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

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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
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Analysis of the Extended Defects in
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My sincere thanks to the following
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OPSOMMING Hierdie dissertasie hande
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4.2.5. Two-Beam Scattering Matrix 4
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Dedicated to my wife and parents
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SUMMARY The dissertation focuses on
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CONTENTS Chapter 1: INTRODUCTION 1
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1 CHAPTER ONE INTRODUCTION Silicon
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2.1. Introduction 3 CHAPTER TWO OVE
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2.2.2 The Zinc-Blende Structure 5 T
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2.3 Point Defects, Defect Migration
Page 23 and 24: v m Em vm0 exp( ) (2.2) kT 9 wher
Page 25 and 26: 11 explained and the concept of par
Page 27 and 28: 13 Straight dislocations furthermor
Page 29 and 30: 2.5 Partial Dislocations and Slip 1
Page 31 and 32: 17 Fig. 2.13. The geometrical setup
Page 33 and 34: 19 extrinsic stacking faults are th
Page 35 and 36: 2.8 Twinning 21 Twinning is a proce
Page 37 and 38: 23 Fig. 2.20. The process of vacanc
Page 39 and 40: S n Td (3.2) 25 and is also referr
Page 41 and 42: 27 where a = a0(Z1 2/3 + Z2 2/3 ) -
Page 43 and 44: 29 Using this expression, curves of
Page 45 and 46: 31 As stated previously hard-sphere
Page 47 and 48: 33 where A is the atomic weight. Th
Page 49 and 50: 35 a vacancy dislocation loop if th
Page 51 and 52: 37 Fig. 4.1. (a) A wave incident on
Page 53 and 54: 39 Consider Fig. 4.2 which illustra
Page 55 and 56: 41 V0 is the mean inner potential o
Page 57 and 58: 43 beam left-hand side g' = 0 g' =
Page 59 and 60: 45 In addition another set of indep
Page 61 and 62: 47 When this is incorporated into t
Page 63 and 64: S ( s , z ) e T i Se ( / 0 )
Page 65 and 66: z0 z2 . xn cos and (4.47) D 1 proj
Page 67 and 68: 5.1 Introduction 53 CHAPTER FIVE LI
Page 69 and 70: 55 different orientations. The inte
Page 71 and 72: 57 Furthermore Pirouz et al. (1987)
Page 73: 59 intersection of the fault, the f
Page 77 and 78: 63 (2000) found that subsequent ann
Page 79 and 80: 6.3.1 Ion Range and Defect Producti
Page 81 and 82: 67 Fig. 6.3. Total number of displa
Page 83 and 84: 7.1 Introduction 69 CHAPTER SEVEN R
Page 85 and 86: Fig. 7.2. Simulated diffraction pat
Page 87 and 88: 73 Fig. 7.3. A HRTEM image of the S
Page 89 and 90: 75 Fig. 7.5. The stacking fault sel
Page 91 and 92: (Si/ni) 2 0.000018 0.000016 0.00001
Page 93 and 94: 79 may be concluded that the initia
Page 95 and 96: 81 Fig. 7.11. Bright field TEM micr
Page 97 and 98: 83 Fig. 7.12 which was obtained by
Page 99 and 100: 85 Fig. 7.13. Bright-field TEM micr
Page 101 and 102: 87 (a) (b) Fig. 7.15. The (a) exper
Page 103 and 104: 89 In the following paragraphs the
Page 105 and 106: Fig. 7.18. CBED pattern taken of th
Page 107 and 108: 93 Table 7.5. The measured paramete
Page 109 and 110: 7.4.2 Results 95 Fig. 7.22. Bright-
Page 111 and 112: 97 Twin platelets on {111} planes
Page 113 and 114: 99 REFERENCES Blumenau, A.T., Jones
Page 115 and 116: 101 Hull, D., Bacon, D.J. : (1984)
Page 117: 103 Smith, D.J., Jepps, N.W. and Pa
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