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Ab initio theory of point defects and defect complexes in SiC [Elektronische Ressource] / vorgelegt von Alexander Mattausch

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197 pages
Ab initio-Theory of Point Defectsand Defect Complexes in SiCDen Naturwissenschaftlichen Fakultätender Friedrich Alexander Universität Erlangen NürnbergzurErlangung des Doktorgradesvorgelegt vonAlexander Mattauschaus AugsburgAls Dissertation genehmigt von den Naturwissenschaftlichen Fakultätender Universität Erlangen NürnbergTag der mündlichen Prüfung: 7. 7. 2005Vorsitzender derPromotionskommission: Prof. Dr. D. P. HäderErstberichterstatter: Prof. Dr. O. PankratovZweitberichterstatter: Prof. Dr. E. PehlkeContents0. Zusammenfassung 11. Introduction 51.1. Defects and diffusion in SiC . . . . . . . . . . . . . . . . . . . . 81.2. Identification of defects by their vibrational modes . . . . . . 101.3. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122. Calculation of defect properties using density functional theory 152.1. Calculation of ground state properties . . . . . . . . . . . . . . 162.1.1. Investigation of defects . . . . . . . . . . . . . . . . . . 172.1.2. Formation energies . . . . . . . . . . . . . . . . . . . . . 212.1.3. Ionisation levels . . . . . . . . . . . . . . . . . . . . . . . 232.1.4. Dissociation energies . . . . . . . . . . . . . . . . . . . . 242.2. Migration barriers . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3. Vibrational spectra . . . . . . . . . . . . . . . . . . . . . . . . . 283. Structural, electronic and vibrational properties of SiC 313.1. Structural properties and polytypism . .
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Ab initio-Theory of Point Defects
and Defect Complexes in SiC
Den Naturwissenschaftlichen Fakultäten
der Friedrich Alexander Universität Erlangen Nürnberg
zur
Erlangung des Doktorgrades
vorgelegt von
Alexander Mattausch
aus AugsburgAls Dissertation genehmigt von den Naturwissenschaftlichen Fakultäten
der Universität Erlangen Nürnberg
Tag der mündlichen Prüfung: 7. 7. 2005
Vorsitzender der
Promotionskommission: Prof. Dr. D. P. Häder
Erstberichterstatter: Prof. Dr. O. Pankratov
Zweitberichterstatter: Prof. Dr. E. PehlkeContents
0. Zusammenfassung 1
1. Introduction 5
1.1. Defects and diffusion in SiC . . . . . . . . . . . . . . . . . . . . 8
1.2. Identification of defects by their vibrational modes . . . . . . 10
1.3. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2. Calculation of defect properties using density functional theory 15
2.1. Calculation of ground state properties . . . . . . . . . . . . . . 16
2.1.1. Investigation of defects . . . . . . . . . . . . . . . . . . 17
2.1.2. Formation energies . . . . . . . . . . . . . . . . . . . . . 21
2.1.3. Ionisation levels . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.4. Dissociation energies . . . . . . . . . . . . . . . . . . . . 24
2.2. Migration barriers . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3. Vibrational spectra . . . . . . . . . . . . . . . . . . . . . . . . . 28
3. Structural, electronic and vibrational properties of SiC 31
3.1. Structural properties and polytypism . . . . . . . . . . . . . . 31
3.2. Electronic pr . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3. Phonons in SiC . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4. Point defects in SiC: properties and migration mechanisms 41
4.1. Vacancies, interstitials and antisites:
the basic intrinsic point defects . . . . . . . . . . . . . . . . . . 42
4.1.1. Effects of the polytypism on point defects . . . . . . . 43
4.1.2. Vacancies . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.1.3. Interstitials. . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.1.4. Antisites . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.5. Abundance of simple point defects . . . . . . . . . . . 60
4.2. Defect migration . . . . . . . . . . . . . . . . . . . . . . . . . . 63
iiiContents
4.2.1. Diffusion of vacancies . . . . . . . . . . . . . . . . . . . 63
4.2.2. Dif of interstitials . . . . . . . . . . . . . . . . . . 67
4.2.3. Self diffusion in SiC . . . . . . . . . . . . . . . . . . . . 70
4.3. Annealing mechanisms of intrinsic defects . . . . . . . . . . . 77
4.3.1. Annealing of silicon related . . . . . . . . . . . 79
4.3.2. of carbon r defects . . . . . . . . . . . 83
4.4. Intrinsic defects and their impact on the dopant diffusion . . 86
4.4.1. The migration of boron . . . . . . . . . . . . . . . . . . 87
4.4.2. The p and n type dopants aluminium, nitrogen and
phosphorus . . . . . . . . . . . . . . . . . . . . . . . . . 96
5. Clustering of carbon in SiC: defect complexes
and their identification 101
5.1. Formation and properties of carbon clusters . . . . . . . . . . 102
5.1.1. Interstitial clusters . . . . . . . . . . . . . . . . . . . . . 103
5.1.2. Antisite . . . . . . . . . . . . . . . . . . . . . . . 110
5.1.3. Impact of the carbon clusters on the annealing . . . . . 115
5.2. Defect identification: vibrational properties of carbon rela
ted defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.2.1. Carbon interstitials . . . . . . . . . . . . . . . . . . . . . 118
5.2.2. di interstitials . . . . . . . . . . . . . . . . . . . 121
5.2.3. Larger interstitial aggregates . . . . . . . . . . . . . . . 123
5.2.4. Di carbon antisite . . . . . . . . . . . . . . . . . . . . . . 125
5.2.5. Clusters of di carbon antisites . . . . . . . . . . . . . . 128
5.2.6. Tri and tetra carbon antisite . . . . . . . . . . . . . . . 130
5.3. Photoluminescence centers . . . . . . . . . . . . . . . . . . . . 133
5.3.1. The D center . . . . . . . . . . . . . . . . . . . . . . . . 134II
5.3.2. The P−T centers . . . . . . . . . . . . . . . . . . . . . . 137
5.3.3. The U center . . . . . . . . . . . . . . . . . . . . . . . . 141
5.3.4. Similarities between SiC and diamond . . . . . . . . . 143
6. Summary 145
A. Basics of the density functional theory 147
A.1. Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
A.2. The Hohenberg Kohn theorem . . . . . . . . . . . . . . . . . . 148
A.3. The Kohn Sham equations . . . . . . . . . . . . . . . . . . . . . 148
A.4. The local density approximation (LDA) . . . . . . . . . . . . . 150
ivContents
A.5. Pseudopotentials . . . . . . . . . . . . . . . . . . . . . . . . . . 152
A.6. Brillouin zone integration . . . . . . . . . . . . . . . . . . . . . 155
A.7. The software package fhi96spin . . . . . . . . . . . . . . . . . 157
B. Accuracy of phonon calculations using the frozen phonon approach159
B.1. Relevance of anharmonic effects . . . . . . . . . . . . . . . . . 159
B.2. Sources of error in the LVM calculations of defects . . . . . . 161
C. Calculational parameters 165
D. Formation energies 167
Bibliography 173
Acknowledgments 185
Curriculum Vitae 187
vContents
viList of Figures
1.1. Experimental implantation profile of boron. . . . . . . . . . . 9
1.2. Vibrational spectrum of the D center in 3C SiC. . . . . . . . . 11II
2.1. Schematic view of the supercell approach. . . . . . . . . . . . 18
2.2. Illustration of the ridge method. . . . . . . . . . . . . . . . . . 27
3.1. Stacking sequence of SiC polytypes 3C, 2H, 4H, and 6H. . . . 32
3.2. Miller indices of the hexagonal crystal structure. . . . . . . . . 34
3.3. Kohn Sham band structure of SiC. . . . . . . . . . . . . . . . . 37
3.4. Phonon dispersion of 3C SiC. . . . . . . . . . . . . . . . . . . . 38
4.1. Local geometry of cubic and hexagonal sites. . . . . . . . . . . 44
4.2. Vacancy defects in 3C SiC. . . . . . . . . . . . . . . . . . . . . . 45
4.3. Formation energies of silicon related defects. . . . . . . . . . . 47
4.4. For energies of carbon r . . . . . . . . . . 50
4.5. Silicon interstitials in 3C SiC. . . . . . . . . . . . . . . . . . . . 52
4.6. Interstitial configurations in 4H SiC. . . . . . . . . . . . . . . . 54
4.7. Carbon interstitial in 3C SiC. . . . . . . . . . . . . . . . . . . . 56
4.8. Defect molecule of the carbon split interstitial C . . . . . 56sph100i
4.9. Migration mechanisms of the self diffusion in SiC.. . . . . . . 64
4.10. of vacancies. . . . . . . . . . . . . . . . 65
4.11. Migration of the silicon interstitial. . . . . . . . . 66
4.12. mechanisms of the carbon split interstitial. . . . . . 69
4.13. Annealing of intrinsic defects in SiC. . . . . . . . 79
4.14. Recombination mechanisms of Frenkel pairs. . . . . . . . . . . 81
4.15. Formation energies of boron interstitials. . . . . . . . . . . . . 89
4.16. For energies of aluminium interstitials in 4H SiC. . . . 97
4.17. Formation energies of nitrogen in 4H SiC.. . . . . 98
4.18. For energies of phosphorus interstitials in 4H SiC. . . 100
viiList of Figures
5.1. Carbon interstitial clusters in 3C SiC. . . . . . . . . . . . . . . 103
5.2. di interstitials in 4H SiC. . . . . . . . . . . . . . . . . . 107
5.3. Tetra interstitial (C ) in 4H SiC. . . . . . . . . . . . . . . 109sp 4,kkhh
5.4. Carbon clusters at carbon antisites in 3C SiC. . . . . . . . . . . 112
5.5. Pair of di carbon antisites [(C ) ] in 4H SiC.. . . . . . . . . . 1132 Si 2
5.6. Antisite clusters at the cubic site in . . . . . . . . . . . 114
5.7. Comparison of the dissociation energies of the clusters. . . . . 116
5.8. Isotope splitting of the LVMs of the di carbon antisite (C )Si. 1282
5.9. of the tri carbon antisite (C ) in 3C SiC. . . 1323 Si
5.10. Comparison of the D spectra in 3C , 4H and 6H SiC. . . . . 135II
5.11. ZPLs and phonon replicas of the P−T centers. . . . . . . . . . 138
5.12. ZPL and r of the U center . . . . . . . . . . . . 142
A.1. Schematic representation of the pseudopotential approach. . 153
B.1. Anharmonic effects in the force and energy calculations. . . . 160
B.2. Defect modes of the di carbon antisite (C ) vs. the defect2 Si
molecule size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
viiiList of Tables
3.1. Experimentally measured structural and electronic proper-
ties of various SiC polytypes. . . . . . . . . . . . . . . . . . . . 34
3.2. Calculated Structural and electronic properties of 3C and
4H SiC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3. Comparison of calculated and measured phonon frequencies. 39
4.1. Ionisation levels of the carbon and the silicon vacancies in
3C and 4H SiC . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2. Bond lengths of the neutral carbon split interstitial. . . . . . . 58
4.3. Migration barriers for the migration of V . . . . . . . . . . . . 65Si
4.4. for the of silicon interstitials. . . 68
4.5. Migration barriers for the migration of carbon . . 70
4.6. Activation energies of the silicon self diffusion. . . . . . . . . 74
4.7. Activation energies of the carbon . . . . . . . . 76
4.8. Energy barriers for the Frenkel pair recombination. . . . . . . 80
4.9. Migration and kick out/kick in barriers for the interstitial
mediated boron diffusion. . . . . . . . . . . . . . . . . . . . . . 91
4.10. Activation energies of the interstitial mediated boron diffu
sion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.1. Dissociation energies of the neutral carbon clusters. . . . . . . 104
5.2. Ionisation levels of selected carbon clusters. . . . . . . . . . . . 105
5.3. LVMsandisotopeshiftsofthecarbonsplit interstitialin3C
SiC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.4. LVMsandisotopeshiftsofthecarbonsplit interstitialin4H
SiC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.5. LVMs of di interstitials in 3C SiC. . . . . . . . . . . . . . . . . 121
5.6. LVMs of in 4H SiC. . . . . . . . . . . . . . . . . 122
5.7. LVMs of tri and tetra interstitials. . . . . . . . . . . . . . . . . 124
5.8. LVMs of (C ) in 3C SiC. . . . . . . . . . . . . . . . . . . . . . 1262 Si
ixList of Tables
5.9. LVMs of (C ) in 4H SiC. . . . . . . . . . . . . . . . . . . . . . 1272 Si
5.10. LVMs of [(C ) ] in 3C SiC. . . . . . . . . . . . . . . . . . . . . 1302 Si 2
5.11. LVMs of [(C ) ] in 4H SiC. . . . . . . . . . . . . . . . . . . . . 1312 Si 2
5.12. LVMs of carbon antisite clusters in 3C and 4H SiC. . . . . . . 132
C.1. Matching radii of the employed pseudopotentials. . . . . . . . 165
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