Ion-surface interactions and limits to s

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Ion-surface interactions and limits to silicon epitaxy at low temperatures
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Murty, M. V. Ramana
(1995)
Ion-surface interactions and limits to silicon epitaxy at low temperatures.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/1vkn-xh33.
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

Low temperature (T [...] 400°C) deposition of Si on Si(001) proceeds epitaxially up to a finite thickness followed by a crystal-state-amorphous-state transition. An atomistic model, the twin-boundary/facet (TBF) mechanism, has been proposed for this transition. The increase in surface roughness during film growth has been directly tied to the breakdown of epitaxy. The mechanism involves the nucleation of a twin boundary on a {111} facet (produced by roughening). When the twinned region meets a different part of the perfect crystal, it inevitably leads to the formation of five- and seven-member rings. These act as nucleation sites for amorphous silicon. Adsorbates such as carbon and oxygen can dramatically increase the surface roughness even at small coverages ([...] 0.01 ML). They thus play an indirect role by accelerating the surface roughening rate.

Films with improved crystalline quality were deposited by ion beam-assisted molecular beam epitaxy. Atomic force microscopy revealed that the main effect of low energy [...] ion irradiation was surface smoothing.

Molecular dynamics simulations suggest that epitaxy on hydrogen-terminated silicon surfaces (at high hydrogen coverage) proceeds by subplantation of the incident Si atom and segregation of [...] units. The remarkable success of sputter deposition in growing epitaxial films on a dihydride-terminated Si(001) surface is explained by the very rapid rise in the subplantation probability with the incident Si atom energy.

An empirical interatomic potential has been developed to describe Si-H interactions. This can be used, with caution, for classical molecular dynamics investigations of hydrogen-terminated silicon surfaces, chemical vapor deposition of silicon and hydrogenated amorphous silicon.

A technique for low temperature Si(001)-2x1 substrate preparation was developed to complement the various low temperature processes that are being developed for device fabrication. This was achieved by low energy noble gas ion ([...] or [...]) irradiation of a nominally dihydride-terminated Si(001)-1x1 surface. Reconstructed Si(001)-2x1 surfaces were prepared at temperatures as low as 100°C. Silicon films deposited on such surfaces were epitaxial.
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
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Research Advisor(s):
Atwater, Harry Albert
Thesis Committee:
Unknown, Unknown
Defense Date:
5 August 1994
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CaltechETD:etd-10262007-111208
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ION-SURFACE INTERACTIONS AND LIMITS TO SILICON EPITAXY
AT LOW TEMPERATURES

Thesis by

M.V. Ramana Murty

In Partial Fulfillment of the Requirements
for the Degree of

Doctor of Philosophy

California Institute of Technology

Pasadena, California

1995

(Submitted August 5, 1994)

M.V. Ramana Murty

ACKNOWLEDGEMENTS

I have benefitted tremendously from interacting with the students and
faculty during my several years at Caltech. It will be difficult to thank
everyone, but I will make an effort. I apologize if I have failed to mention
anyone.

I would like to thank Cho Jen Tsai for showing me the operation of
the MBE system and the X-ray rocking curve system, and Jimmy Yang for
managing the computers and making it a pleasure to write programs and
manuscripts. I was pleased to have colleagues like Jung Shin who gave many
a company in my late night endeavours and Imran Hashim who showed me
cross section TEM specimen preparation and use of the X-ray diffractometer.
I would like to thank Shouleh Nikzad who also showed me many details of
the MBE system. Thanks to Gang He and Selmer Wong for asking me
all kinds of questions, some of which I am still searching for an answer.
Thanks, Sue Melnik and Renato Camata for being kind and patient while
helping me set up the elastic recoil spectrometry system. I also thank John
Nagel for showing me the operation of the AFM. It is also a pleasure to
acknowledge many other fellow students, Howard Lee, Mike Albert, Jim Im,
Byungwoo Park, Kirill Shcheglov, Hyun Joo, Heather Frase, Maggie Taylor,
Ruth Brain, Aimee Smith, Lawrence Anthony, Donald Lie, Jen Sue Chen,
Winston Saunders and Pete Sercel for expressing interest in my work and

clarifying any problem I had.

iil

I wish to specially thank our secretary, Rosalie Rowe, for handling all the
paperwork and making travel arrangements to Conferences.

Setting up the ERS system was a big job and would not have proceeded
far without the help of Mike Easterbrook and Rob Gorris. I would like to
thank Mike Easterbrook for setting up the Pelletron, and for lending a hand
on the ERS system whenever asked and Rob Gorris for machining or fixing
jobs on short notice. I have to thank Joe Fontana at the Keck machine
shop for machining jobs on short notice and fixing what seemed like hopeless
pieces.

I am obliged to Carol Garland for teaching me all the operations in the
TEM lab - from specimen prepartion to use of the electron microscope. I
really enjoyed working in the lab which is one reason why you will see a lot
of TEM images in this thesis. I am thankful to Jan Hutcheon and Alan Rice
for doing SIMS and XPS analysis, respectively, on my samples.

I found many of the graduate courses extremely useful. I enjoyed learning
statistical mechanics from Dr. Corngold. The three courses on diffraction
and TEM by Dr. Fultz and Dr. Ahn showed me the power of TEM. I would
like to thank Dr. Nicolet for teaching me the use of RBS. I am obliged to both
Dr. Nicolet and Dr. Goodwin for helpful suggestions on the ERS system.
I would also like to thank Dr. J.E.E. Baglin and Dr. A.J. Kellock at IBM,
Almaden for the experiments done at their place, and for ideas, and material
support during the building of the ERS system.

I would like to thank the Institute Proofreader, Natalie Gilmore, and Dr.
Atwater for indicating the many grammatical and punctuation errors in the

manuscript.

In doing research and learning new things, I have found Dr. Atwater an
extremely enthusiastic advisor. He showed me how to communicate effec-
tively, had a great belief in what I was doing, and was a great motivator
through good times and especially through hard times. He also gave me
complete independence in choosing an approach to a problem. He was also
the first to credit me for any results that were obtained. He always found
time to discuss any problem, whether of a technical nature or in personal
life.

Science today is advancing through highly specialized disciplines. The
wide ranging research interests of Dr. Atwater has shown me that it is
possible to make contributions in several fields, and that one must make
an effort to explain the relevance of one’s results to people studying closely
related subjects. These are some the things that I take with me as I look
forward toward my career.

Finally, I have to thank my parents and my sister who have always urged
me to reach my dreams and aspirations. It is through their encouragement

and commitment that I have reached so far.

ABSTRACT

Low temperature (T ~ 400°C) deposition of Si on Si(001) proceeds epi-
taxially up to a finite thickness followed by a crystal-state—amorphous-state
transition. An atomistic model, the twin-boundary/facet (TBF) mechanism,
has been proposed for this transition. The increase in surface roughness dur-
ing film growth has been directly tied to the breakdown of epitaxy. The
mechanism involves the nucleation of a twin boundary on a {111} facet (pro-
duced by roughening). When the twinned region meets a different part of the
perfect crystal, it inevitably leads to the formation of five- and seven-member
rings. These act as nucleation sites for amorphous silicon. Adsorbates such
as carbon and oxygen can dramatically increase the surface roughness even at
small coverages (~ 0.01 ML). They thus play an indirect role by accelerating
the surface roughening rate.

Films with improved crystalline quality were deposited by ion beam-
assisted molecular beam epitaxy. Atomic force microscopy revealed that
the main effect of low energy Ar* ion irradiation was surface smoothing.

Molecular dynamics simulations suggest that epitaxy on hydrogen-
terminated silicon surfaces (at high hydrogen coverage) proceeds by subplan-
tation of the incident Si atom and segregation of SiH, units. The remark-
able success of sputter deposition in growing epitaxial films on a dihydride-
terminated $i(001) surface is explained by the very rapid rise in the subplan-

tation probability with the incident Si atom energy.

An empirical interatomic potential has been developed to describe Si-H
interactions. This can be used, with caution, for classical molecular dynamics
investigations of hydrogen-terminated silicon surfaces, chemical vapor depo-
sition of silicon and hydrogenated amorphous silicon.

A technique for low temperature $i(001)-2x1 substrate preparation was
developed to complement the various low temperature processes that are
being developed for device fabrication. This was achieved by low energy
noble gas ion (Art or Het) irradiation of a nominally dihydride-terminated
5i(001)-1x1 surface. Reconstructed Si(001)-2x1 surfaces were prepared at
temperatures as low as 100°C. Silicon films deposited on such surfaces were

epitaxial.

Vil

LIST OF PUBLICATIONS

Parts of this thesis have been published, or will be published under the fol-

lowing titles:

Crystal-state — Amorphous-state Transition in Low Temperature Silicon
Homoepitaxy, M.V. Ramana Murty and H.A. Atwater, Phys. Rev. B49,

8483(1994).

Very Low Temperature (< 400°C) Silicon Molecular Beam Epitaxy: The
Role of Low Energy Ion Irradiation, M.V. Ramana Murty, H.A. Atwater,
J.E.E. Baglin and A.J. Kellock, Appl. Phys. Lett. 62, 2566(1993).

Defect Generation and Morphology of (001) Si Surfaces During Low Energy
Ar Ion Bombardment, M.V. Ramana Murty and H.A. Atwater, Phys. Rev.

B45, 1507(1992).

Empirical Interatomic Potential for Si-H Interactions, M.V. Ramana Murty

and H.A. Atwater, submitted for publication.

Vill

Low Temperature Jon Beam-Induced $i(001)-2x1 Surface Reconstruction,

M.V. Ramana Murty and H.A. Atwater, in preparation.

Epitaxy on Hydrogen-Terminated Silicon Surfaces, M.V. Ramana Murty and

H.A. Atwater, in preparation.

Empirical Interatomic Potential for Si-H interactions, M.V. Ramana Murty

and H.A. Atwater, Mat. Res. Soc. Symp. Proc. 317(1993).

Low Energy Ar lon Bombardment of (001) Si: Defects and Surface Morphol-
ogy, M.V. Ramana Murty and H.A. Atwater, Mat. Res. Soc. Symp. Proc.
223, 21(1991).

Surface and Near-Surface Atom Dynamics During Low Energy Xe Ion Bom-
bardment of Si and fcc Surfaces, M.V. Ramana Murty, H.S. Lee and H.A.
Atwater, Mat. Res. Soc. Symp. Proc. 193, 301(1990).

Contents

1 INTRODUCTION 1
1.1 Low Temperature Silicon Homoepitaxy ............. 1
1.2 Silicon Epitaxy in VLSI Technology ............... 4
1.3 The Silicon Surface... . 2... 2... ee ee 6
1.4 Molecular Beam Epitaxy of Silicon ...........0.2.. 8
1.5 Kinetic Roughening...............2...-0. 0040. 11
1.6 Hydrogen ... 2.2... 2.2.2.0... 0000202000, 00084 13
1.7 Low Energy Ion Irradiation ............--.0.0.4. 14
1.8 Outline of the Thesis .........0...0...0..-2.-0-..000. 16
Bibliography ........0.. 0.020. 02 eee ee ee ee ees 17

2 LOW TEMPERATURE SILICON MOLECULAR BEAM EPI-

TAXY 26
2.1 The Molecular Beam Epitaxy System .............. 26
2.2 Sample Preparation. ..........-....-..022.200. 31
2.3 Silicon Molecular Beam Epitaxy - A Reflection High-Energy

2.4

Electron Diffraction Study .............2.-.2. 0204 32
Conventional Molecular Beam Epitaxy — A Transmission Elec-

tron Microscopy Study ...........-.-.-.-++-2-020- 39

2.5 The Breakdown of Epitaxy at Low Temperatures ....... 43
2.6 Ion Beam-Assisted Molecular Beam Epitaxy .......... 46
2.7 Other Thin Film Characterization Techniques ......... 53

2.7.1 Rutherford Backscattering and Channeling. ...... 53

2.7.2 Secondary Ion Mass Spectrometry. ........... 54

2.7.3. Atomic Force Microscopy. ............+0.-6. 58
2.8 Annealing Experiment ...............-02-0204. 65
2.9 Voids in Low Temperature MBE Grown Silicon ........ 66
2.10 Beam-Induced Desorption of Surface Hydrogen. ........ 68
2.11 Temperature Ramp Experiments ................ 70
2.12 The Crystal-state—Amorphous-state Transition ........ 73
Bibliography 2.2... 1. ee ee 80

LOW ENERGY ION IRRADIATION OF SILICON — A

MOLECULAR DYNAMICS INVESTIGATION 87
3.1 Introduction... ............ 2.0.0. 02202006. 87
3.2 Interatomic Potential for Silicon... . 2... ......0-.4. 89
3.2.1 The Tersoff Potential... ......-.......2040. 89
3.2.2 Description of Silicon. ............2.2.20.4. 91
3.3. Numerical Methods ...........0..-...2..220-. 93
3.3.1 The Algorithm .................2..0.4. 93
3.3.2 The Runge-Kutta-Nystrom Method ........... 96
3.3.3 The Link Cell Method .................. 100
3.3.4 The Cutoff Function ........2-.0..20.0004. 100

3.3.5 Boundary Conditions................-2-6. 101

3.4. Low Energy Ar* Ion Irradiation of Smooth and Rough Silicon
Surfaces 2... ee ee 102
3.4.1 Energy Loss of Ions...............0..00.. 102
3.4.2 Simulation Description .................. 103
3.4.3 Simulation Results .............-.-.-.02.. 106

Bibliography .. 2... 0. ee 115

EPITAXY ON HYDROGEN-TERMINATED SILICON SUR-

FACES 120
4.1 Introduction... .....-.- 0.0.20 0 eee ee ee ee 120
4.2 An Empirical Interatomic Potential for Si~H Interactions . . . 122
4.3 Epitaxy on a Dihydride-Terminated $i(001)-1x1 Surface .. . 134
4.4 Epitaxy on a Monohydride-Terminated 5i(001)-2x1 Surface . 143
4.5 Discussion... 2... 2... ee ee ee 147
Bibliography .. 2... 0... ee ee 149

LOW TEMPERATURE ION BEAM-INDUCED Si(001)-2x1

SURFACE RECONSTRUCTION 155
5.1 Introduction. ..........0.. 2.002200 -2 eee 155
5.2 Beam-Induced Reconstruction of Silicon ............ 157
5.2.1 Sample Preparation... .............0... 157
5.2.2 Reflection High-Energy Electron Diffraction ...... 158
5.2.3 Transmission Electron Microscopy of Silicon Films. . . 159
5.3 Molecular Dynamics Simulations of the Beam-Induced Recon-

5.4

struction... . 20... ee ee 163

Discussion ..... 2. ee kk ee 169

Bibliography .. 2... 2.2.2... 02.02 eee ee ee

6 SUMMARY
6.1 Silicon Molecular Beam Epitaxy .................
6.2 Summary of Results ...............-2-.2-004,
6.3 The Crystal-state—Amorphous-state Transition ........
6.3.1 The Role of Surface Roughness .............
6.3.2 The Role of Low Energy Ion Irradiation ........
6.3.3. The Role of Adsorbates .................
6.4 Other Results... 2... .0.00.002. 0.0.2... 2.0000.
6.4.1 Surface Cleaning of Silicon... ...........0..
6.4.2. Empirical Si-H Interatomic Potential ..........

Bibliography . 2... 2... 2.2 eee

A Chemical Cleaning of Silicon Wafers

Bibliography .. 2... 2... .. 02.20.2000 eee ee ee

B Elastic Recoil Spectrometry
B.1 Introduction. ............ 2.000. eee eee eee
B.2 The Elastic Recoil Spectrometry System ............
B.3 Calibration ...... 0... 0.. 02.0.0... 02.0200.
B.4 Error Analysis... 2... 2... ee ee le
B.5 Hydrogen on Silicon Surface... 2... 2... 2. ee ee
B.6 Conclusion... 2.2... 2... ee

Bibliography ... 2... 2... 2. ee

C Algorithm for Molecular Dynamics Simulations

172

174
174
175
177
177
179
181
184
184
185
187

191
193

194
194
196
203
205
206
209
212

214

Xill

List of Figures

1.1

2.1

2.2

2.3

2.4

2.9

(a) The various geometric features on a vicinal surface. (b)
The terrace and step structure of a vicinal $i(001) surface.
The two different types of monatomic steps, Sa and Sg, are
indicated and the arrow marks the direction of fast diffusion

of adatoms. ...........0.. 000 eee eee ee tee

The molecular beam epitaxy system. ..............
A schematic of the molecular beam epitaxy system. The draw-
ing isnot toscale.. 2. 2... ee ee
The surface net of the (a) unreconstructed $i(001), and (b)
(2x1) reconstructed Si(001). The (2x1) reconstruction is
shown in the x-direction... .........-..-.-2-.2-00-,
The reciprocal lattice corresponding to the (a) unreconstructed

$i(001), and (b) (2x1) reconstructed 5i(001) in the previous
The RHEED pattern of a $i(001)-2x1 surface along the <110>

azimuth with the electron beam incident at (a) 0.6°, (b) 1.5°,

and (c) 2.1° grazing angle... 2.

XIV

2.6

2.7

2.8

2.9

A sequence of RHEED patterns illustrating substrate prepa-
ration and Si MBE at high and low temperatures. RHEED
pattern after (a) chemical cleaning; and (b) complete hydrogen
desorption at 550°C. High temperature buffer layer. RHEED
patterns after (c) 0.5 nm; (d) 30 nm; and (e) 110 nm deposition
at 550°C. Low temperature growth. RHEED patterns after (f)
60 nm deposition; (g) identification of diffraction spots (only
twin spots) in (f); and (h) 200 nm deposition at 300°C. ....
Bright field image of a 220 nm film deposited by conventional
MBE at 370°C. The image was taken under multibeam condi-
tions in the <110> projection. The epitaxial thickness, h,,i,
is estimated to be 83 nm... .. 2... 2-2. eee
(a) High resolution image of a twinned region. (b) A planar
defect believed to be a “hydrogen-platelet.” 2.2... ..02..
High resolution image of a 110 nm film deposited by conven-
tional MBE at 240°C. The image was taken in the <110>

projection. The epitaxial thickness, h.,i, is estimated to be 25

2.10

2.11

2.12

2.13

A possible pathway to the breakdown of epitaxy. (a) Low tem-
perature growth results in three-dimensional islanding with
some {11l}oriented facets. (b) A wireframe model illustrat-
ing the pathway to amorphous silicon. It is postulated that a
©3 coherent twin boundary is formed on a (111) plane. When
this twinned region grows and meets a different plane, say
(111), the atoms do not line up. This necessarily leads to
the formation of five- and seven-member rings and acts as a
nucleation site for amorphous silicon. ..............
(a) High resolution TEM image of an IAMBE film deposited
at 370°C and 0.09 nm/s. The Ar* ion energy was 50 eV and
the ion-to-atom flux was about 0.06. The image was taken in
the <110> projection. (b) An enlarged view of the surface
showing a {311} facet. Both {311} and {111} facets were
observed on the growing front... .............0-.
Epitaxial thickness vs. inverse temperature for conventional
MBE films measured by (a) e cross section transmission elec-
tron microscopy, and (b) o RHEED observations. .......
Epitaxial thickness vs. inverse temperature for (a) e Con-
ventional MBE, (b) © 50 eV Art IAMBE, and (c) A 70 eV
Art IAMBE. The epitaxial thickness was measured by cross

section transmission electron microscopy. ............-

Xvi

2.14

2.15

2.16

2.17

Rutheford backscattering /channeling spectra from (a) a 50 nm
film deposited by conventional MBE at 370°C, and (b) an 80
nm film deposited by IAMBE. The substrate temperature was
370°C for both films. The minimum yield xmin = 0.03 for the
(001) aligned spectra in both cases. It is noted that about (a)
75% and (b) 50% of the signal from the low temperature film
falls within the surface peak... ........-.--.00.4.
The SIMS profiles of H, C and O in (a) conventional MBE
film and (b) IAMBE film. Both films were deposited at 370°C
and 0.09 nm/s. C and O profiles were obtained with a 14.5
keV Cst+ beam; the H profile was obtained with a 10.5 keV
Of beam. Note that the background levels of H and O are
different for (a) and (b). 2... 2. ee ee ee ee eee
AFM images after (a)20, (b)40, (c)60, and (d)80 nm film de-
posited at 325°C by conventional MBE. The growth rate was
0.09 nm/s. (e) AFM image of an IAMBE film after 40 nm
deposition at 325°C. The Art ion energy was 50 eV and the
ion-to-atom flux ratio was about 0.06. The horizontal and
vertical scales are 100 nm/division and 2.5 nm/division, re-
spectively. 2... 2.
RHEED patterns after (a)20, (b)40, (c)60, and (d)80 nm film
deposited at 325°C. (a) RHEED pattern from an IAMBE film
after 40 nm deposition at 325°C. These RHEED patterns cor-

respond to the AFM images in the previous figure. ......

XVil

2.18

2.19

2.20

2.21

2.22

2.23

The rms surface roughness vs. film thickness for different
growth conditions. The roughness was measured over a 300 x
300 nm? area at three separate points on each specimen. Con-
ventional MBE at (a) A, 240°C, (b) ©, 325°C, and IAMBE
at (c) ©, 325°C. The arrows indicate the epitaxial thickness
estimated from the RHEED patterns. The dashed line is the
measured roughness of a high-temperature buffer layer. . . . .
RHEED pattern along <110> azimuth. (a) After depositing
50 nm at 325°C, and (b) after 10 min. anneal at 450°C... . .
(a) Bright field image of a 140 nm buffer layer deposited at
530°C followed by a 340 nm film at 410°C. The image was
taken under multibeam conditions in the <110> projection.
A trail of voids can be seen in the film. (b) The diffraction pat-
tern shows twin spots. (c) An enlarged view (high resolution)
of a defect at the buffer layer/substrate interface. .......
RHEED pattern showing low energy Art ion beam-induced
reconstruction. The substrate temperature was 190°C.
HRTEM image of a film deposited by Het IAMBE. The tem-
perature was dropped at a rate of 9 K/min. starting at 500°C
and the growth rate was 0.02 nm/s. The ECR source was
operated at 130 W and 0.07 Pa He pressure. ..........
HRTEM image of a film deposited by conventional MBE in a
background (0.07 Pa) of He gas. Temperature was dropped at

a rate of 9 K/min. starting at 500°C and the growth rate was

xviii

3.1

3.2

3.3

3.4

3.5

3.6

3.7

The (2x1) reconstructed $i(001) surface viewed along the <110>
axis according to the Tersoff potential. ............. 93

Flow chart showing the major steps in the molecular dynamics

The variation in step size during a simulation of a 10 eV 5i
atom incident on a dihydride-terminated Si(001) surface. ... 99
The three defect structures placed on the $i(001) surface. The
rectangles drawn around each structure indicate the area in
which the ions were incident. All ions were incident at 45°
with respect to the surface normal and the arrows indicate
the azimuths. .. 2... 2... ee 108
The time evolution of displacement yield for argon ions inci-
dent on smooth Si(001)-2x1 surface. The lines are spline fits
to guide theeye. ©... ee 109
The total displacement yield vs. energy for the defect struc-
tures. The lines are spline fits to guide the eye. ........ 112
The distribution of displacements in the substrate at (a) 10
eV, (b) 20 eV, (c) 35 eV, and (d) 50 eV. The four symbols
refer to smooth Si(001) (0), dimer pair (A), dimer string edge
(o), and dimer string center (e). Displacements in layer 0 are

those from the defect placed on the surface. .......... 113

XIX

3.8

4.1

4.2

4.3

4.4

(a) The surface-to-bulk displacement ratio R and (b) the av-
erage number of broken dimers per incident ion (only from the
placed dimers) for the different defect structures. The results
are for the dimer pair (A), dimer string edge (o), and dimer

string center (e). . 2.2.2... . 2... 22.020 202 0200004

The combination of the potentials used for different triples. Lis
the Si-Si potential, [la and IIb are parts of the Si-H potential
and III is the H-H potential... 2.2... .........0.2..
The different hydrogen-induced reconstructions of the silicon
surface. (a) The (2x1) monohydride structure with a hydro-
gen coverage 9 = 1 ML, (b) the (3x1) structure with alter-
nate monohydride and dihydride units at 6 = 1.33, and (c) the
(1x1) dihydride structure with 6 = 2 ML. The dimensions and

angles are according the Si-H potential... ...........

HRTEM image of a silicon film deposited on an initially dihydride-

terminated S$i(001)-1x1 surface. The substrate temperature
was 190°C and the growth rate was 0.09 nm/s. The film is
amorphous. ...... 2.2.2.2... eee eee ee ee
Molecular dynamics simulation of a 0.25 eV Si atom (blue)
incident on a dihydride-terminated $i(001)-1x1 surface. The
atomic positions are at (a) 0 ps, i.e., start of the simulation, (b)
0.15 ps, (c) 0.30 ps, and (d) 1 ps into the simulation. Only the
top layer of silicon atoms (green) and hydrogen atoms (red)

in the region of interest areshown. ...............

4.5

4.6

4.7

4.8

5.1

5.2

Molecular dynamics simulation of a 4 eV Si atom (blue) in-
cident on a dihydride-terminated Si(001)-1x1 surface. The
atomic positions are at (a) 0 ps, i.e., start of the simulation,
(b) 0.05 ps, (c) 0.10 ps, and (d) 1 ps into the simulation. Only
the top layer of silicon atoms (green) and hydrogen atoms (red)
in the region of interest areshown. ..............--
The subplantation probability P, versus incident silicon atom
energy... ee
Epitaxial silicon film deposited on an initially monohydride-
terminated S$i(001)-2x1 surface. The substrate temperature
was 380°C and the growth rate was 0.02 nm/s..........
The atomic positions after 1 ps of simulation for two different
impact points of the incident silicon atom. The incident atom
(blue) is subplanted in (a) but remains at the level of hydrogen
atoms in (b). The incident atom had a kinetic energy of 0.25
eV. Only the top layer of silicon atoms (green) and hydrogen

atoms (red) in the region of interest are shown. ........

RHEED pattern (a) immediately after HF dip; after 50 eV
Art ion irradiation at (b) 190°C, and (c) 100°C; and after
exposure to He* ions at (d) 190°C, and (e) 50°C. .......
HRTEM image of a silicon film deposited after beam-induced
reconstruction using 50 eV Art ions incident at 45° with re-
spect to the substrate normal. The substrate temperature was

190°C and the growth rate was 0.09 nm/s. ...........

161

XX1

5.3

5.4

5.5

5.6

5.7

5.8

B.1

HRTEM image of a silicon film deposited after beam-induced
reconstruction using Het ions. The substrate temperature was
190°C and the growth rate was 0.03 nm/s. ........... 162
Silicon film deposited after beam-induced reconstruction using

50 eV Art ions incident at 65° with respect to the substrate
normal. The substrate temperature was 100°C and the growth

rate was 0.03 nm/s.......-...2..-..-+--0020004 164
Silicon film deposited after beam-induced reconstruction using

Het ions. The substrate temperature was 50°C and the growth

rate was 0.03 nm/s. The thin oxide at the surface is also visible.165
The sputtering yield of hydrogen versus Ar ion energy from

(a) o dihydride-terminated $i(001)-1x1 surface, and (b) e
monohydride-terminated $i(001)-2x1 surface. The lines are
spline fits to guide the eye... . 2.2... ...-2..-02-04. 167
The implantation of surface hydrogen atoms versus Ar ion
energy from (a) o dihydride-terminated $i(001)-1x1 surface,

and (b) e monohydride-terminated $i(001)-2x1 surface. The

lines are spline fits to guide the eye... ............. 168
The silicon sputtering yield from (a) o dihydride-terminated
$i(001)-1x1 surface, and (b) e monohydride-terminated $i(001)-

2x1 surface. The lines are spline fits to guide the eye... .. . 168

A schematic of the elastic recoil spectrometry system. The
line-of-sight port to the substrate is marked by the letter A.
A Kaufman ion source is shown connected at this port. The

drawing is not toscale.. 2... 2... ee ee ee 198

B.2

B.3
B.4

B.5

B.6

The electronics used for the detection of alpha particles and

protons. Both RBS and ERS spectra can be collected simul-

taneously on a single computer. ................. 199

The scattering geometry used in the experiments. ....... 200

The (a) backscattering and (b) forward scattering spectra from
a 100 nm film of (CgHg)n (polystyrene) on Si. The background
subtracted carbon peak is also shown in the RBS spectrum.

Both spectra were collected simultaneously. The incident Het

ion energy was 2.0 MeV. ..........2..02.2000000. 204

The (a) backscattering and (b) forward scattering spectra from
a §i(001) wafer after a dilute (~ 5%) HF dip. Both spectra
were collected simultaneously. The incident Het ion energy
was 2.0 MeV. .. 2... 2... ee
(a) The ERS spectrum from a Si(001) wafer dipped ina ~ 1%
HF + D20 solution for two minutes followed by an overnight
anneal at 200°C. The hydrogen coverage is about 3.0 ML and
the deuterium coverage is about 0.26 ML. (b) The ERS spec-
trum after a 1 ML dose of 50 eV Art ions at a substrate tem-
perature of 200°C. The hydrogen coverage is about 3.3 ML
and the deuterium coverage is about 0.11 ML. The spectra in
(a) and (b) are normalized with respect to the incident He*

dose. The incident Het ion energy was 2.0 MeV.........

208

XXiil

List of Tables

2.1

3.1
3.2

4.1

4.2

4.3

4.4

B.1

The results of temperature ramp experiments. ......... 73

The speed of operation of molecular dynamics codes. ..... 95

Impact parameters used with different surface defect structures. 106

The parameters used in the Si-H interatomic potential along
with the Si-Si and H-H potentials; ............... 127
Properties of some Si,H, molecules. Vibrational wave num-
bers in cm. The bond energy of H2 includes the zero-
point energy. Asterisk (*) indicates a theoretically calculated
value. The Si-H potential was explicitly fitted to the proper-
ties marked by thej sign. ............-2.-.2-004. 129
The energy differences AH for disilane decomposition. The
asterisk (*) indicates a theoretically estimated value. ..... 130
Hydrogen sputtering events during energetic silicon atom de-

position on a dihydride-terminated Si(001) surface. ...... 142

Hydrogen coverage after annealing a dilute HF dipped $i(001)
wafer, 2. ee ee 207

XXiV

Chapter 1
INTRODUCTION

My life is spent in one long effort to escape from the commonplaces
of existence. These little problems help me to do so.

~ Sherlock Holmes, The Red-headed League

Sir Arthur Conan Doyle

1.1 Low Temperature Silicon Homoepitaxy

Anyone who has practiced semiconductor epitaxy must have asked the ques-
tion, “Why does one grow epitaxial films at high temperatures but amor-
phous films at low temperatures?” The usual response is to draw attention
toward the limited adatom mobility at low temperatures. While such an
answer is essentially correct, it is a macroscopic view of the phenomenon. A
more complete description would include the microscopic view — the atomic
arrangements that lead to the breakdown of epitaxy. Such a description is

essential particularly in light of the fact that the crystalline phase is the ther-

Chapter 1

modynamically favored phase. The understanding so gained can be used to
develop techniques to prevent the nucleation of the amorphous phase.

The crystal-state—amorphous-state transition during low temperature
epitaxy is a fundamental phenomenon in semiconductors. Growth at low
temperatures proceeds epitaxially up to a finite thickness followed by a locally
abrupt transition to amorphous film deposition. It has now been observed in
Si, Ge, GaAs and InP. Although semiconductor films have been fabricated
and studied for more than three decades, the discovery of the crystal-state—
amorphous-state transition in physical vapor deposition is a relatively recent
one [1, 2]. Earlier it was believed that growth of semiconductor films always
proceeds epitaxially above a certain temperature, T.,; (with a weak depen-
dence on growth rate), whereas amorphous films would be obtained below
Tepi [3]. In this view, when the diffusion length of an adatom was less than
the nearest neighbor distance on the surface, the adatoms would just stick
where they land. This would lead to an amorphous film in materials with
strongly directional bonds [3]. Applying this criterion to Si on Si(001), we
find T.,; + 300 K using the surface diffusion coefficient (activation energy
0.67 eV and prefactor 10-* cm?/s [4]) and a growth rate of one monolayer
(ML) per second. For Si on Si(001), the transition to amorphous film depo-
sition is observed at temperatures as high as 400°C. Thus the loss of lattice
periodicity occurs even with a large adatom mobility and this has been a
challenge in formulating the growth mechanisms in low temperature epitaxy.

Silicon molecular beam epitaxy (MBE), or vacuum evaporation as it was
called in the early days, has been studied for over three decades. A review

of most of the work done until 1973 can be found in Ref. [5]. Early work

Chapter 1

focussed on epitaxy on Si(111). The films were frequently deposited un-
der high vacuum conditions [6]. Even films deposited at high temperatures
(T > 1000°C) contained defects such as twins and stacking faults [7]. When
ultrahigh vacuum conditions were used, single crystal films were obtained at
550°C on Si(111) [8]. In a transmission electron microscopy study of sili-
con films grown on Si(111)-7x7 using a silane beam, it was observed that
deliberate carbon contamination changed the growth mode from layer-by-
layer to three-dimensional islanding [9, 10]. With the increasing use of MOS
transistors, epitaxy on 5i(001) began to be studied in more detail. Silicon
MBE, as it began to be called in the 1970s, was studied with scrupulous
attention to every aspect of thin film growth — ez situ and in situ surface
cleaning, substrate orientation and vicinality, temperature, growth rate and
effects of doping and ion irradiation. The importance of a clean starting
surface was recognized and the influence of various chemical pre-treatments
(ex situ methods) and ion beam sputtering (in situ methods) were studied.
Surface analytical tools such as X-ray photoelectron spectroscopy (XPS),
Auger electron spectroscopy (AES), low energy electron diffraction (LEED)
and reflection high-energy electron diffraction (RHEED) were employed to
characterize the efficacy of the surface cleaning procedures. The observation
of intensity oscillations of the specular beam in reflection high-energy elec-
tron diffraction, or RHEED oscillations, provided a way to control growth at
the sub-monolayer level [11]. Scanning tunneling microscope (STM) images
revealed a host of phenomena at the silicon surface. The various surface re-
constructions, the terrace and step structure of vicinal surfaces, anisotropic

surface diffusion on S$i(001), anisotropic island shapes and the adsorption

Chapter 1

sites of foreign elements were some of the features observed/revealed by the
STM. Many phenomena on silicon are now known at the atomic scale. There
remain, however, many problems that are still being addressed such as the
improvement in surface smoothness of silicon wafers after chemical cleaning
and growth of lattice-mismatched films on silicon substrates.

Low temperature silicon homoepitaxy has received a lot of attention in
recent years and is the central issue in this thesis. A brief description of the
many features closely related to low temperature silicon epitaxy is given in

the following sections.

1.2 Silicon Epitaxy in VLSI Technology

The ability to grow crystalline semiconductor films at low temperatures has
been considered an important step in the development of future integrated-
circuit technology. Currently, epitaxial silicon films are deposited by chemical
vapor deposition (CVD) from chlorosilane precursors at T > 900°C. Dopant
redistribution and reaction of predeposited layers is quite rapid at such high
temperatures. This has limited the use of epitaxial silicon films in very large
scale integrated (VLSI) circuits. Today, metal-oxide semiconductor (MOS)
devices are frequently fabricated within epitaxial silicon films deposited on
Czochralski wafers. An epitaxial silicon film is also deposited after creating
the buried collector layer for bipolar junction transistors (BJT) [12]. These
films are deposited quite rapidly (several um/min) to prevent contaminant

accumulation. The main reason for this is the high background pressure

Chapter 1

(> 10-® Pa) in the deposition systems. Lower growth rates can be toler-
ated by going to ultra-high vacuum (UHV) systems and this has been a
topic of intense research during the past decade. Silane (SiH,) has been
frequently used as the gas precursor in ultra-high vacuum chemical vapor
deposition (UHVCVD) systems. Excellent epitaxial films can be deposited
at T ~ 500°C. Heterojunction bipolar transistors (HBT), both discrete and
in integrated circuits, have been fabricated [13, 14].

Low temperature epitaxial growth of semiconductor films also generates
a number of new possibilities. One application is the ability to grow delta-
doped structures. The mobility of electrons and holes degrades rapidly as the
doping concentration increases due to the disruption of the periodic poten-
tial. This can be minimized by depositing atomically abrupt dopant layers.
This requires growth at extremely low temperatures to kinetically suppress
the surface segregation of dopant atoms. The deposition temperature must
be less than 300°C for the n-type dopant Sb [15]. Boron delta-doped layers
can be deposited at 400°C [16]. Delta-doped layers with almost unity acti-
vation of the dopant have been demonstrated [17, 18]. Delta-doped layers
can be used to improve the performance of a number of devices such as MOS
transistors, BJTs and ohmic contacts [19].

The prevention of strain relaxation in heterostructures is another moti-
vation. Deposition of group IV alloys and III-V semiconductors on silicon
has received much attention due to the possibility of integrating devices with
different functions on a single chip. The large lattice mismatch between
silicon and other semiconductors has made it difficult to grow thick films

without defects. However, pseudomorphic films exceeding the equilibrium

Chapter 1

critical thickness for misfit dislocation formation can be readily prepared.
Once such films have been deposited, thermal cycling of the wafer must be

minimized to prevent strain relaxation.

1.3. The Silicon Surface

The structure and energetics of silicon surfaces have been studied in great
detail. A clean, low index surface of silicon reconstructs to reduce the number
of dangling bonds. Atoms on a semiconductor surface move a significant
distance to reconstruct. The Si(001) surface usually reconstructs to form a
(2x1) structure. The Si(111) surface forms many reconstructions such as
the (2x1), (5x5) and (7x7) structures. The (2x1) surface of 5i(001) was
first observed in 1959 [20]. The reconstructions on the Si(111) surface have
a similar history, but the actual atomic arrangements for the (2x1) and the
(7x7) structures were reported in 1981 [21] and 1985 [22], respectively.
Silicon wafers are usually made by cutting an ingot with a diamond saw
and chemo-mechanical polishing with silica particles and sodium hydrox-
ide. This usually produces wafers with a small miscut, i.e., the surfaces
are oriented away from a low index crystallographic plane by a small an-
gle. Scanning tunneling microscopy [23] and low energy electron microscopy
(LEEM) [24, 25] images have shown detailed atomic arrangements and the
shapes of steps on such vicinal surfaces. They are characterized by a ter-
race and step structure as shown schematically in Fig. 1.1. The average

terrace size is given by h/tan@ where h is the step height and @ is the angle

Chapter 1

of miscut. Tight-binding calculations have shown that a double step is ener-
getically more favorable than two single steps on the $i(001) surface [26, 27].
Indeed, double steps are found for vicinal angles greater than about 3° [28].
However, for vicinal angles less than about 2°, the surface is dominated by
monatomic steps [28]. This splitting of the double step into two single steps
was explained in Ref. [29] as being due to the surface stress induced by the
dimerization. With double steps, the dimers are all oriented in one direction
whereas with single steps, the dimer direction rotates by 90° at a step. This
relieves some of the strain in the crystal.

The rotation of the dimers at a monatomic step gives rise to two different
types of steps (labeled Sa and Sg (27]) as shown schematically in Fig. 1.1.
The dimers on the top terrace are oriented perpendicular (parallel) to the
step edge in the Sa (Sp) step. The double steps Da and Dg are defined
similarly. Experimentally, it is found that Sp step edges meander a lot but
Sa and Dg step edges are relatively smooth and this has its origin in the kink
formation energies [28]. The step energies in the order of increasing energy
are Sa, Dp, Sp and Dag [27]. Kinks on a Sa step are of Sg type and vice
versa (similarly for Da and Dg steps) which explains the roughness of the
step edges.

Despite the large number of studies of the silicon surface, the surface
energy as a function of orientation is not known. This is due to the inability to
access non-equilibrium orientations and the large amount of mass transport
required to bring a macroscopic crystal into equilibrium. Such knowledge
could be used to determine the equilibrium crystal shape as a function of

temperature [30] and the surface roughening temperature. It would also

Chapter 1

facilitate the study of surface morphology in low temperature epitaxy. The
surface energy for the <100> and <111> orientations was determined in
two recent studies [31, 32]. Both studied the geometry of internal cavities
generated by ion irradiation. The surface energies for the <100> and the
<111> surfaces were estimated to be 1.36 and 1.23 J/m? respectively. The
reconstruction of the internal surfaces in the cavity was not known.

The surface diffusion of adatoms on $i(001) has been studied both ex-
perimentally and theoretically. The adatom diffusion has been shown to be
highly anisotropic with the fast direction being along the dimer rows as in-
dicated in Fig. 1.1. The activation energy and prefactor for diffusion have
been estimated as 0.67 + 0.08 eV and 107° cm?/s respectively [4]. This
corresponds to ~ 1 and ~ 10° jumps/s at room temperature and 300°C re-
spectively. A number of computational studies based on the local density
approximation [33] and empirical potentials [34, 35] have produced similar

numbers for the diffusion constant.

1.4 Molecular Beam Epitaxy of Silicon

Steps on the surface play an important role in epitaxy. This was recognized
early in the development of the theory of crystal growth [36]. The fact that
crystal growth occurs even at small supersaturations was explained by the
diffusion and incorporation of adatoms at steps.

The magnitude of the Péclet number P = jL?/D provides a way to classify

the different growth regimes in molecular beam epitaxy [30, 37]. Here, D is

Chapter 1

step

& adatom
ad-vacancy 7
island
(a)

Figure 1.1: (a) The various geometric features on a vicinal surface. (b) The
terrace and step structure of a vicinal Si(001) surface. The two different
types of monatomic steps, Sa and Sz, are indicated and the arrow marks the
direction of fast diffusion of adatoms.

Chapter 1

the diffusion constant, j is the growth rate in monolayers (ML) per second
and L is the terrace width. When P < 1, the adatoms are able to diffuse
to a step edge and growth proceeds by step flow. There are no RHEED
oscillations. For typical growth rates (~ 1 ML/s) on $i(001), this occurs for
T © 650°C.

For P =~ 1, many atoms diffuse to the step but a significant fraction
also form two-dimensional (2-D) islands on the terrace. The step velocity
alternately rises and falls as it consumes islands until a steady state is reached
and growth is said to occur by convective diffusion. The adatom coverage
and step velocity are fairly well described by an analytical theory [30, 37,
38]. There are a few oscillations of the specular beam intensity in RHEED
before it settles to a steady value. This occurs in the temperature range of
500 © T < 600°C.

At lower temperatures (400 < T < 500°C) for which P > 1, most of
the adatoms nucleate 2-D islands on the terrace. The critical size for a
stable cluster is two [39]. This is the regime of 2-D cluster nucleation and
growth where one observes RHEED intensity oscillations [11]. The island
shapes are highly anisotropic due to differences in the step energies. This
high anisotropy greatly reduces the nucleation of islands on top of islands
and there are never more than ~ 3 incomplete layers [40]. One can grow
crystalline silicon almost indefinitely and persistent RHEED oscillations have
been observed for thousands of cycles [11].

At very low temperatures (T ~ 400°C and P > 1), three-dimensional
(3D) islands are formed. This occurs when the diffusion length of an adatom

is less than the size of a typical island. This is the regime where a crystalline-

Chapter 1

to-amorphous transition is observed after a certain thickness. The RHEED
intensity oscillations damp out after the deposition of a few layers [11]. A
phenomenological or Monte Carlo model to describe the crystal growth would
have to include a number of parameters and rates, many of which are not
known. These include surface diffusion on a flat surface, rate of diffusion
along a step, energy barriers to incorporation at a step, attachment and
detachment rates from a step, surface energies and diffusion rates on various
non-equilibrium orientations, etc. The modification of some of these rates by
adsorbates will further complicate matters. It is these features which have

made the study of low temperature epitaxy an open and challenging problem.

1.5 Kinetic Roughening

When the free energy to create a step at the surface vanishes, islands are cre-
ated spontaneously. This is thermodynamic roughening and the roughening
temperature has been most recently estimated as 1200°C for 5i(001) [41].
Film growth from the vapor phase occurs under highly non-equilibrium
conditions. Since the atoms are not deposited as a sheet, the surface tends
to roughen. Counteracting this roughening are factors like surface diffusion
and desorption which tend to smooth the surface. In this regime, kinetic
roughening dominates, and the surface morphology evolves as a net result
of these different factors. The rate of roughening is frequently expressed (on
long length scales) by w ~ h® where w is the interface width (rms roughness)

and h is the film thickness (for a uniform growth rate, h ~ t, the time of

Chapter 1

film growth). The exponent is calculated for (d + 1) dimensions (d lateral
dimensions plus one vertical dimension) by either performing a Monte Carlo
simulation or solving analytical equations (continuum models). The random
arrival of the incident atoms is expressed by a Poisson distribution (noise
term) [42]. In a simple model, the surface diffusion term is proportional
to V*h where the gradient is taken with respect to the lateral dimensions
[42, 43]. Desorption of adatoms is negligible in the case of molecular beam
epitaxy. In the case of no surface diffusion, the exponent 6 = 1/2. Introduc-
tion of a smoothing term reduces the value of £, i.e., the surface roughens
more slowly. For example, for the Kardar-Parisi-Zhang equation, the expo-
nent 6 = 1/3 ford = 1 and 6 = 0.24 for d = 2 [44, 45]. If surface diffusion is
the only smoothing term, the exponent has been calculated to be B = 0.375
for d = 1 and @ = 0.25 for d = 2 [46, 47].

The study of kinetic roughening during film growth is a very active field
today. It is particularly relevant to low temperature silicon epitaxy because
surface roughness plays a crucial role. As mentioned in the previous Section,
there are a large number of parameters affecting film growth and this has
made even a qualitative description difficult. A combination of experimen-
tal and theoretical work is needed to make progress toward application to

semiconductors.

Chapter 1

1.66 Hydrogen

Silicon is the prototypical semiconductor and hydrogen is the simplest el-
ement [48]. The interaction of these two elements is important in many
processes in VLSI technology. Chemical vapor deposition from silane, an HF
dip, and hydrogenated amorphous silicon are some examples where hydrogen
plays a crucial role.

Hydrogen as an adsorbate has many interesting effects in silicon homoepi-
taxy. Hydrogen-termination of the silicon surface causes a remarkable change
in its reactivity. A bare silicon surface exposed to atmosphere will immedi-
ately form a thin oxide. If the surface Si atoms are terminated with hydrogen
atoms (commonly performed by an HF dip), the oxidation rate is reduced
by several orders of magnitude. Such surfaces are stable in a laboratory at-
mosphere for hours [49]. Recently, it was discovered that dipping a Si(111)
wafer in a high pH solution (pH > 5) of HF and NH,F produces atomically
smooth surfaces [50]. Most of the surface is covered with monohydride species
with very few dihydride and trihydride species. The analogous process with
Si(001) wafers, however, produces relatively rough surfaces. This is believed
to be due to the strong repulsion of H atoms on neighboring dihydride units.
Although the surface is nominally dihydride-terminated, significant amounts
of monohydride and trihydride species may be present [51]. Silicon surfaces
can also be hydrogen-terminated by exposing a clean surface to atomic hy-
drogen, but molecular hydrogen does not adsorb on silicon. Depending on
the hydrogen coverage, the 5i(001) surface can exhibit a (2x1), (3x1) or

(1x1) reconstruction [52].

Chapter 1

Complete hydrogen desorption occurs above 500°C on both Si(001) and
Si(111) [53]. The desorption product is molecular hydrogen. On Si(001), a
dihydride-to-monohydride transition occurs at 350 — 400°C which transforms
the surface from a (1x1) to a (2x1) structure. The desorption of hydrogen
from the monohydride follows first order kinetics on the $i(001) [54]. It is hy-
drogen desorption which limits the growth rate in low temperature chemical
vapor deposition with silanes [55].

Introduction of hydrogen during Si MBE can cause a premature break-
down of epitaxy [56, 57]. It has been shown that even a small coverage of
hydrogen can drastically increase the Si island density during Si epitaxy [58].
At the same time, epitaxy is possible even with a uniform coverage of hydro-
gen [59, 60, 61]. These very interesting observations led us to examine the

influence of hydrogen on the growth process.

1.7 Low Energy Ion Irradiation

Exposure to ions or energetic particles is not an unusual event in device fabri-
cation. Examples include ion implantation to create doped regions, reactive
ion etching to open regions for contacts, sputter deposition of metals, and
plasma-enhanced chemical vapor deposition of amorphous silicon.

Ion beam-assisted deposition has been used to modify thin film microstr-
ucture and properties in a number of materials [62]. Energetic beams of
dopants have been used to deposit heavily doped silicon films by MBE [63].

The surface segregation of dopants is overcome by incorporating them in sub-

Chapter 1

surface sites. lon beam sputtering is frequently used to create clean surfaces
in vacuum. A novel phenomenon in sputtering is the layer-by-layer removal
of silicon with 200 eV Xet ions [64]. Low energy ion irradiation has also been
used to suppress 3-D island formation during the initial stages of growth of
Ge [65], and GaAs [66] on Si(001). This was attributed to the reduction of
surface amplitude fluctuations during the early stages of growth.

The motivation for using ion irradiation in conjunction with silicon ho-
moepitaxy comes from their ability to modify surface kinetics [67]. This
could be used to favor the growth of a crystalline film. Such an approach
has indeed met with success and thick epitaxial films have been deposited at
temperatures as low as 200°C [61]. Silicon films have been deposited by direct
ion beam deposition [68, 69, 70] and sputter deposition [60, 71]. Ion damage
is an important consideration since electrical properties are very sensitive to
beam-induced defects. This limits the maximum ion energy that can be used
to irradiate a growing silicon film [72] and motivates the use of ion energies
below 20 eV. The generation and transport of such ions has proved difficult
due to space charge effects and there have been relatively few investigations
of low energy ion beam-assisted silicon homoepitaxy.

Despite the success with the use of energetic particles, the influence of ion
irradiation on a growing film are relatively unknown. The observation of ion
beam enhanced epitaxial growth of Ge(001) was explained as a balance of ion-
induced vacancy-like defects and growth-induced adatoms and islands [73].
Ion beam-assisted molecular beam epitaxy provides a way to independently
control ion energy, flux and the growth rate. This was used to investigate

the effects of ion irradiation on the surface morphology, film microstructure

Chapter 1

and surface hydrogen.

1.8 Outline of the Thesis

The contents in this thesis are arranged as follows. Chapter 2 describes an ex-
perimental investigation of low temperature silicon molecular beam epitaxy.
The influence of surface roughness, adsorbates and low energy ion irradia-
tion on the crystal-state—amorphous-state transition is discussed. Chapter 3
describes the methods of molecular dynamics and the simulations of low en-
ergy ion irradiation of smooth and rough silicon surfaces. Chapter 4 begins
with the development of an empirical interatomic potential to describe Si-H
interactions. This is followed by a molecular dynamics investigation of epi-
taxy on hydrogen-terminated silicon surfaces. A new technique for preparing
Si(001)-2x1 surfaces at low temperatures is described in Chapter 5. Finally,
Chapter 6 summarizes the main results of this thesis.

There are three appendixes. Appendix A contains a description of the
chemical cleaning procedure for silicon wafers. The computer program SIH
used for molecular dynamics simulations is listed in Appendix B. Lastly,
Appendix C contains the details of an elastic recoil spectrometry system to

measure hydrogen concentrations in thin films and substrates.

Bibliography

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on Si(100) at low temperatures,’ Phys. Rev. B40, 2005(1989).

[2] D.J. Eaglesham, H.-J. Gossmann, and M. Cerullo, ‘Limiting thickness
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[3] J.A. Venables and G.L. Price in Epitazial Growth, ed. J.W. Matthews,
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[4] Y.W. Mo, J. Kleiner, M.B. Webb, and M.G. Lagally, ‘Activation energy
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[5] B.A. Joyce, ‘The growth and structure of semiconducting thin films,’
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[7| See, for example, B.A. Unvala and G.R. Booker, ‘Growth of epitaxial
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Chapter 1

[8] H. Widmer, ‘Epitaxial growth of Si on Si in ultra high vacuum,’ Appl.
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[10] J.M. Charig and D.K. Skinner, ‘Carbon contamination of Si(111) sur-
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[11] T. Sakamoto, N.J. Kawai, T. Nakagawa, K. Ohta, and T.Kojima, ‘Inten-
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[12] B.G. Streetman, Solid State Electronic Devices, Prentice Hall, New Jer-

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[13] B.S. Meyerson, ‘UHV CVD growth of Si and Si-Ge alloys — chemistry,
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[14] B.S. Meyerson, ‘High-Speed silicon-germanium electronics,’ Sci. Am.

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[15] H. Jorke, H. Kibbel, F. Schaffler, A. Casel, H.-J. Herzog, and E. Kasper,
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Chapter 1 19

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Chapter 1

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Chapter 1 21

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[41] R.M. Tromp, E.D. Williams, and J. Tersoff, presented at the 12** Inter-

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Chapter 1 22

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Chapter 1

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S.M. Gates and S.K. Kulkarni, ‘Hydrogen coverage during Si growth
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T. Ohmi, T. Ichikawa, H. Iwabuchi, and T. Shibata, ‘Formation of
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Chapter 1

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Chapter 1

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1793(1990).

Chapter 2

LOW TEMPERATURE
SILICON MOLECULAR
BEAM EPITAXY

When you follow two separate chains of thought, Watson, you will
find some point of intersection that should approzimate to the truth.

- Sherlock Holmes, The Disappearance of Lady Frances Carfax

Sir Arthur Conan Doyle

2.1 The Molecular Beam Epitaxy System

The silicon films were deposited in a custom-built molecular beam epitaxy
(MBE) system. Figure 2.1 shows a view of the ultra-high vacuum (UHV)
chamber. A schematic is shown in Fig. 2.2. The chamber is pumped with
a 330 1/s turbomolecular pump and a 1600 1/s cryogenic pump. The base
pressure in the chamber was around 10~’ Pa. Pressure was measured using a

nude-ion guage. The ion gauge is normally calibrated for nitrogen. The gas

Chapter 2

correction factors were taken as 0.71 for argon and 6.04 for helium [1]. A mass
spectrometer was used for monitoring the residual gas and leak checking. The
residual gas was mostly composed of H,, CO and H20. The silicon wafers
were introduced into the chamber through a load lock, thus preventing the
need to bring the chamber up to air each time. The chamber is equipped with
several valves and shutters to isolate the appropriate parts of the system.

The silicon wafers were held by tantalum clips onto a molybdenum block.
Molybdenum has a negligible vapor pressure and does not react with silicon
at the temperatures of interest (T < 700°C). The substrate manipulator al-
lows angular and azimuthal rotation as well as translation in two orthogonal
directions. The substrate temperature was monitored by a thermocouple at-
tached to the side of the substrate heater block. An optical pyrometer, which
gives more reliable measurements above 300°C, was occasionally used. The
thermocouple was calibrated using the pyrometer measurements and tem-
peratures below 300°C were obtained by an extrapolation of the pyrometer
readings.

The UHV chamber is equipped with two electron guns. They have copper
crucibles with 7 cc pockets to hold the source material. One of these was
used to deposit silicon. The silicon used as source material was obtained
from a high purity silicon ingot. The dopant density in the source was less
than 10!5 cm~%. Silicon was placed in the 7 cc pocket and also in the region
surrounding the pocket to prevent contamination from the copper crucible
[2]. The distance from the source to substrate was about 60 cm. The source
was outgassed extensively before depositing the films. The pressure during

growth was typically 10-® Pa and mainly composed of Hz. A quartz crystal

Chapter 2

sensor was used to record the growth rate. The sensor was calibrated by
cross section transmission electron microscopy (XTEM). The copper crucible
in the electron gun and the quartz crystal sensor were water-cooled during
operation.

For low energy ion beams, two ion sources were employed. A Kaufman
source was used for generating Art ions. The chamber was backfilled with
argon to a pressure of 3 x 10~% Pa during operation. An electron cyclotron
resonance (ECR) source was used to generate He* ions. The starting purity
of both Ar and He gas was better than 99.999%. The gas was passed through
a purifier just before introduction into the ion source. The gas purifier was
rated to give a purity of 10 ppb. The distance from either ion source to the
substrate was about 20 cm. The ion guns were oriented so that the ions were
incident at a 45° angle with respect to the surface normal when the sample
was horizontal.

The sample surface morphology was monitored in situ by reflection high
energy electron diffraction (RHEED) using a 12 keV beam. The RHEED
beam was incident typically at a grazing angle of 0 - 2°. A 50 1/s turbo-
molecular pump was used to differentially pump the RHEED gun so that it
could be used while working at relatively high pressures such as during ion
irradiation of the substrates.

The silicon wafers used in the experiments were of the (001) orientation
with a miscut of less than 1°. They were either n- or p-type with a resistivity

of 10 - 50 Q-cm.

Chapter 2

“Al

Figure 2.1: The molecular beam epitaxy system.

Chapter 2 30

Cryopump

Turbomolecular
pump
Mass Mass
Flow Flow
Controller Controller

Argon Helium | |

Figure 2.2: A schematic of the molecular beam epitaxy system. The drawing
is not to scale.

Chapter 2

2.2 Sample Preparation

Silicon forms a thin (1 - 2 nm) native oxide when exposed to atmosphere.
The surface may also contain metal and organic contaminants. The wafers
were cleaned in chemical solutions before transferring to the UHV chamber.

The procedure used for chemical cleaning of Si wafers is taken from
Ref. [3]. The wafer cleaning procedure is also listed in Appendix A for con-
venience. All ratios mentioned below are by volume and the chemicals are of
the appropriate concentrations available commercially (except HF for which
the actual concentration is given) [4]. The native oxide is first removed by
a dilute HF (~ 1:20 HF : HO) dip. The wafer is then placed for 5 minutes
in a hot alkaline peroxide solution composed of NH4,OH : H202 : H20 ina
1:1:5 ratio. The resulting oxide is then etched by a dilute HF dip and the
process repeated three times. This step removes organic contaminants and
some metals from the surface [5]. The wafer is then placed for 5 minutes in a
hot acidic peroxide solution composed of HCl : H202 : H2O in a 1:1:5 ratio.
The resulting oxide is again etched by a dilute HF dip and the process re-
peated three times. This step removes metal contaminants from the surface
[5]. In the final step, the Si wafer is dipped in dilute HF for 50 to 60s [6].
This results in a nominally dihydride-terminated 5i(001) surface. There are
significant fractions of monohydride and trihydride species on such surfaces
indicating that it is microscopically rough [7]. The wafer is transferred to
the load lock within three minutes after the last step. On the dihydride-
terminated Si(001) surface, hydrogen atoms saturate the dangling bonds of

Si atoms. This passivates the Si surface from oxidation and chemisorption

Chapter 2

of impurities. In fact, such surfaces have been shown to resist oxidation for
as long as 12 hours in the laboratory atmosphere [8].

The silicon wafer so cleaned may still contain physisorbed contaminants.
Prior to epitaxy, the samples were baked at 200 — 250°C for one or more hours.
It has been shown that this low temperature bake removes any physisorbed
hydrocarbons on the surface [9]. The samples are then heated above 500°C to

desorb the hydrogen and obtain a clean, reconstructed $i(001)-2x1 surface.

2.3. Silicon Molecular Beam Epitaxy — A Re-
flection High-Energy Electron Diffrac-

tion Study

Reflection high-energy electron diffraction (RHEED) is an in situ technique
for obtaining information about the sample surface morphology. In our ex-
periments, a 12 keV electron beam was incident at a grazing angle of 0 - 2° on
the sample. The corresponding wavelength of 0.011 nm is seen to be smaller
than the typical bond length of 0.2 nm. This allows one to obtain structural
information about the surface through elastic scattering. The mean free path
of electrons is about 5 nm at 10 keV [10]. Since the electrons are incident
at ~ 1°, most of the electrons are scattered within a 1 nm region near the
surface. This makes RHEED a strong surface sensitive probe. The incident
electrons typically undergo multiple scattering which makes the interpreta-
tion of intensities difficult. Kikuchi lines and other non-kinematic features in

the RHEED pattern can be easily located [11]. However, the elastic scatter-

Chapter 2

ing features can be readily identified and are used here to obtain qualitative
information about the surface morphology.

If the assumption of scattering only from the uppermost surface layer is
made, the reciprocal lattice consists of rods. Since the electron wavelength
A compared to the rod spacing. If the rods were infinitesimally narrow and
the instrumental broadening small, a spotty pattern would be obtained from
an atomically smooth surface. However, in most practical situations nonide-
alities such as steps and islands result in broadening and streakiness of the
rods. This gives rise to the streaks seen in RHEED patterns, particularly at
very glancing incident angles.

The surface unit cell of the unreconstructed Si(001) is a square lattice with
a lattice constant of 0.384 nm as shown in Fig. 2.3(a) [12]. The corresponding
reciprocal lattice is shown in Fig. 2.4(a). Each Si atom on the surface has
two dangling bonds. In vacuum, a clean $i(001) surface reconstructs to form
the structure shown in Fig. 2.3(b). Two Si atoms on the surface move
closer together to form a bond. There is also some inward relaxation of the
surface layer atoms. Now the unit cell is rectangular and the reciprocal lattice
shows extra half-order rods. On a vicinal surface, i.e., a wafer with a slight
misorientation, the (2x1) reconstruction rotates by 90° at a monatomic step.
Thus both (1x2) and (2x1) domains are present on the surface giving rise
to half-order rods in both orthogonal <110> directions.

The RHEED pattern of a reconstructed $i(001)-2x1 surface along the
<110> azimuth is shown in Fig. 2.5(a). The (0,14) and (0, +3) lines can be

seen clearly. The RHEED pattern of the same surface at different incidence

Chapter 2 34

e e e ° e e [110] ee ee o ©
e e e e e e [001] [110] ee ef. e he

Figure 2.3: The surface net of the (a) unreconstructed $i(001), and (b) (2x1)
reconstructed $i(001). The (2x1) reconstruction is shown in the x-direction.

2m on Qn 2n
a z |3,°
OT or
10 oF
00 00 10
1 04
01 , 01 i

(a) | (b)

Figure 2.4: The reciprocal lattice corresponding to the (a) unreconstructed
Si(001), and (b) (2x1) reconstructed $i(001) in the previous figure.

Chapter 2

angles is shown in Fig. 2.5(b)-(c). We see that the streaks decrease with
increasing angle of incidence. The RHEED pattern was monitored along the
<110> azimuth during the experiments because it gives information about
the reconstruction of the surface.

After the chemical cleaning of the silicon wafer as described in the preced-
ing section, we obtain a nominally dihydride-terminated Si(001)-1x1 surface.
The RHEED pattern from such a surface is shown in Fig. 2.6(a). The hy-
drogen coverage is nominally 2 monolayers (ML). The surface changes to
a (2x1) monohydride structure (hydrogen coverage 1 ML) following partial
hydrogen desorption at 350 — 400°C. Complete hydrogen desorption occurs
above 500°C and Fig. 2.6(b) shows the diffraction pattern from a clean, re-
constructed $i(001)-(2x1) surface after heating to 550°C. A buffer layer was
deposited at this temperature. The silicon growth rate was set to 0.09 nm/s.
In Fig. 2.6(c), the RHEED pattern after 0.5 nm growth of Si is shown. A
spotty pattern indicative of three-dimensional island growth is observed. This
is due to small amounts (~ 1 —- 5% of a ML) of carbon and oxygen impurities
at the starting surface and is further discussed in Section 2.7.2. From a ther-
modynamic view [13], one would expect a homoepitaxial film to completely
wet the substrate because the surface energy of both film and substrate is
the same (and interface energy is zero). The islanding is illustrative of the
important role that adsorbates play in silicon homoepitaxy. The C and O
impurities are buried upon further growth and the surface begins to become
smooth. This can be seen in Fig. 2.6(d) which shows the RHEED pattern
after 30 nm deposition. A smooth (2x1) pattern with Kikuchi lines can be

seen in Fig. 2.6(e) after the growth of a 110 nm buffer layer. At this point,

Chapter 2 36

(a) (c)

Figure 2.5: The RHEED pattern of a $i(001)-2x1 surface along the <110>
azimuth with the electron beam incident at (a) 0.6°, (b) 1.5°, and (c) 2.1°
grazing angle.

Chapter 2

growth was interrupted and the substrate temperature dropped to 300°C for
low temperature growth. The cooldown time was about 15 minutes. The
RHEED pattern after 60 nm growth at 300°C is shown in Fig. 2.6(f). There
are no reconstruction lines and the spotty pattern indicates a rough three-
dimensional surface morphology. In addition, extra spots are seen in the
diffraction pattern. This is due to twinning and a complete picture of all the
observed spots is shown in Fig. 2.6(g). During low temperature growth the
twin spots appear suddenly during the course of deposition. Further growth
results in a complete transformation to amorphous silicon deposition. The
ring pattern characteristic of amorphous materials is shown in Fig. 2.6(h).
This was after 200 nm film deposition.

In situ observation of the RHEED pattern shows that growth at low tem-
peratures starts epitaxially. As the film thickness increases, the RHEED
pattern becomes increasingly spotty which is indicative of three-dimensional
islanding. Nucleation of twin boundaries occurs suddenly after a certain
thickness as judged from the appearance of extra spots. The intensity of the
twin spots increases and a ring pattern characteristic of amorphous silicon is
soon visible. Further growth results in a complete transformation to amor-
phous silicon. At very low temperatures (T < 150°C), the transformation
to amorphous silicon is direct and twin spots are not observed. This phe-
nomenon has been studied using a wide variety of techniques to understand
more about the nature of the film and the growing surface, and is the topic

of the next several sections.

Chapter 2 38

dais) *

x7
“AR lg’ AL

x’ eS tA
i” Me !

ON
a he
(g) (h)

Figure 2.6: A sequence of RHEED patterns illustrating substrate prepara-
tion and Si MBE at high and low temperatures. RHEED pattern after (a)
chemical cleaning; and (b) complete hydrogen desorption at 550°C. High
temperature buffer layer. RHEED patterns after (c) 0.5 nm; (d) 30 nm; and
(e) 110 nm deposition at 550°C. Low temperature growth. RHEED patterns
after (f) 60 nm deposition; (g) identification of diffraction spots (only twin
spots) in (f); and (h) 200 nm deposition at 300°C.

Chapter 2

2.4 Conventional Molecular Beam Epitaxy
— A Transmission Electron Microscopy
Study

Transmission electron microscopy (TEM) was performed using a Phillips
EM430 microscope operated at 300 kV. The point-to-point resolution of
0.23 nm is sufficient to obtain lattice-resolved images of silicon. The thresh-
old energy of electrons for production of points defects in silicon is about
200 keV. The incident electron energy of 300 keV was slightly higher, and
imaging was performed before causing any noticeable damage to the speci-
men.

Cross section specimens were prepared by polishing the wafers on a silicon-
carbide paper to ~ 100 um thickness followed by dimpling to create a perfora-
tion. Ion milling was subsequently performed to thin the specimens down to
electron transparency. The maximum temperature during the entire process
did not exceed 200°C. This is well below the solid phase epitaxy temperature
and any annealing of defects in the film may be considered negligible.

Before describing the observations, it is appropriate to define the concept
of epitaxial thickness, h,,;. This is defined as the thickness up to which the
film is defect free. While the region of view is limited in a cross section
transmission electron microscopy (KTEM) specimen (typically 1 um long),
the large number of nucleation sites of the defects makes this a reasonable
definition. This definition also provides an answer to the crystal grower’s
question, “How thick a film can one grow ensuring that it is defect free?”

Other definitions have been used in the literature such as the thickness at

Chapter 2

which half of the deposited material is amorphous [14].

Figure 2.7 shows an XTEM image of a 220 nm film deposited by con-
ventional MBE at 370°C. It is a bright field image taken under multibeam
conditions in the <110> projection. The film growth rate was 0.09 nm/s.
The film/buffer layer interface is visible in some regions due to the contrast
from small amount of impurities accumulated during the growth interrupt.
These impurities are described in more detail in Section 2.7.2. The film ap-
pears defect free up to a thickness, h.,;, of about 83 nm. The film above
that is highly disordered. The presence of twins can be inferred from the
moiré fringes with a spacing of three {111} planes. The high density of twins
gives rise to the extra spots in the RHEED pattern described in the previous
section.

A high resolution image of a twinned region is shown in Fig. 2.8(a). Al-
though not from the above film, this is a typical defect in the disordered
region. The moiré fringes can be seen with a periodicity of three {111}
planes. In addition to twins, isolated planar defects are also visible in the
disordered region. These have been identified as stacking faults and “hydro-
gen platelets.” A through-focus series of images showed that some defects
did not show the contrast typical of a stacking fault or a dislocation. We
believe these are “hydrogen platelet” defects (see Fig. 2.8(b)). Such defects
have been observed after hydrogen plasma-etching of silicon [15, 16, 17].
One model for the hydrogen-platelets involves breaking Si-Si bonds between
neighboring {111} planes and terminating the Si atoms with H atoms [18].

A high resolution transmission electron microscope (HRTEM) image of

a 110 nm film deposited by conventional MBE at 240°C and 0.09 nm/s is

Chapter 2

50 nm

Figure 2.7: Bright field image of a 220 nm film deposited by conventional
MBE at 370°C. The image was taken under multibeam conditions in the
<110> projection. The epitaxial thickness, h.,i, is estimated to be 83 nm.

Chapter 2

bal : aso
ans

nae
bial ae
Tense,
? MASSA

oe Aes yc

Figure 2.8: (a) High resolution image of a twinned region. (b) A planar
defect believed to be a “hydrogen-platelet.”

Chapter 2

shown in Fig. 2.9. The epitaxial thickness is about 25 nm. The crystalline-

to-amorphous transition is seen to be quicker compared to Fig. 2.7.

2.5 The Breakdown of Epitaxy at Low Tem-
peratures

The transition from single crystal silicon to amorphous silicon deposition is a
characteristic of low temperature silicon molecular beam epitaxy. This tran-
sition is abrupt and occurs on a local scale. As seen in the preceding section,
there is a disordered region with a high density of twin planes between the
regions of single crystal and complete amorphous silicon deposition. As the
temperature is reduced, this disordered region gets smaller and the transition
is quicker.

A possible pathway to the nucleation of amorphous silicon is as follows.
Amorphous silicon has short range order but no long range order. The con-
tinuous random network models of amorphous silicon show that besides six-
member rings, it also consists of five- and seven-member rings [19]. Due to
lower diffusivity of Si atoms at low temperatures, growth on Si(001) sur-
faces leads to 3D islanding and the formation of {111} facets. This is shown
schematically in Fig. 2.10(a). Now, £3 coherent twin boundaries can form
on such planes as they cost relatively little energy. At a twin boundary, the
six-member ring structure of silicon is preserved. It is only the third (and
higher) nearest neighbor atoms that are now at a different position. Figure

2.10(b) shows a (111) twin boundary in a wireframe model. While investi-

Chapter 2

5 nm

Figure 2.9: High resolution image of a 110 nm film deposited by conventional
MBE at 240°C. The image was taken in the <110> projection. The epitaxial
thickness, h,,;, is estimated to be 25 nm.

Chapter 2

gating Si(111) homoepitaxy by chemical vapor deposition, it was suggested
in Ref. [20] that twin boundaries can nucleate by adatoms clustering in the
wrong sites. One only needs to take this postulate to its logical conclusion.
When a twinned region grows and meets a different {111} or {001} plane of
the perfect crystal, it inevitably leads to the formation of five- and seven-
member rings. This is shown in Fig. 2.10(b). At very low temperatures
(T Aq 150°C) this rapidly leads to a transformation to amorphous silicon de-
position. At more moderate temperatures (150 ~ T ~ 450°C), a crystalline
film continues to grow after the formation of a grain boundary because a
crystalline network (plus a grain boundary) still has lower energy than an
amorphous network. Eventually the density of defects grows very high, lead-
ing to a transition to amorphous silicon deposition. We will refer to this
mechanism as the twin-boundary/facet (TBF) mechanism. The breakdown
of epitaxy at the edge of a stacking fault or twin boundary has been reported
several times in the past [21, 22].

It was widely believed that semiconductor growth resulted in crystalline
films above a certain “epitaxial temperature” and amorphous films below
that temperature [23]. This epitaxial temperature was estimated by differ-
ent authors to be between 0 and 200°C [24]. Recently, it was shown that the
concept of an epitaxial temperature does not describe semiconductor epitaxy
well. Instead, it was proposed that the epitaxial thickness was a more funda-
mental parameter [6]. It was shown that growth on Si(001) always proceeds
epitaxially up to a certain thickness followed by a crystal-state — amorphous-
state transition [6]. This raised the important question of the relative role

of surface roughness and adsorbates such as carbon, hydrogen and oxygen in

Chapter 2

this transition. It has also been observed that energetic beam techniques such
as ion beam-assisted molecular beam epitaxy, direct ion beam deposition and
sputter deposition produce thicker epitaxial films at very low temperatures.
These important issues in low temperature Si MBE are addressed in the rest

of this chapter.

2.6 Ion Beam-Assisted Molecular Beam Epi-
taxy

Low energy ion beams have been used to modify semiconductor film growth
for several different applications. Heavily doped silicon films have been de-
posited at low temperatures with the use of energetic beams of dopants [25].
The surface segregation problem is overcome by incorporating the dopant
atom in a sub-surface site. Ion beam-assisted molecular beam epitaxy has
been used to modify the strain in Si,_,Ge, films deposited on Si(001) [26].
This was achieved without introducing dislocations. Ion irradiation has also
been used to suppress 3-D island nucleation during the early stages of epitaxy
of Ge [27] and GaAs [28] on Si(001). Energetic silicon ions have been used
to deposit silicon films [29, 30]. In this case, the deposited atoms themselves
carry the energy and the process is referred to as direct ion beam deposi-
tion. Films with improved crystallinity have been obtained by this process
compared to conventional MBE. A chief problem has been the rather low
deposition rates (~ 0.01 nm/s) due to the difficulties in generating mass

separated low energy beams. Sputter deposition has also been reported to

Chapter 2

(111)

(a)

Figure 2.10: A possible pathway to the breakdown of epitaxy. (a) Low tem-
perature growth results in three-dimensional islanding with some {111} ori-
ented facets. (b) A wireframe model illustrating the pathway to amorphous
silicon. It is postulated that a £3 coherent twin boundary is formed on a
(111) plane. When this twinned region grows and meets a different plane,
say (111), the atoms do not line up. This necessarily leads to the formation
of five- and seven-member rings and acts as a nucleation site for amorphous
silicon.

Chapter 2

produce good quality epitaxial films [31, 32, 33]. The sputtered particles
carry a few eV of energy which produces a dramatic improvement in the
film morphology. Closer to our work is the use of Xet+ ions to modify the
surface morphology in Ge(001) homoepitaxy [34, 35]. It was observed that
growth alone or ion bombardment alone led to an increase in surface rough-
ness. However, concurrent ion irradiation during growth resulted in a smooth
surface. It was suggested that this smoothing was a consequence of the an-
nihilation of ion-induced vacancy-like defects and growth-induced adatoms
and small islands.

To understand the influence of ion irradiation, it is necessary to systemat-
ically investigate the role of ion energy in the modification of surface kinetics.
We have used noble gas ions (Ar*+ and Het) because only the physical effects
are important. Concurrent ion irradiation during film growth was employed
to study its effect on surface morphology and film microstructure.

The Art ions were generated by a Kaufman source. The ions were inci-
dent at 45° to the substrate normal along the <100> azimuth. Two different
ion energies, 50 and 70 eV, were employed.

A HRTEM image of a 200 nm film deposited by ion beam-assisted molec-
ular beam epitaxy (IAMBE) at 370°C is shown in Fig. 2.11(a). The Art
ion energy was 50 eV and the ion-to-atom flux ratio was about 0.06. The
film growth rate was 0.09 nm/s. When compared to the conventional MBE
film under similar conditions (see Fig. 2.7), we see that the epitaxial thick-
ness, hep;, of 130 nm for the IAMBE film is higher. The defects are, again,
mostly twin boundaries and stacking faults. An enlarged view of the surface

is shown in Fig. 2.11(b). A {311} facet is marked on the surface. Both {311}

Chapter 2

and {111} facets were observed at the growing front.
The epitaxial thickness for conventional MBE estimated by two methods,
XTEM and RHEED observations, is shown as a function of inverse temper-

ature in Fig. 2.12. The hRHEED for RHEED observations is the thickness at

epi

RHEED

epi values are a little

which twin spots became visible. We see that the h
higher than the XTEM values. At the breakdown of epitaxy, the surface
is faceted and contains amorphous and crystalline regions. As the RHEED
pattern only gives areal-averaged information on ~ 1 mm? of the surface, it is
difficult to pinpoint the time of transition from RHEED observations alone.
However, it does allow a quick determination of the epitaxial thickness.

The variation in h,,; with temperature for IAMBE films is compared with
conventional MBE in Fig. 2.13. Two different Art ion energies of 50 and 70
eV with ion-to-atom flux ratios of about 0.06 and 0.09, respectively, were em-
ployed. The film growth rate was about 0.09 nm/s for all films. We see that
above a certain temperature, there is an increase in the epitaxial thickness.
However, below 300°C, concurrent ion irradiation resulted in a decrease in the
epitaxial thickness. This suggests that annealing of ion damage is incomplete
at these temperatures.

Qualitatively, similar results were observed with IAMBE as in Ref. [34].
Concurrent ion irradiation during growth results in a smoother surface as
observed in RHEED patterns. Ion beam-assisted molecular beam epitaxy
thus produces films with an improved crystalline quality at low temperatures.
The data also suggest that Ar* ion energies lower than 50 eV are required

for improvement in the crystalline quality of films deposited below 250°C.

Chapter 2

5 nm

Film

Buffer

layer

Figure 2.11: (a) High resolution TEM image of an IAMBE film deposited at
370°C and 0.09 nm/s. The Art ion energy was 50 eV and the ion-to-atom
flux was about 0.06. The image was taken in the <110> projection. (b) An
enlarged view of the surface showing a {311} facet. Both {311} and {111}
facets were observed on the growing front.

Chapter 2

Temperature (in °C)
3 400 350 300 250 200
10° -7—J |
e XTEM
O RHEED

10! |
1.4 1.6 1.8 2.0 2.2

1000/T (K~')

Figure 2.12: Epitaxial thickness vs. inverse temperature for conventional
MBE films measured by (a) @ cross section transmission electron microscopy,
and (b) o RHEED observations.

Chapter 2

Temperature (in °C)
400 350 300 250 200

10° —>-—
e MBE
IAMBE, 50 eV Ar™
A IAMBE, 7O eV Ar*®
© i02h 4
Cc
10° 4
| | |

1.4 1.6 1.8 2.0 2.2
1000/T (K7')

Figure 2.13: Epitaxial thickness vs. inverse temperature for (a) e Conven-
tional MBE, (b) © 50 eV Art IAMBE, and (c) A 70 eV Art IAMBE. The

epitaxial thickness was measured by cross section transmission electron mi-

croscopy.

Chapter 2

2.7 Other Thin Film Characterization Tech-
niques

2.7.1 Rutherford Backscattering and Channeling

The XTEM images of low temperature films show that they are free of
extended defects up to the epitaxial thickness. A Rutherford backscatter-
ing/channeling analysis was performed to check the quality of these layers.
The Hett ions were incident normally on the surface and the solid state
detector was at a 170° backscattering angle. With 2 MeV Het** ions, the
minimum yield xmin from a $i(001) wafer for this geometry is about 0.03 [36].
A Xmin Value of 0.03 was indeed obtained with a dilute HF-dipped 5i(001)
wafer. Figure 2.14(a) shows the random and (001) aligned spectra from a
50 nm film deposited by conventional MBE at 370°C. The deposition con-
ditions were identical to the one shown in Fig. 2.7. The xmin value of 0.03
clearly indicates a film with a low defect density. It is noted that about 75%
of the signal from the low temperature film lies within the surface peak. Fig-
ure 2.14(b) shows the result of a similar analysis on an 80 nm JAMBE film
deposited at 370°C. Again, a 0.03 minimum yield indicates that low energy
ion irradiation does not result in the generation of dechanneling defects.

The RBS spectrum of the IAMBE film did not show any Ar peak indi-
cating that the Ar concentration is less than the detection limit of about
0.1%.

In Ref. [37], positron annihilation spectroscopy was used to show that

low temperature Si films have a very low concentration of point defects. The

Chapter 2

authors concluded that the density of point defects was not sufficient to ex-
plain the breakdown of epitaxy. While channeling yield is not sensitive to low
concentrations of defects, the analysis nevertheless indicates that the break-
down of epitaxy is an abrupt phenomenon and not caused by a continuous

increase in the defect density.

2.7.2 Secondary Ion Mass Spectrometry

There are several sources of contamination in an MBE chamber. A typical
pressure during growth was 10~° Pa. This corresponds to a monolayer time,
i.e., the time required to build up one monolayer of contaminants, of about
100 s. Fortunately, the contamination rates are much lower because the
sticking coefficients of most residual gases on silicon are low. Hydrogen is
the main residual gas and comes from extensive outgassing of the source
and surrounding regions. Molecular hydrogen does not react with silicon
but atomic hydrogen which may be produced by cracking of hydrogen and
hydrocarbons at hot filaments and silicon melt has almost unity sticking
coefficient. The next most abundant gases are carbon monoxide, carbon
dioxide and water.

Secondary ion mass spectrometry (SIMS) was performed on a CAMECA
IMS-3f system. The carbon and oxygen profiles were obtained with a 14.5 keV
Cst+ beam and the hydrogen profiles were obtained with a 10.5 keV Of beam.
The sample bias was held at 4.5 keV and the ions were incident nominally at
30°. The sample bias causes a slight deviation in the incident beam which

can be estimated [38]. For the Si signal, the counts of the *°Si isotope were

Chapter 2 55

Energy (in MeV)

0.5 1.0 1.5
3000 t T T

2500 2 MeV He** |
oo
‘'€

> 2000 + Random =
ra

*B 1500+ 4
ro
<<

2 1000 - 7

S00 }- 5

Aligned
0 l n 1
is) 200 400 600 g00 61000
Channel

(a)

Energy (im MeV)
15

0.5 1.0
1.0x10* T T T
—~oak 2 MeV Het*
[=
D> Random
DOB =
0.4 4
Cc
6 02+ 4
Aligned
0.0 1 4.

1 i
“oO 200 400 600 800 1000
Channel

(b)

Figure 2.14: Rutheford backscattering/channeling spectra from (a) a 50 nm
film deposited by conventional MBE at 370°C, and (b) an 80 nm film de-
posited by IAMBE. The substrate temperature was 370°C for both films.
The minimum yield ymin = 0.03 for the (001) aligned spectra in both cases.
It is noted that about (a) 75% and (b) 50% of the signal from the low tem-
perature film falls within the surface peak.

Chapter 2

monitored. The secondary ion yields were converted to atomic densities using

Na = L A, RSFa (2.1)

where Nag is the atomic density of the element A, I, and I, are the yields
of the element A and the °°Si isotope, A, is the relative abundance of the
30Si isotope and RSF, is the relative sensitivity factor of the element A. The
relative sensitivity factors have been experimentally determined for a number
of elements in the Si matrix [38]. The RSF of C and O for the 14.5 keV Cst
beam were taken as 2.4 x 107? and 4.8 x 107? cm~? respectively [38]. Since
the RSF of H atoms with 10.5 keV Of ions was not readily available, the
value from Ref. [38] of 6.2 x 1074 cm~? for 8 keV ions was used. The
relatively modest base pressure of 10-© Pa in the SIMS analysis chamber
limited the sensitivity of the method. A high sputtering rate of ~ 1 nm/s
was used to improve the detection limit. The depth scale was obtained by
using the sputtering rates from previous data [38].

Figure 2.15(a) shows the SIMS profiles of C, H and O from the film
deposited at 370°C by conventional MBE. The C and O profiles show two
peaks at the buffer layer/substrate and film/buffer layer interfaces. This
corresponds to contamination at the initial wafer surface and the contami-
nants accumulated during the growth interrupt after buffer layer deposition.
The total amount of carbon at the buffer layer/substrate and film/buffer
layer interfaces is about 0.02 ML (1 ML = 6.78 x 10!* cm~?) and 0.005 ML
respectively; the corresponding numbers for oxygen are 0.06 and 0.02 ML
respectively. These impurities play an extremely important role in the evolu-

tion of surface morphology. The observation of islanding in the initial stages

Chapter 2

of growth (see Section 2.3 ) can be correlated to these impurities. One way
in which impurities can cause film growth in the Volmer-Weber mode is by
decreasing the surface energy [13]. The islanding in this case, however, seems
to be due to kinetic effects. The extent of islanding can be reduced by going
to slower deposition rates.

The SIMS profiles from the IAMBE film deposited at 370°C are shown
in Fig. 2.15(b). Again, a small amount of C and O is observed at the buffer
layer/substrate interface. The double peak in Fig. 2.15(b) is due to a growth
interrupt during buffer layer deposition. One can also infer a similar con-
tamination peak at the film/buffer layer interface. In addition, the C and O
content in the low temperature film is seen to be higher than the correspond-
ing conventional MBE film. This is probably due to contamination from the
ion beam. Since h,,; for the IAMBE films was higher, this provides some
evidence that C and O contamination is not the direct cause of breakdown
of epitaxy. Another experiment showing that C and O do not directly cause
the crystalline-to-amorphous transition is discussed in Section 2.8.

The hydrogen peak is not observed at either of the two interfaces. This
is not surprising since hydrogen (for coverage < 1 ML) is known to segregate
on the surface during growth [39].

The concentration of all three elements increases toward the surface. This
rise coincides with the observation of defects in these films. The disordered
region of the film contains a high density of dangling bonds. This probably
causes the increase in the impurity incorporation by the diffusion of impu-
rities after exposure to atmosphere and enhanced sticking during growth.

The delayed rise in the H, C and O concentrations in the IAMBE film com-

Chapter 2

pared to the conventional MBE film is consistent with the increased epitaxial
thickness for the IAMBE film.

The SIMS analysis has thus shown that small amounts of C and O are
accumulated during growth interrupts. These impurities can be correlated
with the observation of islanding in the initial stages of Si homoepitaxy. The
increased C and O contamination observed in the IAMBE films is a concern

for the use of ion beams in depositing device quality films.

2.7.3. Atomic Force Microscopy

Even though low temperature growth starts on a planar surface, the surface
does not remain planar during growth. RHEED observations of films de-
posited at different temperatures indicate that the increase in surface rough-
ness strongly correlates with the epitaxial thickness. A scanning probe tech-
nique such as atomic force microscopy (AFM) can provide quantitative in-
formation about the surface roughness.

Atomic force microscopy was performed ez situ using the Digital Instru-
ments, Nanoscope III. The samples were imaged with a metal tip on a SigN,
cantilever. The force constant of the cantilever was 0.58 N/m. Images were
obtained in the contact mode under constant force conditions. A few sam-
ples were imaged with different tips to check for tip artifacts. Similar results
were obtained with the different tips. An atomically resolved image was not
observed.

The Si surface gets oxidized immediately on exposure to atmosphere.

This oxide was removed with a dilute HF dip just prior to imaging. While

Chapter 2 59

22
10

Buffer layer

Film Substrate

1071

Atomic density (cm7*)
oo 8
nv} @ rr}

0 100 200 500 400
Depth (nm)

wey
[o)

Buffer layer | Substrate

oO
nN

—s —v
[o) [e)

a rs)

2,
re

~s
oO

Atomic density (cm7*)

100 200 300 400
Depth (nm)

(b)

Figure 2.15: The SIMS profiles of H, C and O in (a) conventional MBE film
and (b) IAMBE film. Both films were deposited at 370°C and 0.09 nm/s. C
and O profiles were obtained with a 14.5 keV Cst beam; the H profile was
obtained with a 10.5 keV Of beam. Note that the background levels of H
and O are different for (a) and (b).

Chapter 2

Figure 2.16: AFM images after (a)20, (b)40, (c)60, and (d)80 nm film de-
posited at 325°C by conventional MBE. The growth rate was 0.09 nm/s.
(e) AFM image of an IAMBE film after 40 nm deposition at 325°C. The
Art ion energy was 50 eV and the ion-to-atom flux ratio was about 0.06.
The horizontal and vertical scales are 100 nm/division and 2.5 nm/division,
respectively.

Chapter 2

(e)

Figure 2.17: RHEED patterns after (a)20, (b)40, (c)60, and (d)80 nm film
deposited at 325°C. (a) RHEED pattern from an IAMBE film after 40 nm
deposition at 325°C. These RHEED patterns correspond to the AFM images
in the previous figure.

Chapter 2 62

I I t I I

1.5 A MBE, 240°C 4
O MBE, 325°C

IAMBE, 325°C §

1.0 Q é |

R, (nm)
<_—

0.0 -- 4

0 50 100 150 200
Thickness h (nm)

Figure 2.18: The rms surface roughness vs. film thickness for different growth
conditions. The roughness was measured over a 300 x 300 nm? area at three
separate points on each specimen. Conventional MBE at (a) A, 240°C,
(b) O, 325°C, and IAMBE at (c) ©, 325°C. The arrows indicate the epitax-
ial thickness estimated from the RHEED patterns. The dashed line is the
measured roughness of a high-temperature buffer layer.

Chapter 2

this process may change some features on the surface, it does not significantly
affect the conclusions drawn here. This is because the tip-surface convolution
rounds off all the sharp features. While the tip size can introduce artifacts,
it is noted that most of the islands observed in the images were much larger
than the smallest feature observed.

Films of different thicknesses were deposited side by side at 240 and 325°C
by conventional MBE. The substrate shutter was used to block a region of
the substrate after depositing the desired thickness. The growth rate was
0.09 nm/s. The AFM images obtained from the films at 325°C are shown in
Figs. 2.16(a)-(d). One can see 3D islanding even at the smallest thickness
of 20 nm. An increase in surface roughness and island coalescence with film
thickness can also be inferred from the images. The RHEED patterns from
the corresponding surfaces are shown in Figs. 2.17(a)-(d). The width of the
Bragg spots increases with the surface roughness, as expected. Twin spots
were observed in the RHEED pattern after 50 nm deposition. Films were also
deposited by IAMBE at 325°C and 0.09 nm/s using 50 eV Art ions. These
films were deposited separately, as it was not possible to simultaneously block
the ion and growth fluxes in different regions. As a consequence, some sample
variation is expected. Figure 2.16(e) shows the surface of an IAMBE film
after 40 nm deposition. Comparison with Fig. 2.16(b) shows that Art ion
irradiation leads to surface smoothing. This is also evident from the RHEED
patterns in Figs. 2.17(b) and (e).

The rms roughness R, was measured over a 300 x 300 nm? region at
three different points on each specimen. This is plotted as a function of film

thickness in Fig. 2.18. The arrows indicate the epitaxial thicknesses esti-

Chapter 2

mated from the RHEED patterns. We see that the IAMBE film is much
smoother than the conventional MBE film. The rms roughness for the film
at 240°C is seen to rise more slowly than the film at 325°C. This is somewhat
puzzling since surface roughness builds up more rapidly at lower tempera-
tures. For conventional MBE, the ratio of the rms roughness at the epitaxial
thickness R,(370°C)/R,(240°C) = 3. The ratio of the diffusion lengths is
L,(370°C)/L, (240°C) » 3, assuming an activation energy and prefactor of
0.67 eV and 10-* cm?/s for Si adatom diffusion [40]. We see that these ratios
are approximately the same. Although neglecting the effects of adsorbates
and the assumption of a single diffusion constant are oversimplifications, the
ratio of the moments of the surface roughness and the diffusion length de-
serves a further study.

From Fig. 2.18, we can infer a kinetic roughening exponent § ~ 1 for
conventional MBE. The continuum models that describe crystal growth give
B < 1/2 [41] (see Section 1.5 for more discussion). If the arriving atoms are
uncorrelated in space and time, and there is no surface diffusion, 6 = 1/2.
Including surface diffusion only reduces the value of the exponent. Although
one needs data at least over three orders of magnitude in film thickness to
make a good comparison, it is nevertheless significant that the experiment
indicates such a large value for the exponent. This was also noted in Ref. [42].
A possible explanation for this rather large value is the presence of adsor-
bates during growth. Adsorbates such as carbon and oxygen (Section 2.7.2)
and hydrogen [43] can significantly accelerate the surface roughness. This
must be taken into account in the continuum models. In a simple model for

IAMBE, it was shown that R, ~ In h asymptotically [44]. For the IAMBE

Chapter 2

film, we see that the rms roughness remains relatively low up to about 120 nm
film thickness, in agreement with theory. Again, one would need more data
to make a comparison with theory in this case. The rms roughness for the
IAMBE film is seen to rise rapidly with the breakdown of epitaxy. A pos-
sible explanation is that once twins nucleate, adatoms move away from the
positions (re-entrant corners) where they would be forced to form five- and

seven-member rings, resulting in an acceleration of surface roughness.

2.8 Annealing Experiment

The SIMS analysis described in Section 2.7.2 showed that the rise of C,H
and O profiles coincides with the breakdown of epitaxy. However, we believe
the presence of these impurities is an effect and not a cause of the transition.
The conclusive proof that C and O do not cause a breakdown of epitaxy
comes from an annealing experiment first described in Ref. [14]. We have
seen that growth at low temperature proceeds epitaxially up to a thickness
hep; followed by a crystalline-to-amorphous transition. It was found that by
repeating the steps — (a) depositing the film up to h,,;, and (b) interrupting
growth and annealing at 500°C for 1 min. — one can grow crystalline silicon
indefinitely [14]. We found that a 450°C anneal for 10 min. has the same
effect. Now, the temperature of 450°C is too low for desorption of C and O. A
thin SiO layer requires at least 700°C for desorption and SiC, if formed, does
not desorb until the melting point of Si. The RHEED pattern before and after

annealing at 450°C is shown in Fig. 2.19. It is clear that there is remarkable

Chapter 2

smoothing of the surface during the anneal due to island coarsening. The
annealing temperature is also sufficiently high to desorb hydrogen, if the
coverage exceeds 1 ML.

These experiments thus show that the breakdown of epitaxy is not directly

caused by the presence of carbon or oxygen at the observed concentrations.

2.9 Voids in Low Temperature MBE Grown
Silicon

The microstructure of the low temperature deposited silicon films discussed
so far started with single crystal and transformed into amorphous silicon with
an intermediate region consisting of planar defects. Figure 2.20(a) shows an
XTEM image of a film deposited at 410°C and 0.11 nm/s by conventional
MBE. We see that starting at a certain thickness, there is a trail of volume
defects in the film. These defects were identified as voids in Refs. [45, 46]
using positron annihilation spectroscopy. The voids range in size from 1 to
5 nm in diameter. The diffraction pattern from the film is shown in Fig.
2.20(b). The extra spots are twin spots and double diffraction spots.

Is the breakdown of epitaxy due to these volume defects, or voids? The
above film differs from the other films in one important respect — the presence
of defects at the interface, in this case the buffer layer/substrate interface.
An enlarged view of one such defect is shown in Fig. 2.20(c). It appears
that the initial surface of the wafer had some impurities, possibly SiO» or

5iC, around which the film has grown. A twinnned region can also be seen.

Chapter 2

(a)

Figure 2.19: RHEED pattern along <110> azimuth. (a) After depositing
50 nm at 325°C, and (b) after 10 min. anneal at 450°C.

Chapter 2

All reported observations of voids in low temperature silicon films [45, 46]
have had such defects either at the film/buffer layer or buffer layer/substrate
inteface. This was also noted in Ref. [37]. This suggests that film growth on
a surface with such impurities results in a morphological instability causing
void formation. The cause of this morphological instability is not understood
at present. The film morphology is similar to that observed in constitutional
supercooling of binary alloys [47] although it is not clear how far one can
stretch the analog.

It is thus clear that low temperature films can be grown without voids.
The crystalline-to-amorphous transition still occurs and is independent of

void formation.

2.10 Beam-Induced Desorption of Surface
Hydrogen

Surface smoothing by low energy Art ions was shown to be an important
effect in IAMBE films. Another effect of ion irradiation could be sputtering
of impurities. This is indeed the case with surface hydrogen. A nominally
dihydride-terminated Si(001)-1x1 surface was irradiated with 50 eV Art
ions incident at 45° with respect to the substrate normal. The ion flux was
6.8x10'? /cm?-s (= 0.01 ML/s) and the substrate temperature was 190°C.
Figure 2.21 shows the RHEED pattern after a dose of 22 ML. The surface is
(2x1) reconstructed suggesting at least partial hydrogen desorption.

Epitaxy on hydrogen-terminated silicon surfaces and the beam-induced

Chapter 2

Substrate

50 nm 5 nm

Figure 2.20: (a) Bright field image of a 140 nm buffer layer deposited at 530°C
followed by a 340 nm film at 410°C. The image was taken under multibeam
conditions in the <110> projection. A trail of voids can be seen in the film.
(b) The diffraction pattern shows twin spots. (c) An enlarged view (high
resolution) of a defect at the buffer layer/substrate interface.

Chapter 2

reconstruction of silicon is the subject of Chapters 4 and 5. Some important
observations are noted here. Silicon deposition on an initially dihydride-
terminated Si(001)-1x1 surface results in amorphous film growth. However,
Si deposition on a surface after beam-induced reconstruction results in epi-
taxial films. It is also possible to grow an epitaxial silicon film on an initially
monohydride-terminated $i(001)-2x1 surface [6]. In a systematic study of
the influence of hydrogen, it was shown that introduction of atomic hydro-
gen reduces the epitaxial thickness [42]. Thus a high coverage of hydrogen
(> 1 ML) can cause a premature breakdown of epitaxy.

The beam-induced reconstruction experiment also suggested that the
sputtering rate of H was rather low for the flux used. The ion-to-atom flux
ratio in the IAMBE films was typically less that 0.1. The removal of surface
hydrogen due to ion irradiation is thus expected to play a small role in the

evolution of the film microstructure during ion-assisted growth.

2.11 Temperature Ramp Experiments

A clear picture of the difference in growth morphology at different temper-
atures can be seen from a temperature ramp experiment. The temperature
is dropped during deposition at a constant rate starting at a high tempera-
ture, normally in the step flow growth mode. Such a study was first reported
in Ref. [48]. They used an optical reflectivity technique to measure the
crystalline-to-amorphous transition thickness (and hence the temperature).
The transition temperature was a function of both the growth rate and the

temperature ramp rate (48, 49]. Higher growth rates resulted in a quicker

Chapter 2

Figure 2.21: RHEED pattern showing low energy Art ion beam-induced
reconstruction. The substrate temperature was 190°C.

Chapter 2

breakdown of epitaxy.

Temperature ramp experiments were performed for both conventional
MBE and IAMBE. A buffer layer was deposited at high temperature, typ-
ically 550°C. The temperature was then dropped at 9 K per minute. The
appearance of twin spots in the RHEED pattern for the different film growth
conditions is shown in Table 2.1. Both Art and Het ions were used in these
experiments. For the growth rate of 0.09 nm/s, we see that the breakdown of
epitaxy is delayed with the use of ion bombardment. In the case of conven-
tional MBE, the breakdown temperatures are higher than the ones reported
in Ref. [48]. This could be due to the different characterization techniques,
substrate temperature measurement and also other factors such as contami-
nation rates.

The ECR source was used to generate helium ions and the background
pressure during growth was 7 x 10~? Pa. A crude Langmuir probe measure-
ment indicated ion energies in the range 10 - 30 eV. An XTEM image for
the Het IAMBE is shown in Fig. 2.22. This image shows the first defects at
an equivalent temperature of 300°C. The surface is seen to be highly faceted.
To see the influence of any possible contaminants in the He gas, a film was
deposited by conventional MBE in a background of He gas (7 x 10-? Pa)
and the XTEM image of the film is shown in Fig. 2.23. The first defects
are observed at an equivalent temperature of 270°C. Helium ions, because
of their lighter mass, can transfer energy better to the H atoms. Hence, if
H atoms were responsible for the breakdown of epitaxy, one would have ex-
pected to see a significant effect on the transition temperature. This suggests

that H accumulation is not causing the breakdown of epitaxy. However, we

Chapter 2

Table 2.1: The results of temperature ramp experiments.

temperature
ramp rates

MBE -9 0.09 350°C 190°C (-6)

IAMBE, 50 eV Art | -9 0.09 290°C —_—

IAMBE, 70 eV Art | -9 0.09 310°C —

MBE -9 0.02 240°C 260°C (-3)

IAMBE, Het -9 0.02 250°C _—

do not have a good measure of the Het ion flux and hence cannot be certain
about this conclusion. (The Het flux is estimated to be 5 x 10% cm? s7}
to within a factor of 3).

Temperature ramp experiments illustrate the abruptness of the break-
down of epitaxy at low temperatures. Film growth starts in a perfectly
single crystal form at high temperatures and ends with amorphous deposi-
tion at low temperatures. Also, there is no buffer layer/film interface for
contaminant accumulation since there is no growth interrupt. These experi-
ments, however, are harder to interpret because of the different growth modes

encountered in the different temperature regimes.

2.12 The Crystal-state—Amorphous-state
Transition

Based on the above experiments, we can make some observations regard-

Chapter 2

300°C

“OS
Pe

Figure 2.22: HRTEM image of a film deposited by Het IAMBE. The temper-
ature was dropped at a rate of 9 K/min. starting at 500°C and the growth
rate was 0.02 nm/s. The ECR source was operated at 130 W and 0.07 Pa
He pressure.

Chapter 2 75

270°C

500°C

5 nm

Figure 2.23: HRTEM image of a film deposited by conventional MBE in
a background (0.07 Pa) of He gas. Temperature was dropped at a rate of
9 K/min. starting at 500°C and the growth rate was 0.02 nm/s.

Chapter 2

ing the influence of various parameters on the crystal-state—amorphous-state
transition.

The presence of voids, or volume defects, has been mentioned as a cause
of the breakdown of epitaxy [33]. These voids are of sufficiently large size
to be observable in XTEM images. We have correlated these voids with
the presence of defects at the film/substrate interface. The formation of
voids can be prevented by starting with a clean $i(001)-2x1 surface. In
our experiments, the crystal-state—amorphous-state transition was observed
to occur without voids. This agrees with the results of Ref. [37], where
positron annihilation spectroscopy was used to show that the point (and
volume) defect density in the epitaxial layer was too low to account for the
crystalline-to-amorphous transition.

Consider roughness alone as a cause of the breakdown of epitaxy. Surface
roughness has a positive correlation with the temperature dependence of the
epitaxial thickness, h.,;. The roughness increases more rapidly at low temper-
atures due to lower adatom diffusivity. We have also observed through AFM
images and RHEED patterns that concurrent low energy Ar* ion irradiation
during deposition results in surface smoothing. The roughness mechanism
can thus explain the observed increase in h,,; for ion beam-assisted MBE
films. Thus it seems plausible that the twin-boundary/facet (TBF) mecha-
nism described in Section 2.5 is the way the film deposition goes from being
epitaxial to being amorphous.

It is noted that the values of the epitaxial thickness reported by different
groups differ by an order of magnitude for similar growth conditions. Thus

for conventional MBE at 325°C and 0.09 nm/s, we measured an epitaxial

Chapter 2

thickness of about 50 nm. Epitaxial thicknesses of ~ 100 nm (~ 0.1 nm/s,
310°C) and ~ 500 nm (albeit with voids, 0.1 nm/s, 300°C) are reported in
Refs. [50] and [45] respectively. This suggests that some other factor in addi-
tion to surface roughness is playing a role in the breakdown of epitaxy. This
role is best filled by adsorbates. It was observed in SIMS analysis that C
and O accumulate at the surface during a growth interrupt. The initial 3D
islanding observed in silicon films (Section 2.7.2) was correlated with small
amounts of these impurities. Recently it was shown using a scanning tun-
neling microscope that a small coverage of H can dramatically increase the
Si island density during Si MBE [43]. Hence impurities can play an indirect
role in the breakdown of epitaxy by accelerating the surface roughness. Do
impurities such as H, C and O alone cause the crystalline-to-amorphous tran-
sition? From the annealing experiment described in Section 2.8 (and SIMS
analysis), we have seen that a small coverage of C and O does not provide a
site for the nucleation of amorphous silicon. A saturation coverage (~ 2ML)
of hydrogen can result in an amorphous silicon film even without any surface
roughness. At coverages lower than 1 ML, it is known that hydrogen does
not impede the growth of a crystalline film [14, 39]. An unknown quantity is
the hydrogen coverage during growth. A difficulty with the viewpoint that
hydrogen alone causes the breakdown of epitaxy is that hydrogen desorption
is negligible below 350°C on the time scale of film growth. However, h.,;
is observed to exhibit a strong dependence on temperature (Section 2.6 and
Ref. [6]). An indirect role of the impurities is thus more consistent with
the evolution of film morphology in low temperature silicon molecular beam

epitaxy.

Chapter 2

The TBF mechanism for the breakdown of epitaxy raises several interest-
ing issues. It is known that five- and seven-member rings are present at the
5i(001)-2x1 and the Si(111)-2x1 surface. However, they do not seem to act
as nucleation sites for amorphous silicon. The important difference here is
that the five- or seven-member ring is not forced into the film microstructure
by these reconstructions. The rings open up when adatoms are in the vicin-
ity. This is possibly why surface anti-phase domains seem to have no effect
on the film microstructure. The (2x1) reconstruction of the Si(001) surface
results in a lower symmetry (twofold) on the surface than in the bulk (four-
fold). This can cause two independently nucleated islands to be out-of-phase
creating an anti-phase boundary (APB) when they coalesce. Silicon growth
in the 2D nucleation and growth regime will result in a high density of such
APBs. Yet, single crystal can be grown indefinitely in this regime indicating
that the five-member rings open up when adatoms are in the vicinity.

An alternative mechanism for the breakdown of epitaxy was proposed re-
cently in a study of low temperature Ge(001) homoepitaxy [51]. The initial
step was the increase in surface roughness and the formation of {111} facets,
just as in the TBF mechanism. Single adatoms dropped on the $i(111) sur-
face stick in the T, or the H3 site to increase their coordination. Calculations
have shown that the T, site is the lowest energy site for an adatom on the
(111) surface [52]. It was proposed that if the adatom did not have sufficient
time to move out of the Ty, site into its bulk position, it would lead to a
crystalline-to-amorphous transition. At present, I do not see a simple way to
distinguish between the two mechanisms from the existing data. There is cer-

tainly evidence for twinning in the low temperature films. Whereas the TBF

Chapter 2

is active at all temperatures, it is possible that the above mechanism and
also other mechanisms such as the five-member rings on the reconstructed
surfaces could become active at some lower temperature.

Is epitaxial thickness more fundamental than epitaxial temperature? It
was noted in Ref. [6] that the finite h.,; on the Si(001) was due to the
difficulty in nucleating the amorphous phase on this surface. This is borne
by the TBF mechanism which suggests that it is the {111} surface which
is required to initiate the breakdown of epitaxy. This leads us to the very
interesting case of low temperature epitaxy on the Si(111) surface. Since
there is an “infinite” area of the (111) oriented surface, epitaxy must be more
difficult on this surface even if the surface diffusion is more rapid. This indeed
seems to be the case. Using a Rutherford backscattering/channeling study, it
was reported that the films deposited below 400°C on an initially Si(111)-7x7
surface had defects [21]. Another interesting observation is that the stacking
fault in the (7x7) reconstruction (dimer-adatom-stacking fault model [53])
remains intact when Si is deposited at room temperature (22, 54]. Amorphous
silicon starts right at the edge of the stacking fault, just as predicted by the

TBF mechanism.

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Chapter 2

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Chapter 2

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[19] See, for example, F. Wooten, K. Winer, and D. Weaire, ‘Computer-
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[20] G.R. Booker and R. Stickler, ‘Crystallographic imperfections in epitax-
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[22] J.M. Gibson, H.-J. Gossmann, J.C. Bean, R.T. Tung, and L.C. Feldman,
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[23] J.A. Venables and G.L. Price in Epitazial Growth, ed. J.W. Matthews,
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[24] For a survey of estimates of epitaxial temperature, see H.-J. Gossmann
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18, 1(1993).

Chapter 2

[25]

[26]

[28]

[30]

See, for example, W.X. Ni, J. Knall, M.A. Hasan, G.V. Hansson, J.E.
Sundgren, S.A. Barnett, L.C. Markert, and J.E. Greene, ‘Kinetics of
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449(1989).

C.J. Tsai, P. Rozenak, H.A. Atwater, and T. Vreeland, ‘Strain modi-
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system — a kinetic analysis,’ J. Cryst. Gr. 111, 931(1991).

C.H. Choi, R. Ai, and S.A. Barnett, ‘Suppression of 3-dimensional is-
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2826(1991).

R.A. Zuhr, B.R. Appleton, N. Herbots, B.C. Larson, T.S. Noggle, and
S.J. Pennycook, ‘Low temperature epitaxy of Si and Ge by direct ion

beam deposition,’ J. Vac. Sci. Technol. A5, 2135(1987).

K.G. Orrman-Rossiter, A.H. Al Bayati, D.G. Armour, S.E. Donnelly,
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Nucl. Instr. Meth. B59, 197(1991).

Chapter 2

[31]

[32]

[33]

[38]

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T. Ohmi, T. Ichikawa, H. Iwabuchi, and T. Shibata, ‘Formation of
device-grade epitaxial silicon films at extremely low temperatures by

low energy bias sputtering,’ J. App]. Phys. 66, 4756(1989).

D.L. Smith, C.-C. Chen, G.B. Anderson, and $.B. Hagstrom, ‘Enhance-
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beam sputtering,’ Appl. Phys. Lett. 62, 570(1993).

E. Chason, P. Bedrossian, K.M. Horn, J.Y. Tsao, and $.T. Picraux,
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1793(1990).

E.Chason, J.Y. Tsao, K.M. Horn, 8.T. Picraux, and H.A. Atwater, ‘Sur-
face roughening of Ge(001) during 200 eV Xe ion bombardment and Ge
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W.K. Chu, J. W. Mayer, and M.A. Nicolet, Backscattering Spectrometry,
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H.-J. Gossmann, P. Asoka-Kumar, T.C. Leung, B. Nielsen, K.G. Lynn,
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R.G. Wilson, F.A. Stevie, and C.W. Magee, Secondary Ion Mass Spec-
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Chapter 2

[39]

[44]

[45]

M. Copel and R.M. Tromp, ‘H-Coverage dependence of Si(001) homoepi-
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Y.W. Mo, J. Kleiner, M.B. Webb, and M.G. Lagally, ‘Activation energy
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D.P. Adams, 8.M. Yalisove, and D.J. Eaglesham, ‘Effect of hydrogen on
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T. Vasek and M.G. Lagally, presented at the American Vacuum Society
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H. Schut, A. Van Veen, G.F.A. VandeWalle, and A.A. Vangorkum,
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Chapter 2 86

[48] H. Jorke, H.J. Herzog, and H. Kibbel, ‘Kinetics of ordered growth of Si
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[49] H. Jorke, H. Kibbel, F. Schaffer, and H.J. Herzog, ‘Low temperature
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[51] G. Xue, H.Z. Xiao, M.A. Hasan, J.E. Greene, and H.K. Birnbaum, ‘Crit-
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[52] E. Kaxiras and J. Erlebacher, ‘Adatom diffusion by orchestrated ex-
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[53] K. Takayanagi, Y. Tanishiro, S. Takahashi, and M. Takahashi, ‘Structure
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Chapter 3

LOW ENERGY ION
IRRADIATION OF SILICON
— A MOLECULAR
DYNAMICS
INVESTIGATION

And here — ah, now, this really is something a little recherché.

- Sherlock Holmes, The Musgrave Ritual

Sir Arthur Conan Doyle

3.1 Introduction

An atomistic view of film growth, ion-solid interactions or any other physical
process has always been an important goal of condensed matter physics. A lot

of knowledge regarding atomic structure and dynamics has been gained over

Chapter 3

the years through techniques such as X-ray diffraction, electron microscopy,
ion scattering, and infrared and microwave spectroscopies. With the advent
of the scanning tunneling microscope and other scanning probe techniques,
this knowledge base has rapidly increased. This serves as a base both for
constructing models and verifying theoretical predictions.

There are a whole range of computational techniques which one can use
to study a given problem. These include kinetic Monte Carlo simulations
where the atoms are allowed to move between sites with certain rates, clas-
sical molecular dynamics where the atomic motion is governed by a classical
potential and techniques which treat the electronic structure of atoms at
various levels of approximation — tight binding approximation, local density
approximation and ab initio theory. Here, we are primarily interested in
determining the mechanisms of film growth and the influence of low energy
ion irradiation. These processes occur on a time scale and crystal size scale
that is beyond the scope of a first principles calculation on today’s comput-
ers. A classical molecular dynamics technique seems the best approach to
understand the physics of these processes.

Molecular dynamics simulations are generally limited to small ensembles
(10% — 10*) of atoms and short durations, typically a few picoseconds. To
compare the simulation results with an experiment, one must average over
all variables that are also averaged by a given experiment or measurement.
These include the impact parameter, energy and angular spread in the inci-

dent beam for an ion-solid collision.

Chapter 3

3.2 Interatomic Potential for Silicon

3.2.1 The Tersoff Potential

In classical molecular dynamics, the atoms are considered as point masses
whose trajectories are obtained by solving Newton’s equations of motion.
The atoms respond to an interatomic potential which may be a function of
the distance between atoms, angle between a pair of bonds, etc. The set of

differential equations can be written as

dr;(t) _o.
Te = vi(t) (3.1)
dv;(t) _BRle

where

Fi = -—V (= es) (3.3)
i

and ;; is the potential energy between the pair of atoms i and j. Here, r;(t)
and v;(t) are the position and velocity of atom i at time t. The force F; on
atom i is given by the gradient of the interatomic potential.

Silicon has the diamond cubic structure with strongly directional bonding.
A two-body potential V(r) depending only the separation r between atoms
cannot be used to describe such a structure. For a two-body interatomic

potential, the hexagonal close-packed (hcp) structure has the minimum en-

ergy. Hence, an interatomic potential to describe silicon must at least have a

Chapter 3

three-body term. Several interatomic potentials have been developed to de-
scribe silicon and other semiconductors. These include the Keating potential
[1, 2], the Biswas-Hamann potential [3], the Stillinger-Weber potential [4],
the Dodson potential [5] and the Tersoff potential [6]. The Keating potential
expresses the potential energy in terms of the elastic constants. It has been
used with considerable success to study the ordering in III-V alloy semicon-
ductors [7]. Since the potential uses the harmonic oscillator approximation,
deviations far from the equilibrium position are not well described.

A central feature of cascade dynamics is the numerous overcoordinated
and undercoordinated configurations in which the atoms are found. The
chosen interatomic potential must be able to describe not only the atomic
interactions near the equilibrium position, but also the low- and high-density
regions occurring in a collision cascade. The other potentials mentioned
above were developed by fitting to positions far from equilibrium such as
point defects, polytypes and surfaces.

For the molecular dynamics simulations described here, the Tersoff poten-
tial [6] was used to describe silicon. The potential energy between a pair of

atoms is written as

V=>> 4; (3.4)

$; = { Aexp(—Airj) — Boexp(—Aary)(1 + B"G)~> } fe(zy) (3.5)

where

Chapter 3
i= DoE wh+S c [oe(ry — tie) 3.6
Gi — fort c(Tik d2 ~ d2 + (h _ costa)! exp ary — Tik | ( . )
and
1 »ryf.(ry) = 4 $- tsin(m iS) »,R-D0 > Tij >R+D

The interatomic potential thus consists of a many-body term attached to
a Morse-type potential [8]. The potential energy between atoms i and j thus
depends on their separation r and on the position of a third atom k through
the ry, and 6;, terms. Note that the potential is not symmetric, 0; # ©). It
can be made symmetric by defining $; = (6 + ;)/2. Also, the potential
has a many-body term and not a three-body term. The potential energy is
cutoff at a distance of R + D = 3.00 A so that an atom interacts only with
its first nearest neighbors. This is necessary to speed up the computation.

The parameters in the potential are listed in Table 4.1 in Section 4.2.

3.2.2 Description of Silicon

The interatomic potential (eq. 3.4 - 3.7) was fitted to the various high pres-
sure phases of silicon based on the pseudopotential calculations in Ref. [9].
The diamond structure has the minimum energy among all the phases. The
cohesive energy per atom and the bond length are 4.63 eV and 2.35 A respec-
tively, in agreement with experimental values [10]. The radial distribution

function of the amorphous state is also in good agreement with experiment.

Chapter 3

The (2x1) reconstruction on the $i(001) surface is well described. The
atomic rearrangement due to the reconstruction is shown in Fig. 3.1. The
top layer relaxes inward by about 15% and the dimer bond length is 2.37
A. The dimer bond length has been estimated as 2.51 A in ab initio cluster
calculations [11]. The energies of the vacancy and some interstitial sites are
close to the first principles calculations.

There are limitations to the potential, some of which are mentioned here.
The various reconstructions (2x1, 5x5 and 7x7) on the Si(111) surface are
not well described. The potential predicts that the unreconstructed (1x1)
surface has the minimum energy whereas a 7X7 structure is observed experi-
mentally after a high temperature anneal. Due to the neglect of interactions
beyond the first nearest neighbor, the energy of a stacking fault (and also 3
coherent twin boundaries) is zero. Therefore, the energy of both the diamond
cubic structure and the wurtzite structure is the same. The melting point of
silicon is predicted as 2550 K [12] whereas the experimental value is 1685 K
[10].

The size and shape of small clusters is also not well described. The bond
length in the Si, dimer is 2.30 A whereas first principles calculations give
a value of 2.24 A [13]. Another example is the Sig cluster which has been
shown (experimentally) to be planar in the shape of a rhombus [14].

Overall, the Tersoff potential does a fairly good job of describing silicon.

One can obtain a qualitative picture of a phenomenon using the potential.

Chapter 3 93

2.37 A

0.21 A

<__- -—P <—

0.13 A

Figure 3.1: The (2x1) reconstructed $i(001) surface viewed along the <110>
axis according to the Tersoff potential.

3.3 Numerical Methods

3.3.1 The Algorithm

The equations of motion (eq. 3.1 — 3.2) have to be solved numerically. A
flow chart of the algorithm is shown in Fig. 3.2. The main aspects of the
algorithm are a technique for determining all the neighbors of an atom, com-
putation of forces on all atoms and a numerical method for solving the dif-
ferential equations. The neighbors of an atom were determined by the link
cell method. The Runge-Kutta-Nystr6m method [15] was used to solve the
differential equations. An adaptive step size was used to achieve the optimal
speed. These are discussed in more detail in the subsequent subsections.
The computer program SIH for molecular dynamics simulations of Si and
H atoms was written in the C language and is listed in Appendix C. Two

workstations, a DEC3100 and an IBM RS6000/340, were used for performing

Chapter 3

Time ty =0
Step Size h=hyax

Nearest Neighbors List by
Link Cell Method

Calculate Forces on Atoms

Determine new positions
and velocities at t=t)+h

Step Size =h/2 A

Nearest Neighbors List by
Cell Method

Calculate Forces on Atoms

Determine new positions
and velocities at t=tg +h

Is Error < Tolerance ?

Predict new h

Figure 3.2: Flow chart showing the major steps in the molecular dynamics
code.

Chapter 3

Table 3.1: The speed of operation of molecular dynamics codes.

Machine Speed of operation No. of function Ref.
(ms/atom-timestep) evaluations/timestep

DEC3100 8.60 5 this work

RS6000/340 1.70 5 this work

CRAY YMP C90 0.08 i [16]

Special

Purpose Computer 0.40 1 [17]

the simulations. The speed of a program is best described by specifying
the time required per atom per timestep. This is listed in Table 3.1. An
optimum speed of 1.7 ms/atom-timestep was achieved on the RS6000/340
workstation with the Tersoff interatomic potential. The speed dropped to
about 1.9 ms/atom-timestep when the Si-H and H-H interatomic potentials
were included. These are compared to the values of 0.08 ms/atom-timestep
in Ref. [16] on the Cray YMP and 0.40 ms/atom-timestep in Ref. [17] on a
special purpose computer. Both of these references used the Stillinger-Weber
potential [4]. It is noted that the Runge-Kutta-Nystrom method with the
adaptive step size used in our simulations requires five function evaluations
per timestep whereas the Refs. [16] and [17] used a 4° order predictor-
corrector method and the Verlet method [18] respectively which requires only
one function evaluation per timestep. If this factor is included, it is seen that
the speed of the code on the RS6000 compares favorably with the Cray YMP

and the special purpose computer which are inherently faster machines.

Chapter 3

3.3.2 The Runge-Kutta-Nystrom Method

There are several techniques for solving a system of ordinary differential
equations, and the method chosen is usually a compromise between accuracy
and speed. The accuracy is determined by the order of the method. A higher
order method gives more accuracy but also requires more function (in our
case, forces on atoms) evaluations.

There are three classes of methods for solving ordinary differential equa-
tions numerically — Runge-Kutta methods, predictor-corrector methods and
extrapolation methods [15]. For a given order of the method, predictor-
corrector methods require the minimum number of function evaluations.
However, there are two problems with these methods. For an n‘* order
method, the knowledge of the atom positions over the past n steps is re-
quired. Typically in a molecular dynamics simulation, one only knows the
positions and velocities at the start, t = 0. This can be overcome by using
the Runge-Kutta method to generate the first n values. The other problem
with these methods is that it is rather hard to develop an adaptive step size.
We will see that this is an important attribute of a numerical method. With
Runge-Kutta methods, one only needs the positions and velocities at t = 0
to predict the corresponding values at t = h. This is done by evaluating
the function at several strategic points. An adaptive step size can be easily
developed for these methods. However, for a given order of integration, these
methods require higher number of function evaluations.

The third order Runge-Kutta-Nystrém (RKN) method was used to solve

the differential equations [15]. This was combined with Richardson extrapo-

Chapter 3

lation to achieve adaptive step size control {[15, 19]. The RKN method takes
advantage of the fact that the potential is velocity- and time-independent.
The third order is achieved with just two function evaluations. This method

is described here for a simple second order differential equation [15]:

y"(t) = f(y) (3.8)

The position (y) and velocity (y’) are known at time t = to. This infor-

mation is used to evaluate the new values at t = to + h as follows:

kr = Sy'(to) + Zy"(to)h (3.9)

ka = y'(to) +5 (v"to) + ¥"(to + Kah) b (3.10)
= zy" (to) + “y"(to + kh) (3.11)

y(to +h) = y(t) + keh (3.12)

y'(to +b) =y"(t) thib (3.13)

Adaptive step size control is achieved by estimating the error in the above

calculation. Since the RKN method is of third order, an expansion of the

form

y*(to +h) = y(to + h) + a3(to)h? + ag(to)h* +... (3.14)

Chapter 3

holds where the error has been expanded in a Taylor series. Here, y*(to + h)
and y(to + h) are the true and estimated values of y(t) at t = to + h. The
error is estimated by calculating the value of y(to + h) in two ways: the first,
yi, with a step size of h and the second, y2, with two steps of size h/2. Now,
we assume that the error ¢ is dominated by the azh? term and hence is given

y2—-Yy1

If this error is below a certain preset tolerance, the present step size is ac-

(3.15)

cepted. Otherwise, the step size is halved to h/2 and the procedure repeated.
If the step is successful, the next step size is predicted using the value of «€

[19]:

where 7 is the tolerance per unit step and 6 is a constant. The minimum step
size is taken as hain. For a system of differential equations, the maximum
value of € is used. Frequently, one also limits the maximum value of the
step size. In our case, we could keep the step size below a quarter of the
fundamental vibrational period of the atoms.

Finally, this can also be used to get an improved estimate of y(to + h),

often called active extrapolation [19]:

y°"(to +h) =y2+ (3.17)

Note that this correction makes the RKN method with Richardson extrapo-

lation a fourth-order method.

Chapter 3

NooN ww
Oo a Oo

! !

Timestep (in fs)
on

\e) —
uo Oo
eae

2°
ro)

0 200 400 600 800 1000
Simulation time (in fs)

Figure 3.3: The variation in step size during a simulation of a 10 eV Si atom
incident on a dihydride-terminated $i(001) surface.

In the molecular dynamics simulations with the many-body interatomic
potential, a value of @ = 0.7 was found to give a reasonable prediction of the
step size without being too optimistic. A high value of @ can result in an
increased rejection of the step size resulting in more computation time.

The RKN method with Richardson extrapolation thus requires five func-
tion evaluations per timestep. Since this is 2-1/2 times larger than the RKN
method alone, this is profitable only if the step size variations during a sim-
ulation are large. This was indeed the case in many ion-solid collisions. The
step size variation during a 1 ps simulation of a 10 eV Si atom incident on a
dihydride-terminated Si(001) surface is shown in Fig. 3.3. We see that the

step size changes significantly during a simulation.

Chapter 3

3.3.3. The Link Cell Method

For determining the potential energy or interatomic forces, all the neighbors
of an atom within the cutoff distance must be known. A direct way of making
such a list is to compute the distance to all atoms and compare it with the
cutoff distance. This method, sometimes called the Verlet method [18], is of
O(N?) where N is the number of atoms.

An alternate way is to divide the space into cubes, each side equal to the
cutoff distance. Each atom is assigned the address of the cube in which it
resides. Then, an atom will interact only with other atoms in the same cube
and the nearest neighbor cubes. This reduces the search to a great extent.
This method is of O(N).

For many-body potentials, it is essential to store the location of all the
atoms within the cutoff distance of a given atom in an array. After the
computation of the two-body terms, one can use the stored information for

calculating the three- and many-body terms.

3.3.4 The Cutoff Function

The interatomic potential is usually terminated at a certain distance to speed
up the computation. A cutoff function, f,(r), is used to make the potential
vanish after a certain distance. The cutoff function in eq. 3.7 is frequently
used. This function is continuous and has a continuous first derivative at the
boundaries, r= R-D and R + D. It was observed that a better energy and

momentum conservation could be achieved by going to a higher order cutoff

100

Chapter 3 101

function.
1 »r

f.(r) = 4 4— Ssin(a 52) + gsin(8a5sF) , R-D0 »r>R+D

(3.18)
This function with two sinusoidal terms has a continuous third derivative at
the cutoff points. The additional computational expense is minimal, since
at any given time the fraction of atom pairs within the cutoff region is quite
low.

A general n** order cutoff function g,(x) can be obtained from

gn(x) =1— [ sin™t dt (3.19)

This gives a function between 0 and 7 and can be scaled and translated to
the desired region. It is noted that the cutoff function introduces an artificial
barrier centered at x = R, and this becomes more pronounced as the order

of the function increases.

3.3.5 Boundary Conditions

The number of atoms used to describe a crystal is limited by the computing
resources available. Typically, 10? — 10* atoms are used in a simulation of
low energy ion-solid interactions. For silicon, this corresponds to a cube of
side 3-5 nm. A small size of the crystallite can introduce artifacts such
as reflection of energy at the edges and surfaces, distortion due to recon-

struction and relaxation of the surfaces, etc. The distortion of the crystallite

Chapter 3

is circumvented by using periodic boundary conditions in the transverse di-
rections. The bottom two layers of the crystal were also held rigid in some
simulations. The size of the crystallite was chosen to be sufficiently large to

reduce the influence of energy reflections.

3.4 Low Energy Art Ion Irradiation of
Smooth and Rough Silicon Surfaces

3.4.1 Energy Loss of Ions

There is no detailed information available about how ion irradiation affects
the surface kinetics. The energy loss of ions in solids is frequently divided,
for sake of convenience, into electronic and nuclear energy losses. For ion
energies exceeding a few keV, there are “universal” expressions for the energy
loss which give reasonable predictions of the range and straggle for most ion-
target combinations [20]. Scattering of the ion is considered in the binary
collision approximation, in which the ion interacts with one target atom at a
time. Two commonly used programs are TRIM [21, 22] and MARLOWE
[23]. The binary collision approximation cannot be applied at low energies
where many-atom collisions become important. A molecular dynamics (MD)
simulation where the interaction of each atom with all other atoms is taken
into account can provide a better description of the collision cascade. At
present there are no good models to determine what fraction of the ion energy

is channeled into the electronic energy loss, even though several inelastic or

102

Chapter 3

electronic events can occur in a low energy ion-solid collision. Events such
as neutralization of the incident ion, atom excitation, secondary and Auger
electron emission, surface and bulk plasmon excitation and electron-hole pair
creation are considered to be electronic energy loss components. Energy
loss by creation of phonons is also considered as an electronic energy loss
component. Atomic displacements in the surface and bulk, and sputtering,
are considered as nuclear energy loss components. It should be mentioned
that such classification is only for convenience. An example where such a
classification becomes difficult is chemical sputtering, i.e., an enhancement
in the sputtering yield with the use of a reactive ion beam. The computation
of electronic energy loss of ions requires a first principles calculation. With
classical molecular dynamics simulations, one can only study the damage
produced by the ions and the energy loss to lattice vibrations (“heat”) or
phonons. Nevertheless, this provides a qualitative picture of the influence of

ion bombardment.

3.4.2 Simulation Description

A growing Si film does not remain smooth at low temperatures. Surface
roughness was one of the central features in low temperature silicon homoepi-
taxy and is especially clear from the AFM images and RHEED patterns in
Section 2.7.3 . It was also shown that the principal effect of concurrent low
energy Ar* ion irradiation during growth was surface smoothing.

Previous MD studies of silicon include initial stages of epitaxy [24], direct

ion-beam deposition [25], sputtering by keV range Ar* ions [26] and obser-

103

Chapter 3 104

vation of surface channeling on Si(111) [27]. These studies have employed
idealized atomically smooth (001) or (111) surfaces. For real surfaces subject
to ion bombardment at energies near the displacement threshold, some or all
of the effects of ion bombardment could occur preferentially at certain surface
“defect” structures. These include ledges, kinks, dimer strings and 3D islands
with different facets (i.e., local surface orientations). A better understand-
ing of the principal effects of ion bombardment can be gained by studying
the interactions of the ion with a surface containing the above-mentioned
structures.

Ion beam-induced defect production was estimated from a smooth (2x1)
reconstructed Si(001) surface, a dimer pair and the center and the edge of a
dimer string placed on $i(001). The choice of these structures was guided by
the scanning tunneling microscope images of reconstructed 5i(001) surfaces
[28]. There are, in principle, several choices for the position of these defect
structures on the $i(001) surface. The positions shown in Fig. 3.4 correspond
to configurations with minimum energy calculated using the Tersoff potential
and these were used for studying the effects of ion bombardment.

Recent experimental [29] and theoretical [30, 31, 32, 33] studies indicate
that single adatoms are highly mobile at T > 300 K. Adatom diffusion is also
highly anisotropic, the fast direction being along the dimer rows. The acti-
vation energy and prefactor for single adatom diffusion have been estimated
to be 0.67 eV and 10-3 cm?/s respectively [29]. Two atoms, as in a dimer
pair, form a stable cluster on Si(001) [28]. At typical ion fluxes employed
in experiments (~ 1013 — 10!© cm~*s~!), the interarrival time of ions is very

large compared to the lifetime of an adatom. During ion irradiation, the

Chapter 3

probability of striking an adatom becomes significant only at T < 300 K.
The Tersoff potential (Section 3.2.1) was used to model silicon. For the
simulations described below, a sharp cutoff at 3.20 A was used (f.(r) = 1, r

< 3.20 A and f.(r) = 0, r > 3.20 A). The Ar-Si interaction was taken to be

purely repulsive,

Var-si = Aexp(—Ar) (3.20)

with A = 1830.8 eV and \ = 2.00 A~!. The potential had a sharp cutoff at
4.00 A. Note that the value of A is the same as that of the Tersoff potential
and the value of 4; has been scaled to approximately reflect the radius of
the Art ion. The principal idea was to impart some energy to the surface
through an ion and study its evolution.

In the simulations, ions were incident at 45° with respect to the substrate
normal and along the [110], [110] and [100] directions as indicated by the
arrows in Fig. 3.4. Five different ion energies — 10, 15, 20, 35 and 50 eV were
employed. A total of 102 simulations were carried out for each energy with
each structure. The incident ion impact points were chosen at random within
the rectangle drawn around each structure in Fig. 3.4. For the smooth Si(001)
suface, the impact parameter range is the (2x1) unit cell. The average and
the standard deviation of the impact parameter along with the size of the
simulation crystallite for each of the structures is shown in Table 3.2. We
see that these are sufficiently close to make a fair comparison. The initial
substrate temperature was 0 K and simulations were carried out for a period
of 1.0 ps.

In the simulation results described below, the layer containing the atoms

105

Chapter 3

Table 3.2: Impact parameters used with different surface defect structures.

Surface Crystallite Impact parameter
structure size (in unit Average Standard Measured with
cells) (nm) deviation respect to
(nm) atoms in the
Smooth Si(001) 6x6x6 0.116 0.056 (2x1) cell
Dimer pair 6x6x6 0.130 0.064 placed dimer
Dimer string edge 8x8x6 0.112 0.052 placed dimers
Dimer string center 8x8x6 0.115 0.059 placed dimers

placed on the (2x1) surface is referred to as layer 0, the (2x1) surface is

referred to as layer 1, the one below it as layer 2, and so on up to layer 24.

3.4.3. Simulation Results

The typical events observed in a collision cascade include production of
atomic displacements, interstitials and sputtered atoms. Our criterion for
an atomic displacement is met if there is no Si atom within the hard sphere
radius, i.e., a sphere of radius equal to half the equilibrium Si—Si bond length,
within the original lattice site. Figure 3.5 shows the evolution of total dis-
placement yield with time for 10-50 eV ions incident on smooth Si(001)-2x1
surface. The displacement yield rises rapidly in the initial stages and then
falls, first rapidly and then gradually due to replacement collisions and atoms
getting back into their original positions. Figure 3.6 shows the total displace-
ment yield observed at different ion energies for the different structures. The
results here are all averaged over 102 simulations. With 10 eV ions, the yields

from the different ions are spread over a wide range. At higher energies, sur-

106

Chapter 3 107

face displacements constitute a smaller fraction of the total displacements
and the surface defect structure is expected to have a smaller effect on the
collision cascade. This results in a steady decline in the difference in yield
between the different defect structures with increase in energy. The bulk
displacement yield Ep for Si is often taken to be 14 eV. The large spread
in the calculated displacement yields for the different structures at 10 eV is
consistent with this estimate.

Figure 3.7(a) — (d) shows the depth distribution of displacements in the
crystal. With 10 eV ions, the displacements are almost exclusively confined
to the defect layer (layer 0). For ions incident on smooth $i(001), displacment
yields greater than 0.05 were observed up to the third, fourth and fifth layers
with 20, 35 and 50 eV ions, respectively. It should be noted that the number
of displacements in layer 0 can be at most two for the dimer pair. Also,
these displacement yields were observed at the end of the simulation period
of 1 ps. The substrate temperature will determine the annealing dynamics
and, hence, any observable defect generation on a laboratory timescale [34].
The calculated difference in yields from the different defect structures at low
energies indicate that surface displacement yields are site specific, and any
experimental determination of threshold energies must account for this fact.

Sputtering of silicon atoms was not observed from any of the structures
in the energy range considered. An extrapolation of the experimental values
of the sputtering yield of silicon with argon ions gives a value of ~ 0.01 for
50 eV ions [35]. In Chapter 4, we will see that the sputtering yield from a
hydrogen-terminated silicon surface can be very different.

A useful figure-of-merit for the effect of ion irradiation is the surface-to-

Chapter 3

Figure 3.4: The three defect structures placed on the $i(001) surface. The
rectangles drawn around each structure indicate the area in which the ions
were incident. All ions were incident at 45° with respect to the surface normal
and the arrows indicate the azimuths.

108

Chapter 3 109

10 I | | | |
O 10 eV
BL 4 20 eV a
® 35 eV
e 50 eV
L iy
Cc 6K —_
e )
ty
oO
oO Y
SB 4F 4
Qo. Qa
a As AY aR
2K VV OOO _
J GS) DAA A
a Leh bebe tA Ab hb Ah
jn Qa
O FRB... °O-0-3-6-0-6-0-90-0-6-0-O-O-O4)) cc —
| I | ! |

0.0 0.2 0.4 0.6 0.8 1.0 1.2
Time (in ps)

Figure 3.5: The time evolution of displacement yield for argon ions incident
on smooth Si(001)-2x1 surface. The lines are spline fits to guide the eye.

Chapter 3

bulk displacement ratio, R [36]. Here, the surface is taken as layer 0 and
the rest of the crystal is taken as the bulk. Figure 3.8(a) shows the ratio R
from the different defect structures. The ratio changes from about 2 — 3 for
20 eV ions to 0.6 — 0.8 for 50 eV ions. In Fig. 3.8(b), the number of broken
dimers (only from the placed dimers) is shown for the different energies. A
surface-to-bulk displacement ratio greater than unity is observed with ion
energies less than 35 eV. The absolute number of displacements with 10 and
15 eV ions was too low to give a value of R without a large error.

A large surface-to-bulk displacement ratio is desirable because it may al-
low modification of surface kinetics without causing bulk damage. In Chap-
ter 2, an increase in the epitaxial thickness was observed with the use of 50
and 70 eV Art ions. Better results were observed with 50 eV ions. The
observed improvement in the crystalline quality was also a strong function of
the substrate temperature. These observations suggest that at lower temper-
atures and higher energies, there is inadequate annealing of the “damage”
produced by the ions. As mentioned in Chapter 2, RBS/channeling mea-
surements and XTEM images have shown that the IAMBE films are free of
extended defects. At very low temperatures, ions can amorphize the surface
region. This is discussed in more detail in Chapter 5. Recently, successful
epitaxy has been reported at temperatures around 300°C on both clean [37]
and hydrogen-terminated [38] Si(001) surfaces by low energy bias sputtering.
The best quality films were obtained with ion energies less than 30 eV.

In the simulations, observations of Si atom recoils show that, on average,
they move only a lattice site or two from their original position after an ion

impact. Comparison of the recoil atom trajectories and STM-derived kinetic

110

Chapter 3 111

data on adatom diffusion [29] clearly show that the thermal migration of
single adatoms dominates any ion induced migration at T > 300 K. This
suggests that ion irradiation does not enhance the migration component of
diffusion except for ion incidence along special surface channeling directions
[27]. The most important effect of ion irradiation is the beam-induced cre-
ation of single adatoms, which corresponds to the provision of the adatom
formation energy (ledge-terrace desorption energy or dimer-breaking energy).
This can produce smoother surfaces if adatoms produced by breaking 2D and
3D islands can migrate to the step edge. The simulations and the AFM im-
ages in Chapter 2 are suggestive of such a mechanism in ion beam-assisted

molecular beam epitaxy.

Chapter 3 112

10
O Smooth (001) Si
5 A Single dimer
= % Dimer string edge ;
oa e Dimer string center :
otk of, 4
6 Y/Y
.01 |__.
| 10 100

Energy (in eV)

Figure 3.6: The total displacement yield vs. energy for the defect structures.
The lines are spline fits to guide the eye.

Chapter 3 113

2 5 r T T T 2.5 T q U
ool 10 eV . 2.0} 20 eV -
- o
© 4
> 1.54 4 eter
ae) —_!
1.0 7 NOP |
aS) 2
Ov . 4 & 0.5
= 0.5 =
4a,
0.0 b---8:2:—@—~@—_-@ 00-04 0.0
1 1 1 i i . , .
Layer Layer

iS)
x)

Nn
eo
Lj
1.
on
iad
qT

in
tC)

Yield / Layer
Yield / Layer

OSE 05
0.0 0.0
1 i A. a A i iT A.
0 2 ri 6 8 0 2 4 6 7)
Layer Layer
(c) (d)

Figure 3.7: The distribution of displacements in the substrate at (a) 10 eV,
(b) 20 eV, (c) 35 eV, and (d) 50 eV. The four symbols refer to smooth
5i(001) (o), dimer pair (A), dimer string edge (o), and dimer string center
(e). Displacements in layer 0 are those from the defect placed on the surface.

Chapter 3
10 r T T ” 1.0 T T rT
: ;
> ‘ E p
SS % 5 0.8F 7Qo 7
a. @ foi:
ll a 4 0.6 ye 4
N F
1 s 1 § ,
2 & w 0.4 if 4
S, M:
© i;
- Boze sis 4
= 5 ad
0.4 bee Z 0.0 bev
10 100 10 100
Energy (in eV) Energy (in eV)

(a) (b)

Figure 3.8: (a) The surface-to-bulk displacement ratio R and (b) the average
number of broken dimers per incident ion (only from the placed dimers) for
the different defect structures. The results are for the dimer pair (A), dimer
string edge (o), and dimer string center (e).

114

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Chapter 3 116

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[25] M. Kitabatake, P. Fons, and J.E. Greene, ‘Molecular dynamics simu-
lations of low energy particle bombardment effects during vapor phase
crystal growth — 10 eV Si atoms incident on 5i(001)-2x1 surfaces,’ J.
Vac. Sci. Technol. A8, 3726(1990).

117

Chapter 3 118

[26] R. Smith, D.E. Harrison, and B.J. Garrison, ‘KeV particle bombardment
of semiconductors — a molecular dynamics simulation,’ Phys. Rev. B40,

40(1989).

[27] B.W. Dodson, ‘Molecular dynamics simulation of low energy beam de-

position of silicon,’ J. Vac. Sci. Technol. B 5, 1393(1987).

[28] M.G. Lagally, Kinetics of Ordering and Growth at Surfaces, Plenum,
New York, 1990.

[29] Y.-W. Mo, J. Kleiner, M.B. Webb, and M.G. Lagally, ‘Activation energy
for surface diffusion of Si on Si(001) - a scanning tunneling microscopy

study,’ Phys. Rev. Lett. 66, 1998(1991).

[30] G. Brocks, P.J. Kelly, and R. Car, ‘Binding and diffusion of a Si adatom
on the $i(100) surface,’ Phys. Rev. Lett. 66, 1729(1991).

[31] C. Roland and G.H. Gilmer, ‘Epitaxy on surfaces vicinal to Si(001).
1. Diffusion of silicon adatoms over the terraces,’ Phys. Rev. B46,

13248(1992).

[32] D. Srivastava and B.J. Garrison, ‘The dynamics of surface rearrange-
ments in Si adatom diffusion on the 5i(100)(2x1) surface,’ J. Chem.

Phys. 95, 6885(1991).

[33] T. Miyazaki, H. Hiramoto, and M. Okazaki, ‘Ab initio study of ele-
mentary processes in silicon homoepitaxy — adsorption and diffusion on

$i(001),’ Jpn. J. Appl. Phys. 29, L1165(1990).

Chapter 3

[34]

[35]

[38]

S.T. Picraux, D.K. Brice, K.M. Horn, J.Y. Tsao, and E. Chason, ‘Near-
threshold energy dependence of Xe-induced displacements on Ge(001),’
Nucl. Instr. Meth. B48, 414(1990).

N. Matsunami, Y. Yamamura, Y. Itikawa, N. Itoh, Y. Kazumata, S.
Miyagawa, K. Morita, R. Shimizu, and H. Tawara, ‘Energy dependence
of the ion-induced sputtering yields of monatomic solids,’ At. Data Nucl.

Data Tables 31, 1(1984).

D.K. Brice, J.Y. Tsao, and $.T. Picraux, ‘Partitioning of ion-induced
surface and bulk displacements,’ Nucl. Instr. Meth. B44, 68(1989).

G.K. Wehner, R.M. Warner, Jr., P.D. Wang, and Y.H. Kim, ‘Substitut-
ing low energy (< 30 eV) ion bombardment for elevated temperature in

silicon epitaxy,’ J. Appl. Phys. 64, 6754(1988).

T.Ohmi, T. Ichikawa, H. Iwabuchi, and T. Shibata, ‘Formation of device-
grade epitaxial silicon films at extremely low temperatures by low energy

bias sputtering,’ J. Appl. Phys. 66, 4756(1989).

Chapter 4

EPITAXY ON
HY DROGEN-TERMINATED

SILICON SURFACES

“Ts there any point to which you would wish to draw my attention?”
(Inspector Gregory)

“To the curious incident of the dog in the night-time.”

“The dog did nothing in the night-time.”

“That was the curious incident,” remarked Sherlock Holmes.

~ Silver Blaze

Sir Arthur Conan Doyle

4.1 Introduction

Adsorbates play an important role in low temperature silicon homoepitaxy.
Even a small coverage (0.01 - 0.1 ML) of adsorbates can change the evolu-
tion of surface morphology and hence the film microstructure. The common

adsorbates in an ultrahigh vacuum system are carbon, hydrogen and oxy-

120

Chapter 4 121

gen. In a TEM study of silicon films deposited using a silane beam, it was
shown that exposure of a Si(111)-7x7 surface to ethylene (prior to deposi-
tion) changed the growth mode from layer-by-layer to 3-D island nucleation
and growth [1, 2]. A similar conclusion was drawn in Section 2.7.2 for small
coverages (~ 0.01 ML) of carbon and oxygen through in situ RHEED ob-
sevations and ez situ SIMS analysis. Surface hydrogen has received a lot of
attention in recent years. Introduction of atomic hydrogen leads to a pre-
mature breakdown of epitaxy [3]. At the same time, it is interesting to note
that epitaxial silicon films can be deposited by MBE on a surface covered
with 1 ML of hydrogen atoms [4]. Furthermore, sputter deposition results
in epitaxial films even on a nominally dihydride-terminated 5i(001) surface
[5, 6]. What makes these results extraordinary is that there are no dangling
bonds at the surface and hence apparently no adsorption sites. In the only
atomically resolved study (using STM) of MBE on a hydrogen-terminated
Si(001) surface, it was observed that even a small coverage (< 0.1 ML) of
hydrogen atoms could dramatically increase the Si island density [7]. This
was interpreted as hydrogen atoms impeding the diffusion of silicon atoms.
We have used molecular dynamics simulations to understand the atom-
istics of the growth process. The calculations were performed using the Si-Si,
Si-H and H-H interatomic potentials described in Chapter 3. One can en-
vision different models for epitaxy on hydrogen-terminated silicon surfaces.
For example, the incident Si atom could (a) cause the surface hydrogen atoms
to desorb and thus create an adsorption site, (b) recoil implant the surface
hydrogen atoms and create an adsorption site, or (c) “subplant” itself, i.e.,

get implanted one layer below the surface. We will show through molecu-

Chapter 4

lar dynamics simulations that mechanism (c) is the pathway for epitaxy on

hydrogen-terminated Si(001) surfaces.

4.2 An Empirical Interatomic Potential for
Si—H Interactions

We have noted the important role of hydrogen in low temperature silicon
homoepitaxy. Hydrogen and silicon interact in many ways and in many
important processes of device fabrication. Hydrogen plays an important role
in the overall chemical vapor deposition growth mechanism from precursors
such as silane and disilane. Hydrogen in bulk silicon can passivate dopants
and deep level defects. In our work, hydrogen-termination of the surface
has been an important issue. Hydrogen-termination of silicon surfaces prior
to epitaxy in ultra-high vacuum has become increasingly popular due to
the relatively low desorption temperature of the passivation layer. Epitaxial
silicon layers have been deposited on hydrogen-terminated surfaces [5, 6,
4]. A low temperature Art ion beam-induced (2x1) reconstruction from
an initially dihydride-terminated Si(001) surface is discussed in Chapter 5.
Many of these processes occur on a time scale and crystal size scale which is
beyond the scope of a first principles approach but which can be described
with empirical force constants. An empirical Si-H potential is described
here for molecular dynamics simulations of the hydrogen-terminated silicon
surfaces and various gas-surface interactions.

Before proceeding to develop a potential, it is pertinent to ask whether

122

Chapter 4

a classical description of the silicon-hydrogen system is reasonable. A look
at the various configurations of silicon and hydrogen provides a good start.
The Si-H bonding in gas phase molecules and radicals is varied. Saturated
molecules such as SiH, and Si2Hg contain sp?-type bonds whereas p-type
bonds are found in SiH and SiH>. The molecule Si.H, exhibits z-bonding.
Hydrogen adsorption on a silicon surface can result in different reconstruc-
tions depending on coverage. The hydrogen atoms on the surface are quite
localized even at low coverages. Scanning tunneling microscope images at
low coverages reveal the location of hydrogen atoms [8] (or more precisely,
the unpaired electron opposite the hydrogen atom). This is in contrast to
some metals where a delocalized state of the proton has been observed at
low coverages [9]. The properties of hydrogen in bulk silicon depend on its
charge state [10]. An important position is the bond-centered site of atomic
hydrogen where it is bonded to two silicon atoms [11]. It is clear from this
brief description that some aspects, such as the dependence on charge state,
do not allow for a simple solution within a classical adiabatic framework.
Other aspects such as the different types of Si-H bonds and the multiple
bonding of hydrogen in the bond-centered site can be modeled, particularly
by making a special case for them. Finally, the strongly localized bonding of
hydrogen on silicon surfaces and the directional bonds on both the surface
and in molecules are features which readily permit a classical description.
It is clear from the above that this range of silicon-hydrogen interactions
provides a formidable challenge.

Empirical expressions for the Si-H potential have been developed previ-

ously [12, 13]. However, these potentials were not tested over a sufficiently

123

Chapter 4

wide range of configurations to determine their usefulness and limitations.
A classical potential with an expression similar to the one described here
was reported recently [14]. An earlier version of the potential described here
can be found in Ref. [15]. As described in Section 3.2.1, several interatomic
potentials have been developed to model silicon-silicon interactions [16, 17].
The strong directional bonding in silicon is described by a many-body term
attached to a Morse-type potential. The Si potential in Ref. [17] gives a good
description of the different allotropes of silicon and the $i(001) surface. This
has been extended to germanium and carbon [18] and has also been used
to describe the C-H interactions in hydrocarbons [19]. We have chosen this
form to model the Si-H interactions. The total potential energy is written

as a Sul Over pairs:

V=>> 4; (4.1)
i&; = { AF,(N) exp(—Airy) —BoF2(N) exp(—Aary)(1+G?)~* } fe(ry) (4.2)

Gy = DD fe(ta)[e+d{H(N) — cos6ju,}7] explaf(ry—Ry?)— (ra RY )}*] (4:3)
kAij
The valency of hydrogen is set by the parameters a, 6 and H in the many-

body part of the potential. A high value of a and 6 = 1 gives a monovalent
nature to hydrogen while a = 0 and H = —1 in the presence of two Si atoms
describes the bond-centered site in bulk Si. Here, F;, F2 and H are functions
of the coordination Ni, and Ni, of the #* Si atom. To obtain a continuous

function for the coordination, we write [19]

124

Chapter 4

Si Si Si H H Si
I I I Ila Ila Ila
Si Si Si
H H Si Si Si H
Ila Ila Ila IIb Ia nt
Si H H
H Si H H j 9 k
ik
Il Hl il Ill Tij Tik
H H 1

Figure 4.1: The combination of the potentials used for different triples. I is
the Si-Si potential, Ila and IIb are parts of the Si-H potential and III is the
H-H potential.

Nao) = dD £.(), Ng) = > £.(ty) and N = Ny 4NG 6)
j=(H) j=(Si)

(4.4)
1 » Ty < R-—D
f.(ty) = 4 4 — Ssin(n 8) + dsin(3rH®) .R-D0 ,t >R+D
(4.5)

A piecewise linear fit was used to compute the values of F,, Fy and H for
non-integral values of N. Numerical values for the parameters were obtained
by fitting the potential to the various silicon hydride molecules and interstitial
hydrogen sites in bulk silicon. For Si-Si and H-H interactions, the potentials

of Ref. [17] (Section 3.2.1) and Ref. [19] (potential I) were used, respectively.

Chapter 4 126

A combination of the three potentials is used to determine the potential
energy and forces for the different triples such as Si-Si-H, H-Si-H, etc., as
shown in Fig. 4.1. One could, in principle, derive a separate set of coefficients
for each of the triples. It was found that a single Si-H potential gives a
reasonable description in most situations, the exception being the Si-H-Si
triple. The Si-H bond energy of 3.42 eV for silane was obtained from the
heat of formation at 0 K [20], the values of 4.63 eV for Si cohesive energy [21]
and 2.375 eV for hydrogen [20], neglecting the zero point energy correction.
The Si-H bond length for silane was taken [22] as 1.476 A. The parameters
were also adjusted to give a reasonable fit to the stretch and bend modes
of various silicon hydride molecules. The value of 6 was taken to be the
same as that of the H-H potential [19]. The potential was cutoff at 2.00 A.
The parameters of the Si-H potential along with the Si-Si [17] and H-H [19]
potentials are listed in Table 4.1. The interstitial sites of atomic hydrogen
in bulk Si were used to determine the values of the parameters in column
IIb of Table 4.1. It is noted that the parameters in the potential were not
systematically optimized.

The bond lengths, angles and some vibrational wave numbers for the
SimH, molecules and radicals are shown in Table 4.2. The properties explic-
itly fitted to the Si-H potential have been indicated. The properties of the
Sig dimer and the H2 molecule are also included. The geometry and vibronic
properties of most molecules are fairly well reproduced. The bond length in
disilane is 0.07 A higher than the experimental value of 2.33 A [24]. Due
to the neglect of long-range interactions, the potential does not distinguish

between eclipsed and staggered forms of disilane. The experimental value

Chapter 4

Table 4.1: The parameters used in the Si-H interatomic potential along with

the Si-Si and H-H potentials.

Parameter Si-Si Si-H H-H
I Tla Iib | Il
(Ref. [17]) (Ref. [19])

A (eV) 1830.8 323.54 | - 80.07

Bo (eV) 471.18 84.18 | - 31.38

dy (A7}) 2.4799 2.9595 | - 4.2075

d2 (A?) 1.7322 1.6158 | - 1.7956

a (A-! or A~3) | 5.1975 4.00 0.00 | 3.00

B 3 3 - 1

R(®) (A) 2.35 1.475 | - 0.74

c - 0.0216 | 0.70 | 4.00

d 0.160 0.27 1.00 | -

h -0.59826 | - -1.00 | -

R (A) 2.85 1.85 - 1.40

D (A) 0.15 0.15 - 0.30

n 0.78734 | 1.00 - 1.00

5 0.635 0.80469 | - 0.80469

F,(1) - 1.005 | - -

F (2) - 1.109 | - -

F (3) - 0.953 | - -

Fj(n), n>4 - 1.000 ~ -

F2(1) - 0.930 | - -

F2(2) - 1.035 | - -

F2(3) - 0.934 | - -

Fo(n), n>4 - 1.000 - -

H(1) - -0.040 | - -

H(2) - -0.040 | - -

H(3) - -0.276 | - -

H(n), n>4 - -0.470 | - -

127

Chapter 4 128

for the rotation barrier is about 0.05 eV [25]. The predicted wave number of
the torsion mode therefore vanishes, for which a small value of 91 cm7! has
been estimated [22]. The energy differences for the decomposition reactions
of disilane are listed in Table 4.3. The values for the Si,H, and SiH3SiH de-
composition reactions deviate by about 0.7 and 0.4 eV respectively. There is
reasonable agreement between the values calculated from the potential and
the experimental/theoretical estimated values for the other reactions. It is
noted that these are the energy differences between the products and disilane
and not the activation energies for the reactions. The Si-Si bond length in
disilene is also larger than the experimental value. The z-bonding in this
molecule accounts for this large difference. The bond angle and the inver-
sion barrier in SiH3 are 106° and 0.21 eV respectively. The corresponding
experimental values are 110.5° and 0.23 eV respectively [29]. Most of the
vibrational wave numbers are within 15% of the experimental values.
Hydrogen termination of the silicon surface results in different reconstruc-
tions depending on coverage as shown in Fig. 4.2. A clean 5i(001) surface
exhibits a (2x1) reconstruction with the dimer bond along the <110> direc-
tion. The Si-Si interatomic potential gives a dimer bond length of 2.37 A.
For a hydrogen coverage of 1 monolayer (ML), the surface retains the (2x1)
reconstruction with hydrogen atoms terminating the dangling bonds of sili-
con. The Si-Si dimer length increases to 2.43 A. A similar lengthening of the
dimer bond was also reported in the semi-empirical [31] and ab initio cluster
calculations [32]. The H-Si-Si bond angle was found to be 112.4° compared
to the values of 110.2° [33] and 114.7° [31] reported in the literature. The

wave number of the symmetric stretch mode was 2144 cm~* compared to the

Chapter 4 129

Table 4.2: Properties of some Si,,H, molecules. Vibrational wave numbers
in cm~!. The bond energy of Hz includes the zero-point energy. Asterisk (*)
indicates a theoretically calculated value. The Si-H potential was explicitly
fitted to the properties marked by the { sign.

Si-H Expt./ Ref. Si-H Expt./ Ref.
Potential Theory Potential Theory

SiH, SiH

asi-H 1475A 148A [20] ¢ | asi-n 151A 1.51 A [22] *t

Esi-n 3.42eV 3.42eV [20] t | Esi-n 3.10eV 3.14eV [23] t

6y-si-H 109.5° 109.5° [20 tim 2034 2042 [23]

% 2100 2186 [23] t¢

v2 985 972 [23] | SiH,

v3 2151 2189 [23]

V4 913 913 [23] t | asi-w 151A 151A [22] *t
Esi-x 3.42eV 3.49 eV [20] t

SirHe 6y-si-H 92.3° 92.1° [28] ¢
A; sym stretch 2136 2032 = [28]

asi-H 1.48A 149A [24] | Ai bend 878 1004 [28]

asi-si 2.40A 2.33A [24]

6y_si-si 109.4° 110.3° [24]

Aj, Si-H stretch 2110 2163 [25] | SiHs

Ai, SiH; bend 894 920 [25]

Aig Si-Si stretch 387 432 [25] | asi- 1.48A 148A [22] *t

Ay, torsion 0 91 [22] * | Esi-n 3.21 eV 3.25 eV [20] t

E, Si-H stretch 2150 2155 [25] | @x-si-n 106° 110.5° [29]
Inv. barrier 0.21eV 0.23eV [29] t

SipH, vy 2051 —«-1955—[28]

asi-H 148A 148A [22}*| Hp

asi-si 2.36 A 217A {22]*

6y-si-si 106.0° 118.9° [22] * | ax-w 0.74A 0.74A [20]

busi 106.0° 112.8° [22] * | Ex-» 4.75 eV 4.75 eV [20]
PA 4400 4400 [30]

Sip
SiH3SiH

asi-si 230A 2.24A [26] *

Esi-si 2.66eV 3.13 eV [20] | asi-si 2.37A 239A [22] *

4 469 518 [27] | asi-n (1) 148A 148A [22]*
agin (2) 151A 151A [22] *
6y-si-si (1) 109.5° 114.2° [22] *
6y-si-si (2) 92.3° —-89.1° [22] *

Chapter 4

Table 4.3: The energy differences AH for disilane decomposition. The aster-
isk (*) indicates a theoretically estimated value.

Reaction Potential | Literature | Reference

SigHe — SiH35iH + H2| 1.91 eV 2.32 eV
SigHg — SiH, + SiH 2.03 eV 2.17 eV

experimental value of 2099 cm! [32]. At a coverage of 1.33 ML, a (3x1) re-
constructed surface consisting of alternate monohydride and dihydride units
is obtained[8, 34]. The H-Si-H angle in the dihydride units was found to
be 109.5° in agreement with the first principles calculations [35]. At a cov-
erage of 2 ML, the surface reverts to a (1x1) structure. There is strong
repulsion between H atoms bonded to neighboring Si atoms. A canted-row
structure was found to have a lower energy than the symmetric dihydride
structure. The H-Si—-H angle in the canted-row structure is about 106° com-
pared to 100° in the symmetric structure. The Si surface atoms are displaced
by about 0.16 A from their bulk positions in the canted-row structure. Al-
though the difference of 0.02 eV/(1x1) pair is small, it is significant that
a symmetry-breaking displacement produces a structure close in energy to
the symmetric structure. Such a canted-row structure was shown to have a
lower energy using the local density approximation [35]. A somewhat larger
difference of 0.18 eV/(1x1) pair and a Si surface atom displacement of 0.6 A
was reported in these calculations. Experimentally, dihydride-terminated

Si(001)-1x1 surfaces are found to be rough on an atomic scale, presumably

130

Chapter 4 131

due to H-H repulsion [8]. At low hydrogen coverages, hydrogen atoms have
been observed experimentally to pair up [8]. The difference in energy between
an isolated H atom and an H atom in a dimer pair was found to be 0.015 eV,
with the isolated atom having lower energy. This difference, albeit small, is
contrary to the experimental observation. Using the configuration interac-
tion method, it was shown in Ref. [33] that the H atom in a dimer pair had
a lower energy by ~ 0.05 eV. The driving force for pairing of H atoms thus
appears to be small. A 1 ML hydrogen coverage on the Si(111)-1x1 surface
gave a Si-H bond length of 1.48 A and the stretch mode of 2137 cm~!. The
experimental value for the stretch mode is 2084 cm™! [32]. An interesting
result is the possibility of formation of a bond-centered Si-H-Si site on the
surface. Although this has never been observed for silicon, such a bridge-
bonded site was recently observed experimentally on the GaAs surface [36].
It is noted that none of the surface properties were fitted to the Si-H potential
and the above results may be considered as predictions of the potential.

The interstitial positions of hydrogen in silicon have been studied ex-
tensively using first principles techniques. The important sites of atomic
hydrogen can be found in Ref. [37]. All the energies mentioned below are
with respect to H atoms in free space and bulk Si atoms. The minimum
energy site has been shown to depend on the charge state of hydrogen [10].
For both neutral H and Ht, the bond-centered (BC) site is the minimum
energy site [10, 11]. The set of parameters (labeled IIb in Table 4.1) in the
potential were adjusted to produce a minimum energy of atomic H at the
BC site. The Si-H bond length in this site is 1.54 A and the second nearest

neighbor atoms are displaced by 0.10 A. The bridged Si-H bond length in

Chapter 4 132

(a)

(c)

Figure 4.2: The different hydrogen-induced reconstructions of the silicon
surface. (a) The (2x1) monohydride structure with a hydrogen coverage
6 =1 ML, (b) the (3x1) structure with alternate monohydride and dihydride
units at 6 = 1.33, and (c) the (1x1) dihydride structure with @ = 2 ML. The
dimensions and angles are according the Si-H potential.

Chapter 4

the radical H3Si-H-SiH; is 1.58 A. This increase is due to the free motion
of the SiH3 units in the outward direction.

The Si-H bond lengths of 1.58 A and 1.72 A were obtained in the BC site
and the radical, repectively in ab initio cluster calculations [11]. The energy
at the BC site is 1.26 eV compared to 1.05 eV in Ref. [38]. A site near
C (on the line between C and T) was found to be 0.2 eV higher in energy
compared to the BC site. This site was reported to be the saddle point for
H diffusion between BC sites [10] with an activation energy of about 0.2 eV.
Among the other sites, the antibonding site AB was not a metastable site.
At both the tetrahedral interstitial T and the hexagonal interstitial H sites,
the H atom did not interact with any Si atoms. While this is clearly an
oversimplification, ab initzo calculations have shown that there is very little
relaxation of Si atoms when an H atom is placed at these sites [11, 39]. In the
H2 molecule oriented in the <100> direction at the tetrahedral interstitial
site, the H atoms were too far from the Si atoms to interact. The energy
per H atom was therefore 2.38 eV, same as in the free H2 molecule. A value
of 1.92 eV per H atom and an increase of 0.03 A in the H-H bond length
for the Hz molecule was reported with the local density approximation [38].
The energy per H atom in the H} complex (H atoms in adjacent BC and AB
positions) was 1.50 eV compared to 1.65 eV in Ref. [38].

There are several dynamic situations where one could apply the classical
potential described here. A brief analysis of the strengths and weaknesses
of the potential is thus appropriate. An area of considerable interest is the
low temperature chemical vapor deposition of silicon from precursors such

as SiH, and SigHg. The potential might be used to study the dissociative

133

Chapter 4

adsorption of these molecules on the Si(001) surface. However, one must
be more cautious with the dissociation of these molecules in the gas phase
because of the inadequate description of the SipH, molecule and the pres-
ence of ionized species. Hydrogen-terminated silicon surfaces are fairly well
described by the potential. Thus the potential may be used to study various
physical vapor deposition techniques such as molecular beam epitaxy and
sputter deposition of silicon. Another area of application might be modeling
of hydrogenated amorphous silicon. This seems reasonable, since the Si-H
bond lengths and the stretching and bending modes in hydrogenated amor-
phous silicon are not very different from those of the SiH, molecule and the
hydrogen-terminated silicon surface [40].

This potential is used here to study epitaxy of silicon on hydrogen-
terminated silicon surfaces and the beam-induced reconstruction of silicon

in Chapter 5.

4.3 Epitaxy on a Dihydride-Terminated
Si(001)-1x1 Surface

Figure 4.3 shows a HRTEM image of a film deposited by conventional
MBE on a nominally dihydride-terminated Si(001) surface. The growth rate
was 0.09 nm/s. The substrate preparation involved the chemical cleaning
described in Appendix A ending with the HF dip. This was followed by
baking overnight in the UHV chamber at the growth temperature of 190°C.

The deposited film is completely amorphous. Epitaxial silicon films have

134

Chapter 4

been deposited on a similar surface by bias sputtering at 300°C [5] and ion
beam sputtering at 210°C [6]. In Ref. [5], both the Si target and substrate
were biased and rf excitation was used to generate an Ar plasma. In Ref. [6],
a 750-1000 eV Art beam was incident on a Si target and the sputtered Si
was used to form the film. The main difference between conventional MBE
and sputter deposition is the incident particle energy. In MBE, Si atoms are
effused out at the temperature of the source and have an energy of ~ 0.2 eV.
In sputter deposition, the incident particle energy is ~ 5 eV.

In the molecular dynamics simulations, silicon atoms were incident nor-
mally on a dihydride-terminated $i(001)-1x1 surface. The canted-row struc-
ture (see Figure 4.2) was used as it corresponds to the minimum energy
configuration. The substrate had 24 Si layers with 100 atoms/layer. Pe-
tiodic boundary conditions were used in the transverse directions and the
bottom two layers were held rigid. The substrate temperature was held at
0 K and the simulations were followed for 1 ps. The incident atom energies
ranged from 0.25 to 10 eV.

The results of two simulations are shown in Figs. 4.4 and 4.5. These
atomic positions are at the end of 1 ps. In Fig. 4.4, the incident particle
energy was 0.25 eV, typical of conventional MBE. The incident Si atom was
not able to penetrate the layer of H atoms due to steric constraints. In
Fig. 4.5, the incident particle energy was 4 eV, typical of sputter deposition.
In this case, the incident Si atom is “subplanted,” i.e., implanted one layer
below the surface in the lattice. It not only penetrates the layer of H atoms

but also pushes a surface Si atom upward.

135

Chapter 4 136

Film

Substrate

2nm

Figure 4.3: HRTEM image of a silicon film deposited on an initially
dihydride-terminated $i(001)-1x1 surface. The substrate temperature was
190°C and the growth rate was 0.09 nm/s. The film is amorphous.

137

(a)
(b)

138

(d)
Figure 4.4: Molecular dynamics simulation of a 0.25 eV Si atom (blue) incident
on a dihydride-terminated $i(001)-1x1 surface. The atomic positions are at (a)
0 ps, ie. start of the simulation, (b) 0.15 ps, (c) 0.30 ps, and (d) 1 ps into the
simulation. Only the top layer of silicon atoms (green) and hydrogen atoms (red)
in the region of interest are shown.

139

(a)
(b)

140

Figure 4.5: Molecular dynamics simulation of a 4 eV Si atom (blue) incident on
a dihydride-terminated Si(001)-1x1 surface. The atomic positions are at (a) 0
ps, ie. start of the simulation, (b) 0.05 ps, (c) 0.10 ps, and (d) 1 ps into the
simulation. Only the top layer of silicon atoms (green) and hydrogen atoms (red)
in the region of interest are shown.

Chapter 4
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Oo O6F 4
fe)
SS 04-F
5. 0.2 - 5
0.0-F ~

l i

Energy (in eV)

Figure 4.6: The subplantation probability P, versus incident silicon atom
energy.

The subplantation probability P, is plotted as a function of incident par-
ticle energy in Fig. 4.6. The results shown are averages over 50 simulations
at each energy. An incident particle is considered subplanted if at the end of
1 ps it is below a surface Si atom. We see that P, rises very rapidly with inci-
dent particle energy. At 4 eV, which corresponds to the peak in the sputtered
particle energy distribution [41], almost two-thirds of the incident particles
are subplanted. At 0.25 eV, none of the incident Si atoms were subplanted.
Note that these probabilities are at the end of 1 ps and their values may
be different on the time scale of growth (~ 0.01 - 10 s). A small amount
of hydrogen sputtering was also observed and the results are summarized in

Table 4.4,

141

Chapter 4

Table 4.4: Hydrogen sputtering events during energetic silicon atom deposi-
tion on a dihydride-terminated 5i(001) surface.

Incident silicon Number of Number of
atom energy (eV) simulations hydrogen atoms
sputtered

0.25 50 0

2.0 50 0

4.0 50 0

6.0 50 1

10.0 50 4

The simulations suggest that in conventional MBE, the incident particle is
not able to penetrate the layer of hydrogen atoms. There is no good epitaxial
site at the level of the hydrogen atoms. A silicon atom deposited in the first
monolayer will form a stronger bond with the arriving Si atoms than with
the substrate Si atoms. This will result in a randomly networked structure,
or amorphous silicon. In sputter deposition, the SiH, unit segregates to the
surface. How do these results compare with experimental observations? In
Ref. [5], a (1x1) surface was observed in RHEED during the entire growth
of a 200 nm film whereas in Ref. [6], (2x1) spots were observed in low
energy electron diffraction (LEED) after ~ 10 nm deposition. While the
results after deposition of several layers are different in the two cases, it can
be concluded that the surface is (1x1) in the initial stages of growth. This,
together with the observation that the surface remains smooth on an atomic
scale [5, 6], is strongly indicative of surface segregation of hydrogen. The
simulations suggest that the surface Si-H bonds are not broken and it is the
entire SiH, unit that segregates to the surface. A small amount of hydrogen

loss by sputtering was observed in the simulations and this could result in

142

Chapter 4 143

a gradual transformation to a (2x1) structure as reported in Ref. [6]. The
rate of hydrogen loss in an experiment would be quite sensitive to the tail of
the sputtered particle energy distribution and the flux of energetic Ar recoils
from the target.

In the simulations, the incident Si atom does not always end up in an
epitaxial position. It is usually in an interstitial position to maximize the
number of bonds. This is expected since more than one atom would have
to be deposited to get an epitaxial layer. Finally, it is noted that these
simulations only suggest a mechanism for the initial stages of epitaxy. Sputter
deposition also produces epitaxial films at low temperatures and high growth
rates compared to conventional MBE. The energy of the incident particles

thus also serves to smooth the surface during growth.

4.4 Epitaxy on a Monohydride-Terminated
Si(001)-2x1 Surface

Figure 4.7 shows a HRTEM image of a silicon film deposited at 380°C by
conventional MBE on an initially monohydride-terminated $i(001)-2x1 sur-
face. The growth rate was 0.02 nm/s. The substrate preparation involved
the chemical cleaning described in Appendix A ending with the HF dip. The
substrate was then heated and maintained at 380°C for 30 minutes to get
the dihydride-to-monohydride transition. Since complete hydrogen desorp-
tion occurs at a much higher temperature (T ~ 450 - 500°C), the surface
coverage is believed to be close to 1 ML. The XTEM image of the film is

Chapter 4

quite typical of low temperature deposited silicon films. There is an initial
region of epitaxial growth followed by the breakdown of epitaxy. A twinned
region can be seen near the surface. The important observation, however, is
that the initial growth is epitaxial even with 1 ML coverage of hydrogen.

Epitaxial silicon films on a monohydride-terminated $i(001) surface (at
370°C) were first reported in Ref. [4]. More recently, it was observed that
Si films were epitaxial when deposited above 200°C [42]. It was also shown
that hydrogen atoms segregate to the surface during growth [42].

Molecular dynamics simulations similar to the one described in the pre-
vious section were employed to study the atomistics of the growth process.
The substrate size and boundary conditions were the same as in the previous
section. The geometry of the (2x1) surface is shown in Fig. 4.2. The initial
substrate temperature was 0 K. The incident Si atoms had a kinetic energy
of 0.25 eV.

The atomic positions after 1 ps in two simulations are shown in Fig.4.8.
In Fig. 4.8(a), the incident Si atom is subplanted in the lattice whereas in
Fig. 4.8(b), the Si atom is in the same layer as the H atoms. Here, the
subplantation is driven in large part enthalpy difference (4.63 eV) between
a vapor phase and a solid phase silicon atom. The incident atom accelerates
toward the surface as it gains its binding energy and is occasionally sub-
planted. The simulations suggest that it is the SiH unit that segregates to
the surface. The subplantation probability was 0.1 averaged over 50 simu-
lations. While this is rather small, it is possible that simulation at a higher
substrate temperature and for a longer time might result in a subplantation

probability consistent with efficient SiH segregation and Si epitaxy. These

144

Chapter 4 145

10 nm

Film

Substrate

ss
Siento

Figure 4.7: Epitaxial silicon film deposited on an initially monohydride-
terminated $i(001)-2x1 surface. The substrate temperature was 380°C and
the growth rate was 0.02 nm/s.

146

(b)

Figure 4.8: The atomic positions after 1 ps of simulation for two different impact
points of the incident silicon atom. The incident atom (blue) is subplanted in
(a) but remains at the level of hydrogen atoms in (b). The incident atom had a
kinetic energy of 0.25 eV. Only the top layer of silicon atoms (green) and hydrogen
atoms (red) in the region of interest are shown.

Chapter 4 147

results also do not rule out the possibility of an adatom breaking a surface
dimer bond followed by the transfer of a hydrogen atom to the adatom. This

would only result in H segregation but not the SiH unit.

4.5 Discussion

Introduction of atomic hydrogen during low temperature Si MBE can cause
an early breakdown of epitaxy [3]. However, conventional MBE results in
epitaxial films even with a uniform surface coverage of 1 ML [4]. These re-
sults appear to be contradictory but can be explained as follows. At low
surface coverages, hydrogen atoms act as diffusion barriers which results in
a dramatic increase in Si island density [7]. This accelerates the increase in
surface roughness and causes an early breakdown of epitaxy. Our molecular
dynamics simulations have provided some insight into the mechanism of epi-
taxy at large hydrogen coverages. The simulations suggest that the incident
silicon atom is subplanted during epitaxy on hydrogen-terminated $i(001)
surfaces. On the dihydride-terminated surface, it appears that the SiH unit
segregates on the surface which is in agreement with the experimental obser-
vations [5, 6]. The subplantation probability was found to rise very rapidly
with the incident particle energy. On the monohydride-terminated surface,
the results are less conclusive. It appears that the SiH unit segregates to
the surface at least on some occasions. This would be consistent with the
observed surface segregation of hydrogen [42].

It is instructive to compare these results with the case of epitaxy on a

Chapter 4 148

clean $i(001)-2x1 surface. Molecular dynamics simulations have shown the
opening of a dimer when an adatom is in the vicinity [43]. Subplantation
of the incident Si atom has also been observed occasionally [44, 45] in MD
simulations. However, for epitaxial growth it is not necessary for the incident
atom to be subplanted. On a hydrogen-terminated silicon surface (with high
coverage), there are no good epitaxial sites at the level of hydrogen atoms. It
appears that (at least on the dihydride-terminated surface) epitaxial layers
are produced by subplanting the incident silicon atom.

It was mentioned earlier that both the monohydride- and dihydride-
terminated Si(001) surfaces have no dangling bonds. This makes these sur-
faces extremely unreactive. A dihydride-terminated surface can resist oxida-
tion for as long as 12 hours in a laboratory atmosphere [46]. A monohydride-
terminated surface remains (2x1) reconstructed even after exposure to air
for a few minutes [47]. The possibility of doing epitaxy on such surfaces with
sputter deposition is therefore extremely interesting. A problem with sputter
deposition is the implantation of energetic Ar recoils in the film. This can
be overcome with techniques such as pulsed laser deposition which produce
a hyperthermal beam of silicon atoms. One might then be able to deposit

epitaxial silicon films even under high vacuum conditions.

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Chapter 4

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Chapter 4 152

[25] J.R. Durig and J.S. Church, ‘Vibrational spectra of crystalline disilane
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[32] Y.J. Chabal, G.S. Higashi, K. Raghavachari, and V.A. Burrows,‘Infrared
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Chapter 4

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[35] J.E. Northrup, ‘Structure of $i(100)-H — dependence on the H chemical
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[36] H.H. Qi, P.E. Gee, and R.F. Hicks, ‘Infrared study of hydrogen adsorbed
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[37] S.M. Myers, M.I. Baskes, H.K. Birnbaum, J.W. Corbett, G.G. DeLeo,
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153

Chapter 4 154

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[47] M. Hirose, private communication.

Chapter 5

LOW TEMPERATURE ION
BEAM-INDUCED Si(001)-2x1
SURFACE
RECONSTRUCTION

What one man can invent another can discover.

~ Sherlock Holmes, The Adventure of the Dancing Men

Sir Arthur Conan Doyle

5.1 Introduction

Surface cleaning of silicon is a recurring theme during VLSI processing. A
passivating surface layer is always present to protect the underlying silicon
from contaminants. The choice of the passivation layer depends on the pro-

cessing step. The chemical oxide is used prior to the gate oxidation step in

155

Chapter 5

MOS device fabrication, formation of refractory metal silicides such as WSin,
and Ti-W barrier layers. Hydrogen termination is used prior to the deposi-
tion of transition metals to form silicides such as CoSig. The choice of the
passivation layer to form the metal silicides is related to the ability of the
metal atoms to reduce the oxide [1].

A clean silicon wafer is immediately covered with an oxide when exposed
to atmosphere. This native oxide grows to a thickness of ~ 1 —- 2 nm and
passivates the underlying silicon. The surface also frequently contains hydro-
carbons and metal contaminants. A chemical oxide prepared by oxidation in
an alkaline or acidic peroxide solution is frequently preferred over the native
oxide. Another common way of passivating the silicon surface is to terminate
the surface dangling bonds with hydrogen. This is usually achieved by a di-
lute HF dip which etches the oxide and terminates the surface with hydrogen
atoms.

For silicon homoepitaxy, the passivation layer is removed to obtain a
clean, reconstructed $i(001)-2x1 surface. Thermal desorption of the oxide
requires heating to 800°C [2]. Alternatively, the oxide can be removed by
using an ion beam of silicon or a noble gas such as argon. Cleaning with a
silicon beam reduces the desorption temperature to about 700°C [3]. Sputter-
ing with Art ions can be done at ~ 500°C but a high temperature anneal is
frequently required to remove the ion damage. Complete thermal desorption
of hydrogen occurs at ~ 500°C [4].

A number of techniques are being developed to reduce the processing
temperature in epitaxy, oxidation and doping. A method for the preparation

of clean Si(001)-2x1 surfaces at low temperatures is needed to complement

156

Chapter 5 157

these processes. In this chapter, a method analogous to the sputtering of
the SiO, layer with noble gas ions is described to remove the hydrogen from
the surface. Reconstructed Si(001)-2x1 surfaces have been prepared even at
room temperature (~ 50°C) in this way. Silicon films were deposited after

ion irradiation as a test of the cleaning process.

5.2 Beam-Induced Reconstruction of Silicon

5.2.1 Sample Preparation

The chemical cleaning of the silicon wafers is described in Appendix A. After
the dilute HF dip, a hydrophobic, unreconstructed and nominally dihydride-
terminated Si(001) surface is obtained. The wafer was then loaded into the
UHV chamber and baked overnight at the desired ion irradiation tempera-
ture.

The Kaufman source was used to generate Art ions. The Art ion energy
was 50 eV in all experiments, and the ions were incident along the <100>
azimuth within 5°. The incident angle of the beam was varied in some cases
to study the effects. An electron cyclotron resonance source was used to
generate Het ions. The source was operated at 130 W and a pressure of
0.07 Pa. The substrate was oriented at 45° with respect to the axis of the
ECR ion source. Both argon and helium were passed through a gas purifier
rated to give a purity of 10 ppb. The surface morphology was monitored in

situ using RHEED during ion irradiation and subsequent film growth.

Chapter 5

5.2.2 Reflection High-Energy Electron Diffraction

The RHEED pattern along the <110> azimuth from an as-inserted Si(001)
wafer is shown in Fig. 5.1(a). A (1x1) pattern characteristic of a dihydride-
terminated Si(001) surface is observed. The surface was then irradiated with
an ion beam. During ion irradiation, the half-order lines appear gradually
indicating the loss of surface hydrogen. The RHEED pattern after a dose of
1.5 x 10!6 Art ions/cm? and an incidence angle of 45° is shown in Fig. 5.1(b).
The substrate temperature was 190°C. The ion flux was ~ 5 x 10??/cm?-s.

At 150°C and below, we were unable to obtain reconstructed $i(001)
surfaces with 50 eV Art ions incident at 45°. The surfaces gradually became
amorphous upon ion bombardment. However, a more grazing angle of 65°
with respect to the surface normal resulted in a (2x1) reconstructed surface.
A (2x1) surface prepared at 100°C with an Art flux of 2 x 101% ions/cm?-s
for 10 min. is shown in Fig. 5.1(c). The same process at 60°C resulted in
amorphization of the surface region. Thus, with 50 eV Ar?* ion irradiation,
(2x1) reconstructed surfaces were observed at 100°C and above.

Exposure to a helium plasma, generated using an ECR source, also pro-
duced (2x1) surfaces. The ECR source was operated at 130 W and a pressure
of 0.07 Pa. A crude Langmuir probe measurement indicated Het ion energies
in the range of 10 - 30 eV. (The Het flux is estimated to be 5 x 10'%/cm?-s
to within a factor of 3). RHEED patterns after Het ion bombardment for 25
min. at 190°C and 20 min. at 50°C are shown in Fig. 5.1(d) and(e) respec-
tively. To our knowledge, this is the first observation of a (2x1) reconstructed

Si(001) surface produced at “room temperature.”

158

Chapter 5

It is noted that reconstruction lines were clearly visible after a quarter
of the total dose used in the above experiments. It is not possible to dis-
tinguish between a monohydride-terminated surface and a clean $i(001)-2x1
surface from the geometrical features in a RHEED pattern. Molecular dy-
namics simulations described below suggest that the surfaces are almost free

of hydrogen for the dose of ions used in these experiments.

5.2.3 Transmission Electron Microscopy of Silicon
Films

Silicon films were deposited on the S$i(001)-2x1 surfaces produced by ion
irradiation. The deposition temperature was the same as the ion irradiation
temperature. Figures 5.2 and 5.3 show high resolution XTEM images of films
grown on substrates prepared at 190°C by Art and Het™ ion beam-induced
reconstruction respectively. The growth rates were 0.09 and 0.03 nm/s re-
spectively. The film-substrate interface is visible presumably due to car-
bon and/or oxygen impurities. In both cases, the film growth starts out
epitaxially. This is in sharp contrast to the film deposited on a dihydride-
terminated surface (see Fig. 4.3) which is completely amorphous. The films,
however, do contain some defects. A stacking fault is seen to originate at the
film/substrate interface in Fig. 5.3. The crystal-state — amorphous-state
transition is also seen in these films, as expected.

Figure 5.4 shows the high resolution XTEM image of a silicon film de-
posited at 100°C following Art ion beam-induced reconstruction. The film-

substrate interface proved hard to locate due to the thickness fringes. The

159

Chapter 5 160

(e)

Figure 5.1: RHEED pattern (a) immediately after HF dip; after 50 eV Art
ion irradiation at (b) 190°C, and (c) 100°C; and after exposure to Het ions
at (d) 190°C, and (e) 50°C.

Chapter 5 161

Film

‘ Substrate

. ‘

a ate
‘.
tat

sg
ints Se
eae tet

sate
a sg hag ig he

sf,
oe

Se ed eee es

Figure 5.2: HRTEM image of a silicon film deposited after beam-induced
reconstruction using 50 eV Art ions incident at 45° with respect to the
substrate normal. The substrate temperature was 190°C and the growth
rate was 0.09 nm/s.

Chapter 5 162

Film

2 Substrate

5 nm

Figure 5.3: HRTEM image of a silicon film deposited after beam-induced
reconstruction using Het ions. The substrate temperature was 190°C and
the growth rate was 0.03 nm/s.

Chapter 5 163

film was judged to be epitaxial from the measured thickness on the quartz
crystal monitor. The rough crystal-amorphous interface is also indicative of
an initial regime of epitaxial growth. Figure 5.5 shows the XTEM image of
a film deposited at 50°C after exposure to He* ions. The very rapid trans-
formation to amorphous film deposition at such low temperatures makes it
difficult to say if the film is epitaxial. A faint contrast marked by arrows in
Fig. 5 is suggestive of a film-substrate interface and an epitaxial thickness of

about 0.5 — 1 nm.

5.3. Molecular Dynamics Simulations of the
Beam-Induced Reconstruction

To understand the nature of the depletion of surface hydrogen, molecular
dynamics simulations were used. The Si-Si, Si-H and H-H interatomic po-
tentials were described in Chapter 3. The Ar-H and Ar-Si interactions were

taken to be purely repulsive, with Born-Mayer type expressions:

V(r) = Aexp(—Ar)f-(r) (5.1)

For the Ar-—Si potential, the Abrahamson parameters A = 5941.7 eV and
» = 3.6641 A-! were used [5]. The potential was cutoff with R = 3.25 A
and D = 0.15 A. The parameters A = 746.6 eV and \ = 4.1898 A~! for the
Ar-H potential were likewise obtained by combining the repulsive part of the
H-H potential [6] and the Ar—Ar potential [5]. The potential was cutoff with
R = 2.35 A and D = 0.15 A. The cutoff function, f.(r), has the form given
in Eq. 3.18.

Chapter 5 164

Film

Substrate

5 nm

Figure 5.4: Silicon film deposited after beam-induced reconstruction using
50 eV Art ions incident at 65° with respect to the substrate normal. The
substrate temperature was 100°C and the growth rate was 0.03 nm/s.

Chapter 5

5 nm

Figure 5.5: Silicon film deposited after beam-induced reconstruction using
He* ions. The substrate temperature was 50°C and the growth rate was
0.03 nm/s. The thin oxide at the surface is also visible.

165

Chapter 5

In the simulations, Ar ions were incident at 50° with respect to the sur-
face normal and 5° from the <100> azimuth. There were a total of 24
Si layers with 100 atoms/layer in the substrate. The sputtering of H and
Si atoms was estimated from both monohydride- and dihydride-terminated
5i(001) surfaces. Periodic boundary conditions were used in the transverse
directions and the bottom two layers were held rigid. The starting substrate
temperature was 0 K and the simulations were carried out for 1 ps. The
incident Ar ion energy ranged from 15 to 50 eV. The results presented below
are all averaged over 50 simulations at each energy.

On both dihydride- and monohydride-terminated surfaces, hydrogen was
removed by both sputtering and implantation. The hydrogen sputtering and
implantation yield are shown in Figs. 5.6 and 5.7 for the dihydride- and
monohydride-teminated $i(001) surfaces. The sputtered species observed
were atomic H, Ho, and SiH». If sputtering were independent of the bonding
of hydrogen atoms, one would expect the yield from the dihydride surface
to be twice that from the monohydride surface. The hydrogen sputtering
yield from the dihydride surface is seen to be much more than twice that of
the monohydride surface. At 25 eV and below, the sputtering yield from the
monohydride surface is seen to be negligible whereas that from the dihydride
surface is finite. The implantation yields are seen to be comparable to the
sputter yields. Due to the short time period of the simulations, it is not clear
whether the implanted hydrogen would diffuse into the bulk or toward the
surface. Even if all the hydrogen is lost only by sputtering, the calculated
yields suggest that almost all the surface hydrogen was removed by ion ir-

radiation in the experiments described in Section 5.2.2. It was reported in

166

Chapter 5

2.0 i i i i

15 4

Hydrogen Sputtering Yield

Energy (in eV)

Figure 5.6: The sputtering yield of hydrogen versus Ar ion energy from
(a) o dihydride-terminated $i(001)-1x1 surface, and (b) e monohydride-
terminated Si(001)-2x1 surface. The lines are spline fits to guide the eye.
Ref. [7] that Si films deposited on a monohydride-terminated surface were
only epitaxial above 200°C (for a growth rate of 1 ML/min). The growth
of epitaxial films after beam-induced reconstruction (Section 5.2.3) suggests
that most of the surface hydrogen was removed.

A surprising result was the sputtering yield of silicon which is shown in
Fig. 5.8. On dihydride-terminated surfaces, there is strong repulsion between
H atoms bonded to neighboring Si atoms. This gives rise to a rather low
threshold for the sputtering of the SiH, unit. The onset of SiH, sputtering
can be seen at about 25 eV incident ion energy. It is noted that the sputtering
yield of silicon from a clean surface is negligible (< 1%) at these energies [8].
This may be, therefore, considered as a case of chemically-enhanced physical

sputtering of silicon.

167

Chapter 5 168

2.0 i ] T i

Hydrogen Implantation

Energy (in eV)

Figure 5.7: The implantation of surface hydrogen atoms versus Ar ion energy
from (a) o dihydride-terminated $i(001)-1x1 surface, and (b) e monohydride-
terminated 5i(001)-2x1 surface. The lines are spline fits to guide the eye.

1.0 ‘ I i q

0.8 + -

0.6 4

0.4b 4

Silicon Sputtering Yield

O.0 beer Qe etc eenetees -

0 20 40 60 80 100
Energy (in eV)

Figure 5.8: The silicon sputtering yield from (a) o dihydride-terminated
Si(001)-1x1 surface, and (b) e monohydride-terminated Si(001)-2x1 surface.

The lines are spline fits to guide the eye.

Chapter 5

5.4 Discussion

Ion bombardment also results in atomic displacements in the silicon sub-
strate. The surface can be amorphized if the beam flux is too high and
insufficient time is available for annealing. At a more moderate beam flux,
the surface roughens but does not become amorphous. The broadened Bragg
rods in Fig. 5.1(b) and (c) are indicative of rough surfaces. Significant sur-
face and sub-surface atomic displacements can occur with the use of 50 eV
Art ions as seen in Section 3.4. Helium ion bombardment produces more
smoother surfaces compared to argon ions. For a two-body collision, the
energy transfer from an incident atom of mass M, to a target atom of mass
M2 is determined by the y = 4M:M2/(Mi + M2)? factor. Helium ions with
= 0.64 can transfer energy much more efficiently to hydrogen atoms com-
pared to argon ions with y = 0.12. The helium beam-induced reconstructed
surface shown in Fig. 5.1(d) looks similar to a (2x1) surface obtained by
thermal desorption of hydrogen. The “room temperature” surface shown
in Fig. 5.1(e), however, shows some broadening of the Bragg rods. The
improvement in the surface morphology by going to more grazing angles of
incidence can be attributed to the increased energy loss of the ions at the
surface.

After an HF dip, the surface frequently has some amount of physisorbed
hydrocarbons [9]. At the extremely low temperatures used in the experiments
above, these contaminants may not be desorbed during the bake before ion
irradiation. It is remarkable that (2x1) surfaces could still be obtained.

It is possible that small amounts of physisorbed hydrocarbons can also be

169

Chapter 5

removed by the ion beam.

Surface cleaning with remote hydrogen and helium plasmas was reported
at temperatures 250°C and higher in Refs. [10, 11]. A (3x1) reconstructed
surface was obtained after exposure to a remote hydrogen plasma which
changed to a (2x1) structure after exposure to a remote He plasma. The
use of a hydrogen beam had the added advantage of reducing the C and O
contamination at the substrate surface.

The beam-induced reconstruction results suggest that low energy ion
beams can be used to control the hydrogen coverage on the surface. The
preferential removal of dihydride-units can be used to keep the H surface
coverage below 1 ML, which is beneficial for the growth of epitaxial films by
MBE. Another application is the low temperature chemical vapor deposition
of silicon where growth rates are rather low and limited by the hydrogen de-
sorption from the surface [12]. Hydrogen removal with low energy ion beams
can increase the growth rate tremendously.

In conclusion, the removal of surface hydrogen at low temperatures with-
out causing damage to the silicon substrate has been demonstrated. The
use of low energy ions incident at a grazing angle helps to keep most of the
atomic displacements in the top layer(s). Both argon and helium ions have
been used successfully for the beam-induced reconstruction, although helium
ions gave slightly better results. The (2x1) surfaces thus prepared were suit-
able for silicon homoepitaxy. High resolution TEM images of silicon films
have occasionally shown defects originating at the film/substrate interface in-
dicating some ion damage. Molecular dynamics simulations have shown that

sputtering of hydrogen from dihydride units was much higher than monohy-

170

Chapter 5 171

dride units. A chemically-enhanced physical sputtering of silicon was also
observed on hydrogen-adsorbed surfaces.

The phenomenon of beam-induced reconstruction deserves a further study.
The use of lower energy ions and more grazing angles of incidence need to
be investigated. The damage produced by the ions on scales larger than that

observable in an XTEM image will have to be established for any application.

Bibliography

[1] A-H. Reader, A-H. van Ommen, P.J.W. Weijs, R.A.M. Wolters, and
D.J. Oostra, ‘“Transition-metal silicides in silicon technology,’ Rep. Prog.

Phys. 56, 1397(1993).

[2] A. Ishizaka and Y. Shiraki, ‘Low temperature surface cleaning of silicon

and its application to silicon MBE,’ J. Electrochem. Soc. 133, 666(1986).

[3] M. Tabe, ‘Etching of SiO2 films by Si in ultrahigh vacuum,’ Jpn. J.
Appl. Phys. Part 1, 21, 534(1982).

[4] G. Schulze and M. Henzler, ‘Adsorption of atomic hydrogen on clean
cleaved silicon (111),’ Surf. Sci. 124, 336(1983).

[5] A.A. Abrahamson, ‘Born-Mayer type interatomic potential for neutral

ground state atoms with Z = 2 to Z = 105,’ Phys. Rev. 178, 76(1969).

[6] D.W. Brenner, ‘Empirical potential for hydrocarbons for use in simulat-
ing the chemical vapor deposition of diamond films,’ Phys. Rev. B42,
9458(1990).

[7] M. Copel and R.M. Tromp, ‘H-Coverage dependence of $i(001) homoepi-
taxy,’ Phys. Rev. Lett. 72, 1236(1994).

172

Chapter 5

[8]

[10]

[11]

Data Tables 31, 1(1984).

S. Nikzad, 5.5. Wong, C.C. Ahn, A.L. Smith, and H.A. Atwater, ‘In
situ reflection electron energy loss spectroscopy measurements of low
temperature surface cleaning for Si molecular beam epitaxy,’ Appl. Phys.

Lett. 63, 1414(1993).

T. Hsu, L. Breaux, B. Anthony, S. Banerjee, and A. Tasch, ‘Defect
microstructure in low temperature epitaxial silicon grown by RPCVD,.’

J. Elec. Mat. 19, 375(1990).

A. Mahajan, J. Irby, D. Kinosky, R. Qian, S. Thomas, S. Banerjee, A.
Tasch, and T. Picraux, ‘Si atomic layer epitaxy based on SigHs and

remote He plasma bombardment,’ Thin Sol. Fi. 225, 177(1993).

S.M. Gates and $.K. Kulkarni, ‘Hydrogen coverage during Si growth
from SiH, and Si2H¢,’ Appl. Phys. Lett. 60, 53(1992).

173

Chapter 6
SUMMARY

“That is final,” said Lestrade.
“Yes, that is final,” I (Watson) involuntarily echoed.

“It is final,” said Holmes.

- The Adventure of the Norwood Builder
Sir Arthur Conan Doyle

6.1 Silicon Molecular Beam Epitaxy

Historically, advancing integrated circuit technology and understanding the
physics of thin film growth have served as two motivating factors for studying
semiconductor epitaxy. Silicon epitaxy has particularly benefitted from the
concurrence of these factors. This has led to the development of many differ-
ent schemes for silicon film deposition. The optimum ambient conditions for

growing defect-free epitaxial films have been studied in great detail. There

174

Chapter 6

has also been a very consistent drive toward lower growth temperatures.
Molecular beam epitaxy made it possible to grow Si films at temperatures as
low as 500°C. Although not used in the integrated circuit industry because
of low throughput and excessive maintenance costs, the possibility of fab-
ricating layered structures with exceptional control down to the monolayer
level made it popular as a research tool. It also allowed one to control the
different variables associated with thin film growth. As a result, many of the
phenomena associated with the surface and growth at temperatures greater
than about 400°C are known at the atomic scale.

Molecular beam epitaxy at temperatures lower than 400°C proceeds by
the now familiar crystal-state—amorphous-state transition. It was the dis-
covery of this phenomenon [1, 2] which renewed interest in the physics of low
temperature silicon MBE. As discussed in Chapter 1, the number of variables
influencing atom migration on the surface are staggering. Nowhere are these
more important than in low temperature epitaxy. It was the objective of
this work to explain their influence on the film microstructure. The follow-
ing chapter summarizes the current understanding of silicon molecular beam

epitaxy at low temperatures and issues that need to be further addressed.

6.2 Summary of Results

An atomistic model, the twin-boundary/facet mechanism, has been proposed
for the crystal-state—amorphous-state transition observed in low temper-

ature silicon molecular beam epitaxy. The increase in surface roughness

175

Chapter 6

during film growth has been directly tied to the breakdown of epitaxy. Ad-
sorbates such as carbon and oxygen can dramatically increase the surface
roughness even at small coverages (~ 0.01 ML). They thus play an indirect
role by accelerating the surface roughening rate, but do not directly induce
the crystalline-to-amorphous transition on the smooth starting surface, for
coverages of interest here (0 < @ < 0.2 ML).

Molecular dynamics simulations suggest that epitaxy on hydrogen-term-
inated silicon surfaces (at high hydrogen coverage) proceeds by subplantation
of the incident Si atom and segregation of SiH, units. The remarkable suc-
cess of sputter deposition in growing epitaxial films on a dihydride-terminated
Si(001) surface is explained by the very rapid rise in the subplantation prob-
ability with the incident Si atom energy.

An empirical interatomic potential has been developed to describe Si-H
interactions. This can be used, with caution, for molecular dynamics inves-
tigations of hydrogen-terminated silicon surfaces, chemical vapor deposition
of silicon and hydrogenated amorphous silicon.

A technique for low temperature $i(001)-2x1 substrate preparation was
developed to complement the various low temperature processes that are
being developed for device fabrication. This was achieved by low energy
noble gas ion (Art or Het) irradiation of a nominally dihydride-terminated
Si(001)-1x1 surface. Reconstructed $i(001)-2x1 surfaces were prepared at

temperatures as low as 100°C. Silicon films deposited on such surfaces were

176

Chapter 6 177

epitaxial.

6.3 The Crystal-state—Amorphous-state
Transition

6.3.1 The Role of Surface Roughness

We will begin with the central issue of low temperature silicon homoepi-
taxy, namely, the crystal-state—amorphous-state transition. The twin-
boundary/facet mechanism (Section 2.5) accounts for most of the observa-
tions regarding the breakdown of epitaxy. The evolution of surface morphol-
ogy plays a key role in this transition. Due to limited surface diffusion at
low temperatures, adatoms are not able to reach a step edge. Formation of
islands on top of islands, i.e., 3-D islanding, is thus a consequence of limited
adatom mobility. The sequence of atomic force microscope images (see Fig.
2.16) of a film at different thicknesses clearly shows the surface roughening.
This can also be inferred from the broadening of the Bragg rods and the
appearance of a transmission-like pattern in RHEED (see Fig. 2.17). This
roughening is due to kinetic effects although some low index orientations
such as the {111} and {311} will be favored by their lower surface ener-
gies. Such facets can be identified in XTEM images (Fig. 2.11). Now, twin
boundaries can nucleate on {111} oriented surfaces since they cost relatively
little energy. A twin boundary is a mirror image along a {111} plane. The

crystal is still composed of even-member rings after the formation of a twin

Chapter 6 178

boundary (which accounts for its low energy). However, when a twinned
region grows and meets a different surface of the perfect crystal, it inevitably
results in the formation of five- and seven-member rings. At intermediate
temperatures (150 < T < 400°C), crystalline silicon continues to grow after
the formation of a grain boundary because a crystalline network (plus a grain
boundary) has lower energy than an amorphous network. This can be seen
in the XTEM images of films at 240 and 370°C (Section 2.4). Eventually,
the number of such grain boundaries increases and there is a gradual tran-
sition to amorphous silicon deposition. At low temperatures (T < 150°C),
the transition to amorphous silicon seems to be direct (Section 5.2.3). This
could be due to the nucleation and growth of amorphous silicon very rapidly
after the formation of a twin boundary. It is noted that the breakdown of
epitaxy in other semiconductors such as Ge and GaAs can be understood in
an analogous way.

A fundamental difference between crystalline and amorphous silicon is in
the type of ring structures formed by silicon atoms. Crystalline silicon con-
tains only even-membered rings. The continuous random network models of
amorphous silicon show that it consists of five- and seven-member rings in
addition to six-membered rings (and higher odd and even-membered rings).
A mechanism for the breakdown of epitaxy must therefore provide a way for
the nucleation of odd-membered rings. The TBF mechanism leads to the
forced formation of five- and seven-member rings. An alternate mechanism
involving the trapping of an adatom at the T, site on a {111} facet was pro-
posed recently [3]. I do not see a simple way to distinguish between the two

mechanisms from the current data. The low temperature Si films definitely

Chapter 6 179

show twinning. We speculate that the TBF is operative at all temperatures
and the other mechanism becomes active at some lower temperature.

At this point, it is appropriate to consider some of the remarks that have
been made regarding low temperature silicon homoepitaxy. It was noted in
Ref. [4] that epitaxy on Si(111) breaks down at the edge of a twin boundary.
Molecular dynamics simulations also showed the breakdown of epitaxy at
the edge of a stacking fault [4]. In Refs. [5, 6], it was observed that the
stacking fault was preserved during room temperature epitaxy on Si(111)-
7x7. Amorphous silicon starts right at the edge of the stacking fault, just
as expected from the TBF mechanism. It has also been remarked that the
reason for the finite epitaxial thickness on clean $i(001) is due to the difficulty
of nucleating amorphous silicon on this surface [2]. This is borne by the TBF
mechanism which requires the formation of a faceted surface to initiate the

breakdown of epitaxy.

6.3.2 The Role of Low Energy Ion Irradiation

The TBF mechanism is an intrinsic mechanism, i.e., it predicts the break-
down of epitaxy even in the absence of any adsorbates. Thus, if one wants
to deposit epitaxial silicon films on 5i(001) at low temperatures, the sur-
face roughening, and specifically, faceting must be prevented. Concurrent
low energy ion irradiation during growth is one way to reduce the surface
roughening. Films with increased epitaxial thickness were obtained with ion
beam-assisted molecular beam epitaxy compared to conventional MBE. Ar-

gon ions with 50 eV gave slightly better results compared to 70 eV ions.

Chapter 6 180

Improvement in the crystalline quality of the films was only observed above
~ 300°C. This suggests that the dynamic annealing of ion damage was in-
sufficient at the lower temperatures.

Ion bombardment can influence the evolution of surface morphology and
film microstructure in a number of ways. We have observed two effects of
low energy Art ion irradiation — surface smoothing and the removal of sur-
face hydrogen. Surface smoothing can be clearly seen in the AFM images
(Fig. 2.16) and RHEED patterns (Fig. 2.17) comparing the results of con-
ventional MBE and IAMBE. The improvement in epitaxial thickness during
IAMBE is thus explained by the surface smoothing effect of low energy argon
ions. The removal of surface hydrogen is discussed later in this chapter.

Silicon films have now been deposited at low temperatures using energetic
beam techniques in several different configurations. Direct silicon ion beam
deposition has produced films with improved crystallinity [7, 8, 9]. However,
the use of mass separated low energy beams results in rather low deposi-
tion rates (~ 0.01 nm/s). Another concern is the C,O and N contamination
in the film from CO and N2 (both of mass 28 amu) in the beam. In fact,
films deposited with 3°Si have been reported to be superior (in crystal qual-
ity) compared to films with 78Si [8, 9]. Our investigation of IAMBE helped
in determining the most important effect of ion irradiation, namely surface
smoothing. These experiments were also limited by the ion flux and energy
to some extent. Lower beam energies and higher fluxes may produce better
films. Such a beam could be generated with, for example, an electron cy-
clotron source. By far, maximum improvement in crystal quality has been

reported with low energy bias sputtering [10, 11] and ion beam sputtering

Chapter 6 181

[12]. Sputtering produces Si atoms with hyperthermal energies (few eV) and
this seems to be the optimum energy for surface smoothing.

While we have made significant progress toward gaining an atomistic
view of the breakdown of epitaxy, the prediction of surface roughening is
still an open and challenging problem. A prediction of the intrinsic epitaxial
thickness, hpi, would require such an effort. Experiments (Section 2.7.3
and [19]) suggest a value of § closer to 1 (see Section 1.5 for a discussion of
kinetic roughening). If the roughening were only due to the random arrival of
incident atoms, the maximum value of @ would be 1/2. Thus, for describing
practical situations, the effects of adsorbates must be incorporated into the
continuum/Monte Carlo models. The variation in the rms surface roughness
for the IAMBE film was consistent with a simple model which predicted
R, ~ In h asymptotically [13]. However, we had data spanning only one
decade in the thickness h. It would be interesting to see if this were valid for
a larger range of film thicknesses. Almost all the continuum models do not
allow for overhangs. This is usually done to prevent h from being multiply-
valued. However, low temperature Si growth can lead to void formation
under certain conditions (Section 2.9 and [14, 15]). This suggests that one

must allow for overhangs in a complete theory for Si growth.

6.3.3. The Role of Adsorbates

How do adsorbates such as carbon, oxygen and hydrogen influence epitaxy?
Quite a few experiments in the 1960s were done in high vacuum conditions.

As a result, even films deposited at high temperatures (~ 1000°C) often con-

Chapter 6 182

tained defects [16]. It was later shown that deliberate carbon contamination
of the surface results in a change from layer-by-layer growth to 3-D island nu-
cleation and growth [17, 18]. A similar conclusion was drawn from RHEED
observations during low temperature MBE and SIMS analysis (see Section
2.7.2). The SIMS analysis and the annealing experiment (see Section 2.8)
also showed that carbon and oxygen contamination is not the direct cause of
breakdown of epitaxy at low temperatures. However, even a small coverage
(~ 0.01 ML) of carbon or oxygen can accelerate the rise in surface roughness
and hence cause a premature breakdown of epitaxy.

The role of hydrogen is more complex. On one hand, introduction of
atomic hydrogen can lead to an early crystal-state—amorphous-state tran-
sition [19]. On the other hand, conventional MBE gives epitaxial films even
with a uniform surface coverage of 1 ML (Ref. [20] and Fig. 4.7). Finally, ona
smooth, nominally dihydride-terminated Si(001)-1 x1 surface, an amorphous
film is produced (Fig. 4.3). These results might seem contradictory but can
be explained as follows. At low surface coverages, hydrogen atoms act as dif-
fusion barriers which results in a dramatic increase in Si island density [21].
This, in turn, leads to an early breakdown of epitaxy [19]. Our molecular dy-
namics simulations have provided some insight into the mechanism of epitaxy
with large hydrogen coverages. It appears that epitaxial films are obtained
by subplantation, i.e., implantation of the incident Si atom one layer below
the surface. On the monohydride-terminated Si(001)-2x1 surface, the sub-
plantation is driven in large part by the enthalpy difference (4.63 eV) between
a vapor phase and a solid phase silicon atom. The predicted subplantation

probability (0.1) was rather small. It is possible that calculations at a fi-

Chapter 6 183

nite substrate temperature and for a longer time might yield values that are
consistent with epitaxial growth. On the dihydride-terminated $i(001)-1x1
surface, the subplantation probability was observed to increase very rapidly
with the incident particle energy. At thermal energies (0.25 eV), the inci-
dent Si atom is not able penetrate the layer of hydrogen atoms due to steric
constraints. However, at 4 eV almost two-thirds of the incident atoms were
subplanted at the end of 1 ps of simulation. Thus, the remarkable success
of epitaxial films on a dihydride-terminated surface by sputter deposition
[11, 22] can be understood in terms of subplantation probabilities. The sim-
ulations suggest that the SiH and SiH» units segregate during epitaxy on the
monohydride- and dihydride-terminated Si(001) surfaces. This is in agree-
ment with the observations of hydrogen segregation during epitaxy on the
monohydride-terminated surface [23] and the (1x1) RHEED pattern and a
smooth growing front during the initial stages of epitaxy on the dihydride-
terminated surface [11, 22].

The molecular dynamics simulations suggest that the surface Si atom
also segregates during epitaxial growth on hydrogen-terminated surfaces. It
would be interesting to see if this is true experimentally. This could be done
by using an isotope of silicon. Such an experiment would tell whether the
surface hydrogen atom remains bonded to the original Si atom or it bonds
to the incoming Si atom.

The ability to grow epitaxial films on hydrogen-terminated silicon sur-
faces has significant advantages. These surfaces are extremely unreactive
because there are no dangling bonds. While sputter deposition has been

very successful, a chief problem is the embedding of energetic Ar (or any

Chapter 6 184

other primary ion) recoils in the film and production of Si interstitials. This
can be overcome with techniques like laser ablation which produce a hyper-
thermal beam of silicon atoms. This could alleviate the need for ultra high

vacuum conditions.

6.4 Other Results

6.4.1 Surface Cleaning of Silicon

Surface cleaning of silicon has always received a lot of attention because of
potential consequences on further processing steps. The usual procedure is to
generate a surface passivation layer to protect the underlying silicon. The two
common passivation layers are a thin oxide grown chemically and hydrogen
passivation. For some processes, the passivation layer has to be removed
just prior to the process. Low energy ion beam-induced reconstruction is a
promising technique for the production of Si(001)-2x1 surfaces at extremely
low temperatures. Starting with a nominally dihydride-terminated $i(001)-
1x1 surface, both argon and helium ions were succesfully used to remove
the surface hydrogen. Helium ions gave somewhat better results presumably
due to less energy transfer to the substrate silicon atoms. Better results were
also obtained when ions were incident at grazing angles. This is due to the
less energy transfer to atoms in the subsurface layers. Silicon films deposited
after ion irradiation were epitaxial as judged from XTEM images (Section

5.2.3). Molecular dynamics simulations suggest that the ratio of sputtering

Chapter 6 185

yields of hydrogen from dihydride-terminated surface to the monohydride-
terminated surface is much higher than two (with argon ions). This could be
used to preferentially remove dihydride units from the surface.

The phenomenon of beam-induced reconstruction should be studied in
more detail. Ions with even lower energy and more grazing angles of incidence
may produce better results. Besides noble gas ions, the effects of hydrogen
and halogen ions should also be investigated. Hydrogen ions can also remove
C and O impurities from the surface [24]. The damage produced by the
ions on a scale larger than observable in an XTEM image will have to be

established for any possible application.

6.4.2. Empirical Si-H Interatomic Potential

An empirical interatomic potential was developed to describe silicon-hydrogen
interactions. The Si-H potential gives a reasonably good description of the
various gas phase Si,,H, molecules, hydrogen adsorbed on the silicon surface
and interstitial sites of atomic hydrogen in bulk silicon. The interatomic
potential can be further characterized by determining the barriers to sur-
face diffusion of hydrogen and desorption. The potential may be used to
study a multitude of problems such as chemical vapor deposition from silanes,
processing of hydrogen-terminated silicon surfaces, and hydrogenated amor-
phous silicon. However, a note of caution is added since classical potentials
are only a crude approximation to the complete quantum mechanical solu-

tion.

Chapter 6

Finally, one might ask if low temperature silicon epitaxy will ever be
used in a widespread manner for device fabrication. And if so, will the
technique be molecular beam epitaxy? The answer to the first question
definitely seems to be yes. Epitaxy at temperatures as low as 500°C is being
used in some integrated circuits [25]. However, these Si (and Sij_,Ge,) films
are being deposited by UHVCVD. Molecular beam epitaxy systems have low
throughput and are expensive to maintain and it appears that deposition
by CVD is going to be preferred. Molecular beam epitaxy allows one to
precisely control the process parameters and hence is a very good tool for
understanding the physics of film growth. It helps to understand the more

complicated events during chemical vapor deposition.

186

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ular beam epitaxy using a HF dip,’ Appl. Phys. Lett. 59, 685(1991).

[21] T. Vasek and M.G. Lagally, presented at the American Vacuum Society
Meeting, Orlando, 1993.

[22] C.-C. Chen, D.L. Smith, G.B. Anderson, and $.B. Hagstrom, ‘Low tem-
perature epitaxy on H-passivated $i(100) by sputter deposition,’ Mat.
Res. Soc. Symp. Proc. 259, 443(1992).

[23] M. Copel and R.M. Tromp, ‘H-Coverage dependence of $i(001) homoepi-
taxy,’ Phys. Rev. Lett. 72, 1236(1994).

Chapter 6 190

[24] A. Mahajan, J. Irby, D. Kinosky, R. Qian, S. Thomas, S. Banerjee, A.
Tasch, and T. Picraux, ‘Si atomic layer epitaxy based on SipHs and

remote He plasma bombardment,’ Thin Sol. Fi. 225, 177(1993).

[25] B.S. Meyerson, ‘UHV CVD growth of Si and Si-Ge alloys — chemistry,
physics, and device applications,’ IEEE Proc. 80, 1592(1992).

Appendix A

Chemical Cleaning of Silicon
Wafers

The procedure used for chemical cleaning of Si wafers is taken from Ref.
[1]. All ratios mentioned below are by volume. The resistivity of H,O was

15-18 MQ-cm.

Dilute HF dip. The Si(001) wafer is first dipped in a dilute HF solution
(HF : H2O 1:20) for 10 - 15 s to etch the native oxide and then followed with
an H2O rinse (15 ~ 30 s).

Alkaline peroxide solution. The wafer is then placed for 5 minutes in a
hot alkaline peroxide solution composed of NH,OH : H2O2 : H2O in a 1:1:5
ratio. Both NH4,OH and H,O2 are 30% solutions. The temperature was
70 + 10°C. The resulting oxide is then etched by a dilute HF dip (10 - 15s)
and followed by an H20 rinse (15 — 30s). This sequence was repeated three
times. This step removes organic contaminants and some metals from the

surface [2].

191

Appendix A 192

Acidic peroxide solution. The wafer is then placed for 5 minutes in a
hot acidic peroxide solution composed of HC] : H2O2 : H2O in a 1:1:5 ratio.
The temperature was again 70 + 10°C. The resulting oxide is again etched
by a dilute HF dip (10 — 15 s) and followed by an H20 rinse (15 — 30s). This
sequence was repeated three times. This step removes metal contaminants

from the surface [2].

Dilute HF dip. In the final step, the Si wafer is dipped in dilute HF for 50

to 60 s [3]. This results in a nominally dihydride-terminated $i(001) surface.

The wafer is transferred to the load lock within three minutes after the last
step. On the dihydride-terminated 5i(001) surface, hydrogen atoms saturate
the dangling bonds of Si atoms. This passivates the Si surface from oxidation
and chemisorption of impurities. In fact, such surfaces have been shown to

resist oxidation for as long as 12 hours in the laboratory atmosphere [4].

Bibliography

[1] A. Ishizaka and Y. Shiraki, ‘Low temperature surface cleaning of sili-

con and its application to silicon MBE,’ J. Electrochem. Soc. 133, 666
(1986).

[2] W. Kern and D.A. Puotinen, ‘Chemical solutions based on hydrogen
peroxide for use in silicon semiconductor technology,’ RCA Rev. 31,

187 (1970).

[3] D.J. Eaglesham, G.S. Higashi, and M. Cerullo, ‘370°C clean for Si molec-
ular beam epitaxy using a HF dip,’ Appl. Phys. Lett. 59, 685(1991).

[4] T. Takahagi, I. Nagai, A. Ishitani, H. Kuroda, and Y. Nagasawa, ‘The
formation of hydrogen passivated silicon single-crystal surfaces using

ultraviolet cleaning and HF etching,’ J. Appl. Phys. 64, 3516(1988).

193

Appendix B

Elastic Recoil Spectrometry

B.1 Introduction

Hydrogen has always been a hard element to detect. Conventional core loss
techniques such has X-ray photoelectron (XPS) and Auger electron spec-
troscoopies (AES) cannot be used because hydrogen has only one electron
which is involved in bonding. Nevertheless, there are several techniques to
measure hydrogen concentrations — some specific to the Si-H system and
some that are based on physical techniques and are more general. Some
methods specific to the silicon-hydrogen system are infrared spectroscopy
(IR) [1] and high resolution electron energy loss spectroscopy (HREELS) [2].
These techniques are based on the excitation or absorption of Si-H vibra-
tional modes. This makes them rather sensitive to the chemical environment
of the hydrogen atom. While this may be useful for distinguishing various
configurations of H on the surface, it makes it difficult to measure abso-
lute coverages because one has to monitor all possible vibrational modes.
Hydrogen can also be detected by physical techniques such as secondary

ion mass spectrometry (SIMS), time-of-flight medium energy ion scattering

194

Appendix C

(TOF-MEIS) [3] and nuclear reaction analysis (NRA). Secondary ion mass
spectrometry is a destructive method as it relies on analysis of sputtered
particles. The cross sections for most nuclear reactions are rather small. A
commonly used reaction is the !°F(p,a)!©O with a cross section of about
0.5 mb/sr at an incident particle energy of 1.25 MeV [4].

Elastic recoil spectrometry (ERS) is a physical technique for the detec-
tion of atoms lighter than the incident ion. After filtering out the forward
scattered incident beam, the scattered atoms are energy analyzed to deter-
mine their absolute concentration and depth distribution. This technique is
also known as forward recoil spectrometry (FRS) and elastic recoil detection
analysis (ERDA) and is basically an extension of the Rutherford backscatter-
ing spectrometry (RBS). Typically, incident ions with a few MeV are used.
For the detection of hydrogen and its isotopes, ions with atomic number 2 or
higher can be used. Heavy ions such as 78Si+ or *Art can be used to measure
C and O profiles but cause significant damage to the substrate. The damage
with MeV He? ions is comparatively lower, and several uC can be deposited
before any noticeable damage. This allows one to obtain many spectra from
the same sample. The cross sections for elastic scattering are also large. A
typical number is 320 mb/sr for a 2 MeV He? ion and a scattering angle of
25° [5]. There is also a resonance with deuterium at about 2.14 MeV [6]. The
forward scattered Het ions can be separated from the protons either with a
thin Mylar or Al foil or by magnetic deflection. Separation with the stopper
foil depends on the larger stopping cross sections for larger Z particles. A
2 MeV Het ion is completely stopped with a 8 wm Al foil whereas a 1 MeV

H* loses only about 400 keV. The straggling in the stopper foil restricts the

195

Appendix C 196

depth resolution to about 50 nm. A good reference for the optimization of
scattering geometry and the stopper foil for best depth resolution is Ref. [7].
The technique does suffer from rather large data collection times. With a
5 nA beam it takes about 20 minutes to build up good statistics. It is pos-
sible to detect as little as 0.01 ML although practical considerations restrict
the limit to about 0.1 ML. Since the cross sections for light ion scattering
are well known, ERS is one of the best techniques for obtaining absolute

concentrations.

B.2 The Elastic Recoil Spectrometry Sys-
tem

The elastic recoil spectrometry system is designed to measure hydrogen cov-
erage and profiles in thin films and on surfaces. A schematic of the end station
is shown in Fig. B.1. A base pressure of about 2 x 107” Pa is achieved in the
end station when it is isolated from the Pelletron. The chamber is pumped
with an ion pump and two turbomolecular pumps. During operation, the
pressure rises to about 8x 107” Pa due to the Ny» stripper gas used for ion-
izing He atoms in the Pelletron. The pressure in the Pelletron is typically
10-* Pa. An ion gauge is used to measure the pressure and a mass spectrom-
eter is used to monitor the residual gas. The ERS system is connected to the
accelerator beam line through a 4 mm diameter aperture. This serves as a
differential pumping port and helps isolate the high pressure side (the accel-

erator) from the ERS system. The Het beam enters through this aperture

Appendix © 197

and is incident on the substrate at about 78° with respect to the substrate
normal. This angle is obtained by tilting the part of the chamber containing
the sample with respect to the beam axis. The Het beam enters the end
station off-axis to avoid hitting the wall of the chamber. This off-axis dis-
placement is achieved using a bellows arrangement. Solid state detectors are
used to detect the scattered particles. The detectors are bakeable to 200°C.
However, the maximum baking temperature is limited to about 150°C by the
electrical connectors used on the detectors. The samples are inserted through
a load lock. This helps maintain a good vacuum in the chamber for surface
studies. Substrates can be heated for adsorption-desorption studies and film
growth. A reflection high-energy electron diffraction (RHEED) gun is used
(not shown in Fig. B.1) to monitor the surface morhology. An electron beam
deposition source, an effusion cell, an ion gun or an atomic hydrogen source
can be connected at a line-of-sight port shown in Fig. B.1 (marked by the
letter A). The effects of exposing the substrate to different processing condi-
tions can be investigated. A schematic of the electronics for processing the
signals from the detectors is shown in Fig. B.2.

The scattering geometry for hydrogen coverage measurements is shown in
Fig. B.3. The Het beam is incident at 78° with respect to the surface normal.
The nominal backscattering angle is 102° and the solid angle of the detector
is about 2.66 msr. An 8 ym Al foil [8] is used to block the forward scattered
He beam from reaching the forward scattering detector. The nominal forward
scattering angle is 24° and the solid angle of the the detector is 3.60 msr. The
detectors (ORTEC Model U-012-050-100) are circular with an active area of

50 mm?. For optimum depth resolution, a rectangular slit should be used in

Appendix C 198

Figure B.1: A schematic of the elastic recoil spectrometry system. The line-
of-sight port to the substrate is marked by the letter A. A Kaufman ion
source is shown connected at this port. The drawing is not to scale.

Appendix C 199

Detector
Bias Supply
ORTEC 428
RBS
detector
| Pre-Amplifier Amplifier A-D converter =
ORTEC 142A ORTEC 572 Canberra 8075
ERS Computer with
detector multichannel analyzer
Pre-Amplifier Amplifier A-D converter Canberra System 100
| ORTEC 142A ORTEC 572 Canberra 8701]
Detector
Bias Supply
ORTEC 428

Figure B.2: The electronics used for the detection of alpha particles and
protons. Both RBS and ERS spectra can be collected simultaneously on a
single computer.

Appendix C

Substrate

8 pm
Al foil

detector
Qg = 3.60 msr

accor Ml

Qe = 2.66 msr

Figure B.3: The scattering geometry used in the experiments.

front of the ERS detector [9]. This decreases the dispersion in the kinematic
factor of the H atoms. However, we have used the complete detector area
to maximize the counting rate. This gives a measure of the total amount of
hydrogen at the substrate on the surface and in the bulk. The RBS and ERS
spectra are collected simultaneously. The hydrogen counts are thus referred
to a substrate peak and this eliminates the need to measure the incident beam
current. Care must be taken to ensure that the Het beam is not incident
along a channeling direction in the substrate.

The analysis described below is for hydrogen on a silicon surface. Such
surfaces can be prepared by an HF dip or exposing a clean silicon surface
to an atomic hydrogen beam. The yield per channel for backscattering from
the Si substrate is expressed in terms of the incident beam dose Qp, solid
angle Nr, scattering cross section og;, energy per channel € and the stopping

cross section factor [e,] [10]:

QrORosi€
Hy = — B.1
s [€,]cos(61) (B.1)

The stopping cross section factor at the surface, the kinematic factor and the

200

Appendix C

scattering cross section are in turn given by [10]

_ Kgie(Ep) | e(KsiEo)

[eo] = cos(61) cos(62) (B.2)
Ke My,.cosé + M3, — M3,,sin?6 , (B.3)
Mure + Ms;
ZueZsie? \* 1 (Me)
i= ~2 .

The Rutherford scattering cross section is assumed for scattering from
the silicon atoms. Here, e{E) is the stopping cross section for Het ions with

energy E in silicon.

The He* ions recoil scatter protons from the substrate, some of which
are detected by the forward scattering detector. Protons, being lighter than
helium, are only scattered in the forward direction (¢ < 90°). The total
number of protons scattered into the forward detector can be expressed in
terms of the incident beam dose Qg, solid angle Qg, scattering cross section

oy and the surface density (atoms/cm?) of hydrogen atoms Ny :

QrQgcHNy
= B.
Yu cos(6;) (B.5)
The energy transferred to the protons in the collision is given by
4Mu-My 2
E, = ———"——- cos B.6

Typically, 1.9 MeV He* ions are used in the experiments and the pro-

tons on the surface emerge in the directon of the detector with an energy of

201

Appendix C 202

1.01 MeV. Both helium ions and protons are scattered in the forward direc-
tion and have to pass through the Al foil to reach the detector. The energy
loss of light ions (of energy E) is proportional to MiZ?. The range of 1.9
MeV Het? ions, 1 MeV protons and 1.7 MeV deuterons in Al is about 7 wm,
14 wm and 22 wm respectively [11]. A TRIM91 simulation [12] with 1000
He ions incident on a 7 ym Al foil gave a range and straggle of 6.40 wm and
0.17 wm, respectively. The helium ions are thus completely stopped in the Al
foil. A simple calculation assuming Rutherford scattering cross section shows
that the probability of backscattering of 1 MeV protons incident on the the
Al foil is about 0.0002. The protons (and deuterons) lose energy on their
way through the foil but retain sufficient energy to be detected. A TRIM91
simulation with 10000 protons gave a transmission coefficient of 0.9998. The
Al foil thus allows us to separate the forward scattered protons from the He
ions. The surface hydrogen density can be obtained from the eqs. B.1 and
B.5 as

Ny = eR (B.7)

Since the two spectra are collected simultaneously, the quantity Qx/Qr
is close to unity, except for a minor correction factor. The two electronics
chains might have different dead times depending on the arrival rate of the
scattered ions. This is taken into account by replacing Qp/Qz by tr/tz
where tp and tg are the actual collection times (true time - dead time) of
the two chains. Note that this is only a first order correction since the dead
time is not a strictly linear function of the number of ions incident on the

detector. A variation of incident beam current with time will result in non-

Appendix C 203

trivial corrections factors. Fortunately, this factor is close to unity in most
cases and does not introduce a significant error. With this correction, eq.

B.7 becomes

Ny= 2S (B.8)

B.3 Calibration

To calculate the hydrogen coverage with eq. B.8, two quantities need to
be determined — the energy per channel, € in the RBS spectrum and the
ratio of the solid angles, QNR/Qz. The quantity € is determined using a
sample consisting of Au, Rh and Co marker layers. This helps establish the
energy versus channel relation for the RBS spectrum. The ratio of the solid
angles is obtained from a 100 nm (CgHg),, (polystyrene) film (on Si substrate)
consisting of C and H in a stoichiometric ratio of unity. The RBS and ERS
spectra from such a sample are shown in Fig. B.4. The measured ratio,
QRr/Qg, is about 0.76 + 0.05. This is close to the value of 0.74 estimated
from geometry.

As only one sample can be inserted at a time in the chamber, it is not
possible to do a calibration for each sample. Instead, calibration is done
once in a while to check for any changes in the values of € and Qp/OQg. The

variations in their values are usually small.

Appendix C 204

Energy (in keV)

500 1000 1500
8000 ; 1

Oo
oO
oO

4000

Oo
oO

Counts (Arbitrary units)

400 600 800
Channel

(a)

fs
oO
oO
oO

3000 7

NR
[o)
oO
oO

1000 7

Counts (Arbitrary units)

0 | J
0 50 100 150 200 250

Channel

(b)

Figure B.4: The (a) backscattering and (b) forward scattering spectra from
a 100 nm film of (CgHg)n (polystyrene) on Si. The background subtracted
carbon peak is also shown in the RBS spectrum. Both spectra were collected
simultaneously. The incident Het ion energy was 2.0 MeV.

Appendix C 205

B.4 Error Analysis

Hydrogen coverage can be measured with quite high accuracy by elastic recoil
spectrometry. The technique is based on a purely physical process, namely
the transfer of energy in a high-energy collision. This makes it independent
of the bonding environment of the H atoms. Still several factors can intro-
duce errors in the measurement. These include the variation of the position
of the incident beam spot, the sample and detector positions, sample misori-
entation, and the knowledge of scattering and stopping cross sections. It is
useful to distinguish between different types of error when interpreting the
results ~ (a) absolute error, the ultimate confidence that one can place in the
measured values and (b) relative error, the variation in or the ratio of the
measured values from sample to sample, or different spectra from the same
sample.

The hydrogen coverage is expressed in eq. B.8 in terms of the ratio of solid
angles Qp/Oxg, the ratio of scattering cross sections os;/o4 and the stopping
cross section factor [e,].

The scattering cross sections for hydrogen and deuterium have been de-
termined experimentally by using calibrated samples. The values usually
differ from the Rutherford scattering cross sections for MeV alpha particles.
This is expected since the distance of closest approach between a proton and
a MeV alpha particle is comparable to the diameter of a nucleus (~ 107!° m).
In our calculations, we have used the hydrogen scattering cross sections from
Ref. [5] and the deuterium scattering cross sections from Ref. [6]. These

values are probably accurate to within 10%.

Appendix C 206

Sample misorientation (deviation in the angle @, in Fig. B.3) is a major
source of error. A 1° misorientation can result in about 8% change in the
stopping cross section factor [€,]. It is possible to check for sample misorien-
tation by comparing a spectrum with one obtained after a 180° rotation of
the sample. The ratio of solid angles QR/Qg is probably known within 5%.
It can be shown that if the sample and the detector are within 1 mm of their
positions, the errors incurred are less than 4%. Another factor is the large
incident beam spot size (typically 2 x 10 mm?) and its exact locaation on
the sample. Overall, the errors due to small variations in the geometry is
estimated to be about 10%.

The relative error when comparing spectra from two different samples is
estimated to be about 10%. When comparing spectra from the same sample,
the errors are probably less than 5% because the sample misorientation and
the detector and sample positions are also the same. The absolute error in

the measured concentration of hydrogen should be about 20%.

B.5 Hydrogen on Silicon Surface

Figure B.5 shows the backscattering and forward scattering spectra from a
Si(001) wafer after a dilute (~ 5%) HF dip. This corresponds to a hydro-
gen coverage of 5.0 ML. This is an unusually high value. The saturation
coverage of hydrogen on S$i(001) is close to 2.0 ML. A saturation value of
1.85 + 0.18 ML was reported in Ref. [13] after exposing a clean S$i(001)

wafer to atomic hydrogen under UHV conditions. This indicates that the

Appendix C

Table B.1: Hydrogen coverage after annealing a dilute HF dipped Si(001)

wafer.

Process Hydrogen coverage (ML)
as inserted 7.4
100°C, 15 min. anneal 6.8
150°C, 15 min. anneal 6.7
200°C, 15 min. anneal 4.9
200°C, overnight anneal 4.8

surface has a high density of physisorbed hydrocarbons (or any other H con-
taining species). The wafer was exposed to atmosphere for about 10 minutes
after the HF dip and before transfer to the load lock. It is possible that
hydrocarbons accumulate on the surface when the wafer is pulled out of the
HF solution and during the finite time needed to transfer the wafer to the
vacuum system. Performing an RCA clean (see Appendix A) before the di-
lute HF dip did not seem to effect the hydrogen coverage. In all cases, a
sharp (1x1) RHEED pattern was observed along the <110> azimuth.

The hydrocarbon coverage does decrease when the wafer is heated. The
results of one experiment are shown in Table B.1. The hydrogen coverage
goes down from 7.0 ML at room temperature to about 4.8 ML at 200°C. It
has been shown that a low temperature bake can remove hydrocarbons from
the Si(001) surface [14]. Our results are thus consistent with this observation.
Unfortunately, we could not go to higher temperatures to follow the evolution
of hydrogen coverage.

A silicon wafer can be terminated with deuterium atoms by dipping in

a dilute solution (~ 1%) of HF in D20. Deuterium fractions higher than

207

Appendix C 208

Energy (in keV)

1000 1200 1400 1600
5000 T T

aN
oO
Qo
Oo

3000

No
(>)
Oo
Oo

1000

Counts (Arbitrary units)

400 500 600 700 800
Channel

(a)

ui
oO

N W San

co) lo) Oo

I q T
a a

! 1 |

—_
oO

Counts (Arbitrary units)

AA.

H |
50 100 150 200 250
Channel

(b)

[o)
Oo

Figure B.5: The (a) backscattering and (b) forward scattering spectra from
a $i(001) wafer after a dilute (~ 5%) HF dip. Both spectra were collected
simultaneously. The incident He* ion energy was 2.0 MeV.

Appendix C 209

80% were reported in Ref. [15] after such a treatment. Fig. B.6(a) shows a
forward scattering spectrum of a $i(001) wafer dipped in a ~ 1% solution of
HF in D20 for two minutes followed by an overnight anneal at 200°C. We see
two peaks corresponding to H and D atoms. They correspond to a coverage
of about 3.0 ML H and 0.26 ML D atoms. At various times, the deuterium
coverage measured after such a treatment varied between 0.2 and 0.7 ML.
We have seen (Chapter 5) that low energy Art ion irradiation can remove
hydrogen from a Si(001) surface. The ERS spectrum after a ~ 1 ML dose
of 50 eV Art ions on a HF + D2O dipped Si(001) wafer is shown in Fig.
B.6(b). The substrate temperature during ion irradiation was 200°C. The
spectra in Fig. B.6(a) and (b) are normalized with respect to the incident Het
dose. Although we have poor statistics, we see that the deuterium coverage
has decreased significantly (from 0.26 to about 0.11 ML). One would have
expected a similar drop in the 1H coverage. But the 'H coverage increases
from 3.0 to 3.3 ML. This is presumably due to hydrogen adsorption from the

ambient.

B.6 Conclusion

The elastic recoil spectrometry system can be used to measure hydrogen
concentrations in thin films and substrates with quite high accuracy. It is
possible to study the effects of different processes on the hydrogen concen-
tration on the substrate. For surface studies, an improvement in vacuum

conditions is desirable. This is particularly true when the surface is exposed

Appendix C

Counts (Arbitrary units)
r)

re) l
0 50 100 150 200 250
Channel
(a)

2° i i i i]
‘Cc
3 15- 4
hee
war
*9 10 H “
Ne
n — —_—
2° D
7 5 l vi a

0 50 100 150 200 250

Channel

(b)

Figure B.6: (a) The ERS spectrum from a Si(001) wafer dipped in a ~ 1% HF
+ D20O solution for two minutes followed by an overnight anneal at 200°C.
The hydrogen coverage is about 3.0 ML and the deuterium coverage is about
0.26 ML. (b) The ERS spectrum after a 1 ML dose of 50 eV Ar* ions at
a substrate temperature of 200°C. The hydrogen coverage is about 3.3 ML
and the deuterium coverage is about 0.11 ML. The spectra in (a) and (b)
are normalized with respect to the incident He* dose. The incident He* ion
energy was 2.0 MeV.

210

Appendix C 211

for several hours while studying the effects of different processes.

Bibliography

[1] See, for example, Y.J. Chabal, G.S. Higashi, K. Raghavachari, and V.A.
Burrows, ‘Infrared spectroscopy of Si(111) and $i(100) surfaces after HF
treatment: hydrogen termination and surface morphology,’ J. Vac. Sci.

Technol. A7, 2104(1989).

[2] See, for example, J.A. Schaefer, ‘Electronic and structural properties of

hydrogen on semiconductor surfaces,’ Physica B170, 45(1991).

[3] See, for example, M. Copel and R.M. Tromp, ‘H-Coverage dependence
of Si(001) homoepitaxy,’ Phys. Rev. Lett. 72, 1236(1994).

[4] L.C. Feldman and J.W. Mayer, Fundamentals of Surface and Thin Film
Analysis, North-Holland, New York, 1986.

[5] J.E.E. Baglin, A.J. Kellock, M.A. Crockett, and A.H. Shih, ‘Absolute
cross section for hydrogen forward scattering,’ Nucl. Instr. Meth. B64,
469(1992).

[6] F. Besenbacher, I. Stensgaard, and P. Vase, ‘Absolute cross section for

recoil detection of deuterium,’ Nucl. Instr. Meth. B15, 459(1986).

[7] A. Turos and O. Meyer, ‘Depth profiling of hydrogen by detection of
recoiled protons,’ Nucl. Instr. Meth. B232, 92(1984).

212

Appendix C 213

[8] The 8 wm Al foils were obtained from Goodfellow Corporation.

[9] B.L. Doyle and D.K. Brice, ‘The analysis of elastic recoil detection data,’
Nucl. Instr. Meth. B35, 301(1988).

[10] W.K. Chu, J. W. Mayer, and M.A. Nicolet, Backscattering Spectrometry,
Academic Press, New York, 1978.

[11] J.F. Ziegler, J.P. Biersack, and U. Littmark, The Stopping and Range
of Ions in Solids, Pergamon Press, New York, 1985.

[12] J.P. Biersack and L.G. Haggmark, Nucl. Instr. Meth. 174, 257(1980).

[13] K. Oura, J. Yamane, K. Umezawa, M. Naitoh, F. Shoji, and T. Hanawa,
‘Hydrogen adsorption on $i(100)-2x1 surfaces studies by elastic recoil
detection analysis,’ Phys. Rev. B41, 1200(1990).

[14] S. Nikzad, S.S. Wong, C.C. Ahn, A.L. Smith, and H.A. Atwater, ‘In
situ reflection electron energy loss spectroscopy measurements of low
temperature surface cleaning for Si molecular beam epitaxy,’ Appl. Phys.

Lett. 63, 1414(1993).

[15] V.A. Burrows, Y.J. Chabal, G.S. Higashi, K. Raghavachari, and S.B.
Christman, ‘Infrared spectroscopy of Si(111) surfaces after HF treat-
ment: hydrogen termination and surface morphology,’ Appl. Phys. Lett.
53, 998(1988).

Appendix C

Algorithm for Molecular
Dynamics Simulations

The following is a description of the computer program SIH used for
molecular dynamics simulations. The Si and H atoms respond to the
5i-Si, Si-H and H-H interatomic potentials described in Chapter 3. A gen-
eral discussion of the numerical methods is also given in Section 3.3. Briefly,
the Runge-Kutta-Nystrom method with Richardson extrapolation is used to
solve the system of differential equations 3.1 —- 3.2. The nearest neighbors of
an atom are determined using the cell method. Two workstations, DEC3100
and RS6000/340, were used for the simulations. The computation time is
about 9.6 ms/atom-timestep and 1.9 ms/atom-timestep on the DEC3100 and
RS6000/340 workstations, respectively.

The program is written in the C language. A brief description of the
various subroutines and some important variables is given below followed by

the source code.

Subroutines:

214

Appendix B

params

lattice

energy

func

periodic

RKA

Input files:

params.dat

lattice.dat

Output files:

out.dat

final.dat

215

Reads data in the input file “params.dat.”

Reads data the input file “lattice.dat.”

Computes the total kinetic and potential energy of a configu-
ration of atoms.

Computes the accelerations of all atoms for any given config-
uration.

Applies periodic boundary conditions in the transverse direc-
tions (x and y) of the crystallite.

The Runge-Kutta-~Nystrom method for the numerical solution
of the system of differential equations.

: Contains information about the size of the crystallite, dura-

tion of simulation and other variables controlling the flow of
the program. An example is give below.

: Contains the initial positions, velocities and mass of atoms.

This is contained in seven columns as
x y Zz Vx Vy Vz mass

: The position and velocity of atoms (with z < zsave) is

stored at regular time intervals specified in the input file
“params.dat.”

: The position and velocity of atoms is stored at regular time

intervals specified in the input file “params.dat.”

Appendix B 216

Units:
The units for distance, mass and time are A (= 107?° m), fs (= 10-** s) and

amu (= 1.67 x 10-” kg), respectively.

A sample input file params. dat.

auto
2601

1000.0
100.0
10.0
0.01
5.4310
10

-5.00

29.50

10.0

17.00 17.00 -3.00 0.00 0.00 0.20 28.0

Line 1 : There are two possible specifications. Using auto leads to a simula-
tion with adaptive step size control. Using relz leads to a relaxation
of the lattice to a minimum energy configuration. For relaxation, a
simple algorithm is used which sets the velocity to zero whenever
velocity and acceleration are in opposite directions.

Appendix B

Line 2

Line 3

Line 4

Line 5

Line 6

Line 7

Line 8

Line 9,10,11:

Line 12,13

Line 14

Line 15

217

: Number of atoms (including the incident atom) in the simulation.

: Use 0 if there is no incident atom and 1 if there is an incident atom.

: Duration of the simulation (in fs).

: Time-interval at which the atomic coordinates and velocities are

stored.

: The maximum step size allowed (in fs).

: Tolerance (A or A/fs per picosecond).

: Lattice constant of silicon (in A).

Size of the crystallite in unit cells. The primitive cell dimensions
are 3.84, 3.84 and 5.43 A in the x, y and z directions respectively.
The x-direction must be [110] and the z-direction must be [001].

: Atoms with initial z-coordinates less (more) than the value in line

12 (13) are held rigid.

: Only atoms with initial z-coordinate less the value in line 14 are

stored in the output file “out.dat.”

: If there is an incident atom, its position (x,y,z), velocity (vx,Vy,Vz)

and mass are specified here.

#include "stdio.h"

218

#include "math.h"

FILE *parf, *latf, *outf, *finf, *warf, *ranf;

#define MAX 5600

#define MID 2700

#define NN 10

#define SIDEX 30

#define SIDEY 30

#define SIDEZ 15

#define CUBES 13500

short int s,mode,score[CUBES],rigid[MID], zs [MID],tpe[MAX];
int ma,mb,mc,atom, ion;

int m,n, enc [27], val [MAX];

int zone [CUBES] [10], code [MAX];

int SYZ,STD,cu, stor [MAX] [NN];

double A, Bo [NN], ldal, lda2[(NN],b,c,d,Re[NN],eta,R,D;
double alta, alpha, H;

double Al, Bl, H1,As [MAX], Bs [MAX] ,Hs [MAX];

double Au[10}, Bu[10], Hu[10], das [MAX], aBs [MAX], GHs [MAX] ;
double T, interval, hmax, tol, cutoff, sqcut;

double tme,la,rmin,est, zmax, @Aq [MAX], GBg [MAX] , Hq [MAX] ;
double sl,sr,sn,sf, delx, dely, zmin, zsave;

double mass [MID], rx [MAX] [NN] ;

double x [MAX] [3], vx[MID] [3];

double u2 [MAX] [3}, v2 [MAX] [3];

double £ [MAX] [3], vy [MAX] [3];

double ul [MID] [3], V1IMID] 131, we [MAX] [3];

dopble t1[NN] [NN] ,t2[NN] [NN],t3 [NN] [NN];

double g1 INN] [NN] ,g2 [NN] [NN], g3 [NN] [NN] ;

/* we ew ee ow ee i ee a a a a a a re ee ee ee rere trae */

void params (void)

char

short int

c1,c2,c3,c4;
chi, ch2,ch3,ch4,ch5;

int dim;

double xoff,yoff,zoff;

parf = fopen ("params.dat","r");

do {
fscanf (parf,"%c",&cl);
chil = ((cl == ‘A’) [] (cl == ‘a’));
ch2 = ({cl == ‘R’) || (cl == ’r’));

} while ((chl == 0) && (ch2 == 0));

if (chi t= 0) {
fscanf (parf, "$c%ctc",&C2,&C3,&C4) ;
ch3 = ((c2 == ’U’) || (c2 == ’u’));
ch4 = ((c3 == ‘'T’) || (c3 == ‘t’));
ch5 = ((c4 == ‘0’) [| (c4 == '0’));
mode = 0;

if (ch2 != Q) {
fscanf (parf, "tc%ctc",&c2,&c3,&c4);
ch3 = ((c2 == 'E’) |! (c2 == ’e’));
ch4 = ((c3 == ‘'L’) [| (c3 == ‘1’));
ch5 = ((c4 == 'X’) |) (c4 == 'x'));
mode = 1;

219

s = 0;

if ((ch3 == 0) 11 ((ch4 == 0) 11 (ch5 == 0))) {
printf (" Line 1 must be AUTO : automatic step control\n");
printft (* RELX : getting a relaxed lattice\n");
return;

fscanf (parf,"%d",é&n);
if (nm > MID) {
printf (" Number of allowed lattice points = %td\n",MID);

return;

fscanf (parf,"%d",&ion);

if (ion > 1) {
printf (" Only one incident ion is allowed.\n");
return;

fscanf (parf,"%1f",&T);
fscanf (parf,"%1lf",&interval);
fscanf (parf, "$lf£", &hmax);
fscanf (parf,"%1f£",&tol);
fscanf (parf, "$1f£",&la);
fscanf (parf, "td", &ma);
fscanf (parf,"%d",&mb);
fscanf (parf,*%d",&mc);
fscanf (parf, "$1lf",&zmin) ;
fscanf (parf, *$li*,&zmax);
fscanf (parf, *tlf*,&zsave);

Lf (ion) {

fscanf (parf,"tlf lf Slf lf S1lf£ %1f£ %1f"*,&x[n-1] [0], &x[n- yer,
; &x[n-1] (2],&vx{n-1] [0], &vx[n-1] [1],&vx[n-1] [2], &mass [n- -1))
printf ("n = $d T = %£\n",n,T);
fclose (parf);
s=1;

void lattice (void)
register int i;

latf = fopen ("lattice.dat",*r");

for (is 0; ifscanf (latf,"%lf S1f Slf SLE Bl£ Bl£ Bit’, &x{i}][0},&x{i}[(1),&xli} [2],

&vx[i][0],&vxfi}[1],&vx[i] [2],&mass[i]);

};
printf(" Over \n");
fclose (latf);

void energy (void)
register int p,q;

short int ga,qb,qc,rs,sum;

short int Jja,value,l, yard [NN];

int 1,3,Z2, decode, encode, stare[NN];
double axis, ayij, dzij,rsqij,rij;:

220

double dxik,dyik,dzik,rik,nH,nS;

double e, zij [NN], zijn,oc,z,tfc;

double af, af3, bil, bijn,rq,gx,ua,ul,u3,dul,du3;
double xx [NN], yy INN], zz[(NN], fc [NN];

double PE, KE, EN, vsq, St, Px, DY, Dz, rxe [NN];

PE = 0.0;

KE = 0.0;

px = 0.0;

py = 0.0;

pz = 0.0;

for (i=0; i

qa = floor ((x[i} [0] + 12.00) /cutoff);
qb = floor ((x[i]{1] + 12.00) /cutof£);
qe = floor ((x[{i}[2] + 12.00) /cutoff);

encode = qa*SYZ + qb*SIDEZ + qc;

if ((qa < 0) Ii (qb < 0) [I (qe < 0)) encode = 0;
p = score[encode];

zonefencode] [p] = i;

score [encode] ++;
code[{i] = encode - STD;

v (i=0; iif (tpe[i] == 0) {
nS = 0.00;
nH = 0.00;

for (ja=0; ja<27; jat+) {

decode = code[i] + enc[ja];
if ((decode >= 0) && (decode < CUBES)) {

for (1=0; 1 < score[decode]; 1++) {
j = zone[decode] [1];

if (tpe[j] == 0) sqecut = 9.00;
af (tpe[j] == 1) sqeut = 4.00;
dxij = xf{i] [0] - xf{j] [0];
dyij = x[ij[1) - mete

dazij
rsqij = Gxij*dxij + dyij*dyij + dazij*dzij;

if ((rsqij < sqcut) && (rsqij > 0.10)) {
rij = sqrt(rsqij);

if (tpe[j) == 0) f{
R = 2.85;
D = 0.15;

‘3

if (tpe[j] == 1) {
R = 1.85;
D = 0.15;

if (rij >R- D) {
va = 0.5*3.14159*(1.0 + (rij - R)/D);

ul = cos(ua);
u3 = cos(3.0*ua);
tic = 0.5 + 9.0*u1/16.0 - u3/16.0;
} else {
tic = 1.00;
if (tpe[j] == 0) nS += tfc;
if (tpe[j] == 1) nH += tfc;
};
}3
r = floor(nH + nS);
if (r < 0) r = 0;
rq = nH + nS - 1.0*r;
As[i}) = Au[r] + rq*(Au[r+1] - Aulr]);
Bs[{i] = Bulr) + rq*(Buf{r+1] - Bulr]);
Hs[i] = Hu(r] + rq*(Hu[r+1] ~- Hulr]);
};
};
for (i=0; ivalue = 0;
for (ja=0; ja<27; ja++) {

decode = code[i] + enc[ja];
if ((decode >= 0) && (decode < CUBES)) {

for (1=0; 1 < score[decode]; l++) {

j = zone[decode] [1];
rs = 2*tpe[i] + tpe[j];
sqcut = -1.00;

switch(rs + 1) {
case 1 : sqeut = 9.00;

break;
case 2 : sqcut = 4.00;
break;
case 3 : sqcut = 4.00;
break;
case 4 : sqcut = 2.89;
adxij = x{ij [0] - xf} 10];
dyij = xlij{l] - xI3] [1];
azij = xf{i][2] - x[j]{2];
rsqij = adxij*dxij + dyij*dyij + dzij*dzij;

if ((rsqij < sqceut) && (rsqij > 0.10)) {
rij = sqrt(rsqij);

yard{value] = rs;
if (rs == 0) {

A = 1830.8;
ldal = 2.4799;

221

R 2.85;
Dd 0.15;
Re [value]
Bo [value]
1da2 {value
43
if (rs == 1) {
A = As{il;
ldal = 2. 9595;
R= 1.85;
D = 0.15;
Re[value] = 1.47
Bo{value] = Bs [1
; lida2[value] =
if (rs == 2) {
A = As([j];
ldal = 2.9595;
R = 1.85;
D = 0.15;
Re[value] = 1.47
Bo[value] = Bs[j
} lda2[value] = 1.
if (rs == 3) {
A = 80.07;
ldal = 4.2075;
R= 1.40;
D = 0.30;
Re [value]
Bo [value]
; lda2 [value

if (rij > R-
ua
ul
u3

"oi

“HW
Ww
an

cos (ua) ;

} else {

Seem
pay
~]
rary
iw)

5S;
1:
615

cos (3.0*ua);
fc[value] = 0.5 + 9.0*u1/16.0 - u3/16.0;

fce[value) = 1.00;

158;

= 1. 7956;

D) {
0.5*3.14159*(1.0 +

(rij

- R)/D);

PE += A*exp(-ldal*rij)*fc[value] ;

stare[value] = j;
rxe[value] = rij;

xx[value] = dxij;
yy [valuej = dyij;
zz{value] = dzij;
value++;

for (p=0; p < value; p++)
for (p=0; p < value; p++)
j = stare(p];
rij = rxe[p];

zij[p]

for (q=0; q < value; q++)

if (q t= p)
rik = rxe[q];

0.0;

222

223

oc = (xx[p]*xx(q] + yy[pl]l*yy[q] + zz[p]*zz{q])/(rij*rik);
sum = yard[p] + yard[q];

if (sum == 0) {
c = 1.1le-6;
d = 0.1603;
H = ~0.59826;
alpha = 5.1975;
cu = 3;

si;

if ((sum > 0) && (sum < 3)) {
c = 0.0216;
ad = 0.27;
alpha = 4.00;
cu = 3;
H = Hs[il];

if (sum == 4) {
c = 0.70;
dad = 1.00;
H = -1.00;
alpha = 0.00;

) cu = 1;

if (sum > 4) {
c = 4.00;
d= 0.00;
H = 0.00;
alpha = 3.00;
cu = 1;

};

e = c + d*(H - oc)*(H - oc);

df = (rij - Re{p]) - (rik - Re[q]);

if (cu == 3) {

df3 = dfi*df*df;

Zz = exp (alpha*df3);
} else {

z= exp(alpha*df);

zij(p] += fcl[q]*e*z;

‘3
}3

if (value >= 2) {
for (p=0; pif (yard[{p] == 0) {
eta = 0.78734;
dita = -0.5/eta;

} else {

eta = 1.00;

dlta = -0.80469;
33

zijn = pow(zij[p],eta);
bij = “21, 0 + zijn;
bijn = pow(bij,dita);
st = Bo[p] *bijn*exp (-1da2[p]*rxe[p]);
PE -= st*fc(p];

};

} else if (value == 1)
st = Bo[0]*exp(- iaa> [0] *rxet0]);
PE -= st*fc{0];

224

};

};
PE /= 2.0;

for (i=0; ivsq = vx[i] [0] *vx[i] [0] + vxfi][1])*vx[i] [1] + vx{i] [2)*vx[il] [2];
KE += vsq*mass [i];

px += mass[iJ]*vx[ij [0]
py += mass[{i]*vx[i] [1]
pz += mass{i]*vx[ij [2]

KE *= 52.1986;
EN = PE + KE;

fprintf (outf," E = $11.4f eV PE = %11.4f eV KE = %11.4f eV\n",EN, PE,KE);

fprintf (outf," Time = %10.4f fs\n #\n",tme);
printf (" E = $11.4f eV PE = %11.4f ev KE = %11.4f eV\n",EN, PE,KE);

printf (" px = %8.4f py = %8.4f pz = %8.4f£\n",px,py,p2);

we see

func (y,w)

double yI]f{
double w[][3];

3];

short int qa,qb,qc,rs, sum;
short int ja, yard [NN] ;

int i,j,k,1,r,s,decode, encode, min;
double axis, ayij, azis, rsqij,rij;

Gouble dxik,dyik,dzik,rik, zi, qx,rq;

double Fr,fx,fy,f£z,st,fac,stc,nH,nS,tic;
double zij [NN], oc,e,z,zijn,te,ez;

double af, adf2, af3, bij, bijn, vil [NN], vl;
double sx (NN], sy [NN], Sz [NN], £¢[NN] ,dfc(NN] ;
double tx{NN},cty(NN],tz[NN},ti,tm,tr, expo;
double xcl, yel, zcl, xc2, yc2, zc2, ua,ul,u3,dul,du3;
double CX, Cy,CZ,xXax,yay, Zaz, fcx, afcx;
double xx {NN], yy [NN], zz[NN];

for (i=0; i

qa = floor ((y[i] [0] + 12.00)/cutoff);

qb = floor ((y[iJ[1] + 12.00)/cutoff);

ace = floor ((y[i] [2] + 12.00)/cutoff);

encode = gqa*SYZ + qb*SIDEZ + qc;

if (({qa < 0) II (qb < 0) I! (qe < 0)) encode = 0;

p = score[encode];
zone(encode][p] = i;
score [encode]++;
code[i] = encode - STD;

};
for (i=0; iwf{i] [0] = 0.0;
w{i}{1}) = 0.0;
} wl[i][{2] = 0.0;
for (i=0; ism; i++) {
if gepe {a} == 0) {
nS = 0.00;
nH = 0.00;

for (ja=0; ja<27; ja++) {
decode = code[i] + enclja];

if ((decode >= 0) && (decode < CUBES)) {
for (1=0; l

j = zone[decode] [1];

sqcut = -1.00;

if (tpe[j] == 0) sqcut = 9.00;

if (tpe[j}] == 1) sqceut = 4.00;

a@xij = yfi][0] - y[3] [0];

@yij = yfi}{1) - yf3] [1];

dzij = yfij{2) - Yl 121;

rsqij = dxij*dxij + dyij*dyij + dzij*dzij;

if ((rsqij < sqcut) && (rsqij > 0.10)) {

rij = sqrt (rsqij);

stor[iJ[p] = J;
rx[i]{p] = rij;

P+t+;

if (tpe{j] == 0) {
R= 2.85;
D = 0.15;

if (tpe[j] == 1) {
R = 1.85;
D = 0.15;

if (rij > R-D) {
va = 0.5*3.14159*(1.0 + (rij - R)/D);
ul = cos(ua);

u3 cos (3.0*ua) ;
tic = 0.5 + 9.0*u1/16.0 ~ u3/16.0;
} else {
tfc = 1.00;
};
if (tpe[j]) == 0) nS += tfc;
if (tpe[j] == 1) nH += tfc;

225

226

x = floor(nH + nS);
if (r < 0) r = 0;
rq = nH + nS - 1.0*r;

As[i] = Au[r] + xrq* (Au[r+1]}] - Aulr]);
@As(i}] = Au[r+1] - Au[r];

Bs{i] = Bulr] + rq*(Bufr+1] - Bulr]});
@Bs[{i}] = Bu[r+1] - Bufr];

Hs{ij] = Hufr} + rq*(Hufr+1] - Hulr]));
GHs[{i] = Hulr+1] - Hu[r];
}3

if (tpe[i] == 1) {

for (ja=0; ja<27; ja++) {
decode = code[i] + enc[ja];

if ((decode >= 0) && (decode < CUBES)) {
for (1=0; l

j = zone[{decode] [1];
sqcut = -1.00;

if (tpe{j] == 0) sqceut = 4.00;

if (tpe[j] == 1) sqceut = 2.89;

dxij = yf[i][0] - y[3] [0];

dyij = yiil{i] - y{3i{1l;

dzij = yfi][2] - Y(31 (21;

rsqij = Y axij "axl 3 + Gyij*dyij + dzij*dzij;

if ((rsqij < sqcut) && (rsqij > 0.10)) {
rij = sqrt(xrsqij);

stor[il[p] = J;
rx({il{p] = rij;

p++;

valf[i] = p;
}3
for (i=0; i

if (1 >= n) {
min = 1;

for (p=0; pif (min) vaifi] = 0;

for (p=0; pj = stor[i](p];
rij = rx{illpl:;

xx{p] = i} [0] - y[j][0})/ri3
yylp) = (yfiJ{2} - y(j](1))/rij;
zz{ip] = i} [2] - y(3]{2))

227

rs = 2*tpefi] + tpelj];

if (rs == 0)

A = 1830.8;
ldail = 2. 4799;
R= 2.85;
D = 0.15;
Re(p] = 2.35;
Bolp| = 471.18;
ida2[(p] = 1.732
yi
if (rs == 1) {
A = As{il;
ldal = 2.9595;
R = 1.85;
D = 0.15;
Re[p] = 1.475;
Bo[p] = Bs[il;
lda2[p] = 1.6158;
he
if (rs == 2) {
A = As{jl;
idal = 2.9595;
R= 1.85;
D= 0.15;
Re[p] = 1.475;
Botp] = Bs{3];
lda2{p] = 1.6158;
‘3
if (rs == 3) {
A = 80.07;
ldal = 4.2075;
R= 1.40;
D= 0.30;
Re[p] = 0.74144;
Bo[tp] = 31.38;
ida2[{p] = 1.7956;

}3
yard(p}] = rs;

if (rij > R-D) {
0.5*3.14159*(1.0 + (rij - R)/D);
cos (ua);
cos (3.0*ua);
dul = 0.5*3.14159*sin(ua)/D;
du3 = 1.5*3.14159*sin(3.0*ua) /D;
fefp] = 0.5 + 9.0*u1/16.0 - u3/16.0;
Gfc([p] = 9.0*dul/16.0 - du3/16.0;
} else {
fe[p}] = 1.00;
dfc{p] = 0.00;

i)
racy

if (iexpo = exp(-ldal*rij);
st = A*expo;
Fr = ldal*st*fc({p] + st*dfc[p];

fx = Fr*xx([p];
w[i][0}] += £x;
wi3][0] -= £x;

fy = Fr*yy([pl:
w[li][1] += fy;
wifi](1] -= fy;

fz = Fr*zz(pl;
w(i]([2] += £2;
wf{3)[2] -= £2;

if (rs == 1) 8s =i;
if (rs == 2) s = J;
if ((rs == 1) I! (rs == 2)) {

for (q=0; q

k = stor[s
rik = rx{s

xax = (y[s - y[k][0})/rik;
yay = (y[s - y(k] [1])/rik;
zaz = (yls - y{k) [2])/rik;
R = 2.85;
D = 0.15;
} else {
R= 1.85;
) D = 0.15;

if (rik > R-D) {
ua = 0.5*3.14159*(1.0 + (rik - R)/D);
dul = 0.5*3.14159*sin(ua)/D;

au3 1.5*3.14159*sin(3.0*ua) /D;
dficx = 9.0*du1/16.0 - du3/16.0;
} else {
dficx = 0.00;
if (tpe[k] == 0) Fr = fc[p] *expo*dAs [s] *dficx;
if (tpe[k] == 1) Fr = fc{p] *expo*dAs [s] *dfcx;

fx = Fr*xax;
w[s] [0] += £x;
w[k] [0] -= £x;

fy = Frtyay;
wi{s][1] += fy;
w{k] [1] -= fy;

fz = Fr*zaz;
w[s]{2] += £2;
w{k][{2} -= £2;

228

ziji(p]
vij{p]

for
gl
g2
g3

};

0.0;
0.0;

nou

(q=0; acval [i]; q++) {
(p} [a] 0.

{p) [a]
[p] (q]

0. b
0.0;

WoW tt

for (p=0; p

rij

axij
dyij
azij3

for

= rx{i][p);

xx{[p)};

yy(p];
zzip);

wou

(q=0; q

if (q t= Pp)

rik = rxfiliaq);
dxik
ayik
azik

xx{[q];
yylal];
zz{q];

oc = axij*dxik + dyij*dyik + dzij*dzik;

sum = yard[p] + yard[q];

if (sum == 0) {
1.1le-6;
0.1603;
-0. 59826;
ha = 1975;
= 3;

“ap mana
‘On uu

um > 0) && (sum < 3)) {
0.0216;
0.27;
ac=

Hs [i]

if ((s

ph.

= 3;
Hs

1 4.00;

manana

we
Khe.

QP TA.
Gk
oni un

e=c + €*(H - oc)*(H - OC);
af = (rij - Relp)) - (rik - Relq));

if (cu == 3) {

dfi2 ef*af;

df3 af*df2;

z = exp(alpha*df3);
} else {

229

z = exp(alpha*df);

ez = fc[q]*e*z;
fz1 = dfc{q]*e*z;

zij(p] += ez;

if (cu == 3) {
vl = 3.0*alpha*df2*ez;
} else {
vl = alpha*ez;
de
vij{p] += vl;
vil += fzi;
gl{p][q] -= vil*dxik;
g2([p]{q] -= vl*dyik;
g3{pl{q] ~= vi*dzik;
sx[{p] += vl*dxik;
sy{p] += vi*dyik;
sz(p] += vi*dzik;

ti = fcl[q)*z*

if ((sum == 2

2.0*da*(H - oc);
) tt (sum == 1)) {

for (r=0; r

1 = stor[
if (tpe{l
if (tpe[l

gl{p] [r]
g2[p] [r]
g3[p) [r]

sx[p] +=

sy[p] +=
sz {p] +=

tm = ti/rij;

titdfic[r]*dHs[iJ;

j =
] ) tr = ti*dfc[{r)*dHs [i];

tr*xx([r];
tr*yy[r];
tr*zz[r);

oc*dxij;
oc*dyij;
oc*dzij;

tx{p] += tm*xcl;
ty[p] += tm*ycl;
tz{p}] += tm*zcl;

xe2 = dxij - oc*dxik;
ye2 = dyij - oc*dyik;
ze2 = Gzij - oc*dzik;
tm = ti/rik;

tli{p){q] = tm*xc2;
t2{pl{q] = tm*yc2;
t3{p][q] = tm*zc2;

230

231

};

for (p=0; pj = stor[i][p];
st = 0.0;

te = 0.0;

if (val[i}] >= 2) {
if (yard(p] == 0) {
eta = 0.78734;
dita = -0.5/eta;
} else {
eta = 1.00;
alta = -0.80469;
zijn = pow(zij[p],eta);
bij = 1.0 + zijn;
bijn = pow(bij,dlta); __
expo = exp(-lda2[p]*rx[i] [p]);
st = Bo[p]*bijn*expo;
stc = st*fc[p];
te = - 0.5*stc*dlta*eta*zijn/ (bij*zij[p]);
} else if (val[i] == 1) {.
expo = exp(-lda2[p]*rx[{i] [p]);
st = Bo[p]*expo;
ste = st*fc[p];
zijn = 0.00;
bijn = 1.00;

for (q=0; qk = stor[i] {aq};

cx = te*tl[p] [q];
cy = te*t2[p] [q];
cz = te*t3[p) [q];
w[k][0] += te*gl[p][q] - cx;
w[k} [1] += te*g2[p}[q] - cy;
w{k] [2] += te*g3{p][q] - cz;
w[iJ[0] += cx;
w[i][1] += cy;
; w[i][{2] += cz;
Fr = - stc*lda2[p]/2.0 - te*vijip] - st*dfc[p]*0.5;

cx = Fr*xx[p] + te*tx[p];
w{i} [0] += cx + te*sx[p];
w[j] [0] -= cx;

cy = Fr*yy[p] + te*ty[p];
wfi]{1] += cy + te*sy[p];
w[j] [1] -= cy;

cz = Fr*zz[p] + te*tz[p];
w{i][2] += cz + te*sz{p];

wf{j](2] -= cz;

if ((yard{p}] == 1) Il (yard[p] == 2)) {
if (yard[p] == 1) s =i;
if (yard[p] == 2) s = j;

for (q=0; qk = stor[s][q];

rik = rx[s][q];

xax = (y{s] [0] - y[k])[0])/rik;
yay = (y[s] [1] - yk] (1])/rik;
zaz = (y[s)[2]) - y{k][2})/rik;
if (tpe[k] == 0) {

R = 2.85;

D= 0.15;
} else {

R= 1.85;

D= 0.15;
‘i

if (rik > R-D) {
ua = 0.5*3.14159*(1.0 + (rik - R)/D);
dul = 0.5*3.14159*sin (ua) /D;
au3 = 1.5*3.14159*sin(3.0*ua) /D;
dfcx 9.0*dul/16.0 - du3/16.0;
} else
dafcx 0.
3;

if (tpe[k] =
1f (tpe[k] =

Hoon It

00;

tou
eal
3]
Ln]

fx = Fr*xax;
w{s]) [0] += £x;
w[k] [0] -= £x;

fy = Fr*yay;
w(s}{1] += fy;
w(k] [1] -= fy;

fz = Fr*zaz;

w{s][2] += f2;
w(k]} [2] -= f2;

3 i9.5788e-3/mass[i];
] *= fac;

] *= fac;

periodic (r)

double r[}][3];

k =n;
for (1=0; i

(r[i] [0] < sl);
(rf{1} (0) > sr);

ta
tb

- fclp] *expo*bijn*dBs[s] *dfcx*0.5;
- fc[p] *expo*bijn*dBs [s] *dfcx*0.5;

232

233

te = (r[{ij[{1] «< sn);
td = (rf{i}[1] > sf);
if (ta) {
r[{k]) [0] = rf{i]} [0} + delx;
r{k] (1) = r{ij{1)
r{k] [2] = rfi]{2]
tpe[k] = tpe[il;
k++;
if (tc) {
r[{k) [0] = r[ai})[0] + delx;
r({k}{1] = ri} [1] + dely:
r{k]{2] = rfil (2h;
tpe[k] = tpe[i];
k++;
di
if (td) {
r{k] [0] = r[i][0] + delx;
r[{k][1} = r{i}{1] - dely;
rik] [2] = rfij [2];
tpe[k]) = tpe[i];
k++;
3;
if (tb) {
r{k} [0] = r[iJ[0) - delx
r(k} [1] = rfi] (1);
r{k] [2] = rf{i][2];
tpe[k] = tpe([i];
k++;
if (te) {
x[k] [0] = r[i][0] - delx;
r{k) [1] = rf{i}[1] + dely;
rik} {2} = rf{i] {2};
tpe[k]) = tpe[i];
k++;
}i
if (td) {
r({k](0] = r[i])[0] - delx;
v[k}) [1] = rfi][1] - dely;
v[k] [2] = rfi)[2];
tpe[k] = tpe[il];
K++;
};
hi
if (te) { .
rf{k} [0] = rf{i]}[0];
r{k) [1] = rfi] [2] + dely;
r[k] [2] = rf[i}{[2];
tpe(k] = tpe[il;
k++;
}3
1f (td) { .
r[k] [0] = rfi} [0];
rik) [1] = rfi][1] ~ dely;
r{k] [2] = rf[i][2];
tpe[k] = tpe[il;
k++;

if (k > MAX - 4) {
warf = fopen ("*warn.dat*",*w");
fprintf (warf," 2\n");
fprintf (warf,” %5.1f\n",est);
fprintf (warf," k = ¢d\n",k);
fclose (warf);
exit (0);

234

};
}3
m= k;
/* printf (" Number of atoms = %d\n",m); */
/* wee ee ee eee ee ee ew ee ee ee te Oe EE ee eee ee ee */

void RKA (void)

short int cond;

int steps, force;
double pre,sgn,h2,hm,hs, range, gy,vsq:
double third,h,hx,err,z,delta;
double w{MAX} [3],y [MAX] [3];
double u3 (MID} [3];
Gouble v3 [MID] [3];
est = 0.0;
range = -10.00;
rmin = 10.00;
steps = 0;
= hmax;
tme = 0.0;
force = 0;
cond = 1;
for (i=0; irigid[i] = 0;
zs{ijJ = 0;
if (x[i][2] > zmax) rigid[i] = 1;
if (xf{iJ[2] < zsave) zs[i] = 1;
if (zs{ij}) {

fprintf (outf," %6.2f %6.2f %6.2f %7.4f %$7.4f $7.4£ %5.1f\n",x[i] [0],
x[iJ{1],x[i}][2],vx[i] [0],vxfi}[1],vx[i][2],mass[i]);

tpe[i] = 0;

if (mass[{i] < 3.0) tpef{i] = 1;
if ((mass[i] > 5.0) && (mass[i] < 32.0)) tpe[i] = 0;

‘3

me=n;

while ((fabs(T - tme) > 0.0001) && (tme < T)) {

/ \
/ \

steps = steps + 1;
periodic (x);
if (cond == 1) {
energy ();
cond = 0;
func (x,f);

hm = h/3.0;
hs = hm*hm;
h2 = h*h;

for (i=0; i<3; i++) {

235

for (j=0; Jjy(j]{i] = x[j] [i] + 2.0*vx[j] [i]*hm + 2.0*hs*f£[j] [i];
\; cf; (rigid[j]) y[3]} [i] = x{3] [1];
h; ‘

periodic (y);
func (y, w) 7

for (i=0; i<3; i++) {
for (j=0; jul[3] [3] = x3] [i] + vx[j] [i] *h + (£(5] [4] + wfl3] (iJ) *h2/4.0;
vi{j}] [i] = ye + (£[5] [i] + 3.0*w[j] [i])*h/4.0;

if (rigid[j]) {
ul[j]{i] = Pe ]{fil;
vi{3} [i] = vx{3) (al;
3 ‘
};
h 0.5*h
/ \
/ \
do {
hm = h/3.0;
hs = hm*hm;
h2 = h*h;

for (i1=0; i<3; i++) {
for (j=0; jyj] [i] = x[j]fi]_ + 2.0*vx[j][i]*thm + 2.0*hs*f[j] [i];
if (rigid[j]) y[3][i] = x[3] [il];

‘3

periodic (y);
func (y.w);

for (1=0; i<3; i++) {
for (3=0; jen; j++) {
u2[j] [i] = x{3] [i] + vx[{j] fi] *h + (f£[5]) [3] + wi la} )*h2/4.0;
v2{3][3] = yetqi ta) + (£[j] [1] + 3.0*w{[3] [i])* 0;
if (rigid[j]) {.
u2[(j] [i]
v2[3] [1]

Ts
ax

periodic (u2);
func (u2,w);

for (i=0; i<3; i++) {
for (j=0; jy{3]{i] = u2{3} [i] + 2.0*v2[j][i)]*hm + 2.0*w[3] [i] *hs;
b; if (rigid{3]) ylj]{il = x{fj] [il];
‘3

236

periodic (y);
func (y,w2);

for (i=0; on i++)
for (j= j5313) (4) = u2[j
v3[3)[1] = v2{3
if (rigid[j]) {
u3[j] [i] = x[

v3 [3] {i] =

i})*h2/4. 0;

};
‘iG

delta = 0.002*h*tol;

err = 0.0;
for (i=0; i<3; i++) {
for (j=0; jz= fabs( u3{j] [i] - ulf3} (i) );
if (z > err) err = 2;
z fabs( v3[j3]{i]) - vl{3]} [i] );
if (z > err) err = Z;

err = err/7.0;
if ((err > delta) && (force == 0)) {
h = h/2.0;
for (i=0; i<3;: i++)
for (j=0; jul[j)] [i] = u2[j]
vil3] [i] = v2{[3)

) {
fi];
{i};
yi, .

printf (*failed\n");

if (h < 0.0001) {
force = 1;
} while ( err > delta );
force = 0;
; i<3; i++) {
3 J

= u3[J}] [i] + (u3[j] [4] - util
] = v3{3] fi] + (v3[3] [a] - vil

ren
32

if ((ion) && (x{n-1][2] > range)) range = x[n-1] [2];

if (h < 0.000001) {
warf = fopen ("warn.dat","*w");
fprintf (warf," 3\n");
fprintf (warf," %5.1f\n",est);
fclose (warf);
exit(0);

}3
if (mode) {
for (i=0; i<3; i++) {
for (j=0; jsgn = w{j) (i) *vx[j] fil:
if (sgn < 0.00) vx[j]) [i] = 0.00;
};
};

h = 2.0*h;
printf (" Step %d",steps);
printf (" h = %7.4f *,h);
tme = tme + h;
pre = pre + h;
if (fabs(pre - interval) < 0.001) {
pre = 0.0;
cond = 1;
for (i=0; iif (zsf[i]) {

fprintf (outf," %7.3£ %7.3f %7,3£ %9.6£ $9.6£ &9.6£ &5.1f\n",x[il[0l],

x[i] [1] ,xfi)] [2], vx[i] [0], vxfi] [1], vxfi] [2],mass[i]);

; est = tme;

printf (" time = %7.2f fs\n",tme);

hx = delta/err;
*‘h = 0.7*h*pow(hx,0.25);

if ((pre + h) > interval) h = interval ~- pre;
if (h > hmax) h = hmax;

};
periodic (x);
energy ();

if (ion) {
range -= 0.1841;
vsq = vx[n-1]) [0)*vx[n-1) [0]
vsq += vx[n-1]} [2] *vx{[n-1] [2]
gy = 52.1986*vsq*mass{n-1];

+ vx[n-1] [1] *vx{n-1} [1];

fprintf (ranf," Range of incident ion : $6.2f\n", range) ;
fprintf (ranf," Distance of closest approach : %6.2£\n",rmin);
fprintf (ranf," Atom : %d\n",atom);

; fprintf (ranf," %6.2£ %-6.2f (%-d) %6.2f\n\n",range, rmin, atom, gy) ;

warf = fopen ("warn.dat","w");
fprintf (warf," O\n");
fclose (warf);

{* ee a i ee mn mm we

main() {
int ij;
Au[0] = 1.005*323.54;
Au[1] = 1.005*323.54;
Au[2] = 1.109*323.54;
Au[3] = 0.953*323.54;
Au[4] = 1.00*323.54;
Au[5] = 1.00*323.54;
Au[6] = 1.00*323.54;
Au[7] = 1.00*323.54;

237

Bu[0] = 0.930*84.18;
Bull] = 0.930*84.18;
Bul2} = 1.035*84.18;
Bul3] = 0.934*84.18;
Bul4] = 1.00*84.18;
Bu[5] = 1.00*84.18;
Bu(6] = 1.00*84.18;
Bul7] = 1.00*84.18;
Huf[0}] = ~0.040;
Hu[i] = -0.040;
Hu[2] = -0.040;
Hu(3] = -0.242;
Hu[4] = -0.47;
Hu[5] = -0.47;
Hul6] = ~0.47;
Hu[7] = -0.47;
SYZ = SIDEY*SIDEZ;
STD = SYZ + SIDEZ + 1;
for (i=0; i<3; i++) {
enc{i] = i;
enc({i+3] = i + SIDEZ;
enc{i+6] = i + 2*SIDEZ;

for (1=0; 1<9; i++) {
*enc[i+9} = enc{i] + SYZ;
enc[i+18] = enc[i] + 2*SYZ;

params ();

cutoff = 3.00;

if (s == 0) printf (“error\n");
if (s == 1) {

= delx - 2.2*cutoff;
sn = 2.2*cutoff;
= dely - 2.2*cutoff; */

delx = la*ma/sqrt (2.0);
dely = la*mb/sqrt (2.0);
= 2.6*cutoff;

sr = delx - 2.6*cutoff;

sn 2.6*cutof£;

sf dely - 2.6*cutoff;

if (mode == 0) printf (" Mode := AUTO\n");
if (mode == 1) printf (" Mode := RELX\n");

lattice ();

outf

fopen ("out.dat*,"w");

ranf = fopen ("range.dat","w");

RKA ();

fclose (outf£);
fclose (ranf);

238

239

finf = fopen (*final.dat*,*w");
for (i=0; ien; i++) {
fprintf (finf," $11.7£ %11.7£ %11.7£ %8.4f %8.4f $8.4f $5.1f\n",x[i] [0],
x{i}[1],x{i} (2],vx[i} [0],vxfil][1],vxfi] [2],mass[iJ);

fclose (finf);

};