgrew the mask from two sides and shadows the plasma from the substrate.
The diamond does not wet or bond to the Au since there is a gap along most of the Au stripe
edge. The void and gap may help to minimize interfacial tension in diamond. In ELO grown
GaN, strong contact between coalescing regions has been shown to lead to growth-axis tilting148
so that weak contact is advantageous.

138

Figure 9.7 SEM images of a 30-μm thick ELO diamond grown with 4-μm wide Au stripes. (a)
Tilted image, the top surface is the (001) face and the sides are {110} fracture surfaces. The Au
stripes are visible in the lower part of the crystal. (b) Expanded {110} fracture surface at the
region near the Au stripe. The diamond only weakly contacts the Au stripe during overgrowth
and forms a void at the top surface of the gold.

9.1.2.3

Thick diamond growth

Diamond films were grown using Au-masked ELO to 75 and 190 μm thicknesses with 8-μm
wide Au stripes and 4 μm apertures. Figure 9.8 shows an optical micrograph of the 190-μm thick
diamond with the objective focused on the Au stripes through the diamond overlayer. The stripes
are intact, continuous, and appear to be undamaged during growth. The image further
demonstrates the feasibility of using 8-μm wide Au stripes as a mask for diamond under the
present growth conditions.
Examination of films with SEM is restricted to the near surface owing to the relatively
shallow penetration of keV electrons into diamond. In the 75-μm thick diamond film shown in
Figure 9.9(a) there is some evidence for surface roughness arising from dislocation etch pits.
139

However, at both 75 μm and 190 μm thicknesses, Figure 9.9, there are no longer any periodic
surface features that have resulted from ELO growth. It is also likely that the threading
dislocations eventually bend laterally so that the spatial distribution of dislocations at the surface
is fairly uniform. We note that Raman scattering shows no periodic spatial variation in films
once they are thicker than 30 μm.

Figure 9.8 Optical image of Au stripes taken through a 190-μm thick ELO diamond overlayer.
The 8-μm wide stripes are oriented parallel to the <110> diamond direction.

140

(a)

(b)

Figure 9.9 Plan-view SEM images of (a) 75-μm thick ELO diamond with 4-μm wide Au stripes
and (b) 190-μm thick ELO diamond with 8-μm wide Au stripes.
The 190-μm thick ELO diamond film, noted above, did not catastrophically crack or
delaminate from the a-ALO substrate after cooling to room temperature. We noted the
appearance of small cleavage cracks near the ALO substrate which did not propagate to the
surface. This suggests that the internal stress in this diamond sample is small. A lateral Raman
scan, with the laser focused on the diamond surface, across the 8 mm diameter of the crystal is
shown in Figure 9.10. The line center shows small fluctuations about 1332.4 cm-1, corresponding
to a total stress of 0.00±0.16 GPa. This indicates the maximum stress (the upper and lower
uncertainties of the fit) is at least an order of magnitude lower than the thermal stress in a 2 μm
diamond film, Chapter 9.1.2.1. It is not clear how much of the stress relaxation can be attributed
to the ELO growth. In the future, a comparison should be made between ELO and non-ELO
diamond grown under the same conditions to the same thickness.

141

Peak center (cm-1)

1335
1334
1333
1332
1331
1330
-1 0

1

2

3

4

5

6

Position (mm)

7

8

Figure 9.10 Raman center frequency of 190-μm thick ELO diamond with 8-μm wide Au stripes.
The scan covers 8 mm, the diameter of the entire diamond crystal. Very low stress is apparent
from the small Raman shift, 1332.4±0.26 cm-1.
Even with the 100x Raman microscope objective focused at the diamond surface, Raman
signals from well below the surface may contribute to the total intensity. This is because the
spectrometer is not truly confocal; it lacks a pin-hole to collimate the scattered light. This is
problematic for thick crystals, since the Raman signal will be averaged over 50 μm or more. To
obtain reliable Raman data as a function of distance from the top surface, crystals were rotated
by 90 degrees so that the beam was scanned parallel to the growth, or z-axis. Figure 9.11 shows
results for a z-scan for the 75-μm thick ELO diamond with 4-μm wide Au stripes. In Figure
9.11(a), it can be seen that the Raman linewidth decreases more or less continuously as the film
thickens. Figure 9.11(b) indicates that the crystal grows under tensile stress while it is largely
relaxed at the surface. The oscillations may be correlated with small variations in the growth
conditions. The linewidth at the surface is about 1 cm-1 larger than the natural diamond linewidth

142

of 1.65 cm-1. We expect that the linewidth will continue to decrease as crystals are grown to
greater thicknesses.

(a)

(c)

Ir

Dia.

(b)

Figure 9.11 (a) Raman linewidth and (b) Raman frequency vs. thickness of a 75-μm thick ELO
diamond with 4-μm wide Au stripes. The linewidth decreases with thickness and the stress is
mostly relaxed on the top surface. (c) Photograph of diamond {110} surface. The arrow indicates
the scan direction, along [001]dia.

143

9.2 PENDEO for Diamond ELO
The idea of PENDEO lateral overgrowth, previously successful for GaN, see Chapter 6.3.3,
was adapted to diamond. Although it also utilized a Au stripe mask, in this case the Au is used as
an etch mask, unlike the previous method with Au used as a growth mask. The starting point is a
550-nm thick heteroepitaxial diamond film, grown under the conditions described in Chapter 8.5.
The surface is masked with Au stripes, then plasma etched to form a parallel array of trenches,
the Au removed and the diamond stripes then regrown until they coalesce. A part of process of
diamond regrowth after etching is illustrated in Figure 9.12.

(a)

diamond
Ir

(b)

Figure 9.12 Schematic of PENDEO process during diamond growth.
Diamond is readily etched in oxygen or oxygen-containing gas mixtures by electron
cyclotron resonance (ECR), inductively coupled plasma (ICP) or reactive-ion etching (RIE)
systems. Masking materials previously studied are Al,157,158,159,160,161 Au,162,163,164,165 Ti,165
SiO2165,166,167,168 and Si3N4.165 Since no commercial plasma etcher was available, we attempted to
etch the diamond substrate in the CVD reactor at a relatively high temperature, at 500-600 °C, in

144

a hydrogen plasma. An evaporated Au layer was used as the etch mask. As we describe below,
the idea is promising but only a proof-of-principle was demonstrated.
9.2.1

Substrate preparation

The photolithographic process for substrate preparation is illustrated in Figure 9.13. The
diamond substrate was described in Chapter 9.1.1. Surface patterning proceeded as follows.
(1) A 1.3 μm-thick positive PR (Microposit S1813) was spin coated onto the diamond surface
at 5000 rpm for 35 sec diamond substrate covered with the PR layer, then baked in an oven
at 95 °C for 40 min.
(2) The baked PR surface was exposed by the UV light through a photomask for 9 sec.
(3) The exposed sample was developed in Microposit 352 for 30 sec followed by rinsing in
flowing DI water and N2 drying. As this point, the diamond surface was patterned by the
PR layer as shown in Figure 9.13(a).
(4) To remove PR residues in open channels, the substrate was cleaned in the oxygen plasma
etcher at 500 mTorr and 100W for 3 min.
(5) As shown in Figure 9.13(b), a 100-nm thick Au layer was deposited by thermal evaporation
onto the PR patterned substrate.
(6) The Au-covered diamond substrate was immersed in acetone at room temperature for 2030 min. Without a LOR layer, weak ultrasonication was needed to completely lift off the
Au-covered PR. Due to the poor Au adhesion, even weak ultrasonication often causes the
Au layer to delaminate from the diamond as well. The sample was then soaked in IPA for
10 min. Figure 9.13(c) illustrates the sample cross-section after Au lift-off. A final DI rinse
followed.
145

(7) The Au-patterned diamond substrate was etched in an oxygen plasma etcher at 500 mTorr
and 300W for 3 min to completely remove any remaining PR.
A 5 inch diameter PSI chrome stripe mask with a 3.5 μm stripe aperture and 20 μm repeat
was used. After lift-off, the diamond (001) surface was covered with 4-μm wide Au stripes in the
<110> diamond direction.

(a)

PR
diamond
Ir

(b)

Au
PR
diamond

(c)

Figure 9.13 Illustration of sample preparation for PENDEO diamond ELO: (a) a 550-nm thick
diamond substrate patterned with stripes of PR layer by standard photolithography; (b) Au (100
nm) mask layer thermally evaporated on a diamond substrate; and (c) diamond substrate covered
by the Au stripes along the <110> direction. See Figure 9.12 for the two last steps of the process.

146

9.2.2

Diamond plasma etching

The Au-patterned diamond film was etched using a bias-assisted plasma process in the CVD
reactor.169 Due to the low plasma density, the etching was carried out at moderate process
pressure, 1-10 Torr, and temperatures between 500-600 °C. The sample holder geometry for
diamond plasma etching is the same as that for BEN, Figure 8.1.
In the etching experiments, we addressed the following issues: (1) stability of the Au mask
layer; (2) diamond etching rate in H2 or dilute O2/H2 plasma; (3) selectivity, the thickness ratio of
etched diamond to etched Au, in H2 plasma; (4) Au mask removal following etching; (5) damage
to the diamond underlayer; and (6) extent of Au redeposition.
Table 9.2 Conditions of diamond plasma etch in pure H2.

Sample#

Pressure
(Torr)

Power
(kW)

Bias voltage
(-V)

Bias
current
(mA)

Bias
duration
(min)

Note

13-3

18

1.11

133

46-38

5

Au

13-1

18

1.55

150

45-16

30

Au/Ti
bilayer

In the first trial, a Au masked diamond substrate was etched in pure H2 and biased at -133 V
for 5 min. During biasing, a reddish glow appeared above the diamond surface, characteristic of
the cathode glow of a hydrogen plasma. The bias current started at -46 mA again and decreased
to -38 mA gradually. Figure 9.14 shows the steep sidewalls of protected diamond strip,
indicative of the highly directional H2 etching in diamond. In Figure 9.14(b), diamond was only
partly etched forming cone-shape artifacts. Kobashi et al. found that the cone-shape feature was

147

etched diamond covered with a thin layer of graphite,170 which led to a decreased bias current.
After biasing, the Au surface showed damage. This caused some unintentional etching of the
masked region, Figure 9.14(b). After etching the Au was readily removed with a fresh aqua regia
solution.

(a)

(b)

Figure 9.14 (a) Plan-view SEM image of a diamond stripe after etching with Au mask remaining
(center). The Au mask shows damage, with holes visible. (b) 45° tilt SEM image at the boundary
of a diamond stripe and the etched trench. The Au masked diamond stripe is on right side; the
area on the left has been etched. Note the steep sidewalls of the diamond and the cone-like
features in the etched area.
148

The 550 nm diamond substrate was etched by 370 nm, corresponding to an etch rate of 0.80.9 µm/h. During bias, the Au layer was also etched by 30-40 nm. Consequently, the selectivity
was 11, comparable to the ECR technique.165 Inadvertent peeling of Au during bias arises from
poor Au-diamond adhesion. In the next trial, a 5-nm thick Ti layer was evaporated prior to Au
evaporation to improve adhesion. The substrate was biased at -150 Vdc for 30 min. The bias
duration and bias voltage were increased to etch more completely. The bias current started at -45
mA and decreased gradually to -16 mA. After biasing the masked regions were all intact and no
peeling of the Au layer was observed. The diamond in the apertures was etched to the Ir surface,
as shown in Figure 9.15, and no cone-like features on Ir were apparent. The height of the
diamond stripe measured from the Ir was about 500 nm in agreement with the diamond thickness.
Chemical etching in aqua regia solution left a thin residual layer on the diamond surface that
Raman spectroscopy identified as TiCx.171 Apparently, the plasma etching temperature is
sufficiently high that Ti reacts with carbon to form the carbide, which is relatively impervious to
chemical or Ar/O2 plasma etching. Consequently, the adhesion of Au still remains an issue for
this ELO process.

Figure 9.15 Plan-view SEM image of etched area showing the bare Ir surface. Small structures
may be Ir coalescence boundaries. No trace of diamond residues is seen.
149

9.2.3

Regrowth of protected diamond stripes

Regrowth of the etched diamond stripes was carried out under conditions listed in Table 9.3.
After 3.5h of growth, diamond stripes grew uniformly by 2 μm. Flat {111} facets formed on the
sidewalls, Figure 9.16(a). The cone-like features in the etched region turned into (100) diamond
faceted crystallites, Figure 9.16(b). No change in the height of the stripes relative to the aperture
was measured, indicating that both regions had the same growth rate.
Table 9.3 Regrowth conditions of sample 13-3 after H2 plasma etch.

Sample

Pressure
(Torr)

Power
(kW)

CH4
(%)

Growth
temperature (°C)

Stripe direction
(diamond axis)

Reactor

13-3

35

1.55

1

850

<100>

CVD

In Figure 9.16(a), the surfaces along the edge of diamond stripes, i.e., the overgrown regions
are smoother than in the center of non-overgrown region. The different surface roughness is
similar to the observation in Figure 9.4(a), suggesting that threading dislocations have a lower
density in the overgrown area. Further studies aimed at improving Au adhesion and with better
removal of diamond in the trenches are needed. A possible modification is the addition of
oxygen to the plasma which should result in faster diamond etch rates with little effect on the Au
adhesion. It would also be necessary to optimize the vertical and horizontal diamond growth
rates so that overgrowth of the channels occurs before diamond nucleates in these regions.
Nevertheless, this method appears to improve the diamond quality and should be investigated.

150

(a)

(b)

Figure 9.16 Plan-view SEM images of the plasma-etched diamond substrate after regrowth. (a)
A diamond stripe, showing the formation of {111} facets on the side walls. (b) Diamond stripes
and etched areas shown at lower magnification. The diamond grew in the etched areas and
formed oriented crystallites after 3h.

151

9.3 Diamond ELO with SiO2 mask
In this approach, SiO2 was used as a growth mask. In contrast to the method that used Au to
mask a previously grown thin diamond substrate, the SiO2 masks a bare Ir epilayer. After
exposure to the BEN process, it was anticipated that diamond would nucleate and grow from
exposed Ir stripes, eventually overgrowing the SiO2 mask, as visualized in Figure 9.17.
Amorphous SiO2 is a common masking material frequently used in III-V semiconductor ELO,
see Chapter 6. SiO2 has several advantages, particularly its high softening temperature and its
etching properties. The issues to be addressed in this process are similar to those considered
earlier. These are the relative etch rates of SiO2 to diamond and whether diamond nucleates on
SiO2. We found that exposure of the SiO2 to the intense BEN conditions is problematic. Although
this method may prove viable, at the present time this method appears the least favorable
approach.

Figure 9.17 Illustration of diamond ELO with SiO2 mask.

152

9.3.1

Substrate preparation

Figure 9.18 illustrates the sample preparation procedure. This process starts from the
deposition of a SiO2 mask layer on a 2 inch diameter Ir (001)/a-ALO wafer by RF sputtering in
the APX system, Figure 9.18(a). 500 nm SiO2 was deposited at room temperature in 2 mTorr Ar
pressure at 325W yielding a deposition rate of 3 nm/min. The result was a smooth, transparent,
featureless film.
The SiO2 surface was patterned by photolithography, Figure 9.18(b). The steps of the
surface patterning on diamond are described as follows:
(1) The SiO2 surface was treated with HMDS adhesion promoter for 10 min to improve the
adhesion of PR to SiO2 prior to a 1.3-μm thick PR (S1813) spin-coating at 5000 rpm for 35
sec. Then, the coated sample was baked in an oven at 95 °C for 40 min.
(2) The wafer covered with PR was exposed to UV light for 9 sec through the 5-inch diameter
PSI mask, as described in Chapter 9.2.1. The stripes were aligned along the <110>Ir
direction.
(3) Development of the PR in Microposit 352 developer for 30 sec was followed by rinsing in
flowing DI water and N2 blown dry.
(4) To remove the exposed SiO2, the sample was etched in a buffered oxide etch (BOE) with a
ratio of 30:1 (NH4F:HF). The etch rate was 25 nm/min. After the PR layer was stripped in
acetone, the Ir surface was covered by SiO2 stripes with a window/repeat distance of 4/20
µm, Figure 9.18(c).
(5) The patterned SiO2/Ir/a-ALO wafer was coated with PR to protect the Ir during dicing.
Following dicing into 10 10 mm2 chips, the chips were cleaned in solvent and blown dry.
153

SiO2
Ir(001)

(a)

(b)

PR

(c)

Figure 9.18 Steps followed in ELO with the SiO2 mask process. (a) 500-nm thick SiO2, the
masking layer, was sputtered onto a Ir (001) surface, where the lines represent the dislocations
lines in the Ir layer. (b) The SiO2 surface was covered with a layer of PR, patterned by
photolithography. (c) SiO2 in the channels was etched by BOE, forming trenches.

9.3.2

BEN on patterned SiO2/Ir (001)/a-ALO substrates

The SiO2 patterned Ir (001)/a-ALO substrates were subjected to the BEN process, Chapter
8.4, to create diamond nucleation sites on the exposed Ir. Several attempts to carry out this
procedure were unsuccessful. In particular, BEN conditions are appreciably more severe than
those encountered in standard diamond growth. The high voltage applied to the substrate leads to
arcing, SiO2 sputtering, and its re-deposition as small particles on Ir, Figure 9.19. The redeposition inhibits diamond nucleation and further growth. The arcing was observed to damage
the SiO2 and Ir surfaces as shown in Figure 9.20. Attempts to remedy the situation by decreasing
the bias voltage to the threshold for DC glow ignition, and by changing the geometry of substrate

154

Figure 9.19 SEM image of exposed Ir surface after biased, showing nanoparticles randomly
deposited on the surface.

SiO2

Ir

                                                
Figure 9.20 DIC optical image of damaged SiO2 pattern on Ir (001)/a-ALO substrate. After 30
min of -200V bias, the SiO2 and Ir surfaces were eroded by arcing.

155

cap were unsuccessful. Under bias, the highly insulating SiO2 stripes become charged, leading to
electrical breakdown. In some cases, the SiO2 and Ir surfaces were burned off.
This problem could be addressed by insuring that the Ir film has a low resistance connection
to the sample post. This should allow the charge to drain from the SiO2, suppressing arcing.
Since these experiments were conducted on substrates that had not been back-coated with Ir, it is
likely that the circuit had a high resistance, leading to charge buildup on the SiO2. Without
charging, arcing should be eliminated and the particulate deposition should disappear.
We considered that the process might be more successful if the Ir underwent BEN exposure
prior to depositing the SiO2 layer. A substrate was prepared and biased, and then SiO2 was
stripped from half of the substrate, leaving an interface between the biased Ir and the SiO2 mask.
After diamond growth in the CVD reactor under standard conditions, results shown in Figure
9.21 were obtained. The diamond grew close to the boundary between Ir and SiO2 which
indicates that the SiO2 does not sputter onto the Ir. Diamond clusters away from the boundary
grew epitaxially. Figure 9.21(b) shows that oriented diamond grains grew close to the edges of
the SiO2. Furthermore, the biased Ir surface was not damaged by the BOE HF etch. The low
diamond nucleation density observed is attributed to a non-ideal BEN process which was not
optimized in this experiment. These results demonstrate that diamond grown by this method
remains an option although further work is needed for its optimization.

156

(a)

(b)

Figure 9.21 SEM images of diamond growth near a SiO2 boundary. The SiO2 layer is the dark
region in the images. (a) Plan-view and (b) 5° tilt SEM image showing diamond growth adjacent
to SiO2.

157

10. Chapter 10 Conclusions and outlook
This research has been motivated by the prospect of producing single crystal diamond
wafers with the quality of present silicon and gallium arsenide substrates. There had been two
major obstacles in reaching this goal. The first was the inability to grow diamond at the wafer
scale. The second was the poor crystalline structural quality in such materials. To overcome the
first obstacle, heteroepitaxial growth of diamond on sapphire has been investigated, as described
in earlier chapters. A significant advance in nucleating diamond on a thin buffer layer of Ir has
been reached at the 1 cm scale. A high-density nucleation procedure, which proved problematic
in the past, has been placed on a solid foundation, with a highly reproducible process developed.
The initial diamond layer that forms on a buffer layer is always highly defective, so methods to
localize the defects in the vicinity of the substrate have been invented. Several epitaxial lateral
overgrowth methods have been explored, with one method in particular that is simple to
implement and has produced thick diamond films with greatly improved structural quality.
The major results of this work are summarized as follows.
1. Epitaxial Ir growth on sapphire. A robust sputtering process for growing (001) Ir
epitaxial films on a-plane sapphire wafers was developed. By studying Ir on substrates
with different miscut angles by x-ray diffraction, no trace of misoriented grains was
found. In the past, sensitivity to miscut angles and existence of Ir (111) grains had been a
concern.
2. Bias-enhanced nucleation of diamond. A significant advance in increasing the area of
highly nucleated diamond on Ir was made. The reproducibility of the process, which

158

depends critically on control of the plasma in the vicinity of the substrate, was improved
by careful examination of plasma instabilities. This is a key step for producing cm-sized
thin diamond substrates, without which photolithography for lateral overgrowth would
not be practicable.
3. Heteroepitaxial diamond growth of thick films on sapphire. Exposure of sapphire to
the high temperature, highly reactive CVD hydrogen plasma was tested. It had been
unclear whether degradation of the oxide substrate would occur, particularly with growth
times of several days. Sapphire, whether protected by Ir or not, was found to be
unaffected by the plasma chemistry or by thermal shock. As a consequence, non-ELO
growth of CVD diamond on Ir was demonstrated using typical growth rates and
temperatures for films up to 0.1 mm thickness.
4. Diamond epitaxial lateral overgrowth. A photolithographic ELO method using a
simple metal mask was successfully demonstrated. The single prior example of ELO on
diamond had used electron-beam lithography to produce a patterned substrate, a process
which cannot be readily scaled to large substrates. The metal mask is a simple Au film
which can be readily deposited at room temperature by thermal evaporation using
standard equipment. Diamond successfully overgrew and coalesced above the masked
regions. It was shown by a number of methods that dislocations, the source of internal
stress in diamond, were largely excluded from the overgrown regions. By increasing the
relative area of the overgrown region, it was shown that there was a commensurate
improvement of diamond quality, as evidenced by a decreased Raman linewidth.
5. Thermal stress reduction. Thermally-induced stress, caused by the thermal expansivity
mismatch between substrate and diamond, is problematic in heteroepitaxy and in all film

159

growth. The larger contraction of sapphire relative to diamond, when cooled from
growth temperatures of 800 to 1100 oC, generally leads to fracture of film and substrate
or delamination of diamond. A major advantage of Au-masked lateral overgrowth is the
stress relief provided by the ductile Au film in the overgrown film. Whereas non-ELO
diamond on sapphire was always found to fracture and delaminate on cooling. ELOgrown diamond, on the other hand, adhered to the substrate for a large range of
thicknesses. For 2-µm thick ELO diamond, the thermal stress was reduced by a factor of
about 3, even with a relatively small overgrown area. For a 0.2-mm thick ELO diamond
plate, it was found that the growth surface was nearly stress-free, with a stress magnitude
of 0.00±0.16 GPa.
Although dislocation confinement in diamond grown by ELO and the corresponding
reduction of the Raman linewidth in overgrown regions were observed, additional quantitative
evidence of dislocation density reduction is needed. The most direct test is by growth of diamond,
under identical conditions, on ELO and non-ELO prepared substrates. Using interrupted growth
and surface plasma etching, the etch pits that terminate dislocations can be readily counted and
their evolution observed as diamond thickness increases. In a preliminary report, it was inferred
that a dislocation density reduction by two orders of magnitude had occurred on ELO-grown
material before the film thickness grew to 100 μm.172
Because of the dislocation confinement resulting from Au-masked ELO, multiple ELO
processes would be attractive. After a short growth step to the coalescence point, the substrate
could be subjected to another lithography step, with the mask translated to block the previously
unmasked region. Other alternatives are masking patterns with wider stripe to space ratios or a
grid mask pattern for island growth.
160

The two other ELO methods briefly explored are also promising, especially the PENDEO
process. Since the PENDEO process does not require a mask during growth, the temperature can
be increased, leading to a higher growth rate from the onset. Improvements in this process would
benefit from equipment that will allow for more efficient diamond etching.
Ultimately, the overall growth process should be tuned for higher chemical purity of the
resulting diamond. This can be accomplished by slight modifications of growth conditions, along
with greater purity and combinations of feedstock gases. Higher chemical and structural
perfection is important for maximizing carrier lifetimes in particle detector applications. A
program of carrier time-of-flight measurements with feedback to growth variables is needed.
Such systematic research would allow the defects responsible for carrier scattering and trapping
to be identified and eliminated.

161

APPENDIX

162

APPENDIX
Calculations of stress in diamond
The theoretical thermal stress in diamond grown on a substrate can be calculated from
elasticity theory156 by

/ 1

A.1

where σ is the biaxial stress, Δε the thermal strain, E is Young’s modulus and ν is Poisson’s ratio.
The thermal strain from a-ALO substrate to diamond is given by

∝

∝

A.2

where α is the thermal expansivity of diamond (d) and a-ALO (s), T2 is the growth temperature
and T1 is usually room temperature, 25 °C. The thermal expansivities of diamond and sapphire at
different temperatures are listed in Table A.1.

163

Table A.1 Temperature dependent thermal expansion coefficients of diamond and sapphire.173
α/(10-6 K-1)

Material
100K

200K

293K

500K

800K

1100K

1500K

Diamond

0.05

0.4

1

2.3

3.7

4.7

5.6

Sapphire (c-axis)

3.6

4.1

4.8

7.9

8.9

9.8

10.9

Sapphire (m-axis)

3.3

2.2

6.6

7.4

8.3

9.1

10.0

164

By the integration of thermal expansion coefficients between 750 °C and room
temperature from Table A.1, the thermal strains along c-axis and m-axis are -3.75×10-3 and 3.6×10-3, respectively. Since the difference is negligible we use the average strain, -3.68×10-3,
to estimate the thermal stress. The Young’s modulus of diamond is 1140 GPa and Poisson’s
ratio is 0.07.156 As a result, the thin film thermal stress in diamond is -4.55 GPa.

Relations between stress and Raman peak shift
Stress in diamond can be estimated from the shift of the Raman peak position. For
unstressed Type IIa natural diamond, the Raman peak center is located at 1332.4 cm-1. The
relationships between stress and Raman peak shift35 under various conditions are listed below.
A compressive stress corresponds to a blue shift, and a tensile stress to a red shift.

(i)

Hydrostatic stress:

(ii)

⁄

0.31

, ,

(triplet)

A.3

Biaxial stress in (001) plane:

,

0.42

⁄

(doublet)

A.4-1

0.61

⁄

(singlet)

A.4-2

165

(iii)

(iv)

Biaxial stress in (110) plane:

(vii)

A.5-1

0.42

⁄

A.5-2

0.32

⁄

A.5-3

1.49

⁄

(singlet)

A.6-1

0.35

⁄

(doublet)

A.6-2

1.21

⁄

(doublet)

A.7-1

0.64

⁄

(singlet)

A.7-2

Uniaxial stress in [001] direction:

,

(vi)

⁄

Biaxial stress in (111) plane:

,

(v)

1.09

Uniaxial stress in [110] direction:
1.21

⁄

A.8-1

10.78

⁄

A.8-2

0.44

⁄

A.8-3

Uniaxial stress in [111] direction:

,

0.40

⁄

(singlet)

A.9-1

2.97

⁄

(doublet)

A.9-2

166

BIBLIOGRAPHY

167

BIBLIOGRAPHY
1

W. Adam, B. Bellini, E. Berdermann, and P. Bergonzo, Nucl. Instruments Methods Phys.
Res. Sect. A Accel. Spectrometers, Detect. Assoc. Equip. 511, 124 (2003).

2

C. Wild, P. Koidl, W. Müller-Sebert, H. Walcher, R. Kohl, N. Herres, R. Locher, R.
Samlenski, and R. Brenn, Diam. Relat. Mater. 2, 158 (1993).

3

X. Jiang and C.-P. Klages, Diam. Relat. Mater. 2, 1112 (1993).

4

K. Ohtsuka, K. Suzuki, A. Sawabe, and T. Inuzuka, Jpn. J. Appl. Phys. 35, L1072 (1996).

5

K. Ohtsuka, H. Fukuda, K. Suzuki, and A. Sawabe, Jpn. J. Appl. Phys. 36, L1214 (1997).

6

M. Schreck, H. Roll, and B. Stritzker, Appl. Phys. Lett. 74, 650 (1999).

7

F. Hörmann, H. Roll, M. Schreck, and B. Stritzker, Diam. Relat. Mater. 9, 256 (2000).

8

C. Bednarski, Z. Dai, A.-P. Li, and B. Golding, Diam. Relat. Mater. 12, 241 (2003).

9

B. Golding, C. Bednarski-Meinke, and Z. Dai, Diam. Relat. Mater. 13, 545 (2004).

10

Z. Dai, C. Bednarski-Meinke, R. Loloee, and B. Golding, Appl. Phys. Lett. 82, 3847
(2003).
11

S. Gsell, T. Bauer, J. Goldfuß, M. Schreck, and B. Stritzker, Appl. Phys. Lett. 84, 4541
(2004).
12

Y. Ando, J. Kuwabara, K. Suzuki, and A. Sawabe, Diam. Relat. Mater. 13, 1975 (2004).

13

S. Washiyama, S. Mita, K. Suzuki, and A. Sawabe, Appl. Phys. Express 4, 095502 (2011).

14

W. Massa, Crystal Structure Determination (Springer-Verlag, Berlin, 2000).

15

B.B. Pate, Diamond: Electronic Properties and Applications (Kluwer Academic publisher,
1995).
16

J. Isberg, J. Hammersberg, E. Johansson, T. Wikström, D.J. Twitchen, A.J. Whitehead, S.E.
Coe, and G.A. Scarsbrook, Science 297, 1670 (2002).

17

F. Himpsel, J. Knapp, J. VanVechten, and D. Eastman, Phys. Rev. B 20, 624 (1979).

18

M.W. Geis, N.N. Efremow, J.D. Woodhouse, M.D. McAleese, M. Marchywka, D.G.
Socker, and J.F. Hochedez, IEEE Electron Device Lett. 12, 456 (1991).

19

R. Mildren, Optical Engieering of Diamond (John Wiley & Sons, Somerset, 2013).

20

J.L. Warren, J.L. Yarnell, G. Dolling, and R.A. Cowley, Phys. Rev. 158, 805 (1967).

21

M. Liu, L. Bursill, S. Prawer, and R. Beserman, Phys. Rev. B 61, 3391 (2000).
168

22

K. Ishioka, M. Hase, M. Kitajima, and H. Petek, Appl. Phys. Lett. 89, 231916 (2006).

23

K.C. Lee, B.J. Sussman, J. Nunn, V.O. Lorenz, K. Reim, D. Jaksch, I.A. Walmsley, P.
Spizzirri, and S. Prawer, Diam. Relat. Mater. 19, 1289 (2010).

24

S. Solin and A. Ramdas, Phys. Rev. B 1, (1970).

25

F.P. Bundy, H.T. Hall, H.M. Strong, and R.H. Wentorf, Nature 176, 51 (1955).

26

F.P. Bundy, J. Chem. Phys. 38, 631 (1963).

27

R.S. Balmer, J.R. Brandon, S.L. Clewes, H.K. Dhillon, J.M. Dodson, I. Friel, P.N. Inglis,
T.D. Madgwick, M.L. Markham, T.P. Mollart, N. Perkins, G.A. Scarsbrook, D.J. Twitchen,
A.J. Whitehead, J.J. Wilman, and S.M. Woollard, J. Physics. Condens. Matter 21, 364221
(2009).
28

J. Wilks and E. Wilks, Properties and Applications of Diamond, 3rd ed. (ButterworthHeinemann, 1994).

29

A. Khursheed, Scanning Electron Microscope Optics and Spectrometers (World Scientific,
Singapore, 2011).
30

Y. Martin, C.C. Williams, and H.K. Wickramasinghe, J. Appl. Phys. 61, 4723 (1987).

31

Murari Regmi, Ph.D. Dissertation, Michigan State University, 2008.

32

J.R. Ferraro, K. Nakamoto, and C.W. Brown, Introductory Raman Spectroscopy, second
edition (Elsevier, 2003).
33

J. Birman, Phys. Rev. 127, 1093 (1962).

34

R. Loudon, Adv. Phys. 13, 423 (1964).

35

Y. von Kaenel, J. Stiegler, J. Michler, and E. Blank, J. Appl. Phys. 81, 1726 (1997).

36

S. Ganesan, A. Maradudin, and J. Oitmaa, Ann. Phys. (N. Y). 56, 556 (1970).

37

E. Anastassakis, A. Pinczuk, and E. Burstein, Solid State Commun. 8, 133 (1970).

38

J.E. Field, The Properties of Natural and Synthetic Diamond (Academic, London, 1979).

39

M.H. Grimsditch, E. Anastassakis, and M. Cardona, Phys. Rev. B 18, 901 (1978).

40

J. Ager and M. Drory, Phys. Rev. B 48, 2601 (1993).

41

S. Porto, J. Giordmaine, and T. Damen, Phys. Rev. 147, 608 (1966).

42

J.L. Vossen and W. Kern, editors, Thin Film Processes (Academic Press, INC., 1978).

43

M.A. Lieberman and A.J. Lichtenberg, Principles of Plasma Discharges and Materials
Processing (John Wiley & Sons, Inc., New York, 1994).

44

H.V. Boening, Plasma Science and Technology (Cornell University Prss, London, 1982).
169

45

R.E. Clausing, L.L. Horton, J.C. Angus, and P. Koidl, editors, Diamond and Diamond-like
Films and Coatings (Plenum Press, New York, 1991).

46

K. Kuo and J. Asmussen, Diam. Relat. Mater. 6, 1097 (1997).

47

C.R. Bednarski-Meinke, Ph.D. Dissertation, Michigan State University, 2002.

48

J. Asmussen and D. Reinhard, Diamond Films Handbook (CRC press, 2002).

49

J.C. Angus, J. Appl. Phys. 39, 2915 (1968).

50

D.J. Poferl, J. Appl. Phys. 44, 1428 (1973).

51

J.C. Angus and C.C. Hayman, Science 241, 913 (1988).

52

B.V. Spitsyn, L.L. Bouilov, and B.V. Derjaguin, J. Cryst. Growth 52, 219 (1981).

53

M. Kamo, Y. Sato, S. Matsumoto, and N. Setaka, J. Cryst. Growth 62, 642 (1983).

54

A. Sawabe and T. Inuzuka, Appl. Phys. Lett. 46, 146 (1985).

55

C.J. Chu, R.H. Hauge, J.L. Margrave, and M.P. D’Evelyn, Appl. Phys. Lett. 61, 1393
(1992).

56

H. Maeda, K. Ohtsubo, M. Irie, N. Ohya, K. Kusakabe, and S. Morooka, J. Mater. Res. 10,
3115 (1995).

57

I. Sakaguchi, M. Nishitani-Gamo, K.P. Loh, H. Haneda, and T. Ando, J. Appl. Phys. 86,
1306 (1999).
58

J. Achard, A. Tallaire, R. Sussmann, F. Silva, and A. Gicquel, J. Cryst. Growth 284, 396
(2005).

59

T. Teraji, Phys. Status Solidi 203, 3324 (2006).

60

C.-S. Yan and Y.K. Vohra, Diam. Relat. Mater. 8, 2022 (1999).

61

J. Lu, Y. Gu, T.A. Grotjohn, T. Schuelke, and J. Asmussen, Diam. Relat. Mater. 37, 17
(2013).

62

K. Kobashi, K. Nishimura, Y. Kawate, and T. Horiuchi, Phys. Rev. B 38, 4067 (1988).

63

C. Wild, R. Kohl, N. Herres, and P. Koidl, Diam. Relat. Mater. 3, 373 (1994).

64

F. Silva, J. Achard, X. Bonnin, A. Michau, A. Tallaire, O. Brinza, and A. Gicquel, Phys.
Status Solidi 203, 3049 (2006).

65

M. Volmer and A. Weber, A. Phys. Chemie 119, 277 (1925).

66

R. Becker and W. Doering, 24, 719 (1935).

67

J. Frenkel, J. Chem. Phy. 7, 538 (1939).

68

J.B. Zeldovich, Acta Physicochim. USSR 18, 1 (1943).
170

69

L. Zang, Lecture Note: Kinetics (2013).

70

J.A. Venables, Introduction to Surface and Thin Film Processes, 2nd ed. (Cambridge
University Press, 2003).

71

H. Yamada, A. Chayahara, H. Umezawa, N. Tsubouchi, Y. Mokuno, and S. Shikata, Diam.
Relat. Mater. 24, 29 (2012).

72
73

R.J. Jaccodine, Jounral Electrochem. Soc. 110, 524 (1963).
The CVD Diamond Booklet (Freiburg, 2008).

74

P. Becker, P. Scyfried, and H. Siegert, Zeitschrift Für Phys. B Condens. Matter 48, 17
(1982).

75
76

J.W. Arblaster, Platin. Met. Rev. 54, 93 (2010).
Strontinum Titanate-Properties and Applications (Macclesfield, 2013).

77

O. Madelung, U. Rössler, and M. Schulz, editors, II-VI and I-VII Compounds;
Semimagnetic Compounds (Springer-Verlag, Berlin/Heidelberg, 1999).

78

Single Crystal Sapphire (Vancouver, 2012).

79

P.C. Yang, R. Schlesser, C.A. Wolden, W. Liu, R.F. Davis, Z. Sitar, and J.T. Prater, Appl.
Phys. Lett. 70, 2960 (1997).

80

Z. Sitar, W. Liu, P.C. Yang, C.A. Wolden, R. Schlesser, and J.T. Prater, Diam. Relat.
Mater. 7, 276 (1998).
81

S.D. Wolter, B.R. Stoner, J.T. Glass, P.J. Ellis, D.S. Buhaenko, C.E. Jenkins, and P.
Southworth, Appl. Phys. Lett. 62, 1215 (1993).

82

W. Zhu, X. Wang, B. Stoner, G. Ma, H. Kong, M. Braun, and J. Glass, Phys. Rev. B 47,
6529 (1993).
83

X. Jiang, M. Fryda, and C.L. Jia, Diam. Relat. Mater. 9, 1640 (2000).

84

X. Jiang and C.L. Jia, Appl. Phys. Lett. 67, 1197 (1995).

85

C. Jia, K. Urban, and X. Jiang, Phys. Rev. B 52, 5164 (1995).

86

S. Koizumi, T. Murakami, T. Inuzuka, and K. Suzuki, Appl. Phys. Lett. 57, 563 (1990).

87

S. Koizumi, Isr. J. Chem. 38, 33 (1998).

88

W.A. Yarbrough and R. Messier, Science 247, 688 (1990).

89

R.H. Wentorf, Adv. Chem. Phys. 9, 365 (1965).

90

T. Tachibana, Y. Yokota, K. Nishimura, K. Miyata, K. Kobashi, and Y. Shintani, Diam.
Relat. Mater. 5, 197 (1996).

171

91

M. Hansen, Constitution of Binary Alloys, 2nd ed. (McGraw-Hill Book Co., New York,
Toronto, London, 1958).

92

C.H. Lee, J. Qi, S.T. Lee, and L.S. Hung, Diam. Relat. Mater. 12, 1335 (2003).

93

Y. Wu, J. Qi, C.H. Lee, L.S. Hung, W.J. Zhang, I. Bello, Y. Lifshitz, and S.T. Lee, Diam.
Relat. Mater. 12, 1675 (2003).
94

S. Iijima, Y. Aikawa, and K. Baba, J. Mater. Res. 6, 1491 (1991).

95

S. Yugo, T. Kanai, T. Kimura, and T. Muto, Appl. Phys. Lett. 58, 1036 (1991).

96

K. Kobayashi, N. Mutsukura, and Y. Machi, Mater. Manuf. Process. 7, 395 (1992).

97

J.E. Yehoda, R.I. Fuentes, J.C. Tsang, S.J. Whitehair, C.R. Guarnieri, and J.J. Cuomo,
Appl. Phys. Lett. 60, 2865 (1992).

98

S.J. Lin, S.L. Lee, J. Hwang, C.S. Chang, and H.Y. Wen, Appl. Phys. Lett. 60, 1559 (1992).

99

J. Narayan, V.P. Godbole, G. Matera, and R.K. Singh, J. Appl. Phys. 71, 966 (1992).

100

D. Michau, B. Tanguy, G. Demazeau, M. Couzi, and R. Cavagnat, Diam. Relat. Mater. 2,
19 (1993).
101

H. Liu and D.S. Dandy, Diam. Relat. Mater. 4, 1173 (1995).

102

Sz. Katai, A. Kovats, I. Maros, and P. Deak, Diam. Relat. Mater. 9, 317 (2000).

103

S. Yugo, T. Kimura, and T. Kanai, Diam. Relat. Mater. 2, 328 (1992).

104

S. Yugo, K. Semoto, K. Hoshina, T. Kimura, and H. Nakai, Diam. Relat. Mater. 4, 903
(1995).

105

X. Jiang, K. Schiffmann, and C.-P. Klages, Phys. Rev. B 50, 8402 (1994).

106

X. Jiang, W. Zhang, and C.-P. Klages, Phys. Rev. B 58, 7064 (1998).

107

K. Perng, K.-S. Liu, and I.-N. Lin, J. Appl. Phys. 91, 3934 (2002).

108

B.W. Sheldon, R. Csencsits, J. Rankin, R.E. Boekenhauer, and Y. Shigesato, J. Appl. Phys.
75, 5001 (1994).

109

S.P. McGinnis, M.A. Kelly, S.B. Hagström, and R.L. Alvis, J. Appl. Phys. 79, 170 (1996).

110

J. Robertson, Diam. Relat. Mater. 2, 984 (1993).

111

J. Robertson, Diam. Relat. Mater. 3, 361 (1994).

112

J. Robertson, Appl. Phys. Lett. 66, 3287 (1995).

113

Y. Lifshitz, S. Kasi, and J. Rabalais, Phys. Rev. Lett. 62, 1290 (1989).

114

M.D. Whitfield, R.B. Jackman, D. Rodway, J.A. Savage, and J.S. Foord, J. Appl. Phys. 80,
3710 (1996).
172

115

J.A. Mucha, D.L. Flamm, and D.E. Ibbotson, J. Appl. Phys. 65, 3448 (1989).

116

M. Schreck, T. Bauer, and B. Stritzker, Diam. Relat. Mater. 4, 553 (1995).

117

R. Stöckel, K. Janischowsky, S. Rohmfeld, J. Ristein, M. Hundhausen, and L. Ley, Diam.
Relat. Mater. 5, 321 (1996).
118

R. Stöckel, M. Stammler, and K. Janischowsky, J. Appl. Phys. 83, 531 (1998).

119

S. Barrat, S. Saada, I. Dieguez, and E. Bauer-Grosse, J. Appl. Phys. 84, 1870 (1998).

120

Y. Shigesato, R.E. Boekenhauer, and B.W. Sheldon, Appl. Phys. Lett. 63, 314 (1993).

121

Y.-K. Kim and J.-Y. Lee, J. Appl. Phys. 81, 3660 (1997).

122

G. Balestrino, M. Marinelli, E. Milani, A. Paoletti, I. Pinter, A. Tebano, and P. Paroli,
Appl. Phys. Lett. 62, 879 (1993).
123

A. Sawabe, H. Fukuda, T. Suzuki, Y. Ikuhara, and T. Suzuki, Surf. Sci. 467, 845 (2000).

124

K. Ohtsuka, K. Suzuki, A. Sawabe, and T. Inuzuka, Jpn. J. Appl. Phys. 35, L1072 (1996).

125

M. Regmi, K. More, and G. Eres, Diam. Relat. Mater. 23, 28 (2012).

126

F. Hörmann, M. Schreck, and B. Stritzker, Diam. Relat. Mater. 10, 1617 (2001).

127

T. Bauer, S. Gsell, F. Hörmann, M. Schreck, and B. Stritzker, Diam. Relat. Mater. 13, 335
(2004).

128

M. Schreck, T. Bauer, S. Gsell, F. Hörmann, H. Bielefeldt, and B. Stritzker, Diam. Relat.
Mater. 12, 262 (2003).

129

N. Vaissiere, S. Saada, M. Bouttemy, A. Etcheberry, P. Bergonzo, and J.C. Arnault, Diam.
Relat. Mater. 36, 16 (2013).

130

A. Nikitin, L.-Å. Näslund, Z. Zhang, and A. Nilsson, Surf. Sci. 602, 2575 (2008).

131

S. Rey, F. Antoni, B. Prevot, E. Fogarassy, J.C. Arnault, J. Hommet, F. Le Normand, and
P. Boher, Appl. Phys. A Mater. Sci. Process. 71, 433 (2000).
132

A. Chavanne, J. Barjon, B. Vilquin, J. Arabski, and J.C. Arnault, Diam. Relat. Mater. 22,
52 (2012).

133

S. Gsell, M. Schreck, G. Benstetter, E. Lodermeier, and B. Stritzker, Diam. Relat. Mater.
16, 665 (2007).

134

T. Bauer, M. Schreck, F. Hörmann, A. Bergmaier, G. Dollinger, and B. Stritzker, Diam.
Relat. Mater. 11, 493 (2002).

135

S. Gsell, S. Berner, T. Brugger, M. Schreck, R. Brescia, M. Fischer, T. Greber, J.
Osterwalder, and B. Stritzker, Diam. Relat. Mater. 17, 1029 (2008).

173

136

A. Hoffman, S. Michaelson, R. Akhvlediani, N.K. Hangaly, S. Gsell, R. Brescia, M.
Schreck, B. Stritzker, J.C. Arnault, and S. Saada, Phys. Status Solidi Appl. Mater. Sci. 206,
1972 (2009).

137

C. Stehl, M. Fischer, S. Gsell, E. Berdermann, M.S. Rahman, M. Traeger, O. Klein, and M.
Schreck, Appl. Phys. Lett. 103, 3 (2013).

138

D. Hull and D.J. Bacon, Introduction to Dislocations (Elsevier, 2011).

139

F.W. Tausch and A.G. Lapierre, J. Electrochem. Soc. 112, 706 (1965).

140

M. Michelitsch, J. Electrochem. Soc. 112, 747 (1965).

141

D.W. Shaw, J. Electrochem. Soc. 113, 904 (1966).

142

T. Nishinaga, T. Nakano, and S. Zhang, Jpn. J. Appl. Phys. 27, L964 (1988).

143

A. Usui, H. Sunakawa, A. Sakai, and A.A. Yamaguchi, Jpn. J. Appl. Phys. 36, L899
(1997).
144

A. Sakai, H. Sunakawa, and A. Usui, Appl. Phys. Lett. 71, 2259 (1997).

145

A. Sakai, H. Sunakawa, and A. Usui, Appl. Phys. Lett. 73, 481 (1998).

146

Y. Kawaguchi, S. Nambu, H. Sone, T. Shibata, H. Matsushima, M. Yamaguchi, T.
Miyake, K. Hiramatsu, and N. Sawaki, Jpn. J. Appl. Phys. 37, L845 (1998).

147

H. Sone, S. Nambu, Y. Kwawguchi, M. Yamaguchi, H. Miyake, K. Hiramatsu, Y.
Iyechika, T. Maeda, and N. Sawaki, Jpn. J. Appl. Phys. 38, L356 (1999).
148

Y. Honda, Y. Iyechika, T. Maeda, H. Miyake, and K. Hiramatsu, Japanes J. Appl. Phys.
38, L1299 (1999).

149

S. Tomiya, K. Funato, T. Asatsuma, T. Hino, S. Kijima, T. Asano, and M. Ikeda, Appl.
Phys. Lett. 77, 636 (2000).
150

T.S. Zheleva, S.A. Smith, D.B. Thomson, K.J. Linthicum, P. Rajagopal, and R.F. Davis, J.
Electron. Mater. 28, L5 (1999).

151

I. Kidoguchi, A. Ishibashi, G. Sugahara, and Y. Ban, Appl. Phys. Lett. 76, 3768 (2000).

152

T.D. Detchprohm, M. Yano, S. Sano, R. Nakamura, and S. Mochiduki, Jpn. J. Appl. Phys.
40, L16 (2001).
153

X. Zhang, R.R. Li, P.D. Dapkus, and D.H. Rich, Appl. Phys. Lett. 77, 2213 (2000).

154

T. Bauer, M. Schreck, and B. Stritzker, Diam. Relat. Mater. 16, 711 (2007).

155

B. Wölfing, K. Theis-Bröhl, C. Sutter, and H. Zabel, J. Phys. Condens. Matter 11, 2669
(1999).

156

J. Michler, M. Mermoux, Y. Von Kaenel, A. Haouni, G. Lucazeau, and E. Blank, Thin
Solid Films, 357, 189 (1999).
174

157

O. Dorsch, M. Werner, and E. Obermeier, Diam. Relat. Mater. 4, 456 (1995).

158

Y. Ando, Y. Nishibayashi, K. Kobashi, T. Hirao, and K. Oura, Diam. Relat. Mater. 11,
824 (2002).
159

D.S. Hwang, T. Saito, and N. Fujimori, Diam. Relat. Mater. 13, 2207 (2004).

160

J. Enlund, J. Isberg, M. Karlsson, F. Nikolajeff, J. Olsson, and D.J. Twitchen, Carbon 43,
1839 (2005).
161

D.T. Tran, T.A. Grotjohn, D.K. Reinhard, and J. Asmussen, Diam. Relat. Mater. 17, 717
(2008).
162

S.J. Pearton, A. Katz, F. Ren, and J.R. Lothian, Electron. Lett. 28, 822 (1992).

163

A.F. Isakovic, A. Stein, J.B. Warren, S. Narayanan, M. Sprung, A.R. Sandy, and K.
Evans-Lutterodt, J. Synchrotron Radiat. 16, 8 (2008).
164

B.J.M. Hausmann, M. Khan, Y. Zhang, T.M. Babinec, K. Martinick, M. McCutcheon, P.R.
Hemmer, and M. Lončar, Diam. Relat. Mater. 19, 621 (2010).

165

D.T. Tran, C. Fansler, T.A. Grotjohn, D.K. Reinhard, and J. Asmussen, Diam. Relat.
Mater. 19, 778 (2010).
166

S.A. Grot, R.A. Ditizio, G.S. Gildenblat, A.R. Badzian, and S.J. Fonash, Appl. Phys. Lett.
61, 2326 (1992).

167

O. Dorsch, M. Werner, and E. Obermeier, Diam. Relat. Mater. 1, 277 (1992).

168

T. Yamada, H. Yoshikawa, H. Uetsuka, S. Kumaragurubaran, N. Tokuda, and S.I. Shikata,
Diam. Relat. Mater. 16, 996 (2007).

169

B.R. Stoner, G.J. Tessmer, and D.L. Dreifus, Appl. Phys. Lett. 62, 1803 (1993).

170

K. Kobashi, T. Tachibana, Y. Yokota, N. Kawakami, K. Hayashi, K. Yamamoto, Y. Koga,
S. Fujiwara, Y. Gotoh, H. Nakahara, H. Tsuji, J. Ishikawa, F.A. Köck, and R.J. Nemanich, J.
Mater. Res. 18, 305 (2003).
171

R. Hsiao, D. Miller, S. Nguyen, and A. Kellock, Appl. Surf. Sci. 148, 1 (1999).

172

Y.-H. Tang, B. Bi, and B. Golding, MRS Proc. 1734, mrsf14-1734-r05-04 (2015).

173

Y.S. Touloukian, R.K. Kirby, R.E. Taylor, and T.Y.R. Lee, Thermophysical Properties of
Matter (IFI Plenum, New York, 1971).

175