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Microwave plasma-assisted chemical vapor deposition and characterization of (001) homoepitaxial diamond films

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The Pennsylvania State University
The Graduate School
MICROWAVE PLASMA-ASSISTED CHEMICAL VAPOR DEPOSITION AND
CHARACTERIZATION OF (001) HOMOEPITAXIAL DIAMOND FILMS
A Thesis in
Materials
by
Naesung Lee
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor o f Philosophy
May 1996
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UMI Number: 9628125
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We approve the thesis of Naesung Lee.
Date o f Signature
Andrzej R. Badzian
Professor o f Materials
Thesis Advisor
Chair o f Committee
F. Messier
Professor o f Engineering Science
and Mechanics
3 -0
/ TfC
William B. White
Professor o f Geochemistry
Barbara J. Garrigprf
Professor of Chemistry
Id
1/ 3 0 / ? f e
Robert N. Pangborn
Professor o f Engineering Mechanics
Chair of the Intercollege Graduate
Program in Materials
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ABSTRACT
This thesis presents a comprehensive study on the surface morphologies and
structure of (001) homoepitaxial diamond films prepared by microwave plasma-assisted
chemical vapor deposition (MPACVD). A particular emphasis was placed on the
description of the epitaxial growth mechanisms by linking the surface morphologies and
structure to the deposition parameters. This study is expected to make a significant
contribution not only toward establishing the optimum deposition conditions for high-quality
homoepitaxial diamond films but also toward better understanding the growth mechanisms
o f epitaxial diamond films.
A systematic study of the surface morphologies and structure of (001) homoepitaxial
diamond films with the deposition parameters indicates that growth of these films depends
strongly on the surface misorientation angles of substrates toward the [110] or [110]
direction, methane concentrations, and growth temperatures.
Remarkably different surface morphologies were observed on etched substrates and
homoepitaxial diamond films with different misorientation angles. On the etched surface,
the density o f etch pits decreased drastically by increasing the misorientation angles. For the
as-grown films, growth hillocks and macrosteps occurred on the well-oriented and
misoriented substrates, respectively. Step-flow growth resulted in higher growth rates than
hillock growth. The dependence of the etching and growth morphologies as well as the
growth rates on the misorientation angles indicates that surface steps play a significant role
in diamond etching and growth. In this study, therefore, etching and growth mechanisms on
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the diamond (001) surface were considered in terms of the reactions of atomic hydrogen and
hydrocarbon precursors with the atomic steps and terraces on the surface, respectively. It is
proposed that hillock growth occurs through two-dimensional nucleation on terraces when
the density o f surface steps is low, while the step-flow growth proceeds along the
<110> directions on the substrates with the high density of steps.
The homoepitaxial diamond growth with a low methane concentration of 1%
produced macrosteps with the surface close to the single-domain structure, while at high
methane concentrations of 2% and 6%, growth hillocks and random growth features
occurred with the double-domain surface, respectively. The variation of surface
morphologies and structure with the methane concentrations is attributed to lower mobility
and shorter diffusion length of adsorbates on the surface at higher methane concentrations.
During the step-flow growth, step bunching was more apparent at a lower
temperature of 875 °C than at 1200 °C. In terms of surface diffusion o f adsorbates as well
as step bunching, the high temperature growth seems to be more promising for the
deposition of high-quality and smooth films. Step-flow growth with the single-domain
surface is believed to produce higher-quality films with fewer lattice defects than other
growth modes. It is likely that the step-flow growth is favored by increasing the
misorientation angles, lowering the methane concentrations, and increasing the growth
temperatures. This study suggests that the deposition condition for (001) homoepitaxial
diamond films is optimized with misorientation angles of approximately 3-5°, methane
concentrations of less than 1%, and substrate temperatures o f around 1200 °C.
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Reflection high-energy electron diffraction (RHEED) has been used to study the
surface structure of the diamond (001) substrates annealed in H plasma and of as-grown
films. The 2x1 surface reconstruction occurred on all diamond (001) substrates annealed at
650 to 1300 °C in H plasma. It was found that reconstruction takes place at a much lower
temperature in H plasma than in ultra-high vacuum. This indicates that CVD diamond
growth proceeds on the reconstructed surface over the range of temperatures investigated.
The domain and step structure of the diamond (001) surface was investigated by
comparing the intensities of two series of the half-order RHEED spots. The surface
annealed in H plasma showed the transition from the double-domain to the nearly single­
domain structure by increasing the misorientation angles. This transition is temperaturedependent. The as-grown films exhibited the double-domain structure on the well-oriented
surface and the surface close to the single-domain structure on the misoriented surface.
When the surface was close to the single-domain structure, type-A terraces dominated the
H-plasma annealed surface while type-B terraces were the major domain of the as-grown
film surface. This implies that DA and DB steps are present on the H-plasma annealed
surface and on the as-grown surface, respectively. DA steps have never been observed even
on the Si (001) surface. It is inferred that the step formation energies increase in the order
of Da, Sa +Sb, and DB on the surface annealed in H plasma and in the order of DB, SA+SB,
and Da on the as-grown films.
The diamond (001) films which were homoepitaxially grown with boron doping and
subsequently followed by H-plasma annealing, were also investigated using scanning
tunneling microscopy (STM). In this study, an atomic resolution was achieved so that
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individual dimers and even individual atoms in the dimers could be seen. High-resolution
atomic images showed that on the H-terminated diamond (001) surface, the 2x1 :H
monohydride structure was predominant, but the lx l:2 H structure and local 3xl:1.33H
configuration existed only in a very local area and in a very low concentration. For the Hplasma annealed diamond (001) surface, the double-domain structure was observed at a low
misorientation angle while the single-domain structure occurred with type-A terraces and
Da steps at a high misorientation angle. The STM observations of the double-domain and
single-domain structures with the misorientation angles were in good agreement with the
RHEED results. DA steps which were predicted to be present on the single-domain surface
annealed in H plasma by a RHEED study, were confirmed by STM. Atomic images also
revealed several types of surface defects including antiphase boundaries, islands, and dimer
vacancies on the diamond (001) surface.
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TABLE OF CONTENTS
LIST OF FIGURES.......................................................................................................xi
LIST OF TABLES....................................................................................................... xix
ACKNOWLEDGMENTS.............................................................................................xx
PREFACE................................................................................................................... xxi
Chapter 1. GENERAL INTRODUCTION.....................................................................1
Chapter 2. BACKGROUND......................................................................................... 6
2.1. Introduction...................................................................................................... 6
2.2. Surface structure of clean, hydrogenated, and MBE-grown Si (001).............. 7
2.2.1. Surface structure of clean Si (001)......................................................... 7
2.2.1.1. Surface reconstruction of clean Si (001).........................................7
2.2.1.2. Energetical considerations o f step structure
on Si (001) surfaces..................................................................... 10
2.2.1.3. Equilibrium structure o f clean Si (001) surfaces.......................... 17
2.2.2. Surface structure of hydrogenated Si (001)..........................................22
2.2.3. Surface diffusion of Si atoms on Si (001) surfaces.............................. 26
2.2.4. Homoepitaxial growth on Si (001) surfaces
by molecular beam epitaxy....................................................................30
2.3. Chemical vapor deposition of diamond at low pressures................................ 38
2.3.1. History of diamond growth at low pressures..........................................38
2.3.2. Synthesis techniques o f diamond at low pressures................................42
2.3.3. Growth mechanisms of diamond at low pressures............................... 47
2.3.3.1. Role of atomic hydrogen.............................................................. 47
2.3.3.2. Diamond precursors and growth mechanisms............................... 49
2.3.4. Homoepitaxial growth of diamond film s ...............................................56
2.3.4.1. Homoepitaxial diamond growth at different sectors.................... 56
2.3.4.2. (001) homoepitaxial diamond film s ............................................. 60
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2.4. Objectives o f this study..................................................................................65
Chapter 3. EXPERIMENTAL................................................................................... 68
3.1. Introduction.................................................................................................... 68
3.2. Measurement of surface misorientation angles of diamond substrates...........68
3.2.1.
3.2.2.
3.2.3.
3.2.4.
3.2.5.
Principles of back-reflection Laue x-ray diffraction............................. 69
Definition of surface misorientation angles.......................................... 72
Coordinates of back-reflection Laue spots........................................... 76
Description of a computer program...................................................... 82
Experimental details.............................................................................. 84
3.3. MPACVD system for diamond deposition.....................................................88
3.3.1. Description of a tubular MPACVD system.......................................... 88
3.3.2. Diamond deposition procedures ........................................................... 92
3.4. Reflection high-energy electron diffraction (RHEED).................................. 93
3.4.1.
3.4.2.
3.4.3.
3.4.4.
3.5.
3.6.
3.7.
3.8.
3.9.
3.10.
Diffraction from surfaces...................................................................... 96
Construction of RHEED patterns........................................................ 103
Kinematic theory for RHEED intensity............................................... 115
Experimental details............................................................................ 118
Low-energy electron diffraction (LEED)..................................................... 121
Differential interference contrast optical microscopy (D IC M ).....................125
Scanning electron microscopy (S E M )......................................................... 127
Scanning tunneling microscopy (STM )........................................................ 128
Raman spectroscopy..................................................................................... 130
Profilometry for the measurement o f surface roughness............................. 132
Chapter 4. SURFACE MORPHOLOGIES OF (001) HOMOEPITAXIAL
DIAMOND FILM S.................................................................................. 134
4.1.
4.2.
4.3.
4.4.
Introduction.................................................................................................. 134
Literature review.......................................................................................... 135
Experimental details..................................................................................... 138
Results.......................................................................................................... 140
4.4.1. Effect o f surface misorientation angles o f substrates.......................... 140
4.4.1.1. Surface morphologies o f etched substrates................................. 140
4.4.1.2. Surface morphologies of homoepitaxial film s ............................ 144
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4.4.2. Effect of methane concentrations
153
4.5. Discussion.....................................................................................................167
4.6. Summary....................................................................................................... 177
Chapter 5. DIAMOND (001) SURFACE STRUCTURE STUDIED
USING R H EED ....................................................................................... 180
5.1.
5.2.
5.3.
5.4.
Introduction................................................................................................... 180
Literature review........................................................................................... 181
Experimental details...................................................................................... 185
Results........................................................................................................... 186
5.4.1.
5.4.2.
Reconstruction of diamond (001) surfaces in H plasma......................186
Domain structure of diamond (001) surfaces......................................192
5.5. Discussion.................................................................................................... 200
5.5.1.
5.5.2.
5.5.3.
Diamond (001) surface reconstruction................................................200
Diamond (001) surface structure........................................................ 201
Relative stabilities of steps on diamond (001) surfaces.......................205
5.6. Summary....................................................................................................... 211
Chapter 6. STM STUDY OF (001) HOMOEPITAXIAL DIAMOND FILMS
6.1.
6.2.
6.3.
6.4.
6.5.
6.6.
6.7.
212
Introduction................................................................................................... 212
Literature review........................................................................................... 212
Experimental details......................................................................................216
Surface atomic structure o f (001) homoepitaxial diamond film s.................. 217
Domain and step structure of (001) homoepitaxial diamond film s .............. 229
Surface defects o f (001) homoepitaxial diamond film s.................................238
Summary....................................................................................................... 246
Chapter 7. CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK
247
7.1. Conclusions................................................................................................... 247
7.1.1. Surface morphologies o f (001) homoepitaxial diamond film s
247
7.1.2. Surface structure of diamond (001) surfaces....................................... 250
7.1.3. STM study of diamond (001) surfaces.................................................253
7.2. Suggestions for future work.......................................................................... 255
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BIBLIOGRAPHY........................................................................................................ 258
Appendix. COMPUTER PROGRAM FOR THE CALCULATION OF
SURFACE MISORIENTATION ANGLES.............................................274
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LIST OF FIGURES
Figure 1.1 General overview of the research. <j>, CH4, and T denote the surface
misorientation angles of substrates, the methane concentrations in
hydrogen and the substrate temperatures, respectively.................................4
Figure 2.1 Cross-sectional and plan views o f the clean Si (001) surface: (a)
unreconstructed surface, (b) 2x1 symmetric dimer reconstruction, (c)
2x2 alternating buckled dimer reconstruction. Shaded circles denote
the uppermost-layer atoms and in the cross-sectional view, larger
circles represent atoms on an upper terrace or at higher position................8
Figure 2.2 Top views of various steps on the clean Si (001) surface: (a) SA,
(b) SB, (c) Da, and (d) DB steps. Larger circles represent upperterrace atoms and shaded circles denote atoms with dangling
bonds. The dashed lines which run parallel to the step edges,
indicate the step positions (Chadi, 1987).................................................... 13
Figure 2.3 STM image of the clean Si (001) surface (Hamers et al., 1990).
The scan area is 87x87 nm2........................................................................ 16
Figure 2.4 Several hydrogenated Si (001) surface structures: (a) lx l :2H
dihydride structure, (b) 2x1 :H monohydride structure, and
(c) 3xl:1.33H structure. (Boland, 1990)....................................................23
Figure 3.1 Schematic illustration o f a back-reflection Laue technique........................71
Figure 3.2 Definition of a surface misorientation angle <j) with respect to
the crystallographic (001) plane in the principal crystal axes.................... 74
Figure 3.3 Definition of two component angles a and f t resolved toward the
[110] and [110] directions, respectively, o f a surface misorientation
angle (j>. The [001] direction points back from the paper plane..................75
Figure 3.4 Introduction of a new Cartesian coordinate system u vw ............................77
Figure 3.5 Polar coordinates of a plane normal g in the uvw coordinate system
79
Figure 3.6 Coordinates XL and YL o f a back-reflection Laue spot................................81
Figure 3.7 Schematic flow chart o f a computer program for the calculation
of a surface misorientation angle................................................................83
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Figure 3.8 Back-reflection Laue x-ray diffraction pattern o f a diamond (001)
substrate. Part of diffraction spots are indexed. Numbers in
parentheses are the distances o f spots from the center of the
film in mm..................................................................................................87
Figure 3.9 Schematic of the tubular microwave plasma-assisted chemical vapor
deposition system: (a) waveguide for microwave transmission and
(b) reaction chamber................................................................................ 89
Figure 3.10 Schematic arrangement for RHEED experiments.....................................95
Figure 3.11 Construction of the Ewald sphere and geometry of RHEED
from the two-dimensional reciprocal lattice net....................................... 99
Figure 3.12 Geometry of diffraction from the two-dimensional reciprocal
lattice net for the non-zero incidence angle: (a) the Ewald
sphere construction and (b) RHEED pattern.......................................... 105
Figure 3.13 Cross-sectional view of RHEED geometry for the non-zero
incidence angle........................................................................................ 107
Figure 3.14 Unreconstructed and 2x1 reconstructed diamond (001) surface
structures and their reciprocal lattice nets: (a) unreconstructed
surface, (b) 2x1 reconstructed surface, (c) 1x2 reconstructed
surface, (d) reciprocal lattice net o f the unreconstructed surface,
(e) reciprocal lattice net o f the 2x1 reconstructed surface,
(0 reciprocal lattice net of the 1x2 reconstructed surface, and
(g) superposed reciprocal lattice net o f (d), (e), and ( f ) ......................... 108
Figure 3.15 Schematic RHEED patterns predicted from the two-dimensional
reciprocal lattice (a) in the [100] azimuth and (b) in the [110]
azimuth for reconstructed diamond (001) surface. Large closed
circles, small closed circles, and small open circles in the reciprocal
lattice correspond to the fundamental, 2x1 superlattice, and 1x2
superlattice rods, respectively. Their reflections in the pattern are
designated by the same types o f circles...................................................110
Figure 3.16 Schematic illustration of relations betweensurface topography and
RHEED patterns: (a) a surface with high and wide, but thin
protrusions, (b) a surface with low and wide, but thin protrusions,
(c) a surface with multilevel islands, and (d) a flat surface
(Lagally et al., 1988)............................................................................ 114
Figure 3.17 Sample preparation for RHEED using aTEM g rid ................................ 120
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Figure 3.18 Effect o f the step-up and step-down incidences of an electron beam
on the RHEED patterns: (a) step-up incidence and (b) step-down
incidence, and their corresponding [100] azimuthal RHEED
patterns of the diamond (001) surface misoriented 0.8° and 3.0°
toward [110] and [1 1 0 ].......................................................................... 122
Figure 3.19 Schematic o f a LEED system.................................................................124
Figure 3.20 Construction o f the Ewald sphere and geometry of LEED from
the two-dimensional reciprocal lattice n e t.............................................. 126
Figure 4.1 SEM images o f the diamond (001) surfaces etched for 1 hr at
1300 °C and 150 Torr H2: (a) 0.1°, (b) 3.5°, (c) 11.0° o ff substrates,
and (d) high magnification of (a). The directions of images are
designated in Fig. 2 ..................................................................................142
Figure 4.2 DICM images of the surface morphologies of homoepitaxial
diamond films grown at 1200 °C, 90 Torr, and 1% CH4 in H2
on (a) 0.1° o ff (001) substrate for 5 hr, (b) 3.5°, and (c) 11.0°
o ff (001) substrates for 8 hr...................................................................... 145
Figure 4.3 Configuration o f macrosteps for the homoepitaxial growth on
the diamond (001) substrates misoriented toward (a) [110]
and (b) [1001.............................................................................................147
Figure 4.4 DICM images o f the surface morphologies of homoepitaxial
diamond films grown for 15 hr at 1200 °C, 90 Torr, and 1%
CH4 in H2 on (a) 0.1°, (b) 3.5°, and (c) 11.0° o ff (001)
substrates................................................................................................... 149
Figure 4.5 Growth rates as a function of the surface misorientation angles
of substrates at 1200 °C,90 Torr, and 1% CH4in H2.............................. 150
Figure 4.6 RHEED patterns of the (001) film surfaces grown on (a) 0.1°,
(c) 3.5°, and (c) 11.0° o ff substrates at the condition specified in
Fig. 2, taken from [100] for the left and [110] azimuths for the
right patterns. The insets of [110] azimuthal patterns show
magnified views of the zeroth Laue zone. L 1/2 and
denote the
half-order and first-order Laue rings,respectively.................................... 152
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x iv
Figure 4.7 Raman spectra o f the 0.1° o ff (001) substrate and the
homoepitaxial diamond film grown for 15 hr with 1% CH4 in H2
at 1200 °C: (a) spectra taken in the range of 1315-1350 cm '1at
0.25 cm'1 intervals with the slit width o f 100 pm and (b) spectra
taken in the range o f 400-8000 cm'1 at 5 cm’1 intervals with the
slit width o f 200 pm. Numbers in (a) represent the full widths at
half maximum............................................................................................154
Figure 4.8 DICM images of the surface morphologies of (001) homoepitaxial
diamond films grown for 5 hr at 875 °C with CH4 concentrations
o f (a) 1%. (b) 2%. and (c) 6% in H2........................................................ 156
Figure 4.9 DICM images of the surface morphologies of (001) homoepitaxial
diamond films grown for 12 hr at 875 °C with CH4
concentrations
o f (a) 1%, (b) 2%, and (c) 6% in H2........................................................ 158
Figure 4.10 DICM images taken in the same area o f (001) homoepitaxial
diamond films grown at 875 °C with 2% CH4 in H2: (a) 5 hr
and (b) 12 hr. Hillocks in (a) and their correspondence in (b)
are marked A through H ......................................................................... 161
Figure 4 .11 Growth rates as a function o f the CH4 concentrations in H2 at
875 °C, 80 T o r r ...................................................................................... 163
Figure 4.12 Surface roughness o f the diamond substrate and (001)
homoepitaxial films grown for 1, 2, and 5 hr at 875 °C with
1%, 2%, and 6% CH4 in H2. Relative average roughness is a
ratio of average roughness o f a film surface to that of the
substrate.................................................................................................... 164
Figure 4.13 RHEED patterns o f (001) homoepitaxial diamond film surfaces
grown for 30 min at 875 °C with (a) 0.5%, (b) 1.0%, (c)
2.0%, and (d) 6% CH4 in H2, taken with the [100] azimuth.
L 1/2 and L, denote the half-order and first-order Laue rings,
respectively, and arrowheads indicate the 1x2 half-order spots
166
Figure 4.14 Surface adsorbate concentration, n, and supersaturation ratio,
a, as a function o f distance from the steps for two different step
distances, where ns, n0, ac, a s are the adsorbate concentration
at the steps, the steady-state concentration of adsorbate at the
steps, the critical supersaturation ratio for the 2D nucleation,
and the supersaturation ratio at the steps, respectively: (a) a
small distance and (b) large distance between the steps...........................169
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XV
Figure 4.15 Growth mechanisms for two different step distances: (a) stepflow mechanism on a misoriented substrate and (b) hillock
growth mechanism on a well-oriented substrate..................................... 171
Figure 4.16 Surface adsorbate concentration, n , and supersaturation ratio, a,
as a function of distance from the steps for different CH4
concentrations in H2, where ns, n0, ac, a s are the adsorbate
concentration at the steps, the steady-state concentration of
adsorbate at the steps, the critical supersaturation ratio for the 2D
nucleation, and the supersaturation ratio at the steps, respectively:
(a) low, (b) medium, and (c) high CH4 concentrations..........................175
Figure 4.17 Growth mechanisms for different CH4 concentrations in H2, but
for the same misorientation angle o f substrates : (a) step-flow
growth with a low CH4, (b) hillock growth with a medium
CH4, and (c) random growth with a high CH4 concentration..................176
Figure 5.1 RHEED pattern of an acid-cleaned diamond (001) surface
taken with the [100] azimuth..................................................................... 188
Figure 5.2 RHEED patterns of diamond (001) surfaces annealed in H
plasma at (a) 650, (b) 875 and (c) 1000 °C for 30 min, and (d)
1200 and (e) 1300 °C for 10 min, taken with the [100] azimuth.
The left and right patterns are taken from the 0.1° and 3.5° off
substrates, respectively. L1/2 and L] in (b) denote the half-order
and first-order Laue rings, respectively, and arrowheads in (b)
and (c) indicate the type-A 2x1 half-order spots.......................................190
Figure 5.3 Schematic of sample set-up for RHEED, real and reciprocal
lattices, and a predicted RHEED pattern of the diamond (001)
surface : (a) geometry of sample setup for RHEED, (b) unit
cells o f 2x1 and 1x2 structures in the real space, (c) superposed
reciprocal lattice o f 2x1 and 1x2 structures, and (d) a predicted
RHEED pattern with the incident beam along [100] and with the
glancing angle of 0°. The integral-order, type-A 2x1 half-order,
and type-B 1x2 half-order reciprocal rods in (c) and their
reflection spots in (d) are represented by large closed circles,
small closed circles, and small open circles, respectively........................ 193
Figure 5.4 RHEED patterns o f (001) homoepitaxial diamond films grown
for 30 min at 1200 °C, 0.5% CH4 in H2 on (a) 0.1°, (b) 3.5°,
and (c) 11.0° off substrates, taken with the [100] azimuth. The
type-B 1x2 half-order spots in (b) are marked by arrowheads................. 197
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XVI
Figure 5.5 RHEED patterns o f diamond (001) surfaces (a) pre-annealed in
H plasma for 10 min, (b) grown for 30 min with 0.5% CH4 in
H2, and (c) post-annealed in H plasma for 5 min at 875 °C,
taken with the [100] azimuth. Arrowheads indicate the type-A
half-order spots.........................................................................................198
Figure 5.6 Step structures for (a) SA, (b) SB, (c) DA, and (d) DB types with
H atoms bonded to dangling bonds on diamond (001) surface.
Open and closed circles denote carbon and H atoms, respectively.
Larger circles are used for upper-terrace atoms. The dimerization
direction of surface carbon atoms is along the <110> directions............. 208
Figure 6.1 High-resolution STM image of a (001) homoepitaxial diamond
film to show dimer-type 2x1 reconstruction. Individual dimers in
rows are well resolved. A dimer with two bright spots is
outlined by a box. AP2 and L I represent an AP2 antiphase
boundary and the first type of a local 3x1 configuration,
respectively. The scan area is approximately about 5.8x4.4 nm2
218
Figure 6.2 Schematic of various diamond (001) surface structures
terminated by hydrogen or oxygen: (a) 2x1 :H monohydride,
(b) lx l:2 H dihydride, (c) 1x1:0 (bridging), (d) 1x1:0 (double
bond), (e) local 3xl:1.33H configuration, and (f) long-range
order 3xl:1.33H structure. Open, solid, and hatched circles
represent carbon, hydrogen, and oxygen atoms, respectively.
In (e) and (f), dotted boxes denote an unit cell of 3x1
configuration............................................................................................ 220
Figure 6.3 High-resolution STM image of a (001) homoepitaxial diamond
film to exhibit the lx l:2 H dihydride structure, surrounded by the
2x1 :H monohydride structure. The scan area is approximately
9.3x9.3 nm2..............................................................................................222
Figure 6.4 STM image of a (001) homoepitaxial diamond film with local
3xl:1.33H configurations and antiphase boundaries. The
substrate used was misoriented by 1.3° and 0.7° toward the
[110] and [110] directions. Local 3xl:1.33H configurations are
labeled L I, and two types of antiphase boundaries are marked
by API and AP2. The scan area is approximately 12x17 nm2................ 225
Figure 6.5 Schematic o f two types of local 3xl:1.33H configurations (a)
observed near the step edges and (b) observed along API
boundaries. The larger circles denote the upper-layer atoms.
Hydrogen atoms are not shown.................................................................228
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Figure 6.6 Large-area STM image of a (001) homoepitaxial diamond film to
show the 2x1 and 1x2 double-domain surface structure. The
substrate used was misoriented by 1.3° and 0.7° toward the [110]
and [110] directions. Two types o f terraces and single-layer steps
are labeled A and B, and SA and SB, respectively. A double-layer
step running parallel to the dimer rows is denoted by DA. Two
types o f local 3xl:1.33H configurations are marked L I and L2.
The scan area is approximately 20x35 nm2. The distortion o f the
image was caused by instrumental miscalibration................................... 230
Figure 6.7 LEED pattern of the (001) homoepitaxial diamond film shown in
Figure 6.6. to exhibit the 2x1 and 1x2 double-domain surface
structure. Part of LEED spots are indexed..............................................232
Figure 6.8 High-resolution STM image of a (001) homoepitaxial diamond
film to exhibit DA steps between type-A terraces C, D, and E.
The scan area is approximately 15x19 nm2..............................................234
Figure 6.9 STM image of a (001) homoepitaxial diamond film to show the
2x1 single-domain surface structure. The substrate used was
misoriented by 2.3° and 0.2° toward the [110] and [110]
directions. The scan area is approximately 22.9x22.9 nm2...................... 235
Figure 6.10 LEED pattern o f the (001) homoepitaxial diamond film shown in
Figure 6.9, to exhibit the 2x1 single-domain surface structure.
Arrows indicate the absence of one type o f half-order spots.................. 236
Figure 6.11 Schematic o f proposed structures for antiphase boundaries:
(a) two types of antiphase boundaries API and AP2 on (001)
homoepitaxial diamond films and (b) AP2 antiphase boundary
on a MBE-grown nonhydrogenated Si (001) surface. The larger
circles denote the upper-layer atoms. In (a), hydrogen atoms
are not shown......................................................................................... 239
Figure 6.12 High-resolution STM image of a AP2 boundary on (001)
homoepitaxial diamond film. Note that there is no vacancy or
step along the boundary. Lines are drawn on the dimer rows,
and AP2 denotes an antiphase boundary. The scan area is
approximately 5.6x5.0 nm2....................................................................240
Figure 6.13 STM image of a (001) homoepitaxial diamond film to exhibit
dimer vacancies, an island and an extension o f dimer rows. I,
M, and E represent an island, dimer vacancies, and an extended
dimer row. The scan area is approximately 9.4x7.6 nm2........................245
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Figure 7.1 Dependence of surface morphologies and structures o f (001)
homoepitaxial diamond films on misorientation angles of
substrates and CH4 concentrations. Diamond films were grown
at 875 and 1200 °C. Closed and open symbols denote the step
growth, and the hillock or random growth, respectively. S
represents the surface close to the type-B single-domain
structure, and D indicates the double-domain structure.............
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x ix
LIST OF TABLES
Table 4.1 Surface misorientation angles of (001) diamond substrates
towards the [110] and [110] directions, measured from x-ray
diffraction................................................................................................... 139
Table 4.2 CVD conditions for etching and homoepitaxial growth of
diamond (001) surfaces.............................................................................. 141
Table 5.1 CVD conditions for H-plasma annealing and homoepitaxial
growth of diamond (001) surfaces............................................................. 187
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XX
ACKNOWLEDGMENTS
I would like to express my deepest thanks and gratitude to my advisor, Dr.
Andrzej R. Badzian for his support, guidance, and encouragement throughout this
work. I w ill never forget that he has treated me with respect, kindness, and friendship.
Appreciation is extended to my thesis committee members, Dr. Russell F. Messier, Dr.
William B. White, and Dr. Barbara J. Garrison for their invaluable suggestions.
This work has been funded by the National Science Foundation and the Office
of Naval Research. I gratefully acknowledge the Ministry of Education, Korea, for the
financial support during my first three years.
There are many people who have contributed to my thesis. Special thanks go to
Mrs. Teresa Badzian for her kindness and encouragement. I am appreciative of my
interactions with Yalei Kuang who conducted the Scanning Tunneling Microscopy
experiments. Thanks go to Bill Drawl, Phil Swab, and Chris Engdahl for providing
technical support. I would like to extend my gratitude to my office-mates, Brock Weiss
and Greg Barber for their friendship and many useful discussion. 1 thank Dr. Soon
Park for his cheerfulness and helpfulness, and Mrs. Hazel Hunley for her valuable
comments.
This thesis is dedicated to my parents, parents-in-law, brothers, my wife and
only lover, Jinkyung, and our lovely son, Hyunkoo, without whose endless love,
patience, and support all this would never have been achieved. Finally, thanks to God,
and many friends of faith who prayed for me.
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xxi
PREFACE
This thesis research has been carried out during the period o f 1991-1996, under
the guidance of my advisor, Professor Andrzej Badzian, in the Thin Film Group at the
Materials Research Laboratory, The Pennsylvania State University. Part of this work
has been performed in collaboration with Professor Tien T. Tsong’s group in the
Department of Physics, The Pennsylvania State University. The thesis is based in part
on seven papers listed below, some of which have been available in the open literature.
1. N. Lee and A. Badzian, “ Effect of misorientation angles on the surface
morphologies of (001) homoepitaxial diamond thin films” , Appl. Phys. Lett.
66, 2203 (1995).
2. N. Lee and A. Badzian, “ Effect of methane concentrations on surface morphologies
and surface structures o f (001) homoepitaxial diamond thin films” , Appl. Phys. Lett.
67, 2011 (1995).
3. N. Lee and A. Badzian, “ H-plasma annealed and homoepitaxially grown diamond
(001) surface structure studied with reflection high-energy electron diffraction” ,
Phys. Rev. B (in press).
4. N. Lee and A. Badzian, “ Homoepitaxial growth o f diamond thin films on
misoriented (001) substrates” , in Proceedings o f the Fourth International
Symposium on Diamond Materials, edited by K. V. Ravi and J. P. Dismukes, The
Electrochemical Society, Pennington, NJ, Vol. 95-4, 118 (1995).
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5. Y. Kuang, N. Lee, A Badzian, T. T. Tsong, T. Badzian, and C. Chen, “ Study
of antiphase boundaries and local 3x1 configuration on the (001) surface of
homoepitaxial diamond films by scanning tunneling microscopy” , Diamond Relat.
Mater. 4, 1371 (1995).
6. Y. Kuang, Y. Wang, N. Lee, A. Badzian, T. Badzian, and T. T. Tsong, “ Surface
structure o f homoepitaxial diamond (001) films, a scanning tunneling microscopy
study” , Appl. Phys. Lett. 67, 3721 (1995).
7. Y. Kuang, A. Badzian, T. T. Tsong, N. Lee, T. Badzian, and C. Chen,
“ Scanning tunneling microscopy study of antiphase boundaries on the (001) surface
homoepitaxial diamond films” , Thin Solid Films (in press).
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1
Chapter 1
GENERAL INTRODUCTION
Since chemical vapor deposition (CVD) of diamond at low pressures was
successfully accomplished by Soviet researchers in 1970’s, many studies o f CVD
diamond have been undertaken in the past two decades toward its practical application
utilizing the excellent properties of diamond (Spear, 1989; Fujimori and Hara, 1989).
Diamond is the hardest material known, which makes CVD diamond desirable for
applications such as cutting tools and anti-abrasive, wear-resistant coatings. Because it
has the highest thermal conductivity o f any material, diamond is ideal for managing
thermal problems. Optical transparency o f diamond is suitable for infrared, visible
optical windows. Due to its wide band gap and chemical inertness, diamond is an
excellent candidate material for the electronic and optical devices which operate under
severe conditions such as high temperature, chemically harsh, or strong irradiation
environments. Semiconducting diamond is also attractive for high-frequency and highpower devices because o f its high breakdown voltage, high hole mobility, and iow
dielectric constant. Field emission from diamond has recently received much attention
for application since it shows the negative electron affinity for the hydrogenated surface
(Geisetal., 1991; Seal, 1995).
Some o f the more sophisticated diamond applications including those that take
advantage of the excellent semiconducting properties of diamond put rather stringent
demands on the quality o f the deposited diamond films (Gildenblat et al., 1991).
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2
Although polycrystalline diamond films, in particular highly oriented diamond films,
have been pursued toward applications for active electronic devices and have shown
drastic improvement in electrical characteristics, single-crystalline diamond films are
still unmatched for these purposes and remain the best material to meet the
requirements for electronic applications. Single-crystalline diamond films can be
obtained, without difficulty, on single-crystalline diamond substrates by CVD. The
homoepitaxial diamond growth on the (001) sector has been more widely studied than
on other sectors, such as (111) and (110), since high-quality single-crystalline diamond
films can be easily grown on this surface (Badzian and Badzian, 1993). The (001)
diamond homoepitaxy has been achieved by several research groups, but the optimal
growth condition is still far from complete. Moreover, several researches have revealed
inconsistency in the dependence of surface morphologies upon the deposition
parameters such as methane concentrations, substrate temperatures, etc. (e.g., Badzian
and Badzian, 1993; Vitton et al., 1993). Most importantly, the commonly observed
surface morphologies on the (001) homoepitaxial films, macrosteps and growth
hillocks, need to be characterized in terms o f their growth mechanisms.
In the epitaxial growth o f thin films, the growth mechanisms to determine the
surface morphologies and eventually the physical properties of films should be
understood from the point o f view of the atomic structure of surface. Observations of
macrosteps (Badzian and Badzian, 1993; Schermer et al., 1994), growth hillocks
(Everson and Tamor, 1992; Vitton et al., 1993), dimer row extension (Tsuno et al.,
1991; Kawarada et al., 1994), etc., on (001) homoepitaxial diamond films indicate that
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3
steps play a crucial role in the homoepitaxial growth o f diamond films. Little has been
reported in the literature, however, on the step or domain structure of the diamond
(001) surface although they are of great consequence for understanding the growth
mechanisms of CVD diamond films.
Consequently, this thesis research was performed to systematically characterize
the surface morphologies and structure o f the (001) homoepitaxial diamond films as a
function of experimental parameters such as the surface misorientation angles of
substrates, methane concentrations, and substrate temperatures. The general overview
of this thesis is shown in Figure 1.1. A study on the surface morphologies was carried
out in terms of etching and growth processes, which is given in Chapter 4. The etching
and growth morphologies were observed to change remarkably with the experimental
parameters, in particular, misorientation angles. At present, the information on the
domain and step structure of the diamond (001) surface is not available in the literature.
Thus, this study began by investigating other material systems similar to diamond,
especially the Si (001) surface. A review on the Si (001) surface is presented in section
2.2. The diamond (001) surface structure was characterized both for the H-plasma
annealed surface and for the as-grown surface, using reflection high-energy electron
diffraction (RHEED), low-energy electron diffraction (LEED), and scanning tunneling
microscopy (STM), which is described in Chapters 5 and 6. This study revealed both
several similarities and differences between diamond (001) and Si (001) surface
structures.
In this study, a particular emphasis was put on the understanding of growth
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4
MPACVD and characterization of (001) homoepitaxial diamond films
Experimental parameters: </>, CH 4 , T
Surface morphology
Surface structure
No info on diamond surface
Effect of <j>
Effect of C H4 Effect of T
Study on Si (001) surface structure
Etching
Etch pits
Step regression
Growth
Apply to diamond (001) surface
Step-flow growth
Hillock growth
Random growth
H-plasma annealed surface
STM
As-grown surface
RHEED
Effect of <f>, T
RHEED
Effect of
CH4, T
Surface defects
Step structure
Domain structure
Single-layer steps
Double-layer steps
Double domain
Single domain
Relative stabilities of steps
(001) homoepitaxial diamond growth mechanisms
Optimum CVD condition
Figure 1.1 General overview o f the research, if), CH4, and T denote the surface
misorientation angles of substrates, the methane concentrations in
hydrogen and the substrate temperatures, respectively.
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5
mechanisms on an atomic scale by relating the surface morphologies to the surface
structure. This study makes a significant contribution not only toward establishing the
optimal deposition condition for high-quality (001) homoepitaxial diamond films but also
toward better understanding the growth mechanisms of epitaxial diamond films.
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6
Chapter 2
BACKGROUND
2.1. Introduction
The diamond (001) surface structure, in particular domain and step structure,
which not only determine the surface morphologies and physical properties but are also
essential for understanding growth mechanisms of (001) homoepitaxial diamond films,
is just beginning to be studied. Because detailed information on the step or domain
structure of the diamond (001) surface was not available, this study began with a broad
review of other material systems, especially Si since it possesses the same bulk crystal
structure as that of diamond and since both Si and diamond reveal the dimer-type 2x1
reconstruction on the (001) surface. The Si (001) surface has been extensively studied
because the surface structure annealed in ultra-high vacuum (UHV) or grown by
molecular beam epitaxy (MBE) is of great interest from a scientific point of view as
well as for its application. There has been a particular interest in the role of single-layer
versus double-layer steps on the Si (001) surface because growth with maintaining
double-layer steps is in most cases related to the higher quality o f films (Alerhand et
al., 1990; Pehlke and Tersoff, 1991).
In this chapter, therefore, an extensive review is given to what is known about
the Si (001) surface, including the energetics o f steps, clean and hydrogenated surface
structure, surface diffusion of Si adatoms, and homoepitaxial growth o f Si. The second
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7
half of this chapter is devoted to surveying the history of CVD diamond, a variety of
CVD
techniques for diamond growth,
and achievements in the research on
homoepitaxial diamond films to provide the current concerns and problems with
diamond homoepitaxy .
2.2. Surface structure of clean, hydrogenated, and MBE-grown Si (001)
2.2.1. Surface structure of clean Si (0011
2.2.1.1. Surface reconstruction of clean Si (0011
When the Si (001) surface is truncated from a bulk, each atom on the first layer
is bonded to two atoms on the second layer, leaving two dangling bonds on each
surface atom, as shown in Figure 2.1(a). For the clean surface, the high energy
associated with these dangling bonds is lowered by surface reconstruction. The early
LEED studies (Schlier and Farnsworth, 1959) showed that the basic structure o f the
clean Si (001) surface was the 2x1 symmetry, indicating that its periodicity was twice
as long as that o f the bulk in one direction.
To account for the 2x1 surface reconstruction on the Si (001) surface, many
different models have been proposed, but they are broadly grouped into three classes:
vacancy model (Phillips, 1973; Harrison, 1976), dimer model (Schlier and Farnsworth,
1959; Levine, 1973; Appelbaum and Hamann, 1978), and chain model (Seiwatz,
1964). Self-consistent calculations o f the electronic structure for each model have been
performed, concluding that the dimer model was in better agreement with ultraviolet
photoemission spectroscopy (UPS) data than the other models (Appelbaum et al., 1975,
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8
Figure 2.1 Cross-sectional and plan views o f the clean Si (001) surface: (a)
unreconstructed surface, (b) 2x1 symmetric dimer reconstruction, (c)
2x2 alternating buckled dimer reconstruction. Shaded circles denote
the uppermost-layer atoms and in the cross-sectional view, larger
circles represent atoms on an upper terrace or at higher position.
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9
1976). However, the simple dimer model was inconsistent with LEED intensity
analysis.
In 1978, Appelbaum and Hamann found, on the basis of a strain-energy
minimization calculations, that surface dimerization was accompanied by substantial
subsurface distortion extending 4-5 atomic layers into the bulk. This strain-minimized
symmetric dimer structure was shown to be reasonably consistent with LEED intensity
data for
the 2x1-reconstructed
Si
(001)
surface.
Using
energy-minimization
calculations, Chadi (1979) suggested that the surface energy could be lowered further
by allowing the dimers to buckle out o f the surface plane. In order to minimize bondlength distortions, the buckling was accompanied by a lateral shift o f the dimers. In his
2x1 buckled dimer model, all dimers were buckled in the same direction. Later STM
analysis (Tromp et al., 1985; Hamers et al., 1986) observed that alternation of the
buckling direction within a dimer row gave rise to structures with 2x2 and c(4x2)
symmetries which had also been detected with LEED (Jona et al., 1977; Poppendieck
et al., 1978) and helium scattering (Cardillo and Becker, 1980). The 2x1 symmetric
and 2x2 alternating buckled dimer structures are illustrated in Figure 2.1(b) and (c),
respectively.
With the advent of a new surface imaging technique, STM, which makes it
possible to directly probe the atomic structure of a surface with high lateral resolution,
Tromp et al. (1985) and Hamers et al. (1986) provided striking confirmation of surface
dimers on the Si (001) surface. They observed that both symmetric and buckled dimers
were present in roughly equal amounts. This surface had a high density of dimer
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10
vacancies, approximately 10% consisting of individual missing dimers and small
clusters of missing dimers. Dimer buckling was the largest near the missing dimer
defects and gradually decreased with distance away from such defects. It was
concluded, therefore, that dimer vacancies and steps induced or stabilized dimer
buckling and were responsible for the regions of 2x2 and c(4x2) symmetries.
Several calculations of the atomic structure of the Si (001) surface have
suggested
almost
equal
energies
for
the symmetric
and
asymmetric
dimer
configurations (Payne et al., 1989; Roberts and Needs, 1990). By considering spin
correlation in the calculations, the symmetric dimer model was reported to be more
stable than the asymmetric one (Artacho and Yndurain, 1989). Recently, however,
Wolkow (1992) claimed that dimers had an asymmetric character. Using lowtemperature STM, it was observed that at 120 K the number of buckled dimers
increased at the expense o f symmetric dimers. He concluded that at room temperature,
dimers might be seen as symmetric due to the time-averaged configuration of STM
images for the dimers dynamically buckling about the equilibrium configuration on a
time scale which was short compared to the STM measurement time. Although the
dimer model for the 2x1 reconstruction of the Si (001) surface is now commonly
accepted, the detailed dimer configuration is still controversial.
2.2.1.2. Energetical considerations o f step structure on Si (001) surfaces
The bulk diamond-cubic lattice structure of a silicon crystal can be made by
interpenetrating two equivalent face-centered cubic sublattices. On the surface with the
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11
exact (001) plane, thus, any of two equivalent sublattices related to each other by
translation can be revealed with the same probability. The Si (001) surface reconstructs
to form either 2x1 or 1x2 structure, depending on which sublattice appears on the
surface. These two surface structures are identical, but one is rotated by 90° with
respect to the other in bonding geometry. In reality, when one cuts or polishes
surfaces, misorientation from an exact low-index plane is introduced unintentionally or
intentionally. On an annealed or as-grown surface, eventually there appear flat terraces
of a low-index plane separated by atomic steps and kinks, reflecting a macroscopic
surface misorientation. in the thin film growth, steps and kinks play a crucial role by
providing stable incorporation sites for incoming adatoms. The concentrations of steps
and kinks can be controlled at a high level by the surface misorientation angles so that
most crystal growth occurs at these sites (Burton et al., 1951; Lewis and Anderson,
1978).
On the Si (001) surface, a topic of particular interest has been the role of steps
with single-layer and double-layer atomic heights in the epitaxial film growth. Single­
layer steps were found to necessarily introduce antiphase boundaries in III-V
semiconductor films grown on Si (001) substrates, while double-layer steps were
considered to promote the growth of high quality III-V films (Kroemer, 1986). Thus,
the preparation o f the single-domain surface where steps between adjacent terraces have
a double-layer atomic height, has received a great deal of attention. It was reported that
a prolonged annealing of the Si (001) surface with the misorientation angles less than
0.2° at ~1250 K resulted in the single-domain surface (Sakamoto and Hashiguchi,
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1986; Inoue et al., 1987; Doi and Ichikawa, 1989). Recently it has been widely
believed, however, for the clean Si (001) surface that at the misorientation angles o f
less than 2°, single-layer steps occur while at angles of more than 4°, double-layer
steps become predominant.
A substantial effort has been directed toward understanding the fascinating
behavior of steps on the Si (001) surface. Chadi (1987) has performed semiempirical
tight-binding-based total-energy calculations for the formation energies of single-layer
and double-layer steps on the Si (001) surface. These calculations examined two
distinct types each of the single-layer (S) and double-layer (D) steps, labeled in the
following by SA, SB, DA, and DB. For type-A steps, SA and DA, dimer rows on the
upper terraces run parallel to the steps, and for type-B steps, SB and DB, dimer rows on
the upper terraces are perpendicular to the steps. Type-A and type-B terraces are
defined to be the terraces just above type-A and type-B steps, respectively.
Schematics of the four different step configurations that Chadi (1987) considered in
his calculations are shown in Figure 2.2. The edge atoms on SA step are fully bonded,
but each lower edge atom on SB and DA steps and each middle edge atom on DB step
necessarily have a dangling bond. For SB, DA, and DB steps, edge atoms form
dimerlike bonds with lower terrace atoms to satisfy the dangling bonds. The rebonded
step structure shown in Figure 2.2(b), (c), and (d) was found to be more stable as
compared to the non-bonded one. The formation energies per unit length of these four
types of steps relative to the fully relaxed Si (001) surface are given by
MS a) « 0.01 eV,
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13
Figure 2.2 Top views o f various steps on the clean Si (001) surface: (a) SA, (b) SB, (c)
Da, and (d) DB steps. Larger circles represent upper-terrace atoms and
shaded circles denote atoms with dangling bonds. The dashed lines which
run parallel to the step edges, indicate the step positions (Chadi, 1987).
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14
Figure 2.2 (cont.)
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15
X(SB) * 0.15 eV,
MD a) * 0.54 eV, and
\(D B) * 0.05 eV.
(2.1)
The SA step has the lowest formation energy because there is no dangling bond for an
edge atom on this step. For the other three steps, rebonding of an edge atom with the
nearest neighboring atom on the lower terrace eliminates a dangling bond, but induces
bond-length strains. These strains increase in the order o f DB, SB, and DA steps.
For the surface slightly misoriented along the [110] direction, it is impossible to
have only SA steps with the lowest energy. To accommodate the surface misorientation
angle, SA and SB steps have to alternate with each other across terraces. A typical STM
image o f the clean annealed Si (001) surface is shown in Figure 2.3. SA steps are
relatively straight while SB steps are ragged with many kinks. The roughness o f SA and
SB steps results from their formation energies. Thermal fluctuation o f SB steps is
favored because these steps have a low excitation energy for creating SA steps at kinks.
For SA steps, however, the step fluctuation leads to the formation of high-energy SB
steps so that they remain to be relatively straight (Hoeven et al., 1990a; Hamers et al.,
1990).
When the surface is highly misoriented toward the [110] direction, the surface
can have either alternating single-layer steps SA+S B (2x1 and 1x2 double-domain
structure) or double-layer DB steps (1x2 single-domain structure). These two
configurations are different not only in the height o f steps and the width o f terraces but
also in their basic surface structure. Chadi (1987) showed that the double-layer step DB
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Figure 2.3 STM image o f the clean Si (001) surface (Hamers et al.. 1990).
The scan area is 87x87 nm: .
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17
was energetically favorable to alternating single-layer steps SA+SB, based on the step
formation energies for these two cases. Aspnes and Ihm (1986, 1987) also carried out a
similar total-energy calculation, in which a 7t-bonded double-layer step DB was lower in
energy than alternating single-layer steps SA+SB and double- steps DA or DB which
were not rebonded.
2.2.1.3. Equilibrium structure of clean Si (001') surfaces
At the beginning of study on the Si (001) surface structure, several research
groups ( Henzler and Clabes, 1974; Olshanetzky and Shkyalev, 1979; Kaplan, 1980;
Chabal and Raghavachari, 1984) observed, by LEED or RHEED, the single-domain
structure for the clean Si (001) surface with the misorientation angles of more than 4°.
Later, several Japanese researchers (Sakamoto and Hashiguchi, 1986; Inoue et al.,
1987; Doi and Ichikawa, 1989) reported that the well-oriented Si (001) surface had the
single-domain structure after a prolonged annealing at a temperature of 1250 K. In
addition, Aspnes and Ihm (1986, 1987) and Chadi (1987) calculated the step formation
energies, showing that the single-domain surface with DB steps was energetically more
stable than the double-domain one with alternating single-layer steps. Angular profile
analysis of LEED spots (Aumann et al., 1988) showed for the Si (001) surface
misoriented 2.5° along [110] that an extended annealing increased the amount of
double-layer steps at the expense of single-layer steps, finally producing mostly double­
layer stepped structure. This study pointed out that achievement of the equilibrium
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surface structure was a problem in kinetics, with the rate presumably limited by surface
diffusion of Si atoms or evaporation into the vacuum. These early experimental and
theoretical works led to the belief that for the Si (001) surface there was only one
equilibrium structure of the single-domain structure with DB steps.
Swartzentruber and coworkers (1989) found that the Si (001) surface tilted 1°
toward [1101 could not be made to have double-layer steps even with long-term
annealing, indicating that it was not a kinetic limitation that kept this surface from
producing double-layer steps. It was suggested, therefore, that for the surfaces with
small misorientation angles, single-layer steps might be the equilibrium structure
(Swartzentruber et al., 1989; Hoeven et al., 1989a). There were several more reports
that on the well-oriented Si (001) surface, the double-domain structure was always
observed after careful surface annealing, suggesting the presence o f the single-layer
stepped surface as the equilibrium structure.
To figure out the equilibrium structure of the reconstructed Si (001) surface,
Alerhand et al. (1988) and Payne et al. (1989) have pointed out that surface strain
relaxation related to the double-domain structure should be considered in addition to the
step formation energies. Dimerized surface reconstruction induces anisotropic surface
stresses on terraces: tensile and compressive stresses parallel and perpendicular to the
dimerization direction, respectively. On the single-layer stepped surface which has
alternating 2x1 and 1x2 terraces identically matched by 90° rotation, anisotropic
surface stresses cancel each other across the step edges, giving rise to surface strain
relaxation. On the other hand, no strain relaxation occurs on the double-layer stepped
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surface because it comprises the same type of terraces. Thus, the surface strain
relaxation lowers the energy of the single-layer stepped surface. Taking into account
the anisotropic strain effect related to the surface reconstruction, Alerhand et al. (1990)
performed the calculations of energies of the single-layer and double-layer stepped
surfaces. They reported that the surface misorientation angle for the transition between
these two types of surfaces is 0.05° at a temperature of 0 K. On the other hand, Poon
et al. (1990) demonstrated the existence of another interaction between steps in addition
to the surface stain relaxation. It was found that appreciable force dipoles were induced
for the rebonded SB and DB steps, resulting in the step-step interactions. The
misorientation angle for the transition between the single-layer and double-layer
stepped surfaces was predicted to be 1° at 0 K.
Alerhand et al. (1990) and Poon et al. (1990) extended their considerations into
the thermal effect which could stabilize the single-layer stepped surface. A t T = 0 K
steps should be straight, while at T > 0 K steps roughen because atoms may leave the
steps due to thermal motion and move to the environment or to other surface atomic
sites including steps or kinks. An STM image shown in Figure 2.3 reveals that highenergy SB steps are ragged and that low-energy SA steps are straight on the single-layer
stepped surface. Fluctuation of SB steps creates SA steps at kinks but lowers the energy
by increasing an entropy o f steps, leading to reduction o f the total free energy o f the
single-layer stepped surface. For SA steps, the excitation energy is so high that these
steps are relatively straight. On the other hand, DB steps o f the double-layer stepped
surface need much higher excitation energy for roughening since their fluctuation w ill
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20
create high-energy DA steps. Thus, the free energy of the single-layer stepped surface is
lowered rapidly relative to that of the double-layer stepped surface with increasing
temperatures due to the large entropy produced by step roughening of SB steps. Taking
thermal fluctuations into consideration, the transition between the single-layer and
double-layer stepped surfaces moved to higher misorientation angles with increasing
temperatures. The equilibrium phase diagram of the surface as a function of the
misorientation angles and temperatures predicted that at the conventional annealing
temperature of approximately 1200 °C, the transition angle was approximately 2°
(Alerhand et al., 1990) or 3° (Poon et al., 1990).
In a recent work, Tong and Bennett (1991) and Pehlke and Tersoff (1991)
showed that the transition from the single-layer to double-layer stepped surface
gradually occurred with the misorientation angles. As the misorientation angles became
larger, the area of type-B terraces continuously increased and that of type-A terraces
decreased while the surface was single-layer stepped. Above approximately 1.5°,
alternating SA+SB steps started to collapse into DB steps. The content o f DB steps
monotonically increased and finally double-layer steps purely existed above 4-5°.
For the first time, Aspnes and Ihm (1986, 1987) suggested the reconstruction
for D b steps. Based on the fact that the step edge on the (001) surface coincided with
the (111) plane, they proposed a 7t-bonded chain model through which the energy of DB
steps could be lowered. Subsequently Chadi (1987) proposed an alternative model in
which an edge atom was rebonded to an atom on the lower terrace by forming a dimer­
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21
like bond. It was found that these rebonded atoms could lower the step energy even
more than the 7t-bonded chain. STM images obtained by Wierenga et al. (1987) and
Griffith et al. (1988) revealed that the DB step structure observed was consistent with
Chadi’s edge-atom rebonding model given in Figure 2.2.
It was observed that the double-layer stepped surface was quite complex. STM
images o f the Si (001) surface misoriented 4° toward the [110] direction showed that
fairly straight DB steps were evenly spaced and at kinks, DB steps split into single-layer
steps (Wierenga et al., 1987; Griffith et al., 1988, 1989; Swartzentruber et al., 1989).
Kinks are inevitably present along steps when the surface is misoriented toward the
direction away from either [110] or [llO ]. If a double-layer step were maintained at a
kink, a DA step would have to be created along the kink. The formation energy o f the
D a step is the highest, as calculated by Chadi (1987). Thus, the DB step splits into
single-layer steps at kinks to avoid the occurrence of high-energy DA step. As the
misorientation direction is more deviated from either [110] or [ llO ], the double-layer
stepped surface changes to the single-layer stepped surface (Nakayama et al., 1987;
Swartzentruber et al., 1990; Webb et al., 1990; Wasserfall and Ranke, 1994). Using
transmission electron diffraction (TED) and microscopy (TEM), Nakayama et al.
(1987) showed for the Si (001) surfaces tilted 2-5° that steps maintained the double­
layer height when the misorientation directions were deviated less than 20° from [110]
whereas they became single-layer steps for larger deviation. DA steps have never been
reported for the Si (001) surface.
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22
2.2.2. Surface structure of hydrogenated Si (001)
For the interaction of atomic hydrogen with a clean 2x1-reconstructed Si (001)
surface, Sakurai and Hagstrum observed, in 1976, that with increasing exposure time to
atomic hydrogen at room temperature, the 2x1 pattern gradually changed to a sharp lx l
pattern with complete disappearance of the non-integral spots. It was also found that the
2x1 structure of the clean surface did not show any change in LEED patterns by atomic
hydrogen exposure at about 500 K. Based on UPS data, the lx l and 2x1 surface
structures exposed to atomic hydrogen at room temperature and 500 K were assigned to
the dihydride configuration with two H per surface atom and monohydride
configuration with one H per surface atom, respectively, as shown in Figure 2.4(a) and
(b).
For the H-saturated Si (001) surface, a new ordered phase with the 3x1
periodicity was found after being exposed to atomic hydrogen exclusively at 380 K by
Chabal and Raghavachari (1985) using LEED. They also observed the clear lx l
structure by saturation exposure at room temperature. From the IR data showing that
both surfaces had similar hydrogen coverages, it was postulated that the 3x1 unit cell
consisted o f alternating monohydride and dihydride units [Figure 2.4(c)], while the lx l
surface was a disordered phase roughly with an equal number o f monohydride and
dihydride structures, contrary to the traditionally accepted dihydride structure in a
uniform distribution. It was proposed that the formation of a uniform dihydride phase
was prohibited by the repulsive interaction between hydrogen atoms on adjacent
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23
(a)
(b)
(c)
Figure 2.4 Several hydrogenated Si (001) surface structures: (a) lx l:2 H dihydride
structure, (b) 2x1 :H monohydride structure, and (c) 3xl:1.33H structure
(Boland, 1990).
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24
dihydride units.
The 3x1 surface structure with alternating monohydride and dihydride phases
was recently confirmed by STM (Boland, 1990). In addition, this study revealed that
the room temperature lx l surface had the dihydride structure of bulk-like termination
with some defective remnants of the 2x1 configuration. It was concluded that the
hydrogen coverage of the lx l structure was greater than that of the 3x1 structure.
Boland (1992) subsequently made experiments on the stability of the three types
of hydrogenated Si (001) surfaces in an atomic hydrogen environment. Prolonged
exposures of the hydrogenated 3x1 and 2x1 surfaces to atomic hydrogen at 400 K and
600 K, respectively, did not result in the etching o f these surfaces. These surfaces were
stable under the condition in which they were formed. On the contrary, by increasing
the dosing amount of atomic hydrogen, the Si (001) surface with the l x l structure was
degraded, exhibiting etch pits and etch products. The instability of the l x l dihydride
structure was explained in terms of the steric interaction between hydrogen atoms
crowding on this surface. As a result of the steric repulsion, the individual dihydride
units are strained, causing the Si-H bonds of these dihydride units to be weaker than
those found on the 3x1 structure. The strained Si-H bonds and subsequently Si-Si
backbonds are thus weakened and then have lower barriers to reactions, being
susceptible to etching.
To compare the stability of surface structures having different numbers of
hydrogen atoms, Northrup (1991) calculated the surface formation energies for the 2x1,
3x1, and l x l H-terminated surfaces. The 3x1 structure consisting of alternating
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25
monohydride and dihydride configurations was stable with respect to separation into the
2x1 monohydride and the l x l dihydride phases. A canted-row dihydride structure,
which could be obtained by tilting SiH2 groups, was found to be energetically favorable
relative to the symmetric dihydride because it allowed the hydrogen atoms to be further
apart.
A temperature-programmed desorption (TPD) spectrum was obtained from the
l x l dihydride surface by Gates et al. (1989). The first TPD peak appeared at
approximately 700 K, producing the 2x1 monohydride phase. Desorption of hydrogen
atoms from the second TPD peak at about 825 K resulted in the clean 2x1 structure.
TPD experiments were performed for the hydrogenated lx l, 3x1, and 2x1 Si (001)
surfaces (Cheng and Yates, 1991). TPD from the 2x1 monohydride structure yielded a
single H2 desorption peak at about 750 K. Annealing of both H-terminated l x l and 3x1
phases desorbed H2 at about 600 K, restoring a sharp 2x1 LEED pattern with all
hydrogen bonded in the monohydride configuration. However, there was a distinct
difference in two TPD spectra. A very broad H2 desorption feature, ranging from 300
K up to 500 K, was observed for thermal desorption from the lx l surface. Based on
the observation of this broad H2 TPD peak and the liberation of SiH4 species from this
surface, the presence o f a trihydride phase (SiH3) was postulated on the l x l surface.
However, Boland (1990, 1992) showed that the hydrogenated l x l surface was
composed o f mainly bulklike dihydride units even though this surface was poorly
ordered. He claimed that the strained Si-H bonds in the dihydride structure were
responsible for the broad H2 desorption peak at low temperatures.
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26
2.2.3. Surface diffusion of Si atoms on Si (001) surfaces
In a historic paper in 1951, Burton, Cabrera, and Frank introduced the terraceedge-kink model to describe the evolution of the surface structure during crystal growth
in terms of terraces, steps, kinks, adatoms, vacancies and surface imperfections of
dislocations. Thin film growth from the vapor phase begins with the arrival of excess
mobile adatoms at the surface. An atom that has reached the surface undergoes a
random walk, exploring various sites on the surface until it meets a step or another
adatom. How long an adatom moves around before it joins to a step or meets another
adatom is determined by the adatom flux and the diffusivity of an adatom. I f it meets
another adatom, they may cluster together to form a two-dimensional nucleus. This
situation may occur when steps are too widely separated so that adatoms cannot migrate
to the pre-existing steps under a certain deposition condition. In this case, island growth
occurs on terraces and provides additional steps on which adatoms can continue to join.
On the other hand, adatoms may move and be incorporated into the pre-existing steps
rather than meet another adatom. This process, so-called step-flow growth, is the most
important mechanism in the thin film deposition. In both mechanisms of thin film
growth, island growth and step-flow growth, adatoms diffuse to steps, interact with the
steps, and join to the steps, regardless that the steps are pre-existing or newly created
by two-dimensional nucleation. Thus, the diffusion of adatoms on the surface is the
most significant kinetic process to govern the growth of thin films.
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Several different methods have been used to study the surface diffusion.
Macroscopic methods were developed based on the observation of the spreading of an
initially well-defined distribution of adatoms (Butz and Wagner, 1977) or the filling of
a hole (Hall et al.,
1987). However, these methods may be ambiguous and
underestimate the surface diffusivity of adatoms because the interaction of adatoms with
surface defects such as steps cannot be considered. As a microscopic method, field ion
microscopy has been successfully applied so that the positions of single adatoms on a
tip surface are sequentially observed, but this technique is limited to metals because of
the difficulty in making sharp tips and the high field necessary for imaging (Chen and
Tsong, 1990).
Recently, STM has been explored to study migration of adatoms on the surface
because of its atomic resolution and its ability to scan a large area. Mo et al. (1990,
1991, 1992) derived the surface diffusion coefficient o f Si adatoms on the Si (001)
surface by measuring the number o f islands that formed at various substrate
temperatures for a given deposition rate. The surface diffusion coefficient of adatoms
determines how large an area an adatom explores in unit time. The larger the diffusion
coefficient of an adatom,
the fewer islands are formed. At lower substrate
temperatures, more islands with smaller sizes occurred because of the lower diffusion
coefficients. The higher growth rates gave rise to the formation of more islands. For a
silicon adatom on the Si (001) surface, they calculated from the island density as a
function o f temperature that the activation energy for the surface diffusion was
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approximately 0.67 eV and a pre-exponential factor of diffusion coefficient was 10’3±1
cm2/s in room temperature up to 300 °C.
Most semiconductor surfaces reconstruct by dimerization o f surface atoms to
reduce the number of dangling bonds which are created by the existence o f a surface.
In case of Si (001), the surface reconstruction produces a strong anisotropy o f surface
structure with twofold symmetry, which influences drastically the surface diffusion
(Stoyanov, 1989). Most theoretical calculations have shown that the surface diffusion is
faster along dimer rows than across dimer rows on the reconstructed Si (001) surface.
Total-energy calculations o f a Si adatom adsorbed at various symmetric sites gave 0.6
or 0.7 eV/atom for the activation energy for the migration of adatoms along dimer
rows (Miyazaki et al., 1990; Brocks et al., 1991) and 1.0 eV/atom for the diffusion
across dimer rows (Brocks et al., 1991). Molecular dynamics (MD) simulations showed
a similar result of 0.75 eV for the energy barrier for diffusion along dimer rows
(Srivastava and Garrison, 1991). Other theoretical work done by several different
groups using various computer simulation techniques has unanimously agreed that Si
adatoms strongly favor the migration along dimer rows (Zhang et al., 1991; Wang and
Rockett, 1991; Bedanov and Mukhin, 1992; Toh and Ong, 1992; Roland and Gilmer,
1992).
The anisotropy of surface migration of Si and Ge adatoms on the Si (001)
surface was experimentally investigated by STM analysis o f the width o f denuded zones
around atomic steps at substrate temperature of about 300 °C (Mo et al., 1991; Mo and
Lagally, 1991; Mo et al., 1992; Lagally, 1993). A denuded zone is a striped area along
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29
a step in which the island density is much lower than in the areas far from the step. It is
formed because adatoms landing near the step are able to migrate to the step without
colliding with each other to form islands. Therefore, the denuded zones are developed
on the type-B terrace regions near to SB steps where the dimer rows run perpendicular
to the lower step edges, while the type-A terraces with the dimer rows parallel to steps
do not show the denuded zones. The denuded zone analysis by STM suggested that the
surface migration of single adatoms was at least 1000 times faster along dimer rows
than perpendicular to them.
The identification of detailed atomistic mechanisms for the surface diffusion is
one o f the challenging goals in surface science. The best way is to directly observe the
motion of a single adatom on the surface, which unfortunately has not been realized for
Si up to this date. Thus, analytical theories and computer simulations have been carried
out to study the surface diffusion indirectly.
The first-principle total-energy calculation performed by Brocks et al. (1991)
postulated that based on the absolute minimum energy, the binding site for an adatom
appeared just above the second layer atom bonded to a dimer atom, and the surface
diffusion o f the adatom then proceeded from this adsorption site to an equivalent
binding site in the adjacent cell through the top o f a dimer. Similar results have been
reported by Wang and Rockett (1991) and Toh and Ong (1992).
On the other hand, Srivastava and Garrison (1991) and Brenner and Garrison
(1988) showed through MD simulations that although the energy minimum for an
adatom occurred in the trough, the dangling bond site of a dimer atom was the most
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30
probable for adsorption of an adatom because this site provided the largest surface area
for incoming atoms to be funneled. It was also demonstrated that local unreconstruction
(dimer opening) of the otherwise fully reconstructed surface activated the surface
diffusion, which occurred by hopping of an adatom between the neighboring dimer
bridge sites (Srivastava et al., 1989; Srivastava and Garrison, 1991). As for the
adsorption and surface diffusion of a Si adatom on the Si (001) surface, the results
obtained by the Garrison group were confirmed by Monte Carlo and MD simulations
(Zhang et al., 1991) and energy-minimization calculations (Lu et al., 1991).
2.2.4. Homoepitaxial growth on Si (001) surfaces by molecular beam epitaxy
Molecular beam epitaxy (MBE) of Si refers to the growth of silicon or siliconrelated materials via atomic, molecular, or ion beams, at relatively low temperatures,
in a UHV environment. This process has been considered as a low-temperature
alternative to conventional CVD epitaxy, which can lower the growth temperatures and
thus minimize the diffusion effects and autodoping. In addition, the capability to
simultaneously dope a growing silicon film allows for the generation o f sharp doping
profiles with independent dopant beams (Chang and Ludeke, 1975). Although the MBE
technique is capable of the heteroepitaxial growth of other semiconductors,
homoepitaxy is one o f the most important aspects of this technique both for its own
sake and for the integration o f heteroepitaxy with homoepitaxy.
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Interest in the Si MBE on the Si (001) surface for the production of novel
electronic devices has motivated many studies on the initial stages of growth as a
function of process parameters such as the surface misorientation, growth temperatures,
and cleaning treatment. RHEED has been used as a powerful tool to control thin film
growth on an atomic-layer level. Sakamoto et al. (1985, 1987a) for the first time
reported RHEED intensity oscillation o f the specular beam with deposition time during
Si MBE on the Si (001) surface. Using microprobe RHEED, Doi and Ichikawa (1989)
showed that the RHEED intensity oscillation in Si MBE at low temperatures was
related to the alternate growth of 2x1 and 1x2 domains. Almost no oscillation was
observed at higher temperatures because growth occurred via step migration. It was
then concluded that RHEED intensity oscillation took place when growth proceeded by
the layer-by-layer, two-dimensional nucleation (i.e., island growth). Aizaki and
Tatsumi (1986) and Sakamoto et al. (1987b) found that on the misoriented Si (001)
substrate with the double-domain structure, growth occurred preferentially on one of
the two domains at the early stage, leading to the single-domain surface with double­
layer steps. When growth was terminated and the sample was then kept at the growth
temperature in vacuum, the surface was observed to be reversed from the single­
domain to double-domain structure within a few minutes (Sakamoto et al., 1987b).
An STM study of the as-grown surface in a freeze-and-look mode has made
enormous progress in understanding the homoepitaxial MBE growth on the Si (001)
surface. Hoeven et al. (1989a, b, 1990a) observed the initial stage o f Si MBE growth
on the Si (001) surface. At 750 K, growth occurred preferentially at SB steps up to 0.5
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32
monolayer (ML) so that SBsteps caught up with SA steps, giving rise to the formation
of the single-domain surface with an array of evenly spaced straight DB steps, while
later on growth continued with both step flow and island nucleation. At a higher
temperature of about 810 K, the single-domain surface with DB steps was created and
then maintained during growth. This step-flow growth produced the high-quality films
relative to those resulting from the island growth.
Low-temperature MBE growth has been elaborately investigated using STM
(Hamers et al.. 1989, 1990; Hoeven et al., 1990b). At low temperatures between 580
and 750 K, deposition of low coverage less than 0.5 M L Si on the double-domain
surface brought about the two-dimensional nucleation of long and narrow islands on flat
terraces. On the well-oriented surface at relatively low temperatures, the diffusion
length o f Si adatoms was much shorter than the distance between atomic steps. As a
result, nucleation occurred at terraces, forming isolated islands of epitaxial Si. Islands
were often more than 30 times as long as they were wide. As the deposition
temperatures were lowered, the anisotropy of island growth became more outstanding,
and a larger number of smaller islands were formed. Further deposition with higher
coverage induced multilayer growth just above islands before the first epitaxial layer
was completed.
One major important feature o f the surface produced by the low-temperature
epitaxial growth is the presence of antiphase boundaries forming between two islands
with the opposite phases (Hamers et al., 1989, 1990). The surface prepared by the
high-temperature epitaxy is free of antiphase boundaries because growth proceeds by
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33
step-flow mechanism due to the higher diffusion length o f Si atoms than the terrace
width. Antiphase boundaries have also not been observed on the clean surface produced
by the high-temperature annealing (Hamers et al., 1989, 1990). In the low-temperature
epitaxy, however, the surface diffusion is much more suppressed, leading to island
nucleation and, thus, growth on terraces rather than step-flow growth. Epitaxial islands
nucleate randomly, with 50% probability of possessing each o f the two opposite phases
on the same terrace. When two growing islands meet together, there w ill be a 50%
probability that an antiphase boundary is formed at the border between them.
STM investigations o f submonolayer growth showed that subsequent island
nucleation for the second epitaxial layer occurred preferentially along antiphase
boundaries before the first epitaxial layer was completed, giving rise to the multilayer
growth (Hamers et al., 1989, 1990; Hoeven et al., 1990b). The island grew as a single
dimer string until it covered the entire antiphase boundary and then the lateral growth
began. Dimers in a single row grown at an antiphase boundary were found to be
significantly buckled due to the asymmetric strain field produced by the staggering of
dimer rows on either side of the antiphase boundary (Bedrossian and Kaxiras, 1993).
The islands increased in size until they met together on the terrace, forming new
antiphase boundaries for nucleation of the next epitaxial layer. It was found that islands
nucleated at antiphase boundaries accounted for approximately 94% of the area of a
growing layer at 720 K, indicating that antiphase boundaries played a dominant role in
the growth o f multilayer epitaxial films at low temperatures (Bronikowski et al., 1993).
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34
STM observations have clearly indicated an anisotropic growth process which is
intimately related to the reconstructed structure of the Si (001) surface: preferential
growth at the end of dimer rows in both step-flow growth and island growth. The
twofold symmetry of the 2x1-reconstructed surface suggests an anisotropy of the
following properties involved in growth process: surface diffusion of adatoms along
and across dimer rows,
interaction of adatoms with SA and SB steps, and
accommodation (or sticking coefficients) of adatoms at SA and SB steps (Mo et al.,
1989, 1990). There have been several experimental and theoretical studies to explain
the anisotropy of island formation and step-flow growth.
Hoeven et al. (1989a) argued that favoring growth at the ends of dimer rows
resulted from the higher binding energy of adatoms at SB steps because the formation
energy for a SB step was significantly higher than for a SA step. Considering the
energies o f steps bounding an island, Hamers et al. (1989, 1990) postulated that the
anisotropy of islands was determined primarily by thermodynamics rather than kinetics
because an island had the long edges of low-energy SA steps and the short edges of
high-energy SB steps.
On the other hand, STM work and Monte Carlo simulations performed by Mo
et al. (1989, 1990, 1992) showed that anisotropic growth was ascribed to anisotropic
accommodation but not anisotropic interactions or anisotropic diffusion. It was claimed
that adatoms were much more likely to stick to the end o f dimer rows (SB step) than to
the side (SA step) so that SB steps caught up with SA steps in the step-flow growth and
two-dimensional islands grew much faster in the direction of dimer rows at the low-
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35
temperature growth. The probability of crossing a step from one terrace to another has
also been found to be quite different for SA and SB steps. Atoms approaching an SA step
from either above or below were reflected with high probability, while atoms arriving
at an SB step from the top crossed over and had a high probability of being incorporated
at the SB step (Mo et al., 1991).
Contrary to the results of Mo et al. (1991), Chason and Dodson (1991), using
Monte Carlo simulation, demonstrated that the anisotropic island shapes could be
obtained from an anisotropy in either surface diffusion or incorporation rates of
adatoms, although the latter led to much greater shape anisotropy. On the basis of
anisotropic surface diffusion and incorporation, they also simulated the temperature
dependence o f the surface morphologies during growth which showed the transition
from the mode of island growth to step-flow growth mode with
increasing
temperatures.
Elswijk et al. (1991) found in their Monte Carlo simulations that the growth
anisotropy resulted mainly from an anisotropy in both surface diffusion and interaction
energy. Apparent roughening o f SB steps and elongated island shapes were observed by
the introduction of a slight anisotropy in surface diffusion while keeping the anisotropy
of binding energies of a dimer for the two inequivalent single-layer steps (0.04 eV for
SB step and 0.01 eV for SA step). Considering the formation of a bound dimer at the
island edges to be a rate-limiting step for the island growth, another Monte Carlo
simulation (Bedanov and Mukhin, 1993) obtained strong growth anisotropy up to 1/100
in island shapes with the anisotropy of lateral interaction of a dimer being 1:6 for SA
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36
and SB steps, respectively. It was also observed that the migration anisotropy had a
minor effect on the island shapes. In both simulations (Elswijk et al., 1991; Bedanov
and Mukhin, 1993), the interaction energies of a dimer with two types of steps were
deduced from the equilibrium shapes of islands with the aspect ratio of about 2-3 which
were obtained by annealing in UHV (Mo et al., 1989).
The potential energy calculations of single Si adatoms over SA and SB steps
showed that SB steps were good sinks for adatoms while SA steps were poor sinks
(Roland and Gilmer, 1992; Toh and Ong, 1992). It was also found that for SA steps,
adatoms tended to approach to binding sites of the step edges from the lower terraces,
but for SB steps, adatoms tended to come from the upper terraces. Roland and Gilmer
(1992) argued that growth at SB and DB steps took place much more readily than at SA
steps because o f a higher density o f binding sites and lower activation energies for
surface diffusion along the step edges.
There have been studies on the microscopic mechanisms of anisotropic growth
on the reconstructed Si (001) surface. Using MD simulations, Srivastava et al. (1989)
have shown that an anisotropic spread o f dimer opening resulted in the preferential
growth in a direction perpendicular to the dimer rows of a substrate. Adatoms adsorbed
to the dangling bond sites o f dimer atoms underwent a correlated motion in which the
adatoms moved perpendicular to the substrate dimer rows, leading to anisotropic
epitaxial growth through dimer openings. They observed that during the epitaxial
growth, the top layer was constantly dimerizing and the atoms below the top layer were
constantly returning to bulk sites. Metiu et al. (1992) proposed an atomistic
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37
mechanism, so-called exchange mechanism, for the anisotropic island growth. An
adatom approaching the long side of an island stuck to the side and then occupied a
nearest dimer-atom site by the exchange mechanism so that the original dimer atom
climbed onto the dimer row. Once on top of the dimer row, the atom moved along it
fast and then reached the end o f the island to incorporate there, giving rise to the
growth of the island in the length direction.
As reviewed in the above, the detailed mechanisms for epitaxial Si growth on
the reconstructed Si (001) surface are still controversial and not yet completely
understood. However, it is well established that nucleation and growth are governed by
playing between surface diffusion, step and kink density, and deposition rate. These
parameters are determined by substrate temperatures, surface misorientation angles, and
incoming Si flux, respectively. Epitaxial growth may be achieved by island growth
mode, but it may generate defects such as growth hillocks, twinning, and dislocations
in the epitaxial layer. To achieve good crystalline quality, therefore, the step-flow
growth is favorable. For this purpose, proper combination should be made for the
controllable process parameters. In general, the step-flow growth may be achieved with
the slow deposition rates at substrate temperatures above 600 °C for Si (001) substrates
with typical misorientation angles o f 1 to 5° ( Baliga, 1992).
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38
2.3. Chemical vapor deposition of diamond at low pressures
2.3.1. History of diamond growth at low pressures
There has been quite a long history o f the low-pressure synthesis of diamond,
which has been extensively reported in several review papers (DeVries, 1987; Badzian
and DeVries, 1988; Angus, 1989; Spear, 1989). This section presents only a brief
historical perspective which is important in understanding the synthesis of diamond
from the vapor phase at low pressures.
Since it was established in the 18th century that diamond was an allotrope of
carbon, many attempts have been made to synthesize diamond from various forms of
carbon with other structures. As chemical thermodynamics was developed, the
pressure-temperature regime where diamond was thermodynamically stable was
explored. In 1955, General Electric Company announced the success in synthesizing
diamond using a molten transition metal catalyst at high pressures and high
temperatures (Bundy et al., 1955).
Parallel to the efforts for diamond synthesis at high pressures and high
temperatures, several attempts were pursued toward synthesizing diamond at low
pressures in which diamond was metastable with respect to other forms o f carbon. The
first success o f low-pressure diamond synthesis was made in 1952 by Eversole at the
Union Carbide Corporation. In his experiments, seeded diamond crystals were grown
using carbon monoxide and hydrocarbon gases at 900-1000 °C and 100-300 atmosphere
(Eversole, 1962). However, the growth rates were very low and graphitic carbon was
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39
deposited simultaneously. The synthesis process was composed of many cycles of
growth and subsequent etching in hydrogen environment at 1000 °C to remove non­
diamond carbons.
Since 1956, the low-pressure synthesis of diamond from the vapor phase have
been studied by Spitsyn’s group at the Institute o f Physical Chemistry in Moscow
(Spitsyn and Deryagin, 1956). This group have taken many approaches to the lowpressure diamond synthesis, including chemical transport reaction (CTR). These
pyrolysis approaches primarily involved the thermal decomposition of hydrocarbons or
a gas mixture of H2 and hydrocarbons, producing too low growth rates and
codeposition of graphitic carbon as well (Deryagin et al., 1968, 1975; Deryagin and
Fedoseev, 1973). Angus and his colleagues at Case Western Reserve University took a
similar path as that of Eversole (1962) towards growing diamond at low pressures since
the early 1960s. They confirmed Eversole’s results and then demonstrated the growth
of p-type semiconducting diamond from a gas mixture of CH4/ B2H6 (Angus et al.,
1968; Poferl etal., 1973).
For the low-pressure diamond synthesis, these early works usually adopted
thermal decomposition methods of hydrocarbons including CH4 and C2H2 and a gas
mixture of hydrocarbons and H2 over diamond powder without additional activation of
gases. Their results were similar and any group could not produce individual diamond
crystals. The low growth rates less than 0.1 pm/hr and simultaneous deposition of
nondiamond carbons were the common problems. To overcome these problems,
researchers tried to etch as-grown products in a hydrogen environment, but this was not
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40
successful because H2 was not fully dissociated at low temperatures ( ~ 1000°C) used in
their experiments. Throughout the early work, however, the importance o f atomic
hydrogen was recognized in growing diamond at low pressures: atomic hydrogen could
preferentially etch graphite relative to diamond (Chauhan et al., 1974, 1976; Deryagin
and Fedoseev, 1975). The LEED study o f Lander and Morrison (1966) achieved the
most significant results in understanding the role o f atomic hydrogen on the diamond
surface: the unsatisfied dangling bonds on the diamond (111) surface were terminated
with atomic hydrogen, maintaining the bulk-like surface structure. They predicted that
epitaxial growth of diamond on diamond was possible despite the large instability of
bulk diamond with respect to bulk graphite, if the nucleation of graphite was inhibited
while adding carbon atoms to the diamond surface. The growth temperatures o f 9001400 °C and low deposition rates were suggested for the epitaxial diamond growth on
diamond.
In 1976, Deryagin, Spitsyn, and their coworkers for the first time reported the
growth of faceted diamond crystals on nondiamond substrates using CTR at pressures
below 1 atm and a substrate temperature of about 1000 °C. Details on the deposition
method were described later. The use o f atomic hydrogen during growth was
mentioned, and atomic hydrogen was reported to markedly increase the growth rates
and to reduce the codeposition of nondiamond carbon phases (Fedoseev et al., 1978;
Spitsyn et al., 1981). Their findings illustrated that the introduction of atomic hydrogen
during deposition was essential to the growth of high-quality diamond with high growth
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41
rates. The growth of faceted diamond crystals over 30 pm on foreign substrates was
demonstrated by introducing atomic hydrogen during CTR (Spitsyn et al., 1981).
Deryagin and Fedoseev (1977) outlined the three gas activation methods to obtain the
super-equilibrium concentration of atomic hydrogen: catalytic, electrical discharge, and
heated hot filament methods.
In the early 1980s, dramatic successes in the low-pressure diamond synthesis
from the gas phase had been achieved mostly in Japan with the development of a
variety of new gas activation techniques including AC discharge (Mania et al., 1981),
hot filament CVD (Matsumoto et al., 1982), microwave plasma-assisted CVD (Kamo
et al., 1983), r f plasma-assisted CVD (Matsumoto, 1985), DC plasma CVD (Suzuki et
al., 1987), and oxy-acetylene torch method (Hirose and Kondo, 1988). All these
techniques aimed at the efficient decomposition o f reactant gases to produce as large an
amount o f active hydrocarbon species and atomic hydrogen as possible. On the other
hand, active research in the United States started late in 1984 by Rustum Roy at The
Pennsylvania State University just after he visited the National Institute for Research in
Inorganic Materials (NIRIM) in Japan and saw the successful CVD diamond research
of this group. Since then, research on low-pressure diamond growth has been
widespread throughout the world so that now commercial products made from CVD
diamond such as cutting tools, heat sinks, optical windows, etc., are available in the
market.
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42
2.3.2. Synthesis techniques o f diamond at low pressures
To date, the most successful method for diamond synthesis from the vapor
phase is chemical vapor deposition (CVD) techniques using a mixture of hydrocarbon
and H2 gases at low pressures. O f the several CVD techniques developed for the
activation o f source gases, the following methods have been most widely used for
diamond synthesis at low pressures: 1) hot filament CVD; 2) microwave plasmaassisted CVD; 3) r f plasma-assisted CVD; 4) combustion flame CVD; and 5) DC arc
jet CVD.
Hot filament CVD (HFCVD), which was developed by Matsumoto et al.
(1982), is one of the most simple methods for diamond CVD. A key point of this
technique is decoupling of the gas activation temperature and substrate temperature. A
source gas mixture o f hydrocarbon and H2 is decomposed by a hot filament of
refractory metals (tungsten, tantalum, molybdenum, etc.) resistively heated up to 20002500 °C, producing active diamond precursors such as methyl radicals (CH3), acetylene
(C2H2), or other forms of hydrocarbon, and the super-equilibrium concentration of
atomic hydrogen. These active gas species are transported through diffusion and/or
convection to a substrate less than 1 cm apart, which is heated below 1000 °C by
radiation and conduction or sometimes by a separate heater. For this method, a mixture
of less than 2% CH4 in H2 and pressures of less than 40 Torr are typically used, giving
rise to the growth rates of 0.3-4 pm/hr. Sawabe and Inuzuka (1985) biased positively a
substrate in the arragement of HFCVD, where electron bombardment led to the
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43
increase of nucleation density and growth rate. Simplicity and low cost o f the apparatus
and ease of scale-up to the large deposition area are advantageous for this technique.
The major disadvantages are the limited stability and lifetime of the filament due to
carburization and the contamination of growing diamond by filament elements.
Since Kamo et al. (1983) demonstrated the deposition of well-faceted diamond
crystals on non-diamond substrates under microwave glow discharge conditions,
MPACVD has become one o f the most promising techniques for diamond synthesis
because a microwave discharge is very effective in producing atomic hydrogen. The
original design for MPACVD was a tubular system in which a silica glass tube passing
through the applicator served as a deposition chamber. 2.45 GHz microwave field
generated by a magnetron is transmitted to the chamber through a wave guide,
sustaining plasma of a mixture of hydrocarbon and hydrogen inside the cavity which
can be tuned by a tuner and plunger. A substrate may be held inside or remote from the
plasma cavity. Deposition conditions including pressures, substrate temperatures, and
CH4 concentrations are similar to those for HFCVD, but the quality o f as-grown
diamond is generally higher. The typical growth rates are 1-5 pm/hr. For this design,
the substrate size is limited by the tube diameter. The bell jar system developed later by
Bachman et al. and ASTeX, Applied Science and Technology (Bachman et al., 1988),
allowed diamond deposition for up to 5-6 inch diameter substrates. Since then,
continuous modification has been made so that deposition o f an area more than 10
inches in diameter with the growth rates more than 15 pm/hr is achievable by
commercially available high-power MPACVD systems.
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44
Continuous efforts have been made to increase the nucleation density of
diamond crystals on substrates. Through the conventional method of scratching
substrates with diamond powder, the maximum density of diamond nuclei was limited
to less than 109/cm2 in MPACVD. Recently a considerable improvement for the
diamond nucleation was achieved by applying negative dc bias to substrates in
MPACVD (Yugo et al., 1991). The nucleation density as high as 1010/cm2 was
obtained on Si mirror-polished substrates with a bias of -100 V at 40% CH4 in H2and
900 °C. Subsequent improvement was made with the modification of the surface
morphologies using the negative biasing of substrates. This is the growth o f highly
oriented diamond films through the bias-enhanced nucleation technique (Jiang et al.,
1993; Wolter et al., 1993). Applying a negative bias of 100-300 V to a substrate at the
beginning o f deposition in a MPACVD system, highly oriented diamond crystals were
grown on mirror-polished Si substrates with the very high nucleation density of 109n m '2
1U cm
.
1
Diamond was also deposited using low-pressure r f glow discharge of 13.56
MHz (Matsumoto, 1985). The major advantage for using this equipment is an ease of
scale-up for large area deposition. However, the synthesis of high-quality diamond with
low-pressure r f plasma CVD still remains to be achieved and the growth rates are very
low (0.03-0.3 pm/hr). A t the low pressures needed to take advantage o f this type of
glow discharge system, diamond-like carbon rather than diamond is usually formed. To
overcome the low growth rates, atmospheric-pressure r f thermal plasma torches were
developed (Matsumoto et al., 1987; Owano et al., 1991). The gas temperatures in a
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45
thermal plasma are extremely high (usually above 4000 K), and then almost all
molecules are dissociated into atoms, radicals, and ions, resulting in high-quality
diamond films with the very high deposition rates of 60-120 pm/hr. High-rate gas flow
as high as 70,000-80,000 seem is necessary to protect a torch wall and electrode, and
substrates should be externally cooled. The drawbacks with this technology are the
large power and gas consumption, the poor substrate temperature control, and the small
area o f deposition.
Another big step toward increasing the growth rates of diamond was the
introduction of the combustion flame CVD at atmospheric pressure with an oxyacetylene torch (Hirose and Kondo, 1988; Hanssen et al., 1988). The high linear
growth rates o f 50-100 pm/hr were demonstrated using an ordinary welding torch with
a mixture gas o f approximately 50% C2H2 and 50% 0 2 for a total flow rate of
approximately 2,000 seem. Temperatures o f gas phase are as high as 3000 °C, varying
with positions inside the flame. For growing diamond in the combustion flame, it is
necessary to hold a substrate in a reducing C2H2 feather flame and to keep its
temperature at 600-1100 °C. This method is simple and inexpensive, but it is not easy
to control the substrate temperature and the uniformity o f film thickness.
A DC glow discharge is probably the simplest way to obtain a plasma at low
pressures. Several research groups have succeeded in depositing diamond coatings
using this method at low pressures (Pinneo, 1987; Singh et al., 1988; Ravi and
Landstrass, 1989). In this system, DC power is supplied between a cathode and an
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46
anode where a substrate is mounted. For low-pressure and low-power DC plasma
CVD, however, the diamond quality was bad and the growth rates were less than 0.1
pm/hr. Suzuki et al. (1987, 1990) improved the growth rates more than 250 pm/hr
with the quite low gas flow rates of 20-100 seem by increasing the reactor pressure up
to 200 Torr and the DC discharge current density. They also observed that the
nucleation density on mirror-polished Si substrates was about 108 /cm2 and was as high
as that for the scratched surface. The gas temperatures were found to be 4000-6000 °C,
depending on the current densities. A major disadvantage o f high-pressure, compared
to low-pressure, DC plasma CVD is a limitation in the deposition area.
Diamond deposition with high growth rates o f 80 pm/ hr was reported using a
conventional plasma torch commonly used for plasma spraying (Kurihara et al., 1988).
A mixture gas o f CH4 and H2 with the flow rates o f 5,000-20,000 seem was fed
between two electrodes. A plasma jet was generated by DC arc discharge around the
torch nozzle at the pressures of 100-400 Torr and then blown out o f the generator onto
a water-cooled substrate at high velocity. Using an atmospheric DC arc jet CVD, a
much higher growth rate of about 930 pm/hr was obtained (Ohtake et al., 1989). In
this experiment, only H2 and A r were injected through the reactor, and then CH4 was
supplied in the course of the plasma jet. Deposition was performed on Mo and Fe
substrates at atmospheric pressure with 5 % CH4 in H2 and Ar. For this method, the
water-clear transparent diamond films with the highest growth rate are achievable and
pretreatment of substrates prior to deposition is not necessary. However, narrow
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47
deposition area and non-uniformity o f film thickness, and temperature fluctuation over
a substrate are the major limitations.
A variety of methods have been developed to synthesize diamond by CVD from
a mixture o f hydrocarbon and H2. In these CVD techniques, the gas mixture is
dissociated either thermally by means of a hot filament or flame, or in a plasma using
microwave, rf, or DC discharge. It is common for all techniques to produce the super­
equilibrium concentration of atomic hydrogen as well as CH3, C2H2, and other
activated hydrocarbon species. The final goal of these various CVD methods is the
deposition o f high quality diamond on a large area with high growth rates. At present,
some CVD methods such as MPACVD (Raytheon Company, USA; De Beers, UK),
HFCVD (Diamonex Inc., USA), and DC arc jet CVD (Norton Company, USA) are
already well advanced for commercial production of cutting tools, heat sinks, optical
windows, etc. (Bachmann, 1994). From the point of view of these requirements,
however, any technique used so far possesses advantages as well as disadvantages.
Continuous improvement of CVD technologies is in progress for further scale-up.
Which method to choose depends primarily on the specific application intended for the
diamond films.
2.3.3. Growth mechanisms of diamond at low pressures
2.3.3.1. Role of atomic hydrogen
A major breakthrough for the low-pressure diamond synthesis had not been
made until the importance o f atomic hydrogen for reducing codeposition o f non­
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48
diamond carbons and for enhancing the growth rates was suggested (Deryagin and
Fedoseev, 1977). Since then, enormous efforts have been made toward developing
several deposition techniques to create the super-equilibrium concentration of atomic
hydrogen as well as toward understanding the exact role of atomic hydrogen in
diamond growth.
Although the growth mechanisms for CVD diamond are only beginning to be
understood, there has been general agreement on the role of atomic hydrogen in CVD
diamond growth (Badzian and DeVries, 1988; Kondoh et al., 1992); 1) stabilization of
the diamond surface by maintaining sp3 bonding; 2) preferential etching of non­
diamond carbon such as graphite, amorphous carbon, etc., relative to diamond; 3)
generation o f active sites on the hydrogenated diamond surface where the diamond
precursors adsorb, through the abstraction o f surface-bonded hydrogen by atomic
hydrogen from the gas phase; and 4) generation of active hydrocarbon species in the
gas phase responsible for diamond growth. It is implied that sufficient atomic hydrogen
is essential not only for improving the film quality but for increasing the growth rates.
Atomic hydrogen created by various activation techniques mediates the
decomposition o f reactant hydrocarbons, for example CH4, into active species including
CH3 and C2H2 through a series of gas phase reaction (Harris et al., 1988; Goodwin and
Gavillet, 1990; Coltrin and Dandy, 1993). Diamond surfaces are hydrogenated to
satisfy dangling bonds whose saturation depends on the indices of the diamond surface
(Pate, 1986; Hamza et al., 1990). Thus, hydrogenation maintains the sp3 character of
surface carbon atoms on the diamond surface, which is diamond-like rather than
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49
graphitic in terms of the configuration of surface carbon atoms. The hydrogenterminated diamond surface seems to be more stable, compared to the hydrogenated
graphite surface although bulk diamond is thermodynamically metastable with respect
to bulk graphite (Spear, 1987; Badziag et al., 1990; Yarbrough, 1991). Surface
hydrogen atoms may be removed by reaction with hydrogen atoms of the gas phase or
thermal desorption, leaving active surface sites on diamond surface (Frenklach, 1989;
Harris and Weiner, 1990; Garrison et al., 1992; Butler and Woodin, 1994). Active
hydrocarbons w ill be adsorbed on these open sites. I f hydrocarbons are not desorbed
and hydrogen atoms bonded to them are subsequently abstracted, leaving the
hydrogenated surface, growth o f diamond occurs by addition of carbon atoms on the
surface while keeping the starting hydrogenated surface structure. Deposition of
graphite or other non-diamond carbons can be suppressed with the stabilization o f the
diamond surface by sp bonding or with their preferential etching by atomic hydrogen
(Setaka, 1987). Repetition of the above processes would lead to the continuous growth
of diamond by low-pressure CVD under conditions where diamond is metastable
relative to graphite in terms o f bulk property.
2.3.3.2. Diamond precursors and growth mechanisms
Much attention has focused on the identification of growth species in the gas
phase which are responsible for the addition o f carbon atoms to the diamond surface.
For a gas mixture of hydrocarbon and hydrogen, highly controversial arguments have
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50
centered on CH3 (Harris and Martin, 1990; Chu et al., 1990) versus C2H2 as the
growth species (Frenklach and Spear, 1988; Frenklach and Wang, 1991) although the
methyl cation CH3+ (Tsuda et al., 1986) or carbon atom C2 (Raiche et al., 1991) was
considered as well. It was demonstrated that both CH3 and C2H2 were capable of
contributing to diamond growth. However, several experimental studies including
isotopic competition experiments with 13CH4 and 12C2H2 in HFCVD (Chu et al., 1990;
D ’Evelyn et al., 1992) and MPACVD (Martin and H ill, 1990; Harris and Martin,
1990) and resonance-enhanced multiphoton ionization spectroscopy experiments in
HFCVD (Celii and Butler, 1989, 1992; Butler and Celii,
1989) have strongly
supported that CH3 are the dominant growth species for CVD diamond.
In spite o f the extensive research on CVD diamond films, detailed atomistic
growth mechanisms have been rarely studied and are not yet understood. Tsuda et al.
(1986) and Frenklach and Wang (1991) proposed growth models on the diamond (111)
surface using CH3+ and C2H2, respectively. Here, however, only studies on the growth
mechanisms on the diamond (001) surface using CH3 w ill be discussed.
Harris (1990) modeled a diamond growth based on the addition of CH3 to the
hydrogenated diamond (001) surface with the dihydride structure. Bicyclo-nonane
(BCN), which consisted of nine carbon atoms, was considered as a model compound
representing the diamond surface. Using the rate constants estimated from analogous
gas phase reactions and the concentrations of gas phase species from measurements,
this model predicted a growth rate of between 0.06 and 0.6 pm/hr. It was argued that
the calculated growth rates from this model agreed with experimentally measured ones
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51
in HFCVD. For the diamond (001) surface, however, an STM study performed by
Tsuno et al. (1991) showed that epitaxial diamond growth occurred through 2x1
reconstruction. For the diamond (001) surface, the dihydride structure with two
hydrogen atoms per surface carbon atom, which was a basic surface structure o f the
BCN model proposed by Harris (1990), was predicted almost certainly not to exist in a
large area due to strong steric repulsion between surface-bonded hydrogen atoms (Yang
and D ’ Evelyn, 1992a, 1992b).
Garrison and coresearchers (1992) presented elementary reactions starting with
the dimer structure on the reconstructed diamond (001) surface with the monohydride
structure. Using MD calculations, each growth stage was considered, including the
creation of a radical site on the surface, adsorption o f methylene CH2, dimer opening,
and subsequent insertion of CH2 into the dimer bond. It was observed that the insertion
of CH2 into the open dimer site was extremely easy, while the insertion into the trough
site was much slower. This model suggested that the dimer-opening step was the major
atomistic mechanism for CVD diamond growth on the diamond (001) surface. In a
recent paper, Dawnkaski et al. (1995) extended this model for growth on the clean 2x1
reconstructed (001) surface with strained and reactive n bonds.
Following the dimer-opening model o f Garrison et al. (1992), Harris and
Goodwin (1993) carried out a kinetic study for growth on the monohydride (001)
surface which combined alternate sequences of the dimer mechanism and the trough
mechanism following Harris’s original BCN model. They found that the growth rate at
dimer sites was considerably faster than at trough sites between dimer rows. For the
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52
completion of growth o f a new layer occurring half at dimer sites and half at trough
sites, it was postulated that the trough portion o f the mechanism was rate limiting.
STM study on homoepitaxially grown diamond (001) surface (Tsuno et al.,
1991; Busmann et al., 1992) suggested that growth occurred preferentially at steps by
extension o f dimer rows. Garrison et al. (1992) and Harris and Goodwin (1993)
mentioned the step growth a little, but detailed consideration was not given to it.
Tsuda et al. (1992) studied using the ab initio molecular orbital method, a
mechanism for the step growth where carbon atoms were assumed to be the growth
species on the clean 2x1 diamond (001) surface. It was shown that growth at a SB step
occurred via an independent extensions o f individual dimer rows while growth at a SA
step proceeded by the nucleation of a dimer at the SA step edge and by subsequent
propagation of a dimer row along the step edge. This mechanism seems to take after
that of the epitaxial growth o f Si on the clean Si (001) surface. The almost same
atomistic mechanism may be applied to both systems, but it is thought that the different
growing environments of the two systems as well as the most probable growth species
for CVD diamond should have been taken into account.
The step growth mechanism was also studied by Zhu et al. (1993) using
molecular mechanics (MM). They considered adsorption and reactions o f CH3 and
atomic hydrogen at the step edges on the monohydride diamond (001) surface. By
applying the dimer-opening mechanism proposed by Garrison et al. (1992), it was
found that epitaxial diamond growth occurred predominantly by extension of dimer
rows. They claimed that preferential step growth by extension of dimer rows occurred
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53
due to steric and bond-strain constraints on the positions of precursor-addition reactions
and a strong anisotropy in the etching of dimers nucleated at the SA and SB steps. For
the completion of a new layer, this mechanism invoked the etching-away route of
individual dimers formed on terraces rather than surface diffusion o f the growth species
on the diamond surface.
On metals. Si. GaAs, etc., growth is dominantly controlled by surface diffusion
of adatoms to steps or kinks, leading to preferential growth at these sites. In the CVD
diamond growth, however, surface diffusion has been widely believed to be negligible
because the fraction of surface radical sites has been estimated to be rather small, no
larger than 10% (Frenklach, 1992; Brenner et al., 1992; Harris and Goodwin, 1993),
and the migration of the growth species such as CH3 on the hydrogenated surface has
been thought to be energetically unfavorable (Zhu et al., 1993; Harris and Goodwin,
1993). When the growth species land on unstable sites, desorption from these sites has
been generally preferred relative to surface diffusion to the energetically stable sites.
Several experimental observations (Enckevort et al., 1993; Badzian and Badzian,
1993; Vitton et al., 1993), including growth steps and hillocks on homoepitaxially
grown diamond film s, however, have suggested that surface diffusion might play an
important role in CVD diamond growth.
A theoretical approach on surface diffusion of the growth species on the
diamond (001) surface was made by Mehandru and Anderson (1991) using the atom
superposition and electron delocalization molecular orbital method. The migration of
CH3, CH2, and C2H2 was considered on the monohydride (001) surface. In the
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54
presence of hydrogen vacancies, energy barriers were calculated to be high for CH3,
but low for CH2 enough that surface diffusion could occur under CVD conditions for
diamond. The energy barriers for the migration of CH2 along (1.92 eV) and across
dimer rows (2.01 eV) were so close to each other, that it could lead to the conclusion
that there was no preferential diffusion direction on the hydrogenated 2x1 surface. It
was found that C2H2 did not form a strong bond to a surface radical site, but it could
bind strongly by bridging two adjacent radical sites. This structure was considered not
to be involved in the growth mechanism.
Skokov et al. (1994a) and Frenklach et al. (1995) showed in their recent
theoretical analyses that the migration o f CH2 and C2H2 was feasible on the
hydrogenated 2x1 diamond (001) surface and played a crucial role in the CVD diamond
growth. They also proposed a growth model related to their diffusion mechanism. The
growth mechanism was the conversion of dimer sites into bridge sites and surface
migration of bridge sites toward continuous bridge chains.
Under the normal CVD conditions, diamond growth is likely to occur via
extension of dimer rows, as confirmed by STM (Tsuno et al., 1991; Busmann et al.,
1992). There are possibly two ways for the dimer row extension to occur on the
reconstructed diamond (001) surface. One is the propagation of SB steps, and the other
is the propagation of DB steps. In the modeling for diamond growth, however, the
dimer row extension was considered to occur only at SB steps. As reviewed in section
2.2.4, Si growth on the single-stepped Si (001) surface occurs preferentially at SB steps
until approximately 0.5 M L deposition, producing DB steps, and then step flow
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55
proceeds through the propagation of DB steps (Hoeven et al., 1989a, b, 1990a). On the
double-stepped surface, Si growth occurs only at DB steps. Step-flow growth at DB
steps are recommended to obtain high-quality films because this type of growth can
avoid the generation of antiphase boundaries (Hamers et al., 1989, 1990; Hoeven et
al., 1990b). In modeling diamond growth on the diamond (001) surface, therefore, DB
steps as well as SB steps have to be taken into consideration because both Si and
diamond (001) surfaces show a similar surface reconstruction. In order to consider the
step-flow growth at various steps, the step structure o f the hydrogenated or
hydrocarbonated diamond (001) surface and the step form ation energies should be
known. Unfortunately, however, this information is not available at present. In
addition to the step growth, recently there has been increasing concern about surface
diffusion o f hydrocarbon adsorbates on the diamond surface. Theoretical work has
shown that surface diffusion may play a significant contribution to diamond growth
(Mehandru and Anderson, 1991; Skokov et al., 1994a; Frenklach et al., 1995).
Since a study on the detailed atomistic mechanism for the CVD diamond growth
is just beginning, more extensive theoretical and experimental work is needed not only
to better understand the low-pressure diamond growth but also to better control the
CVD diamond quality and growth rates in various CVD techniques.
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56
2.3.4. Homoepitaxial growth o f diamond films
2.3.4.1. Homoepitaxial diamond growth at different sectors
It is quite obvious that single-crystal diamond is the best candidate substrate for
the growth of single-crystal diamond films. Diamond growth on the diamond substrates
proceeds easily. However, there are marked differences between the homoepitaxial
growth on the diamond (001), (111) and (110) sectors.
Single-crystal diamond was already used as substrates in the early work of CVD
diamond. Homoepitaxial growth on the diamond (001), (111) and (110) substrates was
for the first time demonstrated successfully using CTR technique (Deryagin et al.,
1975; Spitsyn et al., 1981). Substrate temperatures were pointed out as one o f the most
important factors which determined the growth rates and film properties. On the (110)
substrates, polycrystalline films were grown at 600°C while highly perfect single­
crystalline layers were obtained at 750 °C. With increasing substrate temperatures, the
growth rates o f homoepitaxial
films
increased and reached a maximum
at
approximately 1000 °C. Further increase in temperature gave rise to reduction of the
growth rates and to codeposition o f graphite inclusions. For the (111) homoepitaxial
films, it was found that excessive stresses in films induced by growth defects caused the
formation of microtwins and the gradual transition from a single-crystalline film into a
polycrystalline one. On the (001) substrates, however, the epitaxial films did not
undergo twinning and then had a high structural perfection.
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57
Experiments on the variation of substrate temperatures using MPACVD
revealed that on the (111) and (110) substrates, single-crystalline epitaxial films were
obtained in the temperature range from 820 to 950 °C while on the (001) surface, the
single-crystalline growth occurred only at 820 °C (Kamo et al., 1988). It was shown
that the growth rates decreased in the order (111) « (110)> (001). Diamond films up to
100 pm thick were grown on the (001) and (111) substrates in the presence of water
vapor at the low CH4 concentrations of 0.5% and 1% at 850 °C (Sato, 1990). Single­
crystal epitaxial films were grown on the (001) substrates whereas on the (111)
substrates, secondary nucleation took place, resulting in polycrystalline particles before
the film thickness o f 100 pm was reached.
The surface morphologies and crystal Unities of homoepitaxial diamond (001)
and (110) films were studied depending on the CH4 concentrations in H2, using
MPACVD (Shiomi et al., 1989, 1990). The epitaxial films grown on the diamond
(110) substrates at 900 °C showed the rough surfaces which were composed of
wedgelike crystal habits in the <100> directions at 2% and of small squares of the (001)
plane at 6% CH4. For the diamond (001) substrates, a smooth, high-quality film
without graphitic component was obtained at 6% CH4 while deposition at 2%, 4%, and
8% CH4 resulted in rough growth surfaces. It was observed that the growth rates of the
(110) films were about twice those of the (001) films.
HFCVD was used to deposit the single-crystal films on the (001), (111) and
(110) substrates with different boron-doping concentrations (Geis, 1990). Lattice
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58
defects, especially dislocation density, increased with higher boron doping. It was
observed that device-quality films were easily obtained on the (001) substrates,
compared to the (111) and (110) substrates.
Badzian and Badzian (1993) also found that epitaxial growth on the (111) and
(110) surfaces was more difficult than on the (001) surface. The (111) films usually
became polycrystalline with a high density of structural defects. For the (111)
substrate, the oriented growth was achieved at 950 °C and 1% CH4, but it was
postulated that epitaxial growth on this surface resulted in a non-cubic form of
tetrahedral carbon. Growth on the (110) substrate resulted in a polycrystalline film at
900 °C, while at 1200 °C a single-crystalline film was obtained, but with microfacets
of {111} planes.
The high growth rates o f 100-200 pm/hr on the (001) and (110) diamond
substrates were achieved using the oxy-acetylene torch method (Snail and Hanssen,
1991). It was observed that the cylindrical-shaped substrate crystals grew into
polyhedral-shaped crystals with {100}, {111}, and {110} faces at 1150-1500 °C. The
(110) homoepitaxial film grown at 1500 °C was confirmed to have a strong graphitic
character. High-temperature growth on the (001) surfaces proceeded mainly via step
propagation, producing high-quality epitaxial films.
Single-crystalline (100), (110), and (111) films homoepitaxially grown with
HFCVD were investigated using atomic force microscopy (AFM) (Sutcu et al., 1992a,
b). Growth on the (001) substrate with 0.3% CH4 at 810 °C produced a rough surface,
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59
exhibiting pyramidal features and penetration twins, while the film grown with 1.6%
CH4 at 1000 °C was nearly atomically smooth. A (111) epitaxial film was rough and
cracked due to the tensile stress, whereas a (110) film was rough on the micron scale
but nearly atomically smooth on the nanometer scale. The growth rates of
homoepitaxially grown films were measured as a function of CH4 concentrations and
substrate temperatures (Chu et al., 1992). The growth rates increased with higher CH4
concentrations in the range less than 0.8% CH4 and at higher temperatures in the range
of 700-980 °C. The growth rates decreased in the order (110)> (001) «(111).
For the homoepitaxial diamond films grown using HFCVD and flame method,
it was reported that crystallographic quality of the epitaxial layers decreased in the
order: flame (001)> H F (110), and flame (110) » HF (001) and HF (111) ( Janssen et
al., 1992; Enckevort et al., 1993; Schermer et al., 1994).
As shown above, despite continuous efforts toward diamond homoepitaxy, there
are still a number of problems to be solved in order to achieve device-quality or gemquality homoepitaxial films. Results on diamond homoepitaxy are not yet conclusive,
and the optimal deposition condition for diamond homoepitaxy remains to be
determined. However, the (001) surface is the first candidate for the growth o f single­
crystalline films, leaving the (111) and (110) surfaces for future investigation.
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60
2.3.4.2. (001) homoepitaxial diamond films
Parametric studies on the morphologies o f the (001) homoepitaxial films have
involved mostly variation of the CH4 concentrations and the substrate temperatures. In
this section, thus, a review will be given mainly on the dependence o f the surface
morphologies upon these two deposition parameters.
The
dependence
of
surface
morphologies
and
crystallinity
of
(001)
homoepitaxial diamond films upon the CH4 concentrations in H2 was investigated in
MPACVD (Shiomi et al., 1989, 1990). For different CH4 concentrations o f 2-8%, all
(001) films grown for 2 hr at 830 °C had no graphitic components, but they showed
different surface morphologies. At 2%, 4%, and 8% CH4, as-grown films showed
rough surfaces with crystallite growth or polishing traces. However, deposition at 6%
CH4 produced a smooth growth surface.
A ir plasma etching was applied to reveal the crystal defects o f the (001)
homoepitaxial films grown by MPACVD (Sato et al., 1991). The epitaxial films grown
up to 20 pm thickness at 860 °C with 3-6% CH4 showed little contrast, smooth growth
surfaces, but plasma etching resulted in characteristics of the films deposited at
different CH4 concentrations. The etched surface grown with 4% CH4 was smooth with
shallow rectangular pits, but all other films grown with 3%, 5%, and 6% CH4 had a
high density o f deep etch pits.
The density of crystallites on top o f pyramidal hillocks, which are the most
common defects on the (001) homoepitaxial diamond films, was studied with variation
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61
of the deposition parameters o f MPACVD (Findeling-Dufour et al., 1995). The density
of crystallites was reduced with a decrease of the substrate temperatures from 950 to
850 °C, an increase o f the CH4 concentrations from 2% to 4%, and an increase of the
microwave power density. It was described that an increase o f the misorientation angles
from 1 to 5° slightly reduced the defect density only at a specific growth condition, but
detailed results were not given.
In a MPACVD experiment, the (001) homoepitaxial film morphology changed
from growth hillocks to step growth with increasing CH4 concentrations (Borst et al.,
1994). Defect density of the (001) homoepitaxial films measured by Rutherford
backscattering decreased at higher CH4 concentrations (Samlenski et al., 1995).
The above results present that the high CH4 concentrations o f 4-6% yield the
optimal properties as to surface morphologies and crystallinity of as-grown films.
However, there have been studies to show that the optimal growth for the (001)
diamond homoepitaxy occurs at lower CH4 concentrations. Transparent and almost
colorless, smooth (001) homoepitaxial films were grown for the CH4 concentrations of
1% or less at 850°C using HFCVD (Avigal et al., 1993). With increasing the CH4
concentrations beyond 1% the films gradually lost transparency and became darker,
until at 4% they looked black and reflective. The films grown with higher CH4
concentrations showed large crystallites with poor faceting. It was postulated that
optimal growth occurred at lower CH4 concentrations o f 0.5-1 %.
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62
An STM and LEED study was performed for the homoepitaxial diamond films
grown on the diamond (001) substrates misoriented 4.3° toward the (110] direction
(Tsuno et al., 1994). In MPACVD at 850-900 °C, the 2x1 single-domain surface was
developed at 2% CH4 while the 2x1 and 1x2 double-domain surface structure was
observed at 6% CH4, suggesting a higher rate of two-dimensional nucleation with
increasing the CH4 concentrations.
Consequently the study o f (001) homoepitaxial diamond growth depending on
CH4 concentrations is still controversial and needs more systematic approaches to
elucidate inconsistency between different groups.
The second CVD parameter important for the diamond growth is the substrate
temperature. Badzian et al. (1991, 1993) investigated the effect o f temperatures on the
surface morphologies of the (001) homoepitaxial films using MPACVD. It was
demonstrated that high-quality single-crystalline diamond (001) films were grown up to
250 pm thickness at 1% CH4 and 850-900 °C. The narrowest full width at half
maximum (FWHM) of Raman spectra was 1.7 cm'1, which corresponds to that of the
best natural diamond. Epitaxial growth on the (001) surface proceeded via step flow
along the <110> directions. But formation o f growth hillocks sometimes disturbed the
epitaxial growth. Craters were formed at the top of growth hillocks on films about 100
pm thick grown at 900 °C. Raman spectra taken at such a crater did not show the 1332
cm'1 peak. On the other hand, growth hillocks which were formed at 1200 °C had a
regular pyramidal shape with a sharp apex. Raman spectra did not show any difference
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63
between the top of hillocks and the flat region of the film. Thus, it was concluded for
the (001) homoepitaxy that deposition at temperatures higher than 1100 °C was
beneficial in terms of the film quality.
In homoepitaxial diamond growth using MPACVD, at temperatures o f 8501000 °C, (001) epitaxial films were composed of growth hillocks with polycrystallites
at their top. At 700-850 °C, however, smooth films were obtained or growth hillocks
were formed with a more regular pyramidal shape and with no polycrystallites atop
(Vitton et al., 1993). The deposition at temperatures below 850 °C was suggested for
the optimal surface morphologies of films.
An AFM study on single-crystalline films grown with HFCVD revealed that at
0.3% CH4 and 810 °C, the (001) homoepitaxial films exhibited growth hillocks with
penetration twins, while at 1.6% CH4 and 1000 °C the films were nearly atomically
smooth (Sutcu et al., 1992a, b). It is not certain in this result whether the smooth
growth surface was attributed to the higher CH4 concentration or the higher substrate
temperature.
The step growth was investigated for the homoepitaxial diamond films grown by
the oxy-acetylene torch method (Snail and Hanssen, 1991). A t high temperatures of
1150-1500 °C, growth on the (001) surface proceeded mainly via step propagation. The
period of steps, the terrace width, increased with the substrate temperatures: 1-2 pm at
1150 °C and 40-60 pm at 1360 °C. The misorientation angles of the substrates involved
were measured, but their relationship with surface morphologies was not found.
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64
Growth hillocks were also observed on the (001) homoepitaxial films (Snail et al.,
1992).
For the homoepitaxial diamond growth using HFCVD and the flame method,
the (001) homoepitaxial films were covered by macrosteps or by numerous shallow
growth hillocks with macrosteps on their side faces (Janssen et al., 1992; Enckevort et
al., 1993; Schermer et al., 1994). The macrosteps in growth hillocks were claimed to
be nucleated at foreign particles or at lattice defects (Enckevort et al., 1993). It was
postulated that in the (001) epitaxial growth, surface diffusion over a distance far less
than the step distances (2-4 nm) was rate limiting. It was also demonstrated that the
mosaic growth on misoriented (001) substrates produced smooth films (Janssen et al.,
1994).
Growth hillocks formed on the homoepitaxial diamond films were intensively
investigated using STM and AFM
(Everson and Tamor,
1992; Tamor and
Everson, 1993). Some pyramidal hillocks had a sharp peak, but most exhibited gross
defects at the top. Gross defects that were not crystallographically related to the
substrate grew more rapidly than the flat region. Each pyramidal hillock showed
several discrete changes in slope in the range of 3-18°.
On the (001) homoepitaxial films, the most commonly occurring morphologies
are macrosteps and growth hillocks. Growth hillocks are frequently accompanied by
polycrystallites that are formed at the top of hillocks by secondary nucleation. The
generation o f polycrystallites disturbs the epitaxial growth o f films whereas step-flow
growth producing flat surfaces or macrosteps results in single-crystalline films with
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65
nearly perfect epitaxy over a whole area. One of the goals in the diamond (001)
homoepitaxy is to achieve the step-flow growth while inhibiting secondary nucleation.
Several studies have been carried out to establish the optimal deposition condition for
the step-flow growth, but they are not yet completed and they also show inconsistent
results between different research groups. The inconsistency in the dependence of
surface morphologies on the deposition parameters may be attributed to different CVD
systems or different CVD conditions involved. However, it may result from other
factors including the surface misorientation angles of substrates. As reviewed in section
4.2, the effect o f surface misorientation of substrates has been well known in other
material systems such as Si, SiC, GaAs, etc. Systematic study o f the deposition
parameters, including the surface misorientation angles o f substrates, should be
performed to establish the optimal condition for the (001) homoepitaxial diamond
growth.
2.4. Objectives o f this study
The (001) diamond homoepitaxy was investigated in this study because nearly
perfect single-crystalline films can be grown on the diamond (001) surface, as
discussed in the previous section. Although extensive studies on (001) homoepitaxial
diamond films have already been performed toward establishing the optimal growth
conditions, understanding the growth mechanisms of CVD diamond, and finally
reaching gem-quality or at least device-quality films, our state o f the art is still far from
the scientific and engineering goals. One o f the most urgent problems to be answered in
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66
the (001) diamond homoepitaxy is to characterize the dependence o f surface
morphologies and film qualities on deposition parameters such as surface misorientation
angles of substrates, CH4 concentrations, substrate temperatures, etc., in order to
establish the optimal CVD condition. Chapter 3 describes a parametric investigation of
the effects o f the deposition processes on the surface morphologies and qualities of
resultant films. In particular, the mechanisms for the hillock growth and step-flow
growth were elucidated in terms of microscopic surface structure.
In the epitaxial growth of thin films, understanding the surface structure is of
great significance because surface morphologies, and eventually physical properties of
as-grown films are determined by surface structure during growth. Although there have
been several kinds of evidence indicating the importance o f steps in CVD growth of
diamond, the role o f steps has not been seriously considered in the CVD diamond
community. As shown in section 2.2 for the Si surface structure, step and domain
structure may be of great consequence for understanding the growth mechanisms of
CVD diamond. Chapter 4 deals with the diamond (001) surface structure o f substrates
annealed in hydrogen plasma and of as-grown films in terms of domain and step
structure using RHEED. The relative stabilities of several types o f steps in the atomic
hydrogen environment and in the CVD environment for diamond growth were
discussed.
For the understanding o f growth mechanisms, the observation o f the growth
surface is a fundamental requirement. Observation with atomic-scale resolution is
highly desirable in order to know the growth processes and the factors important for the
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67
growth, because the crystal growth takes place via incorporation of atoms on the
surface. STM is considered to be one o f the most successful techniques for directly
imaging atomic structure of surfaces. Chapter 5 discusses the atomic structure of (001)
homoepitaxial diamond films observed using STM. Step and domain structure, several
hydrogenated surface structures such as 2x1 monohydride, l x l dihydride, and local 3x1
configurations,
and surface defects including antiphase boundaries,
and dimer
vacancies, are also described.
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68
Chapter 3
EXPERIMENTAL
3.1. Introduction
This chapter presents the experimental techniques used for deposition and
characterization of homoepitaxial diamond films. Detailed descriptions are given for the
theoretical background for the measurement of the surface misorientation angles of
diamond substrates and for RHEED. The tubular MPACVD system used in this study
is stated in detail as well. Characterization techniques such as LEED, differential
interference contrast optical microscopy, scanning electron microscopy, STM, Raman
spectroscopy, and profilometry for the measurement of surface roughness are briefly
mentioned.
3.2. Measurement of surface misorientation angles of diamond substrates
The surface misorientation angles of mirror-polished diamond substrates were
measured by x-ray diffraction, using a home-made back-reflection Laue camera. The
accuracy of the measurements o f the misorientation angles with this camera was within
± 0.1°. Accuracy in the measurement o f misorientation angles seems to be very
important for (001) homoepitaxial diamond growth because in this study these angles
turned out to considerably affect surface morphologies and surface structure such as
step and domain structure. This section describes in detail the principle of back-
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69
reflection Laue x-ray diffraction, the definition o f the misorientation angles, a
theoretical approach towards developing a computer program for the calculation o f the
misorientation angles, and experimental procedures for the measurement.
3.2.1. Principles o f back-reflection Laue x-ray diffraction
The Laue x-ray diffraction is the most convenient method for determining the
orientation and symmetry of crystals. In this method, a parallel beam of white
radiation, the x-ray spectrum with a continuous distribution of wavelength, is directed
onto the surface of a fixed single crystal from an x-ray tube. Thus, the incidence angle
$, the angle between the incident wave and a plane o f reflection, is fixed for every set
of planes in the crystal. Each set of reflecting planes in the crystal diffracts the incident
beam with a particular wavelength X which satisfies the Bragg law,
nX = 2dm sin#,
(3.1)
for the particular value of 0 and the interplanar distance dhU of (hk[) planes in the
crystal, where n is an integer. The diffracted beams, all together forming a diffraction
pattern, reproduce therefore a structure of the crystal (Azaroff, 1968; Cullity, 1978).
There are three types of Laue diffraction techniques, transmission method,
back-reflection method, and cylindrical film method, depending on the relative
positions o f an x-ray source, sample, and film. In the transmission Laue method, they
are placed so that the beams diffracted through the crystal in the forward direction are
recorded on a film. In the back-reflection Laue method, a film is placed between the x-
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70
ray source and the sample to record the beams diffracted in the backward direction. In
the third method, a cylindrical film is used to obtain more diffraction beams around the
sample. The positions o f spots on a Laue pattern are determined by the orientation of
the single crystal relative to the incident beam for both transmission and back-reflection
Laue patterns. The back-reflection method, however, is the more common one. In the
back-reflection method, no special sample preparation is usually required and samples
of any thickness may be used, whereas the transmission method requires relatively thin
samples which can transmit x-rays (Cullity, 1978; Preuss et al., 1974).
The experimental setup for the back-reflection Laue technique is illustrated
schematically in Figure 3.1. The x-ray tube produces a beam of x-rays over a wide
range of wavelength. The pinhole collimator yields a well-collimated beam incident on
the sample. The reflected beams are recorded on the film placed perpendicular to the
incident beam between the x-ray source and the crystal. When a wet-processed film is
used, an appropriate hole is punched at the center of each negative and one corner is
cut for identification.
The orientation of the single crystal can be determined from the positions o f the
back-reflection Laue spots on the film. Knowing the sample-to-film distance df and the
distance / o f a spot from the center o f the film, the Bragg angle 9 is calculated for the
corresponding reflection from the equation
tan (180°-20) = — .
df
(3.2)
But this does not help in identifying the hkl indices of the planes producing a particular
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71
R eflected x-ray beam
Incident
x-ray beam
S am ple
C ollim ator
Film
Figure 3.1 Schematic illustration o f a back-reflection Laue technique.
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72
spot because the wavelength X of the diffracted beam is unknown, which is required to
calculate the interplanar distance dhkl from the Bragg law. However, the orientation of
the normal to the plane producing the spot is known because the normal always bisects
the angle between the incident and diffracted beams. A stereographic projection can be
constructed from the directions of those normals. In the stereographic projection,
angles between plane normals can be measured and compared with a list of known
interplanar angles for the single crystal. Thus, the spots in a Laue pattern can be
indexed with this method.
If the surface of an as-polished diamond substrate coincides with the
crystallographic (001) plane, and an x-ray beam is incident perpendicular to the
surface, a Laue pattern taken from this crystal shows the four-fold symmetrical
distribution o f spots with the 001 reflection exactly at the center of the film. When the
substrate surface is misoriented with respect to the (001) plane, but the x-ray beam is
maintained perpendicular to the substrate surface, all spots move, relative to the center
of the film , in the opposite direction of the misorientation of the sample surface. The
position o f each reflection in the pattern depends on the surface misorientation angle of
the substrate. The surface misorientation angle of the substrate can, therefore, be
measured from its relationship to the positions o f spots with respect to the film center.
3.2.2. Definition o f surface misorientation angles
The bulk diamond structure is built up with tetrahedra whose edges are along
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73
the <110> directions. On the diamond (001) surface, dangling bonds are not only
aligned along the <110> directions, but dimerization, which is made by bonding the
two nearest neighboring surface carbon atoms to lower a surface energy, also occurs
along the <110> directions. On the (001) homoepitaxial diamond films, macrosteps
have been observed to run along the <110> directions (Sutcu et al., 1992a; Maguire et
al., 1992; Badzian and Badzian, 1993; Enckevort etal., 1993; Vitton et al., 1993), and
growth hillocks have a pyramidal shape of four-fold symmetry with their edges parallel
to the <110> directions (Badzian and Badzian, 1993; Schermer et al., 1994). In
studying the diamond (001) surface, therefore, the <110> directions are so important
that the surface misorientation angles o f substrates should be determined in terms of
these directions.
An
as-polished
diamond
single-crystal
substrate which
has a surface
misorientation angle <f>with respect to the crystallographic (001) plane, is illustrated in
the principal crystal axes in Figure 3.2. The surface misorientation angle of a substrate
<f>is a deviation o f the surface normal s from the [001] direction and should be resolved
into two components a and /? toward the [110] and [110] directions, respectively.
Figure 3.3 describes the misorientation angle </> in terms of these two component angles
a and (3. The angles a and (3 are defined so that the surface normal s is tilted by a from
the [001] direction toward the [110] direction and then tilted by P to the [110]
direction from the plane (110) made by the [001] and [110] vectors.
The surface normal unit vector s o f a diamond (001) substrate may be expressed
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74
[001] M
S u b strate
su rface
[010]
[100]
Unit ceil of cubic
crystal system
Figure 3.2 Definition o f a surface misorientation angle <j>with respect to the
crystallographic (001) plane in the principal crystal axes.
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75
[110]
[001]
►
[110]
Figure 3.3 Definition of two component angles a and /? resolved toward the [110]
and [110] directions, respectively, of a surface misorientation angle <j>.
The [001] direction points back from the paper plane.
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76
by
s = hsx + ksy + lsz
(3.3)
with the length o f the vector s, (hs2 + ks2 + l 2) m , equal to a unity, where x , y, and z
are the unit vectors along the principal crystal axes x, y, and z, that is, [100], [010],
and [001], in the cubic crystal system, respectively. The surface normal s specified by
hs ks ls can be described as a function o f the two components a and /? of the
misorientation angle <j>. This description is represented by the equation
s =
sina cos/? + sin/?
x +
sina cos(5 - sin/?
y + (cosa cosy?) z . (3.4)
3.2.3. Coordinates of back-reflection Laue spots
In the cubic crystal system, the (hk[) plane is represented equivalently by its
plane normal unit vector,
hx + ky + Iz
8
(h 2 + k 2 + l 2) W2'
(3.5)
In order to express the plane normal vector g in polar coordinates relative to the surface
normal s of a substrate, which is convenient for the calculation of the coordinates of
Laue diffraction spots, another Cartesian coordinate system uvw is introduced as shown
in Figure 3.4. The v axis is parallel to the incident x-ray beam, which is assumed to be
perpendicular to the sample surface, and the u axis lies in the xy plane. The unit vectors
u, v, and w o f the coordinate system uvw can be described in terms of the xyz system.
The vector v is identical with the normal s o f the surface:
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77
z
v
w
Figure 3.4 Introduction o f a new Cartesian coordinate system uvw.
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78
v = fa x + h y + hz.
(3.6)
The vector u can becomputed from the condition that u is a unit vector in the xy plane,
orthogonal to the vector v. From these relations,
wv = 0
(3.7)
l« l2 = 1,
(3.8)
and
the vector u is determined to be
ks x -
U
hs y
//. 2 , . 2 \l/2 •
(h s 2
(3-9)
+ k s 2 )'
The vector product u x v gives the vector w
-h s
W
h x - ks h y + ( h s 2
,i. 2 , r 2 x 1 / 2
(hs2 + k s 2 ) 1
+ ks2 )
z
•
(3.10)
Generally the surface normal vector s of an as-polished diamond (001) substrate
is not parallel to the z axis, i.e., the [001] direction. In this case, the vector u is
uniquely defined by the restriction that the vector v is identical with the surface normal
s and the vector u occurs in the xy plane. Figure 3.5 shows the polar coordinates o f the
plane normal g in the uvw system. With the unit vectors u, v, and h>, the polar
coordinates y and 8 of the plane normal g can be expressed by the equations:
y = sin'‘(g* >v)
(3.11)
and
i
2
•
U
8 = sin (—— ).
cos^
(3.12)
In the special case where s is parallel to the z axis, the u axis is not uniquely
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79
w
u
Figure 3.5 Polar coordinates of a plane normal g in the uvw
coordinate system.
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80
defined by the condition that the vector u lies in the xy plane because the u axis can
occur anywhere in the xy plane. The u axis is then assumed to coincide with the y axis.
Thus, the u , v, and w axes correspond to the y, z, and x axes, respectively. In this case,
the polar coordinates o f the plane normal g can be expressed with the M iller indices hkl
of the plane in the xyz coordinate system:
(3.13)
and
(3.14)
The coordinates of a Laue spot are illustrated in Figure 3.6. A crystal with a flat
surface is struck by an x-ray beam at normal incidence. The normal g of an arbitrary
crystal plane and the normal s o f the sample surface make the angle c between them.
The Laue spot on a film , arising from this particular crystal plane, appears at an angle
2 c [this angle is represented by (180-2$ in Figure 3.1] from the film center in the gs
plane.
The coordinates XL and YL of a back-reflection Laue spot on a film with respect
to the center of the film can be determined with the polar coordinates y and 8 of the
plane normal g:
XL = /cos//
tan/> tan2c
tanc
(3.15)
and
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81
Laue spot
Sam ple
Figure 3.6 Coordinates XL and YL of a back-reflection Laue spot.
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82
tany tan2cr
cos 8 tancr
(3.16)
where
a = cos'I(cosj/ cos<5)
(3.17)
and I is the distance of the Laue spot from the center of the film and p. the angular
deviation of the Laue spot from the X axis. Following the computation of the
coordinates of the spot, the spot distance I is easily calculated.
3.2.4. Description of a computer program
In the previous sections, the procedures to determine the coordinates o f the Laue
spot o f a plane (hkl) on a film were derived for given surface misorientation angles a
and p. The position of the Laue spot is related to the surface misorientation angles a
and P through equations (3.3) to (3.17). Using these equations, a computer program
was developed to calculate the surface misorientation angles a and P from the
measurements of the distances of Laue spots relative to the film center.
The schematic flow chart of the program is presented in Figure 3.7. The
program begins by reading the input data, namely: the film-to sample distance d f ; the
number of Laue spots to be considered in the calculation of surface misorientation
angles N; the minimum and maximum values o f surface misorientation component
angles a ^ , amax, /?min and /?max; the Miller indices o f a family of planes (/2,-fc,•/,■), and the
measured distances of their Laue spots from the film center /m(/i;fc,7f).
For given surface misorientation angles ccj and pj, the surface normal s is
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In p u t. dp N,
°Tnax’ Amin’ A
Take ccj
04^ , Pj - Pm\
Calculate h~, k „ I,
Calculate «, v, w
Calculate y, 8, a
Calculate XL (h fa lt), Y ^ h ^ l, ) and l^ h fc lj)
Calculate D ,
*7+1 =ocj + A ao r Pj+ 1 ~ P j + ^A
No
* j+ 1 >amax
P j+ 1> Atmax •
Yes
Find a and f t with the smallest D
Figure 3.7 Schematic flow chart of a computer program for the calculation o f
a surface misorientation angle.
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84
specified with equation (3.4). The unit vectors u, v, and w> are calculated using
equations (3.6), (3.9), and (3.10), and y, 5 , and a are then described for the given
planes (/i,fc,/,) following equations (3.11), (3.12), and (3.17), respectively. The
coordinates XL and Y, of the Laue spot of a given plane are calculated thereafter using
equations (3.15) and (3.16). These calculations proceed for all the given number of
planes, usually four planes o f the same family. The next step is to compare the
calculated and measured distances /c(/i,fc,/,) and ^m(^M) ° f the Laue spots of the planes
(h M ,). The comparison is made simultaneously for the four planes o f the same family,
based on the ratios of the distances between Laue spots to remove the influence o f the
sample-to-film distance. For this purpose, the accumulated difference between the
calculated and measured distance ratios is computed by
J
<
Lihikdi)
lm(hJcili)
•
( 3 , 1 8 )
The above calculation and comparison procedures are repeated in a specific increment
0.01° of a and (3, from the minimum value to the maximum value. Finally this
program selects the surface misorientation angles a and P with which Dj in equation
(3.18) is the smallest.
3.2.5. Experimental details
The detailed experimental procedures for the measurement of the surface
misorientation angles of substrates are given here. A back-reflection Laue camera was
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85
made to accurately measure the surface misorientation angles o f diamond (001)
substrates. A diamond substrate was attached to a sample holder which was a round
metal bar of 0.25" diameter and 3" in length. Then the sample holder was fixed into
the 1.5" straight mount with a screw. Using a laser beam, the diamond substrate
surface was precisely adjusted in two directions with two fine resolution mounting
screws of the straight mount so that the substrate surface was parallel to a glass plate
fixed to a sample plate. Following the alignment of the sample, the camera was
mounted to the window o f an x-ray generator (X-ray Diffractis 583, Enraf Nonius). A
continuous x-ray spectrum produced from a copper target passed through the collimator
of 0.5 mm diameter, and was then incident on the sample 20 mm apart from a film. In
this work, the back-reflection Laue patterns were recorded on a wet-processed film for
30 min at 40 kV and 20 mA.
After developing the film , Laue spots were indexed and then the distances of
spots from the center of the film were measured using a ruler with the divisions of 0.5
mm. Four sets o f M iller indices of planes belonging to the same family and the
distances of their spots were input to the computer program, calculating the surface
misorientation angles a and (3 with the smallest difference between the measured and
calculated distances. The surface misorientation angles were averaged for at least 8
different families o f planes.
Following the above-mentioned procedures, the accuracy of this camera in
measuring the misorientation angle turned out to be ± 0.1°, checked using the cleaved
plane of a rock salt crystal, which is much more precise than commercial back-
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86
reflection Laue cameras with the usual precision of ±0.5°. Such high accuracy with this
camera was achievable through 1) precise machining to maintain the perpendicularity of
the film and sample plates to a collimator and 2) using larger films to include more
diffraction spots than Polaroid films utilized for commercial cameras. For the precise
measurement, diffraction spots as far from the film center as possible have to be used
because the farther the spots from the film center the more sensitive to the
misorientation angle of a substrate. It is because the distances of diffraction spots from
the center are determined by the tangent function o f (18O°-20), as shown in equation
(2.2).
An example of back-reflection Laue x-ray diffraction from a diamond (001)
substrate is shown in Figure 3.8. Diffraction spots were indexed with the help of a
standard stereographic projection. The measured distances are given for the family of
224 spots to demonstrate the effect of the surface misorientation on the distances of
these spots from the center. The 224 spot is 64.5 mm apart from the center while the
counterpart 224 spot is located 48.3 mm far from the center. Unequal spacings are due
to the misorientation o f the substrate surface toward the [TlO ] direction. Otherwise,
these two spots would be equally spaced with respect to the center. From the other
distances 51.3 mm and 60.2 mm of the 224 and 2 24 spots, respectively, the surface is
known to be tilted toward the [110] direction. From the comparison o f the two data set,
64.5 and 48.3, 60.2 and 51.3, P is expected to be larger than a. By putting indices of
four spots and their distances into the computer program, a=0.72° and P=-1.30° were
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87
224(51.3)
224(48.3) | 337 H 113
224(60.2)
Figure 3.8 Back-reflection Laue x-ray diffraction pattern o f a diamond (001) substrate.
Part of diffraction spots are indexed. Numbers in parentheses are the
distances o f spots from the center o f the film in mm.
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88
obtained. The surface of this substrate was averaged for 8 sets of families of planes
including {204}, {206}, {228}, {113}, {337}, {224}, {315}, {317} to be misoriented
0.74° toward 1110] and 1.28° toward [ 1 10].
3.3. MPACVD system for diamond deposition
3.3.1. Description of a tubular MPACVD system
A diagram of the tubular MPACVD system used in this study is described in
Figure 3.9. Microwaves were generated by 1.2 kW, 2.45 GHz generator (New Japan
Radio Co.), and its output power was controlled by varying the input voltage supplied
to the generator and displayed by a digital ampere meter. The microwaves generated by
the magnetron were transmitted to the reaction chamber through a set of aluminum
rectangular waveguides, as shown in Figure 3.9(a). An air-cooled isolator allowed the
microwave to pass through from the generator but protected the magnetron by
absorbing reflected microwaves from the applicator. The reflected power was measured
by an analog ampere meter with a sensor built into the waveguide. Three screw tuners
upstream of the applicator were used to minimize the reflected microwave power from
the reaction chamber. The function of these tuners was to improve the energy
efficiency by matching the impedance o f the cavity load (plasma) to that of the
waveguide so that the resonant amplitude was tuned in and the power reflected from the
cavity was minimized. The impedance o f the load and the resonant amplitude were a
function of the type o f gas, pressure, power input, substrate material, and its position
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89
H-bend
wave guide
Tapered
waveguide
Screw tuner
Sliding short
O O
Microwave
generator
2.45 GHz
1.2 kW
Power monitor/
Directional coupler
Applicator
Circulator/
Isolator
(a)
Figure 3.9 Schematic o f the tubular microwave plasma-assisted chemical vapor
deposition system: (a) waveguide for microwave transmission and
(b) reaction chamber.
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90
Prism
Gas inlet
M .
J
Pyrometer
m
<<
Silica tube
Microwave applicator
Plasma
Microwave
'X /vrv/v
2.45 GHz o y v r u x
Plunger
Sample holder
Pressure control system
- > To pump
tr
(b)
Figure 3.9 (cont.)
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relative to the plasma. Therefore, tuning and matching adjustments were necessary to
obtain efficient operations over a wide range o f plasma conditions. At the end of the
wave guide there was a movable plunger which could adjust the antinode of the electric
standing wave to the center of the resonant cavity by its short plate, thus optimizing the
plasma shape and position. It could also be used to reduce the reflected power.
The reaction chamber was a vertically
mounted fused silica tube of
approximately 45 mm inner diameter and 91 cm long, which was placed within the
water-cooled applicator, as given Figure 3.9(b). Both sides of the tube were mounted to
stainless steel pipes with O-rings and clamps. Located at the very top of the tube was a
glass viewport which was used to measure the substrate temperature with an optical
pyrometer (Leeds and Northrup Co.). The reactant gases (CH4 and H2) entered the tube
through the gas inlet at the top. A substrate was placed on a diamond susceptor held at
the top of a 35 cm long fused silica rod. The silica rod was mounted to the end of an
adjustable metal rod feedthrough. The whole assembly was then introduced from the
bottom of the reaction chamber and the feedthrough was clamped into place. The
substrate position was adjusted by moving the metal rod up or down through the
feedthrough.
The total system pressure was monitored by a Baratron pressure gauge (MKS)
and a pressure control system (MKS). A rotary vane mechanical pump (Stokes
Pennwalt) was used to evacuate the system and maintain the required gas pressure. The
lower limit of the system pressure was about 10‘3 Torr. Gas flow rates were controlled
by mass flow controllers (MKS) which were calibrated for the particular gases being
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92
used.
3.3.2. Diamond deposition procedures
The diamond deposition procedures using this tubular MPACVD system are
described as follows:
1) Load a diamond substrate into the reaction chamber. Then adjust the position
of the substrate 1-1.5 cm below the center of the cavity.
2) Switch on the vacuum pump to evacuate the chamber. Turn on the cooling
water for the applicator.
3) Once the chamber is sufficiently evacuated, close the vacuum valve to check
the system leakage. I f there is no leakage, turn on the valve again.
4) Introduce H 2 gas with the flow rate of 100 seem to purge the tube. After
purging twice, ignite a hydrogen plasma at a pressure between 2-10 Torr.
5) As the system pressure continues to rise to the desired set point (80 Torr),
center the plasma ball and minimize the reflected power by adjusting the three tuners
and plunger.
6) Once the desired pressure is reached, adjust the substrate temperature to 900-
950 °C by controlling the microwave power input. The temperature is measured by an
optical pyrometer.
7) Maintain the substrate at a temperature of 900-950 °C for 10 min to clean the
substrate as well as the inside o f the chamber by hydrogen plasma prior to deposition.
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93
8) As soon as the substrate cleaning is completed, switch on the reactant gases
CH4 and HU and adjust the microwave power to reach the desired deposition
temperature. At least 10 min after CH4 gas is introduced, make sure that the substrate
temperature is kept at the desired value during deposition.
9) When the deposition is complete, shut o ff the microwave generator and gas
flows. However, allow a continuous flow of H2 for another 10 min for cooling. Switch
off the H2 gas flow and stop pumping. Vent the system, and the sample is ready for
analysis.
It is to be noted that an effort was made to avoid air leak to exclude any
influence o f oxygen and nitrogen on CVD diamond films. The process for making
diamond can be run successfully only after the optimization of process variables. The
plasma should be as large as possible without touching the tube wall to cover and coat
the substrate uniformly. The most suitable position of the substrate relative to the
plasma ball should be that where the most efficient heating is produced at a given
power and pressure with no partial plasma formed underneath the susceptor or the silica
rod. This is about 1.0-1.5 cm below the center of the cavity. The detailed optimum
deposition parameters are presented in Chapter 4.
3.4. Refection high-energy electron diffraction (RHEED)
For characterizing structure of clean and adsorbate surfaces using electron
diffraction, mainly LEED has been used. Since RHEED in UHV was developed in the
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94
1970s, however, it has turned out to be a technique equivalent to LEED for studying
surface structure (Menadue, 1972; Ino, 1977). To date the RHEED technique has been
successfully applied for surface structure analysis, e.g., 7x7 structure of the Si (111)
surface (Henderson and Polito, 1969), 6x1 structure o f the Si (111) surface adsorbed
with Ag atoms (Ichikawa and Ino, 1980), etc. Because of more convenience in
handling as compared to LEED, recently RHEED has been widely used as an easy in
situ means for thickness control as well as for monitoring thin film crystal growth
during MBE. Also. RHEED can provide information on crystal growth as intensity
oscillation o f the diffraction spots occurs during the layer-by-layer growth o f thin films
deposited by MBE (Joyce et al., 1986; Sakamoto and Hashiguchi, 1986).
It has been known that the glancing incidence o f an electron beam in RHEED
makes it extremely sensitive to details of the surface under study, and so, clearly,
RHEED patterns contain detailed information about the surface structure in addition to
the bulk structure (Ino, 1977; Yagi, 1993). Thus, the periodicity and direction o f the
surface structure relative to the bulk structure can be determined by comparing the
diffraction spots of the surface to those o f the bulk. RHEED is a special case of highenergy electron diffraction (HEED) in that an incident electron beam strikes the surface
of a specimen at the glancing incidence. The RHEED pattern consists of approximately
one half o f a transmission electron diffraction pattern bounded by a shadow edge
parallel to the surface. There are, however, important differences, which depend on the
angle of incidence, surface topography, etc., that strongly influence the character o f the
RHEED pattern. Figure 3.10 shows the schematic arrangement of a RHEED apparatus.
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95
Electron gun
Incident beam
Sample
Reflected beams
Screen
Diffraction spots
Figure 3.10 Schematic arrangement for RHEED experiments.
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96
The incident electron beam strikes the sample surface with the glancing angle less than
a few degrees and is then reflected onto a viewing screen. This section w ill describe
details on the diffraction theory from the surface, the construction o f RHEED patterns,
and the kinematic approach for RHEED intensities.
3.4.1. Diffraction from surfaces
When considering the diffraction from the surface, the assumption of infinite
periodicity is usually made in two dimensions parallel to the surface, but clearly not in
the third dimension which is truncated by the presence of the surface itself. Moreover,
electrons at grazing incidence, even with high energy, penetrate the sample only a short
distance, so the periodicity of the structure beyond the top few layers is relatively
weakly explored in the direction normal to the surface. The crystal structure actually
examined in a typical RHEED (and LEED) study may therefore be considered to be a
slab, infinitely periodic in two dimensions, but comprising only a limited number of
layers in the third dimension, although RHEED provides the information on the bulk
structure together with the surface structure.
The two dimensional lattice of the surface in a real space may be defined by two
lattice vectors a x and a2. A plane wave o f electrons incident on atoms w ill be scattered
in all directions, but the diffraction maxima w ill occur in the direction in which a
constructive interference is made between the waves scattered from all atoms
(Edington, 1975). This requirement is met when the scattered waves from neighboring
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97
atoms differ only by an integral number of wavelength k. This is called the Laue
condition:
ai • (s-s0) = hk
(3.19)
a2• (s-s0) = kk
(3 .20)
where s and sQ are the unit vectors of incident and scattered waves, and h and k
integers. These Laue conditions may be expressed using the reciprocal lattice to easily
visualize and interpret electron diffraction patterns
For the two-dimensional lattice in the real space described by two lattice vectors
a.\ and a2, a corresponding reciprocal lattice is then defined by the basis vectors ax* and
a2 , satisfying the equation
« ,.« / =
= 1,2)
where the Kronecker <5^=0 if
(3.21)
and 8^—1 if i = j . Any vector relating two reciprocal
lattice points takes the form
8hk
= W
+ ka 2 .
(3.22)
On the other hand, the Laue conditions o f equations (3.19) and (3.20) can be described
using the reciprocal lattice vectors:
S
So
— j — = hai
*
*
*
+ ka 2 .
(3.23)
Thus, the diffraction maxima of the scattered beams occur for the directions which are
determined by the following condition:
8hk
s - so
i
•
(3.24)
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98
Equation (3.24) may be simplified by introducing the incident and scattered wave
vectors, k and k0, which are defined as s/A and s0/A, respectively. That is,
ghk = k - k 0.
(3.25)
This means that there is a direct correspondence between the observed diffraction
pattern and the reciprocal lattice of the surface.
The diffracted intensity in the reciprocal space reaches the maxima at the
reciprocal lattice point and then falls very rapidly to zero on moving a small distance
1/N from the point, where N is the number o f the unit cells in the direction along
which the intensity is calculated or measured. Thus, the width of an interference
function associated with the reciprocal lattice point is inversely proportional to the
number o f unit cells in the directions of ax, a2, and a3 (Edington, 1975). Because the
two-dimensional lattice of the surface is defined to be infinite in the ax and a2 directions
and to be infmitesimally thin in the a 3direction, the interference function related to the
reciprocal lattice points are very narrow in the at and a2 directions while they are much
broader in the a3 direction, thereby forming lines perpendicular to the surface. Thus,
the reciprocal lattice points in the two-dimensional lattice are usually called the
reciprocal lattice rods.
Using the so-called Ewald sphere, one can determine the directions for the
diffraction maxima o f the scattered beams and then visualize the construction of
diffraction patterns. The construction o f the Ewald sphere and the geometry of
diffraction from the two-dimensional reciprocal lattice is illustrated in Figure 3.11. A
set of the reciprocal lattice rods is drawn perpendicular to the surface. The incident
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99
Reciprocal lattice rods
Sample
Ewald sphere
Screen
Figure 3.11 Construction o f the Ewald sphere and geometry of RHEED
from the two-dimensional reciprocal lattice net.
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100
wave vector k 0 is drawn in the incident beam direction s0, with the length of 1/A so that
it runs from the point P to the origin O o f the reciprocal lattice. The Ewald sphere with
a radius o f 1/A is then constructed with the center at the point L. A line LG with the
magnitude o f 1/A specifies the scattered wave vector k for a particular g ^ . The
intersections of the Ewald sphere with the reciprocal lattice rods define the directions
and the shape in which the interference maxima o f the scattered beams occur. In other
words, at these intersection points, the diffraction condition of equation (3.25) is
satisfied. For the three-dimensional reciprocal lattice, the reciprocal lattice vector ghkl
runs from the origin to a reciprocal lattice point, and for this case equation (3.25) for
the diffraction maxima is easily figured out at the intersection points. For the twodimensional case shown in Figure 3.11, however, if the vector ghk is directed from the
origin O to a reciprocal lattice point G , strictly speaking, equation (3.25) is not valid.
Considering again the Laue conditions o f equation (3.19) and (3.20), one can infer that
the difference between the components o f the k and k 0 in the a, or a2 directions should
equal an integral number of a * or a2*, respectively, for a diffraction maximum. The
vector gllk from the origin O to a hk reciprocal lattice rod, therefore, may fall anywhere
on this reciprocal lattice rod, leading to the validity of equation (3.25) for the twodimensional lattice.
In electron diffraction from the surface, contribution from the bulk as well as
from the surface should be considered together because the incident electron beam
undergoes penetration through the bulk and interacts with atoms inside the crystal
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101
(Bolger et al., 1988). The layers o f atoms scattering the incident electron beam in
RHEED may be assumed to comprise a surface layer and bulk layers o f a crystal. The
bulk layers are defined as planes parallel to the surface below which the threedimensional bulk periodicity is found, and the surface lattice as the topmost layer above
the bulk layer in which no periodicity exists perpendicular to the surface (May, 1970).
The periodicity of the surface is usually related to that of the bulk. In this case the
superlattice spots resulting from the surface maintain a certain relationship with the
fundamental spots originating from the bulk lattice in RHEED patterns. If possible,
therefore, it is of great advantage to connect the periodicity of the surface lattice with
that of the bulk structure (ErtI and Kuppers, 1985).
When the surface is chemically clean and unreconstructed, the identical
periodicity w ill be found on the surface layer as well as on the bulk layers. An electron
beam k 0 incident on the surface with the lattice vector ax and a2 is partly scattered by
each surface atom, giving rise to diffracted beams khk in the direction for which the
following condition is satisfied:
khk - k 0 = hai* + ka2*.
(3.26)
The diffracted beams propagating backward from the surface are recorded on the
screen. The diffracted beams from the surface layer, propagating forward into the bulk
layers, plus the unscattered part of the incident beam, w ill arrive at the bulk lattice. I f
these beams k hk and kQare incident upon the bulk layer with the same lattice structure, a
new set o f diffracted beams knm may occur:
Km - Kk = nax* + ma2
(3.27)
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102
and
knm - k 0 = nax* + maz*.
(3.28)
Substituting equation (3.26), equation (3.27) and (3.28) may be described by a
equation
Km - K = (n + h)ax* + (m + k)a2*.
(3.29)
Scattering o f the incident beam k 0 in the bulk layer, equation (3.28), can be
mathematically included into equation (3.29) as the case that h = k = 0, because the
unscattered incident beam (fc0) and scattered transmitted beam (khk, h = k = 0 ) are
indistinguishable from each other. In equation (3.29), a new set o f diffracted beams knm
originating from the bulk layer belongs to the same set o f diffracted beams khk which
result from the surface lattice. Scattering from the surface layer and from the
successive bulk layers with the identical lattice structure w ill produce the same set of
diffraction beams without further new diffraction beams, although their intensities are
intermixed (Clarke, 1985).
In the case o f a reconstructed or adsorbed surface, the surface structure differs
from those o f the bulk layers. Let us consider the surface with the lattice vectors bx, b2
and the bulk with the lattice vectors ax, a2. In scattering with the surface layer atoms,
first o f all, beams k hk diffracted backward from the surface w ill appear on the screen by
the relation
K k - k 0 = h b * + kb2 .
(3.30)
The forward diffraction beams k ^ incident upon the bulk layer w ill give rise to a new
set o f scattered beams k nm:
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103
Km ~ Kk = nax* + ma2 .
(3.31)
Substituting equation (3.30) produces
Km - K = na\ + ma2 + h b * + kb2*■
(3.32)
As shown in the previous case, subsequent diffraction through the second, third, etc.,
bulk layers w ill not introduce further new spots as long as they maintain the same
periodicity as the first bulk layer. When h = k = 0 in equation (3.32), scattering from
the first bulk layer results in the fundamental spots characteristic of the periodicity of
the bulk lattice, and then scattering through successive bulk layers will simply increase
their intensities. In the case o f h * 0 or k * 0 , diffracted beams k„m from the bulk layers
w ill be superimposed on the superlattice spots which result from the surface layer,
intermixing their intensities. Considering multiple scattering of electron diffraction, an
accurate analysis o f spot intensities should be performed using dynamic diffraction
theory, which is beyond the scope o f this study.
3.4.2. Construction of RHEED patterns
Figure 3.11 also illustrates schematically the cross-sectional view o f the
geometrical construction of a RHEED pattern. The incident wave vector kQ runs
perpendicularly to the reciprocal lattice rods when the incidence angle is zero. Thus,
the 00 rod at the origin O meets the Ewald sphere tangentially while the other rods
inside the sphere pierce this sphere at points. Each intersection point defines the
scattered wave vector k, specifying the direction of the diffracted beam and the Bragg
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104
angle for a particular reciprocal lattice rod. The diffracted beam which corresponds to
each intersection occurs on the screen at the point where a line extended along k meets
the screen. Fundamentally, because lines intersect a sphere at points, only spots should
appear on the RHEED pattern. In reality, however, streaks elongated along the
direction parallel to the reciprocal lattice rods are usually observed. The closer the
diffraction beams are to the origin the more remarkable the occurrence o f streaking of
spots. This is ascribed to the nonidealities in the instrumentation as well as in the
sample. The instrumental broadening is caused by variation in the wavelength of the
incident electron beams, divergence of the incident, and scattered electron beams due to
defects of the electromagnetic lenses, etc. In particular, spread in the kinetic energy of
the incident electron beams affects the radius of the Ewald sphere, making the sphere
into a thin spherical shell, which is called the dispersion sphere.
The rows o f the reciprocal lattice rods perpendicular to the incident beam are
Laue zones of rods. Among the reciprocal lattice rods belonging to the zeroth Laue
zone, only the rod at the origin meets the Ewald sphere while the others are located
outside the sphere. The instrumental and sample broadening brings several more spots
to the screen. The beam incidence with a non-zero angle onto the surface may make
additional zeroth-order Laue diffraction spots occur as well (Mahan et al., 1990).
For the 0° beam incidence, the zeroth-order spots should occur along a straight
line. In reality, however, the incident beam strikes the surface with a grazing angle of
several degrees. Thus, the Ewald sphere has to rotate upward about the origin of the
reciprocal lattice by a grazing angle. As shown in Figure 3.12(a), this makes the sphere
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105
Reciprocal
lattice rods
L
Ewald sphere
(b)
00
000
Figure 3.12 Geometry o f diffraction from the two-dimensional reciprocal lattice net
for the non-zero incidence angle: (a) the Ewald sphere construction and
(b) RHEED pattern.
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106
cut the zeroth zone o f rods along a ring. The zeroth-order spots move away from the
shadow edge in the direction toward higher order spots and appear along a ring on the
screen. The RHEED pattern to be observed is a plan view projected on the screen of
the intersections of the reciprocal lattice rods with the Ewald sphere, which is given in
Figure 3.12(b).
Figure 3.13 shows in a cross-sectional view the details related to the nonzero
angle of incidence. With increasing the angle o f incidence 9, the intersection points of
rods with the sphere become higher and the corresponding diffraction spots run away
from the shadow edge on the screen. The angle of incidence 9 can be easily calculated
from the position of the 00 spot on the screen:
9 = ta n -'(y ) ,
(3.33)
where R is the distance of the specular 00 spot from the shadow edge of the RHEED
pattern and P the camera length.
Based upon the principles o f RHEED introduced in the above, RHEED patterns
from the diamond (001) surface w ill be constructed. As shown in Figure 3.14(a), the
unreconstructed diamond (001 ) surface is composed of the l x l unit cells with their
dimension of 2.52 A x 2.52 A. But the clean or hydrogenated diamond (001) surface
reconstructs by dimerization of surface carbon atoms along the <110> directions. This
leads to the 2 x 1 or 1x2 surface structure with the unit ceil of 5.04 A x 2.52 A (or 2.52
0
o
A x 5.04 A), depending on the dimerization direction on each terrace [Figure 3.14(b)
and (c)]. In many cases, the 2x1 and 1x2 domains occur alternatively on the adjacent
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107
hk
Reciprocal
lattice rods
00
Shadow
edge
000
Ewald sphere
Screen
Figure 3.13 Cross-sectional view o f RHEED geometry for the non-zero incidence
angle.
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108
2.52 A
A o
o
o
<§
0
o
2. 52 A
9 — 9
o o
2. 52 A
a2
5.04 A
2.52 A
o
0 — 0
o
O
a1
O
O
c f 'b
c f 'b
o
o
O
O
O
c f b
cT " b
o
0
(a)
•
A
w
•
(b)
•
(C)
•
0.40 A-1
tn
<
0.40 A-1
a2
•
o
o
o
•
o
0.20 A"1
•
»
•
&2|
•
•
•
o
0.40 A"1
•
•
(d)
•
•
o
o
Oo
•
o
o
• • I
O ^ O
2
a
0-20oA-1
★
O
O
o
o
o
o
o
o
(f)
•
9
o
o
0.40 A-1 «
* C—
oo
(e)
9
o
o
oo
O
•
•
0“ H
o?
1 o
0.40 A"1
-► [ 110]
• •
° a2 L i° .4 0 ° A - 1
•
•
•—
•
•
it
o
•
o 3-|
o
• • • • • •
o
[110]
(g)
Figure 3.14 Unreconstructed and 2x1 reconstructed diamond (001) surface structures
and their reciprocal lattice nets: (a) unreconstructed surface, (b) 2 x 1
reconstructed surface, (c) 1x2 reconstructed surface, (d) reciprocal lattice
net of the unreconstructed surface, (e) reciprocal lattice net of the 2 x 1
reconstructed surface, (f) reciprocal lattice net of the 1x 2 reconstructed
surface, and (g) superposed reciprocal lattice net of (d), (e), and (f).
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109
terraces, forming the double-domain surface structure (This issue w ill be detailed in
Chapters 5 and 6).
The reciprocal lattice nets of the lx l, 2x1 and 1x2 structures are given in
Figure 3.14(d), (e), and (f), respectively. The basis vectors a * and a 2 o f the l x l net
have the magnitude 0.40 A ' 1 of simply the reciprocals o f the real lattice vectors a x and
a2, and run in the direction of ax and a2, respectively, due to the square shape of a unit
cell. This is applicable to the other basis vectors bx and b2 as well as to C!* and c2 in
the same manner. Consequently, the basis vectors are 0.20 A ' 1 and 0.40 A ' 1 in
dimension for both the 2x1 and 1x2 reciprocal lattices. Assuming the double-domain
structure on the surface, the 2 x 1 and 1x 2 reciprocal lattices of the surface and the lx l
reciprocal lattice of the bulk layers are combined to produce the reciprocal lattice net
for the electron diffraction from the 2x 1 reconstructed diamond surface, as shown in
Figure 3.14(g). By superposition of the three lattices, the basis vectors o f the combined
reciprocal lattice net become a * and a2*.
Figure 3.15 shows the intersection of the Ewald sphere with the reciprocal
lattice rods and the resultant RHEED patterns, when the incident beam is directed along
the [100] and [110] directions with the grazing angle of 0°. In the RHEED experiment,
an accelerating voltage of 40 kV was used, producing the electron beam with the
wavelength o f 0.06015 A. The corresponding Ewald sphere has the radius 16.63 A '1.
The calculation of the spot spacings and radii of the rings in the RHEED patterns was
performed using the relation
R = *P a \
(3.34)
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110
♦
•
o
•
o
«
#
o
•
•
o
*
#
o
•
•
o
*
*
o
•
•
o
»
o
#
o
*
o
«
o
*
•
•
•
•
•
*
o
o
*
•
•
*
o
o
»
•
•
•
*
o
o
*
•
•
*
o
o
#
•
Ewald sphere
o-
1/2
00
4.55mm
< ------ 17.5mm — > j
^ -----------24.7mm ~
(a)
Figure 3.15 Schematic RHEED patterns predicted from the two-dimensional reciprocal
lattice (a) in the [ 100] azimuth and (b) in the [ 110] azimuth for
reconstructed diamond (001) surface. Large closed circles, small closed
circles, and small open circles in the reciprocal lattice correspond to the
fundamental, 2 x 1 superlattice, and 1x 2 superlattice rods, respectively.
Their reflections in the pattern are designated by the same types of circles.
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Ill
•
0
«
0
0
0
9
0
«
0
9
0
*
0
#
o
*
0
0
0
d
0
*
0
*
0
*
0
*
0
«
0
#
0
*
0
«
•
o e o ® o # o # o # o # o ^ o # o # o ® o # o O o # o # o # o # o ® o #
r-L
Ewald
sphere
LL
00
20.8m m
29.3m m
3.25m m
(b)
Figure 3.15 (cont.)
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112
where R is the distance in the screen, P the camera length of an instrument (135 mm in
this study), and a* length in the reciprocal space.
In the RHEED pattern with the [100] azimuth [Figure 3.15(a)], the radii of the
half-order and first-order Laue rings on the screen are calculated to be 17.5 and 24.7
mm, respectively. The spot spacings in the zeroth-order and half-order Laue rings are
given to be 4.55 mm and 2.27 mm from their distances o f 0.56 A ' 1 and 0.28 A"1,
respectively, in the reciprocal space. The zeroth-order Laue spots spread along a
straight line due to the assumption o f the 0 ° incidence, but the half-order and first-order
Laue spots appear along rings. The half-order and first-order Laue rings are composed
of the 16 superlattice spots and 10 fundamental spots, respectively, which are
determined by the intersection of the reciprocal lattice rods with the Ewald sphere.
As shown in Figure 3.15(b), the incidence o f the electron beam along the [110]
azimuth also produces a symmetric RHEED pattern. For the [110] azimuth, the
superlattice spots from the 1x2 domain occur midway between the fundamental spots in
the zeroth-order and first-order Laue zones. The half-order Laue zone consists o f only
the superlattice spots from the other type o f domain, 2 x 1 domain, with the same
spacing as the fundamental spots in the zeroth-order or first-order zone. The spot
spacings and radii o f the Laue rings calculated using equation 3.34 for the same energy
of the incident beam, camera length, and 0° incidence are given in the RHEED pattern.
The number o f Laue rings observed depends upon the dimensions of the screen
and the camera length of RHEED system as well as an accelerating voltage of the
incident beam. As can be seen in Figure 3.15, for studying the diamond (001) surface,
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113
RHEED patterns have to include at least the half-order and first-order Laue rings
because the reciprocal lattice of this surface can be represented by the repeating unit of
the zeroth-order to the first-order zone. In this study, up to the first-order Laue ring
was easily observed both in the [ 100] and [ 110] azimuthal incidences by the
combination o f the accelerating potential o f 40 kV and the camera length of 135 mm
for a given dimension of films 10 cm x 8 cm.
For studying the surface using RHEED,
surface roughness or surface
topography is so important that they drastically affect RHEED patterns (Lagally et al., 1988; Yagi, 1993). Figure 3.16 shows schematically the relations of RHEED with the
surface topography. When there are high and wide, but thin protrusions sitting on a flat
surface [Figure 3.16(a)], the incident beam w ill transmit through the protrusions,
forming sharp transmission diffraction beams. I f the protrusions become lower, the
diffraction beams w ill broaden normal to the surface while keeping the transmission
diffraction pattern, as shown in Figure 3 .16(b). As the area o f flat terraces increases
with decreasing the number of protrusions,
the RHEED pattern will appear
superimposed on the transmission diffraction pattern. As the surface becomes
smoother, transmission spots initially elongate and change continuously into reflection
spots that become shorter until sharp spots along rings are observed for a perfect
surface [Figure 3.16(c) and (d)].
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114
(a)
(b)
(C)
•
•
•
•
e
t
i
•
•
6
•
$
I
(d)
Figure 3.16 Schematic illustration of relations between surface topography and
RHEED patterns: (a) a surface with high and wide, but thin protrusions,
(b) a surface with low and wide, but thin protrusions, (c) a surface with
multilevel islands, and (d) a flat surface (Lagally et al., 1988).
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115
3.4.3. Kinematic theory for RHEED intensity
In the electron diffraction, the incident wave undergoes multiple scattering as
well as inelastic scattering inside a crystal. For a complete structural analysis, i.e., the
determination of the atomic positions within the unit cell, the diffraction intensity
should be calculated using dynamic diffraction theory (Peng and Cowley, 1986;
Ichimiya, 1983; Kawamura and Maksym, 1985). In limited cases, however, the
kinematic calculations have been successfully applied for the analysis of RHEED
intensity (Ino, 1980a, b; Hoiro and Ichimiya, 1989). The intensity o f the superlattice
spots in the RHEED pattern is generally very weak as compared with that o f the
fundamental diffraction spots. In this case multiple scattering of weak superlattice
diffraction beams in the bulk layers can be neglected. The kinematical diffraction
theory seems to be proper for the analysis of weak superlattice diffraction intensities.
The kinematic theory for diffraction intensities is based on the assumption that
the incident electrons interact with atoms very weakly so that only single scattering
processes are considered to give a good approximation. The incident electron beam is
represented by a plane wave with wavelength X running in the direction s0. This wave
may be expressed by the wave function
« / = ^ 0exp(27iik 0-p)
(3.35)
where y/0 and p is the amplitude o f the incident beam and the position o f an atom with
respect to the origin p = 0, respectively. The wave interacts with the atom and then are
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116
scattered in all directions. At a point P far away from the origin, the scattered wave
originating from an atom j at the position Rj may be described by the wave function
GXP(27C2 k * P )
------" ) • f f t o t ) exp[2ni{k-k 0)-Rj\
V=iVo-
(3.36)
where /• is the atomic scattering factor.
Now RHEED intensities from the surface w ill be examined by assuming a twodimensional periodic lattice. Let us consider that the surface whose unit cell is defined
by two lattice vectors a x and a2 is composed o f M -N unit cells. The location of any
atom in the lattice may be represented by the origin of its unit cell (Rp) and its position
within that unit cell (r q). The total scattered wave from a whole of atoms is a
superposition of the waves originating from the single atomswith the corresponding
phase shifts (Clarke, 1985; Ertl and Kiippers, 1985; Yang etal.,1993a):
V x
Z f P.q(ko,k) exv[2ni{k-kQ)-{Rp+ r q)].
(3.37)
PA
The position o f any unit cell, Rp, may be specified by
Rp = max+ na2,
(3.38)
where m and n are integers in the range o f 0 < m < M -\ and 0 < n < N -l. Equation
(3.37) may then be changed to
y/ oc F • 2
ex.p[2ni(k-k0)-Rp]
(3.39)
P
where F is the structure factor. In equation (3.37) the atomic scattering factor/can be
replaced by the structure factor F since F is identical for all unit cells due to the
periodicity o f the lattice. Substituting equation (3.38), equation (3.39) becomes
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117
.tf-1
W x ^ '2
N -1
exp[2;cimax- (k-k0)]
m =0
e\p[2nina2- (k-k0)]
(3.40)
n =0
or
F G
(3.41)
where G is the lattice factor. While the structural factor F is determined by the atomic
scattering factors f j and the positions of the atoms within the unit cell, the lattice factor
G depends on the number of unit cells, surface lattice vectors au az, and (k-k0). The
scattered intensity from M -N unit cells in a given direction is given by
I °c |/r!2 -|G|2.
(3.42)
The intensity calculated by summations is simply
, . 1^2 sin '|W < H i.(& - fco)] sin 2[icNai ■{k - fco)]
r, — 7- 7 7 ' - r - r r--------— 7 7 7 .
sin [Ttai • (k - Ato)]
sm [ 7ta 2 • (At - Aro)]
(3.43)
The intensity maxima are expected to occur for directions k for which the arguments of
the denominators are an integral number o f n, that is
ax- (k - k0) = h anda2• (k - kQ) = k
(3.44)
where h and k are integers. These correspond to the Laue conditions o f equation (3.19)
and (3.20) for the diffraction maxima at the two-dimensional lattice. Using the theory
of diffraction from a plane grating (Jenkins and White, 1976), the maximum intensities
in the directions for which equation (3.44) is satisfied, may be expressed by
/max^ \F\2 (M -N )\
(3.45)
From equation (3.45), one can know that the maximum intensity o f a given diffraction
spot is proportional to the square o f the number o f unit cells as well as the square of the
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118
structure factor. The above kinematic approach for the scattered intensities is valid for
only superlattice spots. This cannot be applied to the intensity calculation of the
fundamental reflections which involve strong dynamic effects.
On the reconstructed diamond (001) surface, the 2x1 and 1x2 terraces which
alternate on the misoriented surface with the single-layer steps generate superlattice
diffraction spots alternately along the half-order Laue ring in a RHEED pattern with the
[100] azimuth, as shown in Figure 3.15(a). Thus, one can know which half-order spot
originates from 2x1 or 1x2 terraces by analyzing a geometry o f a sample set-up. It may
be assumed that the structure factors for the 2 x 1 terraces and 1x2 terraces are
equivalent because the two types o f terraces are identical except for the 90° rotation of
bonding geometry (Martin et al., 1987). Therefore, the intensities of i j and j i half­
order spots are considered to be simply proportional to the square of the areas of the
2x1 and 1x2 domains, respectively. I f the two types o f terraces occupy approximately
the same area, RHEED would show the symmetrical distribution of spot intensities
along the half-order Laue ring in the [100] azimuth. Otherwise, alternate variation of
intensities would be observed along the half-order diffraction spots.
3.4.4. Experimental details
In this study, RHEED experiments were carried out using a conventional TEM
(Philips 420T). In TEM a sample is usually set up with its surface perpendicular to the
beam path, and so it should be thin enough that an incident electron beam is allowed to
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119
transmit. In RHEED, an as-grown or as-treated sample can be used without any special
sample preparation because RHEED utilizes reflected beams from the surface to form a
diffraction pattern. A sample surface should be placed, however, almost parallel to the
beam path so that an incident beam grazes the surface. The procedures for preparing a
sample for RHEED using TEM with the beam running downward, are illustrated in
Figure 3.17. Sides of the hole of a 3 mm TEM slot grid were cut partly and bent up to
make a vertical face relative to grid plane. A sample with dimension of usually 1.4 mm
x 0.6 mm x 0.3 mm was glued to the vertical face o f the grid with conductive paste so
that the surface to be examined was parallel to the incident beam. RHEED patterns
were photographed on films with dimensions o f 8 cm x 10 cm with an accelerating
voltage 40 kV of the electron beam and a camera length of 135 mm.
The beam incidence angles drastically affected the character o f RHEED
patterns. With increasing incidence angles, the half-order Laue spots gradually became
faint with the appearance of strong Kikuchi lines, or sometimes reflection spots
changed to transmission spots, particularly for the relatively rough as-grown films. The
optimal incidence angle for RHEED depended upon the misorientation angles of sample
surfaces and the beam incidence directions. For the well-oriented substrate surface,
RHEED patterns with the maximum intensities for the half-order Laue spots were
obtained at the incidence angle o f approximately 1° both in the [ 100] and [ 110]
azimuths. As the surface misorientation angles increased, the optimal incidence angle
became larger. Let us consider the diamond (001) surface which is misoriented toward
only the [110] direction relative to the crystallographic (001) plane. As noted earlier,
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RHEED grid
Sam ple
Figure 3.17 Sample preparation for RHEED using a TEM grid.
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121
atomic steps or macrosteps would be developed along the [ 110] direction on this
surface. Thus, the optimal incidence angle for this surface would be almost the same as
that for the well-oriented surface if the beam is incident in the step-parallel [ 110]
direction. In the [ 100] azimuthal incidence on such a misoriented surface, however, the
electron beam can strike the surface either in the step-up or step-down directions
although the steps are inclined 45° with respect to the [100] direction. This is illustrated
in Figure 3.18. In the step-up incidence [Figure 3.18(a)], the incidence angle 0 should
be larger than the surface misorientation angle $, but the glancing angle
8
relative to
the crystallographic (001) plane is possibly maintained 1°. In the step-down incidence
[Figure 3.18(b)], the incidence angle Omay be smaller than the surface misorientation
angle ^ , but <5has to be larger than
Thus, the glancing angle
8
of approximately 1°
relative to the (100) plane is out of reach if (p > 1°. The corresponding [100] azimuthal
RHEED patterns for the diamond (001) surface 0.8° and 3.0° misoriented toward the
[110] and [ llO ] directions, respectively, are given in Figure 3.18. Apparently the stepup incidence which was used for this study produces a RHEED pattern containing the
information required for surface analysis.
3.5. Low-energy electron diffraction (LEED)
Despite versatility o f low-energy electron diffraction (LEED) for studying single
crystal surface structure, it was not until the 1960s that considerable advances in UHV
technology, development of electron guns and display systems, and progress in
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Sample
Sa mple
Figure 3.18 Effect o f the step-up and step-down incidences o f an electron beam on the
RHEED patterns: (a) step-up incidence and (b) step-down incidence, and
their corresponding 1100] azimuthal RHEED patterns o f the diamond (001)
surface misoriented 0.8° and 3.0° toward 1110] and 11 10],
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123
specimen preparation allowed LEED to be widely explored as a surface characterizing
tool. Since then, LEED has been successfully applied for investigating not only the
structure o f clean metal surfaces and atom or molecule-adsorbed surfaces but also
reconstructed surfaces of metals, semiconductors and insulators and epitaxially grown
film surfaces (Clarke, 1985; Van Hove and Tong, 1979).
As LEED typically employs low-energy electrons in the range of 20-300 eV,
the elastic scattering occurs strongly from the surface layer so that successive bulk
layers receive the smaller number of incident electrons. Electrons penetrating more than
a few bulk layers have a high probability of losing energy relative to the incident beam
and thus being excluded from the elastically diffracted beams. Consequently, LEED
has a superior surface sensitivity to detect the two-dimensional structure of the top few
atomic layers. For LEED, the kinematic approximation has been shown to be valid as
long as the electron energy is less than roughly 1000 eV (Estrup and McRae, 1971;
Henzler, 1993a).
A schematic diagram of a typical LEED system is shown in Figure 3.19. The
electron gun delivers a beam of typically 1 pA in the 20-300 eV range to the sample.
Electrons scattered or emitted from the sample surface travel in straight lines in the
field free region to the spherical sector grids as the first o f these grids is set to the same
potential as the sample. The next one or two grids are set to retard all electrons other
than those which have been elastically scattered, by applying a potential close to that of
the original electron source. The elastically scattered electrons passing through are then
reaccelerated onto the fluorescent screen applying about 5 kV to the screen, producing
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124
Grids
Fluorescent screen
Electron gun
Sam ple
/ / /
/ / / /
~ 5 kV
-V^+AV
Figure 3.19 Schematic o f a LEED system.
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an image o f diffraction pattern (Clarke, 1985; Ertl and Kuppers, 1985). Due to the
normal incidence, the diffraction geometry for LEED is simpler than for RHEED. As
shown in Figure 3.20, the observed diffraction pattern is simply a projection of the
intersection points of the reciprocal lattice rods with the Ewald sphere at the normal
incidence. LEED experiments were performed in a UHV chamber with a base pressure
o f 1.0xl0'10Torr using an electron beam o f approximately 160 eV.
3.6. Differential interference contrast optical microscopy (DICM)
Optical light microscopy remains the most important tool for the study of
microstructure, despite the evolution o f sophisticated electron microscopes. There are
many different kinds o f imaging techniques for optical microscopy such as bright field,
dark field, polarized, interference contrast, and two-beam and multi-beam interference.
Discussion here is limited to the differential interference contrast optical microscopy
(DICM) used for this study (Carl Zeiss, Axioskop). DICM is an extremely sensitive
image-enhancement technique that utilizes the interference conditions generated by
optical path differences of two beams o f coherent polarized light, and renders visible
details to objects that are generally not revealed by other light optical methods.
Incoming plane-polarized light interacts with a birefrigent prism (Nomarskimodified Wallaston prism) which separates the polarized light into two wave fronts of
similar intensities and vibrating in mutually perpendicular directions. The two coherent
polarized beams are in phase, and their lateral separation is less than the resolving
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126
Screen
Reciprocal lattice rods
Ewald
sphere
O
Figure 3.20 Construction of the Ewald sphere and geometry of LEED
from the two-dimensional reciprocal lattice net.
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127
power of the objective lens. These two parallel and polarized beams are reflected from
the specimen surface, imaged by the objective lens, and recombined by the prism and
analyzer, thereby creating an interference condition. Phase differences between
reflected wave fronts arising from surface irregularities result in a final interference
contrast image. Interference contrast images obtained by this technique have a unique
three-dimensional appearance due to different light intensities on opposite sides of
topographical features. This effect is often helpful in the interpretation of surface
morphologies. Under favorable conditions, DICM is capable of revealing surface
irregularities of the order o f a few tenths of a nanometer, but still limited in lateral
resolution to approximately 0.2 pm. DICM is basically a qualitative interference
technique that converts optical path differences into image contrast. Its chief utility is in
revealing surface morphologies that are not seen vividly by other microscopic
techniques. Details on DICM can be referred to in the work of Holik (1975) and
Richardson (1971).
3.7. Scanning electron microscopy (SEM)
SEM is an imaging technique which can investigate surfaces with sub-pm
features. SEM is often described as bridging the gap between optical microscopy and
TEM. SEM has several advantages over optical microscopy in its high resolution of
about 20-100 nm, high magnification in the range o f 50-100,000X, and high depth of
field at least 300 times or more than that o f optical microscopy. These distinctive
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128
features of SEM result in the characteristic photographs of three-dimensional quality.
Because of the large depth of focus and large working distance, SEM permits direct
examination of rough conductive sample surfaces at all magnifications. For SEM, solid
bulk samples can be used without any necessity of sample destruction, while for TEM,
samples should be thin enough for electrons to transmit.
SEM images are usually formed using either secondary electrons emitted from a
sample or backscattered electrons with approximately the same energy as the primary
electrons. The secondary electron mode has a better resolution than the other (Johari
and Samudra, 1974). In this study, SEM micrographs were made using secondary
electrons to examine the surface morphologies o f diamond substrates etched in H
plasma because fine etch pits were not laterally resolved by DICM. Diamond substrates
were directly observed without any deposition of conductive coatings on the surface,
because hydrogenated diamond surfaces were weakly conductive. SEM microstructures
were investigated using ISI DS 130 microscopy at an accelerating voltage o f 9 kV.
3.8. Scanning tunneling microscopy (STM)
As developed by Binnig and Rohrer (1982), STM allows the direct imaging of
surface structure with a lateral resolution approaching an atomic scale. This method
contrasts other surface science probes which provide a macroscopic average of the
surface under study. Due to its relatively simple construction and operation and its
ability to achieve an atomic resolution, STM has gained worldwide acceptance for
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129
studying the surface.
In STM, a sharp metal tip mounted on three orthogonal piezoelectric drives is
brought close enough to the surface o f a conductive sample so that tunneling of
electrons between the two is made possible. When a bias is applied between the tip and
the sample, electrons can tunnel from one to the other. There are two modes of
imaging techniques in STM, constant height and constant current modes. In the
constant height mode, when the tip is scanned along the surface by means of the X and
Y piezoelectric drives, while maintaining the constant height of the tip, the tunneling
current changes because of surface corrugations and the variation in work function and
electron density. The tunneling current, as a function of the position o f the tip across
the sample, provides an image that reflects the electronic structure and topography of
the uppermost atoms at the surface. In the constant current mode, the tunneling current
is kept constant in a feedback electronic circuit by adjusting the distance between the tip
and sample with the Z piezoelectric drive normal to the surface. When the X and Y
drives scan, the voltage applied to the Z drive is a measure of electronic and
topological changes along the scans. In both modes, the atomically resolved images
give a measure of the local density o f states o f electrons (Golovchenko, 1986; Rohrer,
1994).
In this study, STM experiments were carried out in air at room temperature
using a Nanoscope III (Digital Instruments), and the observations of surface structure
with an atomic resolution were made mostly in the constant current mode. The constant
current mode is more informative particularly when the measurements o f atomic
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130
heights for some features on sample surfaces are necessary. STM images were recorded
using a Pt tip, with a positive bias of 500 mV applied to the sample and with a
tunneling current less than 3 nm. Homoepitaxial films grown on the (001) diamond
substrates were B-doped during deposition using B2H 6 in order to give the electrical
conductivity to the samples.
3.9. Raman spectroscopy
Raman spectroscopy is a technique that uses inelastic light scattering resulting
from the interaction of photons with lattice vibrations or phonons. The phonons are
coupled to the photons through the polarization in molecules or crystals induced by the
electric field o f an intense light beam. When a monochromatic light beam meets a
molecule consisting of electrons and nuclei, the electric field of the light wave will
exert its force on all electrons in the molecule and w ill tend to displace them from their
average position around the positively charged nuclei. The displacements result in an
induced dipole moment P in the molecule that is proportional to the electric field
strength E and polarizability a. Thus,
P = aE.
(3.46)
A lattice vibration is Raman active when the vibration changes the polarizability. An
oscillating dipole radiates energy in the form o f scattered light. Most o f the reemitted
light has the same frequency as the primary light without gain or loss o f energy, which
is known as Raleigh scattering. However, a small fraction of the stored energy is
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131
transferred to the molecule, setting it into vibration. Due to this energy transfer from
the incident light, the corresponding reemitted light has been frequency-shifted by an
amount equal to the vibrational frequency o f the lattice. This shifted frequency is the
Raman scattering. The Stokes scattering is produced when energy is extracted from the
incident light beam and sets it into vibration, whereas the anti-Stokes scattering arises
from the annihilation of the existing thermally excited vibration. Stokes lines are of
greater intensity, and are more often studied (Skoog, 1985: White, 1993).
Raman scattering has become a powerful tool for characterizing CVD diamond
films (Knight and White, 1989). It is very sensitive to the bonding nature o f carbon,
thereby, being able to distinguish various types of carbon: diamond, graphite,
amorphous carbon or hydrogenated amorphous carbon. Both the Raman active firstorder optical phonon mode in diamond at 1332 cm' 1 and in graphite at 1580 cm' 1
provide
the
basis
for
interpreting
the
nature
of
synthetic
diamond
films.
Microcrystalline graphite shows an additional peak at 1357 cm'1. Two broad bands
occur at approximately 1590 cm' 1 and 1350 cm' 1 for amorphous carbon. For diamond­
like carbon which is the hydrogenated amorphous carbon, the broad 1550 cm' 1 band
appears with a shoulder of the 1350 cm' 1 broad band (Knight and White, 1989). Since
the Raman scattering efficiency for graphite is much greater than for diamond, even a
small amount of graphitic carbon in CVD diamond films is readily detected. In
addition, Raman spectroscopy gives information about inherent stresses, impurities, and
structural defects because they give rise to shift and broadening of Raman peaks.
In this study, Raman spectra were measured with an Instruments SA Microfocus
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132
Ramanour U1000 spectrometer using the 514.5 nm line of an argon ion laser with an
output power o f 100 mW. The instrument was equipped with a microscope (objective
40X) with a focal spot size in the range o f a few micrometers. Power at the sample
surface was about 10% of the initial laser power. Data were collected in the ranges of
1315-1350 and 400-8000 cm' 1 at 0.25 and 5 cm' 1 intervals with the monochromator slit
widths of 100 and 200 pm, respectively.
3.10. Profilometrv for the measurement of surface roughness
Surface roughness of diamond substrates and as-grown films was measured by a
profilometer (Alpha-Step 200, Tencor Instruments) with a stylus o f 25 pm-diameter
round tip and a stylus force o f 15 mg over a distance o f 200 pm. A profilometer can
give a quantitative assessment for a surface by scanning its topography with a stylus
being in touch with it. In the instrument used in this study, surface roughness was
given by the arithmetic average (Ra) using the graphical centerline method (ANSI
B46.1-1978). Average roughness Ra is defined as the average deviation of the surface
profile from the centerline,
Ra = 2 f ly, -y |/N ,
(3.47)
where y, and y are the profile height for each point over a measurement distance and
the average profile height obtained by summing yt and dividing by the number of data
points N, respectively. Relative surface roughness, which is a ratio of average
roughness o f a film surface to that o f the substrate, was used to reveal the evolution of
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133
the surface roughness with deposition. Surface roughness measurements were made at
least 5 times for each sample and were averaged.
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134
Chapter 4
SURFACE MORPHOLOGIES OF (001)
HOMOEPITAXIAL DIAMOND FILMS
4.1. Introduction
The extensive literature review on the homoepitaxial growth of diamond films
given in Chapter 2 shows that the characteristics of (001) homoepitaxial diamond films
with the variation of CVD growth conditions are not yet satisfactorily understood. This
chapter concerns the characterization o f (001 ) homoepitaxial diamond films grown on
various substrates and under various CVD conditions mainly in terms of the surface
morphologies, aimed at the understanding of the growth mechanisms and the
establishment o f the optimal deposition condition for (001) homoepitaxial diamond
films.
First o f all, this study emphasized on the effect of surface misorientation angles
of substrates on the surface morphologies of as-grown films because different surface
morphologies have often been observed from sample to sample even in the same
deposition condition. In addition, substrate surfaces were etched in hydrogen plasma
and were examined as a function of the misorientation angles. The second topic is the
effect of CH 4 concentrations on the growth morphologies. Contradicting results were
reported about the dependence o f surface morphologies on CH4 concentrations (Shiomi
et al., 1990; Sato et al., 1991; Avigal et al., 1993; Borst et al., 1994; Samlenski et al.,
1995). It is to be noted that substrates with the same misorientation angle were used in
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135
this study to eliminate the influence o f different surface misorientations in investigating
the effect of CH 4 concentrations. This study is expected not only to enhance our
understanding o f growth mechanisms for (001 ) homoepitaxial diamond films but to
suggest the optimal growth conditions for high-quality films.
4.2. Literature review
Surface morphologies o f (001) homoepitaxial diamond films as a function of
deposition conditions were discussed in Chapter 2. Results available in the literature to
date are unsatisfactory because they are often inconsistent between different groups. In
our experience, it has been frequently observed in regard to (OOl)homoepitaxial
diamond growth that macrosteps and growth hillocks occur on different samples under
the same deposition condition. It has been thought that this may be attributed to the
different features o f substrates used for growth. Several factors o f substrates are
possibly responsible, including the surface misorientation angles, structural defects, and
polishing marks, but the surface misorientation angles of substrates are considered to be
most important. Unfortunately there has been almost no research about the effects of
surface misorientation angles o f substrates on the growth morphologies of CVD
diamond. However, this effect has been extensively studied in other material systems,
including Si, SiC, GaAs, and PbTi03.
Hillock formation in Si (111) epitaxial growth was discussed by Tung (1965).
According to his argument, the deposition rate was subdivided into the decomposition
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136
rate (Rr) of SiCl4 and the surface reaction rate (Rc) for Si atoms to join at the proper
surface sites. These two processes occurred in series, so the slowest would dominate
the total deposition rate. When Rr<Rc, the Si concentration in the gas phase was low,
then the epitaxial layer was smooth. In the case of R,>RC, the Si concentration in the
gas phase was high, and growth hillocks appeared on the growth surface. It was
claimed that growth hillocks were formed on the surface irregularities such as
protrusions or pits under the deposition conditions of the second case. In the
irregularity zones with crystallographic orientations different from
the <111>
orientation, the overall deposition rate under certain conditions could be higher than in
the smooth surface of the substrate.
Later the surface misorientation o f substrates was considered to be one of the
most crucial factors in the growth surface morphologies (Aharoni, 1976). Under the
normal deposition condition, the epitaxial layers which were shiny, smooth and without
hillocks, were grown on the 1° o ff (111) substrates. When the deposition rates were
doubled by increasing the SiCl4 concentrations in H2, however, growth hillocks
appeared. It was found that the higher the misorientation angle o f a substrate, the
higher SiCl4 concentration was needed to obtain growth hillocks. It was postulated,
therefore, that the well-oriented substrates were the worst because growth hillocks were
formed even at very low deposition rates.
In the CVD growth of Si on Si, it has been ascertained that the lateral
movement o f steps is the mechanism that brings about the epitaxial growth of high-
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137
quality films, while hillock growth occurs under inappropriate deposition processes
(Abbink et al., 1968; Joyce, 1974; Ogden et al., 1974). Historically the step-flow
growth has been one of the most important issues in studying crystal growth since the
pioneering work of Burton, Cabrera, and Frank (1951). As for hillock growth,
Chernov (1977) suggested the self-consistent nucleation mechanism, which is basically
almost the same as the 2D island growth on the Si (001) surface discussed in Chapter 2.
The homoepitaxial growth of 6H-SiC (hexagonal structure) by CVD had been
necessarily carried out at high temperatures over 1800 °C to achieve good surface
morphology of as-grown fiims (Muench and Pfaffeneder, 1976; Nishino et al., 1978).
By introducing the surface misorientation to substrates, epitaxial growth temperature
for 6H-SiC could be dropped to 1500 °C or lower while maintaining smooth growth
surface (Shibahara et al., 1987a; Kong et al., 1988a). The step-flow growth was also
demonstrated in the epitaxial growth of 3C-SiC (cubic structure) on misoriented Si
(001) substrates (Shibahara et al., 1987b; Kong et al., 1988b). As the surface step
densities were increased by introducing the surface misorientation, epitaxial layers were
grown laterally from the steps, replicating the structure of the substrates. The step-flow
growth on the misoriented substrates eliminated structural defects such as antiphase
boundaries, dislocations, and stacking faults which resulted in the rough growth
surfaces and the poor electrical properties (Kong et al., 1988a, b).
Concerned with the vapor phase epitaxial growth of GaAs on GaAs (001)
substrates, the misorientation angles of approximately 3° toward <110> were suggested
to obtain smooth growth surfaces free o f growth hillocks (Hollan and Schiller, 1974).
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138
Misoriented SrTi03 (001) substrates were also used to grow PbTi03 thin films (Satoh et
al., 1994). The introduction of surface misorientation o f substrates significantly
reduced crystal boundaries and provided continuous films.
4.3 Experimental details
HP/HT synthetic type lb single-crystal diamonds supplied by Sumitomo
Electric, Japan, were used as substrates for this study because of their better quality
and higher uniformity than natural diamond. Misorientation angles of mirror-polished
substrate surfaces with respect to the (001) plane were determined by Laue x-ray
diffraction. The results o f measurements are given in Table 4.1. To study the effect of
surface misorientation angles, the 0.1°, 3.5°, and 11.0° o ff substrates were either
etched or deposited at the same time, to eliminate any disparity which could happen
between different batches. An investigation of the effect o f CH4 concentrations was
conducted using 3.1° o ff diamond substrates which were obtained by cutting a substrate
into several pieces to maintain the same surface misorientation angle. After measuring
the surface misorientation angles, substrates were cut by a laser and consecutively
cleaned in boiled sulfuric acid saturated with C r03 to remove non-diamond carbon, in
boiled aqua regia and in a 1:1 solution of HF and H N 0 3 to eliminate any metallic
contaminants including Cr, in distilled water, and in acetone for 30 min for each
cleaning process.
Etching and deposition experiments were carried out in an MPACVD system
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139
Table 4.1 Surface misorientation angles o f (001) diamond substrates towards the [110]
and [ llO ] directions, measured from x-ray diffraction.
substrates
misorientation misorientation total misorien­
nominal misorientation
towards [110] towards [ llO ]
direction from [110]
tation angle
0.1° off
0.1°
0.1°
0.1°
45.0°
3.5° o ff
0.2°
3.5°
3.5°
3.3°
11.0° o ff
1. 0°
8.5°
11.0°
39.2°
3.1° o ff
0.8°
3.0°
3.1°
14.9°
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140
with a quartz-tube reactor. CVD conditions are summarized in Table 4.2. Pure H2 gas
was used for etching o f diamond substrates while mixture gases o f 0.5%, 1%, 2%, and
6 % CH4 in H2 were used for diamond deposition. The gas pressure was 80-150 Torr
and the gas flow rate was 100 seem. The substrate temperatures measured by optical
pyrometry were 1300 °C for etching and 875, 1200 °C for deposition.
4.4. Results
4.4.1. Effect o f surface misorientation angles o f substrates
4.4.1.1. Surface morphologies o f etched substrates
The surface morphologies of diamond (001) substrates etched in H plasma at
1300 °C for 1 hr are shown in Figure 4.1. Numerous square-shaped etch pits with four­
fold symmetry are developed on the 0.1° [Figure 4.1(a)] and 3.5° o ff surfaces [Figure
4.1(b)], while few are observed on the 11.0° o ff surface [Figure 4.1(c)]. The edges of
etch pits are parallel to the <110> directions, and their bottom faces are usually flat. A
higher magnification image o f the 0.1° o ff surface [Figure 4.1(d)] shows that welldeveloped etch pits have side faces composed of steps. The number o f etch pits
decreases with increasing misorientation angles. The approximate population densities
of etch pits are 2.1xl07, 7.0xl06, and 1.1x10s cm'2 for the 0.1°, 3.5°, and 11.0° off
substrates, respectively.
Macrosteps developed along the [110] direction are seen in the 3.5° o ff sample,
which are aligned consistently in such a direction as expected from the surface
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141
Table 4.2 CVD conditions for etching and homoepitaxial growth o f diamond (001)
surfaces.
CVD conditions
Effect of misorientation
Effect of CH4
Etching
Growth
concentrations
0.1°, 3.5°,
0.1°, 3.5°,
3.1°
11.0°
11.0°
0% (pure H2)
1%
1, 2, 6 %
Total gas flow rate
100 seem
100 seem
100 seem
Gas pressure
150 Torr
90 Torr
80 Torr
Substrate temperature
1300 °C
1200 °C
875 °C
Misorientation angles of
substrates
CH4 concentration in H2
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Figure 4.1 SEM images of the diamond (001) surfaces etched for 1 hr at 1300 °C and
150 Torr H; : (a) 0.1°. (b) 3.5°. (c) 11.0° off substrates, and (d) high
magnification of (a). The directions of images are designated in Fig. 2.
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143
misorientation o f the substrate. Etch pits and macrosteps indicate that the diamond
(001) surface is etched by the migration o f steps along the <110> directions no matter
how the steps are provided. The origin of these steps are different for the well-oriented
(~ 0° off) and misoriented substrates. For the misoriented substrates the surface
misorientation from the (001) plane w ill provide steps to retreat during etching. The
well-oriented substrates, however, have low densities of steps related to the surface
misorientation and then have very wide terraces. In this case, steps can be created by
nucleation o f etch pits on terraces, and steps in etch pits will make a dominant
contribution for etching over steps provided by the surface misorientation. I t is
concluded therefore that etching o f the diamond (001) surface proceeds in two ways;
(a) regression o f pre-existing steps originated fro m the surface misorientation o f
substrates and (b) creation and regression o f new steps resulting fro m etch pits.
While the highly misoriented (11.0° off) sample was etched predominantly by the
mechanism (a), the well-oriented (0.1° off) surface was etched mainly by the
mechanism (b). The 3.5° o ff substrate is shown to be etched by both processes. Etch
pits might be developed on lattice defects such as dislocations (Mitsuhashi et al., 1992),
but it is thought that the different populations of etch pits in the three samples are
caused by the degree of surface misorientation of substrates rather than by the
difference o f defect densities.
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4.4.1.2. Surface morphologies of homoepitaxial films
The surface morphologies of CVD diamond films grown at 1200 °C change
remarkably with the surface misorientation angles o f (001 ) substrates, as shown in
Figure 4.2. The deposition temperature o f 1200 °C was chosen since (001)
homoepitaxial diamond films could be grown nearly free of twinning at this
temperature (Badzian and Badzian, 1993). Growth on the 0.1° o ff substrate for 5 hr
produced hillocks with a four-fold symmetry which are o f two different sizes (typically
15 pm and 3.5 pm, respectively). The large growth hillocks are usually truncated at the
top where growth of the small hillocks is frequently observed. All edges of growth
hillocks are arranged along the < 110> directions, which indicates the single-crystal
nature of the grown layer. The hillock formation on the diamond (001) substrates at
lower temperatures has been already reported by several research groups using
MPACVD (Badzian and Badzian, 1993; Maguire et al., 1992; Vitton et al., 1993) and
hot-filament-assisted CVD (Sutcu et al., 1992a; Enckevort et al., 1993; Vitton et al.,
1993), but a clear explanation of the origin has not been given. From the present
study, it is believed that the form ation o f growth hillocks is attributed to the low
misorientation angle o f a substrate.
On the other hand, the film grown for 8 hr on the 3.5° o ff substrate [Figure
4.2(b)] shows macrosteps with their edges running parallel to the [110] direction, and is
the smoothest of the three samples. Based on the misorientation angle, the step-down
direction is from the upper right to the lower left of the image. Macrosteps are also
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Figure 4.2 DICM images of the surface morphologies of homoepitaxial diamond films
grown at 1200 °C. 90 Torr. and 1?c CH 4 in H; on (a) 0.1° o ff (001)
substrate for 5 hr. (b) 3.5°. and (c) 11.0° off (001) substrates for 8 hr.
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observed on the film deposited for 8 hr on the 11.0° o ff surface [Figure 4.2(c)]. The
macrostep edges run along the two orthogonal directions of [110] and [llO ], which
makes the step front resemble saw teeth. The step edges are usually a little longer along
[ 110] than along [ 1 1 0 ] in a saw tooth, which agrees with the prediction from the
misorientation angles in the two directions. The steps are going down from the upper
part of the figure to the lower.
The shape of macrosteps are different depending on the nominal misorientation
directions of substrates, as illustrated in Figure 4.3. When the substrate is tilted toward
the <110> direction, macrosteps are likely to have straight edges. On the substrate
misoriented toward the <100> direction, however, macrosteps have zigzag edges. This
is because the homoepitaxial growth on the diamond (001) surface proceeds along the
<110> directions. The diamond (001) surface is reconstructed by dimerization of
surface carbon atoms along < 1 10>. Growth on this surface occurs through the extension
of dimers along the <110> directions (Tsuno et al., 1991; Kawarada et al., 1994;
Frauenheim et al., 1994).
Surface roughness o f as-grown films given in Figure 4.2 was measured by a
profilometer. Average surface roughness Ra was 190-260, 45-55 , 760-850 A for the
0.1°, 3.5°, and 11.0° o ff samples, respectively. The 3.5° and 11.0° o ff films show
remarkably different surface roughness although both were grown by the step-flow
mechanism. Thus, there seems to be an optimal range of the misorientation angles to
produce smooth surfaces while keeping the step-flow growth mode under a given
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147
►
[110]
[110]
(b)
-<
f A
[110]
[100]
^
[1101
Figure 4.3 Configuration of macrosteps for the homoepitaxial growth on the diamond
(001 ) substrates misoriented toward (a) [ 110 ] and (b) [ 100].
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148
deposition condition.
The extended growth under the same CVD condition was performed on the very
same samples shown in Figure 4.2. Figure 4.4 shows the surface morphologies of
epitaxial films deposited for a total of 15 hr. Growth hillocks on the 0.1° o ff film have
a regular pyramidal shape with a sharp apex and become larger in size [Figure 4.4(a)]
as compared to hillocks on the film grown for 5 hr. Small growth hillocks are observed
between large pyramids. Tamor and Everson (1993) measured the slopes of growth
hillocks on (001) homoepitaxial diamond films using STM, which were in many cases
approximately 6 °. Assuming the same angle for the pyramids, growth hillocks shown in
Figure 4.4(a) are expected to be as high as approximately 1.8 pm on an average. The
3.5° o ff film surface is still smooth and macrosteps running along the [110] direction is
preserved even after prolonged growth [Figure 4.4(b)]. The same tendency is kept on
the 11.0 ° o ff film as well, but macrosteps are bunched together to cause much wider
terraces between macrosteps [Figure 4.4(c)].
Growth rates were calculated from the weight gains of samples obtained by
weighing before and after deposition with a microbalance (Micro Gram-Atic Balance,
E. Mettler Zurich, Switzerland). As given in Figure 4.5, growth rates increase with
increasing the misorientation angles. The higher the step density, the larger the
growth rate. It implies that steps (and kinks) are the most active sinks for growth
species to incorporate into a lattice. Thus, step-flow growth producing smooth film s
can be achieved with higher growth rates by an introduction o f the optimal surface
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149
Figure 4.4 DICM images of the surface morphologies of homoepitaxial diamond
films grown for 15 hr at 1200 °C. 90 Torr, and 1% CH4 in H; on (a)
0.1°, (b) 3.5°. and (c) 11.0° off (001) substrates.
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150
0 .7
Growth
Rate
(jam/hr)
0.6
0 .5
0 .4
0 .3
0.2
0.1
0.0
J----- 1------ 1___ .
0
2
I___ i
4
I
6
■
I
8
■1___ L
10
M is o rie n ta tio n A n g le (d e g .)
Figure 4.5 Growth rates as a function of the surface misorientation angles
o f substrates at 1200 °C, 90 Torr, and 1% CH 4 in H2.
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151
misorientation angles to substrates.
The single-crystal nature o f the deposited films was investigated with RHEED.
Figure 4.6 shows RHEED patterns of the films grown for 5 hr on the 0.1° o ff substrate
and for 8 hr on the 3.5° and 11.0° o ff substrates at 1200°C using
1%
CH4. Schematic
RHEED pattern with the [100] and [110] azimuths expected from the superposed
reciprocal lattice of 2x 1 and 1x 2 structures on the reconstructed diamond (001 ) surface
and lx l structure of the substrate layers were given in Figure 3.15(a) and (b). The
observed RHEED patterns agree well with the schematic patterns. The half-order (L 1/2)
and first-order (L)) Laue rings are well resolved in RHEED patterns. The half-order
and first-order Laue spots are observed to be periodically repeated along the Laue
rings. This indicates that the surface lattices as well as the bulk lattices of CVD
diamond maintain nearly perfect crystallinity in a long-range order. These diffraction
patterns are consistent with the well-known 2 x 1 and 1x2 double-domain structure which
had been observed previously by RHEED (Tsuno et al., 1991; Sasaki et al., 1993) and
LEED (Lurie and Wilson, 1977; Hamza et al., 1990; Thomas et al., 1992; Tsuno et
al., 1994). Thus, the as-grown diamond (001) surface consists of two orthogonal
domains with 2 x 1 and 1x 2 unit cells, which have double periodicity along the [ 110] or
[110] directions. There would be many steps of monatomic (single-layer) or oddnumber atomic height dividing 2 x 1 and 1x2 terraces, which are running along the
<110> directions. This microscopic configuration of steps agrees with the macroscopic
observation that the edges o f hillocks or etch pits and macrosteps run along the < 110>
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152
[1101 azimuth
[100] azimuth
Figure 4.6 RHEED patterns of the (001) film surfaces grown on (a) 0.1°. (c) 3.5°,
and (c) 11.0° o ff substrates at the condition specified in Fig. 2. taken from
1100) for the left and [ 110] azimuths for the right patterns. The insets of
1110] azimuthal patterns show magnified views of the zeroth Laue zone.
L, : and L, denote the half-order and first-order Laue rings, respectively.
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153
directions.
Raman spectra were taken to assess the crystalline quality of epitaxially grown
layers because Raman spectroscopy is very sensitive to the presence o f non-diamond
carbon which may be codeposited simultaneously during diamond growth (Knight and
White, 1989). Figure 4.7 shows Raman spectra obtained from a HP/HT synthetic
diamond substrate prior to deposition and from the homoepitaxial film grown on the
0.1° o ff substrate for 15 hr. For the three films, only the 1332 cm' 1 peaks were
observed, and the full widths at half maximum (FWHM) of the as-grown layers were
as narrow as that of a HP/HT synthetic substrate.
4.4.2. Effect o f methane concentrations
The effect of CH4 concentrations on the growth surface morphologies was
studied using the diamond (001) substrates with the same misorientation angle o f 3.1°.
As given in Table 4.1, the mirror-polished diamond substrates have the misorientation
angles of 0.8° and 3.0° toward the [110] and [1 TO] directions. Figure 4.8 shows the
surface morphologies of the films homoepitaxially grown for 5 hr with 1%, 2%, and
6 % CH 4 in H 2 at 875°C. Macrosteps are well developed on the film grown at 1% CH4
[Figure 4.8(a)]. The step-down direction is from left to right of the image. Macrosteps
run mostly along the two orthogonal directions of [ 110] and [ 1T 0 ], but their
morphologies vary from place to place. Macrosteps are aligned in some areas, while
they wave in others. The alignment of macrosteps was found to occur along polishing
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154
14000
12000
Intensity
(A rb .)
10000
8000
cm
6000
cm
4000
S u b strate
2000
Film
1320
1330
1340
1350
R a m a n S h ift (c m -1)
(a)
Figure 4.7 Raman spectra of the 0.1° o ff (001) substrate and the homoepitaxial
diamond film grown for 15 hr with 1 % CH4 in H2 at 1200 °C: (a) spectra
taken in the range of 1315-1350 cm"1 at 0.25 cm"1 intervals with the slit
width of 100 pm and (b) spectra taken in the range of 400-8000 cm' 1 at 5
cm' 1 intervals with the slit width o f 200 pm. Numbers in (a) represent the
full widths at half maximum.
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155
60000
50000
(A rb .)
40000
Intensity
30000
20000
S u b s tra te
10000
Film
2000
4000
6000
R a m a n S h ift (c m -1)
(b)
Figure 4.7 (cont.)
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8000
Figure 4.8 DICM images of the surface morphologies of (001) homoepitaxial
diamond films grown for 5 hr at 875 °C with CH 4 concentrations
of (a) 1%. (b) 2 %, and (c) 6 % in H2.
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157
lines, which is not yet understood. It has been previously reported that macrosteps are
formed by step bunching due to impurity segregation at step edges (Eerden and MiillerKrumbhaar, 1986; Enckevort et al., 1993). The epitaxial films shown in Figure 4.2(b)
and 4.8(a) were grown on substrates with similar misorientation angles and with the
same CH 4 concentration but at different temperatures. Step bunching is more likely to
occur at 875 °C than at 1200 °C. This seems to be because impurity atoms have a
higher sticking coefficient during growth at lower temperatures.
Growth hillocks as well as polishing lines are observed on the film grown with
2% CH4 [Figure 4.8(b)). Some hillocks have flat-topped faces and others have apexes
or particles at the top created by secondary nucleation. Growth hillocks have fourfold
symmetry and are tilted the opposite direction of the surface misorientation. As shown
in Figure 4.2 and 4.4, growth hillocks on the well-oriented substrate have the same
fourfold symmetry, but they are untilted. It seems that tilting o f growth hillocks
depends on the directions and angles o f surface misorientation, and that the flat top
faces of growth hillocks are the (001) plane. On the other hand, the film grown with
6%
CH4 exhibits random growth features (Henzler, 1993a, b) which are elongated
along the nominal surface misorientation direction 15° from [110] toward [100]
[Figure 4.8(c)].
The surface morphologies of epitaxial films produced by an extended growth for
a total of 12 hr under the same CVD conditions are given in Figure 4.9. The film
grown with 1% CH 4 [Figure 4.9(a)] shows much more coarse macrosteps and growth
hillocks which were not observed after the 5 hr growth. On the 2% CH 4 film, growth
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Figure 4.9 DICM images o f the surface morphologies of (001) homoepitaxial
diamond films grown for 12 hr at 875 °C with CH4 concentrations
of (a) 1%, (b) 2 %. and (c) 6 % in H: .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4 .9 (cont.)
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160
hillocks grew to become apparently polycrystalline and lost their fourfold symmetrical
shape [Figure 4.9(b)]. One striking feature of this film is the occurrence o f macrosteps
with the extended growth. Macrosteps on the 2% CH4 film grown for 12 hr look
similar in the appearance to those o f the 1% CH4 film grown for 5 hr, but large
macrosteps with wide terraces are observed frequently. The 1% and 2% CH 4 films
grown for 12 hr show similar overall surface morphologies. However, the differences
observed in the films grown for 5 hr (Figure 4.8) should be noted to understand the
growth mechanisms. For the
6%
CH 4 film , no large difference is found except for the
enlargement of the random growth features after the prolonged growth [Figure 4.9(c)].
One interesting thing is that growth hillocks may disappear with an extended
growth. This is illustrated in Figure 4.10. The surface morphologies were observed in
the same area after 5hr and 12 hr deposition with 2% CH4. Growth hillocks and their
correspondence are marked by A through H in Figure 4.10(a) and (b). Growth hillocks
denoted by A, E, and F disappear in Figure 4.10(b) after the prolonged growth. In the
5 hr grown film, most growth hillocks maintain an epitaxial relation with the film. This
epitaxial relation is lost with the extended growth as secondary nucleation occurs on the
growth hillocks. Polycrystalline crystallites on the 2% CH4, 12 hr grown film are in
many cases found to have a triangular-shaped crystal atop, which seems to be a
{ llljfa c e formed by secondary nucleation. These crystallites are higher in the
elevation than the macrostepped region. It appears that polycrystals with the {111} face
up grow at the same rate or faster than the macrostepped region and then survive in the
growth competition. The growth rates o f polycrystals depend on their surface-normal
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lb !
Figure 4.10 D IC M images taken in the same area o f (001) homoepitaxial diamond
films grown at 875 °C with 2% C H 4 in H: : (a) 5 hr and (b) 12 hr.
Hillocks in (a) and their correspondence in (b) are marked A through H.
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162
directions which are determined by secondary nucleation. Thus, a polycrystal which
has the surface-normal direction with the low growth rate can be defeated by
macrosteps in the growth competition and then buried underneath.
The growth rates measured by a microbalance are shown in Figure 4.11.
Growth rates increase linearly with the higher CH 4 concentrations. The dependence of
the growth rates on CH 4 concentrations can be explained by production of the higher
concentrations of diamond growth precursors with increasing CH 4 concentrations.
Figure 4.12 is the surface roughness for the films grown with the three different
CH4 concentrations. The measurements have been carried out for the substrate prior to
deposition and for the films grown for 1, 2, 5, 12 hr with 1%, 2%, and 6 % CH4. A ll
film surfaces become rougher with increasing deposition time irrespective o f CH 4
concentrations. The film grown with 2% CH 4 has the smoothest surface, whereas the
1% CH4 film is the roughest, which can also be seen from the surface morphologies
shown in Figure 4.8 and 4.9.
Raman spectra were taken in several places including growth hillocks and
polycrystals,
from each sample grown 5 and
12 hr at three different CH 4
concentrations. A ll spectra, which were actually the same as given in Figure 4.7,
revealed only the 1332 cm' 1 diamond peak with FWHM as narrow as that of a HP/HT
synthetic diamond substrate.
Disparities were expected for the different CH 4
concentrations, but within the deposition time up to 12 hr, non-diamond carbon was not
involved in the homoepitaxial diamond growth with the given CH 4 concentrations.
For studying the surface structure o f as-grown diamond films, samples were
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4
JZ
3
E
>3.
0
ro
a:
XT
2
?
o
O
1
0
0
1
2
3
4
5
6
C H 4 C o n c e n tra tio n (%
Figure 4.11 Growth rates as a function of the CH4 concentrations
in H 2 at 875 °C, 80 Torr.
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164
— h— 1 % C H
40
— A— - 2 % C H
U)
<n
—
CD
6% CH
30
O)
3
O
a:
CD
D)
C
D
u.
20
a)
>
<
CD
>
TS
CD
OH
0
2
4
6
8
10
12
D e p o s itio n T im e (h r)
Figure 4.12 Surface roughness o f the diamond substrate and (001) homoepitaxial
films grown for 1, 2, and 5 hr at 875 °C with 1%, 2%, and 6 % CH4
in H2. Relative average roughness is a ratio of average roughness of
a film surface to that o f the substrate.
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165
quickly dropped approximately 40 cm below the center of the plasma cavity inside the
quartz tube of the CVD system during growth so that the topmost surface structure
would be frozen as close to a real growth surface structure as possible. Figure 4.13
contains RHEED patterns of the films grown for 30 min at 875 °C with 0.5%, 1%,
2%, and 6 % CH4, taken in the [100] azimuth. RHEED patterns are consistent with the
schematic pattern given in Figure 3.15(a) which is expected from the superimposed
reciprocal lattice of the 2 x 1 and 1x2 structures on the diamond (001 ) surface and the
l x l structure of the substrate layers. In Figure 4.13, it is noted that the intensity of the
half-order spots decreases with higher CH 4 concentrations. This could result from a
larger number of hydrocarbon species adsorbed on the surface at higher CH4
concentrations or from a disordered layer deposited during dropping of samples, which
would disturb the 2 x 1 surface structure.
As shown in Figure 3.15(a), the 2x1 and 1x2 domains produce diffraction spots
alternately along the half-order Laue ring. In the patterns taken from the films grown
with 0.5% and 1% CH 4 [Figure 4.13(a) and (b)], the 1x2 half-order spots have far
stronger intensities than the 2x1 half-order spots. This implies that the 1x2 domain
dominates these surfaces (Clarke, 1985; Ertl and Kiippers, 1985; Yang et al., 1993a),
as discussed in section 3.4.3. The intensity difference between two series o f the half­
order spots is considerably reduced at 2% CH4 [Figure 4.13(c)] even if the 1x2 half­
order spots are still brighter. The RHEED pattern of the film grown with 6 % CH4
[Figure 4.13(d)] does not show an alternate variation of intensity in the half-order
spots.
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Figure 4.13 RH EED patterns o f (001) homoepitaxial diamond film surfaces
grown for 30 min at 875 °C w ith (a) 0.5% . (b) 1.0%. (c) 3.0% .
and (d) 6% C H 4 in H ; . taken w ith the |100| azimuth. L ,.; and L,
denote the half-order and first-order Laue rings, respectively, and
arrowheads indicate the 1x2 half-order spots.
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167
Although the film surface is close to the 1x2 single-domain structure at low CH 4
concentrations, the 2x1 domain still remains. The presence of the 2x1 domain, even at
low CH 4 concentrations, possibly results from the deviation o f the nominal surface
misorientation direction from the <110> direction. The perfect single-domain structure
would form only when a surface is tilted toward either [110] or [llO ]. Conclusively,
when step-flow growth occurs at low CH 4 concentrations, the surface is close to the
1x 2
single-domain structure, while the
2x 1
and
1x 2
double-domain surface is
developed in h illo c k growth and random growth at high CH 4 concentrations. It is
expected that step-flow growth with the single-domain surface would produce higherquality films with fewer lattice defects than hillock growth or random growth. Our
results are consistent with those of Tsuno et al. (1994) who observed a nearly single­
domain surface in the case of step-flow growth using STM and LEED.
4.5. Discussion
There are similarities and differences between the etched and growth surface
morphologies with the surface misorientation angles o f substrates as shown in Figure
4.1 and 4.2. Both etch pits and growth hillocks on the well-oriented substrates have
similar square shapes with the same orientation, but with concave and convex
morphologies. This suggests that a similar mechanism o f formation could be applicable
to them in spite o f the differences. Both etch pits and growth hillocks are form ed
because o f the low step density on the substrates. Macrosteps causing a rough surface
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168
are notably developed on the highly misoriented surface during deposition, whereas
etching produces a very flat surface on the same substrate. Although they show
different morphologies, etching and growth on the misoriented substrates occur by
lateral movement o f already present steps.
A misoriented surface may be assumed to comprise steps, kinks, and terraces
with a regular distribution, reflecting the macroscopic surface misorientation o f a
substrate from the (001) plane. Diamond growth during CVD occurs by the continuous
adsorption of hydrocarbon precursors and the subsequent abstraction of hydrogen atoms
on this complex surface (Garrison et al., 1992; Harris and Goodwin, 1993; Zhu et al.,
1993). On the surface, steps or kinks are energetically the most favorable sites for
precursors to join the crystal surface (Tsuda et al., 1992; Zhu et al., 1993). F o r the
misoriented substrate where plenty o f atomic steps are available, it can be considered
that the lateral movement o f atomic steps through the continuous supply o f
hydrocarbon precursors into steps makes a m ajor contribution to the growth o f (001)
homoepitaxial diamond. The supply o f hydrocarbon precursors to steps may be
carried out through surface diffusion. It has been found that the surface diffusion of
hydrocarbon adsorbates, in particular CH2, possibly occurs on the hydrogenated
diamond (001) surface and may play a crucial role in the CVD diamond growth
(Mehandru and Anderson, 1991; Skokov etal., 1994a; Frenklach et al., 1995).
Homoepitaxial diamond growth from the vapor phase can be figured out by the
presence of supersaturated concentration of adsorbates on terraces relative to steps
(Chernov, 1977; Nishinaga, 1994). Figure 4.14 illustrates the supersaturation of
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169
(a)
(b)
Figure 4.14 Surface adsorbate concentration, n, and supersaturation ratio, a, as a
function of distance from the steps for two different step distances, where
ns, n0, ac, a s are the adsorbate concentration at the steps, the steady-state
concentration o f adsorbate at the steps, the critical supersaturation ratio for
the 2D nucleation, and the supersaturation ratio at the steps, respectively:
(a) a small distance and (b) large distance between the steps.
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170
adsorbates for different step separations under the same CVD condition, where n , «s,
n0, and a denote the concentration o f adsorbates on the surface and on a step, the
steady-state concentration o f adsorbates incorporating into a lattice at the step, and the
supersaturation ratio of n/n0, respectively. When steps are closely spaced so that the
terrace width is shorter than the diffusion length, as given in Figure 4.14(a), adsorbates
are distributed to a larger number of steps, and then the maximum supersaturation ratio
becomes smaller than the critical ratio ac for the two-dimensional (2D) nucleation
(Nishinaga, 1994). In this case, adsorbates landing on terraces migrate to steps and are
then incorporated into the lattice, leading to the step-flow growth as shown in Figure
4.15(a). The epitaxial growth by step flow is expected to produce a smooth layer of
high quality, as reviewed in section 4.2 for other material systems including Si, SiC
and GaAs.
For the well-oriented surface, however, steps are distributed far apart, giving
rise to a much larger terrace width than the diffusion length of adsorbates under a given
deposition condition. As a result, a higher supersaturation of adsorbates exceeding the
critical supersaturation ratio a c for 2D nucleation would build up on the central region
of a terrace because adsorbates cannot migrate to steps ( Nishinaga, 1994), as given in
Figure 4.14(b). On the terrace region where a > ac, adsorbates meet together to form
stable clusters and stick to the terrace rather than move to the pre-existing steps,
although the pre-existing steps continue to move forward consuming adsorbates in the
area around the step edges. This causes 2D nucleation on the terrace, as discussed in
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171
IQ
O
TCLir-Q
T O ^-O
O
O
TO
Q:
TO.
(a)
f
t
▼
IQ ~*~ Q — C L -- c x fe — - o — »• o o a f e o o
f
oTQ _
2D nuclei
(b)
Figure 4.15 Growth mechanisms for two different step distances: (a) step-flow
mechanism on a misoriented substrate and (b) hillock growth
mechanism on a well-oriented substrate.
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172
section 2.2.4 for the epitaxial Si growth. A 2D nucleus would grow by the joining of
migrating adsorbates onto the newly created steps. This results in lowering the
supersaturation of adsorbates below a c around the 2D nucleus, but the supersaturation
on the upper terrace of the 2D nucleus w ill increase and finally exceed ac as the 2D
nucleus becomes larger. When the nucleus is beyond a critical size, 2D nucleation for
the next layer occurs on the upper terrace of the 2D nucleus. The second layer begins
to grow and the process will be repeated for the third, fourth layers, etc. As the density
o f steps newly created by the repeated 2D nucleation processes exceeds that o f the
pre-existing steps, diamond growth begins to be governed by 2D nucleation. With the
2D nuclei expanding their sizes, they w ill meet together to merge into a larger one,
finally leading to the formation o f a growth hillock (Chernov, 1977). The hillock
growth through 2D nucleation is schematically illustrated in Figure 4.15(b). The
growth by hillock form ation is dom inant over the step-flow growth on the welloriented surface due to the lack o f pre-existing surface steps. Recently, the four-fold
symmetry o f growth hillocks on the diamond (001 ) surface w ; explained with “ a step
interlacing” effect (Enckevort et al., 1993), which can give the 4] symmetry by
assuming the double-layer height o f the growing steps on the four hillock ledges.
It has been discussed above that surface morphologies o f homoepitaxial diamond
films are possibly controlled by diffusion of adsorbates on the surface. For the
misoriented substrates, as the diffusion lengths of adsorbates on the surface are longer
than the terrace width between steps, adsorbates arriving at the terraces diffuse to the
steps, resulting in the step-flow growth. For the well-oriented substrates, however, the
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173
growth is dominated by the hillock formation through 2D nucleation on terraces
because adsorbates far from the already present steps cannot migrate to the steps. These
different growth mechanisms bring about the disparities in growth rates as well as
surface morphologies. As shown in Figure 4.5, the step-flow growth results in higher
growth rates than the hillock growth. In both mechanisms, the growth proceeds mostly
at steps although the origins of steps are different. For the step-flow growth, the steps
are already present due to the surface misorientation, whereas for the hillock growth,
2D nucleation on terraces provides steps. Based on the growth rates, the density o f
steps during growth is higher on the misoriented substrates than on the well-oriented
substrate, no matter whether they are related to the surface misorientation o r i f they
are created by 2D nucleations. I t appears that 2D nucleation is not efficient in
generating steps. For the step-flow growth mode, the nucleation stage can be
neglected, but this stage should be taken into account in the hillock growth, which may
need an incubation time to occur and may contribute to the lower step density and,
consequently, the lower growth rate.
As seen in the previous section, the surface morphologies and structure o f (001)
homoepitaxial diamond films are remarkably different with CH 4 concentrations. The
growth on the 3.1° o ff substrate with 1% CH4 produced macrostep morphology with
the surface close to the single-domain structure, and at 2% and 6 % CH4, growth
hillocks and random growth morphology occurred with the double-domain structure,
respectively, as shown in Figure 4.8 and 4.13, although the extended growth resulted
in similar surface morphologies at 1% and 2% CH4. These disparities would be
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174
attributed to the different surface phenomena occurring during the growth.
A variation of the CH 4 concentrations gives rise to the different fluxes of
hydrocarbon precursors arriving at the surface, which can be known from the higher
growth rates with increasing the CH4 concentrations. As the substrates used for the
deposition have the same misorientation angle, the concentrations of adsorbates on
terraces increase with higher CH4 concentration. When the diffusion length of
adsorbates is longer than the terrace width and the flux is low (e.g., 1% CH4), the
supersaturation of adsorbates on a terrace is maintained below the critical ratio ac for
2D nucleation (Nishinaga, 1994), as illustrated in Figure 4.16(a). In this case,
adsorbates arriving at terraces diffuse to steps, resulting in the step-flow growth as
shown in Figure 4.17(a). The step-flow growth has been known to produce the single­
domain surface structure. This is well documented in the epitaxial growth of Si on Si
(001) using MBE (Hoeven et al., 1989a, b, 1990a). It has been observed for the stepflow growth o f epitaxial Si layers that growth occurs preferentially at SB steps rather
than at SA steps so that SB steps catch up with SA steps at the beginning of deposition,
leading to the single-domain structure.
With a higher CH4 concentration (i.e., 2%), the supersaturation of adsorbates
increases and passes the critical ratio a c as shown in Figure 4.16(b). Adsorbates would
less likely migrate to steps since they could cluster more easily on terraces due to their
higher population (Chernov, 1977). This causes 2D nucleation on terraces, and finally,
growth hillocks result, as illustrated in Figure 4.17(b). When the growth is governed
by 2D nucleation, the double-domain surface structure is supposed to form because of
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175
n
Figure 4.16 Surface adsorbate concentration, n , and supersaturation ratio, a, as a
function o f distance from the steps for different CH 4 concentrations in
H2, where «s, n0, occ, as are the adsorbate concentration at the steps,
the steady-state concentration o f adsorbate at the steps, the critical
supersaturation ratio for the 2D nucleation, and the supersaturation
ratio at the steps, respectively: (a) low, (b) medium, and (c) high CH4
concentrations.
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176
o
O
t
o — *
1 0 -— Q____ CL—
Q.
(a)
1 0 ^ -0
o c fe
V
(b)
O
2 — io « - o
odS b —
o
IQ .
TO ^- O
2D nuclei
O
o
o
o
o
o
(c)
Figure 4.17 Growth mechanisms for different CH 4 concentrations in H2, but for the
same misorientation angle o f substrates : (a) step-flow growth with a low
CH4, (b) hillock growth with a medium CH4, and (c) random growth
with a high CH 4 concentration.
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177
the alternating growth of the 2 x 1 and 1x 2 domains.
As the CH 4 concentration is further increased, a larger number o f adsorbates
occur on the surface, producing much lower mobility and much higher supersaturation
of adsorbates on terraces as given in Figure 4.16(c). Adsorbates w ill meet others as
soon as they land on terraces from the gas phase and then form clusters before they
migrate to the steps newly created by 2D nucleation [Figure 4.17(c)]. Growth hillocks
would lose their fourfold symmetry although they are formed. It is considered that
adsorbates incorporate into the crystal just on the sites where they sit, with almost no
migration. In this case, random growth morphology would eventually result as in the
case of the 6 % CH 4 film.
4.6. Summary
Etching and deposition experiments were carried out on the 0.1°, 3.5°, and
11.0° o ff (001) diamond substrates. The well-oriented surface was etched mainly by
creation and regression o f new steps causing etch pits with the four-fold symmetry,
while the highly misoriented surface was etched dominantly by regression of pre­
existing steps.
Remarkably different surface morphologies were observed on homoepitaxially
grown diamond films with the surface misorientation o f diamond (001 ) substrates:
growth hillocks and macrosteps. Growth hillocks were formed due to the lack of
surface steps on the well-oriented substrate. On the other hand, growth on the
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178
misoriented surface proceeded via step flow along the < 110> directions to produce
macrosteps. Step-flow growth resulted in higher growth rates than hillock growth. High
quality o f films was confirmed with Raman spectra. RHEED showed that the films
were single crystals and that their surfaces were composed of the 2x 1 and 1x2 double­
domain structure.
Homoepitaxial diamond films grown on the misoriented (001) substrates showed
the strong dependence of surface morphologies and structures on the CH4
concentrations. Step-flow growth with the surface close to the 1x2 single-domain
structure was observed after being grown with 1% CH4, while growth hillocks and
random growth morphology with 2 x 1 and 1x2 double-domain surfaces formed when
grown with 2% and 6 % CH4, respectively. However, the extended growth produced
growth hillocks at 1% CH4 and macrosteps at 2% CH4. The dependence of surface
morphologies and structures on the CH4 concentrations are attributed to lower mobility
and shorter diffusion length of adsorbates on the surface at higher CH4 concentrations.
Growth on the misoriented diamond substrates at 875 and 1200 °C showed that
step bunching for macrosteps are more likely to occur at a lower temperature. Taking
into account the surface diffusion as well as the step bunching, the growth at high
temperatures seems to be more promising for the deposition of the smooth, high-quality
films.
Step-flow growth with the single-domain surface is believed to produce higherquality films with fewer lattice defects than other growth modes. It is likely that the
step-flow growth is favored with increasing the misorientation angles, lowering the
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179
methane concentrations, and increasing the substrate temperatures. This study suggests
that the deposition condition for the (001 ) homoepitaxial diamond films is optimized,
from the point of view of surface morphologies, with the misorientation angle of
approximately 3-5°, the methane concentration o f less than 1%, and the substrate
temperature of approximately 1200 °C. However, the optimal deposition condition may
differ, depending on the detailed applications of CVD diamond films. Thus, this
condition has to be established in terms o f each purpose for exploiting the properties or
characteristics ot CVD diamond. Along the line of this study, the electrical properties
of (001) homoepitaxial diamond films w ill be characterized as a function o f deposition
parameters in the near future by measuring
the carrier mobilities and I-V
characteristics.
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180
Chapter 5
DIAMOND (001) SURFACE STRUCTURE
STUDIED USING RHEED
5.1. Introduction
There has been experimental evidence indicating that steps and kinks play a
crucial role in the CVD growth of the (001) homoepitaxial diamond film: macrosteps
(Badzian and Badzian, 1993; Schermer et al., 1994), growth hillocks (Everson and
Tamor, 1992; Vitton et al., 1993), dimer row extension (Tsuno et al., 1991; Kawarada
et al., 1994), etc. Thus, the CVD diamond growth processes have to be considered in
terms of the reaction between the reactive gas species such as atomic hydrogen and
hydrocarbon precursors and diamond surfaces with steps and kinks. Little has been
reported, however, in the literature on the step and domain structures of the diamond
(001) surface.
This chapter addresses the diamond (001) surface structure of substrates
annealed in H plasma and of homoepitaxially grown films, studied using RHEED.
RHEED has been proven to be a useful technique for the investigation of surfaces, as
reviewed in section 3.4. The feature o f glancing incidence makes RHEED sensitive to
the surfaces. Symmetry and intensity distribution o f RHEED spots are related to the
surface structure involved. This study investigated the surface reconstruction and the
domain and step structure of the diamond (001 ) surface by comparing the intensities of
two series of the half-order diffraction spots in RHEED patterns.
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181
5.2. Literature review
On the diamond (001) surface truncated from the bulk, two dangling bonds are
created for each surface carbon atom. This energetically unfavorable situation may be
resolved by termination of dangling bonds with foreign atoms or by reconstruction of
surface carbon atoms, depending on the surface preparation. During CVD diamond
growth, the diamond surfaces are mostly hydrogen-terminated due to the abundance of
hydrogen atoms in the growth environment. Hydrogen atoms are known to stabilize the
diamond surfaces by maintaining sp3 hybridization of surface carbon atoms as well as
to prevent the formation o f graphite (Badzian and DeVries, 1988; Kondoh et al.,
1992). In the presence of the super-equilibrium concentration of atomic hydrogen,
therefore, diamond growth is favored to graphite deposition. Thus, the hydrogenterminated diamond surfaces play an important role in diamond growth by CVD
(Garrison etal., 1992; Harris and Goodwin, 1993; Zhu et al., 1993).
When dosing atomic hydrogen onto the clean 2x1 diamond (001) surface,
hydrogen atoms chemisorb and then profoundly affect the surface structure.
Chemisorption of hydrogen atoms on the diamond (001) surface may take place with
either l x l or 2x1 structure (Hamza et al., 1990; Thomas et al., 1992). The most clear
assignments to the lx l and 2 x 1 structures are a monohydride configuration with one
hydrogen atom per surface carbon atom and a dihydride configuration with two
hydrogen atoms per surface carbon atom, respectively, as shown in Figure 2.4. These
hydrogenated diamond (001) surface structures have been under active debate for many
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years.
In 1977, Lurie and Wilson observed a lx l LEED pattern for the as-polished
diamond (001) surface. I-V measurements in LEED suggested that the l x l surface
structure was that of the truncated bulk. Rutherford backscattering and nuclear reaction
analysis o f the as-polished diamond (001 ) surface showed that this surface was
terminated by hydrogen atoms as well as oxygen atoms (Derry et al., 1983). Using
photon-stimulated desorption spectroscopy, Pate (1986) found that the as-polished lx l
surface was terminated by hydrogen.
On the diamond (001) surface subjected to heating for 5-10 min at 1300 °C in
UHV, Lurie and Wilson (1977) observed that a lx l LEED pattern of the as-polished
surface changed to a 2x1 pattern. Hamza et al. (1990) also investigated the diamond
(001) surface using LEED. The as-polished diamond (001) surface exhibited no LEED
pattern, but l x l patterns occurred with heating to 230 °C in UHV. Upon further
heating, the half-order LEED spots indicating the 2x1 reconstruction of the diamond
(001) surface began to appear at a temperature of 970°C. The 2x1 structure was found
to convert back to the lx l structure by dosing atomic hydrogen at -93 °C and by
subsequent annealing up to 430 °C. Lee and Apai (1993) observed the l x l LEED
patterns from the acid-cleaned diamond (001) surface. Upon heating the surface above
1000 °C, the l x l pattern changed to an apparent 2x1 structure that could be reversibly
converted to the l x l structure by atomic hydrogen dosing. Thomas et al. (1992)
observed the l x l configuration for the acid-cleaned diamond (001 ) surface, which upon
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annealing in UHV began to transform to the 2x1 configuration at a temperature of
approximately 800 °C. It was found, however, that the 2x1 structure did not convert
back to the lx l structure even after substantial dosing with atomic hydrogen at room
temperature.
Hamza et al. (1990) reported temperature-programmed desorption (TPD) results
for the hydrogen-terminated lx l diamond (001) surface, with the desorption peak
occurring around 800 °C. The lx l structure, which was obtained by exposing the 2x1
surface to atomic hydrogen, began to change to the 2x1 structure at 970 °C. The
continued presence of hydrogen on the surface annealed up to 1250 °C was detected by
electron-stimulated desorption. Thus, the TPD peak at 800 °C was assigned to
hydrogen desorption in the lx l dihydride, leaving the 2x 1 monohydride state.
Beginning with the hydrogenated 2x1 diamond (001) surface, on the other hand,
Thomas et al. (1992) observed the desorption peak o f hydrogen near 900 °C. The
surface was kept up with the same 2x 1 structure both before and after the desorption
peak on the diamond (001) surface. It was not clear whether the 2x1 structure after the
thermal desorption corresponded to a clean surface or a monohydride surface.
Direct imaging o f the surface atomic structure revealed evidence for both the
lx l and 2x1 structures o f the as-grown diamond (001) surface. Badzian and Badzian
(1993) obtained atomically resolved AFM images indicating the l x l configuration for
the diamond (001) surface homoepitaxially grown at 0.8% CH4 and 900 °C. However,
the 2x 1 dimerized structure of the as-grown diamond (001 ) surface was observed more
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184
frequently by STM (Tsuno et al., 1991; Busmann et al., 1992 ; Kawarada et al., 1994)
and AFM (Sutcu et al., 1992a, b).
Several theoretical studies on the stability of the hydrogenated diamond (001)
surface have been reported to date. Zheng and Smith (1991) found by SLAB-MINDO
calculations that the stretched lx l dihydride structure had a lower energy than the 2x 1
monohydride structure. Calculations performed by Yang et al. (1993b) using ab initio
methods showed that the lx l dihydride structure was energetically unstable, and the
3x1 structure with alternating monohydride and dihydride was favored over the 2x1
monohydride structure. Using MD simulation, Skokov et al. (1994b) also reported the
3x1 structure with alternating monohydride and dihydride configurations as the most
stable structure for the hydrogenated diamond (001 ) surface.
Yang and D ’ Evelyn (1992a, b) observed in their molecular mechanics (MM)
calculations that the 2 x 1 monohydride structure was the most stable phase over the
temperature range o f 25-1200 °C, followed in stability by the 2x1 clean surface. The
lx l dihydride structure was found to be thermodynamically unstable with respect to
dehydrogenation due to the extremely large steric repulsion between surface hydrogen
atoms. Thus, the monohydride structure was predicted to be the dominant phase under
typical CVD conditions. Mehandru and Anderson (1991) and Jing and Whitten (1994)
also reported that the l x l dihydride phase was unfavorable to the desorption of
hydrogen and the formation of the 2x1 monohydride phase. Overall, theoretical as well
as experimental studies have not yet produced a clear consensus regarding the structure
of hydrogenated diamond (001 ) surface.
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185
As reviewed in section 2.2.1, the step configurations and related domain
structure have been a critical issue for the Si (001) surface because they significantly
affect the epitaxial growth processes and the resultant film qualities. Compared to
studies performed for the l x l and 2 x 1 structures of the diamond (001 ) surface,
however, much less has been known about the step and domain structure of this
surface. There had been almost no concern about step structure and step-flow growth
on the diamond (001) surface until the first STM paper (Tsuno et al., 1991) appeared in
the CVD diamond community. The 2x1 and 1x2 double-domain structure with single­
layer and double-layer steps was not only observed but diamond growth was also found
to occur through the extension of dimer rows on the diamond (001) surface. Since then,
several groups achieved similar observations on this surface (Busmann et al., 1992;
Sutcu et al., 1992a, b; Kawarada et al., 1994). Very recently Tsuno et al. (1994)
observed, using LEED and STM, the 2x1 single-domain structure of the diamond (001)
surface which was homoepitaxially grown on the substrate misoriented 4.3° toward the
[110] direction. Step-flow growth took place on this single-domain surface mostly with
Db steps.
5.3. Experimental details
The surface misorientation angles o f HP/HT synthetic type-Ib diamond (001)
substrates used in this study are given in Table 4.1. Prior to H-plasma annealing or
diamond growth, substrates were consecutively cleaned in boiled sulfuric acid saturated
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186
with C r0 3, in boiled aqua regia, in a 1:1 solution of HF and H N 03, in distilled water,
and in acetone for 30 min for each cleaning process. The H-plasma annealing of
substrates and homoepitaxial diamond growth were carried out using an MPACVD
system with a quartz-tube reactor. CVD conditions were summarized in Table 5.1. The
H-plasma annealing was performed for 10 to 30 min at the substrate temperatures of
650 to 1300 °C with pure H2 gas. Growth experiments were carried out for 30 min at
875 or 1200 °C with the gas mixture of 0.5% CH 4 in H2. In studying the structure of
as-grown diamond surfaces, the turning-off procedure o f plasma is very important
because it may affect the final surface structure. During growth, samples were quickly
dropped down approximately 40 cm below the center o f plasma cavity inside the quartz
tube of the CVD system so that the topmost surface structure could be frozen out as
close to a real growth surface structure as possible.
RHEED was used to characterize the diamond (001) surface structure of
substrates annealed in H plasma and of homoepitaxially grown diamond films. RHEED
experiments were performed using a conventional TEM (Philips 420T). RHEED
patterns were taken in the [100] azimuth with the accelerating voltage o f 40 kV and
with the glancing angles o f 1° to 4 °.
5.4. Results
5.4.1. Reconstruction o f diamond (001) surfaces in H plasma
As given in Figure 5.1, an acid-cleaned diamond (001) surface shows the lx l
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Table 5.1 CVD conditions for H-plasma annealing and homoepitaxial growth of diamond (001) surfaces.
CVD conditions
Misorientation angles of substrates
CH4 concentration in H2
Total gas flow rate
Gas pressure
Substrate temperature
H-plasma annealing
Homoepitaxial growth
0.1°, 3.5°, 11.0°
3.1°
0.1°, 3.5°, 11.0°
3.1°
0% (pure H2)
0%
0.5%
0.5 %
100 seem
100 seem
100 seem
100 seem
80-150 Torr
80 Torr
80 Torr
80 Torr
650, 875, 1000, 1200,
875 °C
1200 °C
875 °C
1300 °C
OO
<1
Figure 5.1 RHEED pattern o f an acid-cleaned diamond (001) surface
taken w ith the 11001 azimuth.
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RHEED pattern. Three possible configurations can be assigned to this surface structure.
One is the dihydride configuration with two H atoms per surface carbon atom (Hamza
et al., 1990), shown in Figure 2.4(a). However, theoretical studies predicted that the
dihydride structure was unstable relative to the monohydride structure because of
severe steric repulsion between surface hydrogen atoms (Yang and D ’Evelyn, 1992a, b;
Mehandru and Anderson. 1991; Jing and Whitten,
1994). The second possible
assignment is the disordered surface structure consisting of both monohydride and
dihydride species. A lack of a long-range order on the surface results in the observation
o f only lx l LEED patterns from the diamond (001) surface (Yang and D’ Evelyn,
1992a). The surfaces of polished diamond (001) samples are considered to be
disordered due to the mechanical damage caused by polishing. The third possibility is
the oxygen-termination of this surface because the samples were exposed to the strong
oxidizing chemical of C r0 3 during the chemical cleaning. The oxygen-terminated
diamond (001) surface was observed to exhibit the l x l structure (Thomas et al., 1992).
Thus, the second or third assignment is more reasonable for this lx l surface structure
although the lx l dihydride configuration may be possible in a local area.
Figure 5.2 shows RHEED patterns of the 0.1° and 3.5° o ff surfaces annealed at
650 to 1000 °C for 30 min and at 1200 and 1300 °C for 10 min in H plasma, taken
with the azimuth of [100]. A ll diamond (001) surfaces annealed in H plasma under the
experimental conditions o f this study exhibit the 2 x 1 configuration where surface
carbon atoms have been known to reconstruct and form the dimerized monohydride
structure with one H atom bonded to each carbon atom in dimers (Hamza et al., 1990;
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190
Figure 5.2 RHEED patterns o f diamond (001) surfaces annealed in H plasma at (a)
650. (b) 875 and (c) 1000 °C for 30 min. and (d) 1200 and (e) 1300 °C for
10 min. taken w ith the [ 100] azimuth. The left and right patterns are taken
from the 0.1° and 3.5° o ff substrates, respectively. L 1/: and L( in (b)
denote the half-order and first-order Laue rings, respectively, and
arrowheads in (b) and (c) indicate the type-A 2x1 half-order spots.
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Figure 5.2 (com.)
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Tsuno et al., 1991; Thomas et al., 1992; Busmann et al., 1992; Kawarada et al.,
1994). Prior to H-plasma annealing, an acid-cleaned substrate revealed the clear lx l
RHEED pattern. After being exposed to H plasma at 650 to 1300 °C, however, all
(001) surfaces of at least 15 substrates investigated till now have been found to show
the reconstructed 2x 1 structure.
In Figure 5.2. the half-order spots indicating the 2x1 reconstruction of the
diamond (001) surface are faint at 650 °C, but become brighter above 875 °C. The
intensity of half-order spots gets weaker again at 1300 °C, which is probably due to the
increased surface roughness caused by H-plasma etching. It was observed that
annealing in H plasma for 1 hr at 1300 °C gave rise to severe etching on these surfaces,
as shown in Figure 4.1. The half-order spots are observed on the surfaces annealed in
H plasma at the low temperature o f 650 °C although they are not bright. Upon
annealing in UHV, Hamza et al. (1990) and Thomas et al. (1992) reported that the
half-order LEED spots began to appear at approximately 800 °C and 970 °C,
respectively.
5.4.2. Domain structure of diamond (001) surfaces
For analyzing RHEED patterns in detail, indexing of diffraction spots has to be
done. Schematic drawings were used to help the understanding of RHEED analysis.
Figure 5.3(a) shows a setup o f a sample misoriented toward the [1 TO] direction for
RHEED, on whose surface steps are down from the lower right to the upper left. For
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193
electron < io o >
beam 1
step down
/ SB * \
O
O
O
O
O
O
O
O
O
O
O
[110]
o
o
o
o
o
o
[ 110]
(b)
(a)
21 10 01 12
11
il o
01
•
1-1
•
•
01*
10
oI q
00
(c)
(d)
Figure 5.3 Schematic of sample set-up for RHEED, real and reciprocal lattices, and a
predicted RHEED pattern o f the diamond (001) surface : (a) geometry of
sample setup for RHEED, (b) unit cells of 2x1 and 1x2 structures in the
real space, (c) superposed reciprocal lattice of 2 x 1 and 1x2 structures, and
(d) a predicted RHEED pattern with the incident beam along [100] and
with the glancing angle o f 0°. The integral-order, type-A 2x1 half-order,
and type-B 1x2 half-order reciprocal rods in (c) and their reflection spots in
(d) are represented by large closed circles, small closed circles, and small
open circles, respectively.
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194
the misoriented (001 ) surface, adjacent flat terraces are assumed to be separated by a
single-layer step. Such an arrangement of the surface introduces two types of terraces
and two types of single-layer steps, based on the dimer-type 2 x 1 and 1x2 reconstruction
of the diamond (001) surface confirmed by STM (Tsuno et al., 1991; Busmann et al.,
1992; Kawarada et al., 1994). Single-layer steps on the diamond (001) surface are
labeled SAand SB, following Chadi’s notation (Chadi, 1987). Terraces are indicated as
type A or B, depending on the relations of dimer row directions with the step edges.
Figure 5.3(b) and (c) show the unit cells of the 2x1 (type-A terrace) and 1x2 (type-B
terrace) structures in the real space and the superimposed reciprocal lattice o f the 2 x 1
and 1x2 structures, respectively. In Figure 5.3(c), reciprocal lattice rods point up out of
paper, and an electron beam grazes the surface in the [100] direction. RHEED under
such a condition produces the pattern schematically drawn in Figure 5.3(d), where
small closed and open circles in the half-order Laue ring (L 1/2) denote the half-order
spots diffracted from the type-A and type-B terraces, respectively. Diffraction spots are
indexed on the basis o f the superposed reciprocal lattice of the 2 x 1 and 1x 2 surface
structure shown in Figure 5.3(c).
In Figure 5.2, the patterns taken from the 0.1° o ff surfaces annealed at 875 to
1300 °C in H plasma show the symmetrical intensity distribution o f the half-order
spots. On the other hand, the 3.5° o ff surfaces reveal, at 875 and 1000 °C, that the
type-A 2x1 half-order spots (indicated by arrowheads) have much stronger intensities
than the type-B 1x2 half-order spots [Figure 5.2(b) and (c)]. A t 1000 °C, however,
intensity difference between the type-A and type-B half-order spots is reduced as
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195
compared to that of 875 °C. Contrarily, at 1200 and 1300 °C, the 3.5° o ff surfaces
exhibit no alternate intensity variation o f RHEED spots along the half-order Laue ring
[Figure 5.2(d) and (e)].
As addressed in section 3.4.3, the kinematic treatment for RHEED intensity
showed that intensities o f the type-A and type-B half-order spots were proportional to
the square of the areas of the type-A and type-B domains, respectively. From the
comparison of intensities between two series of the half-order spots, therefore, the 3.5°
o ff surfaces are close to the 2x1 single-domain structure upon annealing in H plasma at
875 and 1000 °C, on which the type-A terraces are wider than the type-B terraces. On
the 3.5° o ff surfaces at 1200 and 1300 °C and on the 0.1 “o ff surfaces at 875 to 1300
°C, however, the areas o f the type-A and type-B terraces are almost equal (i.e., 2x1
and
1x2
double-domain
structure).
The
surfaces
11.0°
misoriented
toward
approximately the [100] direction were studied at the same temperature range. The
11.0 ° o ff surfaces showed the double-domain structure without the alternate variation
of intensity between two series of the half-order spots at these temperatures.
As shown in Figure 5.2(a), at 650 “C, intensity o f the half-order spots is too
weak to characterize the domain structure. Upon H-plasma annealing, surface atoms
are to be necessarily rearranged or etched out to reach the equilibrium surface
structure. But little surface diffusion or etching is considered to occur at 650 °C even if
the surfaces reconstruct to the 2x1 configuration. This temperature seems to be too low
to obtain the equilibrium surface structure.
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196
Figure 5.4 shows RHEED patterns of the films grown on the 0.1°, 3.5°, and
11.0° o ff substrates for 30 min at 1200 °C with 0.5% CH4 in H2. On the 0.1° o ff film
surface [Figure 5.4(a)], intensities o f the type-A and type-B half-order spots do not
change alternately. On the contrary, the 3.5° o ff film surface [Figure 5.4(b)] reveals
that the type-B half-order spots are far brighter than the type-A spots. The as-grown
surface 11.0° tilted toward the [100] direction [Figure 5.4(c)] shows the symmetric
intensity distribution along the half-order spots. Upon the growth at 1200°C with 0.5%
CH4, therefore, when the misorientation angle is too small (i.e., 0.1° off) or the
nominal misorientation direction is considerably deviated from the < 110> direction
(i.e., 11.0° off), the double-domain structure results. When the surface is misoriented
approximately toward the <110> direction (i.e., 3.5° off), however, the surface is close
to the type-B single-domain structure. It is worth noting that the 3.5° o ff surface
exhibiting the double-domain structure in H plasma at 1200 °C transforms to the
surface close to the single-domain structure during growth at 1200 °C.
The surface structure was investigated in sequence after pre-annealing of a
substrate in H plasma, homoepitaxial growth, and post-annealing o f the as-grown layer
in H plasma at 875 °C. This sample was also set up for RHEED as shown in Figure
5.3. The substrate used is 3.1° misoriented with 0.8° and 3.0° toward [110] and [110],
respectively, as shown in Table 4.1. RHEED patterns taken after each step are given in
Figure 5.5. After pre-annealing in H plasma for 10 min at 875 °C [Figure 5.5(a)],
intensity of the type-A half-order spots is stronger than that o f the type-B half-order
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197
Figure 5.4 RHEED patterns o f (001) homoepitaxial diamond film s grown for 30
min at 1200 °C. 0.5% C H 4 in H: on (a) 0.1°, (b) 3.5°. and (c) 11.0°
o ff substrates, taken w ith the [ 100] azimuth. The type-B 1x2 half-order
spots in (b) are marked by arrowheads.
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Figure 5.5 RHEED patterns of diamond (001) surfaces (a) pre-annealed in H plasma
for 10 min. (b) grown for 30 min with 0.5% CH4 in H2, and (c) post­
annealed in H plasma for 5 min at 875 °C. taken with the [ 100] azimuth.
Arrowheads indicate the type-A half-order spots.
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spots. However, homoepitaxial growth for 30 min at 875 °C with 0.5% CH 4 makes the
type-B half-order spots brighter, as can be seen in Figure 5.5(b). The intensity
alternation between two series of the half-order spots is reversed after homoepitaxial
growth. The as-grown sample was treated again in H plasma for 5 min. The post­
annealing in H plasma converts again the type-B terrace dominant surface developed by
growth to the type-A terrace dominant surface [Figure 5.5(c)]. Consequently, the 3.1°
o ff surface pre-annealed, post-annealed in H plasma, or homoepitaxially grown is close
to the single-domain structure under the above conditions. But it should be noted that
type-A terraces dominate the H-plasma annealed surface while type-B terraces are the
major phase o f the as-grown surface.
RHEED patterns of the films grown on the 3.1° o ff substrates at different CH 4
concentrations were given in Figure 4.13. A t 0.5% and 1% CH 4 [Figure 4.13(a) and
(b)], the type-B spots are bright and the type-A spots are faint. The intensity difference
between two types of the half-order spots is much reduced at 2% CH4 [Figure 4.13(c)]
and the alternate intensity variation o f the half-order spots is not observed at 6 % CH 4
[Figure 4.13(d)]. Thus, the 3.1° o ff surfaces are close to the single-domain structure
with wider type-B terraces on the films grown with low CH4 concentrations of 0.5%
and 1 %, but the double-domain structure is developed on the surfaces grown with high
CH 4 concentrations of 2% and 6 %.
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200
5.5. Discussion
5.5.1. Diamond (001) surface reconstruction
There have been a few experimental studies on the reconstruction of the
diamond (001) surface to date. LEED investigations on the diamond (001) surface
reported that upon annealing in UHV, all substrates did not reveal the conversion of the
lx l structure to the 2x1 structure. Upon heating in UHV for 5-10 min at 1300 °C,
Lurie and Wilson (1977) observed that one out of three samples with the l x l structure
reconstructed to the 2x1 structure. Hamza et al. (1990) found that upon heating in
UHV only 60% of diamond (001) surfaces that had exhibited the l x l
state
reconstructed to the 2x1 state. It was shown that the LEED half-order spots indicating
the 2x1 reconstruction began to appear at 970 °C, with their intensities continuously
increasing on annealing up to 1260 °C. Thomas et al. (1992) also found that not all, but
more than 90% of diamond (001) surfaces showing the lx l configuration transformed
to the 2x1 configuration upon annealing in UHV. In their LEED experiments,
conversion from the l x l structure to the 2x1 structure started at approximately 800 °C
and completed by 1050 °C. Hamza et al. (1990) reported that a higher intensity of
residual oxygen was detected on electron stimulated desorption from the surfaces that
had failed to reconstruct upon heating in UHV.
On the contrary, in this study, annealing experiments in H plasma show
considerably different results. The 2x1-reconstructed structure was observed on a ll
diamond (001) surfaces after being exposed to H plasma at 650 to 1300 °C, as given
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201
in Figure 5.2. The half-order spots indicating the 2x1 reconstruction took place on the
surface annealed in H plasma even at 650 °C whereas upon annealing in UHV, the
transformation of the l x l structure to 2x1 structure began at approximately 800
(Thomas et al., 1992) or 970 °C (Hamza et al., 1990). This disparity in the onset
temperature of reconstruction on the diamond (001) surface is probably due to
differences in the environments o f UHV and H plasma. It is expected that the surface
would be not only more active in H plasma than in UHV but atomic hydrogen might
also play an important role in the reconstruction of the surface. Atomic hydrogen may
eliminate residual oxygen on the surface, making the reconstruction occur more
readily. Thus, reconstruction on the diamond (001) surface occurs at a much lower
temperature in H plasma than in UHV. Accordingly, one can know that CVD
diamond growth in reality proceeds on the reconstructed surface over the range o f
temperatures investigated.
5.5.2. Diamond (001) surface structure
It has been well recognized that the diamond (001) surface reconstructs to the
dimer-type 2x1 structure upon annealing in UHV (Lurie and Wilson, 1997; Hamza et
al., 1990; Thomas et al., 1992) as well as in H plasma (Tsuno et al., 1991; Busmann et
al., 1992; Kawarada et al., 1994; Aizawa et al., 1993; Ando et al., 1994). Not much is
known, however, about the domain or step structure of this surface although this is of
great importance for understanding the growth mechanism of CVD diamond films.
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Thus, it is useful to begin our discussion by briefly summarizing the reports on the Si
(001) surface since it has been intensively studied recently. A full-scale review on the
Si (001) surface was given in section 2.2 and then a brief summary is presented here.
One expects similarities between Si and diamond surfaces because both not only possess
the same bulk crystal structure but also reveal the dimer-type 2x1 reconstruction on the
(001) surface. But there would also be differences due to different bonding energies as
well as to different growth processes such as MBE for Si and CVD for diamond.
Chadi (1987) has performed semiempirical tight-binding-based total-energy
calculations for the formation energies of four different step configurations on the Si
(001) surface. Single-layer SA steps have the lowest formation energy, but double-layer
D b steps are energetically more favorable than alternating single-layer SA+SB steps on
the surface tilted toward [110] or [ 1TO]. It has been found that DA steps are
significantly higher in energy than DB steps and are also unstable relative to alternating
SA+S B steps. The stability of DB steps relative to DA or SA+S B steps on the
misoriented Si (001) surface agrees with experimental observations (Wierenga et al.,
1987; G riffith et al., 1988, 1989; Swartzentruber et al., 1989). But his results could
not account for the presence of alternating single-layer SA+SB steps on the slightly
misoriented surface (Hoeven et al., 1989a, b; Swartzentruber et al., 1989).
To figure out the equilibrium surface structure, Alerhand et al. (1990) and Poon et
al. (1990) have pointed out that surface strain relaxation and thermal roughening of
steps should be considered as well as step formation energies. The dimerized
reconstruction induces anisotropic surface stresses on terraces: tensile and compressive
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stresses along and across the dimerization direction, respectively (Alerhand et al.,
1988; Payne et al., 1989). On a single-layer stepped surface, anisotropic surface
stresses cancel each other across the step edges, but this relaxation does not occur on a
double-layer stepped surface because it comprises the same type of terraces. Thus, the
surface strain relaxation lowers the energy o f the single-layer stepped surface. Thermal
effect also reduces the free energy of the single-layer stepped surface due to an increase
in the configuration entropy associated with ragging o f SB steps. Recent work
elaborated by Tong and Bennett (1991) and Pehlke and Tersoff (1991) has shown that
the transition from the single-layer to double-layer stepped surface gradually occurs
with the misorientation angles. As the misorientation angles increase, the areas of typeB and type-A terraces continuously increase and decrease, respectively, while only
single-layer steps occur. Above approximately 1.5°, alternating SA+SB steps start to
collapse into DB steps. The content o f DB steps monotonically increases until only
double-layer steps exist above 4-5°.
In Figure 5.2, the 0.1° off diamond surfaces annealed at 875 °C and 1000 °C
show the double-domain structure, but the 3.5° o ff surfaces at the same temperatures
are close to the single-domain structure where type-A terraces are dominant. This
indicates th a t the diamond (001) surface is the double domain at small misorientation
angles and the single domain at large misorientation angles. The surface structure
seems to be also dependent upon annealing temperatures. The 3.5° o ff surface annealed
at 875 °C exhibits strong type-A half-order spots and faint type-B spots, but intensity
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difference reduces at 1000 °C and finally no intensity variation is observed above 1200
°C. It can be, thus, postulated that the misorientation angles for the transition between
the double-domain and single-domain surfaces become larger at higher temperatures on
the diamond (001) surface, like the Si (001) surface. The diamond (001) surface during
annealing in H plasma shows almost the same tendency as that of the UHV-annealed Si
(001) surface in the evolution of the surface structure in terms of the domain structure
as a function o f the surface misorientation angles and annealing temperatures, except
for the dominant terrace type. Thus, it is considered that surface strain relaxation and
thermal fluctuation of steps also play an important role in determining the equilibrium
structure of the diamond (001) surface, as they do on the Si (001) surface.
When the diamond (001) surface is close to the single-domain structure, the
type-A half-order spots are stronger than the type-B spots after annealing in H plasma
and vice versa after homoepitaxial growth o f diamond. This implies that the terraces
producing the brighter half-order spots are wider than the other, as addressed in section
3.4.3. Unequal areas of type-A and type-B terraces can be accompanied by either
unequal spacing of SA and SB steps on the single-layer stepped surface or the presence
o f double-layer steps together with single-layer steps. Even if the surface is single-layer
stepped with unequally spaced SA and SB steps, this state is on the way of transition to
the double-layer stepped surface. B u t it is thought that the 3.5° and 3 .1 ° o f f surfaces
which are close to the single-domain structure, comprise double-layer steps mixed
with single-layer steps. The assumption on the existence of double-layer steps on these
surfaces is supported by the results o f Tsuno et al. (1994) and the STM observations of
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205
this study given in Chapter 6. Tsuno et al. (1994) reported that LEED revealed far
brighter intensities in one series o f the half-order spots on the as-grown 4.3° o ff surface
and then STM images showed mostly double-layer DB steps. The transition from the
single-layer to double-layer stepped surfaces with the misorientation angles is presumed
to gradually occur on the diamond (001) surface, as it does on the Si (001) surface. The
3.1° and 3.5° o ff surfaces close to the single-domain structure may lie in the midway of
the transition between the single-layer and double-layer stepped surfaces.
5.5.3. Relative stabilities o f steps on diamond (001) surfaces
It is o f great value to calculate the step formation energies for possible step
configurations, which are not available at the moment for the diamond (001) surface.
But the relative stabilities between several step structures can be inferred from the
RHEED results.
When the surface is misoriented above a critical angle along [110] or [110], the
double-layer stepped surface is more stable than the single-layer stepped surface. I f
kinks are present, however, single-layer and double-layer steps can coexist (Hoeven et
al., 1989a, b; Griffith et al., 1989; Swartzentruber et al., 1990). For the substrates
used in this study, kinks are forcibly introduced because the nominal misorientation
directions are deviated from the exact [110] or [ llO ] direction, as given in Table 4.1.
I f D a steps have the lowest formation energy and then occur on the annealed diamond
(001) surface, DB steps would be created locally along kinks. But if DB steps are higher
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206
in energy than alternating SA+S B steps, DB steps split into SA+SB steps, then DA steps
and SA+SB steps would be present along step edges and at kinked regions, respectively,
on the annealed surface. The fact that alternating single-layer SA+SB steps have a lower
formation energy than DB steps on the annealed diamond (001) surface is supported by
the observation of the double-domain structure on the surface 11.0° tilted toward
approximately the [100] direction. Otherwise, the 11.0° surface would produce a nearly
single-domain RHEED pattern. The same explanation is applicable for the as-grown
surface on which DB steps have a lower formation energy than alternating SA+ SB, and
Da steps have the highest energy. Conclusively, the step form ation energies increase
in the order o f DA, SA+ S B, and DB types on the H-plasma annealed diamond (001)
surface and in the order o f D B, SA+ S B, and DA types on the as-grown diamond (001)
surface.
Double-layer steps occurring on the Si (001) surface are always o f type DB, no
matter whether annealed in U H V (Wierenga et al., 1987; Griffith et al., 1988, 1989;
Swartzentruber et al., 1989) o r grown by M B E (Hoeven et al., 1989a, b, 1990a). The
RHEED results o f this study that the type-A half-order spots are f a r brighter than the
type-B spots on the 3 .1 ° and 3 .5 ° o f f diamond (001) surfaces annealed in H plasma
at 875 or 1000 °C, however, indicate that DA steps can exist on these surfaces. The
question of why DA steps can be stable on the annealed diamond (001) surface is
addressed here.
To consider the stability of DA steps on the annealed diamond (001) surface, it
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207
is better to examine first the step-edge structures on the Si (001) surface. There can be
two different step-edge structures, rebonded and nonbonded, for SB, DA, and DB steps
on the Si (001) surface (Chadi, 1987). For the nonbonded step edges, a dangling bond
is created on each second-layer edge atom for SB and DB steps and on each third-layer
edge atom for DA steps. As shown in Figure 2.2, edge atoms are rebonded to lower
terrace atoms by forming dimer-like bonds, which eliminates dangling bonds o f edge
atoms but creates bond-length strains at the edges. The strains are the smallest in DB
and the largest in DA steps. In rebonding o f edge atoms, the energies relieved by
removing dangling bonds exceed the strain energies. Thus, the step formation energies
increase in the order of SA, DB, SB, and DA types with rebonded structures (Chadi,
1987).
It is to be noted that there are hardly any impurity atoms to satisfy dangling
bonds o f nonbonded edge atoms during annealing Si in UHV or growing Si by MBE. It
is reasonable, therefore, that edge atoms are rebonded to reduce formation energies of
steps on the Si (001) surface. However, the environment of CVD for diamond is quite
different not only during annealing in H plasma but also growing in hydrocarbon
plasma. H plasma of CVD produces plenty o f H atoms, which have been known to
react with the diamond (001) surface to form H-terminated surface with monohydride
structure (Hamza et al., 1990; Aizawa et al., 1993; Ando et al., 1994). Since H atoms
satisfy dangling bonds of edge atoms, rebonding o f edge atoms would not occur. In
Figure 5.6 , the step structures for SA, SB, DA and DB types with H atoms bonded to
dangling bonds are proposed. H termination o f edge atoms appears to change the
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208
Figure 5.6 Step structures for (a) SA, (b) SB, (c) DA, and (d) DB types with H atoms
bonded to dangling bonds on diamond (001) surface. Open and closed
circles denote carbon and H atoms, respectively. Larger circles are used
for upper-terrace atoms. The dimerization direction of surface carbon
atoms is along the <110> directions.
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210
relative stabilities between four types o f steps so that DA steps are more stable than D B
or SA+SB steps on the annealed diamond (001) surface.
The environment during CVD diamond growth in hydrocarbon plasma is quite
complicated because there are hydrocarbon radicals as well as atomic H. Surface
structures would be more complex during diamond growth than during annealing in H
plasma. It is thought that diamond growth occurs at the step edges by adsorption of
hydrocarbon radicals with a subsequent abstraction of H atoms. But detailed growth
mechanisms at the step edges or interaction mechanisms of hydrocarbon precursors
with the step edges are not known at present. However, the fact that the relative
stabilities o f step configurations during growth are different with those of step
structures during annealing in H plasma indicates that hydrocarbon precursors are
adsorbed on the step edges and change the relative formation energies o f steps on the
surface where diamond growth occurs. The RHEED results on the as-grown surface
suggest that the step formation energies become larger in the order o f DB, SA+S B, and
DA steps on the diamond (001) surface during growth.
The diamond (001) surface structure has been discussed from the points o f view
of surface reconstruction and domain and step structure, subject to annealing in H
plasma and growth in hydrocarbon plasma. Because CVD diamond growth occurs
through a series of surface reactions mainly on steps, characterization of the surface in
terms of the step structure is necessary to understand growth mechanisms. Studies on
the step structure of the diamond surface are thought to be a great challenge both to
theorists and experimentalists.
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211
5.6. Summary
RHEED has been used to study the surface structure of the diamond (001)
surface annealed in H plasma and the as-grown film surface. The 2x1 reconstruction
occurred on ail diamond (001) surfaces annealed at 650 to 1300 °C in H-plasma. It has
been found that reconstruction takes place at much lower temperature in H plasma than
in UHV.
The surfaces annealed in H plasma show the transition from the double-domain
to the nearly single-domain structure with increasing the misorientation angles toward
the <110> direction. This transition is temperature-dependent. The as-grown films
exhibit the double-domain structure on the well-oriented surface (0.1°), and the surface
is close to the single-domain structure on the misoriented surface (3.5°). When the
surfaces are close to the single-domain structure, type-A terraces dominate the Hplasma annealed surfaces while type-B terraces are the major domain of the as-grown
film surfaces. It is considered that the step formation energies increase in the order o f
Da . Sa +Sb, and DB on the surfaces annealed in H plasma and in the order of DB,
SA+SB, and DAonthe as-grown films.
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212
Chapter 6
STM STUDY OF (001) HOMOEPITAXIAL DIAMOND FILMS
6.1. Introduction
This chapter concerns the investigation o f (001) homoepitaxial diamond films
using STM which is capable of imaging surfaces on an atomic scale. The principal
power of STM lies in its ability to depict the surface order and disorder in real space in
a local area, which contrasts with diffraction techniques providing averaged surface
structure in a large area. STM is thus the most suitable technique for studying domain
and step structure as well as surface defects on (001) homoepitaxial diamond films.
This chapter reports that surface images with an atomic resolution showed various
surface atomic structures such as lx l, 2x1 and 3x1 configurations. STM and LEED
revealed the double-domain and single-domain structures with single-layer and double­
layer steps, respectively. Several surface defects were also observed, including
antiphase boundaries, islands, and dimer vacancies. This study reported for the first
time the lx l:2 H dihydride structure surrounded by the 2 x l:H monohydride phase, the
local 3xl:1.33H configuration, surface defects of antiphase boundaries and dimer
vacancies, and DA steps on the diamond (001) surface using STM.
6.2. Literature review
Since the 2x1 reconstruction of the diamond (001) surface was first reported
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upon annealing in UHV by Lurie and Wilson (1977), observations o f the same result
were followed by several other groups (Hamza et al., 1990; Thomas et al., 1992; Lee
and Apai, 1993). Studies on the diamond surface had been performed using mostly
electron diffraction techniques such as LEED until STM began to be widely exploited
for investigating the structure of the diamond surface. For the first time, Tsuno et al.
(1991) observed (001) homoepitaxial diamond films on an atomic scale using STM in
air. The dimer-type 2x1 reconstruction o f the diamond (001) surface was confirmed
and this structure was assigned to the 2x1 :H monohydride configuration because the
samples were likely to be exposed to atomic hydrogen during the shutdown o f the CVD
system. The 2x1 diamond (001) surface was found to be stable in air at room
temperature. Since then, the 2x1-reconstructed dimer structure was studied on
homoepitaxially grown diamond (001) films (Maguire et al., 1992; Sutcu et al., 1992a;
Sasaki et al., 1993; Stallcup et al., 1995; Kawarada et al., 1995) and on the (001) faces
of polycrystalline diamond crystals (Busmann et al., 1992; Frauenheim et al., 1993)
using STM and AFM.
Although the 2 x l:H structure has been dominantly observed on the (001)
surface o f CVD diamond films, some studies reported the l x l structure on this surface.
Using AFM, Ravi et al. (1993) observed the coexistence o f the 2x1 and lx l structures
on the same crystal o f polycrystalline diamond films grown by combustion flame
method with a mixture o f oxygen and acetylene and subsequently treated by H plasma.
The l x l structure was postulated to be a result o f oxygen termination of the diamond
(001) surface and the 2x1 structure to be a result o f removal o f oxygen by hydrogen
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214
from the lx l structure. However, their AFM images are completely different from
other STM images, and they might have been created by some artifacts rather than a
real surface structure.
The l x l structure was also observed on a diamond (001) film homoepitaxially
grown with a mixture of CH4 and H2 by Badzian and Badzian (1993) using AFM. It
was considered that this surface would be the H-terminated l x l structure, indicating a
possibility of the existence of the lx l:2 H dihydride structure as a stable or metastable
phase in a local area. Recently Kawarada et al. (1995) observed some rows separated
by a half of the dimer row spacing with STM, which coexisted with dimer rows on
homoepitaxially grown diamond (001) film surfaces. This structure was assigned to the
lx l:2 H dihydride phase, but the image was not clear enough to claim the lx l structure.
The structure of the H-terminated diamond (001) surface has been theoretically
studied, but it has been a matter o f controversy. Zheng and Smith (1991) postulated
that the lx l:2 H dihydride structure was the most stable on the H-terminated diamond
(001) surface, whereas the 2x1 :H monohydride structure was reported to be the most
stable phase by Yang and D’Evelyn (1992a, b), Mehandru and Anderson (1991), and
Jing and Whitten (1994). On the other hand, Yang et al. (1993b) and Skokov et al.
(1994b) found that the 3xl:1.33H structure with alternating dihydride and monohydride
phase was favored over the 2x1 :H monohydride structure.
The domain and step structures on the diamond (001) surface was investigated
using STM. Tsuno et al. (1991) observed the 2x1 and 1x2 double-domain structure
with single-layer and double-layer steps on homoepitaxially grown diamond (001)
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215
films. Dimer rows were found to be extensively extended at SBsteps, as observed at the
initial stage of Si MBE growth on the Si (001) surface. It was argued that diamond
(001) epitaxial films grew through the extension o f dimer rows with the 2x1
reconstruction maintained. They proposed that MBE growth of Si and MPACVD
growth of diamond had a similar mechanism even though one was carried out in UHV
and the other was done in a plasma.
Following the observation of the 2x1 and 1x2 double-domain structure, the 2x1
single-domain structure was demonstrated to form when homoepitaxial growth occurred
on a misoriented diamond (001) substrate (Tsuno et al., 1994). Using LEED, a nearly
perfect single-domain surface was observed on the film grown with 2% CH4 in H2
while the double-domain structure was found with 6% CH4. The STM image taken
from the film grown at 2% CH4 showed that almost all dimer rows aligned in the same
direction and that DB double-layer steps were formed all over the sample. It was
postulated that step-flow growth occurred with the single-domain structure and 2D
nucleation would be dominant on the double-domain surface.
Elongated islands o f dimer rows were observed on the diamond (001) surface
grown by CVD (Busmann et al., 1992; Kawarada et al., 1995), as observed on the
MBE-grown Si (001) surface (Hamers et al., 1989, 1990; Hoeven et al., 1990b). These
islands were always longer in the direction o f the dimer rows than in the direction
normal to the dimer rows. The anisotropic growth was claimed to be attributed to
anisotropic binding energy and anisotropic sticking coefficient of adsorbates at SA and
SB steps, excluding the anisotropic diffusion effect o f adsorbates along and across the
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216
dimer rows, while all three factors were found to affect the anisotropic growth in Si
MBE growth on the Si (001) surface (Mo et al., 1991; Chason and Dodson, 1991;
Elswijk et al., 1991; Bedanov and Mukhin, 1993).
Only a few observations were made for surface defects on the diamond (001)
surface. Antiphase boundaries were reported by Sutcu et al. (1992a, b) and Kawarada
et al. (1995). But high-magnification AFM images obtained by Sutcu et al. were not
well enough resolved in an atomic scale to show clear evidence. In Si MBE growth on
the Si (001) surface, as reviewed in 2.2.4, antiphase boundaries have been known to
form between two islands with the opposite phases (Hamers et al., 1989, 1990) and to
act as nucleation sites for the next layer (Hoeven et al., 1990b; Bronikowski et al.,
1993). Dimer vacancies were also observed on the diamond (001) surface (Kawarada et
al., 1995).
6.3. Experimental details
Type la natural diamond (001) substrates were used for STM study. Following
the measurements of the surface misorientation angles, diamond substrates were
consecutively cleaned in boiled sulfuric acid saturated with C r03, in boiled aqua regia,
in a 1:1 solution o f HF and H N 03, in distilled water, and in acetone for 30 min for
each cleaning process. Homoepitaxial diamond growth was carried out for usually 1 hr
using MPACVD with a quartz tube. A mixture o f 1% CH4 and H2 was used with the
gas flow rate o f 100 seem. For a better electrical conductivity, samples were boron-
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217
doped using 10 and 100 ppm B2H6 in H2 with the flow rates of 20 and 5 seem,
respectively, during deposition, although the undoped, H-terminated CVD diamond
surface is still conductive (Grot et al., 1992). The total pressure was 80 Torr and the
growth temperature was kept at 875 °C. Following the diamond growth, samples were
annealed in H plasma for 5 min to remove nondiamond carbon layers on surfaces that
seem to be formed by residual hydrocarbon gas during the shutdown o f the CVD
reactor. H-plasma treatment was carried out using pure H2 gas with 100 seem at 80
Torr and 830-840 °C.
The surface of (001) homoepitaxial diamond films was characterized using an
atomic-resolution STM (Nanoscope III, Digital Instruments) in air and LEED in UHV.
STM images were taken in the constant current mode, with a positive sample bias of
500 mV and a tunneling current of less than 3.0 nA. The UHV chamber for LEED was
maintained with a base pressure o f l.OxlO'10 Torr and LEED patterns were taken with
an electron energy of around 160 eV.
6.4. Surface atomic structure o f (001) homoepitaxial diamond films
Figure 6.1 shows a high-resolution STM atomic image of a homoepitaxial
diamond (001) film grown by MPACVD. The image consists of dimer rows running
perpendicular to each other in alternate layers. Individual dimers are clearly resolved,
and moreover individual atoms in dimers can be seen. The rows are separated by 5.0
A, while the distance between adjacent dimers in a row is half this distance,
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Figure 6.1 High-resolution STM image of a (001) homoepitaxial diamond film to show
dimer-type 2x1 reconstruction. Individual dimers in rows are well resolved.
A dimer with two bright spots is outlined by a box. AP2 and L I represent
an AP2 antiphase boundary and the first type of a local 3x1 configuration,
respectively. The scan area is approximately about 5.8x4.4 nm2.
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219
approximately 2.5 A. The measurement results are in good agreement with the
theoretical values o f a 2x1 unit cell of the reconstructed diamond (001) surface.
The 2x1 surface structure of Figure 6.1 can be assigned to the monohydride
phase with one hydrogen atom per surface carbon atom, which corresponds to the
2x1 :H structure shown in Figure 6.2(a), because this sample was exposed to the atomic
hydrogen environment at the final stage o f deposition. This assignment may be
supported by the observations of C-H vibration for as-grown (001) homoepitaxial
diamond film surfaces using high-resolution electron energy-loss spectroscopy (Aizawa
et al., 1993; Ando et al., 1994). On the H-terminated diamond (001) surface, dimers
appear symmetric in most cases throughout the observations in this study. The observed
dimer structure is consistent with that of symmetrical dimers unanimously predicted by
theoretical calculations (Verwoerd, 1981; Zheng and Smith, 1991; Yang and D ’Evelyn,
1992a, b; Yang et al., 1993b).
Figure 6.3 presents a high-resolution STM image of a (001) homoepitaxial
diamond film. In the upper left of the image, individual dimers are clearly observed to
be oval and dimer rows seem to run from the upper left. Most interestingly the center
region is not reconstructed and is surrounded by the areas exhibiting the 2x1
reconstruction. In this unreconstructed region, the measured distance, 2.5 A, between
adjacent bright spots agrees well with the theoretical spacing between the nearest
carbon atoms on the unreconstructed diamond (001) surface. Thus, this unreconstructed
region is the l x l structure. This has been the only observation o f the l x l structure in
this study while investigating at least 100 different areas for about 10 samples.
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220
(c)
(d)
Figure 6.2 Schematic of various diamond (001) surface structures terminated by
hydrogen or oxygen: (a) 2 x l:H monohydride, (b) lx l:2 H dihydride, (c)
1x1:0 (bridging), (d) 1x1:0 (double bond), (e) local 3xl:1.33H
configuration, and (0 long-range order 3xl:1.33H structure. Open, solid,
and hatched circles represent carbon, hydrogen, and oxygen atoms,
respectively. In (e) and (f), dotted boxes denote an unit cell of 3x1
configuration.
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221
(e)
n
(f)
Figure 6.2 (cont.)
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222
Figure 6.3 High-resolution STM image of a (001) homoepitaxial diamond film to
exhibit the lx l:2 H dihydride structure, surrounded by the 2x1 :H
monohydride structure. The scan area is approximately 9.3x9.3 mrr.
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Two assignments are possible for this l x l structure. One is that this surface is
H-terminated. The lx l structure is then assigned to the lx l:2 H dihydride phase with
two hydrogen atoms per surface carbon atom, as given in Figure 6.2(b). The other is
the oxygen termination of the l x l region while the surrounding 2x1 region is
terminated by hydrogen atoms. The oxygen-terminated diamond (001) surface was
found to reveal the lx l structure (Thomas et al., 1992), as shown in Figure 6.2(c) and
(d). For the diamond (001) surface grown with a mixture of oxygen and acetylene, the
coexistence o f the lx l and 2x1 structure was already demonstrated (Ravi et al., 1993),
although the possibility that the images reported by Ravi et al. might be artifacts
produced by AFM cannot be excluded. The samples for the STM work of this study
were grown with
1% CH4 in H2, moreover followed by treatment with the
superequilibrium concentration of atomic hydrogen in H plasma. Thus, this surface is
considered to be H-terminated, suggesting an existence of the lx l:2 H dihydride
structure in a local area.
The l x l structure of the film grown with a mixture of CH4 and H2 was
previously observed by Badzian and Badzian (1993) using AFM. The lx l:2 H dihydride
structure was calculated to be more stable with respect to the 2x1 :H monohydride
structure by Zheng and Smith (1991). However, it has been widely accepted that the
2x1 :H monohydride structure is the most stable phase for the H-terminated diamond
(001) surface because the steric repulsion between surface hydrogen atoms is so severe
in the case o f the lx l:2 H dihydride structure (Yang and D ’ Evelyn, 1992a, b;
Mehandru and Anderson, 1991; Jing and Whitten, 1994). Theoretical calculations have
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224
shown that the non-bonded H-H distances range from 1.03 to 1.36 A on the lx l:2 H
dihydride surface, resulting from decrease of the C-H-C bond angle (84°, 86.5°, or
86.9°), shortening of the C-H bond, or twisting of the H-C-H, to reduce the steric
repulsion between the non-bonded hydrogen atoms (Verwoerd, 1991; Mehandru an
Anderson, 1991; Yang and D ’ Evelyn, 1992a). These values are much shorter than the
shortest known non-bonded H-H distances (1.70 A) although they are longer than the
H-H bond length (0.74 A) in H2 (Yang and D ’ Evelyn, 1992a). Thus, Sutcu et al.
(1992a) predicted that if the lx l:2 H dihydride structure really existed, it would be
favored at lower temperatures and then might be created as growth was quenched and
the substrate was cooled. But if present, the l x l :2H dihydride structure would exist in
a low concentration, and the 2x1 :H monohydride structure would be predominant
during the CVD diamond growth. The experimental observations of this STM study are
considered to be in agreement with the prediction of Sutcu et al. (1992a). Consequently
the 2x1 :H monohydride phase is dominant all over the area of the samples, but the
lx l :2H dihydride phase appears to exist in very local areas at very low concentrations.
Figure 6.4 shows an STM image where steps are down from the upper left to
the lower right. Dimer rows are resolved, but individual dimers in a row are not seen.
The running direction of dimer rows alternately change by 90° in the successive layers.
This surface is dominated by the 2x1 dimerized structure, but the narrow rows denoted
by L I can not be explained by the 2 x l:H monohydride structure. Since the width of
these rows is much narrower than that o f dimer rows and the spacing to the next dimer
row is approximately three quarters o f the dimer row spacing, the rows labeled by L I
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225
Figure 6.4 STM image of a (001) homoepitaxial diamond film with local 3x1:1.33H
configurations and antiphase boundaries. The substrate used was
misoriented by 1.3° and 0.7° toward the [110] and [110] directions. Local
3x1:1.33H configurations are labeled L I, and two types of antiphase
boundaries are marked by API and AP2. The scan area is approximately
12x17 nm: .
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226
seem to be not dimer rows, but atomic rows. Considering the H-termination of this
surface, these rows become the dihydride structure. The local 3xl:1.33H configuration
can be assigned to a combination of a dimer row and an atomic row which are the
monohydride and dihydride configurations, respectively, as shown in Figure 6.2(e).
This local structure is quite different from the long-range order 3x1:1.33H structure
[Figure 6.2(f)] in that this configuration is not periodically repeatable. Thus, we call
this structure the local 3xl:1.33H configuration, not the 3xl:1.33H structure. It should
be noted that this configuration is not a periodic structure representing the surface, but
is rather single atomic rows occurring as defects in the 2x1 :H monohydride surface.
The
3x1:1.33H
structure
with
alternating
monohydride
and
dihydride
configurations was theoretically predicted to be the most stable phase for H-terminated
diamond (001) surfaces by Yang et al. (1993b) and Skokov et al. (1994b). On the other
hand, Yang and D ’ Evelyn (1992a) postulated that the 3xl:1.33H structure with
alternating monohydride and dihydride configurations was unstable with respect to the
2 x l:H structure, but a whole family of (2 n + l)x l:(2 n + 2 )/(2 n + l)H
structures,
consisting o f n dimers separated by a dihydride unit, were possibly stable. At some
points, the local 3xl:1.33H configuration observed in Figure 6.4 is close to the
(2 n + l)x l structure, but it is not still periodically repeatable.
The 3xl:1.33H structure was observed on the hydrogenated Si (001) surface by
Chabal and Raghavachari (1985) and Boland (1990, 1992). The 3xl:1.33H structure on
the H-terminated Si (001) surface was found to consist of alternating monohydride
dimer row and dihydride atomic row [Figure 6.2(f)]. In contrast to the 3xl:1.33H
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227
structure existing in a long-range order on the H-terminated Si (001) surface, the local
3xl:1.33H configuration on the hydrogenated diamond (001) surface occurs with a
single atomic row appearing next to several dimer rows, in most cases, at step-edge
regions rather than on flat terraces. This is represented in Figure 6.5(a). In other cases,
the local 3xl:1.33H configuration appears along A PI antiphase boundaries, as
illustrated in Figure 6.5(b). These two types of local 3xl:1.33H configurations are also
seen in Figure 6.6, marked LI and L2. In Figure 6.4, three local 3x1 configurations of
type L2 are about 4.0. 2.0, and 1.5 nm long, respectively. Antiphase boundaries w ill
be discussed in detail in section 6.6.
On the Si (001) surface, as reviewed in section 2.2.2, the lx l:2 H dihydride,
3xl:1.33H, and 2x1 :H monohydride structures were obtained with the exposure of the
clean Si (001) surface to atomic hydrogen at room temperature, 400 K and 600 K,
respectively. The stability of these surface structures is determined mainly by the steric
repulsion between surface H atoms and strain energy related to the surface
reconstruction. On the Si (001) surface, the steric repulsion between surface H atoms
becomes more severe as the surface is more saturated with H atoms but the strain
induced by surface reconstruction is relieved more rapidly by changing the 2 xl:H to
the lx l:2 H structure with decreasing temperatures. On the diamond (001) surface,
atoms are more closely spaced than on the Si (001) surface. Thus, the steric repulsion
between H atoms is expected to be much stronger on the diamond (001) surface. This
seems to be why the lx l:2 H and 3xl:1.33H structures do not exist in a long-range
order on the H-terminated diamond (001) surface.
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228
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Figure 6.5 Schematic of two types o f local 3xl:1.33H configurations (a) observed near
the step edges and (b) observed along API boundaries. The larger circles
denote the upper-layer atoms. Hydrogen atoms are not shown.
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229
In summary, the H-terminated diamond (001) surface is dominated by the
2 x l:H monohydride structure, but the lx l: 2 H
structure and local 3x1:1.33H
configurations exist in very local areas and in very low concentrations.
6.5. Domain and step structure o f (001) homoepitaxial diamond films
Figure 6.6 is a large-area STM image of a diamond (001) surface grown
homoepitaxially and then treated by H plasma. The substrate used was measured to be
misoriented by
1.3° and 0.7°
toward the [110] and [110]
directions
(total
misorientation angle: 1.5°), respectively, by x-ray diffraction. Flat terraces are
averaged to be approximately 34 A wide along [110], separated by single-layer steps
with the height of about 0.9 A. Kinks along SA steps appear roughly every 60 A on an
average. These terrace and kink spacings correspond to the misorientation angles of
1.5° and 0.8° along [110] and [110], respectively. The quite good agreement with the
x-ray diffraction results implies that the observed step distribution reflects the
macroscopic misorientation o f the sample. The step-down direction is from the upper
left to the lower right in the image, that is, toward the major misorientation direction of
[110]. The orientation of dimer rows rotates over 90° at every step, as expected for the
single-layer stepped surface. It can be seen that the shape of steps depends on the
corresponding dimer-row orientation. The steps whose edges are parallel to the dimer
rows on the upper terrace are relatively straight, while the steps with their edges
perpendicular to the dimer rows of the upper terrace are ragged. Following the
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230
Figure 6.6 Large-area STM image of a (001) hoinoepitaxial diamond film to show the
2x1 and 1x2 double-domain surface structure. The substrate used was
misoriented by 1.3° and 0.7° toward the [1 10| and f llO ] directions. Two
types of terraces and single-layer steps are labeled A and B, and SA and Su,
respectively. A double-layer step running parallel to the dimer rows is
denoted by DA. Two types of local 3x1:1.33H configurations are marked
L I and L2. The scan area is approximately 20x35 nm2, The distortion of
the image was caused by instrumental miscalibration.
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notations defined by Chadi (1987), these two inequivalent types of straight and ragged
steps are called SA and SB and the corresponding upper terraces are represented to be
type A and type B, respectively.
The presence of both type-A and type-B terraces indicates that this surface
corresponds to the 2x1 and 1x2 double-domain structure. As given in Figure 6.7, a
LEED pattern taken from the same sample confirms the 2x1 and 1x2 double-domain
structure o f this surface since two different types o f half-order spots show almost the
same intensities. In Figure 6.6, difference in roughness between two types of step
edges implies that the formation energy of SA steps is smaller than that of SB steps.
Fluctuation o f a SB step creates low-energy SA steps at kinks. This w ill increase the
surface energy by increasing the length of the step but lower the surface free energy by
increasing the entropy of the step. The fluctuation o f SB steps totally lowers the surface
free energy. However, excitation of SA steps needs the formation o f high-energy SB
steps at kinks so that SA steps remain relatively straight. The stability of SA steps over
SB steps can be understood even from the step structures given in Figure 5.6. For SA
steps, no dangling bond is present at step-edge atoms, whereas for SB steps, a dangling
bond is generated at each second-layer atom o f the step edges. Although dangling
bonds at SB step edges are satisfied by atomic hydrogen, the formation energy w ill be
higher for SB steps than for SA steps.
In Figure 6.6, type-A and type-B terraces are not uniformly distributed and the
area of type-A terraces seems to be larger than that o f type-B terraces. Interestingly,
the terraces marked by A and A which are separated by a step, are both of type-A.
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Figure 6.7 LEED pattern ot" the (001) homoepitaxial diamond film shown in Figure
6.6. to exhibit the 2x1 and 1x2 double-domain surface structure. Part o f
LEED spots are indexed.
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233
Alternation o f type-A and type-B terraces separated by single-layer steps, which is a
general feature o f the 2x1 and 1x2 double-domain surface, is not obeyed in this local
region. Two type-A terraces are separated by a double-layer DA step which runs along
the [110] direction, as marked DA in Figure 6.6. A DA step with the double atomic
height of about 1.8 A is parallel to the dimer rows on the upper and lower terraces.
Figure 6.8 shows a high-magnification STM image to clearly resolve DA steps. The
terraces labeled by C, D, and E are all type A. Between C and D, D and E, DA steps
are observed locally. In the RHEED study presented in section 5.5.3, DA steps were
predicted to occur on the misoriented diamond (001) surface annealed in H plasma.
Figure 6.9 is an STM image o f a (001) homoepitaxial diamond film which was
grown on a substrate misoriented 2.3° and 0.2° toward [110] and [llO ] (total
misorientation angle: 2.3°), respectively. This sample was also annealed in H plasma
following the growth. Almost all dimer rows are running along the [110] direction.
Unfortunately this surface is atomically very rough, so it is very difficult to identify
steps. However, dimer rows are parallel to step edges, indicating the presence of DA
steps. This surface corresponds to the nearly perfect 2x1 single-domain surface which
consists of only type-A terraces. The single-domain structure is also confirmed by
LEED given in Figure 6.10. The half-order spots coming from the 1x2 terraces, which
are indicated by arrows, completely disappear, implying that only the 2x1 terraces are
present.
The surface with the total misorientation angle o f 1.5° (Figure 6.6) shows the
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8 Hi§h-resoil ■
exhibit o
n STM
ial
D and £ diar.nond
f Htn to
Tlh
scan area
is
m h e r^
ab
Prohib^ m
o u ln
Per^ssio n„
235
Figure 6.9 STM image of a (001) homoepitaxial diamond film to show the 2x1
single-domain surface structure. The substrate used was misoriented by
2.3° and 0.2° toward the [1 10| and (1101 directions. The scan area is
approximately 22.9x22.9 nm'.
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Figure 6.10 LEED pattern of the (001) homoepitaxial diamond film shown in Figure
6.9. to exhibit the 2x1 single-domain surface structure. Arrows indicate
the absence of one type of half-order spots.
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in
2x1 and 1x2 double-domain structure, whereas the 2.3° misoriented surface exhibits the
type-A 2x1 single-domain structure (Figure 6.9). Therefore, as the misorientation
angles increase, the diamond (001) surface annealed in H plasma undergoes the
transition fro m the double-domain structure with single-layer steps to the type-A
single-domain structure with DA steps. The STM observations of the transition of the
surface structure with the surface misorientation angles agree well with the RHEED
results given in section 5.4.2.
On the clean Si (001) surface, when the misorientation angle toward the [110]
or [110] direction is small, single-layer steps dominate the surface, forming the 2x1
and 1x2 double-domain structure. With increasing the misorientation angles, the area of
type-B
terraces
continuously
increase over
that
of
type-A
terraces.
Above
approximately 1.5°, SA+S B steps begin to collapse into DB steps. The content o f DB
steps monotonically increases, and finally, DB steps purely exist above 4-5°, giving rise
to the single-domain structure with only type-B terraces (Tong and Bennett, 1991;
Pehlke and Tersoff, 1991). During MBE Si growth on the double-domain Si(001)
surface, preferential growth occurs at SB steps so that SB steps catch up with SA steps,
leading to the single-domain surface with DB steps (Hoeven et al., 1989a, b, 1990a).
Thus, double-layer steps observed on the Si (001) surface are always o f type DB no
matter whether the surface is annealed in U H V o r grown by M BE. On the
misoriented diamond (001) surface annealed in H plasma, however, DA steps are
observed instead o f DB steps. DA steps seem to be a stable step structure on this
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surface. The observation of DA steps on the diamond (001) surface annealed in H
plasma is consistent with the results o f RHEED investigation presented in section
5.5.3. The reason DA steps are stable over single-layer SA+SB steps and DB steps was
addressed in detail in section 5.5.3. It was also proposed that the step formation
energies increase in the order of DA, SA+S B, and DB steps on the diamond (001)
surface annealed in H plasma.
6.6. Surface defects of (001) homoepitaxial diamond films
In Figure 6.4, two types of antiphase boundaries are observed, denoted as API
and AP2. A schematic of API and AP2 boundaries is shown in Figure 6.11(a). The
API boundary runs parallel to the dimer rows where two adjacent dimer rows separated
by the boundary are 3aQapart from each other (aQ is the lattice constant of the diamond
(001) surface, 2.52 A) while the dimer rows are separated by 2a0 on the 2x1
reconstructed region free of antiphase boundaries. A row of vacancies appears along
the A P I boundary. In some cases, an atomic row with dihydride configuration occurs
along this boundary, resulting in the local 3xl:1.33H configuration denoted by L2, as
shown in Figures 6.5(b) and 6.6. The AP2 boundary runs perpendicular to the dimer
rows. The dimer rows with one phase are misaligned with a shift of a0 relative to those
in the opposite phase so that the dimer rows on one side of the AP2 boundary meet the
troughs between the dimer rows on the other side.
A high-resolution image of the AP2 boundary on the diamond (001) surface is
shown in Figure 6.12. Dimer rows are observed to run through the boundary with a
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239
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Figure 6.11 Schematic of proposed structures for antiphase boundaries: (a) two types
o f antiphase boundaries A PI and AP2 on (001) homoepitaxial diamond
films and (b) AP2 antiphase boundary on a MBE-grown nonhydrogenated
Si (001) surface. The larger circles denote the upper-layer atoms. In (a),
hydrogen atoms are not shown.
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240
•v virsMijw
Figure 6.12 High-resolution STM image of a AP2 boundary on (001) homoepitaxial
diamond film. Note that there is no vacancy or step along the boundary.
Lines are drawn on the dimer rows, and AP2 denotes an antiphase
boundary. The scan area is approximately 5.6x5.0 mrr.
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241
shift of half the dimer row spacing a0 without any interruption such as vacancies or
steps. The structure o f AP2 boundaries on the diamond (001) surface are similar to that
of AP2 boundaries on the H-terminated Si (001) surface (Boland, 1992), but quite
different from that of AP2 boundaries on the MBE-grown non-hydrogenated Si (001)
surface (Hamers et al.. 1989, 1990). A schematic of the AP2 boundary on the MBEgrown Si (001) surface is illustrated in Figure 6.11(b). This structure is considered as
two SB steps separated by 5a0, with a single array of dimers approximately at the
center. On the Si (001) surface, each second-layer edge atom at SB steps has a dangling
bond and then is rebonded with the nearest atom on the lower terrace in the UHV
environment (Chadi. 1987), as shown in Figure 2.2. Strain induced by rebonding of
edge atoms at SB steps seems to result in such a unique structure for AP2 boundaries on
the MBE-grown Si (001) surface. On the diamond (001) surface, however, dangling
bonds of edge atoms created at SB steps can be satisfied with hydrogen atoms or other
hydrocarbon adsorbates so that rebonding does not have to occur. This situation
produces the structure o f AP2 boundaries which is unique to the diamond (001)
surface grown in the environment quite different from that o f Si M B E growth.
Antiphase boundaries have been investigated in detail for the Si (001) surface
epitaxially grown by MBE, using STM. Antiphase boundaries have been known to be
characteristic o f the island growth through 2D nucleation on the 2xl-dimerized Si (001)
surface (Hamers et al., 1989, 1990; Hoeven et al., 1990b). In the low-temperature
epitaxy where surface diffusion length is much shorter than the terrace width, epitaxial
islands nucleate with 50% possibility to possess each o f two possible phases on the
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same terrace. When two growing islands with the opposite phases coalesce together, an
antiphase boundary is formed at the border. Antiphase boundaries act as nucleation
sites for islands of the next layer. Islands nucleated at antiphase boundaries were
observed to account for approximately 94% of the area o f a growing layer at 720 K in
MBE growth (Bronikowski et al., 1993).
In this study, it is not yet clear whether antiphase boundaries were formed
during growth or during subsequent H-plasma treatment.
However, from the
observation that antiphase boundaries have not been found on the clean Si (001) surface
annealed at high temperatures in UHV (Hamers et al., 1990), antiphase boundaries
present on (001) homoepitaxial diamond films are considered to be formed during
growth. It implies that the diamond film given in Figures 6.4, 6.6, 6.8, and 6.12 (these
images were taken from the same sample) was grown by the island growth mechanism
through 2D nucleation. In section 4.4.1, on the other hand, hillock growth and stepflow growth were observed on (001) homoepitaxial diamond films at low and high
misorientation angles, respectively. In addition, the double-domain and single-domain
structures occurred on as-grown diamond films with the surface misorientation angles,
as shown in section 5.4.2. Thus, it seems that island growth proceeds on substrates
with small misorientation angles while step-flow growth occurs at large surface
misorientation angles.
Recently Kawarada et al. (1995) observed antiphase boundaries on (001)
homoepitaxial diamond films which were grown with a mixture o f CO and H2 and
subsequently treated by H plasma. It was concluded that surface diffusion length of
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243
adsorbates was so short that surface diffusion played a negligible role in diamond
growth by CVD. It may be applicable in some cases. In this study, however, the
observations of the step-flow growth and the single-domain surface indicate that surface
diffusion may play a considerably important pan in CVD diamond growth. The effect
o f the misorientation angles on surface morphologies and structure suggested that
diamond growth should be considered with the relation o f surface diffusion length to
terrace width under a given deposition condition.
This study shows that the surface morphologies and structure of homoepitaxial
diamond films vary, depending on the deposition parameters such as the misorientation
angles, methane concentrations, substrate temperatures, etc. It seems that the island
growth mode (or hillock growth mode) changes to the step-flow growth mode with
increasing the surface misorientation angles, decreasing the methane concentrations,
and increasing the substrate temperatures. Therefore, the step-flow growth free of
antiphase boundaries can be achieved by optimizing the diamond deposition conditions.
Figure 6.13 is an STM image to exhibit surface vacancies created by missing of
dimers, as marked M. The diamond (001) surface has fewer dimer vacancies o f less
than 1% compared with those on the Si (001) surface. The Si (001) surface showed a
high density of dimer vacancies o f approximately 10%, which consisted of individual
missing dimers or small clusters o f missing dimers (Tromp et al., 1985; Hamers et al.,
1986). The formation of dimer vacancies is a thermally activated process and its
concentration on the surface is then determined by an Arrhenius’ equation of the
formation energy of a dimer vacancy. Considering much higher bonding energy
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between atoms in diamond (3.6 eV for C-C bond) than in Si (1.8 eV for Si-Si bond)
(Kittel, 1976), a much lower concentration of dimer vacancies on the diamond surface
is easily understood.
An island o f a single dimer row is observed at the center o f Figure 6.13,
marked I. The island is elongated along the dimer row with an aspect ratio of
approximately 1:7. Dimer rows are strongly extended, as marked D. Dimer row
extension is a common phenomenon at SB steps, as can be seen in Figure 6.6. Taking
into account that this surface was annealed in H plasma following the epitaxial growth,
the island and extended dimer rows are anticipated to form by etching rather than
surface diffusion because atomic hydrogen etches the diamond surface as demonstrated
in Figure 4.1. Thus, this surface would be closer to an etching shape than an
equilibrium shape. In many respects, the etching or evaporation shape of a crystal is
closely related to the growth shape because etching or evaporation is a kind of a reverse
process o f growth. It is then expected that during diamond growth, islands also have
the strong anisotropic shape and dimer rows are extended along the rows, as given in
Figure 6.13. Growth anisotropy can result from several factors including the
anisotropic surface diffusion along and across dimer rows (Chason and Dodson, 1991;
Bedanov and Mukhin, 1993); anisotropic interaction o f adsorbates at SA and SB steps
(Elswijk et al., 1991); and anisotropic sticking coefficients o f adsorbates at SA and SB
steps (Mo et al., 1989, 1990, 1992). Growth anisotropy on the diamond (001) surface
such as elongation of islands and extension of dimer rows at SB steps is expected to be
considerably affected by these anisotropic factors although surface diffusion may not
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Figure 6.13 STM image of a (001) homoepitaxial diamond film to exhibit dimer
vacancies, an island and an extension of dimer rows. I, M, and E
represent an island, dimer vacancies, and an extended dimer row.
The scan area is approximately 9.4x7.6 nm".
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246
show the strong anisotropy on the diamond (001) surface (Mehandru and Anderson,
1991).
6.7. Summary
Using STM. an atomic resolution was achieved for the diamond (001) surface
so that individual dimers and even individual atoms in dimers were resolved. Highresolution atomic images showed that on the H-terminated diamond surface, the 2xl:H
monohydride structure was predominant, but the lx l:2 H structure and local 3xl:1.33H
configuration occurred in a very local area and in a very low concentration. For the Hplasma annealed diamond (001) surface, the double-domain structure was observed at a
low surface misorientation angle while the single-domain structure occurred with typeA terraces and DA steps at a high misorientation angle. The STM observations of the
double-domain and single-domain structures with the misorientation angles agreed well
with the RHEED results given in Chapter 5. DA steps running parallel to dimer rows of
the upper and lower terraces were observed. Atomic images also revealed two types of
antiphase boundaries, islands and dimer vacancies on the diamond (001) surface.
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247
Chapter 7
CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK
7.1. Conclusions
A comprehensive study on the surface morphologies and surface structure of
(001) homoepitaxial diamond films has been accomplished in this
thesis. Aparticular
emphasis was placed on the characterization o f the deposition mechanisms for (001)
homoepitaxial diamond growth by relating the film morphologies and surface structure
to the deposition parameters. This work is expected to make a significant contribution
not only toward better understanding the growth mechanisms o f epitaxial diamond films
but also toward
establishing
the optimum
CVD
conditions
for high-quality
homoepitaxial diamond films. The conclusions of this study are presented here in
detail.
7.1.1. Surface morphologies of (0011 homoepitaxial diamond films
A systematic study of the surface morphologies and structure
of (001)
homoepitaxial diamond films with the deposition parameters indicates that growth of
these films depends strongly on the surface misorientation angles o f substrates toward
the [110] or [110] direction, methane concentrations, and growth temperatures.
To characterize the effects o f the misorientation angles, etching and deposition
experiments were carried out using pure hydrogen gas and a mixture of methane and
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248
hydrogen in plasma, respectively. By increasing the misorientation angles, the density
of etch pits with the fourfold symmetry drastically decreased on diamond (001)
substrates. This indicates that the etching o f diamond substrates depends on the density
o f surface steps reflecting the macroscopic surface misorientation. It is proposed that
the well-oriented surface is etched mainly by creation and regression o f new steps
causing etch pits, while the highly misoriented surface is etched dominantly by
regression of pre-existing steps.
The surface morphologies of (001) homoepitaxial diamond films changed
remarkably with the misorientation angles. Growth hillocks and macrosteps were
observed at the low and high misorientation angles, respectively. Growth rates
increased with larger misorientation angles. These observations imply that surface steps
play a significant role in the surface reaction of hydrocarbon precursors in the diamond
growth. It is thus proposed that (001) homoepitaxial diamond growth is governed by
the relation of the surface diffusion length of adsorbates with the terrace width on the
surface. When the terrace width is larger than the diffusion length, two-dimensional
nucleation occurs on the terraces, resulting in growth hillocks. By increasing the
misorientation angles, however, the terraces become narrower than the surface
diffusion length, and adsorbates arriving at the terraces migrate to the steps, leading to
the step-flow growth along the <110> directions. The step-flow growth was more
efficient than hillock growth in depositing epitaxial diamond films from the gas phase.
From the etching and deposition experiments, it was found that the etching
morphologies are strongly correlated with the growth morphologies. Etch pits versus
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249
growth hillocks at low misorientation angles, and flat or macrostepped etching and
growth morphologies at high misorientation angles indicate that surface steps play a
similar role in both etching and growth.
The methane concentrations were observed to significantly affect the surface
morphologies and structure of (001) homoepitaxial diamond films. On the misoriented
substrates, macrosteps occurred at 1% CH4, whereas growth hillocks and random
growth morphology were developed at 2% and
6%
CH4, respectively. RHEED
investigation revealed that the surface was close to the 1x2 single-domain structure at
0.5% and 1% CH4, but the 2x1 and 1x2 double-domain structure resulted at 2% and
6% CH4. These indicate that the step-flow growth proceeds by maintaining the single­
domain structure and that the hillock or random growth occurs with the double-domain
structure. When the surface diffusion length is larger than the terrace width, the stepflow growth takes place. By increasing the methane concentration, as the adsorbate
concentration on the terraces exceeds a critical value, the two-dimensional nucleation
occurs on the terraces, giving rise to growth hillocks. Further increase of the methane
concentration results in random growth on the terraces with almost no surface
migration of adsorbates. The dependence o f surface morphologies and structures on the
methane concentrations are attributed to lower mobility and subsequently shorter
diffusion length of adsorbates on the surface at higher methane concentrations.
Growth on the misoriented diamond substrates at 875 and 1200 °C showed that
step bunching for macrosteps is more likely to occur at a lower temperature. Taking
into account the surface diffusion of adsorbates as well as the step bunching, the growth
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250
at higher temperatures seems to be more promising for the deposition of the highquality films.
Step-flow growth with the single-domain structure is believed to produce
higher-quality films with fewer lattice defects than other growth modes. The
dependence of surface morphologies and structures o f (001) homoepitaxial diamond
films on misorientation angles of substrates and methane concentrations is shown in
Figure 7.1.
It is likely that the step-flow growth is favored with increasing
misorientation angles, lowering methane concentrations, and increasing substrate
temperatures. The correlation of surface morphologies and structures indicates that the
step-flow growth is associated with the type-B single-domain structure, and the hillock
or random growth with the double-domain structure. This study suggests that the
deposition condition for (001) homoepitaxial diamond films is optimized with
misorientation angles of approximately 3-5°, methane concentrations of less than 1%,
and substrate temperatures o f approximately 1200 °C.
7.1.2. Surface structure of diamond (001) surfaces
In this thesis, RHEED was successfully used for investigating the surface
structures of diamond (001) substrates annealed in H plasma and (001) homoepitaxial
diamond films. A ll diamond (001) surfaces annealed at 650 to 1300 °C in H plasma or
grown epitaxially revealed the 2x1 reconstruction. The surface reconstruction took
place at a much lower temperature of 650 °C in H plasma than at a temperature of 800
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C H 4 concentrations
(% )
251
6
-
5
-
4
-
©
o
8 7 5 °C
^
a
1 2 0 0 °C
R a n d o m g ro w th
D
o
H illo c k g ro w th
3
-
2
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1
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J
0
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i.
2
X
4
6
8
10
12
M is o rie n ta tio n a n g le s o f su b stra tes (° )
Figure 7.1 Dependence o f surface morphologies and structures of (001) homoepitaxial
diamond films on misorientation angles of substrates and CH4
concentrations. Diamond films were grown at 875 and 1200 °C. Closed and
open symbols denote the step growth, and the hillock or random growth,
respectively. S represents the surface close to the type-B single-domain
structure, and D indicates the double-domain structure.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
or 970 °C in UHV. It is considered that the surface would not only be more active in H
plasma than in UHV but also that atomic hydrogen may eliminate residual adsorbates
such as oxygen on the surface, making the reconstruction occur more readily.
Consequently, CVD diamond growth, in reality, is known to proceed on the
reconstructed surface over the range of temperatures investigated.
The domain and step structure of the diamond (001) surface was characterized
by comparing the intensities between two series of the half-order RHEED spots. Upon
annealing in H plasma, the diamond (001) surface showed considerably different
domain structure with the annealing temperatures and misorientation angles. The welloriented surface exhibited the 2x1 and 1x2 double-domain structure irrespective of the
annealing temperatures. On the other hand, the misoriented surface was close to the
type-A 1x2 single-domain structure at low temperatures of 875 and 1000 °C, but was
the double-domain structure at high temperatures of 1200 and 1300 °C. Thus, the
single-domain structure is favored at larger misorientation angles and at lower
temperatures, while the opposite conditions are true for the double-domain structure.
This indicates that the surface annealed in H plasma undergoes the transition from the
double-domain to the nearly single-domain structure by increasing the misorientation
angles. This transition was discussed in terms o f the formation energies of single-layer
and double-layer steps, strain energies related to the surface reconstruction, and
entropies created by the thermal fluctuation of steps.
The H-plasma annealed surface close to the single-domain structure was
dominated by type-A terraces. It is implied that this surface is composed of mainly
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253
double-layer DA steps. The step formation energies are proposed to increase in the
order of DA, SA+SB, and DB on the H-plasma annealed surface. To date, DA steps have
never been observed even on the Si (001) surface. For the first time, this RHEED study
suggests the presence of DA steps on the H-plasma annealed diamond (001) surface.
The transition of the double-domain to the single-domain structure with the
misorientation angles and the existence of DA steps were confirmed by STM
observations in this study.
The as-grown film surface exhibited the double-domain structure at a low
misorientation angle while the film surface was close to the single-domain structure at
high misorientation angles. When the growth surface was close to the single-domain
structure, type-B terraces were the major domain on this surface. On the as-grown
films, the step formation energies are considered to increase in the order of DB,
SA+SB, and DA.
7.1.3. STM study of diamond (001) surfaces
An STM study was carried out for the diamond (001) surface homoepitaxially
grown with boron doping and subsequently followed by H-plasma annealing. In this
work, an atomic-scale resolution was achieved so that individual dimers and even
individual atoms in dimers could be seen. On this surface, high-resolution atomic
images showed,
in most areas, the dimer
rows
indicating the 2x1 surface
reconstruction, but showed, in some local areas, the bulk-truncated unreconstructed
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254
structure or the single atomic rows adjacent to several dimer rows. These structures
were assigned to the 2 xl:H monohydride structure, lx l:2 H dihydride structure, and
local 3xl:1.33H configuration, respectively. On the H-terminated diamond (001)
surface, therefore, the 2 xl:H monohydride structure is predominant, but the lx l:2 H
dihydride structure and local 3xl:1.33H configuration occur in a very local area and at
a very low concentration.
STM revealed the domain and step structure o f the diamond (001) surface in a
real space. The H-plasma annealed diamond (001) surface at a low surface
misorientation angle consisted o f alternating type-A and type-B terraces separated by
single-layer steps. The area o f type-A terraces seemed to be larger than that of type-B
terraces. SA steps with their edges parallel to the dimer rows on the upper terraces were
relatively straight whereas SBsteps with their edges normal to the corresponding dimer
rows were ragged. The different edge roughness o f two inequivalent single-layer steps
suggests that SB steps have higher formation energy than SA steps. A t a higher
misorientation angle, on the other hand, the surface showed the single-domain structure
with type-A terraces, and consequently, DA steps. The double-domain and single­
domain surface structures with the misorientation angles were confirmed with LEED.
The STM and LEED observations on the domain and step structure agreed well with
the RHEED results. In particular, D A steps, which were predicted to be present on the
H-plasma annealed surface with
the large misorientation angles by
RHEED
investigation, were observed.
The STM study also showed several types of surface defects on (001)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
homoepitaxial diamond films. Two types of antiphase boundaries, A PI and AP2, were
observed to run parallel and perpendicular to the dimer rows, respectively. These
antiphase boundaries seem to form during the island growth through two-dimensional
nucleation on the 2x1 reconstructed diamond (001) surface. It is considered that
antiphase boundaries can be prohibited from forming during growth by optimizing the
diamond deposition conditions toward the step-flow growth, as mentioned in section
7.1.1. On the diamond (001) surface, dimer vacancies were observed to exist at a very
low concentration compared to the Si (001) surface, probably due to the much higher
bonding energy between atoms in diamond. It was found that islands and dimer rows
were remarkably extended along the dimer rows, indicating the strong growth
anisotropy on the diamond (001) surface.
7.2. Suggestions for future work
Although this thesis provides new insight for studying homoepitaxial diamond
growth, there are many issues and problems which remain to be solved in the current
field of CVD diamond deposition before CVD diamond growth can be completely
understood and before homoepitaxial diamond films can be grown with the best quality.
Some suggestions are presented here for future work, along the lines of this research,
to reach the goals of a detailed basic and applied understanding of (001) homoepitaxial
diamond growth.
1)
Further systematic studies on (001) homoepitaxial diamond growth are
necessary to clearly elucidate the dependencies of the surface morphologies and
with permission of the copyright owner. Further reproduction prohibited without permission.
256
structures upon various experimental parameters and process variables. This thesis
strongly emphasized the effects of surface misorientation angles of substrates and
methane concentrations on the growth morphologies and structure, but only a partial
investigation was performed for the other important CVD parameter, substrate
temperatures, because of experimental difficulties in decoupling the temperature and
microwave power. To vary only the substrate temperatures in the MPACVD system,
the external heating or cooling for substrates is required to be used inside a plasma. It
should also be noted that the heating or cooling system may cause metallic
contamination to diamond films. Characterization of the effects of the growth
temperatures is expected to give some invaluable information regarding the surface
diffusion on diamond surfaces.
2) In this study, RHEED and STM results revealed several types of steps and
the relative stabilities between them on the H-plasma annealed and as-grown diamond
(001) surfaces. These observations need to be confirmed by theoretical approaches such
as the calculation of formation energies for various step configurations and the
anisotropic surface stresses related to reconstruction on the diamond (001) surface,
which remain a challenging task to theorists.
3) Unfortunately, the STM study was limited to the H-plasma annealed surface,
although the atomic images were taken from CVD diamond layers. An attempt was
made to image the as-grown diamond surface, but the disordered layer at the top,
which seemed to form during the shutdown o f the CVD reactor, interfered with the
STM observation o f this surface. Several approaches are under examination at present,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
257
including the growth at the methane concentrations a little beyond the border between
etching and growth, and the annealing of as-grown samples in UHV, to overcome the
problems related to the disordered layer at the top o f as-grown films and to finally
image growth surfaces.
4)
The major application of homoepitaxial diamond films is for active electronic
devices. The electrical properties of CVD diamond films are expected to change with
the surface morphologies and structure. Measurement of electrical properties such as
carrier concentrations, carrier mobilities, I-V characteristics, etc., has to be carried out
to fully characterize the effects of various experimental parameters and to establish the
optimum deposition conditions from the point of view o f practical applications for
homoepitaxial diamond films. This work is in progress in collaboration with the
Samsung Advanced Institute of Technology, Korea.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
258
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274
Appendix. COMPUTER PROGRAM FOR THE CALCULATION OF
SURFACE MISORIENTATION ANGLES
THIS IS THE COMPUTER PROGRAM TO CALCULATE THE SURFACE MISORIENTATION
ANGLES OF DIAMOND (001) SUBSTRATES, MADE BY NAESUNG LEE, MRL, THE
PENNSYLVANIA STATE UNIVERSITY.
THIS PROGRAM IS DESIGNED TO CALCULATE THE ANGLES IN THE ORDER OF
0.02 DEGREE. FOUR SETS OF DATA MAY BE INPUT AT THE SAME TIME, THAT IS,
FOUR hkl VALUES AND THE DISTANCES OF THEIR DIFFRACTION SPOTS FROM THE
CENTER OF A FILM TAKEN BY LAUE X-RAY DIFFRACTION. THE RANGE OF THE ANGLES
TO BE INPUT IN THIS PROGRAM, (A L P H A m a x - ALPHAMlN) AND (B E T A m a x - B E T A m in ), IS NO
MORE THAN 1 DEGREE.
CLS
pi = 3.14159: filmd = 20!
minSRDEV = 1000: m inSRDEVI = 1000: minSRDEV2 = 1000: minSRDEV3 = 1000:
minSRDEV4 = 1000: minSRDEV5 = 1000:
increment = 1
start:
INPUT "NUMBER OF SPOTS="; NUMBER
OPEN "samp1.txt” FOR INPUT AS #1
IN P U T #1, alpmin, alpmax, betamin, betamax
CLOSE #1
LOCATE 2, 1: PRINT "Alpha Min= alpmin
LOCATE 2, 20: PRINT "Alpha Max= "; alpm ax
LOCATE 3 ,1 : PRINT "Beta Min= betamin
LOCATE 3, 20: PRINT "Beta Max=
betamax
LOCATE 2, 12: INPUT "", alpmin$
IF alpmin$ = "" THEN ELSE alpm in = VAL(alpmin$)
LOCATE 2, 31: INPUT
alpm ax$
IF alpmax$ = THEN ELSE alpm ax = VAL(alpmax$)
LOCATE 3, 12: INPUT
betamin$
IF betamin$ = "" THEN ELSE betamin = VAL(betamin$)
LOCATE 3, 31: INPUT "", betamax$
IF betamax$ = "" THEN ELSE betam ax = VAL(betamax$)
IF NUMBER = 1 THEN GOTO zz1:
IF NUMBER = 2 THEN GOTO zz2:
IF NUMBER = 3 THEN GOTO zz3:
IF NUMBER = 4 THEN GOTO zz4:
zz4:
OPEN "samp5.txt" FOR INPUT AS #5
IN P U T #5, h(4), k(4), L(4), DM(4)
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275
zz3:
OPEN "samp4.txt" FOR INPUT AS #4
INPUT #4, h(3), k(3), L(3), DM(3)
zz2:
OPEN "samp3.txt" FOR INPUT AS #3
INPUT #3, h(2), k(2), L(2), DM(2)
zzT.
OPEN "samp2.txt" FOR INPUT AS #2
INPUT #2, h(1), k(1), L(1), DM(1)
CLOSE #2, #3, #4, #5
FOR i = 1 TO NUMBER
LOCATE i + 3, 1: PRINT "h("
LOCATE i + 3, 3: PRINT i
LOCATE i + 3, 6: PRINT ")=
h(i)
LOCATE i + 3, 15: PRINT "k("
LOCATE i + 3, 17: PRINT i
LOCATE i + 3, 20: PRINT ")=
k(i)
LOCATE i + 3, 30: PRINT "l("
LOCATE i + 3, 32: PRINT i
LOCATE i + 3, 35: PRINT ")=
L(i)
LOCATE i + 3, 45: PRINT "DM("
LOCATE i + 3, 48: PRINT i
LOCATE i + 3, 51: PRINT ")= DM(i)
LOCATE i + 3, 9: INPUT
h$(i)
IF h$(i) = "" THEN ELSE h(i) = VAL(h$(i))
LOCATE i + 3, 23: INPUT
k$(i)
IF k$(i) = THEN ELSE k(i) = VAL(k$(i))
LOCATE i + 3, 38: INPUT
L$(i)
IF L$(i) = "" THEN ELSE L(i) = VAL(L$(i))
LOCATE i + 3, 54: INPUT
DM$(i)
IF DM$(i) = "" THEN ELSE DM(i) = VAL(DM$(i))
NEXT i
OPEN "samp1.txt" FOR OUTPUT AS #1
PRINT #1, alpmin, alpmax, betamin, betamax
CLOSE #1
IF NUMBER = 1 THEN GOTO zzz1:
IF NUMBER = 2 THEN GOTO zzz2:
IF NUMBER = 3 THEN GOTO zzz3:
IF NUMBER = 4 THEN GOTO zzz4:
zzz4:
OPEN "samp5.txt" FOR OUTPUT A S #5
PRINT #5, h(4), k(4), L(4), DM(4)
zzz3:
OPEN "samp4.txt" FOR OUTPUT AS #4
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276
PRINT #4, h(3), k(3), L(3), DM(3)
zzz2:
OPEN "samp3.txt" FOR OUTPUT AS #3
PRINT #3, h(2), k(2), L(2), DM(2)
zzz1:
OPEN "samp2.txt" FOR OUTPUT AS #2
PRINT #2, h(1), k(1), L(1), DM(1)
CLOSE #2, #3, #4, #5
M = INT((alpmax - alpmin) * 5 0 + 1 )
N = INT((betamax - betamin) * 50 + 1)
DIMESION STATEMENT
IF increment >= 2 THEN GOTO skip2:
DIM alpha(M), beta(N)
DIM X(NUMBER), Y(NUMBER), D(M, N, NUMBER), RD(M, N, NUMBER)
DIM RDM(NUMBER)
DIM RDEV(M, N, NUMBER), RDEV2(M, N), SRDEV(M, N)
skip2:
FOR i = 1 TO M
alpha(i) = alpmin + (i - 1 ) * .02
F O R j = 1 TO N
beta(j) = betamin + (j - 1) * .02
hs = (SIN(pi / 180 * alpha(i)) * COS(pi / 180 * betaG)) + SIN(pi / 180 * betaQ))) / SQR(2)
ks = (SIN(pi / 180 * alpha(i)) * COS(pi / 180 * beta(j)) - SIN(pi / 180 * betaG))) / SQR(2)
Is = COS(pi / 180 * alpha(i)) * COS(pi / 180 * beta(j))
dd1 = 1 / SQR(hs A 2 + ks A 2)
ux= ks*d d 1
uy = -hs *dd1
wx = -hs * Is * dd1
wy = -ks * Is * dd1
wz = (hs A 2 + ks A 2) * dd1
RDEV2(i, j) = 0
FOR a = 1 TO NUMBER
dd2 = 1 1SQR(h(a) A 2 + k (a )A 2 + L(a) A 2)
gux = h(a) * dd2 * ux
guy = k(a) * dd2 * uy
gu = gux + guy
gwx = h(a) * dd2 * wx
gwy = k(a) * dd2 * wy
gwz = L(a) * dd2 * wz
gw = gwx + gwy + gwz
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277
gamma = A T N (gw /S Q R (1 - g w A 2))
tt1 = gu / COS(gamma)
delta = ATN(tt1 / SQR(1 - tt1 A 2))
tt2 = COS(gamma) * COS(delta)
sigm a = ATN(SQR(1 - tt2 A 2) / tt2)
IF sigma < .001 AND sigma > -.001 THEN
X(a) = 0: Y(a) = 0
GOTO skii:
END IF
X(a) = TAN(delta) * TAN(2 * sigma) / TAN(sigma) * film d
Y (a) = TAN(gam m a) * TAN(2 * sigma) / COS(delta) / TAN(sigm a) * filmd
D(i, j, a) = SQR(X(a) A 2 + Y(a) A 2)
R D (i,j, a) = D(i, j, a) / D(i, j, 1)
RDM(a) = DM(a) / DM(1)
RDEV(i, j, a) = RD(i, j, a) - RDM(a)
RDEV2(i, j) = RDEV2(i, j) + RDEV(i, j, a) A 2
skii:
NEXT a
SRDEV(i, j) = SQR(RDEV2(i, j) / NUMBER)
inc = inc + 1
IF minSRDEV > SRDEV(i, j) THEN
minSRDEV = SRDEV(i, j): XLength = i: YLength = j
beta = beta(j): alpha = alpha(i)
END IF
NEXT j
NEXT i
FOR i = 1 TO M
FOR j = 1 TO N
IF SRDEV(i, j) <= minSRDEV THEN GOTO s k i:
IF m inSR D EVI > SRDEV(i, j) THEN
m inSR D EVI = SRDEV(i, j): XLength 1 = i: YLength 1 = j
betal = beta(j): alph al = alpha(i)
END IF
s k i:
NEXT j
NEXT i
FOR i = 1 TO M
FO R j = 1 T O N
IF SRDEV(i, j) <= m inSRDEVI THEN GOTO sk2:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IF minSRDEV2 > SRDEV(i, j) THEN
minSRDEV2 = SRDEV(i, j): XLength2 = i: YLength2 = j
beta2 = beta(j): alpha2 = alpha(i)
END IF
sk2:
NEXT j
NEXT i
FOR i = 1 TO M
FOR j = 1 TO N
IF SRDEV(i, j) <= minSRDEV2 THEN GOTO sk3:
IF minSRDEV3 > SRDEV(i, j) THEN
minSRDEV3 = SRDEV(i, j): XLength3 = i: YLength3 = j
beta3 = beta(j): alpha3 = alpha(i)
END IF
sk3:
NEXT j
NEXT i
FOR i = 1 TO M
FOR j = 1 TO N
IF SRDEV(i, j) <= minSRDEV3 THEN GOTO sk4:
IF minSRDEV4 > SRDEV(i, j) THEN
minSRDEV4 = SRDEV(i, j): XLength4 = i: YLength4 = j
beta4 = beta(j): alpha4 = alpha(i)
END IF
sk4:
NEXT j
NEXT i
PRINT
PRINT "=================="
PRINT "=== Results ==="
PRINT "=================="
FOR b = 1 TO NUMBER
PRINT "hkl("; b ; " ) : h(b); k(b); L (b );" DM(”; b ; D M ( b ) ; " RDM("; b ; R D M ( b )
NEXT b
PRINT
PR| NT
PRINT
PRINT
PRI NT
PRINT
PRINT
PRINT
PRINT
PRINT
PRI NT
"=========================="
"minSRDEV alpha
beta "
"
("; a l p m i n ; a l p m a x ; b e t a m i n ; b e t a m a x ; ")"
"=========================="
USING
##.### ##.### "; minSRDEV; alpha; beta
USING "#.####### ##.### # # . # # # m inSRD EVI; a lp h a l; betal
USING "#.####### ##.### ##.### "; minSRDEV2; alpha2; beta2
USING "#.####### ##.### ##.###"; minSRDEV3; alpha3; beta3
USING "#.####### ##.### ##.###"; minSRDEV4; alpha4; beta4
"=========================="
LPRINT
LPRINT "
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279
LP R IN T "
=== Results ==="
LP R IN T "
=================="
FOR b = 1 TO NUMBER
L P R IN T "
hkl("; b ; " ) : h(b); k(b); L(b); " DM("; b ; D M ( b ) ; " RDM("; b ; R D M ( b )
NEXT b
LPRINT
LPRINT
LPRINT
minSRDEV alpha
beta "
LPRINT
("; a l p m i n ; a l p m a x ;
b e t a m i n ; b e t a m a x ; ")"
LPRINT
#.####### ##.### # # .# # # "; minSRDEV; alpha; beta
LPRINT USING "
#.####### ##.### ##.### "; m inSR D EVI; a lp h a l; betal
LPRINT USING "
#.####### ##.### # # .# # # "; minSRDEV2; alpha2; beta2
LPRINT USING "
LPRINT USING "
#.####### ##.### ##.### "; minSRDEV3; alpha3; beta3
#.####### ##.### # # .# # # "; minSRDEV4; alpha4; beta4
LPRINT USING "
LPRINT
LPRINT CHR$(12)
PRINT : PRINT : INPUT 'T o Save (Y /N )"; sav$: sav$ = UCASE$(sav$)
IF sav$ = 'Y " THEN ELSE GOTO sk10:
PRINT ; INPUT "File Name : " , f$: f$ = f$ + ".lau"
OPEN f$ FOR OUTPUT AS #1
PRINT #1, h(1), k(1), L(1)
PRINT #1, h(2), k(2), L(2)
PRINT #1, h(3), k(3), L(3)
PRINT #1, h(4), k(4), L(4)
PRINT #1, USING '#.####### m .m #
P R IN T #1, USING "#.####### m.m#
PRINT #1, USING '#.#####m ##.###
PRINT #1, USING "#.####### ##.###
PRINT #1, USING "#.####### m.m#
CLOSE #1
# # .# # # ";
# # .# # # ";
##.### ";
# # .# # # ";
# # .# # # ";
minSRDEV; alpha; beta
m inSR DEVI; alphal; betal
minSRDEV2; alpha2; beta2
minSRDEV3; alpha3; beta3
minSRDEV4; alpha4; beta4
sk10:
PRINT ; INPUT "Re-start (Y/N)", ans$: ans$ = UCASE$(ans$)
IF ans$ = ’Y " THEN GOTO ZZZ:
END
ZZZ: CLS
increment = 3: GOTO start;
END '====== end of main
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
VITA
Naesung Lee was bom in Kyunggi, Korea, on December 12, 1961. He
graduated from Hwanil High School in Seoul, Korea, in 1980, and received a B.S.
degree in Metallurgy from Seoul National University, Seoul, Korea, in 1984. He
attended Korea Advanced Institute of Science and Technology, Seoul, Korea, from
1984 to 1986, graduating with a M.S. in Materials Science and Engineering. He had
been employed by Korea Institute o f Machinery and Metals, Changwon, Korea, from
1986 to 1989, and by Korea Gas Corporation, Ansan, Korea, from 1990-1991, in the
field o f research and development of materials. In the fall o f 1991, he enrolled at The
Pennsylvania State University in Materials, where he has studied at the Materials
Research Laboratory under the direction of Andrzej Badzian, Professor of Materials.
He is currently a member of the Electrochemical Society, and has published
several papers in the open literature.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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