Polytypism and One-Dimensional Disorder in Silicon Carbide – a Study using Synchrotron Edge Topography

 

 

 

 

 

 

James Francis Kelly

 

                                       

 

 

 

 

 

          

A thesis submitted to the University of London for the degree of Doctor of Philosophy in the Faculty of Science

 

 

 

September 2002

 

 

 

 

 

Industrial Materials Group

School of Crystallography

Birkbeck College

University of London

Malet Street

London WC1E 7HX

 

Abstract

 

Silicon carbide (SiC) originated before the birth of our solar system, formed in red giant carbon stars and became trapped as interstellar grains in primitive meteorites roaming through the Milky Way for billions of years.  Isotopic analysis of meteoritic SiC is thus offering a new and exciting tool for exploring the structure and evolution of our galaxy. Artificial carborundum on the other hand, manufactured as a substitute for diamonds initially, has proved more useful for the abrasives industry, the main commercial use of SiC today. Nevertheless interest in Moissanite gemstone production is reviving interest in this burgeoning semiconductor material.

The current widespread interest in SiC as a high-temperature power semiconductor can be attributed to its wide band gap (Eg ~3 eV) electronic properties. Despite this potential, device development has been handicapped by the presence of defects and the tendency for SiC to form so many polytypes. The phenomenon of polytypism, first observed in SiC ninety years ago by Baumhauer, has been studied extensively and a full explanation for its existence still remains elusive today. The problem is essentially that the one-dimensional ordering arrangement in SiC has produced over 150 different layer periodicities based on the simple ABA… ABC… stacking sequences found in close packed structures. This arises from the large number of possible repeat sequences, the largest reported spacing in SiC being 3015 Å. Besides these long-period ordered structures one-dimensional disorder (1DD), when there is no finite lattice repeat, is also a prevalent feature in silicon carbide.

A significant gap in our understanding of polytypism exists, caused in part by the lack of experimental data on the spatial distribution of polytype coalescence and also by lack of knowledge of the regions between adjoining common low-period polytypes (6H, 15R and 4H) and 1DD. Few observations detailing the relative location of different polytypes in the same crystal have been reported. This shortcoming has been properly addressed for the first time by constructing morphologically accurate models of the layer-stacked SiC edges. With the advent of synchrotron radiation source x-ray diffraction edge topography (SRS-XRDT) and the improved resolution currently available, finer features have been revealed at polytype boundaries. Diffraction contrast is provided from the edges rather than the more substantial faces of the hexagonal crystals and it is now possible to identify and confidently resolve thin one-dimensionally disordered layers (as thin as 5 µm) and regions of high defect density as well as long period polytypes (LPP’s).

The next nearest polytype relationships between the common polytypes are important clues to the growth scenario of Lely vapour grown SiC. A unique database on these adjoining polytype patterns has prompted the author to develop a classification scheme and propose a non-degenerate polytype-polytype configuration termed a sandwich model. These ubiquitous features are illustrated with several examples and some general trends and rules of polytype coalescence in SiC are presented.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Acknowledgements

The EPSRC for funding, CLRC for facilities, Prof. Paul Barnes for encouragement and friendship over many years, Dr. Graham Fisher for guidance and tuition in the early days, Dr. Graham Clark and Dr. David Laundy for help on station 7.6 of the Daresbury Laboratory SRS, Emeritus Prof. Alan MacKay for some critical inspiration and the Industrial Materials Group Birkbeck for their humour and support, in particular Dr. Jeremy Cockcroft for helpful discussion throughout my time at Birkbeck College. I am indebted to Juliet Munn, Andy Beard and Martin Vickers for their help in the SEM work.

 

I would also like to take this opportunity to thank the following institutions and organizing committees for the financial support and opportunity they granted me, during the course of this project, to attend the conferences and meetings listed:

Aperiodic 2000 organizing committee

Birkbeck College Awards

The British Crystallographic Association (BCA) in particular Prof. Chick Wilson

The Engineering and Physical Sciences Research Council (EPSRC)

The European Crystallographic Association

The Institute of Physics (IoP)

 

Meetings:

BCA meeting 3-5 April 2000 Edinburgh

APERIODIC 2000 conference 4-8 July 2000 Nijmegen, Netherlands

IoP EMAG meeting 6 September 2000 London

IoP CMMP conference 18-21 December 2000 Bristol

Royal Society discussion meeting 21 February 2001 London

BCA/CCG course 30 Mar-7 April 2001 Durham

BCA meeting 7-10 April 2001 Reading

SiCEP program 31 May-10 June 2001 Linköping/Stockholm, Sweden

ECM20 conference 25-31 August 2001 Kraków, Poland

Higher European Research Course for Users of Large Experimental Stations  (HERCULES) course 17 Feb-28 Mar 2002 Grenoble, France

 

 

Contents

 

Abstract       2         

 

Acknowledgements          4

 

List of Figures         8

 

List of Tables        10

 

List of Abbreviations and Symbols    11

 
 
 
Chapter 1. Literature Review
                                       

1.1          Background – A brief History of Silicon Carbide           12

 

1.2          Introduction      17

                                                                       

1.3     A description of silicon carbide           22

                       

1.4     On the origins of polytypism    27

 

1.5   Axial Next Nearest Neighbour Ising model (ANNNI)     37

 

1.6     Methods to study polytypes      46

 

1.7     Current Research      52

 

 

 

Chapter 2. X-Ray Diffraction Topography–Methods of Analysis

 

2.1          Introduction       54

 

2.2     The Early History of Topography 54

         

2.3          Development of Instrumental Techniques 58

         

2.4          Topographic Contrast          61

 

2.5          Synchrotron Radiation Sources      65

 

2.6          Synchrotron Topography 69

 

2.7     Edge Topography 75

         

2.8          Photographic emulsions           78

         

2.9     Standard Indexed Topographs 80

           

2.10   Polytype Identification 83

         

2.11          Measuring Long Period Polytypes    88

         

2.12          Resolution Limit in Synchrotron Topography of SiC     90

         

2.13          Orthogonal Configuration          92

         

 

 

Chapter 3. Edge Topography Survey Results

                                       

3.1     A Brief History of the Project          94

 

3.2     In Search of a Polytype Neighbourhood Classification Scheme       107

                       

3.3     Polytype Coalescence Sandwich Models       112

                       

3.4     Edge Morphology           117

                   

3.5     Defect Density Bands          122

 

3.6     The Missing Piece Method of Polytype Identification           128

 

3.7     One-Dimensionally Disordered (1DD) Layers          139

 

3.8     Long Period Polytypes (LPP’s)       146

 

3.9     Statistical Trend of Polytypism 154

 

 

 

Chapter 4. Silicon Carbide Cathodoluminescence

                                       

4.1          Objectives       158

 

4.2          Experimental    158

 

4.3     Electron Microscopy of SiC    159

 

4.4     Locating Cathodoluminescence        161

 

4.5          Luminescence from 1DD layers 165

 

 

Chapter 5. The Phenomenon of Polytypism

                                       

5.1     Summary           166

 

5.2     Chaotic behaviour – a model for polytypism? 168

 

5.3     Future work  172

 

5.4          Conclusions     174

 

 

 

Bibliography        176

 
 
 
Appendix 1

Table A1 Indexed reflections from the 31.l diffraction row for the common polytypes   184              179

Figure A1     Graphs of INDTOP/WRIST output for 6H+4H and 6H+15R polytypes. 185

 

Appendix 2

Table A2 Polytype content from GRF samples (pre HBL) 186

Table A3 Polytype content from GRF samples - amended (post HBL) 187

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

List of Figures

 

Chapter 1

1.1         The Hertzprung-Russell diagram               13

1.2         A typical silicon carbide hexagonal platelet     15

1.3         The zig-zag chain structure of hexagonal SiC               18

1.4         The relation between structure and temperature of occurrence in SiC         20

1.5              Atomic model of the 6H polytype of SiC          22

1.6         A two-dimensional representation of the 1 1`20 plane in SiC 25

1.7         The spiral growth pattern of carborundum 28

1.8         Screw dislocations in silicon carbide 6H           30

1.9              Variation of entropy with disorder in SiC         34

1.10       The interaction scheme for the ANNNI model              39

1.11       The ground state phase diagram of the ANNNI model     41

1.12              Schematic phase diagram of the ANNNI model at temperature kT          42

1.13       Mean field phase diagram of the ANNNI model              43

1.14              Energy band-gap diagram   50

1.15       In-situ X-ray topography of SiC single-crystal Lely growth    53

             

 

Chapter 2

2.1         Berg-Barrett geometry     59

2.2         Lang camera    61

2.3              Schematic representation of the spectral output of the SRS       67

2.4         Graph of the Photon flux v Energy for station 7.6 of the SRS  70

2.5              Synchrotron Radiation Source ring at the Daresbury Laboratory 71

2.6         7.6 Topography hutch experimental layout      74

2.7              Photograph of station 7.6 hutch    77

2.8              Schematic of experimental geometry used on station 7.6               78

2.9         Ilford L4 emulsion (full plate edge topograph of sample J50) 79

2.10              INDTOP/WRIST Simulation of 6H polytype 82

2.11              Indexed full plate topograph of 6H polytype (J112)     85

2.12              Indexed full plate topograph of 4H and 15R polytypes (J14)               86

2.13              Multipolytypic topographs of 6H, 15R and 4H coalescence: (J52, J57)   87

2.14              Optical microscopes used in the analysis of the photographic plates       88

2.15              Magnified long period repeat of J26 (152H/456R)              89

2.16              Geometric factors affecting resolution in a topographic experiment  91

2.17              Orthogonal geometry – schematic diagram  92

2.18              Indexed full plate topograph (#389) of J26 using orthogonal geometry    93

           

 

Chapter 3

3.1              Photograph of samples J1-J120 used in the edge topography survey     96

3.2              Enlargements from a white radiation synchrotron edge topograph of J67      106

3.3              Schematic of the non-degenerate polytype sandwich configurations in SiC      109

3.4              Photograph of a doubly filled sandwich configuration J33          111

3.5              Simple sandwich model 6H + 1DD + 6H of crystal J6   113

3.6              Standard example of the American club sandwich model (crystal J12)         115

3.7         A topograph of J2 showing the layer indexing of the 15R polytype 116

3.8              Topographs and model of J26 containing an LPP assigned 152H/456R               118

3.9         Full plate edge topograph of J24 (asymmetric sandwich) 121

3.10              Topograph and American club sandwich model of sample J52 123

3.11       A 1200μm thick SiC crystal containing the 6H polytype (J47)       125

3.12              Topograph and model of J36 showing the presence of defect bands               127

3.13              Illustration of the “missing piece” method of polytype identification of J13          130

3.14       A “3-D” map of the polytype content of J13              131

3.15              Missing method applied to crystal J15 133

3.16              Unambiguous spatial polytype relationships determined for J29          135

3.17              Multipolytypes in syntactic coalescence (J20)       137

3.18       An example of a highly disordered silicon carbide crystal (J59)               140

3.19              Distribution of 1DD layer thicknesses (μm) in the XRDT survey              142

3.20       A thin (147μm) sandwich model of J64 containing the LPP 42H   143

3.21              Enlargements from a 6H polytype (J45) containing thin 1DD layers               144

3.22a              Current status of polytype model building from SiC synchrotron topographs 147

3.22b              Current status of polytype model building from SiC synchrotron topographs 148

3.23       LPP 201H/603R measured in sample J105               149

3.24       LPP layer widths (μm) displayed as a function of c-repeat spacings  152

3.25              Frequency of low period polytypes (6H, 15R, 4H) observed in the study       153

3.26       Pie chart depicting the abundances of the various coalescence models     155

3.27              Distribution of the crystal edge thickness data               156

 

 

Chapter 4

4.1              Photograph of Joel JSM-35CF Scanning Electron Microscope               159

4.2              Scanning electron micrographs of relatively thick SiC crystal edges       160

4.3              Various micrographs of SiC crystals (J15, J52, J57, J20)         161

4.4              Complementary combined imaging modes applied to sample J59 162

4.5         SEM and cathodoluminescence images of J40          163

4.6              Cathodoluminescence visible in sample J20 164

4.7              Enlarged area SEM micrograph and CL image of J57         165

 

 

Chapter 5

5.1              Poincaré section of a chaotic attractor (due to Ueda) 171

5.2         A waveform plot of a solution of the Duffing oscillator 172

5.3         Plot of LPP widths against number of layers  173

 

 

 

 

 

 

 

 

 

 

 

 

List of Tables

 

1.1              Electronics for Extreme Environments (E3)         16

1.2              Theories of polytypism  19

1.3              Notations used to describe polytypes    23

1.4              Physical properties of silicon carbide              26

1.5              Structure series of polytypes    31

1.6              General experimental techniques for studying polytypes    49

 

 

2.1         A chronological summary of laboratory topography techniques    57

2.2              Calculated X-ray photon flux on station 7.6 SRS              70

2.3              INDTOP/WRIST output for 6H polytype 81

2.4              Systematic absences for 6H polytype              84

2.5         Beam size comparison (Pre/Post HBL data)        91

 

 

3.1              Detailed assignment of all the 135 crystals used in the XRDT survey      97

3.2         Long period polytype assignments 146

3.3              Statistical frequency of the common 6H, 15R and 4H polytypes              153

3.4              Statistical distribution of polytype models    155

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

List of abbreviations and symbols

 

 

A – Atomic weight (g/mol ASiC = 40.10, AC = 12.01, ASi = 28.09)

B – Magnetic flux density (Wb m-2)

B – Brilliance of synchrotron source

c – Velocity of light in vacuum » 3x 108 m s-1

C – Polarization factor (C=1 for s polarization, C= |cos 2qB| for ppolarization)

Cd – Contrast factor

d – lattice plane spacing (Å)

δ – Specimen-to-plate distance (mm)

D – Source-to-specimen distance (m)

e – Electronic charge = 1.6 x 10-19 C

Eb – Electron beam energy (keV)

F – Structure factor (Fh)

h – Planck’s constant  =  6.6 x 10-34 Js

h,k,l – Miller indices

I – Integrated Intensity

I o – Incident beam intensity

l - Wavelength (nm, Å)

m – mass (kg)

m - Linear absorption coefficient (cm-1)

x - Extinction distance

P(l) – Power in synchrotron beam

ρ – Density (g/cm3 for SiC ρ = 3.217)

re – Classical electron radius (e2/mc2)

R – Resolution (Rs)

Re – Depth of electron in material (μm)

s - Standard Deviation (S.D.)

S – Source size

t - Thickness of sample

T – Period of oscillation

q - Bragg angle (qB)

V – Volume of unit cell

VD – Volume of defect

ω – angular frequency

Z – Atomic number (Z = 20 for SiC, Zc = 6, ZSi = 14))

[ ] – denotes a Figure in the thesis