Diamond surfaces : interactions with hyd

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Diamond surfaces : interactions with hydrogen and halogens
Citation
Melnik, M. Susan
(1997)
Diamond surfaces : interactions with hydrogen and halogens.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/gdrt-7n92.
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

Absolute deuterium coverage on the diamond C(100) surface has been measured under a variety of dosing conditions by nuclear reaction analysis (NRA) using [...]. The (2x1) surface with ~1.0 D per surface C is produced under typical dosing conditions. However, at unusually high filament temperatures circa 2000°C, coverages up to 1.34 ± 0.09 D per surface C are observed. Coverage is calibrated by comparing to a standard containing 1.5x[...] D/[...]. Signal from subsurface deuterium is estimated to be negligible by comparison to previous scattering experiments and by secondary-ion mass spectroscopy of a homoepitaxial CVD (100) sample. D breakage of surface dimer bonds at high filament temperature is proposed as a mechanism to generate surface dideuterides. The relevance of dimer breakage and dihydride formation to recent experiments on surface degradation is briefly discussed.

Previous models of hydrogen reactions with C(100) are substantially revised to include all types of sites on the reconstructed terrace, and it is shown that saturation coverage determines the ratio of site-averaged abstraction rate to site-averaged recombination rate, [...]. NRA coverage measurements of 0.95 ± 0.04 D per surface C imply a [...] of 0.06 ± 0.04 at 1800°C gas temperature and 360°C surface temperature. Results indicate that thermochemical kinetic models overpredict by a factor of ~20 the fraction of sites available for growth during diamond CVD.

In a separate issue, C(110) surface mobility is demonstrated by calculating activation energies for the migrations of H, F, and Cl with quantum chemical methods using hydrocarbon cluster models. The calculations included extensive basis sets with many-body effects at the level of single and double excitations from Hartree-Fock and Complete-Active-Space wavefunctions. Intra-chain migrations of H along [...] carbon chains and nearest-neighbor F migration are found to be too slow to compete with thermal desorption. However, inter-chain migrations of H and Cl are calculated to be sufficiently fast to compete with thermal desorption under ultrahigh vacuum conditions and with gas-surface reactions under typical diamond growth conditions. This was the first study to consider migration rates as well as barriers, establishing mobility's competitiveness during diamond growth. [...]/[...] is estimated to be [...]. Finally, a kinetic Monte-Carlo algorithm is presented to directly combine mobility with gas-surface reactions in the same iteration step when simulating hydrogen processing of diamond.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Applied Physics
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Goddard, William A., III (advisor)
Goodwin, David G. (co-advisor)
Thesis Committee:
Goddard, William A., III (chair)
Rossman, George Robert
Atwater, Harry Albert
Tombrello, Thomas A.
Defense Date:
21 May 1997
Record Number:
CaltechETD:etd-01162008-075117
Persistent URL:
DOI:
10.7907/gdrt-7n92
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Diamond Surfaces: Interactions with Hydrogen

and Halogens

Thesis by

M. Susan Melnik

In Partial Fulfillment of the Requirements
for the Degree of

Doctor of Philosophy

California Institute of Technology

Pasadena, California

1997
(Submitted May 21, 1997)

M. Susan Melnik

ili

Acknowledgements’

Kudos to all my mentors for their incredible dedication to education and science:
my co-advisor Prof. William A. Goddard, III, of Caltech, Drs. Satoshi Koizumi
and Yoichiro Sato of the National Institute for Research in Inorganic Materials (aka
Mukizai-ken) in Japan, Dr. John N. Russell, Jr., of the Naval Research Laboratory
(NRL), and Dr. O. Wayne Holland of Oak Ridge National Laboratory (ORNL). I ac-
knowledge my co-advisor Prof. David G. Goodwin for introducing me to the fascinat-
ing subject of diamond growth, and I especially thank him for funding my attendance
at several conferences. Graduate school is a means to do science and become inte-
grated into the scientific community, and national conferences are absolutely essential
to the latter and therefore the former.

I thank the other members of my thesis committee, Profs. Harry A. Atwater and
George R. Rossman. I am especially grateful to Prof. Thomas A. Tombrello for his
careful reading of the thesis and for asking many tough, good, and fair questions in
the thesis exam. TAT, you are an educator in the truest sense of the word. I only wish
I had met you sooner in my graduate studies. HAA, thank you for welcoming me into
your lab and especially for introducing me to the Materials Research Society. I also
thank Prof. Marc-Aulet Nicolet for welcoming me to the pelletron lab and providing
me with an office. GRR, thanks for several useful and enjoyable discussions about
diamond, IR, and SIMS.

Thanks to all the people who read and critiqued drafts of the thesis: Profs. David
G. Goodwin and William A. Goddard, III, Dr. Robert M. Housley, Drs. David B.
Poker and David M. Zehner of ORNL, and especially, especially Dr. John N. Russell,
Jr., of NRL. JNR, Jr., many thanks for all those hours of telephone conferencing to
debug experiments at ORNL and ideas at Caltech.

‘Funding agencies and individuals specific to certain projects are acknowledged at the end of the
corresponding chapters and appendices.

I thank the United States and Japanese government laboratories which facilitated
the majority of the experiments reported here. Diamond surface science is notoriously
expensive and proceeds at a snail’s pace relative to silicon without lots of money and
spare parts to facilitate it. Except for the handful of universities with enough re-
sources, | believe that government laboratories are the only place to do graduate
experiments in diamond surface science. Many diamond theses have benefitted from
collaborations with government laboratories, including SLAC, NRL, Lawrence Berke-
ley, and ORNL, and I heartily recommend them to future students.

I thank Dr. Rodney C. Chin, formerly of Lawrence Berkeley National Laboratory
and the University of California at Berkeley, for many useful discussions about each
of our diamond projects, and for commiseration through the downside of graduate
school. Thanks also to my Caltech officemate, Ms. Ruth Ann Bertsch, and all of the
Goddard group for stimulating scientific discussions and mutual support. I could not
have done it without you. Thanks to Dr. Dana L. Roth for fielding many questions
and providing excellent scientific references.

The production of the manuscript was aided by many friends. Thanks especially
to Mrs. Beth Hasler, who became my hands for 3 months when my wrists could no
longer stand the strain of typing and grading. Thanks to Ms. Jerri Greene of the
Caltech Student Affairs Office for arranging to fund a good deal of her time. Thanks
to Mr. Jeremy Kua and Ms. Laurine Tuleja for additional typing. I am grateful to
Mr. Gary Holt for many latex and postscript debugging sessions, and for working late
into the night to typeset transparencies for the defense. I thank Mr. Glenn C. Smith
for technical assistance in producing the central figure of Chapter 3.

Thanks to my undergraduate advisors, Profs. Eli Reshotko and Thomas Eck of
Case Western Reserve University, who taught me the love of physics and teaching,
and who occaionally served as surrogate advisors in my graduate studies. Although
graduate school forced teaching to the back burner, I hope to one day join your ranks
at an undergraduate institution. Thanks to Prof. James A. Yorke, of the University
of Maryland, for introducing me to the scientific community of nonlinear dynamics

and for being the best boss I ever had.

Finally, thanks to God for seeing to it that I never lacked for food, water, and a
place to lie my head (though the floor was sometimes harder than I wanted it to be)
through even the most dire times of graduate school, and for keeping the government
labs open long enough to be there when the experiment needed them. Graduate
school did not take anywhere near the course I had originally intended, but God
has been there all along and seen me through it. I also thank my parents, Dr. and
Mrs. Walter and Martha L. Melnik, for endless encouragement and generous financial

support, and the rest of my family for their love.

Abstract

Absolute deuterium coverage on the diamond C(100) surface has been measured under
a variety of dosing conditions by nuclear reaction analysis (NRA) using ?D(*He,p)*He.
The (2x1) surface with ~1.0 D per surface C is produced under typical dosing condi-
tions. However, at unusually high filament temperatures circa 2000°C, coverages up
to 1.34+0.09 D per surface C are observed. Coverage is calibrated by comparing to a
standard containing 1.5x10'8 D/cm?. Signal from subsurface deuterium is estimated
to be negligible by comparison to previous scattering experiments and by secondary-
ion mass spectroscopy of a homoepitaxial CVD (100) sample. D breakage of surface
dimer bonds at high filament temperature is proposed as a mechanism to generate
surface dideuterides. The relevance of dimer breakage and dihydride formation to
recent experiments on surface degradation is briefly discussed.

Previous models of hydrogen reactions with C(100) are substantially revised to
include all types of sites on the reconstructed terrace, and it is shown that satura-
tion coverage determines the ratio of site-averaged abstraction rate to site-averaged
recombination rate, k4/ke. NRA coverage measurements of 0.95 + 0.04 D per sur-
face C imply a ka/kp of 0.06 + 0.04 at 1800°C gas temperature and 360°C surface
temperature. Results indicate that thermochemical kinetic models overpredict by a
factor of ~20 the fraction of sites available for growth during diamond CVD.

In a separate issue, C(110) surface mobility is demonstrated by calculating acti-
vation energies for the migrations of H, F, and Cl with quantum chemical methods
using hydrocarbon cluster models. The calculations included extensive basis sets with
many-body effects at the level of single and double excitations from Hartree-Fock and
Complete-Active-Space wavefunctions. Intra-chain migrations of H along [110] car-
bon chains and nearest-neighbor F migration are found to be too slow to compete
with thermal desorption. However, inter-chain migrations of H and Cl are calculated

to be sufficiently fast to compete with thermal desorption under ultrahigh vacuum

vii
conditions and with gas-surface reactions under typical diamond growth conditions.
This was the first study to consider migration rates as well as barriers, establishing
mobility’s competitiveness during diamond growth. Dyjq)/Dioo1 is estimated to be
~10*. Finally, a kinetic Monte-Carlo algorithm is presented to directly combine mo-
bility with gas-surface reactions in the same iteration step when simulating hydrogen

processing of diamond.

vill

Contents

Acknowledgements
Abstract

1 Introduction

1.1 Diamond Surface Science... 2 0. ee el
1.1.1 Structure of the three major faces... . 2... ....00..
1.1.2 Thermal desorption... 2... .. 0.0.0.0. 0000. eae
1.1.3 Atomic hydrogen exposure: surface reconstruction and degra-
dation 2...
1.1.4 Molecular hydrogen exposure .............. 0004
1.1.5 Experimental technique .........0.0. 0.000000 0s

1.1.6 Rate parameters and dynamics of reactions with H(D)
1.2. Diamond Growth Experiments... .........0.....02004
1.2.1 Experimental challenges .................200.-
1.3 Thesis Overview... 0... ee

References... 00 kk ee

ili

oO WB let

2 Deuterium Reaction with C(100): Ion-Beam Scattering Experiment 27

2.1 Introduction... 2... 2. 2 ee
2.1.1 Hydrogen coverage ... 0... ee
2.1.2 Abstraction and recombination reaction rates .........
2.1.38 Chapter overview... 2.0... ee

2.2 Experimental procedure ..... 20.0.0... 00. e eee eee
2.2.1 Sample preparation... 2... 2.0.0... eee ee
2.2.2 Deuterium dosing .. 2... 0...

ix
2.2.3 Coverage measurement and calibration .............
2.3 Results... 2. ee
2.3.1 Surface reconstruction . 2... 0.0... 0.0. eee ee
2.3.2 Coverage at 1800°C 2... ee
2.3.3 Coverage at low surface temperature ..............
2.3.4 Coverage at high filament temperature .............
2.4 Analysis of deuterium coverage .........0. 02.0000. 08
2.4.1 Subsurface deuterium signal... 2.2... .......00..
2.4.2 Subsurface deuterium diffusion .................
2.4.3 Negligibility of elemental tungsten exposure ..........
2.4.4 Estimated atomic deuterium flux during dosing ........
2.4.5 Proposed effect of dosing on dihydrides and degradation
2.5 Analysis of reaction-rate ratio... 2 ee

2.5.1 Relationship between surface coverage and gas-surface reaction

2.5.2 Negligibility of inverse abstraction rates... ..........
2.5.3 Comparison to reaction rateson C(111) ........00...
2.5.4 Comparison to reaction rates in growth models ........
2.6 Conclusions ... 2...
2.7 Acknowledgements .. 2.0... 0. 0

References... 0... nk es

Migration on the C(110) Surface: Ab-initio Computations

3.1 Introduction...) 2. ee

3.2 Computational method... 2... 0.0.00. 0000. eee ee
3.2.1 Calculation of the electronic wavefunction ...........,
3.2.2. Optimization of cluster geometries ...............

3.3 Results... ee
3.3.1 Comparison of SD-HF to SD-CAS energy. ...........

3.3.2 Determination of ground and excited transition states... . .

3.3.3 Activation energies 2... 103
3.4 Analysis... 103
3.4.1 Predicted characteristic migration times ............ 104

3.4.2 Comparison of migration times to thermal desorption times. . 104

3.4.3 Comparison of migration times to gas-surface reaction times . 105

3.5 Conclusions .. 2... 107
3.6 Acknowledgements ........0. 00.0000 000. eee eee 108
References 2. 109
Figures... 0 127
SIMS profiles of hydrogen and deuterium in diamond 127
A.l Introduction... 2... 0.0.0. 0 127
A.2 Sample synthesis .......0.0..0.0.00 000000000. eee 127
A.3 Results... ee 128
A.4 Conclusions... 133
A.5 Acknowledgements .......0.0.0 2000000000 eee eee ee 134
References. 2... 135

Design of pelletron endstation for Elastic-Recoil Spectrometry 137

B.1 Motivation. 2... ee 137
B.2 Experiment in old endstation ............0.0000 00004 140
B.3 Design of new endstation. .. 2... 0... 144
B.4 Conclusions .. 0... 145
B.5 Acknowledgements ... 0.0.0.0. 00. cee ee ee 146
References 2... ee 150

Kinetic Monte-Carlo algorithm to simulate deuterium reaction with

diamond (100) (2x1) 152
C.1 Reaction mechanism .. 1... 2 152
C.2 Kinetic Monte-Carlo algorithm .........0..0...0000 0004 152

References... 0. ke 157

xi
D Off-axis potential for hydrogen abstraction from constrained isobu-
tane 158
D.1 Introduction... 2... 0... ee 158
D.2 Off-Axis GVB-CAS potential

References

List

2.1
2.2
2.3
2.4
2.5

2.6
2.7

2.8
2.9
2.10
2.11
2.12
2.13

3.1
3.2
3.3
3.4
3.9
3.6
3.7
3.8
3.9

of Figures

Atomic-scale geometry of C(100) 2.2... ee ee ee.

NRA chamber configuration .. 0... 2 ee
NRA spectrum of D-terminated C(100)................0..
NRA spectrum of calibration standard ................0.
Deuterium coverage vs. exposure at Tsy,p=360°C and Tg=1800°C . .
Deuterium coverage vs. flashing temperature subsequent to exposure
at Tyurp=S860°C 2 ee
Deuterium coverage vs. exposure at Tsyrp=80°C and Tg=1800°C. . .
Deuterium coverage vs. flashing temperature subsequent to exposure
at Tsurp=80°C 2 ee
AFM image of sample subsequent to NRA experiment. ........
AFM image of mica... 2. ee ee
Deuterium coverage at high filament temperature ...........
Upper bound for W exposure during outgas ............4..
Upper bound for W exposure during dose... .............
Proposed effect of Tpitament ANd T surface during dosing. ........

Computational cluster for (1,2) migration... ..........0..
Computational cluster for (1,3) migration... ..........00.0.
Computational cluster for (1,4) migration... .........0...
Potentials of excited transition state for (1,2) F migration ......
Potentials of excited transition state for (1,4) F migration ......
Labels of atomic centers in transition-state clusters .........,
Estimated characteristic reaction times... 2.2... .......0.4
Potentials of reactant state for (1,2) Cl migration ...........

Potentials of ground transition state for (1,2) Cl migration ......

3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
3.23
3.24
3.25
3.26
3.27
3.28
3.29
3.30

Al
A.2
A.3
AA
A.5

B.1
B.2
B.3

Xili

Potentials of repulsive states for (1,2) Cl migration ..........
Potentials of excited transition state for (1,2) Cl migration ......
Excited transition state for (1,2) Cl migration: absolute energies . . .
Ground transition state for (1,2) Cl migration: absolute energies . . .
Potentials of reactant state for (1,2) F migration. ...........
Potentials of ground transition state for (1,2) F migration. ......
Repulsive states for (1,2) F migration: absolute energies .......
Potentials of excited transition state for (1,2) F migration ......
Excited transition state for (1,2) F migration: absolute energies

Ground transition state for (1,2) F migration: absolute energies

Potentials of reactant state for (1,4) Cl migration ...........
Potentials of ground transition state for (1,4) Cl migration ......
Potentials of repulsive state for (1,4) Cl migration... ........,
Potentials of excited transition state for (1,4) Cl migration ......
Excited transition state for (1,4) Cl migration: absolute energies . . .
Ground transition state for (1,4) Cl migration: absolute energies . . .
Potentials of reactant state for (1,4) F migration. ...........
Potentials of ground transition state for (1,4) F migration. ......
Potentials of excited transition state for (1,4) F migration ......
Excited transition state for (1,4) F migration: absolute energies

Ground transition state for (1,4) F migration: absolute energies

Impurity layers grown into the diamond sample. ............,
SIMS profile of subsurface deuterium content... ...........
SIMS profile of near-surface region (high background H signal)... .
SIMS profile of near-surface region (lower background H signal)

SIMS profile of CVD film (lowest background H signal) ........

Schematic of old ERS endstation ........... 005.5 0000.5
ERS spectrum of unheated diamond sample ..............

RBS spectrum of unheated diamond sample ..............

D.1 GVB-CAS potential for H abstraction from constrained isobutane . .

List of Tables

1.1

2.1
2.2
2.3

2.4
2.9

3.1

3.2
3.3
3.4
3.9
3.6
3.7

C.l

D.1

Kinetic parameters for thermal desorption from various diamond surfaces 5

Comparison to previous experiments ........0.....00004 Al
Rough estimate of atomic D exposure... ............00.4 57
Comparison between k4/kp of previous experiments and molecular dy-

NAMICS 2. 71
Effect of activation barrier on extrapolated open-site fraction... .. 73
Effect of experimental uncertainty on extrapolated open-site fraction 73

Summary of excited and ground transition-state results for halogen

migrations 2. 99
Summary of transition-state results for H migrations ......... 99
Configurations of ground transition states for (1,2) migrations .... 100
Configurations of ground transition states for (1,4) migrations .... 101
Summary of activation barriers .... 0.0.0.0... 000 eee 103
Characteristic times for surface migrations at 900°C .......... 103
Characteristic times for gas-surface reactions at 900° ........., 106
Mechanism for reaction of hydrogen with C(100) (2x1) ........ 153

List of CAS-GVB energies as a function of attacking hydrogen position 162

Chapter 1 Introduction

Diamonds have fascinated humans since their discovery near Golconda, India in the
7th Century B.C. The Greco-Romans termed them “adamas,” meaning unconquer-
able, for their ability to withstand blows from a sledgehammer without fracturing.'
Rarely used as gemstones, and then only by the very wealthy, they often functioned
as hard components of cutting and polishing tools, and they were highly valued for
their mythical ability to ward off diseases and evil spirits [2]. In the 1870s the dia-
mond market was flooded by the discovery of the prodigious Kimberly mines in South
Africa. To preserve the industry, de Beers introduced a centrally-controlled cutting
and polishing, sales and distribution system [2, pp. 202-205], and they developed an
entirely new market through campaigns to sell diamonds to the masses in the form
of jewelry and engagement rings [3].

Recently diamond has attracted a great deal of attention because its unique ma-
terial properties make it an excellent candidate for high-technology commercial ap-
plications such as heat sinks, wear-resistant and low-friction coatings, and electron
emitters for flat-panel displays. As a semiconductor with one of the least number
of electrons, diamond is also an excellent candidate for theoretical investigations of
surface chemistry relavant to low-pressure growth. Despite the commercial and the-
oretical importance of diamond, very little is currently understood about two of the
reactions central to its processing and chemistry: hydrogen recombination with and

abstraction from the diamond surface,

Hes + CS AB, CH + hyphonon (1.1)
H.8s 4 C—Heet aan Cosa 4 Hees (1.2)
kia

‘Pliny the Elder wrote that the best way to test diamonds is “upon an anvil, and they are so
recalcitrant to blows that an iron hammer head may split in two and even the anvil itself be unseated.
Indeed the hardness of adamas is indescribable.” [1]

where C-! represents a radical surface site and C-H™ represents a hydrogenated
surface site.”

These reactions determine key parameters in low-pressure diamond growth [4, 5],
surface science [6, 7, 8], and tribology [9]. In diamond chemical-vapor deposition
(CVD), reactions between the surface and gas-phase atomic hydrogen determine the
number of surface sites available for growth.’ In diamond surface science, the hy-
drogen coverage determines the number of surface sites available for reconstruction.
In tribology, hydrogen recombination with reactive radical sites reduces friction and
wear on sliding surfaces [10]. Nevertheless, there is very little data on the rates of
these hydrogen reactions with diamond. Diamond growth modelers have found it
necessary to estimate gas-surface reaction rates from the data of analogous gas-phase
reactions [11]. The lack of rate data limits the accuracy of the growth models as well
the understanding of surface reconstruction and wear processes.

Rate data is also quite scarce in the case of adsorbate diffusion on diamond sur-
faces. Although diffusion plays a key role in determining surface structure in silicon
growth, before 1990 diffusion had not been considered possible on diamond [12].
Some studies considered only the activation barriers to migrations [12] and growth

reactions (13, 14, 15] and often concluded that migrations were negligibly slow due

?Reactions 1.1 and 1.2 are highly simplified models and do not account for the many types of
sites present on a typical diamond surface. Chapter 3 analyzes the (100) surface in detail and shows
that these simplified models yield the abstraction and recombination rate constants averaged over
all types of surface sites present.

3The number of radical surface sites is determined by the rate equations for reactions 1.1 and 1.2.

—fpsurf

d(C i ] = kp[C 8") [H-8*5] _ ka[C—H"]/H-25]. (1.3)
In steady state this reduces to [C-H*™!] = §2[C“*]. For [C5"*] = 1 —[C-H*""] (once again

neglecting other types of surface sites; see chapter 3 for a more thorough analysis),

_pysurfy
[C-H I= ayy (1.4)

Therefore the abstraction and recombination rates determine the coverage of surface radical sites
available for growth.

to their high barriers. The study described in chapter 3 [16, 17, 18] compared the
migration rates to gas-surface reaction rates and was instrumental in demonstrating
the competitiveness of diffusion on diamond surfaces.

The present research focuses on understanding diamond surface processes, such as
diffusion and hydrogen abstraction, at a microscopic level. Diamond surface science
is fundamental to this investigation, and a broad overview of it is presented in sec-
tion 1.1. The relevance of this investigation to diamond CVD is briefly discussed at
several points in the text, and a short introduction to CVD is presented in section 1.2.

Finally, section 1.3 gives an overview of the thesis.

1.1 Diamond Surface Science

1.1.1 Structure of the three major faces

The diamond surface is typically formed by cleaving the crystal and then polishing
with diamond grit in an olive oil lubricant. On (110) and (111) the dangling bonds
produced by cutting the bulk crystal are typically saturated by hydrogen which pre-
sumably derives from the olive oil. However, complete saturation is not possible on
the (100) surface because the diamond lattice is too tight, i.e., the hydrogen nuclei
on neighboring carbon centers would be less than 1 A apart. Therefore the surface
reconstucts to the (2x1):H structure shown in fig. 1.1 [19]. A (3x1) reconstruction
is also possible on the (100) surface [20] but has never been observed experimentally.
The (111) surface desorbs hydrogen upon heating to about 1000°C and reconstructs
to the (2x1) structure [21, 22]. The (100) [23, 24, 25] and (110) [26, 27] surfaces
also desorb hydrogen upon heating but no major reconstructions occur.*

The foregoing picture is highly oversimplified. In reality, some freshly-polished

samples reconstruct upon heating, while as many as 40% do not [21, 24]. Clean,

smooth samples are difficult to produce reliably, and reconstruction is sensitive to

“One group [26] has reported the appearance of faint half-order LEED spots upon heating the
(110) surface to 1227°C. This indicates a partial (2x1) reconstruction. The half-order spots were
removed by adsorption of approximately 0.1 H per surface C.

100

O11

(a) 2 x 1 reconstruction of C(100).

Figure 1.1: Atomic-scale geometry of the diamond (100) (2x1) surface. The large
grey spheres represent carbon centers, and the small white spheres represent hydrogen
centers. The arrows indicate the crystallographic directions.

surface roughness as well as to small amounts of contamination from the polishing
process or the vacuum chamber. Oxygen contamination has been associated with
the inability of a (100) surface to reconstruct [24], and exposure to atomic oxygen
has been found to destroy the (2x1) LEED pattern on the (100) surface [23]. The
mechanism by which oxygen interferes with reconstruction is unknown; however, ad-
sorption of oxygen at a bridge site affects the adjacent surface dimer [28]. Even when
parts of the sample are locally reconstructed, oxygenated sites might possibly inter-
fere with long-range reconstruction by allowing uncorrelated surface domains. If the
resulting domain size were less than 100 A, then the local reconstruction would not

be detectable by LEED [29].

Surface | A(s') Eq (kcal/mol) Order — Method Ref.
(100) 1013 4 72.7 1 TPD [23]
103 79.5 1 TPD [30]
1013 ¢ 71 1 TPD? [31]

3 x 10° 37 1 TPD (24, 25]
(110) 1913 @ 75 1 TPD [27]
5x10! gh £5 1 TPD (26)
(111) 1913 4 78 1 TPD [32]
105+? 92+9 13+0.3 SFG [33]

polycrystalline | 1019599 69 +6 1 TOF-SARS [7, 34]
5 x 107 51 1 TPD* [35]

“The prefactor was assumed to be 10!% s7?!.

’D» desorption from a D-terminated surface.

“In addition to Dz, HD and He desorption resulted from background hydrogen present during
deuterium exposure. All three species gave the same desorption parameters.

Table 1.1: Kinetic parameters for thermal desorption of hydrogen from various di-
amond surfaces. TPD is temperature-programmed desorption, SFG is the surface-
spectroscopic technique of sum-frequency generation, and TOF-SARS is time-of-flight
scattering and recoil-ion spectroscopy.

1.1.2 Thermal desorption

On the three major faces, adsorbed hydrogen desorbs as molecular hydrogen upon
heating to ~1000°C in vacuum. The rate of thermal desorption is first order in surface

coverage, 1.e.,

“u = —Aexp Pa/kT gn (1.5)
where n = 1 for first-order desorption and 6 is the areal density of surface hydrogen.
The values for activation barrier, Ey, and the pre-exponential factor, A, vary from
experiment to experiment and are summarized in table 1.1.

Although thermal desorption spectra often show a single peak characteristic of
a single desorption mode, some spectra exhibit an additional peak at lower tem-
perature [27, 30, 31, 32]. The first peak is attributed to desorption from adjacent
monohydride sites. On silicon surfaces the second peak is attributed to the presence

of dihydride sites, with a desorption barrier lower than that of monohydrides. In some

diamond cases, the second peak does not appear until a series of exposures to several

times the amount of H necessary to saturate the surface. Both a mechanical polishing
during sample preparation and a slow etching by atomic hydrogen during dosing can
cause surface roughness, leading to dihydrides. Therefore surface degradation may
generate dihydrides, causing a second thermal desorption peak to develop. All data
reported in table 1.1, except that of refs. [30] and [32], were based on spectra with

single desorption peaks.

1.1.3 Atomic hydrogen exposure: surface reconstruction and

degradation

Exposure to gas-phase atomic hydrogen changes the reconstruction of the (111) sur-
face. Chemisorption of ~0.05 D per surface C onto a bare (111) surface starts to
rapidly transform the surface from (2x1) to (1x1) [22, 33], presumably by unzipping
the w-bonded chains. The (2x1) reconstruction is restored by thermally desorbing
the deuterium upon heating the sample to 1420 K in vacuum. Subsequent expo-
sure to atomic D returns the surface to a (1x1) state. These adsorption-induced
phase transitions have been studied by thermal desorption spectroscopy (TDS), X-
ray photoemission spectroscopy (XPS), Auger electron spectroscopy (AES), second-
harmonic generation (SHG) and LEED [22, 33, 36], and by sum-frequency generation
(SFG) [33, 36].

Some experiments have found that cycling the diamond surface through a series
of atomic hydrogen exposures followed by desorption (thermal annealing) degrades
the sharpness of the (2x1) LEED pattern [21, 24]. However, other experiments found
the (2x1) pattern to be completely reproducible when the sample was heated during
dosing to 800-850°C [33] or 500°C [36]. Degradation might be caused by surface
roughness. Since mechanical polishing likely produces a rougher surface than plasma
treatment, Hoffman et al. [31] compared polished surfaces to plasma-treated ones.
They found that polished C(100) degrades upon cyclic deuterium adsorption and
desorption, even for doses performed at surface temperatures up to 800°C. How-

ever, no degradation is reported for C(100) samples prepared by hydrogen-plasma

treatment [19, 31], even when the sample temperature was as low as 27°C during
dosing. The ability of heating during dosing to prevent degradation in some cases,
and its inability in other cases, might also be explained by surface roughness. The
experiments which found no surface degradation when the sample was heated during
dosing [33, 36] were performed on polished C(111), whereas experiments which found
surface heating unable to prevent degradation were performed on polished C(100).
As a cleavage plane, polished C(111) is likely to be smoother than polished C(100).

Surface roughness has also been proposed to explain the need for ~1000°C anneal-
ing to produce the (2x1) LEED pattern on polished surfaces [19]. Whereas plasma-
treated C(100) exhibits a sharp (2x1) LEED pattern [19] upon insertion into the
vacuum chamber, mechanically-polished samples give a (1x1) pattern [23, 37, 38, 39],
though sometimes only after heating to 400-500°C [21, 24]. The (2x1) pattern does
not emerge until annealing to 800°C [23], 1200°C [39] or 1227°C [24].

The (1x1) LEED pattern also degrades upon cyclic H exposure and desorption,
again possibly due to the roughness of mechanically polished surfaces. Hamza et
al. [24] found that exposing the polished C(100) surface to large doses of atomic hy-
drogen at -93°C destroyed even the (1x1) pattern. Although the (1x1) pattern was
later restored by annealing to 427°C, heating to 1227°C did not produce a fully recon-
structed surface. The (1x1) LEED pattern further degraded upon successive cycling
through thermal desorption and atomic hydrogen exposure, necessitating periodic
repolishing of the sample.

In some experiments, surface degradation causes a second peak to appear in ther-
mal desorption spectra, possibly by generating dihydride sites, as discussed in sec-
tion 1.1.2.

In summary, surface degradation is a complex, poorly-understood process. Sur-
face roughness, as caused by mechanical polishing or adsorption-desorption cycling
below T, of 500°C, appears to be a prerequisite for degradation. Cycling the sur-
face above a temperature of 500°C causes negligible degradation, possibly due to
self-healing of local roughness by surface migration [40]. The physical mechanism for

degradation has yet to be identified, but may involve local graphitization, slow etch-

ing of the surface by atomic or molecular hydrogen, or rupture of surface C-C bonds.
Carbon-carbon bond breakage is likely a slow process initiated by (-scission through
H abstraction [{11, 41], or C-C bond breakage may be catalyzed by contamination

originating from the atomic hydrogen source [Chapter 2].

1.1.4 Molecular hydrogen exposure

Molecular hydrogen does not dissociatively chemisorb on either bare or hydrogenated
diamond surfaces below 400°C [21, 23, 27, 33, 42, 43]. However, hydrogenated dia-
mond powders become fully deuterated after one hour of exposure to Dg at 700°C [43].
Since the experiment reported in chapter 2 saw desorption above 450°C, desorption
may preceed deuteration. If desorption activates the reaction, then holding the sur-
face temperature below 450°C would preclude diamond from reacting with gas-phase
D2. Above 840°C, mass spectroscopic analysis gives evidence for the evolution of small
quantities of CD, from deuterated diamond [43]. This may indicate local reconstruc-
tion of the diamond surface followed by graphitization and subsequent etching by D»
at elevated temperatures. Annealing of diamond powders above 900°C causes local
graphitization, as detected by Raman spectroscopy [44], and heating CH,-covered
C(111) to 1200°C converts part of the CH, into graphitic carbon, as detected by
AES [22]. However, any graphitization is limited below 860°C, as the weight gained
by the powders (determined by thermogravimetric analysis) is exactly what would
be expected from replacing the surface hydrogens with deuterium [43]. Therefore,
any graphitization and subsequent vaporization to CD, would be below the detection

limit of the gravimetric instrument [43].

1.1.5 Experimental technique

Diamond surface science experiments are limited by the difficulty in preparing reli-
ably clean surfaces [6, 21]. Over the years samples have been prepared by a variety
of methods, including polishing with diamond grit lubricated by olive oil, boiling in

acids to remove metal contaminants, and ultrasonic rinsing in solvents to remove hy-

drocarbons. Plasma treatment has arisen as one of the most reliable ways to clean
diamond. The hydrogen plasma smooths the (100) surface and causes it to recon-
struct to (2x1):H [45], a surface which remains stable even in air. During experiments
physisorbed contaminants are eliminated by heating, and surface cleanliness is typi-
cally checked via XPS or HREELS. Auger spectroscopy is minimized to avoid surface
damage or degradation [31].

Diamond experiments are also challenged by the difficulty in accurate temperature
measurement. The emissivity of clear, polished diamond is typically much lower than
that of the sample holder material. Therefore, pyrometers measure the temperature of
the sample holder, usually rough molybdenum or tantalum, rather than the diamond
itself. Since thermocouples do this job just as well without requiring line-of-sight
access or viewport corrections, the majority of diamond surface science experiments
measure temperature by attaching a thermocouple to the sample holder. However,
thermocouples clamped to sample holders can be greater than the actual diamond
temperature by as much as 150°C [19] to 200°C [46]. The best accuracy is obtained
by positioning the thermocouple inside of a hole laser-drilled into the side of the
sample [46]. The graphitized surface of the hole radiates as a black-body, producing
good thermal contact, and diamond’s high thermal conductivity assures a uniform
sample temperature.

One might question why issues such as reliable sample preparation and repro-
ducible results, problems long since solved in the silicon field [47], remain central to
diamond experiments. Diamond differs fundamentally from silicon in that it graphi-
tizes upon damage or heating, transforming the sp*? bonds into sp? hybridization.
Therefore, a process commonly used to clean silicon surfaces, sputtering and anneal-
ing, destroys diamond surfaces [37, 38]. Moreover, the high-pressure process used to
grow diamond commercially produces crystals of a much smaller size and higher defect
density than the float-zone method of growing silicon crystals. Therefore, the results
of diamond experiments are much more sample-dependent than those of silicon.

The extreme physical properties that make diamond an attractive material com-

mercially also make it difficult to investigate scientifically. As the hardest natural

10
material in the world, diamond is difficult to cut and polish smooth crystal faces. As
one of the widest-bandgap semiconductors, it is difficult to probe with charged par-
ticles. Most surface analysis techniques utilize charged beams, and sample charging
becomes a significant problem when one moves from silicon to diamond. Moreover, as
a semiconductor which forms one of the strongest bonds with hydrogen and cannot
be sputter-cleaned, diamond must be heated to at least 1000°C in vacuum to desorb
the surface hydrogen. At such an extreme temperature most materials have intoler-
ably high vapor pressures, and the materials available to fabricate ultrahigh vacuum
components for diamond are severely limited compared to those for sputter-cleaned
silicon. Diamond sample holders typically consist of molybdenum, which is easier to
machine than tungsten and which outgasses orders of magnitude less hydrogen than
does tantalum [25]. However, molybdenum is itself difficult to machine, and square
corners and intricate grooves must be cut electrochemically to avoid chipping.® The
myriad of unusual challenges faced by diamond surface experiments makes them more

rare and less reproducible than those of silicon.

1.1.6 Rate parameters and dynamics of reactions with H(D)

Since molecular hydrogen has been found to be unreactive with diamond at room
temperature [21, 23, 48], reaction rates are typically investigated using atomic hy-
drogen. Atomic hydrogen is commonly produced by passing Hy over a hot tungsten
filament. The tungsten catalyzes the cracking of Hy and desorbs atomic hydrogen
equilibrated to the temperature of the tungsten, typically 0.1 to 0.2 eV. To mini-
mize tungsten transfer to the sample, hot tungsten capillary sources are shielded by a
cooled copper block [49]. Hyperthermal hydrogen has also been produced in the case
of silicon experiments by laser photolysis of a pulsed free-jet expansion of HI [50].
However, the interaction of hyperthermal beams with diamond surfaces has yet to be

investigated.

> Moreover, sample manipulator parts which are standard in stainless steel are either unavailable or
custom in molybdenum. For example, the sample holder of chapter 2 was electrochemically machined
from molybdenum plate and was clamped together with threaded rod and nuts, molybdenum screws
being rarely available commercially and prohibitively expensive.

In theory, once atomic hydrogen has been formed, the sticking probability on the
various crystal faces can be measured. However, the difficulty in calibrating H flux has
thus far prevented this from being accomplished. For a hot tungsten filament source,®
H flux calibration requires an elaborate differentially-pumped mass spectrometer with
careful analysis of a modulated hydrogen beam to account for entrapment of radicals
on the vacuum chamber walls [55, 56].

Even though absolute sticking or recombination rates have not been measured,
reaction-rate ratvos may be measured. Two particularly important reactions are hy-
drogen abstraction from and recombination with the diamond surface. The ratio
of the rates of these two reactions, k4/kpr, determines the fraction of surface sites
available for growth during CVD. Two groups have measured k4/kp, one by high-
resolution electron energy-loss spectroscopy (HREELS) [8] and time-of-flight scat-
tering and recoil spectroscopy (TOF-SARS) [7], and the other by sum-frequency
generation (SFG) [33]. The SFG results are inconsistent with the others, and all
three disagree with a value commonly used in diamond growth models [11]. Due to
the dearth of gas-surface reaction-rate data, diamond growth modelers extract their
rates from analogous gas-phase reactions [11, 57]. However, surface reactions differ
from gas-phase reactions due to the presence of surface phonons and the strain of
the underlying lattice. The models approximate surface effects by taking the high-
pressure limit of gas-phase rate constants, and the inconsistencies between the model
rate constants and the experimental rate constants may have been due in part to
this approximation. Nevertheless, this does not explain the differences between the
HREELS and SFG results, and further experiments are necessary to resolve the in-
consistencies.

Measuring the reaction rate for a range of gas-phase and surface temperatures

SLangmuir presents quite an elegant analysis of the degree of dissociation of molecular hydrogen
by a hot tungsten filament [51]. However, due to the vacuum practice at the time [52], the initial
rates of dissociation he obtained may have been affected by oxygen contamination [53]. Brennan
and Fletcher [54] investigated the effect of oxygen contamination and extended the work to cleaner
vacuum. They found that on clean W filaments the measured rate of atomization was consistent
with atomic and molecular hydrogen desorbing from the W surface in their equilibrium ratio. The
equilibrium constant is determined by the temperature of the filament and the pressure of the
molecular hydrogen.

gives information about the mechanism by which hydrogen reacts with the diamond
surface. It has recently been suggested that hydrogen reacts with diamond via a gen-
eralized Eley-Rideal (ER) mechanism [8]. In contrast to the Langmuir-Hinshelwood
mechanism, where the reactants fully accomodate to the surface before reacting, in
the ER mechanism the gas-phase reactant does not equilibrate with the surface. In-
stead the incident H provides the energy for surmounting the activation barrier, and
the reaction rate depends on the temperature of the incident H rather than on the
temperature of the surface. Each diamond experiment to date has investigated only
a single gas-phase temperature and the types of samples (single vs. poly-crystalline)
have varied across experiments. A single experiment investigating a range of gas-
phase and surface temperatures on the same sample would strengthen the evidence
for the ER mechanism.

The dynamics of hydrogen reactions with diamonds have yet to be investigated.
In the ER mechanism, the majority of the reaction energy is deposited into molecular
excitations of the gas-phase products rather than into the surface. For example, in
the abstraction of H(D) on D(H)/Cu(111), which has recently been shown to be an
ER reaction [58], approximately all of the available reaction energy is deposited into
the HD product in the form of translational, vibrational, and rotational excitation.
H abstraction of hydrogen and halogens from Si(100) has also been proposed to pro-
ceed via a generalized ER mechanism [59, 60], and the lack of sample heating by
this process makes it an attractive candidate for low sample-temperature cleaning of
semiconductor surfaces [59].

In summary, issues surrounding rate parameters and dynamics of diamond surface
reactions with atomic hydrogen have yet to be resolved. A single experiment inves-
tigating a range of gas-phase temperatures would resolve inconsistencies in previous
rate measurements. Future experiments could extend the data to include abstraction
barriers and dynamic effects by investigating reaction rates over a wide range of inci-
dent atomic hydrogen energies, from thermal energies relevant to hot-filament CVD
to hyperthermal energies relevant to plasma-enhanced deposition [61]. Results will be

vital to the development of accurate computer models of surface processing and low-

13
pressure diamond growth as well as to the development of theoretical understanding

of radical-surface reaction dynamics.

1.2 Diamond Growth Experiments

Attempts to grow diamonds artificially date back to the early 1800s. In 1796, Smith-
son Tennant, building on the research of Sir Isaac Newton and Antoine-Laurent
Lavoisier, discovered that diamonds consisted of the same material as charcoal (car-
bon) [62]. Growth methods then focused on hydrocarbon feedstocks. Early workers
tried a variety of methods to grow diamond including crystallizing it out of carbon-rich
aqueous solutions [63]’ and producing electrical discharges across carbonaceous mate-
rials [65, 66]. In the 1870s researchers realized that diamonds were made in volcanoes®
and created various types of ovens and explosions to mimic their high-temperature,
high-pressure conditions. This yielded large quantities of soot and some small stones
rumored to be diamond [2]. The technology at the time did not allow high pressures to
be sustained for long enough to grow significant amounts of diamond, and before the
advent of Raman spectroscopy it was difficult to establish growth by distinguishing
between polycrystalline diamond and amorphous carbon. Researchers refined their
growth technique and in the 1950s developed a method to produce diamond at high
pressure using Fe or Ni as a catalyst [67].

Attempts to grow diamond from low-pressure reacting gases began as early as
1911, when J. W. Hershey experimented with an oxy-acetylene blowtorch [68]. Al-
though his attempts were unsuccessful, in 1988 researchers succeeded in growing

diamond films from blow torches [69, 70].

"Due to the lack of high-pressure conditions, it is unlikely that the few crystals produced in
1828 [63] actually consisted of diamond. Recently, Zhao et al. [64] succeeded in growing diamond
from seed crystals in a solution of nickel and glassy carbon in water. However, their growth occured
at 1.4 kbar and 800°C, vastly higher pressures and temperatures than the atmospheric conditions
used in 1828.

’Before the 1860s, diamonds were panned from rivers or found scattered on beaches. Water had
washed these diamonds from their sources, volcanic ducts, so long ago that the sources were no
longer evident. In the 1860s, the first primary source of diamonds, the Kimberly mines in South
Africa, were discovered, and researchers realized that diamonds were made in volcanoes. [2, p. 199]

In the 1960s, Eversole [71] patented a method to grow diamond at low pressure and
high temperature by passing methyl-containing gas over diamond powder at ~1000°C.
Under these conditions black carbon grew along with diamond, and Eversole found
it necessary to interrupt the growth periodically and clean off the amorphous carbon
by heating the powder in hydrogen gas at about 50 atmospheres. In the past two
decades researchers have combined the cleaning and growth steps by diluting the
hydrocarbon gas in Hy [4, 72, 73, 74]. To eliminate the need for high pressure, the gas
is activated by cracking hydrogen over a hot tungsten filament [75] or in a microwave
plasma discharge [76]. The atomic hydrogen in turn activates the hydrocarbon gas
and the growing surface by abstracting hydrogen from them to produce radical sites.
Methyl radicals in the gas grow the diamond by recombining with surface radical
sites [4, 11, 57]. A series of abstractions and rearrangements subsequently bond
the methyl carbon to the other carbons in the diamond lattice. Similar reaction
mechanisms have been proposed for diamond growth from acetylene [77, 78].

In low-pressure CVD reactors, feedgas composition is typically 1% methane or
acetylene and 99% hydrogen. Higher methane fractions give rougher growth sur-
faces [79] and codeposition of amorphous carbon. Diborane and phosphine have also
been included in the feedgas at the ppm level to p- or n-dope the diamond either for
electronic applications or to simply increase the conductivity to allow ex-situ SEM
observation [80]. However, n-doping has not yet been reported to be sucessful. Sub-
strate temperature is typically 700-1000°C during growth. Reducing the substrate
temperature from 700°C to 400°C decreases the growth rate from 0.1 wm/hr to 0.006
pm/hr [81].

1.2.1 Experimental challenges

In-situ growth monitoring is difficult; high temperature and atomic hydrogen are not
particularly welcoming to many probe materials. Non-intrusive optical techniques
such as REMPI [82] have been the most successful at gaining information about

the gas-phase growth environment. The gas composition at the growing surface has

15
been measured quite elegantly, by drilling into the substrate an entrance hole to
a molecular-beam mass spectrometer [83]. McMaster et al. have built upon this
technique to measure the gas-phase concentrations of H, CH3, CH4 and C2Hp» in
MWCVD [84] and HFCVD [85] reactors.

One of the challenges in growth experiments is temperature measurement. The
diamond temperature is usually measured by optical pyrometers or thermocouples.
There is a temperature gradient over the substrate, and quoted growth temperatures
are often averages over the substrate area, in the case of pyrometric measurement,
or the thermocouple locations, in the case of thermocouple measurement.? Thermo-
couple measurements are complicated by thermal gradients between the sample and
junction. Gradients can be minimized by inserting the junction directly into a hole
drilled in the diamond [46]. However, typical diamond samples are too small to
contain holes for thermocouple junctions, and thermocouples are usually located on
the sample holder. Optical pyrometric measurements are complicated by diamond’s
low emissivity. The emissivity is so low that most of the radiative flux impinging on
the pyrometer originates from the material directly behind the substrate. Typically
the emissivity of the sample holder is assumed to be constant, neglecting the variation
with temperature, chemical state and roughness of the surface.

In practice temperatures are measured to ensure repeatable results between growth
runs rather than to identify the exact surface temperature. For example, in Kamo-
type reactors there is no temperature control independent of the plasma, and the
microwave power and cavity length are adjusted during the run to produce the desired
temperature. This is an important point to keep in mind when comparing theoretical
predictions to experimental data.

Measurement questions aside, growth experiments are time-consuming. Unlike
silicon, where huge market forces have reduced sample preparation to a fine art, dia-
mond sample preparation is generally done by “cut and try.” Moreover, investigating

the effect of growth conditions on growth rate or film quality requires a large num-

°For example, in MWCVD experiments performed by the author at the National Institute for Re-
search in Inorganic Materials, temperatures typically varied by 30°C over the area of the 6 mm x6 mm
substrate. Temperatures were measured pyrometrically assuming a constant emissivity of 0.5.

16
ber of runs to span the huge parameter space of temperature, pressure, flow rate,
and gas-phase composition. The difficulty of preparing samples and optimizing the

growth experimentally motivated the development of diamond growth models [4, 11].

1.3. Thesis Overview

The present research addresses some of the challenges in diamond surface science and
uncovers new ones. In chapter 2, measurements of absolute deuterium coverage on
C(100) by nuclear reaction analysis (NRA) are reported. This is the first time ab-
solute coverage has been measured on a (2x1) surface with LEED characterization,
confirming the (2x1):D reconstruction. Previous models of hydrogen reactions with
C(100) are substantially revised to include all types of sites on the reconstructed
surface, and it is shown that steady-state coverage measurements give the ratio of
site-averaged abstraction rate to site-averaged recombination rate, k4/kp. The cov-
erage measurements are analyzed to determine k4/kp at 1800°C filament temperature
and 360°C surface temperature. Absolute deuterium coverage is also reported under
a variety of dosing and annealing conditions. However, high filament temperature
during dose produced unexpectedly high coverage, and D breakage of surface dimer
bonds is proposed as a mechanism to increase coverage. The relevance of dimer break-
age and dihydride formation to recent experiments on surface degradation are briefly
discussed. All NRA measurements reported in Chapter 2 were completed at the Oak
Ridge National Laboratory in Oak Ridge, Tennessee.

Issues related to the NRA measurements are addressed in the appendices. In
appendix A, the question of subsurface signal in the NRA spectra is addressed by mea-
surements of subsurface deuterium content via secondary-ion mass spectroscopy(SIMS).
To prevent charging during SIMS, boron-doped samples were grown by microwave-
plasma CVD. Sample growth and SIMS measurements took place at the National
Institute for Research in Inorganic Materials, Tsukuba, Japan. In appendix B, a
summary is given of the design and development of an ultrahigh vacuum endstation

to perform measurements equivalent to NRA in the Caltech Pelletron.

The question of surface mobility at growth temperatures is addressed in chapter
3. Mobility is demonstrated by calculating activation energies for the migrations of
H, F, and Cl on the C(110) surface by quantum chemical methods using hydrocarbon
cluster models. The calculations included extensive basis sets with many-body effects
at the level of single and double excitations from Hartree-Fock and Complete-Active-
Space wavefunctions. The calculated activation barriers for the (1,2) migrations of H,
F and Cl and the (1,3) migration of H indicate that such migrations are too slow to
compete with thermal desorption. The (1,4) migration of F is also slow. However, the
(1,4) migrations of both H and Cl are calculated to be sufficiently fast to compete with
thermal desorption under ultrahigh vacuum conditions and with gas-surface reactions
under typical diamond growth conditions. Previous studies had considered only the
activation barriers to migrations [12] and growth reactions [13, 14, 15] and often
concluded that migrations were negligibly slow due to their high barriers. This was
the first study to consider the migration rates and establish that they were sufficiently
fast to compete with gas-surface reactions during growth [16, 17, 18]. Implications
of mobility for thermal desorption and diamond growth are briefly discussed. In
appendix C, a kinetic Monte-Carlo algorithm is presented which incorporates mobility
into diamond surface reaction models. The algorithm cuts in half the number of
required integrations by addressing migration in the same iteration step as gas-surface

reactions and developing a general scheme to weight reaction probabilities accordingly.

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7577 (1994).

Chapter 2 Deuterium Reaction with

C(100): Ion-Beam Scattering Experiment

2.1 Introduction

Diamond surface experiments have attracted attention in recent years [1], fueled by
the relevance to models of low-pressure diamond thin-film growth [2, 3, 4] for elec-
tronic and industrial applications. Although the experiments have increased our
understanding of diamond surface processes, several issues remain unresolved. These
include absolute hydrogen coverage on C(100) and the rates of abstraction and re-
combination with gas-phase atomic hydrogen. Absolute coverage is an important
parameter in diamond surface models, and predictions for the (100) face range from
0 to 1.33 hydrogen per surface carbon [5, fig. 4]. A coverage of two hydrogen per
surface carbon has also been proposed, but has been found to be unstable due to
the steric crowding of the hydrogens [5, 6]. Reaction rate constants are intimately
related to coverage, in that they determine the saturation coverage under typical hy-
drogen dosing conditions and the fraction of sites available for growth during thin-film
deposition. Issues relating to hydrogen coverage are reviewed in section 2.1.1, and
reaction-rate research is discussed in section 2.1.2. Section 2.1.3 concludes with an

overview of the chapter.

2.1.1 Hydrogen coverage

Measurements of absolute hydrogen coverage are rare. Relative coverages may be
measured by intergrating peaks generated by surface spectroscopies or temperature-
programmed desorption (TPD), but the normalization factors are difficult to cali-

brate. In contrast, ion-beam scattering techniques are easily calibrated by compari-

son to ion-implanted standards, and nuclear sensitivity assures that the measurement
integrates equally over all bonding configurations. Derry et al. [7] measured coverage
on polished C(100) by nuclear reaction analysis and found 2 H per surface C. However,
the sample was unheated and may have contained physisorbed hydrocarbons. Yagi et
al. [8] found 3-4 H per surface C on MWCVD homoepitaxial C(100) by elastic-recoil
spectrometry. Their samples were also unheated. Dollinger et al. [9] found a cover-
age of 1 H per surface C on plasma-treated C(100) by medium-energy ion-scattering
(MEIS). The exact value of hydrogen coverage on C(100) remains unresolved.

The coverage is modified when diamond is dosed with atomic hydrogen gas, due
to abstraction and recombination reactions. The absolute saturation coverage from
dosing has not been measured but may be estimated from reaction-rate ratios implied
by relative coverage measurements. Thoms et al. [10] obtained a ratio implying
0.95 + 0.01 D per surface C on polycrystalline diamond by high-resolution electron-
energy loss spectroscopy (HREELS). The gas-phase temperature was equal to the
filament temperature, 1800°C, and the surface temperature was 80°C in one set of
experiments and 600°C in another. Both surface temperatures implied the same
coverage. Koleske et al. [11] obtained a ratio implying 0.97 + 0.01 D per surface
C at a filament temperature of 1560°C from time-of-flight scattering and recoil-ion
spectroscopy (TOF-SARS). However, Chin e¢ al. [12, 13] measured a ratio implying
0.83 H per surface C from sum-frequency generation (SFG) spectroscopy of hydrogen-
dosed diamond (111). Chin’s filament was at 1800°C during dosing, and his surface
temperature varied from room temperature to 200°C due to radiative heating by the
hot filament. The saturation coverage may vary with filament temperature, surface
temperature, hydrogen isotope and crystallographic orientation of the surface. Full
characterization of the effect of dosing parameters on absolute coverage has yet to be

accomplished.

Monohydride vs. dihydride production by dosing

Although the (100):(21) surface contains up to 1 H per surface C, hydrogen coverage
can be greater than 1 due to the presence of dihydrides. The (100) crystal plane cuts

2 bonds for each carbon, leaving enough unpaired electrons to form up to two CH
bonds, or 2 H per surface C. However, the steric crowding of neighboring hydrogen
centers makes this surface unstable to reconstruction to a (2x1) structure, with up
to 1 H per surface C, or a (3x1) structure, with up to 1.33 H per surface C [5, fig. 4].
The carbon centers on the (21) surface form rows of dimer bonds with monohydride
termination, and those of the (3x1) surface form rows of dimer bonds alternating
with undimerized dihydrides. Low-energy electron diffraction (LEED) distinguishes
between the (21) and (3x1) structures. However, for small surface domains less than
~100A across, LEED shows only the (1x1) pattern of the underlying bulk atoms. Re-
ported LEED patterns of C(100) include both the (1x1) [14, 15, 16, 17, 18], consistent
with disordered dihydrides or monohydrides, and (2x1) [17, 18, 19, 20], consistent
with ordered monohydrides. Sample preparation [16, 19], surface roughness [12], and
surface temperature during hydrogen dosing [13] have all been found to affect recon-
struction and surface quality. The existence of dihydrides cannot be established by
LEED, and conditions which generate dihydrides remain controversial.

Infrared spectroscopy is able to distinguish between mono- and di-hydrides and
has the advantage of good resolution, ~6-20 cm~!. Infrared sum-frequency generation
(SFG), a nonlinear optical effect, is symmetry-forbidden in the bulk and therefore has
excellent surface sensitivity. Chin [12] found peaks with shoulders in the CH stretch
region on polished C(100) by SFG. However, he was unable to observe bending modes,
and he interpreted the spectra as indicating monohydrides with two different bonding
arrangements. Fourier-transform infrared spectroscopy (FTIR) has good resolution
but poor surface sensitivity. Surface sensitivity is increased by performing multiple-
internal-reflection FTIR (MIRIRS). Yang et al. [5] found a CD deformation mode at
901 cm~! on polished C(100) by MIRIRS following exposure to atomic deuterium.
However, they were unable to distinguish surface CH stretches from background due
to hydrocarbon impurities.

HREELS identifies hydrides by assigning loss peaks to CH and CH, stretch and
deformation modes. However, peak assignment is rendered difficult by poor reso-

lution, typically 60-100 cm7? [21]. For a surface with a mixture of mono- and di-

hydrides, CHg symmetric and antisymmetric stretches may be indistinguishable from
the CH stretch peak. Spectral deconvolution and off-specular collection are two of the
most powerful tools in interpreting spectra. However, specular deconvolution which
assumes dipole selection rules is invalid on C(100), and impact scattering selection
rules are difficult to apply [22]. When dipole scattering dominates, on-specular col-
lection gives sensitivity to modes with dynamic-dipole moments perpendicular to the
surface, namely CH stretch and CH, symmetric stretch. However, in off-specular col-
lection, impact scattering increases relative sensitivity to CH» antisymmetric stretch.
Therefore, dihydrides may be identified by a splitting in the CH stretch peak as the
collection moves from on-specular through off-specular angles.

HREELS experiments show evidence for both mono- and di-hydrides. Lee and
Apai [17] performed spectral deconvolution on data from polished C(100) and con-
cluded that the (1x1) surface contained mono-, di- and tri-hydrides. However, the
assumption of dipole selection rules may be inaccurate [22]. Heating the sample
to 1200°C produced a (2x1) surface which was concluded to be totally free of hy-
drogen from the lack of any CH stretch modes near 2900 cm~!. Dosing the sam-
ple with atomic hydrogen reproduced the (1x1) pattern and the original spectra
with multiple-hydride modes. Results were completely reproducible upon repeated
dosing-annealing (adsorption-desorption) cycles. Aizawa et al. [23] found no split-
ting of the CH stretch peak at off-specular angles and concluded that the surface
contained only monohydrides. Their sample was grown by microwave-plasma CVD
on a (100) substrate. Sun et al. [24] assigned modes to the features in their specu-
lar HREEL spectra and concluded that the surface contained dihydrides. However,
the assumption of dipole selection rules may again be inaccurate. The sample was
facetted (100) grown by hot-filament CVD on a silicon substrate. Thoms et al. [19]
detected no CH peak split at off-specular angles and concluded that their sample
was terminated by monohydrides. The sample was hydrogen-plasma treated C(100).
The sample remained (2x1) even upon hydrogen dosing, and spectra were completely
reproducible upon repeated adsorption—desorption cycles.

Evidence for mono- and di-hydrides has been found by temperature-programmed

desorption (TPD) and electron-stimulated desorption (ESD). TPD spectra from C(100)
typically show a single peak near 900°C assigned to Hy desorption from monohydride
sites [20]. However, Yang et al. [5] observed a low-temperature shoulder in the des-
orption peak from polished C(100) and suggested dihydrides as a cause by analogy
with $i(100).' Hoffman et al. [27] found two desorption peaks from C(100):(1x1).?
Double desorption peaks appeared after repeated adsorption—desorption cycles, cou-
pled with electron bombardment, which may indicate dihydride generation. Hamza
et al. [18] observed two H* peaks in time-of-flight ESD on polished C(100):(1x1)
and assigned the fast peak to dihydrides. Upon annealing to 900°C the fast Ht peak
disappeared, the surface displayed a (2x1) LEED pattern, and the remaining peak
was assigned to monohydrides. Dosing the sample with atomic hydrogen returned the
surface to a (1x1) structure and reproduced the original ESD peaks. After repeated
adsorption—desorption cycles, the (2x1) pattern was no longer generated.

Clearly, both monohydrides and dihydrides exist on the C(100) surface, and the
conditions to generate dihydrides remain unclear. The greater roughness of polished
surface increases the probability of dihydrides. However, even a smoother H-plasma
treated samples can exhibit double TPD peaks upon repeated adsorption—desorption
cycling (coupled with electron-beam irradiation) [27]. Conditions under which dihy-

drides appear upon adsorption—desorption cycling have yet to be understood.

2.1.2 Abstraction and recombination reaction rates

The ratio of the rate constant for hydrogen abstraction (k,4) to that for recombination
(kr), when averaged over all surface sites, is important in both diamond surface
science and diamond growth experiments. In diamond surface science it determines
the maximum surface coverage attainable by typical hydrogen dosing conditions, and

in diamond chemical-vapor deposition (CVD) it determines the fraction of surface

‘Butler et al. [25] also published desorption peaks with distinct shoulders from C(110), and
Hagstrom et al. [26] found double desorption peaks from C(111).

“Hoffman [28] recently found low and high-temperature desorption peaks from C(111) and as-
signed them to desorption from dihydride dimers at steps and monohydride sites on terraces, re-
spectively.

32
sites available for growth.

Recently several groups have measured the ratio, k4/kz. The results are not di-
rectly comparable across experiments due to variations in crystallographic orientation
of the sample surface, hydrogen gas temperature and hydrogen isotope. However, all
experiments disagree by an order of magnitude with a ratio commonly used in dia-
mond growth models. Thoms e¢ al. [10] inferred a k4/kp of 0.05+0.01 from HREELS
of deuterium-dosed polycrystalline diamond. Due to the low pressure in the reaction
chamber, the gas-phase temperature was equal to the filament temperature, 1800°C,
and the surface temperature was 80°C in one set of experiments and 600°C in an-
other. Both surface temperatures gave the same k4/kp. Koleske et al. [11] obtained
a similar reaction-rate ratio of 0.03 + 0.01 at a filament temperature of 1560°C from
TOF-SARS. However, Chin et al. [12, 13] obtained a ratio of 0.2 from SFG spec-
troscopy of hydrogen-dosed diamond (111). Chin’s filament was at 1800°C during
dosing, and his surface temperature varied from room temperature to 200°C due to
radiative heating by the hot filament. On the other hand, reaction rates typically
used in thermochemical kinetic diamond growth models [29, 30] give a ratio of 2.14
at 1800°C. These rate constants were estimated from gas-phase data, where the hy-
drogen temperature is the same as that of the alkane modeling the surface.

Due to the dearth of gas-surface reaction-rate data, diamond growth modelers
extract their rates from analogous gas-phase reactions [29, 31]. However, surface
reactions differ from gas-phase reactions due in part to steric hindrance from sur-
rounding surface atoms and the strain of the underlying lattice. Surface effects are
approximated by taking the high-pressure limit of gas-phase rate constants [29, 31],
and errors are introduced by the inadequacy of this approximation. Moreover, due
to the exponential dependence on temperature and the variation across experiments,
many gas-phase rate constants are not known to better than a factor of five. There-
fore the ratio of rate constants taken from gas-phase data may be in error by an order
of magnitude. Directly measuring the ratio of recombination to abstraction rate
constants on a diamond surface would improve the accuracy of growth models.

Nevertheless, reaction rates measured by surface-science experiments are difficult

33
to apply to CVD conditions. Surface-sensitive techniques such as HREELS, TOF-
SARS, and SFG require low pressure to minimize beam attenuation and ultra-low
pressure to avoid surface contamination. At such low pressures the mean free path
of the gas molecules is much larger than the size of the vacuum chamber itself. Al-
though this gives surface-science experiments the unique ability to separately control
gas and surface temperatures, the large difference between gas and surface tempera-
ture make the data difficult to apply to continuum reactions. To date all experiments
have fixed the gas temperature and most have investigated only one or two surface
temperatures. Only the TOF-SARS experiment has measured reaction rate for a
series of surface temperatures and found an apparent activation barrier of 0.8 + 0.2
kcal/mol, suggesting a direct (Eley-Rideal) reaction upon impact with the surface,
with an early transition state. In contrast, in a Langmuir-Hinshelwood mechanism
the gaseous species equilibrates with the surface before reacting, and the rate is de-
termined by the surface temperature, T;. Measuring k4/kp for a series of gas and
surface temperatures would tell which mechanism is active or whether both partici-
ka —E, —E

pate to a degree, e.g., — = Aexp —— exp ~. It would also clarify the relevance
kr kpT, kpT,

of low-pressure data, where T, # T,, to diamond growth, where T, = Ts.

The effect of isotope on reaction rate is unknown. Some experiments exposed a
deuterated diamond surface to hydrogen gas while others exposed a hydrogenated
diamond to deuterium gas. Most groups assume ky = kp when reducing their data,
and in some cases the isotopic effect has been investigated and found to be small.? In
SFG experiments Chin et al. [13] found the rate of reaction of gas-phase H with C(111)
to be similar to that of gas-phase D. However, Koleske et al. [11] measured the rate of
D(g) abstraction of surface-bonded H to be 2-4 times the rate of H(g) abstraction of
D on polycrystalline diamond. They suggest that on C(111)-like sites, D(g) is more
efficient at abstraction because its higher momentum allows it to impart a greater
displacement to the surface carbon, establishing a weak z-bond between the surface

and neighboring carbon atoms. It has yet to be determined whether the isotopic effect

*In the case of a surface-surface reaction, thermal desorption, Schulberg et al. [32] observed no
isotopic effect on desorption of Hy, HD and Dg from polycrystalline CVD diamond.

34
varies with crystallographic orientation. On a surface analogous to C(100), Si(100),
Sinniah et al. [33] found an isotopic effect opposite to that on polycrystalline diamond:
the rate for D(g) abstraction of surface-bonded H was only 0.2 times the rate for
H(g) abstraction of D. Thus, the isotopic effect on diamond surface reactions remains

unresolved, and its dependence on surface orientation requires further investigation.

2.1.3 Chapter overview

The issues of absolute coverage on C(100), its dependence on dosing conditions, and
the reaction-rate ratio k4/kpr are addressed by measuring the amount of deuterium
on the diamond surface by nuclear reaction analysis (NRA). Absolute deuterium cov-
erage is reported under a variety of sample annealing and atomic deuterium dosing
conditions. The experimental procedure is described in section 2.2, and results are re-
ported in section 2.3. Coverage is measured for dosing at 1800°C filament temperature
and 360°C surface temperature. However, an attempt to identify the effect of gas and
surface temperatures on reaction rates revealed unexpectedly high coverages at high
filament temperature. A generic mechanism to generate high coverage at high fila-
ment temperature is proposed in section 2.4.5 and compared to the results of previous
dosing experiments. In section 2.5 previous models of hydrogen reactions with C(100)
are substantially revised to include all types of sites on the reconstructed terrace, and
it is shown that steady-state coverage measurements give the ratio of site-averaged
abstraction rate to site-averaged recombination rate, k4/kpr. Section 2.5 discusses
the relevance of the results to chemical kinetics models of diamond growth. Finally,

section 2.6 summarizes the conclusions.

2.2 Experimental procedure

Unless otherwise noted, all experiments were performed at the Surface Modification
and Characterization (SMAC) Research Center of Oak Ridge National Laboratory in
Oak Ridge, Tennessee.

2.2.1 Sample preparation

The sample was a type ITA natural diamond cut along (100) + 3° by Harris Diamond
Corporation. In a prior experiment at Caltech, the sample had been bombarded
with 1.9 MeV “He* at 5nA for ~50 minutes to obtain RBS and ERS spectra. The
bombardment produced some lattice damage and turned the sample from colorless
to light grey.

To clean the surface for the NRA experiment, the sample was hydrogen-plasma
treated in an Astex reactor at the Gas/Surface Dynamics Section of the Naval Re-
search Laboratory. Hydrogen plasma treatment is one of the most reliable methods to
prepare diamond samples. Plasma treatment smooths the (100) surface and causes
it to reconstruct to (2x1):H [34]. Prior to treatment the sample was boiled for 15
minutes in a solution of 3 parts HCl to 1 part HNO 3 aqua regia, followed by boiling
for 18 minutes in a solution of 3 parts H2SO, to 2 parts HNO3. The sample was then
hydrogen-plasma treated at 750°C and 10 torr for 20 minutes. The microwave power
was 600 W, and the hydrogen flow rate was 500 sccm. The temperature was measured
by a thermocouple located behind the substrate heater; the actual diamond surface
temperature was estimated to be 800°C. The reactor contained a CVD-diamond-
coated substrate holder to minimize sample contamination. Finally, the back side of

the sample was also plasma treated.

2.2.2 Deuterium dosing

The sample was mounted on an all-molybdenum holder and installed in a stainless
steel ultrahigh vacuum chamber (fig. 2.1). The chamber was pumped by turbomolec-
ular and ion pumps. The base pressure was 2.0 x 10~!° torr, and the dosing pressure
was 5.0 x 10~® torr. During sample annealing, the pressure momentarily rose to
~2x1078 torr, presumably due to outgassing of D2 from the ceramic beads insulating
the thermocouple leads. The sample was heated by electron bombardment of the
back of the molybdenum holder. The sample temperature was measured by an E-

type thermocouple clamped to the front of the sample holder about 3 mm from the

Pyrometer
window
To Mass
‘urbomolecular spectrometer
pump
Deuterated
diamond
Wy \
* He’ HES
0.7 MeV i”
os Stopper foil
Detector
Deuterium
doser
LEED

Figure 2.1: NRA set-up.

sample. The filament’s brightness temperature was measured via optical pyrometry,
and values were converted to absolute temperature [35, p. 10-283] without correcting
for viewport bias. The sample temperature during bake-out was similar to that of
the rest of the chamber, and the sample surface and doser filament were annealed
prior to each dose. The ion pump was valved-off during dosing, to extend its life, and
during annealing, to minimize the partial pressure of Do.

Prior to each dose, the sample and doser filament were annealed simultaneously to
avoid cross-contamination. Before annealing the sample was positioned to face ~180°
away from the doser. Then the doser filament was outgassed at 2220°C for 2 minutes
in order to desorb any tungsten oxide [36, 37]. After 2 minutes, the sample was flashed

to 990°C and held between that and ~1050°C for about 2 minutes to desorb the

surface hydrogen. (Thoms e¢ al. [19] conclude from their HREEL spectra that C(100)
is free of adsorbed hydrogen upon heating to 1050°C for approximately one minute.)
Then the heater bias voltage was turned off, and the hot filament was decreased
to ~50°C above the filament dosing temperature. Once the sample had cooled to
a few degrees above the surface dosing temperature, the filament temperature was
decreased to its dosing value, and the D2 leak valve was opened. After the pressure had
stabilized to 5.0 x 10~® torr, the sample was quickly rotated into the dosing position.
About 3 seconds were required to rotate the sample into position, and exposures were
not corrected for the rotation time. In the dosing position, the distance between the
sample surface and doser filament was about 4 cm. Throughout dosing the sample
temperature was maintained to within 38°C of the desired surface dosing temperature
by radiative heating from behind. Upon completion of dosing, the sample was quickly
rotated to face ~180° away from the doser, the leak valve was simultaneously closed,
and then the doser filament amperage was turned off.

During exposure the surface temperature was either 80° + 3°C or 360° + 3°C,
and the filament temperature was 1735° + 20°C, 1800° + 20°C, 1975° + 20°C, or
2025° + 20°C. The true filament temperature is higher than the measured value by
about 50°C due to viewport bias [38].

2.2.3 Coverage measurement and calibration

The total deuterium coverage, 9p, was measured by counting the protons produced
by the nuclear reaction *D(*He, p)“He. The incident "Het beam energy was 0.740.003
MeV, the current was typically 1 nA, and the beam spot diameter at the sample was
2mm. Collection time for each spectrum was about 100 seconds. Relative beam dose
was measured by accumulating backscattered ions from a gold-plated beam chopper
rotating at ~10 Hz. The beam was incident normal to the sample, and the proton
spectra were collected by four solid-state detectors located about 2 cm in front of the
sample. Stopper foils of 25.4 zm thick nickel were placed in front of the four detectors
to filter out backscattered *He* ions and pass the ~13 MeV protons [39, p. 238]. The

38
deuterium doser filament, which was located a few cm from the four detectors, was
turned off during NRA to keep the spectrum’s proton peak well-separated from the

thermal noise peak.

10 F ai
a |
8 C
7 oc cecceedeceecectescesdecessetecssilescseecstsebececesissesesbeccsessssecteesen
gL 6 : coe
g c
3 5
O " Area of Peak
4 S597 E90 D/C
E surf
SF Average of 7 spectra NO
2 ban 55.6+£3.3 DIC... oe ne
Po Eeerercnereecbesesceceeeeefeencsneccceeefesceeseccteenpeceecennnes Co a a 4
0 200 400 600 800 1000
Channel « E

proton

Figure 2.2: NRA spectrum of D-terminated C(100). The quoted errors represent
the resolution in the measurement due to the finite number of events counted. For
example, a total of 44 events were detected in this spectrum. The spectrum was
collected subsequent to 1500L exposure at a filament temperature of 1800°C and a
surface temperature of 360°C, followed by a series of anneals to 800°C and 630°C.

The sample was aligned with respect to the beam spot by scanning in the two
directions perpendicular to the beam, y and z, and by rotating the sample about
the z axis. Coverage values peaked on the sample and decreased when the beam
was scanned off the sample onto the holder. After alignment, spectra were typically
collected at two to four locations completely on the sample, and often more than
one spectrum was taken at any one location. The spatial deuterium distribution was
uniform over the sample to within the scatter from spectrum to spectrum at any one
location. The coverage is assigned to be the average value of all the spectra taken at
the two to four locations. The resolution in the coverage measurement is taken to be
£p. where 8p is the measured coverage, and N is the total number of events counted.

VN?
Deuterium coverage was calibrated by comparing the total counts from the sample

1000 F
900 F |
800 Fo Aréa of Peak
700 F=(1:506*-0:006) ‘0! pyem’
2 600 r_...... iverage of 7 spectra
: 500 f= (i:307 £.0.002) 10° D/cm
Y 400 E
300 :
200
100 E
0 200 400 600 800 1000
Channel « E

proton

Figure 2.3: NRA spectrum of calibration standard. The quoted errors represent the
resolution in the measurement due to the finite number of events counted. A total of
70873 events were detected in this spectrum.

to the total counts from a secondary standard. The secondary standard was an a-C
film chemically vapor-deposited in deuterium atmosphere on a Si substrate. In a
prior experiment the D incorporation in the film was measured to be (1.5 + 0.01) x
10'* D/cm? by comparison to a primary (ion-implanted) a-C standard. In the NRA
experiment, the (secondary) standard was first located with respect to the beam spot
by scanning in the y and z directions. Spectra were then collected at four locations
on the standard, and the resulting deuterium distribution was uniform to within 3%.
The average of the total counts in the four spectra was taken to be equivalent to
1.5 x 10'° D/cm?. Calibration spectra were collected several times over the course
of the experiment, and the average value varied by only about ~1%. The error in
the calibration factor is taken to be 1%. Sample NRA spectra are shown in figs. 2.2
and 2.3.

Deuterium coverages are reported in units of D per surface C, where the areal
density of surface carbons is assumed to be that of an ideal (100) surface, 1.566 x
10° /cm?,

The lower detection limit of NRA is determined by the background cosmic radia-

40
tion incident on the detectors. For spectral collection times typical to this experiment,
the spectrum for no incident helium ions consisted of one count, implying a lower de-

tection limit of 0.02 x 10’°D/cm? or 0.013 D per surface C.

2.3 Results

2.3.1 Surface reconstruction

Due to the hydrogen-plasma pretreatment, the sample surface was reconstructed upon
insertion into the vacuum chamber [34]. The (2x1) reconstruction remained even
after several thousand langmuirs (L) of deuterium dosing. After about 10* L of
exposure, the surface reconstruction was characterized via LEED at ~115 V, and a
(2x1) pattern was clearly evident. During LEED the sample was heated to ~100°C

to avoid charging.

2.3.2 Coverage at 1800°C

Figure 2.4 shows deuterium coverage after dosing at a filament temperature of 1800°C
and a surface temperature of 360°. Coverages are reported in units of monolayers,
where one monolayer is one D per surface C, and the atomic density is taken to be
that of the ideal (100) surface, 1.57 x 10'°C/cm?. An exposure of 2500L appears
to be sufficient to reach saturation coverage. The saturation coverage of 0.95 + 0.04
agrees with the coverage of 0.95 + 0.01 implied by Thoms et al.’s [10] analysis of
their HREELS data.* The saturation coverage differs from the value of 0.83 implied
by Chin et al.’s [12, 13] data for C(111), and the significance of the difference is
discussed in section 2.5.3. Table 2.1 compares the saturation coverages implied by

previous experiments to that obtained by NRA.

“During NRA the sample was cooling subsequent to exposure, and the sample temperature was
decreasing between 285° and 40°C.

Dosing Conditions for T, 360°C

1.5
r : * T.1800°C
fil
S)
g 1 ;
£ ;
wn
eel
ov
Du .
Q 0.5
fan)
0 500 1000 1500 2000 2500 3000

D , exposure (L)

Figure 2.4: Deuterium coverage as a function of exposure at a filament temperature
of 1800°C and a surface temperature of 360°C. Each point represents an independent
experiment. The sample was not annealed after exposure. The error bars represent
the resolution in the coverage measurement. For example, a total of 697 events were
detected in the 2500L case. The error due to the number of events counted was
greater than the error in the calibration factor.

Reference Surface Tsurtace Tflament Ka/kR Saturation coverage
Koleske [11] poly 500°C =1560°C )=—00.03 £0.01 0.97 + 0.01 D/surf C
Thoms [10] poly 80-600 1800 0.05+0.01 0.95+0.01

NRA (100) 360 1800 0.06+0.04 0.95+0.04

Chin [13] (111) s«:25-200 1800 0.204? «08347? H/swfC

Table 2.1: Comparison to coverages implied by previous experiments. The reaction-
rate ratios measured by previous experiments were converted into coverages via
eq. 2.27.

Thermal desorption

The sample was heated subsequent to dose, and coverages were measured as a function
of heating temperature. Results are shown in fig. 2.5. For heating temperatures under
200°C, the sample was heated at a rate of ~10°C/sec and held at the annealing
temperature for about 2-5 minutes. Below 200°C the annealing time did not affect
coverage. For temperatures over 200°C, the sample was flashed to a temperature of
Trash at a rate of ~10°C/sec, and heating was turned off within seconds of attaining
Trash. The amount of deuterium desorbed between 470°C and 800°C in fig. 2.5
implies a desorption barrier of 3.0 eV, assuming first-order desorption with a pre-
exponential factor of 10'%/sec and a heating rate of 10°C/sec. The desorption barrier
of 3.0 eV agrees with the barrier of 3.08 eV implied by the temperature-programmed
desorption data of Hoffman et al. [27] for D2 desorption and Thomas e¢ al. [20] for He
desorption. However, any rate parameters calculated from the NRA flashing results
are less reliable than those of TPD experiments because the NRA heating rate was
not carefully controlled.

Note that 10%+7% of a monolayer desorbs upon heating to ~600-620°C, whereas
a negligible amount of deuterium desorbs at temperatures below 450°C. Hoffman
et al. [27] also detected desorption at 600°C from a plasma-pretreated, undegraded
C(100):D sample. Thomas et al. [20] found desorption from C(100) at 600°C after
~1000 L hydrogen exposure. However, Thoms et al. [10] found negligible desorption
at 600°C from polycrystalline diamond. The reason for the discrepancy is unknown.
The lower limit of the NRA desorption value, 3% ML, may be within the exper-
imental uncertainty of the HREELS measurement. The HREELS coverages were
uncalibrated, and no error bars were reported.® It is also possible that the (100)

samples contain a small fraction of dihydride sites, yielding low-temperature des-

> Temperature measurements across experiments using different sample holders and different ther-
mocouple locations are not directly comparable. Other experiments have found imperfect thermal
contact to cause temperature variations between a diamond and the sample holder where the ther-
mocouple was located. Smentkowski et al. [40] found that a thermocouple attached to the the sample
heater registered a temperature up to 200°C greater than one inserted into the diamond sample.
In a separate experiment, Thoms eé al. [19] found thermocouple measurements to be 100-150°C
greater than pyrometric measurements at sample temperatures above 1000°C.

Dosing Conditions for T._, 360°C

1.5 ant
- ° Ta 1800°C ; 1500L] -
* T fl 1800°C; 2500L
S)
¥ 1 ; t
2 os :
a :
ran)
a) i i H i
0 200 400 600 800
Tash (°C)

Figure 2.5: Deuterium coverage as a function of flashing temperature subsequent to
exposure at a surface temperature of 360°C. The heating rate was appproximately
10°C/sec. The error bars represent the resolution in the coverage measurement.

orption. Ez-situ AFM found an upper bound to the surface roughness of the NRA
sample, indicating a maximum macroscopic step coverage of ~4%. However, even
with 4% dihydride sites, the D coverage of monohydride sites would still lie within

the error bars of the measurement, 0.95 + 0.04 D per dimerized carbon.

2.3.3 Coverage at low surface temperature

Figure 2.6 shows deuterium coverages resulting from dosing at a surface temperature
of 80°C and a filament temperature of 1800°C. An exposure of 1500L appears to
be sufficient to reach saturation coverage. The coverages at 1500L and 2500L are
within the error bars of the corresponding coverages obtained by dosing at a surface
temperature of 360°C. Since both of these surface temperatures are low enough for
migration and desorption to be inactive, coverage is expected to be insensitive to
surface temperature. The HREELS data of Thoms et al. [10] also indicate little

difference in k4/kp between a surface temperature of 80°C and one of 600°C, implying

little difference in saturation coverage.

Dosing Conditions for T,_, 80°C

1.5
x T. 1800°C
' fil
L Fe t
v 1 x
Q T t
D L
nm
+ Lo
Vv
a L
A 0.5
en) =
0 i
0 1000 2000 3000 4000 5000 6000

D, exposure (L)

Figure 2.6: Deuterium coverage as a function of exposure at a filament temperature
of 1800°C and a surface temperature of 80°C. Each point represents an independent
dosing experiment. The sample was annealed at up to 200°C after exposure. The
coverages reported are averages of the annealed values. The error bars represent the
resolution in the coverage measurement.

One major difference between the 360°C amd 80°C exposures is that the cooling
time prior to dose is an order of magnitude longer for the latter. The majority of
the cooling time is spent between the temperatures of 360°C and 80°C, and during
this time the sample is exposed to ~0.9 L of total background gas, based on ion-
gauge pressure. Thoms et al. [19, 41] cleaned their samples by a similar annealing
procedure and found that after cooling to 80°C a small amount of hydrogen was
evident on the surface, possibly due to readsorption from the background gas during
cooling. However, any hydrogen would be replaced by deuterium during dosing,
and the steady-state NRA coverages are not expected to be affected by small initial

coverages of hydrogen.®

°If anything, the error bars of the 80°C D coverages fall slightly above the error bars of the 360°C
data, indicating no interference to D adsorption by any potential surface-bonded H.

Thermal desorption

After deuterium dosing, the UHV chamber with base pressure of 2 x 107!° torr was
opened to the NRA beamline, whose pressure was about 8 x 1078 torr. During NRA
the sample was sometimes cooled with £Neg, and at sample temperatures below ~30°C
the deuterium coverage was found to rise. Since the coverage would subsequently
decrease upon heating to temperatures less than 200°C, the rise was presumably due
to physisorption of DO from the gas in the beamline.’ Derry et al. [7] also used a
€Nz2 dewar in their vacuum chamber and sometimes found coverages greater than one
D per surface C. The high coverages might also have been caused by physisorption of

water.

Dosing Conditions for T,_, 80°C

1.5 | * T,,1735°C; 3000L }
L | x T fil 1800°C; 1500L, 2500L, and 5000L].
v 1 Pk ee entree Toeeccsceeeseeeesseepecssssesssnessesssssaeeseeses deeceeeeeeeees
& , + *
fot
ian} L
i?a)
te L.
ov
Oo. .
So Le
a L.
0 I i i
0 200 400 600 800
Tash ( C)

Figure 2.7: Deuterium coverage as a function of flashing temperature subsequent to
exposure at a surface temperature of 80°C. The error bars represent the resolution in
the coverage measurement due to the limited number of events counted.

To avoid surface contamination subsequent to dose, the sample was heated and

coverages were measured as a function of heating temperature. Results are shown

“Russell [42] has found water to physisorb on diamond at £N2 temperatures and desorb above
-93°C.

46
in fig. 2.7 for heating subsequent to exposures at a surface temperature of 80°C. For
heating temperatures under 200°C, the sample was heated at a rate of ~10°C/sec
and held at the annealing temperature for about 2-5 minutes. For temperatures over
200°C, the sample was flashed to a temperature of Tgash at a rate of ~10°C/sec.
Annealing up to 200° did not significantly change coverage, except in cases where the
sample was annealed after £No cooling. Therefore, little or no DO contamination
is expected to be physisorbed on the surface in the uncooled cases or in the low-

temperature annealed cases, and all data reported herein are for such cases.

2.3.4 Coverage at high filament temperature

Saturation coverages at filament temperatures above 1800°C ranged up to 1.34+0.09
D per surface C. The high coverages might have been caused by surface dihydrides,
such as those present on a disordered surface or an ordered (3x1) reconstruction.®
Since NRA is a nuclear-sensitive technique, it cannot distinguish between mono- and
di-hydrides. Although Thoms et al. [19] saw no HREELS evidence for dihydrides
on C(100) after dosing at a filament temperature of 1800°C, dihydrides may be pro-
duced through an activated process at higher filament temperatures. Sakurai and
Hagstrum [43] proposed that adsorption of H onto a Si(100) (2x1):H surface breaks
the silicon dimer bonds, and Si dimer-bond breakage and etching by exposure to
atomic hydrogen have been widely supported by other studies [44, 45]. It is possible
that atomic D also breaks carbon dimer bonds on diamond (100). Although bond
breakage may be too slow to detect at typical filament temperatures of 1500-1800°C,
elevated temperatures may activate the process.

Other possible causes of high deuterium coverage are considered to be less likely.
The deuterium doser contains a molybdenum collimation tube behind the hot fila-
ment, and radiative heating of the tube increases as the fourth power of the filament
temperature. Elements such as C and O are present at the 0.01% (atomic) level

in bulk molybdenum [46], and at elevated temperatures C and O can diffuse to the

8A (3x1) reconstruction cannot be established because no LEED was performed after the high-
temperature exposures.

molybdenum surface and desorb as CO. Surface dihydrides may then be produced
on the diamond by CO activation of surface dimer bonds. Although very high fil-
ament temperatures may activate CO desorption from the molybdenum tube, the
flux of CO reaching the sample is negligible. For example, even at a molybdenum
temperature of 500°C, less than 0.006 ML of C would desorb from the molybdenum
and directly impinge on the sample during the longest dosing times. A previous ex-
periment in the same set-up confirmed negligible oxygen production by the doser by
mass-spectroscopic analysis. Outgassing of O (or CO) was detected only after the fil-
ament had been heated for several hours at ~2000°C [47]. In the present experiment,
all high temperature exposure times were less than 0.2 hr, and O and CO outgassing
are expected to be negligible.

Elemental tungsten is also generated at too low of a rate to accumulate in signifi-
cant amounts on the sample. The vapor pressure of elemental tungsten is greater than
10~!° torr above 1900°C, implying a total evaporation at the filament of 0.3 L during
the 1975°C exposure and 0.45 L during the 2025°C exposure. However, the flux of
tungsten decreases with the square of the distance from the filament. The shape fac-
tor describes the decrease in radiative flux from the filament to the diamond, and an
upper bound is estimated in section 2.4.3. It is shown that total direct exposure to
elemental tungsten is less than 0.0002 monolayers during both deuterium dosing and
filament outgassing. Therefore, contamination by elemental tungsten is negligible.

Another possible cause of high deuterium coverage is the presence of molybdenum
or tungsten-deuteride on the sample. However, hydrogen has not been reported to
etch tungsten [48]. Moreover, ex-situ XPS of the sample performed at Caltech subse-
quent to the NRA experiment showed no evidence for the presence of molybdenum or
tungsten. The detection limit was ~0.1% (atomic) W.° Therefore, if the sample were
in fact contaminated by molybdenum or tungsten-deuteride, any contaminant must

have desorbed upon the final 700°C anneal prior to removal from the NRA chamber.

°The only elements detected on the diamond surface were C (90.97% £0.10%), O (7.16% +0.10%)
and Si (1.87%+0.10%). The composition was calculated from the area of the C(1s), O(1s) and Si(2p)
peaks. The source of the oxygen may have been contamination received in transit from the NRA
to XPS chambers, and the source of the silicon may have been pump oil in the XPS chamber. The
sample was not heated to desorb physisorbed contaminants prior to XPS.

A fourth possible cause of high coverage, macroscopic surface roughness, is pre-
cluded by ez-situ atomic-force microscopy (AFM). Detected roughness levels were too
low to produce excess coverages of 0.3 D per surface C. Fig. 2.8 shows AFM images of
regular grooves spaced approximately 330 A apart and about 4 A high. These mea-
surements were performed at room temperature in contact mode in an atmospheric
AFM (Digital Instruments Nanoscope® III). The AFM measurements were taken at
Caltech subsequent to the NRA experiment.

Fig. 2.9 shows a flat surface of mica scanned at the same rate (5 Hz) as the di-
amond sample. No smoothing was performed on either image. The fact that the
local roughness (or noise) in the mica image is similar to the roughness in the dia-
mond image demonstrates that the atomic-scale roughness of the diamond is below
the detection limit of the AFM. The absence of regular grooves in the mica image
demonstrates that the diamond grooves are not an artifact of the imaging process.
Diamond grooves were found at all scan rates used and at all locations scanned. The
spacing of the grooves ranged between 330 and 450 A, and the apparent peak-to-valley
height ranged up to 14 A at the highest scan rate.

0.5 nm
0.2 new
0.0 nm

WU OO'T

Figure 2.8: AFM image of diamond sample subsequent to NRA experiment. The
image is slightly distorted between x = 75 and 100 nm due to the reversal of the tip’s
direction of travel during the scan(fig. 2.9).

a) wn
5 x = wo
c Cc Pa _
Fe) N r=] 3
fo] o o Wi
Bo & mn
AaNero
Om CS
O Wem he by
“Hw oOo oa
=} ocacre
Cora t
al soUaoSs
ZAWHNZE
wn

100
nm

Figure 2.9: AFM image of mica. The absence of regular grooves in the mica image
demonstrates that the grooves in the diamond image are not an artifact of the scan-
ning process. The bump at the end of the mica scan is an artifact of reversing the
tip’s direction of travel during the scan. The location of the bump changes with the
location of the end of the scan. The actual mica sample is flat between x = 75 and

100 nm.

Thermal desorption

Dosing Conditions for T, 360°C

° Orn,
15 T,, 1977°C ; 3000L
b 8 T, 2025°C; 1500L
o 5 , 4
u 5 eee Sea EE EEE SSE EEESESOSESSCSESSOSSSCOSSOSSSSSSESS SSSEEESSSSESSSSSOSOSSNOTSEOSEE EEEESNESESSON
; §
1? 8)
el
z 5
Qo
Oo
0 | |
0 200 400 600 800

(°C)

anneal

Figure 2.10: Deuterium coverage as a function of annealing temperature subsequent
to exposure at a surface temperature of 360°C. The error bars represent the resolution
in the coverage measurement.

Fig. 2.10 shows coverage as a function of annealing temperature subsequent to
dose. The sample was heated at a rate of approximately 10°C/sec, and to minimize
the effect of variations in heating rate, the sample was held at the annealing tem-
perature for 2-2.5 minutes. Holding the sample at the annealing temperature allows
better equilibration between the thermocouple and the sample and more accurate
measurement of temperature-time history. Therefore, these desorption measurements
are more reliable than those performed by flashing the sample in section 2.3.2. The
highest three anneals imply an average activation barrier of 2.9 eV, assuming first
order desorption and a preexponential factor of 10'%/sec. The barrier does not differ
significantly from the value of 3.0 eV implied by the exposures at T4 of 1800°C, where

the barrier calculation is less accurate due to the shorter anneal times (~1 sec).

52
2.4 Analysis of deuterium coverage

2.4.1 Subsurface deuterium signal

Since the resonance producing the nuclear reaction is broad [49, fig. A11.23, p. 568],
NRA suffers from large sampling depth. The incident 7>He* energy drops from 0.70
to 0.37 MeV before the nuclear-reaction cross section drops to half its peak value.
Taking an average stopping power of 37 eV/(10!° atoms/cm?) [50], the ion travels
6750 A through the diamond before losing 0.33 MeV. Therefore, in addition to the
surface deuterium, the spectra integrate over the top 6750 A of bulk deuterium. A
rough upper bound for the subsurface deuterium content in natural diamond may be
estimated from the measurements of Sellschop et al. [51]. Although their technique
suffers from poor depth resolution, their results imply an upper bound of about 31
monolayers of bulk hydrogen in the top 6750 A. The upper bound for the deuterium
content is then 31 times the isotopic abundance of 1.5 x 10~* [52], or about 0.005 D
per surface C.

Subsequent experiments on CVD diamond gave a more exact estimate of subsur-
face deuterium content. In the case of homoepitaxial diamond (100), the experiment
of Appendix A estimated the H content to be 0.30 H per surface C in the top 6750 A.
The deuterium content in the top 6750 A was estimated to be 0.003 D per surface
C. In the case of polycrystalline CVD diamond, Dollinger et al. [9] detected less than
10-8 hydrogen content below the top 10-20 A, with a depth resolution of 10 A. There-
fore, the hydrogen content in the first layers below the surface may be approximated
to be the same as that in the bulk. The total subsurface deuterium content in the
top 6750 A of the Dollinger sample is then less than 7.6 monolayers times the iso-
topic abundance [52], or 0.0011 D per surface C. Therefore, the total contribution of
subsurface deuterium to the NRA spectra is taken to be 0.0011 D per surface C.

The lower detection limit of the NRA system is determined by the background
cosmic radiation incident on the detectors. For beam parameters typical to this
experiment, our lower detection limit is 0.013 D per surface C. When compared to

the lower detection limit, subsurface deuterium contributes negligibly to the surface

deuterium spectrum.

2.4.2 Subsurface deuterium diffusion

NRA spectra showed negligible increases in D coverage between 1500 and 5000L ex-
posures, indicating negligible diffusion or incorporation into the subsurface region
during exposure. At filament temperatures below 1975°C, coverages were close to 1.0
D per surface C, consistent with the (2x1):D structure and no subsurface deuterium
content. At filament temperatures above 1975°C, coverages ranged up to 1.34 + 0.09
D per surfcace C, consistent with the (3x1):1.33D structure and no subsurface deu-
terium content. Therefore, all coverage measurements are consistent with negligible D
diffusion from the surface to the subsurface region, and no such diffusion is expected.
Smentkowski et al. [40] recently suggested deuterium penetration into the subsur-
face region as one possible cause of sharpening of the Cls transition in XPS data.

However, the NRA measurements show no direct evidence for subsurface diffusion.

2.4.3 Negligibility of elemental tungsten exposure

Although the vapor pressure of W becomes significant (> 1x 107!°torr) above 1900°C,
the flux of W at the sample is negligible. Figure 2.11 shows an upper bound for the
direct W exposure at the sample during outgassing prior to dosing, and fig. 2.12 shows
the estimated direct W exposure during dosing. Exposures were estimated via the

equation

Agia
w = lweadia TrmwkT;

where ew is the total elemental W exposure, [wegig is the elemental W flux at the

Aft P. Pw (T
paPw (Ts) (2.1)

diamond, t is the exposure time,'® Ayy and Agjq are the tungsten and diamond surface

areas, respectively, Fg is the shape factor, Py(T;) is the vapor pressure of elemental

10F xposure times prior to dosing are taken to be 1020 s, the maximum sample cooling time
between flashing and dosing, below the filament outgassing temperature (Tp = 2200°C) and 360 s,
the maximum filament outgassing time, at the outgassing temperature. Exposure times during
dosing are the maximum dose times: 600 s at 1735°C, 1000s at 1800°C, 600 s at 1977°C, and 300s
at 2025°C,

OG 0.01¢
Fs
< 0.001 & ‘
a e
5 ODO OD Berend eee eer rece tce cee ence ce ereeneneeneencaneveadeeseecenenestnenarneaneraesfeneeerteeneees x
ae c ;
SE 10°: ne ee J
24 °
ae a 4
£8
er 107 be Oooo eee eee ces fececeeenceneeneeneeteseereeefeseseesestessesteneereeee 4
=> E e
& 10°
+9
ae; 10
S E : :
= yo? Fei
1600 1800 2000 2200 2400
(°C)

filament

Figure 2.11: Estimated direct elemental W exposure of back side of sample prior to
dosing. The front side of the sample was out of line-of-sight of the doser, and thus
received an even lower exposure.

tungsten at filament temperature Ty, mw is the mass of W, and k is the Boltzmann
constant.

The factor il Fg accounts for the decrease in direct radiative flux from the fila-
ment surface to the diamond location. The exact shape factor is difficult to calculate
for the case of the NRA doser, with a pancake, spiral-wound filament. However, an
upper bound is obtained by treating the filament as a disk of diameter 0.635 cm, the
diameter of the doser collimation tube behind the filament. The diamond is treated
as a disk 0.5 cm in diameter, parallel to the plane of the filament and 4 cm away
for the dosing exposures and 20 cm away for the outgassing exposures. Fyq is then
0.0039 for dosing and 0.00016 for outgassing [53, p. 32]. These shape factors are upper
bounds for Fyg. The actual shape factors may be lower due to the fact that the hot
part of the filament occupies less area than the exit of the collimation tube.

W exposures of the back side of the sample during outgas (fig. 2.11) are less than
0.0007 W per surface C, and those of the front side during dose (fig. 2.12) are less
than 0.00012 W per surface C. Figure 2.11 shows the exposure of the back side of

O 0.01 g —
& .
S 0.0015
& E
i} Cc H :
wa ' :
5 0.0001 & : ‘ ve
ou E J
EE 10° pms i a 3
y= of ° ;
BB 108 penn annie Se ; a
aA af ° i
Sf 10° pe coperrnrnrcrnrc prrrememernrntns eeeaereencnenerne 3
= c 1
& 10° Brccccsrsrrnysrrsneeesennseseessccs
g 10°
S E
2 10° ;

1600 1800 2000 2200 2400

CC)

filament

Figure 2.12: Estimated direct elemental W exposure of the sample during dose.

the sample during outgas. The exposure of the front side of the sample is far less.
Assuming a C-WDs surface moiety, direct W contamination during dose accounts for
less than 0.0006 D per surface C. Therefore, contamination by elemental tungsten is

negligible during both outgassing and dosing.

2.4.4 Estimated atomic deuterium flux during dosing

The atomic deuterium flux incident on the sample was not measured. In the absence
of a calibration, a very rough estimate may be obtained by considering the flux at

the filament surface. The flux of atomic deuterium out of the filament is given by

Tp = 28mPal Doincas ; (2.2)

out@fil

where s,, is the sticking coefficient of Dz on the tungsten, P, is the atomization
probability, and Tp,,. 9, is the flux of D2 incident on the filament.

In steady-state mass flow, the flux of D2 out of the filament is determined by the

difference between the incident Dy flux and the outgoing D flux,

= —_i
P Do sueeei _— SmI Doincaal 5 Deaton (2.3)

Atomic and molecular deuterium desorb from the filament in their equilibrium ratio

given by eq. 2.37,

/ P
Dout@al ; + 4ROR K (2.4)
\ MDo 2BK Fe

pout = Vi +4ee + Vi +4ee + L

Combining these three equations, one obtains

™MDo

mp P
4/\/(BK)? +42K — 2K) + (M222 2rmp,kTincat

Pp , (2.5)

out@fl ~~ 5m (

where Tincagi 18 the temperature of the deuterium incident on the filament, 25°C. The
sticking coefficient, s, is estimated to be 0.3 at 2300°C [54] and is assumed to be
temperature-independent [55].

The deuterium flux directly incident at the diamond is lower than that emitted
at the filament by the shape factor, Fg, and the exposed area ratio, Afi/Aaia,

_ Api
Dinc@dia ~~ Ad
2:

Prat’ (2.6)

out@fil*

The shape factor may be roughly estimated, as in section 2.4.3, by treating the
filament as a disk of 0.635 cm diameter and the diamond as a disk 0.5 cm in diameter,
parallel to the filament and 4 cm away. Fq is then approximately 0.004 [53, p. 32].

Table 2.2 estimates Ip, 44, from the shape factor and eqs. 2.5 and 2.6. All
exposures are on the order of 10 D per surface C, indicating a D flux sufficient to
obtain monolayer coverages with a reasonable sticking coefficient of atomic deuterium
on bare diamond. The D exposures given in table 2.2 are intended to check the
sufficiency of dosing and should in no way be taken as an accurate estimate of the

actual D exposure. Accurate D flux can be measured by installing a differentially-

Rough order-of-magnitude estimates for D flux and exposure

PDoince fit” Ty PDinceoaia t exposure Dexposure
torr °C =—ML/s s ML
1x107° 1735 2.40 x 107? 600 14
1800 2.41 1000 24

1975 2.42 600 15

2025 2.42 300 7

°Pressure of D2 at room temperature incident on filament,
corrected for an ion gauge sensitivity to D2 of 0.5 [56]. Ion
gauge pressure was 5 x 107° torr.

Table 2.2: Very rough estimate of D exposure. One monolayer (ML) is defined to be
1 D per surface C, or 1.566 x 10!°D/cm?.

pumped mass spectrometer at the location of the diamond, with a beam chopper to
distinguish between deuterium desorbing directly from the filament and background

deuterium bouncing off the chamber walls.

2.4.5 Proposed effect of dosing on dihydrides and degrada-
tion

Coverages up to 1.34+0.09 D per surface C were found at filament temperatures circa
2000°C, indicating the possibility of surface dihydride generation. Surface dihydrides
are proposed to form at high filament temperature through breakage of dimer bonds
by hot atomic deuterium. Sakurai and Hagstrum [43] proposed that adsorption of
H onto a Si(100) (2x1):H surface breaks the silicon dimer bonds, and dimer bond
breakage and etching of silicon surfaces by atomic hydrogen has been supported by
many studies [44, 45]. Although bond breakage may be slow at typical filament
temperatures of 1500-1800°C, elevated temperatures may activate the process.

The results of several previous experiments are consistent with dimer-bond break-
age during dosing. Lee and Apai [17] found that a polished (100) (2x1) surface

converted to a (1x1) structure upon atomic hydrogen dosing.'! Heating the sample

'\ The filament temperature was not reported, and the sample temperature during dosing was not
specified.

to ~1200°C desorbed hydrogen and restored the (21) pattern, and the adsorption-
desorption process was completely reversible. To destroy the (2x1) reconstruction, it
is necessary to break carbon-carbon bonds, and on terraces, dimer bonds, being the
most strained, are likely to be among the first to be broken. Lee and Apai suggested
the conversion of C-C bonds to C-H bonds, eventually leading to CH4. Sun et al. [57]
dosed a (100)-facetted polycrystalline sample at 2000°C filament temperature in 107°
torr Dy. They interpreted their on-specular HREEL spectra to indicate surface mono-
hydrides and dihydrides and suggested H breakage of dimer bonds. However, dipole
selection rules were used when interpreting the spectra, and Thoms ez al. [22] later
demonstrated that dipoe selection rules are not applicable on the smooth C(100):H
surface.

Hamza et al. [18] also found that a polished C(100) (2x1) surface converted to a
(1x1) structure upon dosing. Again, this can be caused by dimer-bond breakage. The
filament temperature and dosing time were not reported. Pate found atomic hydrogen
dosing to convert the (2x1) surface to a (1x1) structure at a filament temperature
of 1800°C. Subsequent annealing did not restore the (2x1) LEED pattern, and Pate
suggested etching or roughening of the surface by the single adsorption-desorption
cycle. Dimer-bond breakage is consistent with all of these findings.

Filament temperature is not the only factor determining whether evidence of C-C
bond scission will be seen. Once broken by adsorption of hydrogen, dimer bonds
may be subsequently restored by thermal desorption of the hydrogen, freeing the
carbon electrons to re-pair. Since surface temperature determines desorption rate,
it is a second factor affecting whether C-C scission is detected. Although Pate saw
indications of bond breakage on C(111) at 1800°C, Chin et al. [13] found no such
indications when dosing at the same filament temperature. However, Pate’s surface
temperature was < 100°C, and Chin et al.’s was 800-850°C during dose. In a separate
experiment, Chin e¢ al. [13] found surface CH3 species to desorb upon annealing
to 400°C. It is possible that Pate’s low surface temperature stabilized di- and tri-
hydrides, preventing reformation of C—-C bonds after scission. At surface temperatures

below 200°C, Chin et al. found repeated adsorption—desorption cycles to degrade the

surface. The CH stretch peaks in the SFG spectra broadened, and other (unspecified)
hydrocarbon features appeared in the spectra, consistent with C-—C bond scission
and the stabilization of broken bonds by formation of di- or tri-hydrides. Dosing
at 800-850°C was found to completely regenerate the surface, consistent with the
desorption of di- and tri-hydrides and destabilization of broken C-C bonds. Since
surface temperature determines desorption rate, it must be considered in addition
to filament temperature when searching for evidence of dihydride formation through
dimer-bond scission.

Indications of thermal desorption from dihydride sites on the C(100) surface have
been found by TPD. Yang e¢ al. [5] found a low-temperature shoulder in the ther-
mal desorption peak and suggested desorption from dihydride sites by analogy with
Si(100). Hoffman et al. [27] found a peak at 710°C and one at 900°C. Therefore, dihy-
dride desorption may occur when dosing the sample at medium surface temperature,

restoring broken C—C bonds.

A :
m~/ \I\O 3 \AN/ \/\O
Dig) + C Cc —~c Cc : Dig) + C Cc —~ Cc Cc
/ \/ wy
C stable Cc — C+D 8
Ty feccecssseseesseecessseceesseseconsssennnsssnensssnnseesssdecesessseeeessnnseesssnsseessanenseensseetsnaserseaneeestnesfeessees
Cc C stable : Cc C stable
i \7 “
C stable : C —= Cc +D,{8)
Ta Ta

surface

Figure 2.13: Proposed effect of T pitament ANd T surface On dimer breakage and hydrogen
desorption from dihydride sites.

60
Figure 2.13 shows the proposed effect of the filament and sample temperatures
on surface sites during dosing. The reactions of abstraction and recombination with
unsaturated sites are omitted for clarity. Four temperature regimes are shown, with
Ta and Ty being the temperatures at which Hy desorbs from monohydride and
dihydride sites, respectively. Significant thermal desorption begins when the dosing

time reaches the characteristic thermal desorption time, i. e.,
tose = Aage Pe /Mours, (2.7)

where taose is the dosing time, Ty, y is the surface temperature during dosing, and Ago
and Ege are the pre-exponential factor and barrier, respectively, to thermal desorption
from dihydride sites. Dihydride desorption parameters have not been measured on
(100), but parameters have recently been caculated for a low-temperature peak on
C(111) [28]. For a dosing time of 1000 sec, these give a Ty. of ~630°C.

The filament temperature at which dimer-bond breakage becomes active, Tp, is
determined by the dosing time and hydrogen flux. Assuming dimer bond breakage
proceeds via

Dé + DC-cD™* 4; cpsf + cp", (2.8)
the rate of change of dimer coverage is given by

Apeqce = -—0lpPpc-cp. (2.9)

Here @p¢—cp is the number of monohydride dimerized surface carbons per surface
C, oy is the total dimer-scission reaction cross-section, and I'p is the flux of atomic
deuterium incident on the surface. The number of dimer breakage events during
dose becomes significant when the dosing time is equal to the characteristic time,
tdose = 1/(oT'p).! Higher filament temperatures will give higher o, and Tp and

therefore shorter dosing times to dimer breakage. Therefore, two experiments using

™ Assuming ky = Aye~”*/*T1, the characteristic temperature, Ts, is determined by the transcen-

61
the same filament and surface temperatures may obtain conflicting results if one of
them is dosing for long enough or at a high enough flux to break a significant number
of dimer bonds while the other is not.

Surface roughness also affects the time to attain significant dimer breakage. Pol-
ished surfaces typically have smaller terrace domains than hydrogen-plasma treated
samples, and therefore fewer dimer bonds must be broken in order to have a signifi-
cant effect on the LEED pattern. However, polishing roughness can be compensated
for by decreasing the filament temperature. Thomas et al. [20] found polished (100)
to remain in the (2x1) state even after 4 x 104 L exposure to Ha. The filament
temperature was 1500°C, and the rate of dimer breakage at this temperature may
be too slow to affect the LEED pattern within the dosing time. Polishing rough-
ness can also be compensated for by increasing the surface temperature during dose.
Employing dosing parameters within the (medium surface temperature, low filament
temperature) region of fig. 2.13 allows surface dihydrides to desorb faster than they
are formed by dimer breakage.

Hydrogen-plasma pretreatment is recommended for studying dimerized monohy-
dride sites. Thoms et al. [19] saw no HREELS evidence for dihydride production on
C(100) (2x1) after dosing at a filament temperature of 1800°C. Spectral interpreta-
tion was reliable in that it did not assume any dipole selection rules. The rate of
dimer production is therefore small at 1800°C for their dosing flux.

Hydrogen reactions with dimerized sites may be characterized by choosing dosing
parameters in the lower left quadrant of fig. 2.13. However, long dosing times bring T,
down and eventually result in dimer scission. Dosing at higher surface temperatures,
in the lower right quadrant, is recommended for dynamically restoring broken bonds
by desorbing from dihydrides. Dosing in the upper left quadrant is recommended
for studying dimer breakage, as this preserves evidence of C-C bond scission by

precluding desorption from dihydrides. Dosing above the monodydride desorption

dental equation

2am
Ey/kT, —_ Dr 2.10
€ = kT; DAstaose- ( )

62
temperature may allow a disordered surface to be restored to a (2x1) reconstruction
by reorganizing the dimer rows. These hypotheses may be tested by performing SFG
on C(100) under various dosing conditions and observing the effect on CH symmetric
and antisymmetric and CH stretch signals. SFG has the resolution to distinguish these
peaks, and because it is based on a process that is symmetry-forbidden in the bulk,
SFG has excellent surface sensitivity.

In summary, the following interpretation of degradation is suggested. Degradation
is the result of a dynamic competition between two processes: C-C bond breakage by
insertion of atomic hydrogen from the gas phase, and C-C bond restoration initialized
by desorption of molecular hydrogen from the dihydride C. If the rate of dimer bond
breakage exceeds the rate of reformation, then the surface degrades and the (2x1)
LEED pattern is eventually destroyed. The rate of dimer bond breakage is expected
to depend mainly on filament temperature, flux of atomic hydrogen to the surface,
and coverage of DC-CD sites. The rate of dimer bond reformation is expected to
be limited by the rate of hydrogen desorption from the dihydride site, controlled by
surface temperature. This interpretation is consistent with the NRA measurements
of high deuterium coverage at high filament temperature, the findings of Lee and
Apai [17] that the (2x1) LEED pattern can be destroyed by exposure to atomic
hydrogen, the findings of Chin et al. [13] that the surface eventually degrades after
low-surface-temperature exposures and is regenerated by high-surface-temperature
exposures, and the findings of Hoffman [28] that low-surface-temperature exposures
result in multiple peaks in thermal desorption spectra while 800°C exposures result

in single desorption peaks.

63
2.5 Analysis of reaction-rate ratio

2.5.1 Relationship between surface coverage and gas-surface

reaction rates

Total deuterium coverage is determined by the reaction of gas-phase atomic deuterium
with the diamond surface. There are three types of sites on a fully reconstructed (100)
surface: fully deuterated dimers, DC-CD™", half-deuterated dimers, DC—C.™", and
pi-bonded dimers, -C—C-"*, Gas-phase atomic deuterium recombines with surface

sites and abstracts deuterium from them.

Recombination :
D885 +. C-Cpt Frm DpDCc—cp™* (2.11)
Des + C—CO.surt Fre, DC—cC.sut (2.12)

Abstraction :
kat
De +DC—-CD™" == D§* + -C-CD™" (2.18)
kag

De 4 DC-csef A pss 4 .c_c.sut (2.14)

kan

In addition, chemisorbed deuterium migrates from surface site to surface site and is

thermally desorbed.

Migration :
kufh
DC-CcD™ +.C-cD™ = Dc-c-™f+DC-cD™ (2.15)
ku fh
ka fp '
DC-—cD™ +.c-cs™! =s pc-cof+DC-C (2.16)
k_M fp

_ surf _ surf KMhh _ surf _ surf

-C-CD™ +-C-cD™? = .c-cs“f +DC-CD (2.17)
k_Mhh
kMhp

.C-CD™f 4 .O—C.surt = C-CsHt 4 DC C.sut (2.18)

k_Mhp

Desorption :
kps
DC-—cDp™! = ‘C-Ceut + D5" (2.19)
-—Df

Summing the rate equations for reactions 2.11 through 2.19, one obtains

d6p — d0p_p 1 fd@p_, | di,_p
dt — dt 5 ( di’ di ) (2.20)

+{k_anbs—s + ght (@p—« + #.-p) }T pn,

—{kafOp-p + gan (Op-+ + Op) }Tp — kpsOp-p,

where @p is the number of deuterium per surface carbon, @p_p is the number of fully-
deuterated dimers per pair of surface carbons, 8p_, is the number of half-deuterated
dimers per pair, 0,—, is the number of pi-bonded dimers per pair of surface carbons,
Ip is the atomic deuterium flux at the sample surface, [p, is the molecular deuterium
flux, and kz, is the total reaction cross section, or the rate constant expressed in terms
of (1/flux/time).

Note that all surface migration terms have cancelled out of eq. 2.21. Surface
migration conserves total deuterium coverage as it redistributes deuterium among the
various surface sites. Migration affects overall coverage only indirectly, by determining
the balance between @p_p, Op-«, and 0_, and by producing DC-CD™" sites for
thermal desorption. For example, migration tends to convert half-deuterated dimers
into pi-bonded dimers, weighting the kr, term more heavily than the kg», term in the
first line of eq. 2.21. The balance between @p_p, Op_., and 0,_, affects total coverage
because the rates of abstraction and recombination are expected to vary with surface
site. For example, Dawnkaski et al. [58] estimated the probability for recombination

with a w-bonded site to be 1.7 times that for recombination with an isolated radical

65
site.3

Writing eq. 2.21 in terms of average rate constants and overall coverages,

dép

= keOP py + k-a8.0'b, — kad — kv spp, (2.22)

where 0, is the number of unsaturated bonds per surface carbon and

ke = K pp9x—» + 5k rn (Op—« + Op) (2.23)

k_4nOs—« + $k—as (Op-« + 9s—D)

(2.24)

and

ky = wasp + akan (Op—« + @.—D) (2.25)
p-p + 5 (@p-s + 6—p)

Since no study has detected thermal desorption below a surface temperature of
450°C, the desorption term in eq. 2.22 may be neglected. For a fully-dimerized surface
6, = 1—Op. In steady state, the left hand side of eq. 2.22 is zero, and the steady-state

coverage, 6, is

kelp + k_aYp,
(ke +ka)Tp — kal,

0; (2.26)

As discussed in section 2.5.2, the mole fraction of D®** is likely to be large enough

'3These probabilities were calculated at 1527°C, with the surface temperature equal to the gas
temperature, from molecular dynamics simulations using the Brenner potential [59].

66
for Pp/Tp, > k-a/kr (or W/mp,/mp x [D%*]/[D2] >> k_a/kp). Then eq. 2.26

reduces to

O, = (2.27)

Here k, and kp are the steady-state site-averaged abstraction and recombination rate
constants. Therefore, the steady-state deuterium coverage, 0;, gives the ratio of the
average abstraction rate constant to the average recombination rate constant, where
the averages are weighted over all sites present in the steady state on a fully-dimerized

surface with negligible thermal desorption.

Deconvolving individual reaction-rate constants
When the site-averaged reaction rates are constant in time, eq. 2.22 may be integrated

to give

Ap = Oy + (Oo _ Oye, (2.28)

where Op is the initial coverage and a is the decay constant,

Q = (ke + ka) Tp - k_aYp,. (2.29)
kelp + kal,

. 2.30
(kr + ka) Fp —k_alp, (2.30)

Once again, as discussed in section 2.5.2, the mole fraction of D®* is likely to be
large enough for 'p/Tp, >> k_a/kr (or /mp,/mp x [D9**|/[De] >> k_4/kp). Then
eqs. 2.29 and 2.30 reduce to

a = (ke tka) Tp. (2.31)

(2.32)

Therefore, the time-rate-of-change of the coverage gives the sum of the abstraction
and recombination rate constants times the deuterium flux via eq. 2.31. Measuring
6;, aw, and Ip would enable the individual values of the average rate constants to
be deconvolved from their ratio when the site-averaged rates do not vary with time.
However, this has yet to be accomplished due to the difficulty of measuring Tp,

absolute atomic deuterium flux [54, 60).

2.5.2 Negligibility of inverse abstraction rates

The assumption [p/lp, >> k_a/ker in section 2.5.1 amounts to neglecting the in-
verse abstraction rate relative to the recombination rate. Goodwin [61] has estimated
[D85]/[Ds] (or /mp/mp, x Tp/Tp,) to be >> k_4/kg under diamond CVD con-
ditions, where T, = T;. Since deuterium flux was not calibrated and gas-surface
reaction rates have not been measured under UHV conditions, where T, > Ti, the
ratios Pp/Tp, and k_4/kpr cannot be accurately calculated under the NRA dosing
conditions. In the absence of data, a rough estimate is obtained by comparing to
tungsten cracking experiments and molecular-dynamics simulations of gas-surface re-
action rates.

Low-pressure tungsten cracking experiments [54, 62] found that atomic and molec-
ular hydrogen desorbed from the filament in a ratio consistent with their equilibrium
ratio, where the equilibrium constant is determined by the filament temperature and
the incident hydrogen pressure. Therefore, the outgoing flux of atomic and molecular

deuterium at the filament, ['p,. es, and ['p....09)) respectively, may be estimated as

PD .uveat PD2oue/\/2MD_kTy
/ P,
— MD Dout 2 4
MDo PDoout ( 3 )
— mp Xp
= (BP AR. (2.35)

Pp wees _— _Podout/+f2ampkTy (2.33)

68
Here Pp,,, and Pp,,,, are the partial pressures of the desorbing atomic and molecular
deuterium, respectively, mp and mp, are the atomic and molecular masses, k is the
Boltzmann constant, and Xp is the mole fraction of desorbing atomic deuterium. In

equilibrium,

Xp =i Exp rahe -12

—=—K 2.
=k, (2.36)

2V°P P

where K is the equilibrium constant at the filament temperature and reference pres-
sure, Po, and P is the pressure of D2 incident on the filament (5 x 107° torr for the

NRA dosing conditions). Substituting eq. 2.36 into eq. 2.35 yields

/ Po
Pessoa [Mp __Y1* RK" (2.37)

P Dp cutest ™D2 2a —,/1+ dpe +1

The smallest Up, om /P Douro OCCULS at the lowest filament temperature, which in the

NRA experiment is 1735°C. Woolley et al. [63] calculated the equilibrium constant for
deuterium dissociation from spectroscopic data and statistical mechanics. They found
K at 1727°C and 760 torr to be 2.227 x 10-®. Substituting these values into eq. 2.37
yields a Vp, eq /UDoomom Of 240. Therefore, only a small fraction of the deuterium
desorbs from the filament as molecular deuterium, and the NRA experiment probes
mainly atomic deuterium reactions with the diamond surface.

The ratio of atomic to molecular deuterium flux incident on the sample, ['p/Tp,,
is

r Vow +P

where I"p,,, is the atomic deuterium flux impinging on the sample directly from the
filament, Ip,,,,, is the atomic deuterium flux impinging on the sample from the vacuum
chamber walls, Cp, out is the molecular deuterium flux impinging on the sample directly
from the filament, and V'p.reftectead is the molecular deuterium flux reflected from the
filament (not adsorbed and desorbed). The Dy which does not strike the tungsten
filament is at room temperature. Since Ando et al. [64] found diamond powder to be

unreactive with D2 below 400°C and since the temperature of the diamond surface is

69
less than 400°C, the rate of reaction of room-temperature Dy with the diamond may
be neglected. Moreover, the temperature of the Dg reflected from the tungsten is less

than 170°C, assuming a thermal accomodation coefficient of 0.07 [54].‘4 Therefore,

the reactions of Do, ,, and Do,.,..,., With the diamond surface are neglected, yielding
P Pr r P
D =— Dout + Dwall > Dout . (2.39)
lp, PDs out PDoout

The Tp incident on the sample is lower than the amount emitted at the filament
by the shape factor describing radiative transfer from one to the other. However,
since [‘p, incident on the sample also decreases by the same amount, shape factor is

irrelevant to the ratio of fluxes. Therefore,

Up 5 Powe _ Po
lp, PDoout

owhl > 940), (2.40)

Deout@al

k_a/kp may be estimated by the molecular-dynamics calculations of Dawnkaski
et al. [58]. At 1527°C (k_4 x T'y,) varied between 6.5 x 107° and 2.3 x 1073/s/site
at 0.1 torr partial pressure of Hz, depending on the type of surface site. (kp x Ty)
varied between 0.023 and 0.039/ys/site at 18 torr partial pressure of H. Therefore,

the maximum site-specific k_4/kp is

k_a 2.3 x 1078 Pu mH. 4
Pe | ZH = 7.6 x 10 2.41
kr 0.023 Pu, \) ma * (2.41)

where Py is 0.1 torr and Py, is 18 torr. These rate constants were calculated assuming

gas temperature equal to surface temperature and so are not directly applicable to
the NRA conditions, where T, > T,. Therefore, these rate constants are merely a

qualitative estimate of k_4/kp.

‘4Recently, Eenshuistra et al. [65] detected vibrationally-excited H2(v"’) effusing from a metal
oven containing hot filaments. They attribute the excited molecules to atomic H desorbing from the
filament and recombining with wall H in an Eley-Rideal reaction. The NRA dosing pressure was two
orders of magnitude lower than Eenshuistra et al.’s pressure, and the flux of Dout@ai incident on the
walls was many times lower in the NRA case due to the larger vacuum chamber. Therefore, the NRA
experiment is likely to produce a significantly lower flux of vibrationally-excited D2. Although its
presence cannot be ruled out, in the absence of spectroscopic data, the reaction of vibrationally-hot
Dz is neglected in the present analysis.

70
Therefore, the best available estimates for Pp/T'p, (>240) and k_4/kp (7.6 x 107*)
indicate that the assumption [p/I'p, >> k_4/kr is likely to be satisfied under NRA
dosing conditions. In other words, the inverse abstraction rate may be neglected

relative to the recombination rate.

2.5.3 Comparison to reaction rates on C(111)

The deuterium coverage on C(100) saturates at 0.95+0.04, for exposure at a filament
temperature of 1800°C and a surface temperature of 360°C. This saturation coverage
agrees with the coverage of 0.95+0.01 implied by Thoms et al.’s [10] HREELS data on
polycrystalline diamond. However, the saturation coverage disagrees with the value of
0.83 implied by Chin et al.’s [12, 13] data for C(111). Chin et al. estimated coverage
by comparing the rate at which atomic hydrogen replaced chemisorbed deuterium on
C(111) to the rate at which atomic hydrogen recombined with clean C(111). Although
in the NRA experiment atomic deuterium reacted with diamond, the deviation is un-
likely to be an isotopic effect; for Chin states that the rate at which atomic deuterium
reacted with the diamond surface was similar to the rate at which atomic hydrogen
reacted.

The discrepancy is most likely due to a variation between site-specific reaction
rates on C(100) and C(111). Dawnkaski et al. [58] recently estimated the recombina-
tion and abstraction probabilities for several types of sites on the (100) (2x1) surface
and the (111) (1x1):0.75H surface from molecular dynamics calculations using the
Brenner potential [59]. At 1527°C their reaction probabilities imply a saturation hy-
drogen coverage of 0.84 for C(100) and 0.70 for C(111)..° Since Dawnkaski et al.
assumed a surface temperature equal to the gas temperature, their results are not
directly comparable to the experiments, where surface temperature was < 360°C and
the gas temperature was 1800°C. Nevertheless, their calculations do imply a varia-

tion between site-specific reaction rates on C(100) and C(111), one large enough to

These coverages were calculated by eq. 2.27 using Dawnkaski et al.’s probability for abstraction
from the C(100) (2x1):0.94H surface and for recombination at an isolated radical site on the same
surface,

Reference Surface Tsurface Thiament Ka/KR Saturation coverage
Experiment

Koleske [11] poly 500°C =1560°C §=0.03+0.01 0.97+0.01 D/surf C

Thoms [10] poly 80-600 1800 0.05+0.01 0.95+0.01

NRA (100) 360 1800 0.06+0.04 0.95 + 0.04

Dawnkaski [58] (100) 1527°C =1527°C —:0.09/0.46 =: 0.84.-—-H/surf C

Dawnkaski (58) (111) 1527 1527 ~——-0.14/0.32—0..70

Table 2.3: Comparison to reaction-rate ratios obtained by previous experiments. Re-
action rates are converted into coverages via eq. 2.27. The experimental uncertainty
is not specified in the work of Chin e¢ al. [12, 13].

qualitatively explain the difference between the experimental saturation coverages of

0.95 + 0.04 on C(100) and 0.83 on C(111). Results are summarized in table 2.3.

2.5.4 Comparison to reaction rates in growth models

Thoms et al. [10] found k4/kpr to be independent of surface temperature below 600°C,
indicating that at temperatures low enough to neglect migration and thermal desorp-
tion, filament temperature controls the net rate of reaction on diamond. Abstraction
on Si(100) has also been shown to be independent of surface temperature [66]. Al-
though Koleske et al. [11] found a slight surface-temperature dependence in ka, this
dependence has a negligible effect on the extrapolation of NRA data, as shown at the
end of this section. Therefore, gas temperature is likely to control the rate of reaction
with the diamond surface, and filament temperature is used to extrapolate the NRA
data down to diamond growth temperatures.

The NRA reaction-rate ratio of 0.06 at 1800°C is extrapolated down to a growth
temperature of 927°C by assuming an activation barrier of 7.3 kcal/mol [29, table I].
The resulting ratio is 0.017 at 927°C, compared to a ratio of 0.59 in thermochemical

kinetic models of diamond growth on C(100) [29].1° These reaction rates may be

16Since the present work expresses reaction-rate constants on a per C-D basis and the thermo-
chemical model expresses rate constants on a per cluster basis, the thermochemical abstraction rates
must be divided by the number of equivalent C-H bonds in the cluster to convert to the conventions
of the present work. The resulting k4 is that of reactions a, d, and o in ref. [29], or half of the rate

72
converted to open-site fraction via eq. 2.27 assuming 6, = 1 — 6,. The NRA ratio
implies an open-site fraction of 1.6% + 1.1% at 927°C, whereas the growth model
ratio implies an open-site fraction of 37%. Therefore, the extrapolated NRA data
indicate that the thermochemical growth model overpredicts the fraction of surface
sites available for growth by a factor of ~20.

Molecular dynamics simulations based on the Brenner potential [59] obtain a
ka/kpr consistent with the extrapolated NRA ratio. Dawnkaski et al. [58] determined
the abstraction and recombination reaction probabilities at various sites on a slab
modeling the C(100) surface. The slab contained 3 rows of 3 dimers on the surface and
7 layers in the bulk. At 927°C the ratio of reaction probabilities on half-deuterated
dimers gave a k4/kp of 0.041." Reaction-rate ratio is converted to coverage via
eq. 2.27, and the coverage is converted to open-site fraction by assuming 0, = 1 —
Op. The molecular-dynamics k4/kpz implies an open-site fraction of 4.0%, in much
better agreement with the NRA fraction of 1.6% + 1.1% than thermochemical kinetic
models.

Due to the distance between the filament and the sample, the velocity of the
incoming deuterium in the NRA experiment is more predominantly perpendicular to
the surface than that of a Maxwell-Boltzmann distribution. Since the abstraction
transition state is collinear with (111) [67, 68], the (100) directionality of the NRA
deuterium would tend to slightly decrease ky. Therefore, it is not surprising that
the molecular dynamics calculations obtained a higher k,4 for a Maxwell-Boltzmann
distribution of incoming H velocities.!8 The higher k4 accounts in part for the larger
open-site fraction obtained by molecular dynamics simulations.

Table 2.5.4 summarizes the dependence of open-site fraction on the activation

barrier to abstraction, E4. Chang et al. [68] determine E4 for a hydrogen bonded to

of reaction A in ref. [29]. Likewise, kp is the rate of reactions b, e, g, n, p, and r in ref. [29].

‘7Since Dawnkaski et al. [58] express reaction probability on a per C-H basis, their reaction-rate
ratios may be directly compared to those of the present work.

18 The magnitude of the directionality effect may be estimated by repeating the molecular-dynamics
simulations for the NRA conditions. The velocity distribution of the incoming D may be generated
by approximating the filament source as a disk ~0.625 cm in diameter, ~4 cm from the sample and
parallel to it.

Experiment Ey (kcal/mol) k4/kr(1800°C) 0,.(927°C)
Chang et al. [68] 10.61 0.06 0.9%
Dawnkaski et al. [58] 7.84-9.69 1.1-1.5%
Harris et al. [29] 7.30 1.6%
Krasnoperov et al. [69] 6.21-7.15 1.7-2.0%

Table 2.4: Effect of activation barrier on the extrapolation of open-site fraction from
NRA filament temperature down to diamond-growth temperature.

Experiment Ex (kcal/mol) ka/kp(1800°C) 9,(927°C)
Chang et al. [68] 10.61 0.02-0.10 0.3-1.5%
Dawnkaski et al. [58] 7.84-9.69 0.4-2.4%
Harris et al. [29] 7.30 0.5-2.7%
Krasnoperov et al. [69] 6.21-7.15 0.6-3.2%

Table 2.5: Effect of experimental uncertainty in NRA coverage measurement on ex-
trapolated open-site fraction.

an sp° surface carbon from quantum wave packet calculations based on an empirical
potential for hydrocarbons [59]. Dawnkaski et al. [58] calculate E4 from molecular
dynamics simulations on C(100)(2x1) and C(111). Harris e¢ al. [29] take E4 from
analogous gas-phase data, and Krasnoperov et al. [69] measure the reaction of gas-
phase hydrogen with polycrystalline diamond at ~2 torr. The resulting activation
barriers range from 6.2 to 10.6 kcal/mol. However, the range of activation barriers
changes the extrapolated open-site fraction by only a small amount, less than 1%.
Although the uncertainty in the NRA value for k4/kz has a larger effect on open-site
- fraction, table 2.5.4 shows that the extrapolated open-site fraction remains one to
two orders of magnitude lower than predicted by the thermochemical growth model.
The better agreement between the NRA data and molecular-dynamics simulations
indicate that molecular dynamics more accurately simulates surface effects than ther-
mochemical kinetic models. In molecular dynamics, surface effects are approximated
by calculating the interaction of the surrounding slab with the gas-phase species and
surface sites. On the other hand, thermochemical kinetics models take their surface
reaction rates from analogous gas-phase reactions. Surface effects are approximated

by taking high-pressure rate constants and accounting for the strain of the surround-

74
ing lattice when calculating AG to find the reverse rate constants.

Thermochemical models assume that the total reaction cross section per surface
site equals the total reaction cross section per equivalent site in an analogous gas-
phase reaction [29, 30]. However, the disagreement with the NRA data implies that
the two cross sections differ. There are several mechanisms by which a gas-surface
reaction cross section differs from an analogous gas-gas reaction cross section. The
diamond atoms surrounding the surface site change the reaction cross section by
constraining the geometry of the transition state and the angle of approach of the
incoming hydrogen. The surface also lacks the kT of translational energy that the
analogous gas-phase species would contribute to the reaction. All of these effects
are accounted for by the molecular-dynamics simulations and are absent in thermo-
chemical models. Therefore, molecular dynamics rate constants based on well-tested
potentials are likely to model diamond growth more accurately than rate constants
of analogous gas-phase reactions. These physical reasons and the consistency with
the NRA data suggest that molecular-dynamics rate constants be incorporated into

diamond growth models to improve reliability.

Extrapolation from dosing temperatures to diamond growth temperature

The quantitative relationship has not yet been determined between reaction rates
under dosing conditions, where T, > T;, and rates under CVD conditions, where T,
= T,. In the absence of data, the following method is proposed for extrapolating
from dosing conditions to diamond growth conditions.

The gas and surface temperature dependence of the ratio k4/kp may be expressed

as
ka Ag,e7 #94 /[kTy As,e7 4 /kTs

7, _ _ ;
kr Agpe Fan/kTy Ae Es p/kTs

(2.42)

where A,, is the pre-exponential factor for the gas-phase temperature (T,) depen-
dence of the rate constant for reaction X, A;, is the pre-exponential factor for the
surface temperature (T,) dependence, E,, is the activation barrier associated with

the gas-phase temperature, and E,, is the activation barrier associated with the

75
surface temperature. Eq. 2.42 assumes that the modes are separable into gas and
surface, occupied according to the thermal distribution of states at T, and Ts, re-
spectively. Eq. 2.42 holds for a Langmuir-Hinshelwood reaction, where the gas equi-
librates with the surface before reacting and F, = 0, and holds for some Eley-Rideal
direct reactions, where the gas-phase reactant forms a product immediately upon
striking the surface.'? Experiments performed with T, = T, measure activation bar-
rier Ex = Ey, + Es, and pre-exponential factor Ax = Aj, x As,. The effective

activation barriers for the ratio k4/kp are

= _ qe —(Eo4—Egp)/bTy (Es, ~Esp)/RTs (2.43)
The net activation barrier associated with the surface temperature, F, = E,, —
E,,, is estimated as follows. Koleske et al. [11] found a slight surface-temperature
dependence for the rate of abstraction from polycrystalline diamond, with an apparent
E,, of 0.80.2 kcal/mol. An E,, of 0.6 kcal/mol falls closer to the range of the data
Thoms et al. [10], which found k4/kp at 600°C to be at most 1.5 times that at 80°C.
Dawnkaski et al. found the probability of recombination with C(100) and C(111)
to decrease between 927°C and 1527°C [58, fig. 3]. Taking Ag to be constant, the
decrease implies an Eg between 0.0 and ~-1.5 kcal/mol.?° The HREELS experiment
of Thoms et al. [10] found the probability of recombination to differ negligibly at
80°C from 600°C. From the error bars of the HREELS analysis, |E,,,| is less than 0.2
kcal/mol. Therefore, E,, is taken to be zero. The net surface activation barrier for
the ratio k4/kp is then E, = E,, — E,, ~ 0.6 kcal/mol.
The net activation barrier associated with the gas temperature, KE, = Ey, — En,
is estimated as follows. As in the preceding paragraph, Ep is estimated to be -1.5

kcal/mol from the recombination probabilities of Dawnkaski et al. (58, fig. 3]. Since

18Reactions with hot precursor mechanisms, where the reactant is trapped on the surface for a
time then reacts before fully equilibrating with it, may have several modes not thermalized to either
temperature and may not be well-described by eq. 2.42.

(927 Cc ~Ep,/(k-1200K)
20The activation barrier, Ep, was calculated by nee = i500 S=Es7@eiso0Ky » Where k is the

Boltzmann constant and pp is the probability of recombination at an isolated radical site on C(100)
taken from fig. 3 of ref. [58).

76
E, is small, Ep is taken to be Ey,, or Ey, * —1.5 kcal/mol. E,, is taken from
experiments performed with T, = T,, which measure Ey, = E,, + E,,. E;, has not
been measured for C(100) or C(111). In the absence of data, E,, is taken to be 0.6
kcal/mol, as in the preceding paragraph. Therefore, the net gas activation barrier for
ka/kr is Ey ~ (E4 — 0.6) +1.5 = BE, +0.9 kcal/mol, where E4 is the abstraction
activation barrier when T, = Ts.

The net gas and surface temperature dependence of k4/k,z is

k A A _ E,at0.9 kcal/mol 0.6 keal/mol
WA ny Sat sa ET eT (2.44)
Kr AgpAsn

where Ey, is the abstraction activation barrier when T, = T,. Taking the pre-
exponential factors to be temperature-independent, k4/kp at NRA dosing temper-

atures (Tyi, Ts:) may be extrapolated to k4/kp at diamond growth temperatures

(Tyo, Tse) via

ka ka _Egt0.9 keal/mol; 1 1) _ 0.6 keal/moly 1 1
k (Ty2, Ts2) & k (Zoi, Tsi)e ; Ta Tai ¢ a
R R

The 0.9 kcal/mol is a correction term to account for the negative barrier to recombi-
nation, as well as for the fact that the measured FE, includes not only the gas- but
also the surface-temperature dependence of abstraction. Since this correction factor
is approximate, and since the 0.6 kcal/mol correction term was chosen from data on
polycrystalline diamond, the exact values of the 0.9 and 0.6 correction terms will
change as data become available for E,, on C(100) and C(111), but the magnitudes
are expected to remain small.

Since the 0.9 kcal/mol term in eq. 2.45 decreases k4/kp and the 0.6 term increases
ka/kp, the net effect on the extrapolation to diamond growth temperatures is small.
Numerical calculation of eq. 2.45 for the activation barriers in table 2.5.4 reveals a

negligible change in open-site fraction.

77
2.6 Conclusions

The absolute deuterium coverage on the diamond (100) surface was measured via
NRA, and for the first time absolute coverage was studied as a function of deuterium
exposure. The saturation coverage is 0.95 + 0.04 D per surface C upon exposure to
deuterium at 1800°C and a surface temperature of 360°C.

Subsurface deuterium content was estimated to be negligible by comparison to
SIMS of microwave plasma-treated C(100) (Appendix A) and to results of previous
scattering experiments [9, 51]. The maximum coverages measured by NRA were
consistent with negligible diffusion or incorporation into the subsurface region during
NRA. Therefore, no deuterium diffusion is expected into the subsurface region.

The coverage was measured for a range of dosing parameters, gas-phase (Ty) and
surface (T,) temperatures. At high filament temperatures circa 2000°C coverages up
to 1.34 + 0.09 D per surface C were observed, consistent with the presence of sur-
face dihydrides. A mechanism for dihydride production is suggested: insertion into
the dimer bond by hot D from the filament, and a working hypothesis is suggested
to explain the surface-temperature dependence of degradation in previous experi-
ments [13]. Despite the high filament temperatures, exposure to elemental tungsten
is negligible, and ez-situ XPS showed no evidence for the presence of W or Mo (less
than 0.1% atomic W) on the sample subsequent to NRA. At low filament tempera-
tures (< 1800°C), saturation coverages were close to the expected value of 1 D per
surface C. Coverage measurements for the range of Ty and T, extend the work of
Thoms et al. [10] and Koleske e¢ al. [11], which investigated a single T;, and the work
of Chin et al. [12, 13], which measured reaction-rate ratio at a single T,.

Coverage was studied as a function of anneal temperature subsequent to dosing,
and desorption was seen at temperatures above 450°C. Anneals subsequent to the
1800°C exposures gave a thermal desorption barrier of ~3.0 eV assuming first-order

‘consistent with the barriers

desorption with a pre-exponential factor of 10/2 s~
obtained from TPD by Hoffman et al. [27] and Thomas et al. [20].

Hydrogen abstraction and recombination with the diamond surface are two of the

most important reactions in diamond CVD, as they determine the number of sites
available for growth. The NRA results imply that the ratio of recombination rate to
abstraction rate on C(100) is 0.06 +0.04 at 1800°C. The measured reaction-rate ratio
provides a consistency check for the set of reaction parameters used in diamond CVD
models. The NRA data are extrapolated down to diamond growth temperatures
(927°C) and compared to growth models of C(100) based on analogous gas-phase
reactions [29]. Results indicate that thermochemical growth models overpredict the
fraction of radical surface sites available for growth by a factor of ~20. Molecular-
dynamics simulations [58] are in better agreement with the NRA results, and their
reaction parameters are recommended for use in diamond CVD models.

At a filament temperature of 1800°C, the measured ratio of reaction rates, 0.06 +
0.04, agrees with the HREELS result of Thoms et al. [10] and the TOF-SARS mea-
surements of Koleske et al. [11]. However, it differs from the value of 0.2 obtained
by Chin et al. [12, 13] on C(111), possibly due to a variation between site-specific
reaction rates on C(100) and C(111), re. Appendix D.

Recommendations for future work

A working hypothesis is suggested to explain the high coverages at high filament
temperatures in the present experiment and to explain the surface-temperature de-
pendence of degradation in other experiments [13]. This hypothesis may be tested by
dosing the sample in the four different filament and surface temperature regimes and
monitoring the coverage.

Further experiments could also be performed to confirm assumptions made here.
For example, subsurface deuterium content could be confirmed to be negligible by
heating the sample to 1000°C and taking an NRA spectrum to see zero coverage.
Negligible contamination by trace elements may be confirmed by performing NRA
in a chamber equipped with an X-ray photoelectron spectrometer (XPS). XPS could
be performed as a function of sample cooling time without dosing, to eliminate the
possibility of contamination during cooling time.

Filament temperatures up to 1800°C are expected to preserve the surface re-

construction, and are recommended for studying reactions with a dimerized surface.
However, filament temperature may be raised to > 2000°C to investigate the po-
tential process of dimer-bond cracking by hot D emitted from the filament. Low
surface temperatures may stabilize dihydrides by precluding D, desorption and are
recommended for preserving evidence of dimer-bond breakage. Medium surface tem-
peratures may activate D2 desorption from dihydrides and are recommended for main-
taining a dimerized surface. High surface temperatures (2800°C) activate desorption
from monohydrides and may restore a disordered, degraded surface to the (2x1):D
reconstruction.

The reaction of molecular deuterium with the diamond surface may be studied
by keeping the filament temperature low enough to minimize atomic D formation (<
1000°C). Although room-temperature D2 and Hy are unreactive with the diamond
surface [13, 16, 20, 25, 41, 64], molecular D2 reacts with diamond powder above
450°C at atmospheric pressure [64]. In UHV hot D2 may react with bare diamond
by inserting into surface 7-bonds. This hypothesis may be tested by exposing a bare
sample to Dz at low filament temperature and investigating coverage as a function of
temperature.

On the issue of reaction-rate measurements, future studies of atomic D reactions
with diamond could determine not only the value of k4/kp but also the activation
barrier. This could be accomplished by dosing at a series of filament temperatures
while keeping the surface fully dimerized. I suggest filament temperatures up to
1800°C, where D cracking of dimer bonds is expected to be negligibly slow, and a
surface temperature at or above 360°C, where background gas exposure, prior to dos-
ing, is minimized. However, at filament temperatures below ~1200°C, the hydrogen
cracking efficiency is small [70]. Reaction rates of molecular hydrogen may be studied
at lower filament temperature. To obtain data more directly comparable to diamond
CVD conditions (700-1000°C), an UHV-compatible radio-frequency glow discharge
oven may be fabricated to produce lower-temperature atomic hydrogen [71].

Finally, future work could extend the NRA experiment by separately determining

the individual reaction rates, k4 and kp, in addition to their ratio, k4/kpz. These

80
parameters can be measured by calibrating the atomic deuterium flux via a chopped,
differentially-pumped mass spectrometer and by performing the analysis described
in section 2.5.1. The resulting site-averaged reaction rates may be compared to site-
specific rates by modeling site-specific coverages via the kinetic Monte Carlo algorithm
of Appendix C. Diamond surface science is one area where neither modeling nor
experiment alone can yield all the relevant reaction mechanisms and parameters, but

only the two working in concert.

2.7 Acknowledgements

The diamond sample was provided by the California Institute of Technology. I thank
Dr. Lou Troilo and Dr. James Butler, for help in plasma treating the sample at the
Naval Research Laboratory, and Mr. Robert Rossi, for imaging the sample via AFM
at Caltech. Iam especially grateful to Dr. John N. Russell, Jr., of the Naval Research
Laboratory for many useful discussions throughout the course of the experiment.

The NRA experiment was facilitated by the Surface Modification and Charac-
terization (SMAC) Research Center of Oak Ridge National Laboratory. I gratefully
acknowledge the help of Drs. David B. Poker and David M. Zehner, the technical sup-
port of Mrs. Gary Ownby, Dale K. Hensley, and Darrell K. Thomas, and the general
support of all SMAC members.

The work at ORNL was sponsored by the Division of Materials Sciences, U. S.
Department of Energy, under contract DE-AC05-960R22464 with Lockheed Martin
Energy Research Corp. Travel and local transportation were provided through the
personal funds of M. Susan Melnik, Dr. Walter L. Melnik, Dr. Ernest N. Prabhaker,
Mr. Glenn C. Smith; the hospitality of Dr. Gary Farlow, Dr. Wayne Holland, Dr.
Youlian Davidov, Dr. Jay Jellison, and Dr. John Budai; and the general funds of the
Engineering and Applied Sciences Division of the California Institute of Technology.
Local housing was provided in part by the hospitality of Mrs. and Mr. Katherine and
Jonathan Fain. Additional funds were provided by the ARCS Foundation, ONR and
NSF.

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Chapter 3 Migration on the C(110)

Surface: Ab-initio Computations

3.1 Introduction

Mobile surface adsorbates play a key role in surface processes of semiconductors such
as silicon and gallium arsenide. However, before this work was first published [1]
diamond surface science studies had generally assumed mobility to be low [2], and
diamond chemical-vapor deposition (CVD) studies had not established the competi-
tiveness of surface migration with gas-surface reactions. In diamond surface science,
the thermal desorption of Hz from C(100) was found to obey first-order rate kinet-
ics [3, 4]. Desorption from Si(100) was also first-order, and a pre-pairing mechanism
had been proposed to explain why the two-body desorption was not second-order [5].
However, the possibility of pre-pairing on diamond had not been investigated, and
a mobility mechanism to produce the pre-pairing had not been established. In dia-
mond chemical-vapor deposition studies, activation barriers to migration of surface
CH» and CHz3 [6] had been calculated, yet the competitiveness of these migration
rates with gas-surface reaction rates had not been demonstrated. One particular step
in an acetylene growth mechanism, two-center ring closure, had been proposed to
proceed via a concerted reaction involving hydrogen transfer [7]. However, Chang et
al. [8] later performed a thorough search of the potential energy surface about the
transition state and found that ring closure was more likely to proceed via gas-phase
hydrogen abstraction than surface migration. Thus, diamond surface models had yet
to establish a mobility mechanism to produce pre-pairing, and diamond CVD models
had concentrated on gas-surface reactions [9, 10] and gas-phase dynamics [11] rather
than surface migrations. |

Diffusion of chemisorbed species can occur on the diamond surface by insertion

into a C-H bond or migration to a neighboring radical site. We restrict attention to
the latter. Migration was considered to be negligible under typical CVD conditions
because the majority of diamond surface sites have neighbors which are terminated
by hydrogen, which blocks migration pathways. In CVD environments containing
halogens [12], a fraction of the surface sites may also be terminated by fluorine or
chlorine. Nevertheless, during growth some fraction of the surface terminator is miss-
ing, exposing open surface radical sites. The surface coverage is determined by a
balance of abstraction by gas-phase radicals and recombination onto radical sites.
Under hydrogen-based CVD conditions, the experiment of chapter 2 suggests that
2% of the surface sites are open, and modeling studies suggest that up to 40% are
open [13]. If the surface-terminating species are mobile, then the open radical sites
may be regarded as mobile. This would clear pathways for hydrocarbon adsorbate
diffusion.

Even when surface coverage limits mobility to short-range diffusion, surface migra-
tion may have implications for diamond growth mechanisms. Before this work [1, 14],
no proposed growth mechanism had included simple migration of surface termina-
tors!. These studies often found pathways which were blocked due to steric hindrance
from neighboring terminators, or concluded that the reaction must proceed through
a highly strained intermediate. Both of these conclusions could be radically altered
by even a small degree of mobility of surface terminators.

To demonstrate mobility and its competitiveness with gas-surface reactions, we
calculated the ab initio quantum chemical activation barriers to migration of H, F,
and Cl on a diamond surface. Attention is restricted to the (110) surface, which has
a higher growth rate than either the (100) or (111) surfaces [16]. (110)-type sites
also appear at steps on the (100) and (111) surfaces. Our results were summarized

in previous publications [14, 17], and more complete details are given here.

‘Huang and Frenklach [15] had calculated a barrier to migration on the (100) (1 1):2H surface by
semi-empirical MNDO methods. However, their emphasis had been the calculation of the energetics
for several possible reaction steps in diamond growth from addition of methyl, CO, and acetylene;
and none of these calculations included migration within the reaction pathway.

91
3.2 Computational method

3.2.1 Calculation of the electronic wavefunction

The Schrodinger equation was solved for a cluster of atoms modeling each migration
using standard ab-initio techniques [18]. The nuclear kinetic energy was neglected,
and the Hamiltonian included all coulomb interactions and the kinetic energy of the

electrons.

Hej vi Yo Se gt hE es ar: By)

i j

where H is the Hamiltonian, E is the total energy, |W) is the electronic wavefunction,
n is the number of electrons and N the number of nuclei, and Z is the atomic number.
All quantities are expressed in atomic units.

The spatial orbitals, ¢, were expressed in terms of Gaussian basis functions, x,

centered on the nuclei,
100

6 = SY GX:
p=l

Two basis sets were used in these calculations. A valence triple-zeta (VTZ) set with
polarization? was included for the two carbons directly involved in the migration. A
VTZ basis with polarization? was included for the migrating hydrogen. The fluo-
rine and chlorine basis sets were VTZ plus polarization*. The Dunning double-zeta

contraction® was used on all peripheral carbons and hydrogens.

?The carbon triple-zeta basis set consisted of a diffuse s function, exponent 0.0474, and a diffuse
p function, exponent 0.0365, in addition to a double-zeta (9385p) /[3s2p] contraction from ref. [19].
The carbon polarization function was d-type with an exponent of 0.75.

3The exponents for the hydrogen triple-zeta basis set were taken from the (6s) set of Table V
of ref. [20]. The four smallest coefficients were also taken from this reference. The coefficients for
the two most diffuse functions were 1.0 each. Thus the hydrogen triple-zeta basis set consisted of a
(6s) /[3s] contraction. The hydrogen polarization function was p-type with an exponent of 0.6.

“The fluorine triple-zeta basis set was the (11s7p) /[5s3p] contraction from ref. [21]. The exponent
for the fluorine (1d) polarization function was taken from ref. [22]. The chlorine triple-zeta basis set
was the (12s9p)/[6s5p] contraction from ref. [23]. Chlorine polarization was d-type with an exponent
of 0.6.

°The carbon double-zeta basis set was the (9s5p)/[3s2p] contraction from ref. [19]. The hydrogen
double-zeta basis set was the (4s)/[2s] contraction of ref. [19] with scale factor of 1.2.

92
I approximated each electron as interacting only with the mean field of all other

electrons, producing the Hartree-Fock (HF) wavefunction,

yy =A { (TI aaa ona) . (3.2)

where A is the antisymmetry operator, m is the number of spatial orbitals (n/2 +1),
and a and £ are up and down spin eigenfunctions, respectively.

Next I correlated the electrons directly involved in the reaction at the Generalized-

Valence-Bond (GVB) or Complete-Active-Space (CAS) level, where
m—2

(TI aaa
wl

and Nactive is the number of active electrons. The GVB-CAS calculation optimizes

pu) = A S- Chri

fj +fhr +h =Nactive

(ono thst) ace)
(3.3)

inactive

the configuration coefficients, C;., and the orbital coefficients, c;,,. For the hydrogen
migrations, the GVB-CAS active space included 3 electrons in 3 orbitals (3 in 3),
and the wavefunction has the orbitals optimized for all seven spatial configurations
(8 spin eigenfunctions).

An active space was developed for the halogen migrations by testing several cases,
including 3 in 3, 5 in 5, and 7 in 7. In all test cases the GVB-CAS determined sim-
ilar weight distributions for the three most important configurations. In subsequent
calculations, 7-in-7 active spaces were generally used, to include 4 of the electrons in
the halogen’s outer-shell as well as the 2 in the carbon-halogen bonding orbital and
the 1 in the carbon radical orbital.

Finally, given the HF or GVB-CAS wavefunction, I included further correlations
between electrons by carrying out Configuration-Interaction (CI) calculations in which
all single and double excitations were allowed from all non-core occupied to all virtual

orbitals. These wavefunctions are denoted as SD-HF and SD-CAS respectively and

93

written as

pwr?) = A S° Ca (Deore ()imactive (P)active () virtua)

single
excitations

+ S° Ca \(P) come (9) mactive (9) cctive (9) virtual)

single
excitations

+ S° Ca \(P) core ()imactive (2) active () virtua)

double
excitations

+ S° Co l(P)come (9) inactive (9) active (9) virtwat)

double
excitations

+ » Co (Peone (9) inactive (9) active (®) virtuat) ‘ (3.4)

double
excitations

Here (¢)core are the orbitals of the inner-shell carbon and halogen electrons, and the
* superscript represents the excitation of a single electron into a virtual orbital. The
SD-HF and SD-CAS calculations fix the orbital coefficients, c;,,, and optimize the Cl
coefficients, C,. Thus the major purpose of the HF and GVB-CAS calculations is
to obtain optimal orbitals upon which to base the CI calculations. The CI active
space included 3 electrons in 3 orbitals for the H migrations and 5 in 5 for the
halogen migrations. To include the most important higher-order correlations for the
H migrations, the CI calculation was based upon a 3-reference wavefunction where
the 3 references were the configurations with the highest weight in the GVB-CAS
calculation.

The GVB-CAS calculation often diverged unless it included the halogen’s outer-
shell s electrons in the active space. To make convergence automatic, most halogen
GVB-CAS calculations were performed from the SD-HF CI numbers as the starting
wavefunction. These calculations are denoted CAS-CI.

All calculations were performed using a modified version of the MOLECULE/SWE-
DEN suite of codes [24]. For H migration, I used both SD-HF and SD-CAS wavefunc-
tions. For the halogens, my final results included only SD-HF wavefunctions. The

choice of SD-HF or SD-CAS wavefunction is explained in section 3.3.1.

94

3.2.2 Optimization of cluster geometries

As a model for the (110) surface, we consider constrained clusters in which all surface
C-C bonds not involved in the reaction are replaced by C-H bonds. This leads to the
clusters shown in figs. 3.1a-3.3a. The internuclear C-C distances were fixed at 1.54 A,
the value for bulk diamond [25]. All C-H bond lengths on the peripheral hydrogens
were fixed at 1.10 A, a value typical for hydrocarbons. In large-scale multireference
configuration interaction calculations of (1,2) Cl migration, Engels et al. [26] found
that variations in the CH bond length had “minor influence on the total energy.” The
only atom whose coordinates were optimized during our calculation was the migrating
X (H, F, or Cl).

The transition-state geometry was determined by placing the migrating atom at
several positions along the symmetry axis, for the (1,2) and (1,4) migrations, or sym-
metry plane, for the (1,3) migration. The position was optimized to give the minimum
energy, and the resulting geometries are shown in figs. 3.1b-3.3b. The reactant ge-
ometry was determined by placing the migrating atom in a bonded position, at a
tetrahedral geometry from one of the primary carbon centers. The active C-H, C-F
and C-Cl bond lengths were then optimized for the reactant clusters.® The activation
energy was the difference between the transition-state energy and the reactant energy.

In several cases the geometry of the transition and reactant states was confirmed
by least-squares fitting a parabola to the energies of the four geometries closest to the
state. The parabola’s minimum was within 0.01 A of the minimum determined by
the single-point calculations. The geometry resolution of the single-point calculations
produced an uncertainty in the activation energies of about 0.05 eV.

Since the (1,4) H migration required the largest CI calculations, I optimized its
transition-state geometry at the SD-CAS single-reference level and calculated the
energy of that geometry at the triple-reference level. I also took the reactant energy

to be equal to the SD-HF reactant energy, which makes my estimate for the SD-CAS

®The active C-F and C-Cl bond lengths were optimized individually for each reactant cluster.
The active C-H bond length was optimized for the reactant cluster of the (1,2) migration, and the
bond length for the (1,4) and (1,3) H migrations was taken to be the same as that of the (1,2)
migration.

95

\ itt H wit H
/ —_—_ Zz —=__—_>
Hi H
(a) Reactant (b) Transition State (c) Product

Figure 3.1: Cluster for (1,2) migration. X represents H, F, or Cl, and (110) lies in
the plane of the paper. The origin bisects the surface C-C bond, and the z axis is
perpendicular to the surface (110) plane.

la / /
yw Hw 2 Heer C
A H
\ sane wt 2) H fr \ cant wit \ caw
ra H yw” “ H oman
(a) Reactant (b) Transition State (c) Product

Figure 3.2: Cluster for (1,3) migration. (110) lies in the plane of the paper. The
midpoint between C, and C2 determines the origin, and 6=0 lies in the C,C2C3
plane. The (r,@) plane is perpendicular to the surface (110) plane.

H H H H
lt / Slt /
H Clin Cg CainXmeC
yw" n wer
HON HH ‘Ny
(a) Reactant (b) Transition State (c) Product

Figure 3.3: Cluster for (1,4) migration. X represents H, F, or Cl, and (110) lies in
the plane of the paper. The origin is located halfway between C,; and C2, and the z
axis is perpendicular to the surface (110) plane.

96

activation barrier too low by about 0.1 eV/cluster for (1,4) H migration.

3.3 Results

3.3.1 Comparison of SD-HF to SD-CAS energy

The SD-CAS wavefunction gives an energy closest to the actual activation barrier.
Therefore it was used in all cases where computationally feasible. As the H migrations
had only 3 electrons directly involved in the reaction, it was straightforward to de-
termine the appropriate orbitals for the active space of the GVB-CAS wavefunction.
In this case the calculated energies behaved as expected: the calculated activation
barrier at the HF level was higher than that at the GVB-CAS level which was in turn
higher than that at the SD-CAS level, the best level of approximation.

However, the outer-shell electrons of F and Cl participated in their migrations,
making it difficult to design an active space that was large enough to be physically
reasonable and small enough to be computationally feasible. Figs. 3.4 and 3.5 show
that in a few cases SD-CAS energies were actually higher than SD-HF energies. Here
the SD-CAS calculations were based upon a single-reference wavefunction, the dom-
inant configuration of the 5-in-5 GVB-CAS. A multi-reference CI would have more
effectively included interactions with the halogen outer-shell electrons, and multi-
reference SD-CAS energies are expected to be lower than SD-HF energies. However,
since multi-reference CIs were computationally impractical for the halogen migrations,

these reactions were calculated at the SD-HF level.

97

¢ ° £E (HE)-E_ (HEF) “*B(7,6) |
[ trans reac |
7.5 a E (SD-CAS)-E (SD-CAS) he
| trans reac 4
«+ E (SD-HF)-E (SD-HF) ;
_~ trans reac
ft 7 rN
2 7.0-+—- +
3 [
Oo
o [
on 6.5 ° as
> L °
wv g
oa r &
<1 6.0
| ¢
1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

z (A)

Figure 3.4: Computed potentials of an excited transition state for (1,2) F migration.
The HF configuration was ?B(7,6), and the active space of the GVB-CAS and SD
calculations included 5 electrons in 5 orbitals. The z axis is defined in fig. 3.1 .

7.04 eet ; =
° E ansee) - ECAP) B(11,10) 1
a E ans’ D-CAS) - E tS D-HF)
6.5 * E (SD-HF)-E_ (SD-HF) /T
3 vans reac
a 6.0 besecssceneeseeerefenseneeseneneenss
ae L
jon
a 5 5 & 2
~ ~ g
an
<1 a Ed +
ee L
4.54 a a
0.8 1 1.2 1.4 1.6 1.8 2 2.2

z (A)

Figure 3.5: Computed potentials of an excited transition state for (1,4) F migration.
The HF configuration was ?B(11,10), and the active space of the GVB-CAS and SD
calculations included 5 electrons in 5 orbitals. The z axis is defined in fig. 3.3 .

98

3.3.2 Determination of ground and excited transition states

Although physical considerations narrow the field, one cannot determine the ground
electronic configuration a priori. I calculated the energies of several configurations
closest to the expected ground state for the halogen migrations, where outer-shell
electrons complicate the reaction. Results are summarized in table 3.1, and details
are given at the end of the chapter in figs. 3.8 to 3.30. The calculations were guided by
GVB-CAS results, which determine whether nearby configurations of the same sym-
metry type are more stable. To assure reliability, all symmetry types were computed,
and both the ground and excited transition states were identified. Here a transition
state is an energy minimum along the z axis, and the ground transition state is the
state with the lowest energy minimum.

As table 3.1 indicates, several halogen-migration configurations did not lead to
transition states but gave potentials that were purely repulsive in the region of calcu-
lation. In general, lack of identification of a transition state does not necessarily mean
lack of existence. Rather it could simply mean that the transition state is not located
within the computational subspace searched. However, my configurational search was
sufficiently broad to identify two transition states for each halogen migration.

The configurations for the ground transition states are listed in tables 3.3.2 and
3.3.2. The unpaired electron’s orbital could have been either symmetric or antisym-
metric with respect to rotation about the z axis. Both cases were calculated, and
the ground configuration was determined to be ?A for the F migrations and Cl (1,2)
migration and 7B for the Cl (1,4) migration.

The H migrations were electronically simpler, as H contains no lone pairs. Only 7B
and *A” configurations were considered, and results are shown in tables 3.2 through
3.3.2. The GVB-CAS calculations confirmed that within this symmetry the assumed

configurations dominated.

99

Dominant GVB~CAS

Atom Migration HF Configuration E, Za Configuration
Cl (1,2) 7 A(10,7) 3.71eV 2.20 A J
2 A(9, 8) x x 2 A(10, 7)
* B(9, 8) 3.72 2.00 J
* B(10, 7) x x 2 B(9,8)
F (1,2) 7 A(8,5) 4.68 eV 180A J
2 A(7,6) x x 2 A(8, 5)
* B(7, 6) 5.44 1.70 J
*B(8, 5) x x 2 B(8, 5)/?B(7, 6)
Cl (1,4) ?.B(13, 12) 2.29eV 1.70 A Jf?
?B(14, 11) x x div?
2 A(14, 11) 2.45 1.5 J
F (1,4) ?.A(12, 9) 3.41eV 1.0A J
* B(11, 10) 4.65 1.40 JV

“Preference of the HF orbital energies. The GVB-CAS calculation was not performed.
’The HF calculation preferred the ?A(14,11) state, and the GVB-CAS calculation
diverged due to the high HF energy.

Table 3.1: Calculated activation barriers, E,, and geometries, z,, for HF configu-
rations near the ground state. \/ denotes that the GVB-CAS calculation confirmed
that the reference configuration dominated. x denotes that the potentials were purely
repulsive in the region of calculation.

Dominant GVB-—CAS

Atom Migration HF Configuration E, Za Configuration
H (1,2) ?B(5,4) 3.24eV 114A J
(1,3) ?.A”(8,5) 3.56 eV 1.11 A, 44° J
(1,4) ?B(9,8) 2.24eV 0.71 A J

Table 3.2: Calculated activation barriers, E,, and geometries, z,, for H migrations.
The geometry for the (1,3) migration is given in terms of (r,@) coordinates defined in
figure 3.2b. \/ denotes that the GVB-CAS calculation confirmed that the reference
configuration dominated.

100

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101

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tH s€ 10 ott “dz 4 He 8% A omngs
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“dé 10
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--- ~ ww --- --- Pyy-ehy — Sy By byy-y + eyy-By

a ~~ --- -~-- eny-Usy — BH-BS eHT-Sy +L RyY-By

a --- ~-- a WB yV-My = UO-My AD-B + Q-H1

--- --- @Iy-14

~— e --- “ae ~—s bapy-%1 — eqp-Hs bapy-e19) + BqET-FIg

--- -~-- --- --- CAET- TI TAPZ-TAy) C4Y-SA 4 TAPZ-TA | PaMPDUIG
“d@ 10 “dz 10
‘dz 10 8% 10

--- --- --- --- sTsy — stg sTsg + stl

~-- --- ~-- ~-~ ste — szplig stot + spa

dTpUIUTASTIUY OT}OUIUIAG ILIaUIULASTUY OLIyaUIUAAG oLIyeuIWASTIUY DLIOWIUAS

moreIsIW 1D

woes

WOryeIsTA, H

(a) (1,2) migration

102

Fpy2 Hy
x ‘ toa /
Cpzinnns Cy
His a\E \
\ Hig

ceesans eal mp4

/ tl
Hf 03 H b1

(b) (1,4) migration

Figure 3.6: Labels of atomic centers in transition-state clusters for (1,2) and (1,4)
migrations. X represents H, F, or Cl, and (110) lies in the plane of the paper. The
origin is located at the midpoint between the two surface carbons. The z axis is
perpendicular to the surface (110) plane.

103

3.3.3 Activation energies

The predicted activation energies are shown in table 3.5. The calculated barriers are
upper bound to the actual barriers, and the computational precision is about 0.1 eV
for the H (1,4) migration and 0.05 eV for all other migrations. The barrier height
for (1,4) migrations is at least 1 eV lower than for (1,2) and (1,3) migrations for all
three systems. This is consistent with combustion experiments, where (1,4) hydrogen

migrations occur while (1,2) and (1,3) migrations remain too slow to be detected [27].

Migration (1,2) (1,3) (1,4)
H 3.24eV 3.56eV 2.24 eV
Cl 3.71 a 2.29
F 4.68 — 3.41

Table 3.5: Calculated activation energies for surface migrations. The calculations are
performed at the SD-CAS level for hydrogen migrations, and at the SD-HF level for
halogen migrations. Barriers to (1,3) migration of Cl and F were not calculated.

Migration (1,2) = (1,3) (1,4)
TH 3.2 sec 95sec 180 x 107° sec
Tol 440 — 340 x 107°
TR 6 x 10° — 200

Table 3.6: Order-of-magnitude estimates of characteristic times for surface migrations
at 900°C.

3.4 Analysis

Since migration reactions are unimolecular and gas-surface reactions are bimolecular,
rate comparisons must account for concentration and frequency factors in addition
to barrier heights. Accounting for pre-exponential factors and barrier heights, order-
of-magnitude estimates were obtained for the characteristic migration times. This
was the first study [1] to compare characteristic times directly instead of only barrier
heights. Previous studies [2, 28] had obtained “extrordinarily high” barriers to mi-

gration and were not able to establish its competitiveness with gas-surface reactions.

104

3.4.1 Predicted characteristic migration times

The predicted activation barriers are converted to characteristic migration times using

the approximate transition-state theory expression

keT
ne BoP thar (3.5)

where r is the characteristic migration time, E, is the activation energy (from ta-
ble 3.5), kg is Boltzmann’s constant, T is the temperature (1173 K), and h is Planck’s
constant. This simple expression for the pre-exponential factor may be in error by
a factor of about five. Moreover, the barrier height on a real diamond surface may
be lower than our computed E, due to the cluster approximations and their overly-
constrained geometries. Thus these estimates for 7 may be in error by an order of

magnitude. The predicted migration times are shown in table 3.6.

3.4.2 Comparison of migration times to thermal desorption

times

For migration to be significant in diamond surface science, it must compete with
thermal desorption. Although the rates of halogen desorptions are unknown, Butler
et al. [29] have measured the rate of hydrogen desorption from C(110). The corre-
sponding desorption time is calculated from t = 1/kg, where kg = Ae~"4/*T is the
desorption rate constant. Figure 3.7 compares the temperature dependence of the
hydrogen (1,4) migration time with that of the surface desorption time. Here the
(1,4) migration times are calculated by equation 3.5, which is an order-of-magnitude
estimate. The migration times shown in fig. 3.7 are several orders of magnitude faster
than desorption times. Therefore the (1,4) migration of hydrogen is sufficiently fast to

occur before desorption and sufficiently fast to pre-pair the hydrogens for desorption.

Sati : ° H (1,4) Migration Time
Characteristic Times , Cl (1,4) Migration Time
x H Thermal Desorbtion (110)
5 t + H Thermal Desorbtion (100)
VOD prc pepe ° Lifetime of Surface C*
soe cave °* Lifetime of Surface C-H
1 0’ weeeee x. ‘ r cette te ecedeeececaeeecceeeeerdevecceeesecsetensedeseaaeeeseceeecened ‘ eee :
— 10 . Ry '
© ~~ ~ ~ * + X
E a a Seg
oy +. x x
oe ~ —— pan anna nnnnnnn I SOnSRIIRRIRIOIIES
iS 1) pene “$ $ Posten ran ia *
a3) $4 .
Bot enn Pe, i
am "$4
of an
YQ pred 2.0 ee. CCR} CCS SCE aE SES eee SEDS SE SOEDEEEEEEEES
sosad PeCeTerereee re Te
"bas
10° 1 4. it roan oo real . a
600 700 800 900 1000 1100 1200 1300 1400
Temp (K)

Figure 3.7: Estimated characteristic reaction times.

3.4.3 Comparison of migration times to gas-surface reaction

times

For surface migration to be significant during growth, it must compete with gas-
surface reactions. Otherwise, a surface hydrogen will be abstracted by gas-phase
atomic hydrogen before it has a chance to migrate. Alternatively, a surface radical
site will disappear upon recombination with a gas-phase hydrogen atom before a
neighboring H can hop into this site. The characteristic lifetimes of surface hydrogen
and radical sites are unknown for C(110). However, Belton and Harris [13] have
estimated reaction rates for the (110) surface, using rate constants for analogous
gas-phase reactions. The corresponding lifetimes are shown in table 3.7. These are
order-of-magnitude estimates, calculated using 7~! = ky x [H8*], where ky is the
forward rate constant at 900°C (taken from table I, reactions (2) and (3) of ref [13].),

and [H®**] is the gas-phase concentration of atomic hydrogen just above the surface.

106
(H®**] is taken to be 5.5 x 1071? mol/cm? at 20 torr [30].

Gas-Surface Reaction T
Hs + C—ysut > Hs" + Cysurt 390 Us
Heas + Cysurt + C— Het 180 US

Table 3.7: Order-of-magnitude estimates of characteristic times (r) per surface site
for gas-surface reactions at 900°C [13].

The gas-surface reaction times are four to six orders of magnitude faster than any
of the (1,2) or (1,3) migration times. Thus these migrations are too slow to play a
role in CVD of diamond. The characteristic time for (1,4) migration of F is also too
slow. However, our estimates for the (1,4) migration times of H and Cl are within
the uncertainty of the estimated surface site lifetimes. Thus (1,4) migration of both
HA and Cl is sufficiently fast to compete with gas-surface reactions and play a role in
diamond CVD.

A sequence of (1,4) migrations down zig-zagged carbon chains yields diffusion
in the [110] direction, whereas a series of (1,2) hops across carbon chains followed
by (1,4) hops between chains yields diffusion in the [001] direction. Thus table 3.6
indicates that diffusion occurs at least 10* times faster in the [110] direction than
in [001]. Although migration may occur in diamond CVD, we do not expect long-
range surface transport. It is interesting to note that if other growth conditions could
be found where surface diffusion dominated, this anisotropy would greatly enhance
surface transport from terraces to steps with edges parallel to [001]. The [001] steps
would then be rough and grow at a much higher rate than the smooth [110] steps.

Figure 3.7 compares the temperature dependence of the hydrogen (1,4) migra-
tion time with that of gas-surface reaction times. Here the (1,4) migration times
are estimated by equation 3.5. The gas-surface reaction times are calculated using
T = ky x (H8*], with [H®*] = [H®*](1173K) x 1173/T (K) (ideal gas). This is an
order-of-magnitude estimate, since it does not account for chemical reactions which
may modify the temperature dependence of [H8*5]. Nevertheless, the gas-surface re-

action times and migration times shown in fig. 3.7 are comparable only at surface

107
temperatures where diamond grows, i.e. 700°C to 1000°C. This suggests the possi-
bility that the temperature for diamond growth must be sufficiently high for (1,4)
migration to be activated. Possible roles of migration include annealing the surface,
allowing it to relax from strained structures, and increasing methyl incorporation rate
relative to desorption rate by allowing surface hydrogens near the adsorbed methyl

to move away and decrease the steric crowding of the methyl.

3.5 Conclusions

Ab initio calculations were carried out to estimate activation energies for the mi-
gration of H, F, and Cl on the diamond (110) surface, or (110)-like sites on steps
on other surfaces. Accounting for pre-exponential factors and barrier heights, order-
of-magnitude estimates were obtained for the characteristic migration times. This
was the first study [1] to compare characteristic times directly instead of only barrier
heights. The estimated times for (1,4) migration of both H and Cl are of order 10~* s.
Under UHV conditions, these characteristic migration times are orders of magnitude
faster than characteristic thermal-desorption times. Therefore (1,4) migration is suf-
ficiently fast to pre-pair the surface hydrogen, allowing first-order desorption kinetics.
Under diamond CVD conditions, the characteristic times for (1,4) migrations of H
and Cl are of the same order of magnitude as estimated surface-site lifetimes. There-
fore (1,4) migrations of H and Cl are sufficiently fast relative to gas-surface reactions
to play a role in diamond CVD.

After this work was published [31] several groups investigated the potential role
of migration in diamond CVD. In the case of growth on the (100) surface, direct-
simulation kinetic Monte Carlo studies [32] found that surface migration opened a
pathway for pi-bonded sites to grow to bridged sites four to six orders of magnitude
faster than the rate at which isolated radical sites grew without migration. Other
simulations [33] found migration to be a key step in enabling atomically smooth

growth of the (100) surface.

108
3.6 Acknowledgements

Useful discussions with Jason K. Perry are gratefully acknowledged. This work was
supported in part by the Office of Naval Research under contract N00014-90-J-1386.
The computer facilities for the studies were supported by grants from the National

Science Foundation (CHE 91-00284, GCAG ASC-9217368).

109

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M. Tsuda, M. Nakajima and 8. Oikawa, “Epitaxial growth mechanism of dia-
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(24) MOLECULE/SWEDEN is a system of electronic structure codes written by J.
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112
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113

as © E\(HF) - E, , (HF)
0.64 | ¢ E\(SD-HF) - E, ,,(SD-HF)
= 0.5+
Hn -
= 0.4
o E
i L
v 5
a. 0.3 ce ne
> t
2 [
in 0.2+ es ee
<1 t
0.14 a
ee oe
1.6 1.7 1.8 1.9 2
log (A)

Figure 3.8: Computed potentials of the reactant state for (1,2) Cl migration. The
SD-HF was 5-in-5. Io_c is the length of the active C-Cl bond.

6.0 ap __
I ° E (HE)-E (HF) 7A(10,7)| |
trans reac
i * E (SD-HF)-E_ (SD-HE) | |
5.5 . trans reac aan
a : ° ° °
3 4.54. oo @ A
4.0-+ Saini Sa RR oo $ an

1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1
z (A)
Figure 3.9: Computed potentials of the ground transition state for (1,2) Cl migration.

The HF configuration was ?A(10,7), the GVB-CAS calculation was 7-in-7, and the
SD-HF was 5-in-5. The z axis is defined in fig. 3.1.

114

25.0 ° HE *A(9,8) ° HEF *B(10,7){.
x CAS-CI + CAS-CI
8 * SD-HF ° SD-HE
3 21.0 i:
a ° 5
~ co]
g 17.04 wl
2 .
LY +
a 13.0---
ae
as
a L
Vo QO Reneeeeeeee eetteteer deer eeenetentecnnibesnetceeecantecneebeneees
E [ i ° 3 Ad ¢
cone [ . |
5.0

1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1
z (A)
Figure 3.10: Computed potentials of repulsive states for (1,2) Cl migration. The

HF configurations were *A(9,8) and ?B(10,7), and the GVB-CAS calculations were
7-in-7, and the SD-HFs were 5-in-5. The z axis is defined in fig. 3.1 .

6.0
t ° E (HE)-E_ (HF) 7B(9,8)
trans reac
i * E (SD-HF)-E_ (SD-HE)
5.5+-- trans reac |
= i
YX L
4 L
5 5.0
ft
ov °
QO,
% 4.5-+ ° 2
= |
<4 4
re en

1.7 19 241 #23 #25 27 29 3.1
z (A)

Figure 3.11: Computed potentials of an excited transition state for (1,2) Cl migration.
The HF configuration was 7B(9,8), and the SD-HF was 5-in-5. The z axis is defined

in fig. 3.1.

115

oe peng ° 2 Le

= + SD-HF
je)

2 21.0

i)

o 17.04

jon u~L

> ° ° °

YL L
ea 13.0
Os
As

aye r

", ee

py L

5.0
r ° + ° + °
1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1
z (A)

Figure 3.12: Computed potentials of an excited transition state for (1,2) Cl migration.
The HF configuration was ?B(9,8), and the SD-HF was 5-in-5. The z axis is defined

in fig. 3.1.

05 olin te) «CCF *A 00,7),
“Tt x CAS-CI
> * SD-HF
2 21.0
3 17.04
On meni
ca 13.0 [ ¥. > a x a eeeeneans ane . D4 eT
feb“ t
- a
5 L
ee a
+ e é . e e + e °
1.7 19 241 #23 #25 27 29 3.1
z (A)

Figure 3.13: Computed potentials of the ground transition state for (1,2) Cl migration.
The HF configuration was ?A(10,7), the GVB-CAS calculation was 7-in-7, and the

SD-HF was 5-in-5. The z axis is defined in fig. 3.1.

116

: © E (HF) - E, ,,(HF) |
Os Saas Ge | * E(SD-HF) - E, ,,(SD-HF)/+
_~ a ee 4
Song iL
a4 C
4 L
= 0.4
v [
bes [
Y L
o i ee
> t
4 t +
i ea see ceneeeeeeneeneneenefoetrtintnteneeeenteenfeets
< : >
OD perc teecetetssttntnnntfntntnnnnnennen a
0.0-+4 voce Be
1.2 1.3 1.4 1.5 1.6
log A)

Figure 3.14: Computed potentials of the reactant state for (1,2) F migration. The
SD-HF was 5-in-5. lc_p is the length of the active C-F bond.

707———+— ¢ & (HE)-E (HE) 7A(85)~
[ trans reac
* E (SD-HF)-E_ (SD-HF)
trans reac
6.5
4 °
ra} 6.0 *
5)
o.
> 7 ° °
wy a uu
< « ‘ :
5.0 | be
r bd ra ° :
1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8
z (A)

Figure 3.15: Computed potentials of the ground transition state for (1,2) F migration.
The HF configuration was ?A(8,5), and the SD-HF was 5-in-5. The z axis is defined

in fig. 3.1.

117

° HF 7A(7,6) ° HF *B(8,5)

25 Qh x CAS-CI + CAS-CI
t ° ¢« SD-HF « SD-HF
+ 21.0
a °
a 17.0 nae
sy 13.0-+-- ae seecteeeseseecensedeeneenrenssetietaeeheneeeneenees +
Ty
a § ee
fe L ¢ °
ty 9.0 Fosccccssscessene
§ [ é hd e
ay ° e
sO [es Uc nent cn ne SnnE nets SenESEEEESSS SSO SNRESEOEEE

1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8
z (A)
Figure 3.16: Computed potentials of repulsive states for (1,2) F migration. The HF

configurations were ?A(7,6) and ?B(8,5), the GVB-CAS calculations were 7-in-7, and
the SD-HFs were 5-in-5. The z axis is defined in fig. 3.1 .

118

rt * EB (HE)-E, (HE) 7B(7,6)
7.5-+4 s E__,,(SD-CAS) -E_ (SD-CAS) ob

+E. (SD-HF)-E_ (SD-HE) |

3 7.0 a vende

3 [ i 1

1]

a [ :

Qu oe nnn nee geeereenbeseeeee vesseeteesbesenntennenes

> L °

wv é

tx [ + :

<4 6 nee eneec cee eeedecee cence eeceeeeeeebcneeeceenneneeaceabeceaeeeeneens
if ° ca

12 14 #16 #18 #2 22 24 26 28
z (A)

Figure 3.17: Computed potentials of an excited transition state for (1,2) F migration.
The HF configuration was ?B(7,6), the GVB-CAS was 5-in-5, and the SDs were 5-in-5.

The z axis is defined in fig. 3.1.

119

pepe | 8 CHE 7 B(7,6) 4
25.0 + GVB-CAS [°T
_ = S§D-CAS |
2 21.0 ° SD-HF pp
io]
el 7 °o °
go 17.0-+ +
<7 [ + 4
i" 13.0 a eee oe Se +
B_§
oaks t
- 9.0
all r ; é 3
5.0 a aed
1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8
z (A)

Figure 3.18: Computed potentials of an excited transition state for (1,2) F migration.
The HF configuration was 7B(7,6), the GVB-CAS was 5-in-5, and the SDs were 5-in-5.
The z axis is defined in fig. 3.1.

25.0-- ° HEF 7A(8,5)
_~ x CAS-CI
to
g 21.0 * SD-HF
or)
fo
oo 17.0-fon ¢ : ° a
% t ® x x
ce, 13.0
oan
RS
pj"
9.0
& i
rx] L ; +
12 14 #16 441.8 2 22 24 26 28
z (A)

Figure 3.19: Computed potentials of the ground transition state for (1,2) F migration.
The HF configuration was 7A(8,5), the CAS-CI was 7-in-7, and the SD-HF was 5-in-5.

The z axis is defined in fig. 3.1.

120

— _
© E (HF) - E, so¢FF)
0.6+ * E(SD-HF) - E, ,,(SD-HF)|+
= 0.5--
<2 L
a 0.4
Y E
g &
Oy 0) Qi nneeneeeeeediceseneeeetenneneeeentnentedeeunnnntentenaneeeeettunnndeerettetnnteneeetneeesetes AL
LY t
a 0.24
<1 ; |
a a 6
0 ee Se |
1.6 1.7 1.8 1.9 2
loa (A)

Figure 3.20: Computed potentials of the reactant state for (1,4) Cl migration. The
SD-HF was 5-in-5. loc is the length of the active C-Cl bond. 7-in-5 SD-HF calcula-
tions were also performed at lc_c; = 1.80, and the energy was the same as the 5-in-5
energy.

121

4.5 __
i > EL ne(HtF) - E.,, (HP) *B(13,12)} 7
L * E (SD-HF)-E (SD-HF)
7 tans reac LL
a [
3 L 4
a 3.5 eee ees es eee tea +
a .
Qn
iS B.0-be ren es
™ I
2.5 Ss q
2.0L. |

11 13 15 17 19 24 23 25
z (A)

Figure 3.21: Computed potentials of the ground transition state for (1,4) Cl migration.
The HF configuration was 7B(13,12), and the SD-HF was 5-in-5. The z axis is defined
in fig. 3.3. 7-in-5 SD-HF calculations were also performed at z = 1.90, and the energy
was the same as the 5-in-5 energy.

122

° HEF *B(14,11)

25.0- es a | « SD-HE +
_ |
x 21.0 2
vv
v 17.0
a, AT
xv L :
ws 13.0 Se a me
RS
po + *
‘sy 9.0-+. i" i
a 2 : e
ca [ '
5.0+—-
i T

1100643 46145 #4.7 19 #24 #23 2.5
z (A)
Figure 3.22: Computed potentials of repulsive state for (1,4) Cl migration. The HF

configuration was ?B(14,11), and the SD-HF was 9-in-5. The z axis is defined in
fig. 3.3.

4.54 et
f° ° EHF) - E.,, (HP) 7A (14,11)
[ * E (SD-HF)-E (SD-HF)
4.0 trans reac
ran ; : r
2 ° °
5 :
7 3.5 : sessessesafeseesesnessssasessduesssarscseerecseeapeneensces
5 [
am [
% CO en nn ee en -L
2.5 i Me secsscetseceespectnseeeeseeeeefaceenssetnee +

110464.3 4145 1.7 41.9 24 #23 25
z (A)

Figure 3.23: Computed potentials of an excited transition state for (1,4) Cl migration.
The HF configuration was 7A(14,11), and the SD-HF was 9-in-5. The z axis is defined

in fig. 3.3.

123

° HE *A(14,11)|_

25.0 Rn nee manne een + CAS-SD =
* SD-HF
£ ee ne
cs) °
o 17.0-+ :
Ou oT
c 13.0
As
WY
mt L
_ 9.0
ma” L
5.0 id
b » cd
i . . . ry > . . ; ?
i]

1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5
z (A)
Figure 3.24: Computed potentials of an excited transition state for (1,4) Cl migration.

The HF configuration was 7A(14,11), the CAS-CI was 11-in-11, and the SD-HF was
9-in-5. The z axis is defined in fig. 3.3 .

° HE 7B(13,12)_

25.0 I + SD-HF +
4 21.0 +
=I
ae)
@ 17.04 _
a Fs eae Senn RS ERC SERED ER
wv |
ty 13.0
BS
me r
' 9.0
fy |

5.0

1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5
z (A)

Figure 3.25: Computed potentials of the ground transition state for (1,4) Cl migration.
The HF configuration was 7B(13,12), and the SD-HF was 5-in-5. The z axis is defined

in fig. 3.3.

124

OPT 9B (HE) - E, , (HF)
0.64 * E(SD-HF) - E, ,,(SD-HF)L
~ 0.5+ ae
na L
5 0.4
(s) L
Sed L
v L
a 0.3+4 _
> i"
iS t ?
1 Ors aes
0.1-— a ae ae r
0.0+ o¥
1.2 1.3 1.4 1.5 1.6
Le, (A)

Figure 3.26: Computed potentials of the reactant state for (1,4) F migration. The
SD-HF was 5-in-5. lc_p is the length of the active C-F bond.

° E (HE)-E_ (HE) 7A(12,9)
5.5 trans reac
; * E,_,(SD-HF) - E (SD-HF)
g 5.0-+ ne ae
Nn r ‘ °
a) ‘
1)
Est L
a. 4.5
> [
YX
jaa] iL
a 4.0--
4 ¢
3.54 ee
Le +
0.8 { 1.2 1.4 #16 1.8 2 2.2

z (A)

Figure 3.27: Computed potentials of the ground transition state for (1,4) F migration.
The HF configuration was ?A(12,9), and the SD-HF was 7-in-7. The z axis is defined

in fig. 3.3 .

125

7.0 a > \_
° E. ansHlF) - E (HF) B(11,10) | |
[ 8 E ans? D-CAS) - E ato D-HF)
_ 6.5- * £E,(SD-HF)-E(SD-HF) (7
g :
B [
Oo 6.0
a [
<0)
a.
3 5 Bae o. 2
~ ~ q i
< B icy °
5 Oeste reeeeee renee ferceceeceesecteedceeettneeectnnedbesnsectenseenefoserrernnecereasdaseecstneereeteedeecstnueesertnsesbacesenees —
4.54 1 + fs
0.8 1 1.2 1.4 1.6 1.8 2 2.2
z (A)

Figure 3.28: Computed potentials of an excited transition state for (1,4) F migration.
The HF configuration was ?B(11,10), the GVB-CAS was 5-in-5, and the SDs were
o-in-5. The z axis is defined in fig. 3.3 .

25 Q-p epee innnnnnpennnnennteee ° HE ?B(1,10)
i + CAS-CI

> [ e S§D-CAS
= 21 Openness 6 ee * SD-HF
Vv

© 17.0-+

Qa en
ve L
ws 13.04 fe
Ey L
RS

fy* L

‘, 9.0

& L
wy [
ro ae @ De mane Seceeeneeranee , Gog By
0.8 1 1.2 1.4 1.6 1.8 2 2.2
z (A)

Figure 3.29: Computed potentials of an excited transition state for (1,4) F migration.
The HF configuration was ?B(11,10), the GVB-CAS was 5-in-5, and the SDs were

d-in-5. The z axis is defined in fig. 3.3 .

126

25.0 ~ ° HF *A(12,9)/7
= | x CAS-CI
2 21.0 ! + SD-HF 4
a | : }°
3 J
a) i
@ A ne
a. ani
Lv L |
ty Vee eee ee eee tte ec treet ctte cceernrcenetsnanbeeneetsaaetcteedecceescnneceneeeedeseeneneeenerttentdieeseteeeeesenty ae
ae : 4
As
wv
po :
hy 9.0 _ seteretheveentetenecteaeebeseceeeesattettidesectntcneecectenedeeceee

& L
aa [
5.0
| ¢ ry ° ¢
0.8 1 1.2 1.4 1.6 1.8 2 2.2

z (A)

Figure 3.30: Computed potentials of the ground transition state for (1,4) F migration.
The HF configuration was ?A(12,9), the CAS-CI was 13-in-13, and the SD-HF was

7-in-7. The z axis is defined in fig. 3.3 .

127

Appendix A SIMS profiles of hydrogen

and deuterium in diamond

A.1 Introduction

A diamond sample containing layers of various deuterium concentrations was grown
by microwave-plasma chemical-vapor deposition. Growing impurities into the dia-
mond allows it to be doped without the lattice damage that accompanies ion-beam
doping. Impurity levels were profiled as a function of depth from the diamond surface
using Secondary-Ion Mass Spectroscopy (SIMS). Boron doping was necessary to avoid
sample charging during SIMS. SIMS confirmed the presence of the layers. The SIMS
profile of hydrogen will enable experimentalists to deconvolve surface D from bulk D
when performing Nuclear Reaction Analysis (NRA) and surface H from bulk H when
performing Elastic-Recoil Spectrometry (ERS).

A.2 Sample synthesis

A B-doped sample was synthesized by microwave-plasma chemical-vapor deposition
(MWCVD). The deposition chamber was a Kamo-type reactor, consisting of a quartz
tube with diamond-coated quartz substrate holder. The substrate was a natural type
IB (100) diamond. First the substrate was deuterium-plasma treated at 925°C and 43
torr for 10 minutes, with a Dz flow rate of 10 sccm. Secondly the substrate was cooled
to 785°C and exposed to a mixture of 10% D2/89% H2/1% CH, and 2ppm B2H,g for
10 minutes. The total flow rate was 100 sccm. Next the mixture was changed to
99% H»2/1%CHy, and 2ppm ByH,g for 2 hours at 100 sccm. Finally, the sample was

deuterium-plasma treated at 926°C and 42 torr for 10 minutes, with a flow rate of

128

D surface cover

H layer, B-doped diamond

Buffer H/D layer

D layer

Natural (100) diamond substrate

Figure A.1: Impurity layers grown into the diamond sample.

10 sccm. Between each growth or plasma-treatment step, it took several minutes to
adjust the pressure and sample temperature, controlled by leak-valve position and
microwave power, and re-attain steady state. Growth and treatment times reported
omit the adjustment periods. Sample temperature was measured via optical pyrom-
etry, assuming an emissivity of 0.5 due to the polycrystalline diamond coating on
the quartz sample holder. The resulting layered structure is shown schematically in
fig. A.1.

The “D surface cover” marks the diamond surface so that it can be distinguished
from hydrocarbon contamination during SIMS. The B doping increases conductivity,
to avoid sample charging during SIMS. The middle D layer is simply a D2 plasma-
treated substrate. The “buffer layer” is a B-doped layer grown with 10% Dg in the
feedgas, to ensure that H does not etch away all the D in the “D layer” during growth.

A.3 Results

Scanning electron microscopy of the sample showed a very smooth surface. There are
some small crystallites on the edges and two small regions of polycrystals near the
middle, but the rest of the surface looks perfectly smooth on an SEM length scale

(>300 nm). SEM indicated the presence of parallel ridges on the surface; however, the

129
ridge height was unresolvable on an SEM length scale. Dektak profilometry showed
that the typical peak-to-valley height was about 300 A.

SIMS profiles are shown in figs. A.2 and A.3. A primary beam of 10 keV Cs*
was scanned over a 400 um x 400 ym area. A constant etch rate was assumed in
converting the time axis to units of depth. The overall depth of the SIMS trench in the
sample was measured by Dektak profilometry. The growth rate of the boron-doped
layer was 0.3 wm/hr, assuming it occurred during the 2-hour deposition.

The width of the surface deuterium peak in fig. A.3 is about 300 A. The majority
of the deuterium in this peak is expected to have originated from the surface. One
would expect the width of the hydrogen surface peak to be the same as that of
deuterium. There is a small surface hydrogen peak in fig. A.2, but it is about one-
third narrower than the deuterium peak. Presumably the signal from the background
hydrogen in the SIMS chamber is eclipsing the signal from the sample hydrogen. No
surface hydrogen peak is evident in fig. A.3, where the slower etch rate decreased the
sample H signal to below background hydrogen levels. Therefore, the (background) H
signal in fig. A.3 should be taken as an upper bound to the actual hydrogen content

in the sample.

10

10° 5

L\ oO
wel \ ne

10° F

40° F

SECONDARY ION ZNTENSITY (cte/sec)

tk D/H,

_ | iy i Hadi iy

i 4,
o 2000 4000 so000 8000
DEPTH (sngatroma)

49

Figure A.2: SIMS profile of subsurface deuterium content.

130

SECONDARY ION INTENSITY (cte/eec)

8 B

10! Na Ai , ‘

DEPTH {engetroma)

Figure A.3: SIMS profile of near-surface region.

Count rate may be roughly converted to density by

I, RSF;

i, = x ~133 A.l
p To-13 RSFo_1s PC~13 ( )

where p; is the impurity atom density, J; is the secondary ion intensity of the impurity,
and RSF is the relative sensitibity factor describing the secondary ionization yield.
The RSF depends on the matrix material and incident beam and was not calibrated
for the SIMS conditions. In the absence of a calibration for the 10 keV beam, RSF is
taken from data for a 14 keV Cst beam incident on a separate diamond [1, p. E-3].
The RSF for 8C is 1.8 x 107%, for H is 4 x 103, and for 0 is 2.3 x 107°. In fig. A.3,
1.3 x 10° cts/s corresponds to the density of ¥C in diamond, which for an isotopic
abundance of 1.1% [2, p. 344] [3] is 2x 10?! particles per cm?. Therefore, 1.3 x 10° H~
cts/s corresponds to a density of approximately 0.88 x 1074 H/cm? taking into account
the relative RSF factors. The density of H in the top 500 A is then ~1.7-3.3x 107
H/cm?,

A bulk density on the order of 107° H/cm?® is consistent with the bulk hydrogen
content found in other experiments. Dollinger et al. [4] measured hydrogen content

by elastic-recoil detection on polycrystalline diamond grown by MWCVD on a silicon

131
substrate. They found a bulk hydrogen content of of 1.4 x 107° H/cm?. Madiba et
al. [5] used nuclear reaction analysis to measure a bulk density of 8.8 + 2.6 « 109
H/cm? in a high-pressure synthetic diamond. Although a bulk density of 1.7-
3.3x 10°? H/cm? is consistent with hydrogen densities measured in diamond by other
techniques, it is only an upper bound to the actual H content in the sample due to
the presence of background hydrogen in the SIMS signal.

The depth resolution of ERS profiles is approximately 500 A in diamond for an
8-4 Al stopper foil and 2.0-MeV incident Het beam. Integrating the H signal over
the top 500 A and converting cts/s to density as earlier, the H content is 1.3 x 1045
H/cm?. Therefore, an upper bound to the total subsurface H contribution to ERS
profiles is 0.8 H per surface C on the (100) surface.

The density of D at the surface is approximately 6.7 x 10!8/cm?, assuming the same
secondary ionization yield for D as for H. Assuming a linear drop to 3.3 x 10!7/cm?
at 300 A and 1.7 x 10!7/em? at 500 A, the total deuterium content is less than
1.1 x 10'8/cm?. Therefore, the total contribution of subsurface deuterium to ERS
profiles is approximately 7 x 107° D per surface C on the (100) surface.

The depth resolution of NRA in diamond is approximately 6750 A for an 0.7-MeV
incident 7Het beam.! Taking density to be constant from 500 A to 6750 A, the total
contribution of subsurface deuterium to NRA profiles is 0.014 D per surface C.

Figure A.4 gives a better estimate of the sample H signal. The width of the surface
H peak is approximately the same as that of the surface D peak, indicating a lower
background H level. The spectrum in fig. A.4 was taken with a higher etch rate than,
and several hours after, the spectrum of fig. A.3, allowing a lower base pressure in
the SIMS chamber and lower background levels in the spectra. Converting the count

rate to density as before, the H content in the top 500 A is 0.30 H per surface C,

'The NRA depth resolution is determined by the width of the resonance producing the nuclear
reaction [6, fig. A11.23, p. 568]. The incident ?Het energy drops from 0.70 to 0.37 MeV before the
nuclear-reaction cross section drops to half its peak value. Taking an average stopping power of
37 eV/(10* atoms/cm?) [7], the ion travels 6750 A through the diamond before losing 0.33 MeV.
Therefore, in addition to the surface deuterium, the spectra integrate over the top 6750 A of bulk
deuterium.

132
and the D content is 0.0034 D per surface C. The total deuterium content in the top
6750 A is 0.0050 D per surface C.

10 «=
= L +13
n :
~ 4° eget battled eed bith hice iebethtdebel Cc
Hn - : 3
S 10° [ese
o F +s :
= 1000 & eee H
fon E q
° E q
2 E
me [
= Le occ os en
E io)
z pO
9 t OQ, | . 4
9 Lccesseesecsveseese 5 ceceseguee cebeestaetteh tate cee te aete td B
H 105 % ote ee es oe ni i ae
1 Oo © ° q
++ Or a :
[ ° J
1 + jt & 600.0 5 22 D/H,
0 200 400 600 800 1000
Depth ( )

Figure A.4: SIMS profile of near-surface region with lower background hydrogen
levels.

In fig. A.5 the boron signal drops to zero unexpectedly soon, about 1000 A before
the H/D buffer layer. The reason for the drop is unknown. It is possible that growth
occurred during the 40-minute adjustment period when the Dy and H2/Dz plasmas
were hot but had not attained steady state, yielding 1750 A of growth with no B
incorporation. If this is the case, the growth rate in the low-B-density layer was 0.1
pum/hr, and the source of the hydrocarbon was the polycrystalline-diamond-coated
sample holder. However, it is unlikely that background hydrocarbons could cause
such a high growth rate.

A more plausible explanation for the drop in B density at 6000 A is the delay
time necessary to attain steady-state gas-phase concentrations in the reactor. If the
entire region above 7750 A grew during the 2 hours that the CH, was flowing, then
the undetectably low B density between 7750 A and 6000 A, as well as the slow
increase in B concentration between 6000 A and 3000 A, may reflect the time it took

the reactor gas to attain steady-state concentration of B. A Kamo-type reactor has

133

Secondary Ion Intensity (cts/s)

0 1000 "2000 3000 4000 5000 6000 7000 8000
Depth (angstroms)

Figure A.5: SIMS profile of film with best background hydrogen levels.

large volume due to a stainless-steel sleeve at the bottom for feedthroughs. The total
volume of the reactor was on the order of 55,000 cm?, and with a flow rate of 100 sccm
the order of 50 minutes was required to attain steady-state B concentrations. The
average growth rate between 7750 and 3000 A was then ~0.5,um/hr, and the average
growth rate during steady-state B incorporation was ~0.3~m/hr. Locher et al. [8]
found an approximately linear dependence between the film’s boron density and the
(steady-state) gas-phase B concentration between 0.2 and 30 ppm. Therefore, the B
density likely began to rise at the beginning of growth (presumably 7750 A), reaching
detectable levels at 6000 A, and attaining steady-state at 3000 A.

A.4 Conclusions

A diamond sample containing layers of various deuterium concentrations was grown
by MWCVD on the C(100) surface. Boron doping avoided the sample charging that
usually accompanies SIMS profiling of diamond. SIMS confirmed the presence of the
layers. SEM and Dektak profilometry indicated the presence of parallel ridges on the

134
surface averaging about 300 A in height.

Secondary ion intensities in SIMS profiles were converted to approximate atomic
densities using relative sensitivity factors for a 14 keV Cst beam incident on diamond.
For use in deconvolving surface hydrogen on the (100) face from bulk hydrogen in ERS
spectra, hydrogen density was integrated over the top 500 A. The total deuterium
content in the top 500 A is approximately 0.003 D per surface C. In initial spectra,
the background hydrogen eclipsed the sample’s H signal, yielding an upper bound to
the hydrogen content in the top 500 A of 0.8 H per surface C. The final spectrum
showed a lower background H signal, and the hydrogen content in the top 500 A is
0.30 H per surface C. For use in deconvolving surface deuterium on the (100) face
from bulk deuterium in NRA spectra, hydrogen densities were integrated over the
top 6750 A. In initial spectra, the total deuterium content is approximately 0.014 D
per surface C, and an upper bound for the H content is 7.5 H per surface C. In the
spectrum with the lowest background H signal, the total deuterium content in the
top 6750 A is 0.0034 D per surface C, and the total H content is 0.30 H per surface
C.

A.5 Acknowledgements

I gratefully acknowledge the Japanese National Institute for Research in Inorganic
Materials (NIRIM) for facilitating the project. The work was supported in part by
the U.S. National Science Foundation and the Japanese Institute for Science and
Technology under the 1995 Summer Institute in Japan for U.S. Graduate Students
in Science and Engineering. I gratefully acknowledge Drs. Y. Sato, M. Kamo and M.
Nishitani for welcoming me into their lab, I. Sakaguchi for performing SIMS, and T.
Ando and S. Koizumi for getting me started on and trusting me with their growth
chamber and SEM. I thank all the members of NIRIM’s High-Temperature Materials
Research Lab and TEM group for their hospitality. Valuable discussions with Dr.
Gary R. Huss of Caltech are gratefully acknowledged.

135

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ysis, edited by J. R. Tesmer and M. Nastasi, Materials Research Society, Pitts-
burgh, PA (1995), pp. 549-568.

J. F. Zeigler, “Helium stopping powers and ranges in all elements.” In The Stop-
ping Powers and Ranges of Ions in Matter, Pergamon Press, New York (1977),

volume 4. See p. 30 for conversion between *He and “He stopping powers.

136
[8] R. Locher, J. Wagner, F. Fuchs, M. Maier, P. Gonon and P. Koidl, “Optical and

electrical characterization of boron-doped diamond films.” Diam. and Rel. Mat.

4, 678-683 (1995).

137

Appendix B_ Design of pelletron

endstation for Elastic-Recoil Spectrometry

B.1 Motivation

Although kinetics models are powerful tools to understand diamond surface reac-
tions and growth, many of the parameters used in them have yet to be measured
experimentally. Here I report the design of an ultrahigh vacuum system to study the
kinetics of H reactions with diamond, important processes in diamond chemical-vapor
deposition (CVD), and to measure absolute hydrogen coverage, an important param-
eter in diamond surface models. The system will measure the amount of hydrogen
on the C(100) surface by elastic-recoil spectrometry (ERS), an ion-beam scattering
method to detect atoms lighter than the incident ion [1, 2, 3]. Relative coverages
have previously been measured through electron or photon spectroscopy, but here
absolute coverage will be measured, to within about 5% of a monolayer. Measuring
hydrogen coverage in UHV as a function of temperature tells the absolute saturation
coverage of the (100) surface produced by plasma pre-treatment. The system will be
designed to heat the sample in order to study surface reactions at diamond growth
temperatures (~1000°C). Sample heating will also be necessary to desorb physisorbed
contaminants and to prevent sample charging during electron diffraction.

The vacuum system will include a reflection high-energy electron diffraction
(RHEED) system to allow hydrogen coverage to be correlated with surface reconstruc-
tion. Chin et al. [4] recently correlated (111) surface reconstruction with hydrogen
coverage via sum-frequency generation and found that adsorption of 0.05 H per sur-
face C was sufficient to revert the (21) surface to a (1x1) structure. The experiment

reported in chapter 2 investigated deuterium coverage of the C(100) surface via nu-

138

clear reaction analysis (NRA). The surface was initially a (2x1) structure, with ~1
D per surface C. However, after exposure to filament-cracked hydrogen at an unusu-
ally high filament temperature of 2025°C, coverages up to 1.3 D per surface C were
measured. This indicated the possibility of a (3x1) structure, a reconstruction which
has been investigated theoretically [5] but not yet observed experimentally. RHEED
observations in the ERS endstation will allow further investigations of the (100) sur-
face structure and its evolution upon exposure to gas-phase H. Due to diamond’s low
conductivity, the sample will be heated to avoid charging during RHEED.

In other diamond experiments, cycling the sample through a series of hydrogen
exposures and thermal desorptions degraded the surface LEED pattern. Adsorp-
tion/desorption cycling also caused a second peak to arise at lower temperatures in
thermal desorption spectra, indicating the possibility of dihydride sites on the sur-
face. RHEED observations coupled with ERS measurements will allow degradation
to be quantified, and coverages greater than 1.0 H per surface C would strengthen
the argument for the association of degradation with surface dihydrides.

The system is also designed to study reaction kinetics by measuring the hydrogen
coverage of diamond upon exposure to atomic H at various gas and surface temper-
atures. As shown in chapter 2, absolute coverage data allows one to calculate the
ratio of the abstraction rate constant to the recombination rate constant, both aver-
aged over all surface sites present. These two reactions control the fraction of surface
sites available for growth during diamond CVD. Measuring rate data as a function
of temperature extends other experiments [4, 6, 7], which investigated a single fila-
ment temperature and low surface temperature, by allowing activation barriers to be
obtained.

Measuring rate data as a function of temperature also gains information about
the dynamics of reactions on diamond surfaces. For example, at temperatures low

enough for migration and desorption to be inactive, the reaction

gas _ oO surf kan gas o_o, surf
He" + HC—C — Hs" +-C-C (B.1)

139
is expected to be Eley-Rideal, where the gas-phase reactant provides the energy to
surmount the activation barrier and rate depends solely on gas temperature. (Here
HC—C-* denotes a half-hydrogenated dimer on the C(100) (2x1) surface, and
-C—CS"? denotes a pi-bonded dimer.) However, at higher temperatures, surface-
surface reactions participate in the conversion of atomic to molecular hydrogen, and
conversion rates are expected to develop a dependence on surface temperature. Above
~600°C desorption becomes active, opening a pathway for reaction B.1 to occur not
only through direct abstraction but also through a sequence of recombination and

desorption steps,

Kran

Hes +HC-C —} HC-CH™ (B.2)
HC-CH™ + HE +-C-C."", (B.3)

where kpp is the recombination rate constant and kp is the desorption rate constant.
Reactions B.2 and B.3 represent a Langmuir-Hinshelwood mechanism, where the gas-
phase reactant comes into equilibrium with the surface before reacting (desorbing)
and therefore the rate of Hy formation depends on surface temperature.

The chamber is designed to expose the diamond to atomic hydrogen several times,
each at a different surface or filament temperature, and measure the resulting cover-
age. Desired surface temperatures are 200°C, 500°C, 700°C, and 1000°C, and filament
temperatures are 1560°C, 1800°C, and 2100°C. The sample will be cooled before each
ERS measurement to avoid light noise in the RBS detector and to keep the hydrogen

signal well-separated from the thermal noise peak of the ERS detector.

140
B.2 Experiment in old endstation

Procedure

The sample was natural type ITA diamond, cut and mechanically polished to a surface
plane of (100) + 3° by Harris Diamond Corporation. The as-received samples were
ultrasonic-rinsed in ethanol before attaching to the sample holder. The samples were
glued to the holder with household paraffin, and no plasma-treatment was performed.

The ERS set-up is shown in fig. B.1. Hydrogen coverage was measured by collect-
ing H* ions forward-recoiled from an incident “He* beam. The energy of the incident
helium beam was 1.9 MeV, and the current was 5 nA. Forward scattered helium ions
were filtered by a 8-4m aluminum foil placed in front of the ERS detector. Spectral
area was converted to absolute hydrogen coverage by comparison to a polystyrene
standard of 1000 A (CgHg), on a Si substrate. RBS and ERS spectra were collected
simultaneously, and the ERS spectral area was normalized by the height of the RBS
carbon edge, thus eliminating the need to measure beam current incident at the sam-
ple. Channel number in the RBS spectrum was converted to energy by comparison

to a sample containing three marker layers (Au, Rh, and Co) on top of a Si substrate.

Results

Fig. B.2 shows a spectrum of elastic recoils from an unheated diamond sample in the
old endstation. About eight monolayers of hydrogen are present, presumably due to
hydrocarbon contamination physisorbed to the surface. The sample must be heated
in order to desorb the contamination.

The hydrogen spectrum contains an asymmetric surface peak with a low-energy
tail, similar to the ERS spectra obtained by Ingram ez al. [8] on microwave-plasma
CVD diamond. Ingram et al. estimated the sum of surface and subsurface H to be
1.5%, or about 7.5 H per surface C. The bulk H content was estimated to be 0.3%.
Assuming the subsurface H fraction in the top 500 A was the same as that of the

bulk, the total contribution from subsurface hydrogen in the top 500 A is 1.5 H per

141

Sample
Manipulator

Sample heater
Thermecouple

He current
measurement

To Mass Spectrometer

th ) Gate

Backscettered
4tHe* j
brd-Scattered
t +
4H
RHEED
Beam

%;

UALIDISITIOLIESS ERS detector
motion feedthrough

6 Turbo Pump +

Figure B.1: Schematic of old ERS endstation.

surface C. Therefore, there are approximately 6 H per surface C on the surface of
the Ingram sample. Allowing 1-2 monolayers of surface-chemisorbed hydrogen, the
remaining 4-5 H per surface C were presumably due to hydrocarbon contamination.
The Ingram sample was also unheated.

The ERS results are also consistent with those obtained by Yagi et al. [9] on
MWCVD homoepitaxial C(100). Yagi et al. found 3-4 H per surface C on their sam-
ples. The samples were unheated, and therefore presumably contained 2-3 monolayers
of hydrocarbon contamination, in addition to 1 monolayer of chemisorbed hydrogen.
The working pressure was 8 x 107° torr. Yagi et al. argue that surface hydrocarbon

contamination can be neglected since the area of their H peak did not vary signifi-

142
Energy (MeV)

0.0 0.5 1.0 1.5 2.0
300 iy q i LI
250k -
200 —_— Heurtace —
<_<
Oe al
5 150 -
oO
700 ~~
50 -- a
Hout
o li } i } 3
Oo 200 400 600 800 1000 47200
Channel

Figure B.2: ERS spectrum of unheated diamond sample obtained in old endstation.

cantly with beam dose between 2 x 10'* and 12 x 10!* ions/em?. However, constant
coverage may simply indicate that steady-state was attained, i.e., pumping rate was
equal to the hydrocarbon condensation rate.

The present results are consistent with those of Ingram et al. [8] and Yagi et al. [9]
and indicate that several monolayers of hydrocarbons are physisorbed on the diamond
surface. Sample heating is necessary to desorb the contamination and to measure the
true coverage of chemisorbed hydrogen on diamond by ERS.

Fig. B.3 shows the RBS spectrum of the diamond substrate. A carbon edge is
clearly resolved at 0.88 MeV. During RBS the beam occasionally oscillated off the
sample, and a small signal from the stainless-steel sample holder is evident at 1.69
MeV. However, the ratio of the height of the holder edge to that of the carbon
edge indicates that the holder received only ~0.0005 the beam dose of the sample.!

Assuming the holder contained 10% (atomic) hydrogen, the holder’s contribution

‘The small dose received by the holder is consistent with the pattern of radiation damage evident
in the sample. Before RBS the sample was clear and colorless, and upon RBS a grey elliptical region
appeared in approximately the same location as the beam spot. The grey region was darkest near
its center and was located in the center of the sample. No grey was evident on the sample edges,
indicating little beam oscillation off the sample.

143
Energy (MeV)

42:0 0.5 1.0 1.5 2.9
1.0x10 T T T T

0.8 - ~
2 0.6 - “
wd
Lo]
SP o4- Cyurtace edge 4

0.2 f =

Coute
0.0 T T uy —T T
° 200 400 600 800 1000 1200

Channel

Figure B.3: RBS spectrum of unheated diamond sample obtained in old endstation.

to the spectral area of the surface hydrogen peak is only ~0.002 of the sample’s
hydrogen contribution. Therefore, the stainless steel’s hydrogen was neglected when

deconvolving the sample’s surface H peak.

Subsurface hydrogen contribution

Low depth resolution is a problem inherent to elastic-recoil spectrometry. Straggling
in the aluminum stopper foil reduces the depth resolution to about 500 A. Therefore
the top 500 A of bulk hydrogen must be subtracted from the spectra to obtain the
amount of surface hydrogen. Sellschop et al. [10] have measured hydrogen in natural
diamond crystals via nuclear reaction analysis (NRA). Although NRA also suffers
from poor depth resolution, their results imply an upper bound of about 8.1 mono-
layers of bulk hydrogen in the top 500 A, where one monolayer is one H per surface
C on the (100) plane. Subsequent experiments on diamond grown by chemical-vapor
deposition (CVD) obtained a more exact estimate of subsurface hydrogen content. In
the case of homoepitaxial CVD diamond, the experiment of Appendix A estimated
the total hydrogen content to be 0.30 H per surface C in the top 500 A. In initial
spectra, the background hydrogen eclipsed the sample hydrogen signal, giving an up-

144

per bound of 0.8 H per surface C in the top 500 A of the sample. In the case of
polycrystalline CVD diamond, Dollinger et al. [11] detected less than 107? hydrogen
content below the top 10-20 A. Their hydrogen content was calibrated by comparison
to an ion-implanted standard, and the depth resolution was 10 A. Therefore, I ap-
proximate the hydrogen content in the first layers below the surface to be the same as
that in the bulk, and I assume that the ERS sample has 107° bulk hydrogen content.
The total subsurface hydrogen content in the top 500 A of the ERS sample is then
approximately 0.6 monolayers.

Even with 0.6 monolayers of subsurface hydrogen and 1 monolayer of surface hy-
drogen, there were still 6.4 monolayers of hydrogen from physisorbed contamination.

The sample must be heated to desorb the contamination.

B.3 Design of new endstation

Due to radiative losses, the old heater was unable to attain temperatures greater
than 250°C. Although a higher-temperature heater was available, the old endstation
(fig. B.1) was too small to contain the high-temperature heater and holder within
its 3.3-cm central cross.* Therefore, I custom-designed an entirely new endstation,
including a 20.3 cm vacuum chamber and sample holder, along with RHEED and
ERS/RBS geometries. The new endstation (fig. B.4) has a simplified geometry,
allowing easier bake-out and potentially better vacuum. The new system also locates
the ERS detector closer to the sample, yielding shorter data collection times. Previous
collection times were typically 30 minutes per coverage measurement. In addition, the
atomic hydrogen/ECR port has been moved closer to the sample. The new vacuum
chamber hardware is shown in fig. B.5.

The new chamber was designed to fit into the same space as the old endstation.
The distance between the new chamber’s beam and ERS-detector ports is the same

as the distance between the old endstation’s beam port and gate valve, plus 1”.

?Moreover, the old heater occupied so much of the volume of the central cross that it caused
significant outgassing of the cross walls during heating.

145
The extra inch allows enough room between the vacuum chamber wall and the ERS
detector flange for installing bolts into the flange, while keeping the chamber diameter
large enough to support all 3” ports.? The similar size of the new chamber to the
old endstation not only conserves space but also preserves the alignment of the old
endstation with respect to the helium beam during new-chamber installation.*

The new design incorporates a high-temperature (1000°C) sample heater and
holder. The holder consists completely of molybdenum, to minimize vapor pres-
sure at high temperature. The resistive heater is a thin plate of CVD graphite coated
with pyrolytic BN, approx. 1.9 cm x 4.3cm x 0.3cm. (The length of 4.3 cm includes
space for the electrical leads.) The heater itself consumes about 10 amps at 30 volts,

and the hot zone is about 1.7 cm in diameter, ample for the 15 mm x 5 mm sample.

B.4 Conclusions

Hydrogen coverage of the diamond C(100) surface has been measured by elastic-recoil
spectrometry. Results show several monolayers of surface contamination, consistent
with the measurements of Ingram et al. [8] and Yagi et al. [9]. Since ERS is a
nuclear-sensitive technique, it cannot distinguish between physisorbed contamination
and chemisorbed hydrogen. Sample heating is necessary to desorb the contamination
and to allow the true coverage of chemisorbed hydrogen on diamond to be measured
by ERS.

To decrease contamination, the pelletron endstation has been custom-redesigned

to attain better vacuum and higher-temperature sample heating. In addition to des-

Space is further conserved by building the support structure for the new endstation upon the
cart which housed the old one. The new chamber will be held by clamps at the four 90° ports shown
in fig. B.4a, and the clamps will be bolted to a unistrut cage built upon the cart.

“The alignment will be preserved as follows. First the cross behind the gate valve of the old
endstation (the load-lock cross) will be moved back by 1”, to make room for the new chamber, by
inserting a one-inch through flange between the gate valve and load-lock cross. The load-lock cross
will then be fixed to the unistrut cage before removing the part of the old endstation ahead of the
gate valve. Finally, the new endstation will be aligned by bolting to the fixed load-lock cross. (A
reducing flange was custom-designed to mate the load-lock cross to the detector port of the new
endstation while ensuring proper vertical alignment of the new endstation.)

146
orbing surface contamination, heating is necessary to avoid sample charging during
RHEED and to study diamond surfaces at CVD growth temperatures. The new de-
sign allows sample heating to 1000°C as well as RBS, ERS, RHEED, and hydrogen
or deuterium exposure studies.

The new endstation will allow the study of abstraction and recombination, key
radical-surface reactions in diamond chemical-vapor deposition, and thermal desorp-
tion, key reactions in diamond surface science. Studying these reactions as a function
of separately-controlled gas and surface temperatures will permit the identification of
the regime in which the reactions are Eley-Rideal and the regime in which they are
Langmuir-Hinshelwood.

The new endstation will also allow absolute hydrogen coverage to be measured
on the reconstructed C(100) (2x1) surface. Coverage measurements and RHEED
observations will permit the evolution of the surface structure to be investigated as
a function of exposure to gas-phase H. Upon repeating the high-temperature dosing
conditions which produced coverages of 1.3 D/surface C in chapter 2, RHEED obser-
vations can determine whether the (3x1) surface appears. The (3x1) reconstruction
has been investigated theoretically [5], but its electron diffraction pattern has not yet
observed experimentally. Furthermore, correlating absolute coverage with RHEED
patterns will allow surface degradation to be quantified. Coverages greater than 1.0
H per surface C would strengthen the argument for the association of degradation
with surface dihydrides, and the relationship between degradation and roughness can

be determined by exz-situ atomic-force microscopy.

B.5 Acknowledgements

This work was funded in part by ONR and NSF. I would like to acknowledge Profs.
Harry A. Atwater and David G. Goodwin, for reviewing preliminary designs, and
Prof. Marc A. Nicolet, for his hospitality in the pelletron laboratory. I also thank

Dr. Ramana Murty for training me to operate the old endstation, and I thank Dr.

147
Hyun Lee and Mrs. Michael Easterbrook, Jeffrey Atkinson, Robert Gorris and Roy

Andrews for technical advice and design assistance.

148

Gun

Sap) mae ERS
He Detector
Feedthrough

Hot Filament
Feedthrough

(a) Top view.

Diamond

Sample [—
dayt
4 ERS
He Defector
uF
RBS

Detector

Hydrogen doser
i and ECR source

| |

i t

(b) Side view, with 45° ports omitted for clarity.

Figure B.4: Schematic of new endstation.

149

Figure B.5: Custom 8” vacuum chamber and multiport flange for the new ERS
endstation, surrounded by standard hardware. The ruler at the base of the flange is
six inches long.

150

Bibliography

(1) J. E. E. Baglin, A. J. Kellock, M. A. Crockett and A. H. Shih, “Absolute cross
section for hydrogen forward scattering.” Nucl. Instr. and Meth. B 64, 469-474
(1992).

[2] F. Besenbacher, I. Stensgaard and P. Vase, “Absolute cross section for recoil

detection of deuterium.” Nucl. Instr. and Meth. B 15, 459 (1986).

[3] A. Turos and O. Meyer, “Depth profiling of hydrogen by detection of recoiled
protons.” Nucl. Instr. and Meth. B 232, 92 (1984).

[4] R. P. Chin, J. Y. Huang, Y. R. Shen, T. J. Chuang and H. Seki, “Interaction
of atomic hydrogen with the diamond C(111) surface studied by infrared-visible
sum-frequency-generation spectroscopy.” Phys. Rev. B 52, 5985-5995 (1995).

[5] Y. L. Yang and M. P. D’Evelyn, “Theoretical studies of clean and hydrogenated
diamond (100) by molecular mechanics.” J. Vac. Sci. Technol. A 10, 978-984
(1992).

(6] B. D. Thoms, J. N. Russell, Jr., P. E. Pehrsson and J. E. Butler, “Adsorption
and abstraction of hydrogen on polycrystalline diamond.” J. Chem. Phys. 100,
8425-8431 (1994).

[7] D. D. Koleske, S. M. Gates, B. D. Thoms, J. N. Russell, Jr. and J. E. Butler,
“Hydrogen on polycrystalline diamond films—studies of isothermal desorption

and atomic deuterium abstraction.” J. Chem. Phys. 102, 992-1002 (1995).

[8] D. C. Ingram, J. C. Keay, C. Tang, M. L. Lake and J. M. Ting, “Trapping of
hydrogen in diamond.” Diam. Rel. Mat. 2, 1414-1419 (1993).

[9]

[11]

151
H. Yagi, K. Tanida, K. Nishimura, A. Hatta, T. Ito and A. Hiraki, “Elastic re-

coil detection analysis for hydrogen near the surface of chemical-vapor-deposited

diamond.” Jpn. J. Appl. Phys. 34, L577—L579 (1995).

J. P. F. Sellschop, S. H. Connell, C. C. P. Madiba, E. Sideras-Haddad, M. Stem-
met, K. Bharuth-Ram, H. Appel, W. Kundig, B. Patterson and E. Holzschuh,
“Hydrogen in and on natural and synthetic diamond.” Nucl. Instr. Meth. B 68,
133-140 (1992).

G. Dollinger, A. Bergmaier, C. M. Frey, M. Roesler and H. Verhoeven, “Impuri-
ties of light elements in CVD diamond.” Diam. Rel. Mat. 4, 591-595 (1995).

152

Appendix C Kinetic Monte-Carlo
algorithm to simulate deuterium reaction
with diamond (100) (2x1)

C.1 Reaction mechanism

The interaction of gas-phase deuterium with the diamond surface is modeled via an
abridged version of the reaction mechanism of Dawnkaski et al. [1], table C.1. The
Dawnkaski mechanism includes only reconstructed terrace sites, and our abridgement
excludes the surface methyls. The resulting deuterium coverage, @p(t, Tyas, Turf);
may be calculated via a time-dependent Monte Carlo algorithm. I present an algo-
rithm to rigorously weight the competition between gas-surface reactions and surface
migrations within the same iteration step. Addressing migrations in the same itera-

tion as gas-surface reactions cuts in half the number of required iterations.
C.2 Kinetic Monte-Carlo algorithm

The model calculates the deuterium coverage as a function of time. At each time step,
a grid of surface sites is cycled through in random order. Each surface site has several
possible reactions that can occur. For example, an isolated radical site can undergo
gas-surface reactions R1 and -A1 or if neighboring sites are deuterated the deuterium

may migrate via reactions MO1t, MO1T, M11t, or M11T. Each of these 6 reactions

bt
T(dex)j

is assigned a probability pidex)j; = , where ot is the computational timestep and

153

Reaction Label
H atom recombination
With an isolated C radical R1

With one C atom in a 7-bond R2
H atom desorption

To form an isolated radical D1
To form a 7-bond D2
H atom abstraction

To form an isolated radical Al
To form a 7-bond A2
Hz deposition of a H atom

At an isolated radical ~Al
At one C atom in a z-bond -~A2
Hy» desorption DO
Hy adsorption -D0
H atom hop to a radical site

Across dimer MOid
Across trough Molt
Parallel to trough MO1T
H atom hop to form a 7-bond

Across trough Milt
Parallel to trough M11T
H atom hop to break a z-bond

Across trough M10t
Parallel to trough M10T
CH3 hop to a radical site

Across dimer MO1ldm
Across trough MO01tm
Parallel to trough M01Tm

Table C.1: Reaction mechanism of Dawnkaski et al. [1] for interaction of hydrogen

with diamond (100) (2x1). Nomenclature and labels have been changed to correspond
to the present text.

154

T(dex)j 18 the characteristic time for reaction j on site (dcx). The timestep is chosen
so that }7,p; < 1. The p; along with the probability of no reaction, 1 — yy Pi
define bins between 0 and 1. A random number is then generated and the bin into
which it falls determines which event occurs. The site, and its neighbors in the case
of migration, are updated, and the entire process repeated for the next site.

This algorithm affords the advantage of allowing all possible reactions for a given
site to compete with each other. The list of sites is cycled through once for each
dt, and the migration reactions are treated in the same manner as the gas-surface
reactions. This contrasts with the Dawnkaski algorithm, which separates migration
events from gas-surface events and cycles through the list of surface sites twice for
each dt.

For a given site, the set of all possible reactions is determined not only by the
site type but also by the neighboring site types. When a site at time ¢t undergoes a
reaction, both it and its neighbors are immediately updated to their states at time
t+0dt. As the algorithm continues cycling through the list of sites, it eventually reaches
one of the neighboring sites, whose clock was already updated to time ¢t + d¢. It then
determines the set of all possible reactions for that site by examining its neighbors,
some of whose clocks are at time t and some at time t + 6t. However, in the physical
system sites interact with their present neighbors, not future neighbors, and all sites
are updated simultaneously, not serially. One way to resolve this inconsistency is to
choose a computational timestep, dt’ ~ 6t/N, so small that only one site of the entire

grid is likely to undergo a reaction. However, a faster solution is to pick a surface site

155

at random and allow it to undergo a reaction with large probability, weighted by the
reactivity of the site, and then advance all site clocks by ét/N and iterate. However
under this scenario some sites will never be picked or allowed to react. To ensure
that all sites are picked, the list of surface sites is randomized and all sites are cycled
through in random order.

To weight the probability that a site reacts by its reactivity, d¢ is chosen as follows.
The relative probability for reaction j to occur on site J is py; = o, where 7; is the
characteristic time for reaction j on site J. This probability is normalized by choosing

dt so that the probability for no reaction, pyo = 1— > j Psj, 18 positive. We arbitrarily

choose min, psp to be rae =: Then
bt ot
1p (a)
Fi Tj Max jj Tj
or
bt < (C.2)

_ l 1 .
yy TIj + maxy; Ty

To ensure that d¢ simultaneously normalizes reaction probabilities for all site types,

l 1

ot < .
maxy i757 + maxy; Tyj

(C.3)

Thus the normalization, or timestep dt, is determined by the site with the highest
reactivity. Using the same timestep for all site types ensures that sites with lower
reactivity have proportionately lower probablilities to react.

Since every site type has some probability to undergo no reaction, the algorithm

may skip every s; = gint(1/pjo) site of type J and automatically update it as having

156

undergone no reaction. In this case the reaction probabilities for the unskipped sites

must be divided/renormalized by 1 — 1/s; to account for the fact that they must

react.

157

Bibliography

[1] E. J. Dawnkaski, D. Srivastava and B. J. Garrison, “Time dependent Monte Carlo
simulations of H reactions on the diamond {001}(2x1) surface under chemical

vapor deposition conditions.” J. Chem. Phys. 102, 9401-9411 (1995).

158

Appendix D Off-axis potential for
hydrogen abstraction from constrained
isobutane

D.1 Introduction

Hydrogen abstraction from the diamond surface is a key reaction in chemical-vapor
deposition. The abstraction process is sensitive to angle of approach at terrace
sites [1, 2], and this sensitivity changes reaction probabilities at steps and overhangs.
Analogous gas-phase models do not include the geometric constraint of the surround-
ing diamond surface and of the surface terminators, such as H, Cl and F. Here sen-
sitivity to angle of approach is demonstrated by calculating the GVB-CAS energy
at several off-axis geometries near the transition state. The diamond (111) surface
is modelled by constrained isobutane. The transition-state geometry is that of Page
and Brenner [1]. To approximate the constraint of the surrounding diamond surface,
the isobutane atoms are fixed at their transition-state positions while the abstracting
hydrogen is placed at several off-axis positions approaching the transition state. The
GVB-CAS energy is calculated for hydrogen displacements up to 0.7 A along the

central axis and +0.7 A perpendicular to the axis.

159
D.2 Off-Axis GVB-CAS potential

The GVB-CAS potential is depicted in fig. D.1, and the energies at the 59 calculated
geometries are listed in table D.1. The central z axis lies along the line joining the
central carbon to the abstracted H. The origin is at the center of mass, 0.209 A directly
below the central carbon. The surrounding three carbons have C3, symmetry; the
yz plane is chosen to contain one of these carbons. The (x,y,z) coordinates given are
those of the abstracting hydrogen. All other atoms are located in the transition-state

geometry given by Page and Brenner [1].

Energy (kcal/mol)
he]

y (A)

z (111) (A)

Figure D.1: GVB-CAS potential for H abstraction from constrained isobutane. The
CH bond being broken lies along the z-axis at y=0. Energies are plotted relative to
the energy at (y=-0.7, z=3.25).

The CH bond which is being broken lies along the z axis at y=0, and the sur-

160

rounding surface carbons lie behind the potential shown in fig. D.1, at z < 2.4 A.
The axis of the potential-energy saddle lies along the z axis, and therefore, incident
H atoms with velocities along the z axis require the least increase in energy to reach
the barrier. In contrast, H atoms with velocities along [100] (55° to the z axis), and
impact parameters with z < 2.8 A, must surmount the sides of the saddle to reach
the transition state. Therefore, the reaction cross-section is likely to be greater for
incident velocities along [111] than for velocities along [100], allowing for a difference

between UHV measurements of reaction rate on the (100) and (111) surfaces.

161

Xx Y Z CAS-GVB Energy
0.000000 0.000000 2.548904 -157.6745924933
0.000000 0.100000 2.548904 -157.6744589664
0.000000 -0.100000 2.548904 -157.6744596675
0.000000 0.200000 2.548904 -157.6740622211
0.000000 -0.200000 2.548904 -157.6740677456
0.000000 0.300000 2.548904 -157.6734249359
0.000000 0.500000 2.548904 = -157.6717219386
0.000000 0.700000 2.548904 -157.6703469720
0.000000 -0.700000 2.548904 -157.6705266513
0.000000 0.000000 2.648904 -157.6741381841
0.000000 0.100000 2.648904 -157.6740209914
0.000000 -0.100000 2.648904 -157.6740214853
0.000000 0.200000 2.648904 -157.6736853620
0.000000 -0.200000 2.648904 -157.6736892235
0.000000 0.300000 2.648904 -157.6731811622
0.000000 0.500000 2.648904 -157.6720266869
0.000000 -0.500000 2.648904 -157.6720790470
0.000000 0.700000 2.648904 -157.6714252572
0.000000 -0.700000 2.648904 -157.6715487308
0.000000 0.000000 2.748904 -157.6735438862
0.000000 0.100000 2.748904 -157.6734736709
0.000000 -0.100000 2.748904 -157.6734740047
0.000000 0.200000 2.748904 -157.6732787122
0.000000 -0.200000 2.748904 -157.6732813511
0.000000 0.300000 2.748904 -157.6730049823
0.000000 -0.300000 2.748904 -157.6730135780
0.000000 0.500000 2.748904 -157.6725120326
0.000000 -0.500000 2.748904 -157.6725477137
0.000000 0.700000 2.748904 = -157.6725920540
0.000000 0.000000 2.848904 -157.6734484000
0.000000 0.100000 2.848904 -157.6734245955
0.000000 -0.100000 2.848904 -157.6734248133
0.000000 0.200000 2.848904 -157.6733642455
0.000000 -0.200000 2.848904 -157.6733660187
0.000000 0.300000 2.848904 -157.6732988188
0.000000 -0.300000 2.848904 -157.6733046089

162

Xx Y Z CAS-GVB Energy
0.000000 0.500000 2.848904 -157.6733361453
0.000000 -0.500000 2.848904 -157.6733601972
0.000000 0.700000 2.848904 -157.6738652318

0.000000 0.000000 3.048904 -157.6749364064
0.000000 0.100000 3.048904 -157.6749616189
0.000000 -0.100000 3.048904 -157.6749617154
0.000000 0.200000 3.048904 -157.6750396615
0.000000 -0.200000 3.048904 -157.6750404369
0.000000 0.300000 3.048904 -157.6751771024
0.000000 -0.300000 3.048904 -157.6751796428
0.000000 0.500000 3.048904 -157.6756608970
0.000000 -0.500000 3.048904 -157.6756715862
0.000000 0.700000 3.048904 -157.6764379998
0.000000 -0.700000 3.048904 -157.6764637238

0.000000 0.000000 3.248904 -157.6772756745
0.000000 0.100000 3.248904 -157.6773047747
0.000000 -0.100000 3.248904 -157.6773048280
0.000000 0.200000 3.248904 -157.6773916833
0.000000 -0.200000 3.248904 -157.6773920175
0.000000 0.300000 3.248904 -157.6775350743
0.000000 -0.300000 3.248904 -157.6775361464
0.000000 0.500000 3.248904 -157.6779791101
0.000000 -0.500000 3.248904 -157.6779836436
0.000000 0.700000 3.248904 -157.6785929685
0.000000 -0.700000 3.248904 -157.6786040453

Table D.1: Calculated CAS-GVB energies as a function of attacking hydrogen position
(x, y, z). Coordinates are in A; energies are in hartrees.

163

Bibliography

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