Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...

Analysis of the Extended Defects
in 3C-SiC
by
Ezra Jacobus Olivier
Submitted in partial fulfilment of the
requirements for the degree
Magister Scientiae
in the Faculty of Science at the
Nelson Mandela Metropolitan University
Supervisor: Prof J.H. Neethling February 2008
PDF processed with CutePDF evaluation edition www.CutePDF.com

Dedicated to my wife and parents

My sincere thanks to the following people:
ACKNOWLEDGEMENTS
- My supervisor, Professor J.H. Neethling for his guidance and encouragement
throughout this project.
- Any of the staff or students from the NMMU Physics Department whom
played a contributing role in any way during my research
- SANHARP for their financial assistance
- My parents, brother and sister for encouragement and support throughout
- My wife for her understanding, support and love
The assistance of the following people is also gratefully acknowledged:
- Dr Anna Carlsson at FEI Company in Eindhoven for the HRTEM results
- Dr Chris Franklyn at NECSA for doing the proton implantation
- NovaSiC for supplying the SiC used in the study
- Johan Westraadt for the annealing of the samples at the University of the
Witwatersrand

SUMMARY
The dissertation focuses on the analysis of the extended defects present in as-grown
and proton bombarded β-SiC (annealed and unannealed) grown by chemical vapour
deposition (CVD) on (001) Si. The proton irradiation was done to a dose of 2.8 × 10 16
protons/cm 2 and the annealing took place at 1300°C and 1600°C for 1hr. The main
techniques used for the analysis were transmission electron microscopy (TEM) and
high resolution TEM (HRTEM).
From the diffraction study of the material the phase of the SiC was confirmed to be
the cubic beta phase with the zinc-blende structure. The main defects found in the β-
SiC were stacking faults (SFs) with their associated partial dislocations and
microtwins. The SFs were uniformly distributed throughout the foil. The SFs were
identified as having a fault vector of the type 1/3 with bonding partial
dislocations of the type 1/6 by using image simulation. The SFs were also
found to be predominantly extrinsic in nature by using HRTEM analysis of SFs
viewed edge-on. Also both bright and dar-field images of SFs on inclined planes
exhibited symmetrical and complementary fringe contrast images. This is a result of
the anomalous absorption ratio of SiC lying between that of Si and diamond.
The analysis of the annealed and unannealed irradiated β-SiC yielded no evidence of
radiation damage or change in the crystal structure of the β-SiC. This confirmed that
β-SiC is a radiation resistant material. The critical proton dose for the creation of
small dislocation loops seems to be higher than for other compound semiconductors
with the zinc-blende structure.

OPSOMMING
Hierdie dissertasie handel oor die uitgebreide defekte in β-SiC gegroei deur middel
van chemiese damp neerslag op (001) silikon substrate. Transmissie
elektronmikroskopie is ook gebruik om die defekte in proton bestraalde beta
silikonkarbied (nie uitgegloei en uitgegloei) te ondersoek. Die beta silikonkarbied is
bestraal met 400 keV protone tot ’n dosis van 2.8 × 10 16 protone/cm 2 .
Die uitgloeiing van die materiaal het plaasgevind by 1300°C en 1600°C vir een
uur. Hoë resolusie transmissie elektronmikroskopie is ook aangewend om die
stapelfoute in SiC te analiseer.
Met behulp van elektron diffraksie en hoë resolusie transmissie
elektronmikroskopie is die fase van die silikonkarbied bevestig as die kubiese
beta fase. Die hoof defekte wat gevind is in die SiC was stapelfoute met hul
geassosieerde parsiële ontwrigtings en mikro-tweelinge. Die stapelfoute was uniform
gespasieer deur die material. Dit is bevestig deur die gebruik van beeldsimulasie dat
die stapelfoute ‘n fout vektor van die tipe 1/3 en
bindings parsiële ontwrigtings van die tipe 1/6 het. Verder is ook vasgestel, met
behulp van hoë resolusie transmissie elektronmikroskopie dat die stapelfoute
hoofsaaklik ekstrinsiek is. Beeld simulasie van stapelfoute het aangetoon dat die
ligveld en donkerveld beelde van die foute semetries en komplimentêre is. Dit is as
gevolg van die waarde van die anomale absorpsie koefficient van die silikonkarbied
wat tussen die van silikon en diamand lê.
Die analise van die uitgegloeide en nie-uitgegloeide bestraalde beta silikonkarbied het
geen tekens van stralingskade of fase verandering getoon nie. Dit het net weereens
bewys dat beta silikonkarbied ‘n bestralings weerstandige materiaal is en dat die dosis
van protone wat nodig is vir die vorming van klein ontwrigtings lussies heelwat hoër
is vir die materiaal as vir ander saamgestelde halfgeleiers met die sink-blende
struktuur.

CONTENTS
Chapter 1: INTRODUCTION 1
Chapter 2: OVERVIEW OF CRYSTAL DEFECTS IN β-SIC 3
Page
2.1. Introduction 3
2.2. Cubic and Zinc-Blende Crystal Structures 3
2.2.1. The Face-Centred Cubic Structure 3
2.2.2. The Zinc-Blende Structure 5
2.3. Point Defects, Defect Migration and Annealing Behaviour 7
2.3.1. Introduction 7
2.3.2. Point Defects 7
2.3.3. Defect Migration and Annealing Behaviour 8
2.4. Dislocations 10
2.4.1. Introduction 10
2.4.2. The Dislocation Line and Burgers Vector 11
2.4.3. Motion of Dislocations 13
2.5. Partial Dislocations and Slip 15
2.6. Dislocations in the Zinc-Blende Structure 16
2.7. Stacking Faults 18
2.8. Twinning 21
2.9. Vacancy and Interstitial Loops 22
Chapter 3: ION IMPLANTATION AND RADIATION DAMAGE 24
3.1. Introduction 24
3.2. Ion Ranges 24
3.2.1. Introduction 24
3.2.2. Range Calculations 25
3.2.3. The Linhard, Scharff and Schiott (LSS) Theory 26
3.3. Defects Created by Ion Implantation 30
3.3.1. Introduction 30
3.3.2. Theory of Displacement Damage 30
3.3.3. Defects 34
3.3.3.1. Defects Created During Irradiation 34
3.3.3.2. Aggregation of Point Defects and Growth of Defect 34
Clusters during Heat Treatment
Chapter 4: DYNAMICAL THEORY OF ELECTRON DIFFRACTION 36
AND IMAGE SIMULATION
4.1. Introduction 36
4.2. Theory of Electron Diffraction 36
4.2.1. The Direct Space Bragg Equation 36
4.2.2. The Bragg Equation in Reciprocal Space 38
4.2.3. Darwin-Howie-Whelan Equations 40
4.2.4. DHW Equations: Two-Beam Case 42

4.2.5. Two-Beam Scattering Matrix 44
4.2.6. Crystal Defects and Displacement Fields 45
4.3. Image Contrast for Selected Defects 47
4.3.1. Line Defects 47
4.3.2. Stacking Faults 47
4.3.3. Fringe Contrast Observed from Twinning 51
Chapter 5: LITERATURE REVIEW OF SiC 53
5.1. Introduction 53
5.2. CVD Growth of β-SiC on Si 53
5.3. Crystal Defects in β-SiC 56
5.3.1. Introduction 56
5.3.2. Accommodation of Misfit and Interfacial Twinning 57
5.3.3. Mechanisms for the Formation of Stacking Faults 58
5.3.4. Stacking Fault Energy in β-SiC 61
5.4. Ion Implantation and Radiation Damage in β-SiC 61
Chapter 6: EXPERIMENTAL DETAILS 64
6.1. Introduction 64
6.2. CVD Growth of β-SiC 64
6.3. Proton Implantation in β-SiC 64
6.3.1. Ion Ranges and Defect Production 65
6.4. Annealing Procedure 67
6.5. Sample Preparation 68
Chapter 7: RESULTS AND DISCUSSION 69
7.1. Introduction 69
7.2. Extended Defects in β-SiC Grown by CVD on (001) Si 69
7.2.1. Crystal Structure and the SiC/Si Interface 70
7.2.2. Stacking Faults and Partial Dislocations 74
7.2.3. Twinning 82
7.3. Hydrogen Implanted β-SiC 83
7.3.1. Unannealed 83
7.3.2. Annealed at 1300°C 84
7.3.3. Annealed at 1600°C 85
7.4. Reassessment of Unimplanted Sample 94
7.4.1. Overview of Investigation 94
7.4.2. Results 95
Chapter 8: CONCLUSION 96
8.1. Introduction 96
8.2. TEM Analysis of β-SiC Grown on (001) Si by CVD 96
8.3. TEM Analysis of β-SiC Proton Bombarded and Annealed 97
β-SiC
References 99

Analysis of the Extended Defects
in 3C-SiC
by
Ezra Jacobus Olivier
Submitted in partial fulfilment of the
requirements for the degree
Magister Scientiae
in the Faculty of Science at the
Nelson Mandela Metropolitan University
Supervisor: Prof J.H. Neethling February 2008

Dedicated to my wife and parents

My sincere thanks to the following people:
ACKNOWLEDGEMENTS
- My supervisor, Professor J.H. Neethling for his guidance and encouragement
throughout this project.
- Any of the staff or students from the NMMU Physics Department whom
played a contributing role in any way during my research
- SANHARP for their financial assistance
- My parents, brother and sister for encouragement and support throughout
- My wife for her understanding, support and love
The assistance of the following people is also gratefully acknowledged:
- Dr Anna Carlsson at FEI Company in Eindhoven for the HRTEM results
- Dr Chris Franklyn at NECSA for doing the proton implantation
- NovaSiC for supplying the SiC used in the study
- Johan Westraadt for the annealing of the samples at the University of the
Witwatersrand

SUMMARY
The dissertation focuses on the analysis of the extended defects present in as-grown
and proton bombarded β-SiC (annealed and unannealed) grown by chemical vapour
deposition (CVD) on (001) Si. The proton irradiation was done to a dose of 2.8 × 10 16
protons/cm 2 and the annealing took place at 1300°C and 1600°C for 1hr. The main
techniques used for the analysis were transmission electron microscopy (TEM) and
high resolution TEM (HRTEM).
From the diffraction study of the material the phase of the SiC was confirmed to be
the cubic beta phase with the zinc-blende structure. The main defects found in the β-
SiC were stacking faults (SFs) with their associated partial dislocations and
microtwins. The SFs were uniformly distributed throughout the foil. The SFs were
identified as having a fault vector of the type 1/3 with bonding partial
dislocations of the type 1/6 by using image simulation. The SFs were also
found to be predominantly extrinsic in nature by using HRTEM analysis of SFs
viewed edge-on. Also both bright and dar-field images of SFs on inclined planes
exhibited symmetrical and complementary fringe contrast images. This is a result of
the anomalous absorption ratio of SiC lying between that of Si and diamond.
The analysis of the annealed and unannealed irradiated β-SiC yielded no evidence of
radiation damage or change in the crystal structure of the β-SiC. This confirmed that
β-SiC is a radiation resistant material. The critical proton dose for the creation of
small dislocation loops seems to be higher than for other compound semiconductors
with the zinc-blende structure.

OPSOMMING
Hierdie dissertasie handel oor die uitgebreide defekte in β-SiC gegroei deur middel
van chemiese damp neerslag op (001) silikon substrate. Transmissie
elektronmikroskopie is ook gebruik om die defekte in proton bestraalde beta
silikonkarbied (nie uitgegloei en uitgegloei) te ondersoek. Die beta silikonkarbied is
bestraal met 400 keV protone tot ’n dosis van 2.8 × 10 16 protone/cm 2 .
Die uitgloeiing van die materiaal het plaasgevind by 1300°C en 1600°C vir een
uur. Hoë resolusie transmissie elektronmikroskopie is ook aangewend om die
stapelfoute in SiC te analiseer.
Met behulp van elektron diffraksie en hoë resolusie transmissie
elektronmikroskopie is die fase van die silikonkarbied bevestig as die kubiese
beta fase. Die hoof defekte wat gevind is in die SiC was stapelfoute met hul
geassosieerde parsiële ontwrigtings en mikro-tweelinge. Die stapelfoute was uniform
gespasieer deur die material. Dit is bevestig deur die gebruik van beeldsimulasie dat
die stapelfoute ‘n fout vektor van die tipe 1/3 en
bindings parsiële ontwrigtings van die tipe 1/6 het. Verder is ook vasgestel, met
behulp van hoë resolusie transmissie elektronmikroskopie dat die stapelfoute
hoofsaaklik ekstrinsiek is. Beeld simulasie van stapelfoute het aangetoon dat die
ligveld en donkerveld beelde van die foute semetries en komplimentêre is. Dit is as
gevolg van die waarde van die anomale absorpsie koefficient van die silikonkarbied
wat tussen die van silikon en diamand lê.
Die analise van die uitgegloeide en nie-uitgegloeide bestraalde beta silikonkarbied het
geen tekens van stralingskade of fase verandering getoon nie. Dit het net weereens
bewys dat beta silikonkarbied ‘n bestralings weerstandige materiaal is en dat die dosis
van protone wat nodig is vir die vorming van klein ontwrigtings lussies heelwat hoër
is vir die materiaal as vir ander saamgestelde halfgeleiers met die sink-blende
struktuur.

CONTENTS
Chapter 1: INTRODUCTION 1
Chapter 2: OVERVIEW OF CRYSTAL DEFECTS IN β-SIC 3
Page
2.1. Introduction 3
2.2. Cubic and Zinc-Blende Crystal Structures 3
2.2.1. The Face-Centred Cubic Structure 3
2.2.2. The Zinc-Blende Structure 5
2.3. Point Defects, Defect Migration and Annealing Behaviour 7
2.3.1. Introduction 7
2.3.2. Point Defects 7
2.3.3. Defect Migration and Annealing Behaviour 8
2.4. Dislocations 10
2.4.1. Introduction 10
2.4.2. The Dislocation Line and Burgers Vector 11
2.4.3. Motion of Dislocations 13
2.5. Partial Dislocations and Slip 15
2.6. Dislocations in the Zinc-Blende Structure 16
2.7. Stacking Faults 18
2.8. Twinning 21
2.9. Vacancy and Interstitial Loops 22
Chapter 3: ION IMPLANTATION AND RADIATION DAMAGE 24
3.1. Introduction 24
3.2. Ion Ranges 24
3.2.1. Introduction 24
3.2.2. Range Calculations 25
3.2.3. The Linhard, Scharff and Schiott (LSS) Theory 26
3.3. Defects Created by Ion Implantation 30
3.3.1. Introduction 30
3.3.2. Theory of Displacement Damage 30
3.3.3. Defects 34
3.3.3.1. Defects Created During Irradiation 34
3.3.3.2. Aggregation of Point Defects and Growth of Defect 34
Clusters during Heat Treatment
Chapter 4: DYNAMICAL THEORY OF ELECTRON DIFFRACTION 36
AND IMAGE SIMULATION
4.1. Introduction 36
4.2. Theory of Electron Diffraction 36
4.2.1. The Direct Space Bragg Equation 36
4.2.2. The Bragg Equation in Reciprocal Space 38
4.2.3. Darwin-Howie-Whelan Equations 40
4.2.4. DHW Equations: Two-Beam Case 42

4.2.5. Two-Beam Scattering Matrix 44
4.2.6. Crystal Defects and Displacement Fields 45
4.3. Image Contrast for Selected Defects 47
4.3.1. Line Defects 47
4.3.2. Stacking Faults 47
4.3.3. Fringe Contrast Observed from Twinning 51
Chapter 5: LITERATURE REVIEW OF SiC 53
5.1. Introduction 53
5.2. CVD Growth of β-SiC on Si 53
5.3. Crystal Defects in β-SiC 56
5.3.1. Introduction 56
5.3.2. Accommodation of Misfit and Interfacial Twinning 57
5.3.3. Mechanisms for the Formation of Stacking Faults 58
5.3.4. Stacking Fault Energy in β-SiC 61
5.4. Ion Implantation and Radiation Damage in β-SiC 61
Chapter 6: EXPERIMENTAL DETAILS 64
6.1. Introduction 64
6.2. CVD Growth of β-SiC 64
6.3. Proton Implantation in β-SiC 64
6.3.1. Ion Ranges and Defect Production 65
6.4. Annealing Procedure 67
6.5. Sample Preparation 68
Chapter 7: RESULTS AND DISCUSSION 69
7.1. Introduction 69
7.2. Extended Defects in β-SiC Grown by CVD on (001) Si 69
7.2.1. Crystal Structure and the SiC/Si Interface 70
7.2.2. Stacking Faults and Partial Dislocations 74
7.2.3. Twinning 82
7.3. Hydrogen Implanted β-SiC 83
7.3.1. Unannealed 83
7.3.2. Annealed at 1300°C 84
7.3.3. Annealed at 1600°C 85
7.4. Reassessment of Unimplanted Sample 94
7.4.1. Overview of Investigation 94
7.4.2. Results 95
Chapter 8: CONCLUSION 96
8.1. Introduction 96
8.2. TEM Analysis of β-SiC Grown on (001) Si by CVD 96
8.3. TEM Analysis of β-SiC Proton Bombarded and Annealed 97
β-SiC
References 99

1
CHAPTER ONE
INTRODUCTION
Silicon carbide (SiC) is a wide band gap semiconducting ceramic with excellent
thermal, mechanical and electrical properties. It has a wide range of applications,
which include its use as structural material for high temperature applications in
aggressive environments (Eveno et al. (1992)). It is proposed as an encapsulating
material for nuclear fuel in light water and gas-cooled fission reactors due to its good
resistance to neutron radiation damage and also as material to be used in fusion
environments due to its excellent thermal stability. Hence the study of this material
and its structural integrity under different conditions similar to that experienced in the
reactor environment is important. A detailed knowledge of the extended defects
present in the SiC after the growth process is required together with the study of the
evolution of the micro and nano-structure of SiC at high temperatures and irradiation
conditions.
This dissertation focuses on a transmission electron microscopy (TEM) study of the
extended defects in 3C-SiC prepared by chemical vapour deposition on silicon (Si)
substrates, as well as the investigation of the defects produced in this material by 400
keV hydrogen implanted to a dose of 2.8 × 10 16 protons/cm 2 . The effects of post
irradiation annealing on the implanted material was also investigated for samples
annealed at temperatures of 1300°C and 1600°C for one hour. Silicon is the preferred
substrate for the CVD growth of single crystalline 3C-SiC and due to the lattice
mismatch between SiC and Si, the twins, stacking faults, partial dislocations and
misfit dislocations present in the SiC will be similar to the lattice defects present in
SiC grown on other substrates. In a nuclear reactor such as the pebble bed modular
reactor, the SiC layers in the nuclear fuel particles are irradiated with high energy
neutrons. The point defects produced by the neutrons will be the same type as those
produced by high energy protons. In this investigation SiC were bombarded with
protons and then annealed to determine the critical proton dose needed to produce
extended defect clusters during post-implantation annealing. The annealing at
elevated temperatures also allowed the investigation of possible phase transformations
in the 3C-SiC.

2
The characteristics of two-beam diffraction contrast TEM images of stacking faults
(SFs) and thin twin platelets in SiC were investigated by using image simulation.
Since it is expected that the anomalous absorption ratio of SiC should lie between that
of diamond and Si, it is important to investigate how the value of this ratio would
affect the symmetry of bright and dark-field TEM images of SFs in SiC. Image
simulation was carried out using the software developed by Head et al. (1973)
published by Marc De Graef (2003).
The outline of the dissertation is as follows. In Chapter 2 a brief discussion of the
crystal defects found in face-centred cubic (fcc) and zinc-blende crystal structures is
given. Emphasis is placed on the extended defects found in 3C-SiC. Defects created
during ion bombardment and their migration during heat treatment is also discussed in
general. Chapter 3 discusses the theory of ion implantation and radiation damage in
materials. Fundamental theories used in calculating the ion ranges and displacement
damage are given and the coalescence of point defects leading to the formation of
defect clusters during heat treatment is discussed. Chapter 4 deals with the theory
relating to the method of image simulation. This is done by briefly discussing the
dynamical theory of electron diffraction and the derivation of the Darwin-Howie-
Whelan (DHW) equations. A simple method for calculating a line profile across the
fringes of a stacking fault is also given. Chapter 5 is a literature review of previous
research done on 3C-SiC focusing on crystal growth, crystal defects and behaviour
under irradiation conditions. Chapter 6 gives the experimental details of the current
investigation on 3C-SiC. Chapter 7 contains the results of a transmission electron
microscopy (TEM) study of the as-grown and implanted 3C-SiC along with the
discussion of the results. Chapter 8 lists the conclusions derived from the results of
this dissertation.

2.1. Introduction
3
CHAPTER TWO
OVERVIEW OF CRYSTAL DEFECTS IN 3C-SiC
In this chapter a short overview of the types of crystal defects found in 3C-SiC is
presented. The content presented is by no means complete but focuses on the
important aspects needed to understand the analysis of the experimental results later
on. The reader is advised to consult other references written specifically for this
purpose if a deeper understanding is required (Hull et al. (1984)). This chapter
focuses mainly on the defects found in the zinc-blende structure since this is the
crystal structure of 3C-SiC. The structure itself is explained firstly by referring to a
more simple structure i.e. the fcc structure with special attention given to the atomic
stacking sequences in the principal crystallographic directions. Furthermore the types
of point defects found in SiC are discussed and their diffusion characteristics are
reviewed. Finally the nature of the extended defects present in 3C-SiC is discussed.
2.2. Cubic and Zinc-Blende Crystal Structures
2.2.1 The Face-Centred Cubic Structure
The unit cell of the face-centred cubic (fcc) structure is a cube with atoms situated at
the corners and centres of the cube faces as illustrated in Fig. 2.1. It contains four
1
atoms in positions 000 ; 0
1 1
2 2 ; 2 2
1 1 1
0 and 0 2 2 , with the smallest translation vectors
being of the type (1/2). This corresponds to half a surface diagonal of the unit
cell.

Fig. 2.1. The face-centred cubic structure with shortest translation vector ½
4
Furthermore all next larger translational vectors such as that of the and
type can be decomposed into vectors of the type (1/2) for example:
(1/2)[110] + (1/2) 110]
= [100]
[ _
(1/2)[110] + (1/2) [110] = [110]
The stacking sequence of the {100} and {110} planes are ABABAB…and that of the
{111} planes ABCABC…. (termed close-packed planes). The two stacking sequences
are shown in Fig. 2.2.
(a) (b)
Fig. 2.2. The stacking sequences of (a) the {100} and (b) the {111} planes in a fcc
structure.
A
B
A
B
A
B
A
B
A
B
C
A
B
C

2.2.2 The Zinc-Blende Structure
5
The zinc-blende structure can be seen as composed of a basic fcc framework with
atoms situated at positions as discussed above, with the addition of a further set of
1 1
atoms situated at positions 4 4 4
1 3 1 1 3 1 3
3 3
; 4 4 4 ; 4 4 4 and 4 4 4
3 . The two sets of atoms may be
of the same type as for example in diamond (carbon), silicon, germanium or it may
consist of a composition of different elements such as for GaAs, ZnS and SiC. The
unit cell consists of 8 atoms and can be seen as two interpenetrating fcc lattices
a
displaced by a translation of 111 as shown in Fig. 2.3.
4
Fig. 2.3. The SiC zinc-blende unit cell with the smaller atoms being the carbon and
the larger silicon.
The stacking sequence of the zinc-blende structure for the {100}, {110} and {111}
planes are analogous to that of the fcc-structure with the only difference being that the
two sets of atoms create a doubling of the stacking sequence in the sense that in the
{100} and {110} cases one obtains a sequence AA'BB'AA'… and in the {111} a
sequence AA'BB'CC'… is seen (where the ' denotes the alternate set). This is shown
in Fig. 2.4 for the stacking of the {100} and {111} planes.

(a) (b)
6
Fig. 2.4. Stacking sequences of the zinc-blende structure for the (a) {100} and (b)
{111} planes
A
A'
B
B'
A
A'
B
B'
A
A'
B
B'
The two consecutive layers of the constituent atoms in the same type of configuration
are considered as a single plane consisting of a double layer of Si and C atoms. Thus a
ABABAB… or ABCABC… stacking sequence as in the case for the fcc structure
results with the only difference being that a layer contains both the constituent atoms.
-SiC is a cubic phase of SiC with a zinc-blende structure as shown in Fig. 2.3. The
{110} planes consist of double layers of Si and C atoms. Also the stacking sequence
for the {100} and {110} planes are AA'BB'AA'… and AA'BB'CC' for the {111}
planes (where the ' denotes the stacking sequence of the alternate set of atoms). Note
also that the consecutive layers of the silicon and carbon atoms in the sequence for
e.g., AA' is closely spaced and thus the stacking sequence can be generalized to be
ABABAB… and ABCABC… in the {100}, {110} and {111} case respectively by
combining the two closely spaced layers to form one plane.
A
B
A
B
A
B
A
A'
B
B'
C
C'
A
A'
B
B'
C
C'
A
B
C
A
B
C

2.3 Point Defects, Defect Migration and Annealing Behaviour
2.3.1 Introduction
7
In this section the different types of point defects in a crystal lattice are discussed.
Fundamental statistics on their concentration in the lattice are presented and their
diffusion mechanisms are considered. In general the diffusion behaviour of point
defects in SiC cannot be fully explained yet, since it is a complex process that is still
being researched.
3.2 Point Defects
A point defect is defined as the insertion or absence of an atom in a crystal lattice
uncharacteristic to that of the normal atomic sites. When the defect is a result of atoms
comprising of the parent lattice it is termed an intrinsic defect and when the atom is an
impurity it is termed extrinsic. Intrinsic point defects may further be characterised as
being vacancy or interstitial, vacancy being the absence of an atom in a regular atomic
site and an interstitial the insertion of an atom into a non-lattice site. This is depicted
in Fig. 2.5.
Fig. 2.5. The intrinsic defects, vacancy and interstitial present in a lattice (from Hull
et al. (1984))
Extrinsic point defects may be characterised as substitutional, where an atom of the
parent lattice lying in a lattice site is replaced by an impurity atom, or interstitial,
where the impurity atom is at a non-lattice site (Fig. 2.6).

8
Fig. 2.6. The extrinsic defects, substitutional and interstitial present in a lattice (from
Hull et al. (1984))
Vacancies and interstitials can be produced by plastic deformation and also due to
high-energy particle irradiation. Also intrinsic defects are produced by virtue of
temperature, a thermodynamically stable concentration of these defects are always
present above 0 K. The equilibrium fraction of point defects is given by the relation,
n
eq
E f
nt
exp( )
(2.1)
kT
where nt is the total number of atomic sites, k Boltzmann’s constant and Ef the energy
of formation of one defect. For a vacancy, the energy is that required to remove one
atom from the lattice and place it on the surface of the crystal, and for the interstitial it
is the energy required to remove one atom from the surface and insert it into an
interstitial site. Typically the vacancy formation energy is two to four times less than
that of the interstitial and consequently the concentration of interstitials is far lower
than that of vacancies at a certain temperature T.
2.3.3 Defect Migration and Annealing Behaviour
In general point defects are continuously attempting to migrate, the success of which
critically depends on the defect migration energy Em and is largely determined by the
specimen temperature. Strain induced motion is also possible but it is the aim of this
section to discuss the former. The atomic jump frequency at temperature T of a point
defect is given by,

v
m
Em
vm0
exp( )
(2.2)
kT
9
where Em is the migration energy of the point defect, either vacancy or interstitial and
υm0 is the atomic vibration frequency. This atomic jump frequency is a measure of
how often it is expected for atoms to leave their normal positions but it does not say
anything about the direction the atom will take for any particular jump. The atom
accordingly takes a very haphazard path as it wanders through the crystal and this
path is termed a random walk and could be correlated or uncorrelated depending on
the type of defect in question since the probabilities of motion for each are different.
A substitutional impurity jumping through a vacancy mechanism for example is said
to have a correlated random walk because there is not an equal probability of its
nearest neighbours being vacant.
Thus if a region in a crystal contains a concentration of point defects all of these
defects will perform random walks but will also eventually disperse and spread
throughout the crystal causing a net transport of matter. This happens since there is a
difference in concentration of defects in the crystal causing a concentration gradient.
This net transport of matter is described by Fick’s first law,
dc
J D
(2.3)
dx
dc
where J is the flux, the concentration gradient and D the diffusion coefficient,
dx
which depends on the mechanism of diffusion, type of crystal structure and jump
frequency. This equation can also be given in a more useful form known as Fick’s
second law,
2
dC d C
D
(2.4)
2
dt
dx

10
in which the rate of change of the concentration with time is described. This is useful
since it enables the change in concentration to be determined at different time
intervals. Furthermore the diffusion coefficient may be given as,
D
Q
/ kT
D0e
(2.5)
where D0 is called the pre-exponential factor and is temperature independent and Q is
the energy of activation for diffusion which depends on the diffusing species.
In general the formation energy of interstitials is considerably higher than that of
vacancies but their migration energy is far lower. This is due to the considerable
lattice strain created by the interstitial and thus relieving this strain by means of
migration should be highly probable. If interstitials are formed thermally or by other
means they will rapidly migrate to sinks. Such sinks will include the surface, other
interstitials or vacancies and extended defects. If the interstitials come into contact
they will form stable clusters and if they come into contact with vacancies mutual
annihilation will occur. If two interstitials form a cluster it is termed a di-interstitial
and if three form a cluster it is a tri-interstitial etc. The probability of migration of
these clusters within the lattice become increasingly less probable as they increase in
size and will when reaching a sufficient size act as a sink for the migration of other
point defects. The same process holds for vacancy migration with the only difference
being that the migration energy for vacancies are much higher than that of interstitials.
In general the migration energy of substitutional impurities in the lattice is also higher
than that of the interstitial.
2.4. Dislocations
2.4.1 Introduction
In this section the theory of dislocations is presented. Concepts of dislocation line and
Burgers vector are explained and also different types of dislocations in a crystal are
discussed. The motion of dislocations through the processes of glide and climb is

11
explained and the concept of partial dislocations and slip discussed since it is
important in the understanding of the formation of stacking faults.
2.4.2. The Dislocation Line and Burgers Vector
To understand the concept of the dislocation line and Burgers vector the following
geometrical analogy may be followed and is shown in Fig. 2.7. Imagine a dislocation
being produced by making a cut in a perfect crystal. Following this the two sides of
the crystal are shifted with respect to one another by a translation vector of the lattice.
Then the missing material is added or surplus material removed. The shifted surface
of the cut may grow together in such a way that the cut is no longer discernable. Thus
at the inside of the crystal, at the edge of the former cut surface, a line of strongly
disturbed material remains. This line is called the “dislocation line”.
(a) (b)
(c)
Fig 2.7. The geometrical analogy of a Volterra-cut describing a dislocation present
in a crystal (from Bollmann (1970)). (a) A cut is made in a perfect crystal. (b) The two
sides of the crystal are shifted with respect to one another by a translation vector of
the lattice. (c) The shifted surface of the cut may grow together in such a way that the
cut is no longer discernable.

12
The dislocation is surrounded by perfect but elastically deformed material and the cut
is called a “Volterra-cut”. Within a crystal, dislocations are characterised by two
parameters:
1. the path of the line in the crystal,
2. the Burgers vector (a measure of the strength of the dislocation).
Also the material in the immediate surroundings of the dislocation is called the
“dislocation core”. The Burgers vector is defined by comparing the disturbed crystal
with the perfect. An arbitrary line sense is attributed to the dislocation line. A closed
circuit in the sense of a right-handed screw is then made around the dislocation line in
an area of unperturbed material. This closed circuit is then repeated step by step with
reference to the perfect crystal in which the circuit will remain open. The vector
pointing from the end to the beginning in the reference crystal is defined as the
Burgers vector. The procedure is shown in Fig. 2.8.
(a)
(c)
(b)
(d)
Fig. 2.8. The Burgers circuit used in defining the Burgers vector of a dislocation
(from Bollmann (1970)). (a) A closed circuit in the sense of a right-handed screw is
made around the dislocation line in an unperturbed material. (b) The closed circuit is
repeated step by step with reference to the perfect crystal in which the circuit will
remain open. The vector pointing from the end to the beginning in the reference
crystal is defined as the Burgers vector. (c) and (d) The same procedure is followed
with the circuit being closed in the distorted crystal.

13
Straight dislocations furthermore can be categorised into edge and screw dislocations.
An edge dislocation may be seen as a result of an extra plane inserted into the material
and a screw as a shear of two consecutive planes such that it seems that two original
parallel crystal planes are now joined as a helical surface (shown in Fig. 2.9.).
Fig. 2.9. A geometrical description of a screw dislocation present in a crystal (from
Bollmann (1970)). (a) A cut is made in the perfect crystal. (b) The two sides of the
crystal is sheared by a translation vector of the lattice.
The dislocation line and Burgers vectors of an edge dislocation are always normal to
one other and those of a screw dislocation are parallel. In general a dislocation may be
seen as a combination of edge and screw dislocations with associated edge and screw
Burgers vector components given by,
a) screw component bscrew = b·cos(α)
b) edge component bedge = b·sin(α)
where α is the angle between the dislocation line l and the Burgers vector b of the
dislocation.
(a) (b)
2.4.3. Motion of Dislocations
It is possible for a dislocation to move within a material under plastic deformation.
This may be understood by the concepts of glide and climb of a dislocation.

14
Dislocation glide takes place on the slip plane which is the {111} for fcc and zinc
blende structures and is a result of atoms above and below the plane being displaced
by b with respect to one another.
Fig. 2.10. A representation of the process of glide in a crystal (from Bollmann
(1970))
If a dislocation climbs it moves perpendicular to the glide plane. It is only possible if
the dislocation has an edge component and if the temperature and stress is sufficient
for diffusion to be possible.
Fig. 2.11. A representation of the process of climb in a crystal (from Bollmann
(1970))
In general glide is the only mechanism present at low temperatures during plastic
deformation. Also from these mechanisms the definition of the slip plane may be
made. It is defined as the plane which contains both the dislocation line and Burgers
vector of the dislocation.

2.5 Partial Dislocations and Slip
15
In the fcc structure slip occurs on the close-packed planes {111} with the slip
direction . Slip involves the sliding of close-packed planes of atoms over each
other. To see how this can occur the following may be done. Consider that the close-
packed planes can be simulated by a set of hard spheres.
Fig. 2.12. The simulation of close-packed planes by a set of hard spheres to describe
the concept of slip in a crystal lattice (from Hull et al. (1984))
The full circles represents the A layer, the sites marked B the B layer and C the C
layer. Consider next the movement of the layers when they are sheared over each
other. It will be found that that the B layer of atoms will first move to the nearby C
site and then to the next B site instead of directly moving from B site to B site. Thus
the unit lattice displacement b1 is achieved by two movements about the C positions
represented by b2 and b3. If one considers the movement of the unit 1/2
dislocation in the fcc lattice it implies that the motion will take place via two
dislocations termed partial dislocations with Burgers vectors b2 and b3 in a reaction of
the type,
1
2
110
1 1
211 121
6 6
(2.6)
This occurs since it is energetically favourable for the edge dislocation to dissociate
according to Frank’s rule with b 2 edge = a 2 /2 which is greater than bp1 2 + bp2 2 = a 2 /3.

16
2.6 Dislocations in the Zinc-Blende Structure
As in fcc metals, slip occurs in the zinc blende structure on close packed planes along
close packed directions. The predominant slip system is {111} with the
majority of dislocations lying along and directions.
The asymmetry in the zinc-blende lattice causes two possible dislocations in the
lattice for identical Burgers vector and dislocation line direction. As discussed earlier
the {111} layers consist of sets of closely spaced double layers of the constituent
atoms with small internal spacing
a 3a
and large external spacing of . The glide
4 3
4
of a dislocation can then either cut through the small internal spacing or large external
spacing. Two sets of dislocations are thus generated depending on the glide system.
The set of dislocations causing slip between the closest spaced layers is called the
glide set while the other called the shuffle set. The shuffle set is commonly assumed
to be the correct description since fewer bonds have to be broken for the dislocations
to move across the {111} planes.
The properties of dislocations in the zinc-blende structure may be explained in terms
of the concept of a 60° dislocation. In this configuration the slip plane is of the {111}
type with the dislocation line and Burgers vector making an angle of 60° with one
another. This is illustrated in Fig. 2.13.

17
Fig. 2.13. The geometrical setup of the sixty degree dislocation in a zinc-blende
crystal lattice (from Stirland et al. (1976))
There are three possible sixty degree dislocations that could lie on one {111} plane.
The core of the dislocation contains atoms with broken bonds and the axis of
the dislocation lies along a set of identical type atoms. If GaAs is used as an example,
the broken bonds may belong to either Ga or As atoms. The dislocations are called an
α and β dislocation respectively depending on whether the broken bonds belong to Ga
or As atoms respectively. This situation is illustrated in Fig. 2.14.
Fig. 2.14. The (a) α and (b) β type sixty degree dislocations in a zinc-blende crystal
lattice (from Stirland et al. (1976))

18
The polarity of the broken bonds in both situations differ and thus the α dislocation is
positive and the β negative. Accordingly they will have different mobilities and
activation energies. The dotted lines in the figure indicate the extra (double) half-
planes of Ga-As atoms which generate the edge component of the two types of
dislocations.
2.7 Stacking Faults
A stacking fault is a planar defect in which the regular stacking sequence of a local
region within the crystal has been disrupted. These faults are mainly introduced due to
plastic deformation through mechanical or thermal strain but may also be introduced
into a crystal during a CVD growth process. Stacking faults are not expected in an
ABABAB… type stacking sequence since no alternative configuration for an A layer
resting on a B exists. However stacking faults are possible in the ABCABC… type
stacking sequence since alternate stacking configurations do exist. This is frequently
seen in the close-packed {111} planes for the fcc and zinc-blende structures.
Fig. 2.15. The (a) intrinsic and (b) extrinsic stacking faults in an fcc lattice (from Hull
et al. (1984))
(a)
(b)
Two types of stacking faults are possible, termed intrinsic and extrinsic. Intrinsic
stacking faults are formed as a result of the removal of a layer in the stacking
sequence, as shown in Fig. 2.15(a) where part of a C layer has been removed, and

19
extrinsic stacking faults are the inverse of intrinsic and relates to the insertion of an
extra layer between two existing layers as in Fig. 2.15(b) where an A layer has been
inserted between a C and B.
Fig. 2.16. A description of the modification of the stacking sequence in a lattice due to
the presence of intrinsic and extrinsic stacking faults (from Käckell et al. (1998))
Furthermore if an intrinsic stacking fault is introduced by the removal of a B layer for
example, it creates a stacking sequence ABCA/CABC which correlates to only one
modified layer (Fig. 2.16.). When a C layer for example is inserted between an A and
B such as in the case of an extrinsic stacking fault it creates a stacking sequence
ABCA/C/BCABC which implies the modification of two layers.

20
(a) (b)
Fig. 2.17. The dissociation of (a) an edge dislocation in an fcc lattice into (b) two
partial dislocations bounding between them a ribbon of stacking fault (from Hull et
al. (1984))
A stacking fault is generated by the dissociation of an edge dislocation into two partial
dislocations by a reaction of the type,
_ _ _
b edge b p b 1 p2
(2.7)
An edge dislocation present in the crystal with Burgers vector of the type 1/2
(Fig. 2.17(a)) dissociates into two partials with Burgers vector of the type 1/6
type through a reaction shown in equation 2.7 (Fig. 2.17(b)). With the dissociation the
two partial dislocations leave between them a stacking fault and are in turn referred to
as the bonding partials. The associated energy per unit area γ of a stacking fault is
known as the stacking-fault energy and is given by the relation,
[ E ( faulted)
E(
perfect)]
/ A
(2.8)
with E being the energy and A the area. Values typically lie in the range 1-1000
mJ/m 2 .

2.8 Twinning
21
Twinning is a process in which a region of the crystal is deformed through a
homogenous shear process. This produces the original crystal structure but in a
different orientation. The simplest case is the result in which the twinned area is a
mirror image of the original crystal. This is depicted in Fig. 2.18.
Fig. 2.18. A geometrical description of twinning in a crystal lattice (from Hull et al.
(1984))
The open circles represent the position of the atoms before twinning and the filled
circles after. The line x-y is termed the twin boundary with atoms above and below it
mirror images of one another. Twinning may occur due to plastic deformation or
introduced into the material during the CVD growth process. It differs from the
process of slip since no rotation of the lattice is taking place. In the fcc and zinc-
blende structures twinning takes place on the {111} system. It is as a result of
a shear causing a displacement of 1/6 on each consecutive plane and can be
seen as the motion of partial dislocations with b = 1/6 on consecutive {111}
planes lying parallel to x-y.
Furthermore a modification to the electron diffraction pattern obtained from a twinned
area in a crystal also occurs. The twinned sections generate a different set of
diffractions spots according to its crystallographic orientation which are superimposed
onto the diffraction pattern from the perfect crystal. Such a situation is depicted in
Fig. 2.19.

22
Fig. 2.19. The modification of the diffraction pattern due to twinning in a crystal with
the electron beam along the (from Hirsch et al. (1965))
The final orientation of a twin platelet and corresponding twin spots may be obtained,
in the case of fcc crystals, by a 180° rotation of the lattice about the {111} planes.
This is seen by rotating the diffraction pattern from the perfect crystal by 180° and
superimposing it onto the original (Fig. 2.17). This example is called primary
twinning in fcc materials.
2.9 Vacancy and Interstitial Loops
If a material contains a concentration of vacancies and interstitials in excess of the
equilibrium concentration these point defects may diffuse and coalesce to form
clusters and precipitate as platelets which will collapse to form a dislocation loop as
they grow larger as shown in Fig. 2.20.

23
Fig. 2.20. The process of vacancy loop formation in a lattice (from Hull et al. (1984))
This figure depicts the process for vacancy loop formation. The vacancies cluster to
form a platelet with the subsequent collapse of the planes inward to form a dislocation
loop. The dislocation loop may under certain conditions enclose an area constituting a
stacking fault. The stacking fault may be removed by the motion of a partial
dislocation across the loop. Furthermore, loops in general lie on close-packed planes.

3.1. Introduction
24
CHAPTER THREE
ION IMPLANTATION AND RADIATION DAMAGE
In this chapter a model of the implantation of ions into matter and the subsequent
radiation damage is presented. Theories for the calculation of ion ranges are discussed
and reference is made to the most popular approach, that of the LSS theory, to
illustrate the procedure taken in doing such a calculation. The result shown in Chapter
6 was however obtained using software developed by Ziegler et al. (1985) using
Monte Carlo methods. Following this theory of displacement damage and annealing
of defects are presented.
3.2. Ion ranges
3.2.1 Introduction
During ion implantation, the implanted species can lose energy to the target atoms in
two ways, namely electronic excitations (inelastic) and nuclear collisions (elastic). At
higher energies the ion is stripped of some or all of its electrons and multiply ionized
at which stage the energy loss is mainly due to inelastic processes, i.e. electronic
excitation. Occasionally the moving atom will interact directly with lattice atoms and
collisions of the Rutherford type results. As the kinetic energy of the moving atom
decreases its degree of ionization does as well until the atom essentially becomes
neutral at which stage collisions of the hard-sphere type will dominate. The rate at
which energy is lost is given in the following form,
dE
N[
S n ( E)
Se
( E)]
(3.1)
dx
where N is the number of target atoms per unit volume, Sn(E) and Se(E) defined as the
nuclear and electronic stopping powers respectively. The nuclear stopping power
Sn(E) is given by,

S n Td
(3.2)
25
and is also referred to as the stopping cross-section. T is the energy transferred and dσ
the differential cross-section. The electronic stopping power is proportional to the
velocity of the incoming ion and thus is proportional to E kin , the kinetic energy of
the particle. Using equation 3.1 the implanted range R is given by,
0
1
( ) ( )
E
dE
R (3.3)
N S E S E
0
n
e
with E0 being the energy of implantation.
3.2.2 Range Calculations
The first step taken in finding the equation relating the nuclear stopping power is by
solving the scattering integral (equation 3.4) for the centre of mass system scattering
angle θ given by,
U m
du
2 p
(3.4)
0 V ( u)
2 2
1
p u
E
r
where p is the impact parameter, u = 1/r with r the distance between colliding atoms.
V(u) the interatomic potential and
energy. Also Um satisfies the following,
1
V ( U
)
p
m 2 2
U m
E
r
0
E r
M 1M
2
E
with E the projectile’s
M M M )
1(
1 2
which represents the reciprocal of the minimum distance of approach.
(3.5)
Solving this integral the scattering angle θ is then used to obtain the energy
transferred to a struck atom by the relation,

4M 1M
2 2
2
T E
sin T sin
2
m
(3.6)
( M M ) 2 2
1
2
26
From this the differential cross-section d 2pdp
may be obtained using the
impact parameter p which in turn is determined by using equation 3.6. Following this
the nuclear stopping power Sn(E) may be determined by solving equation 3.2 between
the limits 0 to the maximum energy transferred
4M
M
E
1 2
Tm (3.7)
2
( M 1 M 2 )
In finding Sn(E) the differential cross-section dσ is found which in turn depends
heavily on the choice of the interatomic potential V(r) used. Also in most cases the
scattering integral cannot be solved analytically and numerical methods should be
employed which brings with it an added complexity. The most widely used theory in
the prediction of ion ranges in a solid is the LSS theory developed by Linhard, Scharf
and Schiott. In the following section the main results of this theory will be discussed
but it is left to the reader to consult further references for a more detailed
understanding.
3.2.3. The Linhard, Scharff and Schiott (LSS) Theory
The LSS theory uses a Thomas-Fermi model of the interaction between heavy ions to
derive a nuclear stropping power Sn and electronic stopping power Se. The electronic
stopping power is proportional to the velocity of the moving atom since the process of
energy loss is dependent on the kinetic energy of the moving atom and the nuclear
stopping power is obtained through the procedure shown in the previous section.
The interatomic potential used has the form,
2
Z1Z
2e
r
V ( r)
(3.8)
4 r a
0

27
where a = a0(Z1 2/3 + Z2 2/3 ) -½ and is the Thomas-Fermi screening function which is
tabulated numerically. An approximation to the function is also given by,
r
r
a
(3.9)
2 1
a r 2 2 [ c ]
a
with c 3 resulting in the best average fit to the potential.
Using approximation methods in finding the solution the LSS theory predicts a
nuclear stopping power Sn of the form shown in Fig. 3.1.
Fig. 3.1. Nuclear and electronic stopping powers in reduced units. Full-drawn curve
represents the Thomas-Fermi nuclear stopping power, the dot and dash lines the
electronic stopping for k=0.15 and k=1.5. The dashed line gives the nuclear stopping
power for the r -2 potential (from Carter et al. (1976))
The energies and distances are expressed in terms of dimensionless parameters ε and
ρ given by,
aM 2
E
(3.10)
2
Z Z e M M )
1
2
( 1 2
M M
RN4a
(3.11)
2 1 2
and 2
( M 1 M 2 )

28
The nuclear stopping power Sn is thus given by these dimensionless parameters as
d
which is a function of ε only. The electronic stopping power Se is given by,
d
d
d
n
e
k
1
2
1 2 1 2
3 2
1 0.
0793Z1
Z 2 ( M 1 M 2 )
6
with k Z1
2 3 2 3 3 4 3 2 1 2
( Z1
Z 2 ) M 1 M 2
(3.12)
(3.13)
A universal curve cannot be obtained for the electronic stopping power since k
depends on the colliding atoms. Fig. 3.1 shows the electronic stopping power plotted
for two values of k being 1.5 and 0.15. The straight line indicates the dependence on
velocity.
Fig. 3.2. Reduced range-energy plots for various values of the electronic stopping
parameter k (from Carter et al. (1976))
The average total path length ρ is then given by,
0
d { S n ( )
S e ( )}
(3.14)

29
Using this expression, curves of ρ versus ε can be plotted by use of numerical
integration for specific k values as illustrated in Fig. 3.2.
If R is expressed in µg/cm 2 and E in keV then equations 3.11 and 3.10 become,
166
M
1
R
(3.15)
2 / 3 2 3
2
( Z
(
1 Z 2 ) M 1 M 2 )
and
32.
5
M 2
E
(3.16)
2 3 2 3 1 2
Z Z ( Z Z ) ( M M )
1
2
1
2
1
2
The range R is then calculated for a specific Z1, Z2 and E combination by calculating ε
and k and simply reading ρ from the graph using equation 3.11 for the conversion.
Fig. 3.3. The geometrical description of the projected and lateral ranges Rp and R
(from Neethling (1980))
In practice the average projected range Rp is usually measured. It is defined as the
component of the range R parallel to the ion beam direction. The lateral range R is
the component of R perpendicular to the ion beam direction. This is depicted in Fig.
3.3. At energies sufficiently high the ion tends to move in a straight line and only
undergoes appreciable angular deflection when the energy is reduced such that the
dominating process of energy loss is due to hard-sphere collisions. Under these
circumstances the average total path length R and average projected range are
approximately the same.

3.3 Defects Created by Ion Implantation
3.3.1 Introduction
30
This section discusses in short the main aspect of the theory of displacement damage.
The concept of threshold displacement energies (TDE) is discussed and the different
processes involved in the slowing down of the ion in the lattice are explained. A
simple calculation is used to determine the number of displaced atoms per incoming
ion. The type of defects created in the damage process is discussed and their evolution
with annealing is explained.
3.3.2 Theory of Displacement Damage
The effect of atoms being displaced during irradiation with high energy ions is
perhaps the most important process taking place. The displacement of an atom from
its regular lattice site depends on a value Ed which is the minimum energy that is
required to displace the atom from its site. If the atom receives energy in excess of Ed
it is possible that further displacements may result from the movement of the primary
displaced atom. If a hard-sphere approximation and classical non-relativistic
mechanics is used, the maximum energy transferred to a stationary atom by a particle
with mass M1 and energy E is given by equation 3.7,
Thus the minimum incident energy required to displace an atom is given by,
E
m
2
( M 1 M 2 )
Ed
(3.17)
4M
M
1
2
To determine the number of displacements produced by an incoming ion Nd it is
important to understand the amount of energy transferred to the atom through
collisions in the process of slowing down.

31
As stated previously hard-sphere collisions at the lower end of the energy range
dominate as the process for atomic displacements. This occurs since the kinetic
energy of the ion is not sufficient to penetrate the electron cloud of the stationary
atom. If the kinetic energy is sufficient to penetrate the electron cloud collisions of the
Rutherford type dominate. To approximate the transition from hard-sphere scattering
to Rutherford scattering a theory developed by Kinchin and Pease (1955) is
considered.
The theory assumes that the presence of the electron cloud cuts off the Coulomb
interaction between the nuclei of the moving and stationary atoms at a distance r0
given by,
r
0
a
(3.18)
3 3 1 2
( Z Z )
2
1
0
2
2
Thus if the kinetic energy of the ion is less than the Coulomb potential between the
moving and stationary nuclei it is assumed that the collisions are of the hard-sphere
type. If the kinetic energy is greater than the Coulomb potential then the collisions are
of the Rutherford type. A kinetic energy LA at which this transition occurs is defined
and given by,
L
2 3 2 3 1 2
2E
RZ
1 Z 2 ( Z1
Z 2 ) ( M 1 M 2 )
A (3.19)
M 1
where ER is the Rydberg energy and M1 the mass of the stationary atom. Seitz and
Koehler (1956) also showed that the assumption of Rutherford scattering is only valid
for scattering angles of the order b/a, where b is the distance of closest approach.
Thus at smaller angles the effect of screening electrons is still felt. Therefore
collisions only occur for impact parameters less than r0, at which the minimum energy
which can be transferred is,
E
*
2
2
2
2
3
2
3
4E
R Z1
Z 2 ( Z1
Z 2 ) M 2
( )
(3.20)
E
M
1

32
Thus if E * >Ed all Rutherford collisions displace atoms, but an energy LB exist above
which only some of the Rutherford collisions do so. LB is given by,
L
B
2
ER
2 2 2 3 2 3 M 2
4 Z1
Z 2 ( Z1
Z 2 )( )
(3.21)
E
M
d
1
Thus to summarize at higher energies the ion undergoes Rutherford collisions and in
some cases atoms are displaced. If the energy falls below LB all Rutherford collisions
displace atoms. The reason why only some Rutherford collisions displace atoms at
energies E>>LB is since half the energy lost to atoms which receive energy less than
Ed and are thus not displaced. This energy loss is dissipated through lattice vibrations
termed thermal spikes.
As the energy of the ion decreases further the importance of energy loss due to hard-
sphere collisions become more important than that of electronic energy loss and for
this reason Kinchin and Pease (1955) defined a transition energy LC. It is a defined as
the energy above which all energy loss is due to electronic excitation and below
which is due to hard-sphere collisions. The value of LC is difficult to obtain in general
but is approximated for insulators as,
1 M
LC
E
m
4 e
G
(3.22)
where ΔEG is the band gap between valence and conduction band, me electron mass.
For metals the relation is,
1 M
LC
m
4 e
f
where εf is the Fermi level but in general LC may be approximated by,
(3.23)
LC A keV (3.24)

33
where A is the atomic weight. Thus in general it is found that the number of atoms
displaced by an incoming ion Nd depends firstly on its energy. If its energy is less than
LC the number of displaced atoms is determined as follows. Consider an atom with
initial energy T < LC moving in a solid. The first collision then results in a sharing of
the energy T with the struck atom which on average is half that of T. Both atoms will
then continue with energy 1/2T and collide with one atom each sharing their energy
with the struck atom with a factor of an half on average. This process will continue
until the average energy of the struck atoms falls below 2Ed and if this occurs after q
groups of collisions the total amount of displaced atoms will be given by,
q
N d 2 ( T 2Ed
)
(3.25)
This expression is valid if T is greater than 2Ed, if T is between Ed and 2Ed only one
atom is displaced and below Ed obviously no atom is displaced. If T is bigger than LC
the expression becomes LC/2Ed.
If the energy of the atom is bigger than LC and LB Kinchin and Pease showed that the
moving atom will displace ΔN atoms in losing energy ΔE, where
N P E
E
(3.26)
and P is given by,
d
meZ
1[
1
ln( E 2Ed
]
P (3.27)
2
4M
( Z / Z)
ln( 4m
E / M I )
1
effective
4M
M
1 2
with
and 2
2
( M 1 M 2 )
ion is light the expression may be simplified to,
N
d
P E LC
) bL
Ed
e
2
I 8. 8Z
the mean ionization potential. If the implanted
( 0 C
(3.28)

34
where b = 0.5 if LB > LC and b = 0.25 of LB

35
a vacancy dislocation loop if the cluster growth takes place in the presence of a gas.
Instead gas bubbles or voids may form, if the gas eventually diffuses out of the
bubble.

36
CHAPTER FOUR
DYNAMICAL THEORY OF ELECTRON DIFFRACTION AND IMAGE
SIMULATION
4.1 Introduction
This chapter discusses in basic terms the technique of image simulation of two-beam
TEM images of defects. The theory presented is taken from the book “An
Introduction to Conventional Electron Microscopy” written by Marc de Graef (2003)
and it is once again left to the reader to consult this book for any further information.
The theory of electron diffraction is discussed from a dynamical point of view
introducing the concepts of the Bragg equation, reciprocal space and the Ewald
sphere. This is then used to derive the Darwin Howie Whelan equation which in turn
is used for image simulations. Only the two-beam case is considered and the
scattering matrix approach is explained. Finally a simple method to obtain line
intensity profiles from stacking faults and twinned areas on inclined planes is shown.
4.2. Theory of Electron Diffraction
4.2.1 The Direct Space Bragg Equation
Although the process of electron scattering within a crystal is in general a complicated
process it may be explained in a simple way through the Bragg relation. Consider Fig.
4.1.

37
Fig. 4.1. (a) A wave incident on a set of hkl planes at an angle θ, (b) the incident and
diffracted directions and the plane normal must lie in a planar section through a
conical surface with its top in the plane (from De Graef (2003))
A wave is incident on a set of planes with indices (hkl) at an angle θ. Assuming the
planes to be semi-transparent mirrors, part of the intensity of the wave will be
transmitted through the first plane and part of it reflected. If Snell’s law is applied
since an ideal mirror was assumed, the incident and reflected angles must be the same,
and both directions of the wave must be coplanar about a normal n to the (hkl) planes.
Next, if the reflected waves from the first and second planes are considered it is seen
that there is a difference in path length between the two which relate to the waves
being in or out of phase. This path length difference is given by the sum of the
distance PO’ and O’Q which in turn is related to the interplanar spacing dhkl and the
angle θ as follows:
PO'O'Q d
hkl
2d
sin d
hkl
sin
hkl
sin
(4.1)
For in-phase propagation of the two reflected waves, known as constructive
interference, the path length difference should be an integral number of wavelengths
and thus for constructive interference the relation is,
2 sin n
(4.2)
d hkl

38
which reduces to, 2d hkl sin for use in the electron microscope since the n is
incorporated into the value of dhkl using the Miller index notation . It should be noted
that the Bragg equation only describes the geometric representation of diffraction and
does not give any information on the intensity of the diffracted wave. The equation is
derived with respect to a specific plane and states that the incident and diffracted
waves must travel in directions which lie on a conical surface with top in the
diffracting plane and opening angle π/2-θ as illustrated in Fig. 4.1(b).
4.2.2 The Bragg Equation in Reciprocal Space
The direct space Bragg equation however elegant and simple is not useful when the
absolute direction of a diffracted wave needs to be determined. To do this the Bragg
equation should be reformulated in terms of reciprocal space which in turn leads to
the Ewald sphere construction.
From the de Broglie relation it is known that a plane wave may be represented by its
momentum vector p = hk where k has units of reciprocal length and that λ = 1/|k|. k
fully characterises the direction and wavelength of the plane wave with respect to the
crystal reference frame and thus a reciprocal space equivalent of the Bragg equation
can be derived since the plane (hkl) may be represented by the vector ghkl in
reciprocal space.
Fig. 4.2. (a) The incident and diffracted wave vectors with reciprocal lattice vector g,
(b) The redrawn vector construction (from De Graef (2003))

39
Consider Fig. 4.2 which illustrates the wave vectors of the incident and diffracted
waves in Fig. 4.1 with the reciprocal lattice vector g. By redrawing the vector
construction such that k' starts at point C Fig. 4.2 (b) is obtained which shows the
relation,
k' k
g
(4.3)
This is equivalent to the direct space Bragg condition and is shown by projecting the
above equation onto the vector g,
k'
g k
g
g
g;
k g sin k g sin g
sin sin 1
d
hkl
2
(4.4)
from which the Bragg equation follows. The Bragg condition is thus satisfied
whenever the point C falls on the perpendicular bisector plane of the vector g. The
perpendicular bisector plane to the vector ghkl consists of all points that are at the
same distance from the origin of reciprocal space and the reciprocal lattice point hkl.
This leads to a simple geometric construction for the direction of a diffracted wave
when the incident wave vector and crystal orientation are given. This is known as the
Ewald sphere and is depicted in Fig 4.3.
Fig. 4.3. The Ewald sphere construction (from De Graef (2003))

40
The following procedure is followed. First draw the reciprocal lattice with origin O.
Then draw the incident wave vector k such that its end point coincides with O. The
point C is then taken as the center of a sphere with radius |k|. Whenever a reciprocal
lattice point falls on this sphere, the Bragg condition is satisfied and a diffracted
vector k+g may occur. Note also that more than one reciprocal lattice point may lie on
the Ewald sphere which indicates that multiple beam diffraction may occur. This is
due to a relaxation of the Bragg condition due to the sample geometry causing the
reciprocal points to extend into rods (see Hirsch et al. (1965)).
4.2.3 Darwin-Howie-Whelan Equations
Bragg’s law shows that electrons are diffracted in directions k' given by k+g for all
reciprocal lattice points g lying on the Ewald sphere. Hence it may be anticipated that
the total wave function at the exit surface of the crystal will be a superposition of
plane waves, one in each of the directions predicted by the Bragg equation. All that
remains is the computation of the complex amplitudes of each of the diffracted waves
which are given by the Darwin-Howie-Whelan (DHW) equations:
d
dz
g
2is
g
g
i
i
g g
'
e
' g q '
g g
'
g
(4.5)
These DHW equations are derived from the Schrödinger equation for dynamical
electron scattering,
2
2 2
2 8
me
4 K 0 4
U ( r)
V ( r)
2 c
(4.6)
h
where Vc is a complex electrostatic lattice potential Vc=V + iW. The Fourier
transform of which is given by,
V ( r)
V V
'(
r)
iW ( r)
V
c
0
0
2igr
Vg e i
g0 g
W
g
e
2igr
(4.7)

41
V0 is the mean inner potential of the crystal and is positive and causes acceleration of
the electrons and hence the relativistic acceleration of the electron increases to,
^ ^
C
V
(4.8)
0
from which the wave number k0 is given by,
k
0
^
2me
(4.9)
h
which in turn is used to simplify the Schrödinger equation to,
2 2
2
4
k 4
[ U iU ]
(4.10)
with,
0
2me
U ( r)
2
h
g 0
V
2 igr
ge
; (4.11)
igr
g e W
2me
2
U ' ( r)
; (4.12)
2
h
g
To solve equation 4.10 an empty crystal approximation (i.e. U+iU’= 0) is used to
obtain a general solution of the form,
r ( )
g
(4.13)
i k g r
g e
2 ( 0 )
which upon substitution into equation 4.10 and using a high energy approximation the
DHW equations are obtained. To follow the complete derivation the reader is referred
to de Graef (2003). The symbol θg in equation 4.5 is known as the phase factor, sg is
the deviation from the Bragg condition and,
1 1 e
i
q
g
g '
g
i
g
'
g
(4.14)

'
with ξg the extinction distance, g the absorption length and g g
g
'
.
The extinction distance and absorption length is given by the following,
1 U g
k g cos
g
'
1 U g
'
k g cos
g
42
The extinction distances as calculated by Electron Diffraction (2003) is given in Table
4.1. for commonly used reflections for 3C-SiC.
Table 4.1. – The extinction distances in 3C-SiC at 200 kV as calculated by Electron
Diffraction (2003).
4.2.4 DHW Equations: Two Beam Case
Index ξg (in Å)
111 622
220 825
200 1915
400 1383
113 1431
When the special case in which the intensity of the incident beam is shared only
between the transmitted ψ0 and one diffracted beam ψg is considered, the DHW
equations are given by two coupled differential equations. They are,

43
beam left-hand side g' = 0 g' = g
g
d 0
e
0: 2 is 0
0 0 i
'
g (4.15)
dz
q
0
i g
d g
e
g: 2 is g
g i 0 ' g
(4.16)
dz
q
These equations may be written in the form,
dT
dz
dS
dz
i
isgT
S ; (4.17)
q
g
i
is g S T ; (4.18)
q
g
by means of the following substitution,
)
z
0 T ( z e ; (4.19)
i
g z
g S(
z e e ; (4.20)
)
i
with i(
s ) ' g . This is done to remove the dependence on the normal
0
absorption length and to render the equations more symmetric. Thus following this
procedure the solution to the problem is derived as follows. Equation 4.17 is written
as,
q
g dT
S s gq
gT
; (4.21)
i
dz
and
dS
dz
2 q
g d T
sg
q
i
dz
2
g
dT
dz
g
i
g
0
(4.22)

44
Substituted into equation 4.18 and rearranged to give,
2
d T 2 2
T 0
(4.23)
2
dz
with
s
2
g
1
q q
g
g
This is the differential equation for the harmonic oscillator with general solution,
T ( z)
Acos(
z) B sin( z)
(4.24)
From the boundary condition at the entrance surface T(z = 0) = 1 the value of A is
found to be 1. The value for B is found by computing dT/dz and substituting into the
equation for S above and applying the boundary condition S(z = 0) = 0 which leads to
B = -isg/σ and thus,
is g
T ( s,
z)
cos( z) sin( z)
; (4.25)
i
S(
s,
z)
sin( z)
; (4.26)
q
g
These are the general solutions to the dynamical two-beam equations including
absorption. Note also that σ is complex.
4.2.5 The Two-Beam Scattering Matrix
In Section 4.2.4 the solutions to equations 4.17 and 4.18 was found by using the
following initial conditions:
T ( s,
z 0)
1;
S ( s,
z 0)
0 ; (4.27)

45
In addition another set of independent initial conditions can be used to obtain a special
solution:
T '( s,
z 0)
0 ;
S '( s,
z 0)
1;
(4.28)
which shows that it is assumed that all the incident amplitude is in the direction of the
scattered beam rather than the transmitted beam. Using this it is found that the
solutions to T' and S' is given by,
'
T ( s,
z)
S(
s,
z)
;
'
S ( s,
z)
T(
s,
z)
; (4.29)
Thus the expressions for transmitted and scattering amplitudes are swapped and the
sign of the excitation error changed. From equation 4.26 it is also seen that S(-s,z) =
S(s,z). The amplitude at the exit plane of the crystal with thickness z0 is then given by,
0
g
z
z
0
e
(
'
0
) z
( )
where T T(
s,
z)
.
S
( s,
z ) e
0
T
Se
i
T
Se
(
0
) z0
scat 0
i
'
g
g
Se
T
Se
T
i
( )
g
i
( )
g
0
g
z0
(4.30)
(4.31)
Sscat is known as the scattering matrix and is obtained by the knowledge that the
general solution to a system of N first-order differential equations may be written as a
linear combination of special solutions, where the special solutions can be obtained by
stating N independent boundary conditions. Thus in the case for N = 2 two sets of
independent boundary conditions given by equations 4.27 and 4.28 are used to find

46
solutions which in turn are combined to give a general solution from which the
scattering matrix is obtained. The general solution may then be written as follows,
z ) S scat ( s,
z ) (
0)
(4.32)
( 0
0
It should also be noted that the scattering matrix is a complex matrix of the form,
S S iS
(4.33)
scat
r
i
4.2.6 Crystal Defects and Displacement Fields
The presence of a defect in a crystal causes a disruption in the positions of the atoms
as predicted by the Bravais lattice translation vectors. The atoms are displaced from
their positions by a vector R which is a function of position r. This vector field R(r) is
known as the displacement field and relates the displaced position r’ of the atom to
the ideal position r by,
r '
r R(r)
(4.34)
Also the presence of this displacement field causes a deviation in the potential of the
crystal from the perfect crystal at the deformed position given by,
'
V ( r) V ( r R)
V
0
V
0
g
g
V
V
g
g
e
e
2ig(
rR
)
2igR
e
2igr
(4.35)
which shows that the electrostatic potential is modified by a phase factor αg as
follows,
V
g
i
(r)
g
V e with ( r) 2g
R(r)
g
g (4.36)

47
When this is incorporated into the Darwin-Howie-Whelan equations it modifies the
equations to be,
d
dz
g
2i(
s
g
i
g g
'
e
' g q '
g
g
dR
g ) g
i
'
(4.37)
g
dz
which only constitutes a change in the excitation error to an effective excitation error
given by,
dR(r)
( r) s g
(4.38)
dz
eff
sg g
4.3. Image Contrast for Selected Defects
4.3.1 Line Defects
As discussed in section 2.4 a dislocation is a linear lattice defect which may be
characterised by a Burgers vector b and a dislocation line direction u. It may be
characterised as being of edge character with b·u = 0 or screw character with b || u or
a mixture of both. In general the displacement field of a dislocation is given by,
1 sin 2
1
2
cos
R b
be
b u
ln r
(4.39)
2
4(
1
)
2(
1
)
4(
1
)
where υ is Poissons’s ratio, be the edge component of the Burgers vector and (r,θ)
polar coordinates in a plane perpendicular to the dislocation line direction.
4.3.2 Stacking Faults
The aim of this section is not to describe the full process of simulating an inclined
stacking fault with its associated partial dislocations but rather to describe a relatively
easy way of obtaining one-dimensional intensity profiles of stacking fault fringes. The
procedure uses a scattering matrix approach discussed in Section 4.2.5 with the

48
associated displacement field of the stacking fault to obtain a line intensity profile of
the fringes.
As discussed in Section 2.6 stacking faults are produced by a disruption of the regular
stacking sequence of a material. It can also be seen as two regions of the crystal
having been shifted relative to one another by a distance given by a displacement
vector R which may be a non-lattice translation as shown by Fig. 4.4. The
displacement vector has a component parallel to the fault plane R|| and normal to it
R . Thus the presence of this fault will introduce a phase shift α = 2πg·R which
modifies the solution to the DHW equations for the bottom section (section II) of the
crystal. If α is an integer multiple of π no defect contrast will be seen which shows
that R is a lattice translation vector and effectively no modification of the solutions to
the DHW equations result. If R is a non-lattice translation, α is not an integer multiple
of π and image contrast of the form of alternating light and dark fringes will be
formed.
Fig. 4.4. (a) Schematic illustration of a planar defect separating crystal sections I
and II; (b) inclined planar defect combined with the column approximation (from De
Graef (2003))
To simulate such an intensity profile the following procedure is used. Consider a
crystal with thickness z0 containing a stacking fault as shown in Fig. 4.4 (b). Region 1
has been shifted with respect to region II by a vector R. The top section of the crystal
(region 1) is defect free and is described by a scattering matrix Sscat(s1.z1) where z1 is
the distance from the top surface to the fault. The bottom section is shifted with
respect to the top and is described by a different scattering matrix M(s2.z2) since it lies
in a different orientation with respect to the top. The two scattering matrices are as
follows,

S
( s , z ) e
T
i
Se
(
/ 0
) z1
scat 1 1
M ( s , z ) e
2
2
'
0
(
/ ) z
'
2
T
i
Se
g
g
Se
T
Se
T
i
( )
i
g
( )
M can further be decomposed into,
i
g
1
0
T S e 1 0
2 2
M M P(
g ) S 2P(
g )
i g i
g ( )
i
g
0
e S
e T 0
e
2
2
g
49
(4.40)
(4.41)
2 (4.42)
with P being the defect phase shift matrix,
1
0
P(
)
(4.43)
i
0
e
Using this, the transmitted and scattered amplitudes at the exit plane of the crystal are
obtained by the product of the scattering matrices for each section using the initial
condition (1,0) T ,
0
g
1
(
g ) S 2P(
) S1
0
P g
From this the intensities are obtained by squaring the wave functions.
(4.44)
Note that the values of z1 and z2 depend on the incoming beam direction B, foil
normal N and the plane normal P of the plane in which the fault lies, note also that the
extinction distance used depends on the diffraction vector g. Thus to solve the
problem the following geometrical setup is used and shown in Fig. 4.5.

50
Fig. 4.5. The geometrical setup used in simulating a line intensity profile of a
stacking fault
Firstly the projected foil thickness zproj and range Dproj of the stacking fault in the
direction of the beam is determined. This is done by finding the angle between the
foil normal N and the beam direction B, θ, from which zproj is determined by the
trigonometric relation,
z0
z proj (4.45)
cos
and the projected lateral range Dproj by the relation,
D proj
with
N.
D tan. z
(4.46)
z0
0
D where α is the angle between the plane normal P and the foil normal
tan
Following this, the lateral range is divided into n equally spaced points as shown in
Fig. 4.5 (b). The number n determines the resolution of the solution to the problem but
also influences the computing time. Next the values of z1 and z2 are determined
through the relations for each point,

z0
z2 . xn
cos
and (4.47)
D
1
proj
z z proj z
(4.48)
2
51
Hence z1 and z2 are used with the values of s1 and s2 and the extinction distance in the
scattering matrices to determine the exit plane waves which in turn is used to
determine the intensity at each point xn used. Also in general the excitation errors s1
and s2 for the two regions do not differ significantly and may be assumed to be equal.
The foil thickness for this derivation was also assumed to stay constant but is not
necessarily true which in turn adds another element of complexity to the problem.
4.3.3 Fringe Contrast Observed from Twinning
Twinning as explained in Section 2.7 is a region in which part of the crystal is
displaced through a homogenous shear process to produce the original crystal
structure but in a different orientation. Thus a similar geometrical situation as for
stacking faults may occur but with the difference that one part of the crystal (region 1
or 2) will be twinned with respect to the original crystal. This causes a change in that
the excitation error of the twinned area and will be different to that of the normal
crystal and should be incorporated into the scattering matrix for that region. To
simulate such a situation the same procedure is used as for a stacking fault with the
only difference being that the excitation error changes.

52
Figure 4.6 – The geometrical considerations for simulation of a line intensity profile
of a narrow twin
Furthermore a different situation (depicted figure 4.6) may occur in which a narrow
twinned section is present within the material. In this case the crystal has three regions
in which a scattering matrix should be calculated and also three sections where the
plane wave propagates through the original crystal and then twinned crystal (section
1), original crystal then twinned crystal and then original crystal again (section 2) and
finally through a twinned crystal and then through the original crystal (section 3). This
will produce an interesting fringe contrast image divided into three sections. To
simulate such a situation is similar to that of the stacking fault with the only
difference being that the calculations are done for each section and that for section
two, three thicknesses of the regions z1, z2 and z3 should be determined. Also the
excitation error of the twinned region should be taken into account. In general such a
calculation is not as trivial as discussed above but the section is given to aid in the
understanding of what such a calculation might entail. Factors such as the calculation
of the deviation parameter of the twinned section with reference to the bulk crystal
structure must be done. In addition, care must be taken that the correct two-beam
condition is used to form the image.

5.1 Introduction
53
CHAPTER FIVE
LITERATURE REVIEW OF SiC
The following chapter consists of a literature review of earlier work done on 3C-SiC
with regards to growth by CVD on Si substrates, crystal defects and defect generation
by ion irradiation. A literature review was also done with regard to diffusion
characteristics but it is presented together with the discussion of the results of proton
bombarded 3C-SiC in Chapter 7 since it makes more sense to do so.
5.2 CVD Growth of SiC on Si
The CVD growth of 3C-SiC {001} on Si {001} takes place through the classical
mechanism of nucleation and growth. During the first step of the process only
propane is introduced at 1100°C leaving only the substrate as a source of Si after
which the substrate is ramped up to the growth temperature of 1380°C and the silane
introduced.
Pirouz et al. (1987) explained that this two-step process causes the formation of two-
dimensional nuclei on the substrate. Assuming then a “pill box” shape with height h
(of the order of one or a few monolayers), the critical radius r of the nuclei is given
by,
r h
hH
( )]
(5.1)
f / g /[ f / g f / s s / g
with γf/g, γf/s, γs/g the film/gas, film/substrate, substrate/gas interfacial energies per unit
area respectively and ΔH the enthalpy change per unit volume between the reactants
and the product. The energy barrier for the formation of a stable nucleus ΔG is given
by,
(5.2)
G hr
f / g

54
The critical radius and energy barrier for the formation of stable nuclei both depend
on γf/s. The film/substrate interfacial energy in turn depends on the bonding across the
interface where the existence of elastic strains and dangling bonds increases its value
and thus increases r and ΔG. Consequently epitaxially oriented nuclei will have a
lower interfacial energy and a smaller critical radius and energy of formation barrier.
Misoriented nuclei will have a larger interfacial energy with a larger critical radius
and energy of formation barrier than oriented nuclei and will be subcritical and
dissolve away. The rate of nucleation, N, is proportional to exp(-ΔG/kT) and thus
many more oriented than misoriented nuclei will form.
However the film/substrate interfacial energy is expected to be a function of
temperature and its contribution to the energy of formation barrier decreases with
increasing temperature. This in turn reduces the anisotropy between oriented and
misoriented nuclei formation and it is expected that at higher temperatures their
deposition rates become more equal. This is evidenced by the fact that the growth of
SiC at higher temperatures results in a polycrystalline structure. If the film/substrate
energy is considered the energy of oriented nuclei will be in a global minima of the
energy function with an orientation relationship between the substrate and nucleus of
(001)Si||(001)SiC ; 110]
Si|| 110]
SiC. However Pirouz et al. (1987) mentioned that local
[ _
[ _
minima in the energy function also exists for other orientations. For example a nuclei
twinned on a 111)
plane relative to an epitaxial one will have the orientation
( _
relationship with respect to the substrate as (001)Si|| 221)
SiC ; 110]
Si|| 114]
( _
[ _
[ _
SiC .
These types of nuclei are expected to have a lower film/substrate interfacial energy
than misoriented nuclei but higher than oriented. Thus a fraction of the stable nuclei
will have a twinned orientation relationship. Further, the lateral growth of the twinned
nuclei will be slower than that of the oriented ones and will grow easier in directions
inclined to the interface. As a result they tend to growth thin and long within the film.
Growth at 1380°C results in migration of the twinning boundaries and the
consumption or decrease in the volume of the twins.
Powell et al. (1987) in a different publication explains that during the initial stages of
deposition a large number of supracritical nuclei form on the Si substrate with

55
different orientations. The interfacial energy of the epitaxially oriented nuclei is lower
than that of the misoriented ones and as a result the former nuclei will have a
relatively faster lateral growth whereas the latter grows preferentially in vertical
directions. Once the different nuclei meet a grain boundary stress results between the
nuclei which tends to cause the epitaxial nuclei to grow at the expense of the
misoriented. This is proportional to the difference in interfacial energies between the
two nuclei, the surface areas of the grains and the grain boundary energy.
If the substrate is heated to the growth temperature and the silane and propane are
introduced, the nuclei will grow vertically and laterally in a three dimensional manner
called one-step deposition. This causes the vertical growth of the grains to occur faster
than lateral growth of the epitaxially oriented ones causing a polycrystalline
aggregate.
In the two-step process, the island nuclei start forming during the ramping process at
much lower temperatures with their growth being predominantly two-dimensional
with Si coming from the substrate. In the extreme case where only propane is
admitted in the ramping stage with no Si present in the vapour phase vertical growth
is inhibited. Due to the predominant lateral growth, epitaxially oriented nuclei grow
much faster than misoriented ones which rapidly consume misoriented grains before
bulk deposition takes place.
Fig. 5.1. Atomic force microscopy images of 3C-SiC epilayers having different
thicknesses: (a) 0.08; (b) 0.13; (c) 0.7 and (d) 3.7 µm (from Yun et al. (2006)).

56
Yun et al. (2006) used AFM to show the process of nucleation and growth at different
stages during growth. The images show isolated nuclei forming on the substrate at an
epilayer thickness of 0.08 µm during the initial stages of deposition. The nuclei merge
at a thickness of 0.13 µm and develop further to form a continuous {100} faced
surface at 0.7 µm. They explained that the driving force for the growth to take place
through this process is a result of the lattice mismatch between the SiC and Si as well
as thermal mismatch.
Finally the researchers Sudarshan et al. (2006), Nagasawa et al. (2002), and Jacob et
al. (2000) all presented results that are consistent with what is discussed above.
5.3 Crystal Defects in SiC
5.3.1. Introduction
The main crystal defects found in epitaxially grown 3C-SiC are stacking faults with
their accompanying partial dislocations, twins and inversion domain boundaries.
In a TEM study by Jacob et al. (2000) on epitaxially grown 3C-SiC on Si(001) a high
density of planar defects lying on {111} planes was found. Defects included stacking
faults and microtwins and the authors suggested that the defects were introduced
during the growth process to accommodate the large lattice and thermal mismatches
between the crystals.
Similar findings were reported by Stoemenos et al. (2004) in a TEM study on 300µm
thick freestanding 3C-SiC. Microtwins, stacking faults and inversion domain
boundaries were observed and their presence attributed to the same reasons as above.
Powell et al. (1987) in an extensive microscopy study on 3C-SiC found microtwins,
stacking faults and also misfit dislocations accommodating the lattice mismatch. They
presented possible mechanisms for the nucleation and growth of the defects and these
will be discussed in Sections 5.3.2 and 5.3.3.

57
Furthermore Pirouz et al. (1987), Ho et al. (1999) and Nagasawa et al. (2002) all
studying epitaxially grown 3C-SiC on Si (001) found microtwins and stacking faults
as the predominant defects in the SiC and attributed their presence to lattice and
thermal mismatch.
5.3.2 Accomodation of Misfit and Interfacial Twinning
The mechanism for the accommodation of misfit during growth and its relationship to
interfacial twinning has been thoroughly explained by Powell et al. (1987). The total
misfit, f, between an epilayer and substrate is accommodated by the elastic strain, ε,
of planes in the regions of good register and by interfacial dislocations, δ. The spacing
of misfit dislocations with Burgers vector b would be S = b/δ. The Si/SiC system has
a lattice mismatch of about 20% (f ≈ 0.2). Assuming that the entire misfit is
accommodated by misfit dislocations, f = δ and S ≈ 5b. Thus an array of edge misfit
dislocations in SiC parallel to the interface with b = a/2 [110] at a spacing of S ≈ 5d110
would accommodate all the misfit.
Furthermore it is also frequently observed that where misfit dislocations become
irregular, twinning occurs. The twins nucleate at the interface due to coherency
stresses resulting from the lattice mismatch. Twinning may be thought of as the
motion of partial dislocations with b = a/6 on consecutive {111} planes.
Considering the substrate plane to be (001), a pure misfit edge dislocation with
Burgers vector a/2 110]
[ _
would be the most efficient type of dislocation to
accommodate the lattice mismatch having strength 2a / 2 according to Frank’s rule.
A shear type dislocation gliding on the (111) plane for example with b = a/2 101]
will have an edge component along the 110]
direction of half the strength of the pure
[ _
edge with 2a / 4 . Thus the shear type dislocation is only half as efficient as the edge
misfit dislocation in accommodating the misfit. On the other hand partial dislocations
of the type a/6 121]
or a/6 211]
gliding on a (111) plane will also have an edge
[ _
[ _
component with strength 2a / 4 and is just as efficient as the shear type dislocation
in misfit accommodation. Furthermore a twin as discussed above may be considered
[ _

58
as the propagation of a number of partials with the width of the twin determined by
the number n of the partials. Such a system can be considered having Burgers vector
equal to that of a superdislocation with b = na/6 121]
[ _
having strength n 2a / 4 . Thus
a twin formed by glide of these partials is much more efficient in mismatch
accommodation than the edge misfit and shear dislocations.
It is necessary to consider the lattice mismatch in the 110]
also. A set of pure edge
[ _ _
dislocations with b = a/2 110]
at a spacing of 5d {110} orthogonal to the first array
would satisfy the mismatch strain along this direction also. The strength of the edge
_ _
[ _ _
component of an a/6 [ 121]
partial along the 110]
[ _ _
direction is 2a / 12 and thus the
twin needs to be six (111) layers thick to be able to accommodate the mismatch along
[ _ _
the 110]
direction as efficiently as an edge misfit dislocation having b = a/2 110]
. In
another publication Powell et al. (1987) presented high resolution TEM results of
misfit dislocations present at the SiC/Si interface. They found the dislocations occur
on average every four lattice fringes.
5.3.3. Mechanisms for the Formation of Stacking Faults
The mechanism of formation of stacking faults in SiC is still widely debated. It is
obvious that the driving force behind the process is the low stacking fault energy in
SiC but the exact process of formation of the SFs during growth seems not to be as a
result of one thing but rather a combination of different processes during growth. The
possible mechanisms are discussed by Powell et al. (1987) and Pirouz et al. (1987).
(a) Firstly if it is assumed that the process of growth of the material occurs through
the formation of discrete nuclei on the substrate surface, it can be envisioned that
some of the nuclei may be deposited on incorrect sites forming surfaces of mismatch
boundary. When the correctly deposited islands meet the incorrectly deposited islands
an inverted pyramid of stacking fault could result growing on the inclined {111} faces
with its {001} base at the interface. Using a simple geometric consideration (depicted
in (e)) it can be shown that depending on the nature of the dislocations at the
[ _ _

59
intersection of the fault, the faces of the pyramid would either be all of the same
nature or alternatively intrinsic and extrinsic faults. It can also be shown that the
measurement of the width of the fault at the surface of the foil enables one to measure
the point of nucleation.
(b) It is possible for interfacial stacking faults to have formed during the cooling
stages due to the lattice mismatch between the substrate and film. In this case, the
stacking fault would nucleate at the interface during the cooling stages and
subsequently propagate into the bulk by glide of partial dislocations. However the
activation energy of dislocation motion in SiC is very high and it is unlikely that the
stacking fault nucleated would propagate throughout the bulk of the layer. Thus the
faults are limited to a region close to the interface with the bonding partial
dislocations parallel to the interface.
(c) The next possibility is the spontaneous generation of dislocations at the interface
as soon as the epitaxial layer begins to grow. Conditions on the interface such as
contamination, roughness, moderate stresses would enhance the generation at lower
temperatures of growth. According to Booker et al. (1978) the dislocations always
form in pairs and once the dislocations are generated they split into two Shockley
partials bounding a ribbon of stacking fault between them.
(d) The fourth possibility is that dislocation loops are generated within the bulk of the
material presumably during the cooling stages by the stresses caused by the thermal
mismatch between the substrate and film. Following this, the glide dislocations would
split up into Shockley partials bounding wide ribbons of stacking fault between them
since the stacking fault energy in SiC is very low. The interaction between partials
gliding on different {111} planes would give rise to intersecting faults.

60
Fig. 5.2 A schematic diagram of the fault on the (111) planning assuming that it has
nucleated at point O. W1 and W2 are the widths of the fault on the top and bottom of
the foil respectively.
(e) The last possibility is that stacking faults arise during the growth of the film due to
incorrect deposition of some nuclei on the surface of the growing film. This could be
as a result of a rapid deposition rate, inhomogeneities in the film or impurities in the
carrier gas. Furthermore diffusion rates in SiC are very low at the temperature of
deposition and thus the nuclei would not have enough time to readjust themselves to
the correct position. Once a mismatch boundary has formed stacking faults will grow
on the {111} faces with further growth of the film. A schematic illustration of this is
given in Fig. 5.2. It is assumed the stacking fault nucleated at point O due to some
inhomogeneity and grow wider as the layer thickened in the [001] direction. Since the
directions are parallel to the Peierls valleys in crystals with sphalerite structure,
and the Peierls energy is expected to be very high in SiC, the growth occurs such that
the partials bounding the stacking fault lie along these directions. Measuring the width
of the fault at the top of the foil, W1 enables one to determine the depth below the
surface, h, at which the stacking fault nucleated,
h W1
/
2
Yun et al. (2006) explained that the stacking fault formation is a result of a large
number of twins forming on {111} planes during the early stages of growth prior to
the coalescence of nuclei. The atomic stacking errors may form on {111} planes of

61
each nuclei because of the low surface energy of the plane. The atomic errors lead to
twin formation and stacking faults appear at twin boundaries.
5.3.4. Stacking Fault Energy in SiC
The stacking fault energy in SiC has been found to be very low and this is one of the
main reasons for the large number of hexagonal polytypes that are found in SiC. For
3C-SiC the stacking fault energies have been theoretically calculated by Denteneer et
al. (1987), Iwata et al. (2002), Käckell et al. (1998) and Lindefelt et al. (2003).
Denteneer et al. (1987) used an adaptation of the ANNNI (axial next-nearest-neigbour
Ising) and found the stacking fault energy γesf for the extrinsic fault as -15 mJ.m -2 and
for the intrinsic γisf = 12 mJ.m -2 . This is interesting since the value for the extrinsic
fault is negative which shows that the formation of the fault is energy efficient.
Denteneer explains that this is an indicator of the occurrence of polytypism in SiC.
Iwata et al. (2002) also found a negative stacking fault energy in 3C-SiC of -2.70
mJ.m -2 and -6.27 mJ.m -2 using two different methods which are the supercell and
ANNNI method respectively. Käckell et al. (1998) using a scheme based on density-
functional theory and the local-density approximation found values of -28 mJ.m -2 and
-3.4 mJ.m -2 for extrinsic and intrinsic faults respectively.
Furthermore Denteneer et al. (1989), Karch et al. (1994) and Cheng et al. (1990)
found values of 13.8 mJ.m -2 , 11.1 mJ.m -2 , -7.1 mJ.m -2 for intrinsic and -6.1 mJ.m -2 ,
-15.4 mJ.m -2 and -32.3 mJ.m -2 for extrinsic faults respectively. The negative SF
energy values for the extrinsic fault is suggested to be due to the fact that the stacking
sequence of the extrinsic fault is close to the bulk stacking sequence of the more
stable hexagonal polytypes of SiC.
5.4 Ion Implantation and Radiation Damage in SiC
The process of energetic displacement cascades in SiC is not a trivial process. There
is anisotropy between the threshold displacement energies (TDE) of the two
subsystems and also a difference in recovery of the subsystems after the
displacements has taken place. The TDE is also highly directional varying greatly

62
with direction. Values published by Perlado et al. (2000) range from 42 – 112 eV for
Si and 26 – 58 eV for C depending on the direction. Heinisch et al. (2004), in a study
on displacement damage in SiC in fission reactors, stated that the displacement value
for Si could be taken as 35 eV and for C as 20 eV since these are the average values
taken over all directions in the SiC the also stated that there are actually four
minimum recoil damage energies that should be considered to create displacements in
SiC, depending on the projectile/target combinations: 41 eV (C/Si), 35 eV (Si/Si), 24
eV (Si/C) and 20 eV (C/C). Vladimirov et al. (1998) used values of 93 eV for Si and
16.3 eV for C in their calculations as well as Ryazanov et al. (2002).
Thus it is obvious that there is still a lot of uncertainty about the correct values for
TDE to be used in calculations for SiC and is as mentioned before, a result of the
anisotropy within the material. Hence the method of computer simulation is used to
determine the displacement mechanisms and TDE in the material.
Gao et al. (2001) used molecular dynamics (MD) software to simulate Si
displacement cascades in SiC. Their simulation showed that during a high energy Si
primary knock on atom (PKA), multiple sub-cascades were generated. This prevented
both a compact structure of displaced atoms to form during the collision phase and a
high-energy density during the thermal spike. They attributed this to the light masses
of the SiC system and small scattering cross-sections of the Si and C atoms.
Furthermore the high melting temperature of the SiC also inhibits the development of
a liquid like cascade which results in a very short lifetime of the thermal spike. This
along with the formation energies of defects provide a physical basis for defect
production and clustering in the material. They found that at the peak of the thermal
spikes the number of displaced Si and C atoms are essentially the same but that the Si
sublattice partially recovers as the energy of the cascades dissipate into the lattice,
while the damage in the C sublattice does not. The number of Si interstitials surviving
after the cascade was on average three times smaller than for C. This is possible since
most silicon atoms are only displaced a short distance from their lattice positions and
recombine during the thermal spike phase. They explain that as a consequence of the
above facts, the formation of a dispersed cascade is seen with defects spread over the
simulation box, and most interstitials remain as single defects. Only a small fraction
of interstitials form clusters, the biggest being four atoms. Furthermore Perlado et al.

63
(2000) found that subsequent annealing of their simulated cascades yielded no
considerable change in the defect configuration. Thus it may be concluded that almost
all interstitials are generated during the early stages of the cascade and then directly
quenched into their final arrangements. When considering vacancies the same results
are seen as for interstitials.
Gao et al. (2001) also simulated high energy cascades in the SiC created by Au ions.
They found a disordered region with a very high defect concentration but also with a
large anisotropy regarding the amount of interstitials of Si and C. It clearly
demonstrated that a heavy energetic ion can create a large disordered cluster in SiC.

6.1 Introduction
64
CHAPTER SIX
EXPERIMENTAL DETAILS
This chapter deals with the experimental procedures used in this investigation.
Specifics on the growth process, ion implantation, annealing procedure and the TEM
sample preparation are given.
6.2 CVD Growth of SiC
The 3C-SiC used in this study was grown by NovaSiC in France using H2 as carrier
gas and C3H8 (propane) and SiH4 (silane) as precursors on a silicon substrate. The
layer deposition was carried out at 200 mbar. The first step of the process consisted of
a carbonisation of Si at 1100 °C under a mixture of H2 and C3H8 and the second step
was the epitaxial growth, performed at 1380 °C with a growth rate of 2 µm/h.
6.3 Proton Implantation in SiC
To investigate the damage created by light ion bombardment in 3C-SiC the material
was implanted with 400keV protons to a total dose of 2.2 × 10 16 over a 1cm diameter
region. The 400 keV protons were generated by implanting the material with 800 keV
H2 + ions which upon entering the material splits up into 400 keV H + . The implantation
was done at NECSA (National Energy Corporation of South Africa). SRIM
(Stopping Ranges of Ions in Matter) developed by Ziegler et al. (1985) was used to
calculate the proton range. This software uses Monte Carlo methods to determine the
ion range and defect production within the material.

6.3.1 Ion Range and Defect Production
65
Fig. 6.1. A plot of the ion distribution of 400 keV protons implanted into 3C-SiC
obtained by using SRIM
Fig. 6.1. shows a SRIM plot of the hydrogen ion distribution of 400 keV protons
implanted into 3C-SiC. The plot shows a maximum concentration of ions at 2.87 µm.
This is within the thickness of the SiC layer used for this study. Fig. 6.2. shows SRIM
plots of the numbers of Si and C vacancies produced for displacement energies given
by Heinisch et al. (2004) and Vladimirov et al. (1998).

(a)
(b)
66
Fig. 6.2. (a) Si and C vacancies produced per unit distance in 3C-SiC using
displacement energies of 35 eV and 20 eV respectively (Heinisch et al.); (b) Si and C
vacancies produced per unit distance in 3C-SiC using displacement energies of 93 eV
and 16.3 eV respectively (Vladimirov et al.)
SRIM gives the number of vacancies produced per ion for the two sets of
displacement energies to be 13.2 and 10.1 respectively. It is also evident from Fig.
6.2. that the number of Si vacancies is always less than that of the C due to its
displacement energy being higher. In the case of Fig. 6.2 (b) the anisotropy is very
high with an order of magnitude difference in the numbers produced. Fig. 6.3. shows
a plot of the number of displaced atoms per unit distance per incoming ion for the
displacement energies used by Heinsich et al. (2004).

67
Fig. 6.3. Total number of displacements produced in the 3C-SiC per incoming ion per
Angstrom.
If an area around the peak of the projected range is selected, as indicated on the above
figure, an estimate of the total number of displacements per unit volume around the
damage region can be obtained for the dose used by assuming that the number of
displacements per incoming ion per angstrom to be constant over this region.
Multiplying it by the dose and dividing it by the volume which in this case is a disc
with thickness of the area selected and diameter of 1 cm. The number of
displacements per cm 3 is then found to be 9.5×10 21 in the damage region. This is
about an order of magnitude lower than the concentration of atoms per unit volume in
SiC which is 9.6×10 22 .
6.4 Annealing Procedure
After the proton implantation two sets of samples were sent to the University of the
Witwatersrand for annealing at 1300 °C and 1600 °C for 1 hr. The annealing was
done in vacuum.

6.5 Sample Preparation
68
For the analysis in the TEM, samples were prepared in cross-section as illustrated in
Fig.6.4. Two sections with dimensions 3mm by 0.5 mm were cut from the irradiated
area of the SiC samples. The two sections were then glued together using an epoxy
solution with the faces of the irradiated surfaces facing towards one another.
Following this two sections of the same dimensions as before of Si were cut and glued
to either side of the SiC sections for extra support. The samples were then
mechanically thinned to approximately 250 µm by means of wet sandpapering
followed by polishing on a rotating pad using a 3 µm diamond grit solution to remove
any residual surface damage from the sandpapering. This was then mounted on a
copper microscope grid using an epoxy solution with the polished face on the grid.
The other side of the sample was polished using the same procedure as before to a
total thickness of approximately 50 µm. The samples were finally milled using a
Gatan PIPS (Precision Ion Polishing System) by means of the simultaneous
bombardment of the top and bottom surfaces with 5 kV argon-ion beams at an
incident angle of 6°. The milling continued until a small hole appeared in the sample.
Fig. 6.4. Schematic representation of the steps in the preparation of a (110) cross-
sectional sample (Neethling (1980)).

7.1 Introduction
69
CHAPTER SEVEN
RESULTS AND DISCUSSION
The following chapter contains the results obtained from a TEM investigation of the
as-grown and ion bombarded 3C-SiC. The results of this investigation are also
compared with findings of other researchers.
7.2 Extended Defects in -SiC Grown by CDV on (001) Si
A cross-sectional sample of 3C-SiC grown on Si by CVD was prepared using the
technique described in Section 6.5. Following this an investigation was done by using
transmission electron microscopy (TEM) as well as high-resolution TEM (HRTEM).
From these results the phase of the SiC was determined to be the cubic (3C-SiC) zinc-
blende structure with a lattice parameter of 4.35Å . The interface between the SiC and
Si was also investigated. It was found from diffraction data that parallel epitaxial
orientation between the two materials was obtained during growth. The consistency
along the interface was also investigated and it was seen to contain a reasonable
amount of inhomogeneities. Examples of very thin twinned sections originating at the
interface were also found. In the bulk of the material a large density of stacking faults
was observed lying on the {111} close-packed planes with bonding partials of the 1/6
type. The stacking faults observed in an edge-on orientation showed an
interesting feature in that they generate satellite streaks in a diffraction pattern. This is
consistent with what is normally seen in materials containing narrow planar
precipitates. This is due to the shape of the precipitate being similar to that of a plate
like crystal (see p.97 Hirsch et al. (1965)). Furthermore these stacking faults were
investigated using HRTEM and found to be extrinsic in nature. These findings agree
with that found by previous researchers (Sections 5.2-5.3).

70
7.2.1 Crystal Structure and the SiC/Si Interface
Fig. 7.1. Bright field TEM micrograph of the Si/SiC interfac. B = [011], g =
≥ 0. Inserted are SAD patterns taken from the bulk of the SiC and over the interface
_
11 1,
s
Fig. 7.1. shows a bright-field TEM micrograph of the SiC/Si interface (in figure
caption). The beam direction B is [011] with diffraction vector g = [ 111]
deviation parameter s ≥ 0. The inserts are selected area diffraction (SAD) patterns
taken of the areas indicated and are rotated to reflect the correct directions as in the
micrograph since there is a rotational relationship between diffraction and image
planes in the TEM. This rotation relationship has been tabulated for the TEM for
various magnifications and is used for the correction. In this particular case the
rotation could also be found easily due to the direction of growth of the 3C-SiC being
known. The left hand SAD pattern is consistent with the 3C-SiC phase with beam
direction B = [011] and lattice parameter 4.35 Å. The camera length of the TEM was
calibrated using the Si substrate as reference. This diffraction pattern (right hand)
corresponds to the superposition of the two sets of diffraction patterns of the Si and
SiC, with the pattern containing the shorter set of reciprocal lattice vectors being that
of the SiC and the other that of the Si. The following procedure was followed.
_
and

Fig. 7.2. Simulated diffraction pattern of the [011] zone axis of 3C-SiC.
71
Fig. 7.2 shows an indexed simulated diffraction pattern of the [011] zone axis of 3C-
SiC. From diffraction theory it is known that the diffraction patterns obey the
following relation (Hirsch et al. (1965)),
L Rd hkl
where λ is the electron wavelength, L the camera length, R the distance from the
transmitted or central diffraction spot to the diffraction spot in question and dhkl the
interplanar spacing given by (Hirsch et al. (1965)),
d hkl
h
2
a
k
2
l
2
with a the lattice parameter of the material and h,k,l the Miller indices of the
diffraction vector used. Using these relations the lattice parameter of a crystal can be
determined from a diffraction pattern provided the camera constant λL is known.
R

72
Table 7.1. The values used in calculating the camera length. Rm is the measured
values in arbitrary units using measuring software and R is the actual values in
meters obtained by using the scaling factor. A value of 5.43Å was used for the lattice
parameter of Si.
Index Rm R (in m) λL (in m 2 )
93.49 0.007805 2.45E-12
93.49 0.007805 2.45E-12
91.39 0.00763 2.39E-12
91.39 0.00763 2.39E-12
107.27 0.008956 2.43E-12
107.27 0.008956 2.43E-12
Average 2.42E-12
Table 7.2. The values used in calculating the lattice parameter of SiC. Rm is the
measured values in arbitrary units using measuring software and R is the actual
values in meters obtained by using the scaling factor.
Index Rm R (in m) dhkl (in m) Lattice parameter (in m)
116.37 0.009715 2.49E-10 4.32E-10
115.86 0.009673 2.51E-10 4.34E-10
115.90 0.009676 2.50E-10 4.34E-10
114.67 0.009573 2.53E-10 4.38E-10
133.69 0.011161 2.17E-10 4.34E-10
132.43 0.011056 2.19E-10 4.38E-10
Average 4.35E-10 ± 0.02E-10
Using this procedure, the lattice parameter of the SiC was determined by taking an
average of the parameters obtained using all the and diffraction spots
present in the pattern. The lattice parameter was found to be 4.35Å ± 0.02Å.
Furthermore from the orientation relationship between the two sets of diffractions
spots it is clear that exact epitaxial orientation between the two materials were
obtained during growth with the following orientation relationship {001}Si || {001}SiC
and Si || SiC.
Fig. 7.1 also shows evidence of planar defects originating at the interface and
extending into the bulk of the SiC. This was confirmed by a high resolution TEM
study of the interface shown in Fig. 7.3.

73
Fig. 7.3. A HRTEM image of the SiC/Si interface with FFTs taken of the Si and SiC
(inserted)
The inserts are the images obtained from fast Fourier transforms (FFT) taken of the
areas indicated. These FFTs are essentially reconstructed images of diffraction
patterns of the areas resulting from the fact that in a TEM the images in the diffraction
plane are Fourier transforms of that in the image plane and vice versa. Thus these
patterns may also be used to determine the lattice parameter of the SiC. Using the
same technique as above and a value of 4.35ű 0.01Šwas found.
Evidence of defects originating at the interface and propagating along {111} planes is
seen. The origin of these defects has been ascribed by Powell et al. (Section 5.3.2) to
the accommodation of the lattice and thermal mismatch between the SiC layer and Si
substrate. This process takes place through the introduction of misfit dislocations and
twins. Due to the high density of twins and stacking faults at the SiC/Si interface the
misfit dislocations could not be resolved at the interface.

74
The absence of an intermediate polycrystalline layer along the interface shows that the
growth did take place according to a two-step process with an initial carbonisation
step achieved by only introducing the propane.
7.2.2 Stacking Faults and Partial Dislocations
Fig. 7.4. Bright field TEM micrographs taken from the bulk of the 3C-SiC sample. B
= [011], g =
SF selected
_
11 1,
s ≥ 0
Fig. 7.4. shows a set of low magnification bright-field TEM micrographs of different
areas in the 3C-SiC representative of the bulk of the material. A high density of
stacking faults (SF) are seen lying on the four {111} planes. Fringe contrast typical of
stacking faults lying on inclined and edge-on planes is seen. The stacking faults are
uniformly distributed throughout the foil.
The preliminary results of tilting experiments in the electron microscope showed the
fault vector of the SF to be of the type 1/3 with bonding partials of the type
1/6 i.e. the partials are of the Shockley type. This indicates that the fault was
not formed as a result of the aggregation of point defects, which would form a Frank
loop with Burgers vector of the type 1/3.

75
Fig. 7.5. The stacking fault selected for simulation with arrows pointing to the
thickness fringes used for foil thickness determination
To verify the suggested nature of the fault image, simulation and matching was
performed. Fig. 7.5. shows a magnified bright field TEM micrograph of the SF shown
in Fig. 7.4. This fault was selected for the simulation and the assumed fault vector and
partial dislocation burgers vectors were used. Following this, the unknowns of the
problem were determined starting with foil thickness. This was done using the
thickness fringes present in the micrograph as well as the technique of convergent
beam electron diffraction (CBED) (De Graef (2003)).
Thickness fringe method
Consider Fig. 7.5. It is known that the thickness fringes present in a bright field (or
dark field) micrograph follow in increments of 1/2ξ (ξ is extinction distance) for each
successive bright to dark fringe starting from the edge of the material (Hirsch et al.
(1965)). Thus in this case the foil thickness was found to be approximately 2.75 ξ at
the point of the fault using the thickness fringes as indicated. Using this and the
extinction distance of the {111} reflection in 3C-SiC the thickness was determined to
be ~ 188 nm. A value of 622 Å was used for the extinction distance and was found
using Electron Diffraction (2003).
3 ξ
~2.75 ξ
2 ξ
5/2 ξ
3/2 ξ

CBED
76
Fig. 7.6. shows an annotated micrograph of a CBED pattern recorded using a 400
reflection at the area containing the stacking fault.
Fig. 7.6. An annotated CBED micrograph used in the determination of the foil
thickness
The distances measured on the original negative are indicated on the figure. The
values calculated according to the technique outlined in De Graef (2003) are given in
Table 7.3 with corresponding plotted values and the associated linear trend line given
in Fig. 7.7.
Table 7.3. The measured parameters with calculated variables used in obtaining Fig.
7.7.
ni Δθi Si (nm -2 ) 1/ni 2 (Si/ni) 2 (nm -2 )
2 0.36 0.0050 0.250 6.31667E-06
3 0.80 0.0111 0.111 1.38637E-05
4 1.13 0.0157 0.063 1.55589E-05
5 1.47 0.0205 0.040 1.68515E-05

(Si/ni) 2
0.000018
0.000016
0.000014
0.000012
0.00001
0.000008
0.000006
0.000004
0.000002
0
77
y = -4.99E-05x + 1.89E-05
R 2 = 9.95E-01
0 0.05 0.1 0.15 0.2 0.25 0.3
(1/ni) 2
Fig. 7.7. The plotted values of Table 7.1 with the linear trend line used to determine
the foil thickness and extinction distance
From the trend line the values of extinction distance and foil thickness can be
determined from the slope and y-intercept of the graph respectively by taking the
square root of the inverse of the associated value. The extinction distance was found
to be 142 nm and foil thickness 230 nm. Electron Diffraction (2003) calculates the
extinction distance of the 400 reflection in 3C-SiC to be 138 nm and is thus in good
agreement with the obtained value. The value found for foil thickness using the
thickness fringe method agrees well with that of the CBED technique but the value
found by the latter should be taken as the more accurate one.
Following this the anomalous absorption ratio of the material was chosen. This ratio
affects the image contrast characteristics in the bright and dark-field image and may
lead to incorrect conclusions if the wrong value is used for the image simulations. A
value between that of diamond and silicon was assumed since no theoretical value
could be found in literature. A value of 0.055 was used. The values of diamond and
silicon are ~ 0.01 and ~ 0.1 respectively and can be calculated by finding the ratio of
the absorption length to that of the extinction distance which in turn could be found
by various software packages such as JEMS - Electron Microscopy Software.

78
After determining all the variables of the problem the fault was simulated using
software developed by Head et al. (1955) using a technique analogous to that
discussed in Section 4.3.3.
Fig. 7.8. The bright field and dark field TEM micrographs with their corresponding
simulated images of the stacking fault selected.
Fig. 7.8. shows both bright and dark field TEM micrographs of the stacking fault with
the corresponding simulated images. Excellent agreement is seen in both cases and it

79
may be concluded that the initial identification of the fault was correct. Also the
fringes in the bright and dark-field images are complementary and symmetrical in
both cases. This being a direct result of the magnitude of the anomalous absorption
ratio for SiC which differs from that of heavier elements. The complementary and
symmetrical nature of bright and dark-field SF images of SiC is not true in general for
the heavier elements (Hirsch et al. (1965)).
SF viewed edge on
Fig. 7.9. Bright-field TEM micrograph of narrow planar defects viewed edge-on. B =
[011], g =
_
11 1,
s ≥ 0. Inserted is the SAD pattern taken over the area indicated and
below the dark field image obtained by using the spot indicated.

80
Fig. 7.9. shows a bright-field TEM image obtained from an area within the material
containing narrow planar defects. A SAD pattern of this area showed additional
streaks between the diffraction spots. Using one of these streaks to form a dark field
image resulted in an inversion of the contrast indicating that the defects are the origin
of the streaks. This is similar to streaks produced by thin precipitates viewed edge-on.
A further investigation was conducted by means of HRTEM and it was found that the
streaks are a result of extrinsic stacking faults present in the SiC viewed edge-on.
Fig. 7.10. HRTEM image and magnified view of a fault present in the 3C-SiC sample
with a FFT taken over the area indicated
{111}
Fig. 7.10. shows a high resolution TEM image of the sample with a planar defect
viewed edge-on. The {111} planes run in directions indicated on the figure. The insert
is a magnified view of the area indicated with its associated FFT.
From the magnified view it is clear that the defect is an extrinsic stacking fault. Two
displaced {111} layers are seen as described in Section 2.7. Furthermore streaks
similar to that seen previously in the SAD pattern are found in the FFT image,
indicating that the defect is the same type as that observed in Fig. 7.9.

81
Fig. 7.11. Bright field TEM micrograph of the 3C-SiC sample. B = [011], g = _
11 1,
s ≥ 0
The high density of stacking faults in the crystal is attributed to the very low stacking
fault energy in SiC. The fact that the faults shows different characteristics in terms of
lengths and combinations of partials, along with its uniform distribution throughout
the crystal suggests that their formation is not a result of only one process (e.g. misfit
strain) but rather a combination of processes during growth and possibly post growth.
Firstly pyramidal stacking faults are seen (indicated by the arrow in Fig. 7.11.) in the
sample supporting the theory of formation by the incorrect deposition of nuclei during
bulk growth as explained by Powell et al. (1987). Secondly wide ribbons of stacking
fault along with intersecting faults in the form of stair-rod structures (indicated by the
arrow in Fig. 7.11.) are also seen supporting the theory of spontaneous generation of
dislocation loops during the cooling stages of growth due to thermal mismatch.The
subsequent splitting of glide dislocations into partials leads to the formation of wide
ribbons of stacking fault and the interactions of moving partials results in intersecting
faults (explained by Powell et al. (1987)).
Furthermore, the extrinsic faults seen in the high resolution TEM images support the
theory that extrinsic faults have a much lower energy than intrinsic SFs. This may be
due to the fact that the stacking sequence of the extrinsic fault is close to the bulk
stacking sequence of the more stable hexagonal phases of SiC.

7.2.3 Twinning
Fig. 7.12. Bright-field TEM micrograph of a twinned area in the 3C- SiC lattice.
B = [011], g =
82
_
11 1,
s ≥ 0. The insert is a SAD pattern of the area with the
corresponding dark-field micrograph obtained using the twin spot indicated
Fig. 7.12. shows a bright-field TEM image of an area close to the SiC/Si interface in
the SiC where twins are present. The twins were identified by analysing the extra
spots in the SAD pattern shown in Fig. 7.12. The extra spots are consistent with a
180° rotation of the lattice about a {111} plane. Also the dark-field image shown in

83
Fig. 7.12 which was obtained by using one of the extra spots showed an inversion of
the contrast over the area indicating the twinned regions. The twins are long, very
narrow, originate at the interface and extent only a short distance into the bulk of the
material from the interface.
The presence of twins is consistent with the theories of nucleation and growth and
accommodation of lattice misfit presented in Sections 5.2. and 5.3.2. The twins are
most probably introduced during the growth process. Since the film/substrate
interfacial energies of the twinned nuclei is higher than that of the epitaxial ones the
epitaxial ones will have a faster lateral growth than the twinned nuclei and will also
cause the twins to grow along inclined {111} planes. This is exactly what is seen in
results and supports the theory presented in Sections 5.2 and 5.3.2.
7.3 Hydrogen Implanted -SiC
In this section the results of the investigation of proton irradiated 3C-SiC to a dose of
2.8 × 10 16 protons/cm 2 at 400 keV are presented. Implanted samples that were
unannealed and annealed at 1300 °C and 1600°C for one hour were prepared in cross-
section and analysed by TEM. In the unannealed sample no noticeable change in the
microstructure of the SiC was seen showing the same characteristics of the
unimplanted SiC sample. Also no effect due to implantation was seen in any of the
annealed samples. No evidence of a damage region was seen or of defects having
formed as a result of the irradiation process. The structure of the SiC remained
crystalline with the cubic 3C phase for every sample even those annealed at 1600°C.
7.3.1 Unannealed
The unannealed sample yielded no difference from the characteristics seen in the
unimplanted sample. No evidence of radiation damage or a damage zone was seen
with the SiC remaining crystalline throughout. The main defects seen were stacking
faults with their associated partial dislocations and twins originating from the
interface and extending only a limited distance into the bulk of the SiC layer.

84
These results agree well with the theories proposed by Gao et al. (2001) and Perlado
et al.(2000) from their molecular dynamics simulations of displacement cascades in
SiC. It shows that the proton does not impart to the lattice enough energy to create
vast displacement cascades capable of creating an amorphous region. This is due to its
small mass compared to the constituent atoms and also due to the high threshold
displacement energies of the atoms, especially the Si. The anisotropy of the
displacement energies between the constituent atoms also play a big role and their
difference in recovery after the thermal spike prevents large defect clusters to form
during the radiation process. It also causes the cascade to be dispersed, containing
only single point defects and small point defect clusters. Finally the results also show
that a significantly higher proton dose should be used if any form of visible radiation
damage is to be produced.
7.3.2 Annealed at 1300°C
No evidence of radiation damage was observed after a 1hr anneal at 1300°C. Bright-
field TEM images using all the reflections 200, 111, 220 and 311 showed no
significant changes in the characteristics observed in the unimplanted or implanted
unannealed samples. Fig. 7.13. shows a bright field TEM image of the sample using a
311 two-beam condition. This image is similar to that obtained with other two-beam
conditions. Only thin twins, edge-on stacking faults and inclined stacking faults were
seen and no damage region or dislocation loops due to the clustering of point defects
were observed.

85
Fig. 7.13. Bright-field TEM micrograph of 3C-SiC sample annealed at 1300°C for 1
hr. B = [011], g = 311, s ≥ 0. The insert is a SAD pattern of the two beam condition
used.
7.3.3 Annealed at 1600°C
For the analysis of this sample a beam direction was used since the sample was
most electron transparent in this direction. Also it was assumed that if the effects of
radiation damage was to be seen in the sample it would be in the form of dislocation
loops which would lie on the {111} close packed planes. These loops will be strongly
visible using 220 type reflections which in turn are easily accessible using a
beam direction. However extensive examination of the sample using all of the 220
reflections showed no evidence of a damage region or dislocation loops having
formed due to the clustering of intrinsic point defects. The only defects found were
stacking faults with their associated partial dislocations and interesting dislocation
complexes such as shown in Fig. 7.14.

86
(a) (b)
Fig. 7.14. (a) Bright-field TEM micrograph of the bulk of the 3C- SiC sample
annealed at 1600°C for 1 hr. (b) Bright field micrograph showing dislocation
complexes in 3C-SiC sample annealed at 1600°C for 1 hr. B = [111], g = 220, s ≥0.
The dislocation complexes seen in Fig. 7.14 (b) were initially not observed in the
unimplanted sample and it was initially thought that they might have formed due to
either the irradiation or annealing process. This was found not to be the case since a
reassessment (Section 7.3) of the unimplanted sample in the {111} beam direction
showed similar defect complexes.
Furthermore an electron diffraction investigation was done to confirm that no phase
change occurred during the annealing of the sample at 1600°C. A diffraction pattern
of the zone axis was taken and matched with simulated patterns. This was done
for the since this direction allows an unambiguous differentiation between
cubic and hexagonal SiC phases. Excellent agreement was found and it was
concluded that the crystal structure remained that of the cubic 3C phase. The results
are shown in Fig. 7.15.

87
(a) (b)
Fig. 7.15. The (a) experimental (b) simulated SAD pattern of the [110] zone axis in
the 3C-SiC sample annealed at 1600°C for 1 hr
To explain the results obtained for the implanted SiC the following is proposed.
During proton implantation point defects (interstitial atoms, vacancies and hydrogen
atoms) are generated simultaneously in the specimen. In the case of SiC the interstitial
atoms and vacancies are from both sublattices, i.e. silicon and carbon. Since
interstitials and vacancies can have a charge, they can trap electrons or holes. Point
defects produced by irradiation can be trapped by a number of sinks of which the
following are the most important:
1. Interstitial and vacancy recombination will result in mutual annihilation.
2. Some vacancies may trap hydrogen atoms leading to the formation of gas filled
bubbles or two dimensional platelets.
3. Interstitials and vacancies can be trapped by dislocations, dislocation loops and
voids.
In order for the displaced atoms and hydrogen to interact during post irradiation
annealing, they must be mobile enough to migrate to the various sinks.
Since dislocation loops on {111} and {110} planes consist of double layers of silicon
and carbon atoms charge neutrality is maintained. This is a result of the Coulomb
repulsion in dielectric ionic materials which ensures that interstitial coalescence into a
dislocation loop remains stoichiometric (Ryazanov et al. 2002). The same argument
would apply to vacancy loops.

88
Therefore, for dislocation loops to grow, it is required that both Si and C interstitial
atoms be present at the loop nucleation site. For SiC, there is a big difference in the
generation rates for Si and C atoms due to the large difference in threshold
displacement energies in SiC (one source gives Ed = 93 eV for Si and 16 eV for C,
Vladimirov et al. (1998)). About 5 times more carbon than silicon interstitials are
produced during irradiation and the carbon interstitials are also more mobile than the
silicon interstitials as can be seen from the following data.
Table 7.4. Diffusion coefficients for Si and C interstitials in SiC
Si interstitials C interstitials Temperature Reference
D = 9 x 10 -6 cm 2 /s
(Em = 0.51 eV)
D = 10 -4 exp (-0.3/kT)
= 3 x 10 -6 cm 2 /s
D = 1 x 10 -5 cm 2 /s
(Em = 0.55 eV)
D = 10 -4 exp (-0.2/kT)
= 9.8 x 10 -6 cm 2 /s
1500 K Salvador et al. (2004)
1000 K Ryazanov et al. (2002)
Using the diffusion coefficients for interstitial Si and C from Ryazanov et al. (2002).,
the average diffusion distance for Si in SiC at 1000 K for 30 minutes is found to be
x Dt ~ 700 m.
For carbon interstitials the average diffusion distance is found to be approximately
1300 m.
From the above calculation is it clear that Si and C interstitials are already mobile
enough at 1000 K for the nucleation and growth of dislocation loops. The fact that no
dislocation loops were observed in the samples analysed in this investigation, most
likely indicates that the proton dose was below the critical dose required for
interstitial coalescence. SiC is a very radiation resistant material which makes it ideal
for use in fission end fusion reactors.

89
In the following paragraphs the analysis and attempted identification of an interesting
defect in the SiC sample is presented. The identification is interesting since it shows
that the defect is an edge dislocation with Burgers vector and dislocation line
combination uncharacteristic of that usually found in 3C-SiC and in zinc-blende
structures. The simulated image of the defect agrees closely with the experimental one
but the nature of the defect could not be proved conclusively through experimental
techniques in the microscope due to the thickness of the sample prohibiting it from
being studied in different beam directions. A further investigation on this type of
defect will be conducted in future.
Fig. 7.16. Bright-field TEM micrograph of an area containing a defect indicated by
the black arrow. B = [111], g = 220, s≥0. The white arrow indicates and area
containing residual contrast possibly showing a nucleation point.
Fig. 7.16 shows a bright-field TEM micrograph of the area in the material where the
dislocation is present. The dislocation is indicated by the black arrow. The beam
direction is [111] and the reflection 220. The bright field image was taken such that
the Kukuchi line was present on the outside edges of the diffraction spots to obtain the
best contrast. Also present in the image is a stacking fault which may be used to

90
determine the orientation of the micrograph accurately since it is known that the
stacking fault is lying on the {111} planes.
The dislocation has a zig zag image character indicating that the dislocation line is
inclined extending most probably from top to bottom of the foil. Also the projected
image of the dislocation line is perpendicular to the fringes of the stacking fault. All
of these facts along with the visibility and invisibility of the defect using the different
220 reflections pointed towards the dislocation being a 60° type commonly found in
zinc-blende structures with the Burgers vector of the type ½ and the dislocation
line in a direction making an angle of 60° with the Burgers vector.
However the projected length of the dislocation is 397 nm, which gives a foil
thickness of 561 nm by using the beam direction [111] with the dislocation line [110].
This foil thickness is too thick to be electron transparent. The geometrical setup used
is shown in Fig. 7.17.
Fig. 7.17. The geometrical setup used to infer the foil thickness from an assumed
dislocation line direction
Next the foil thickness was determined by using CBED. The CBED micrograph taken
of the area of the dislocation is shown in Fig. 7.18.

Fig. 7.18. CBED pattern taken of the area of interest using a 220 reflection
91
From the figure a line profile was obtained using a Matlab method developed for this
purpose along the line indicated. This was done to aid in the identification of the
positions of the minima’s and maximums used in the calculations. The profile is
shown in Fig 7.19 with identifications of the maximums and minima’s shown.

Intensity
92
Fig. 7.19. The intensity profile of the CBED pattern along the line indicated on Fig.
7.18.
The measurements and subsequent calculated variables of the technique are given in
Table 7.3 (the units and scale used in determining the θi’s are irrelevant since it is the
ratio of that to the Bragg angle that is important). The plotted values are shown in Fig.
7.20.
2θB
Position
etc.
θ1
θ2
θ3

93
Table 7.5. The measured parameters with calculated variables used in obtaining Fig.
7.20
(Si/ni) 2
ni Δθi Si (nm -2 ) 1/ni 2 (Si/ni) 2 (nm -2 )
4 13 0.0044 0.063 1.22975E-06
5 28 0.0096 0.040 3.65112E-06
6 38 0.0130 0.028 4.66997E-06
7 49 0.0167 0.020 5.70487E-06
8 58 0.0198 0.016 6.11964E-06
9 67 0.0229 0.012 6.45229E-06
10 76 0.0259 0.010 6.72476E-06
11 86 0.0293 0.008 7.11641E-06
12 95 0.0324 0.007 7.29683E-06
13 105 0.0358 0.006 7.59524E-06
0.000008
0.000007
0.000006
0.000005
0.000004
0.000003
0.000002
0.000001
0
y = -1.09E-04x + 7.94E-06
R 2 = 9.93E-01
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
(1/ni) 2
Fig. 7.20. The plotted values of Table 7.3 with the linear trend line used to determine
the foil thickness and extinction distance
Once again from the slope and y-intercept of the linear trend line the extinction
distance and foil thickness were obtained by taking the square roots of their inverses.
The value obtained for the extinction distance is 96 nm and the foil thickness is 355
nm.
The foil thickness determined is too thin for the dislocation line direction to be that of
a type since the projected length of the dislocation is too long. The only option

94
left is that the line direction is of the type. The [100] makes an angle of 54.74°
with the [111] direction and if one infers the foil thickness from the projected
dislocation length, a thickness of ~280 nm is found. Thus it is possible that the
dislocation line direction is of the 100 type with the dislocation not running
completely from top to bottom in the foil but rather having been nucleated at a defect
somewhere within the foil. A possible nucleation point is shown on the micrograph in
Fig. 7.16. by the white arrow. Some form of residual contrast is visible which may
indicate a defect which acted as nucleation point.
Fig. 7.21. The simulated image of the dislocation indicated on Fig. 7.16.
None the less, the identification of the dislocation was done by simulation and the
results are shown in Fig. 7.21. Excellent agreement is seen but the true nature of the
defect will have to be established in a future study.
7.4 Reassessment of Unimplanted Sample
7.4.1 Overview of Investigation
The unimplanted SiC sample was investigated again, using a beam direction,
to determine whether similar dislocation complexes to those observed in the hydrogen
implanted SiC sample annealed at 1600°C was present. It was found that the same
dislocation structures are present in the unimplanted sample and it was concluded that
dislocation complexes was not introduced as a result of the irradiation or annealing
process.

7.4.2 Results
95
Fig. 7.22. Bright-field TEM micrograph of the unimplanted 3C-SiC sample viewed
under a beam direction with g = 220, s≥0.
Fig. 7.22 shows a bright field TEM micrograph of the unimplanted sample recorded
using a beam direction with a g = 220 two-beam condition. The quality of the
micrograph is poor since the sample was very thick in this direction but none the less
it is sufficient to show that the same dislocation complexes are present in this sample
as was observed in the annealed one. Their presence is most likely due to the growth
process and they are identified as predominantly partial and 60 degree type
dislocations.

8.1 Introduction
96
CHAPTER EIGHT
CONCLUSION
In this chapter the conclusions that are reached from the study are dealt with in two
sections. Section 8.2 lists the main results and conclusions for the unirradiated and
unannealed samples and Section 8.3 the main results and conclusions for the proton
bombarded 3C-SiC. All the results listed and conclusions are from a TEM study of
the samples.
8.2 TEM Analysis of ß-SiC Grown in (001) Si by CVD
The phase of the SiC was confirmed by electron diffraction and HRTEM to be
the cubic ß phase with a lattice parameter of 4.35 0.01 Å.
The SiC layer was single crystalline with the same orientation as the Si
substrate.
HRTEM indicated that planar defects on inclined {111} planes were generated
at the Si/SiC interface and propagate through the SiC layer.
The SiC layer contained a high density of SFs which were uniformly
distributed through the foil.
By simulating SFs and matching it with observed SFs, it was found that the
SFs have a fault vector of the type 1/3 with bonding partial dislocations
of the type 1/6 .
Inclined SFs exhibited symmetrical and complementary fringe contrast images
in both bright and dark field two-beam imaging conditions.
SFs viewed edge-on generated streaks in the diffraction pattern similar to that
generated by a thin precipitate viewed edge-on.
HRTEM imaging of SFs viewed edge-on indicated that the SF were extrinsic
in nature. FFTs obtained of the HRTEM image of these SFs produced streaks
similar to those observed in the selected area electron diffraction patterns of
edge-on SFs.

97
Twin platelets on {111} planes were observed in the SiC layer. These narrow
twins nucleate at the interface and extend only a short distance into the SiC
layer.
The extended defects observed in the SiC layers were most probably introduced
during the CVD growth process as a result of the lattice mismatch between the SiC
epitaxial layer and the Si substrate. This inference is strengthened by the fact that
hexagonal 6H-SiC, which are grown by a different technique, can be prepared with an
extremely low extended defect concentration. Furthermore, it is known that stacking
faults form readily in ß-SiC due to the very low (negative) stacking fault energy of
this compound. Twins on the other hand can also relieve misfit stress and it is
therefore expected that twins would be generated at the Si/SiC interface as was
observed in this investigation.
High resolution transmission electron microscopy analyses of stacking faults viewed
edge-on indicate that the SFs are extrinsic in nature, i.e. it consists of two displaced
layers yielding a stacking sequence in the direction of …ABCA/C/BCAB…
The symmetrical and complementary nature of two-beam bright and dark-field
diffraction contrast images of inclined SFs indicate that SiC has an anomalous
absorption ratio between that of Si and diamond. This conclusion was confirmed by
matching simulated SF images with experimental SF images, where the best match
was obtained for an anomalous absorption ratio of 0.016 for SiC. The values for Si
and diamond are 0.1 and 0.01 respectively.
8.3 TEM Analysis of Proton Bombarded and Annealed ß-SiC
ß-SiC samples were implanted with 400 keV protons to a total dose of 2.8 ×
10 16 protons.cm -2 . Post-implantation annealing was carried for 1 hour at 1300
and 1600 ºC.
In all the implanted samples, annealed an unannealed, no evidence of radiation
damage was observed. The radiation damage that one would expect to find in proton

98
implanted and annealed materials could include self interstitial dislocation loops,
hydrogen platelets or bubbles, vacancy loops and voids. The possibility that the high
density of stacking faults and twin platelets could have acted as sinks for the radiation
induced interstitials and hydrogen and thus preventing self interstitial coalescence and
loop formation is ruled out by the fact that the same proton bombardment and
annealing treatment was also performed on semiconductor grade 6H-SiC (hexagonal
phase with no visible lattice defects) and no radiation damage was detected in this
case also. The TEM results of the 6H-SiC were not included in this dissertation since
no lattice defects were observed in these samples.
The calculation of the average migration distance for silicon and carbon interstitial
atoms at a 1000°C revealed that the interstitial atoms are mobile enough to migrate
over large distances and thus could form dislocation loops if present in large enough
concentrations after annihilation by vacancy interstitial recombination.
The proton implanted and annealed ß-SiC samples also exhibited no evidence of
phase transformation or an increase in lattice defect concentration compared to the
unimplanted samples.
The results of this investigation confirm the notion that SiC is a radiation resistant
material. The critical proton dose for the creation of small dislocation loops seems to
be higher than for other compound semiconductors with the zinc-blende structure.
This is most probably due to the very high displacement energies of Si and C atoms.
The large difference in displacement energies for Si and C would also retard the
formation of dislocation loops since equal numbers of Si and C are required for a loop
to nucleate and grow. The difference in lattice recovery for the Si and C sub-lattices
after the thermal spike produced during ion implantation is another factor which
would retard dislocation formation and hence contribute to the radiation resistance of
SiC.
Future work on SiC will include the use of higher proton doses to establish the critical
dose required for dislocation loop formation. The proton induced radiation damage at
higher doses will also be compared with radiation damage produced by high energy
neutrons in SiC.

99
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