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Intrinsic point defects in zinc oxide [Elektronische Ressource] : modeling of structural, electronic, thermodynamic and kinetic properties / vorgelegt von Paul Erhart

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Intrinsic Point Defects in Zinc Oxide:Modeling of Structural, Electronic, Thermodynamicand Kinetic PropertiesVom FachbereichMaterial- und Geowissenschaftender Technischen Universit˜at Darmstadtzur Erlangung des Grades Doktor-Ingenieurgenehmigte Dissertationvorgelegt vonPaul ErhartReferent: Prof. Karsten AlbeKorreferent: Prof. Heinz von SeggernTag der Einreichung: 18. Mai 2006Tag der mundlic˜ hen Prufung:˜ 5. Juli 2006Darmstadt, 2006D17ContentsList of Figures VList of Tables VIIList of Abbreviations IXAbstract XIIII. Introduction 11. Motivation 32. Modeling of materials 72.1. Simulation techniques in atomic scale modeling . . . . . . . . . . . . . . . 72.2. Bridging length and time scales . . . . . . . . . . . . . . . . . . . . . . . . 9II. Quantum mechanical modeling of intrinsic point defects 133. Density functional theory 153.1. General aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2. Exchange-correlation functional . . . . . . . . . . . . . . . . . . . . . . . . 163.3. Plane wave basis sets and pseudopotentials . . . . . . . . . . . . . . . . . . 174. Structure and stability of vacancies and oxygen interstitials 194.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19IContents4.2. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.4. Discussion .

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Intrinsic Point Defects in Zinc Oxide:
Modeling of Structural, Electronic, Thermodynamic
and Kinetic Properties
Vom Fachbereich
Material- und Geowissenschaften
der Technischen Universit˜at Darmstadt
zur Erlangung des Grades Doktor-Ingenieur
genehmigte Dissertation
vorgelegt von
Paul Erhart
Referent: Prof. Karsten Albe
Korreferent: Prof. Heinz von Seggern
Tag der Einreichung: 18. Mai 2006
Tag der mundlic˜ hen Prufung:˜ 5. Juli 2006
Darmstadt, 2006
D17Contents
List of Figures V
List of Tables VII
List of Abbreviations IX
Abstract XIII
I. Introduction 1
1. Motivation 3
2. Modeling of materials 7
2.1. Simulation techniques in atomic scale modeling . . . . . . . . . . . . . . . 7
2.2. Bridging length and time scales . . . . . . . . . . . . . . . . . . . . . . . . 9
II. Quantum mechanical modeling of intrinsic point defects 13
3. Density functional theory 15
3.1. General aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2. Exchange-correlation functional . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3. Plane wave basis sets and pseudopotentials . . . . . . . . . . . . . . . . . . 17
4. Structure and stability of vacancies and oxygen interstitials 19
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
IContents
4.2. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5. Role of band structure, volume relaxation and flnite size efiects 37
5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.2. Band structure of zinc oxide . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.3. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6. Migration mechanisms and difiusion of intrinsic defects 55
6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.2. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.3. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.4. Oxygen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.5. Zinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.6. Potential sources of error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
III. Interatomic bond-order potential for zinc oxide 85
7. Review of potential schemes 87
7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.2. Metallic and covalent bonding . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.3. Bonding in compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8. Pontiflx/Pinguin: A code for fltting analytic bond-order potentials 93
8.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
8.2. Analytic bond-order potential formalism . . . . . . . . . . . . . . . . . . . 95
8.3. Fitting methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8.4. Features of Pontifix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
II8.5. An illustrative example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
8.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
9. Bond-order potential for zinc oxide 103
9.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
9.2. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
9.3. Zinc oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
9.4. Zinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
9.5. Oxygen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
9.6. Point defects, thermal properties, and cutofi parameters . . . . . . . . . . 115
9.7. Irradiation of bulk zinc oxide. . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.8. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
9.9. Appendix: Total energy calculations . . . . . . . . . . . . . . . . . . . . . 120
Conclusions 123
Outlook 125
A. Appendix: Methods 129
A.1. Molecular dynamics simulations . . . . . . . . . . . . . . . . . . . . . . . . 129
A.2. Phonon dispersion relations . . . . . . . . . . . . . . . . . . . . . . . . . . 130
A.3. Overview of external codes . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Danksagung { Acknowledgments 133
Erkl˜arung { Disclaimer 135
Curriculum vitae 137
Bibliography 141List of Figures
4.1. Geometric structure of oxygen and zinc vacancies . . . . . . . . . . . . . . 24
4.2. of oxygen interstitial conflgurations . . . . . . . . . . 25
4.3. Variation of point defect formation enthalpies with Fermi level . . . . . . 26
4.4. Electron density of oxygen vacancy conflgurations . . . . . . . . . . . . . . 30
4.5. Geometry and electron density of dumbbell interstitial conflguration . . . 31
4.6. Simplifled molecular orbitals scheme of oxygen dumbbell bond . . . . . . . 32
4.7. Relative net charge and variation of oxygen separation with charge state . 33
4.8. Electron counting scheme for rotated dumbbell oxygen interstitial . . . . . 34
5.1. Band structure calculations with the GGA+U method . . . . . . . . . . . 41
5.2. Comparison of band structure calculations for zinc oxide . . . . . . . . . . 42
5.3. Scaling behavior of formation enthalpies with concentration . . . . . . . . 45
5.4. Variation of point defect formation volumes with charge state . . . . . . . 48
5.5. V of point defect enthalpies with Fermi level . . . . . . 50
5.6. Stability map of intrinsic point defects . . . . . . . . . . . . . . . . . . . . 51
5.7. Comparison of point defect transition levels . . . . . . . . . . . . . . . . . 52
5.8. Variation of equilibrium defect transition levels with isostatic pressure . . 53
6.1. Schematic of a one-dimensional potential energy surface . . . . . . . . . . . 58
6.2. Sc illustration of the nudged elastic band and the dimer method . 59
6.3. Vacancy migration paths . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.4. Energy pathway for oxygen vacancy in-plane migration . . . . . . . . . . . 62
6.5. Oxygen interstitial migration paths . . . . . . . . . . . . . . . . . . . . . . 64
6.6. Charge state dependence of oxygen interstitial migration enthalpies . . . . 66
6.7. Schematic of the energy surface for oxygen interstitial migration . . . . . . 67
V6.8. Modifled migration paths for negatively charged oxygen interstitials . . . . 71
6.9. Dependence of oxygen difiusivity on chemical potential and Fermi level . . 72
6.10.Temperature dependence of oxygen self-difiusion coe–cient . . . . . . . . 73
6.11.Charge state dep of migration enthalpies for zinc difiusion . . . . . 74
6.12.Zinc interstitial migration paths . . . . . . . . . . . . . . . . . . . . . . . 76
6.13.Site-projected density of states for zinc interstitial migration . . . . . . . . 77
6.14.Dependence of zinc difiusivity on chemical potential, Fermi level and tem-
perature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
8.1. Flow chart of the Pontifix fltting algorithm . . . . . . . . . . . . . . . . 98
8.2. Pauling plot for silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
9.1. Pauling plot for zinc oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
9.2. Energy-volume curves for bulk phases of zinc oxide . . . . . . . . . . . . . 108
9.3. Phonon dispersion relations for zinc oxide . . . . . . . . . . . . . . . . . . 109
9.4. Energy-volume curves for bulk phases of zinc . . . . . . . . . . . . . . . . 111
9.5. Pauling plot for oxygen . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
9.6. Probability to form a defect during a recoil event as a function of energy . 119
A.1. Flow chart of molecular dynamics simulation . . . . . . . . . . . . . . . . . 130List of Tables
4.1. Formation enthalpies of intrinsic point defects . . . . . . . . . . . . . . . . 28
4.2. First and second nearest neighbor relaxations around the oxygen vacancy 29
5.1. Formation enthalpies of intrinsic point defects . . . . . . . . . . . . . . . . 47
5.2. F volumes of intrinsic point defects . . . . . . . . . . . . . . . . . 49
6.1. Energy barriers for oxygen vacancy and interstitial migration . . . . . . . 63
6.2. Parameters for derivation of oxygen defect difiusivities . . . . . . . . . . . 70
6.3. Energy barriers for zinc vacancy and interstitial migration . . . . . . . . . 75
9.1. Analytic bond-order potential parameter sets for zinc oxide . . . . . . . . . 104
9.2. Summary of properties of the ZnO dimer . . . . . . . . . . . . . . . . . . . 105
9.3. of bulk properties of zinc oxide . . . . . . . . . . . . . . . . . . . 107
9.4. Summary of bulk properties of zinc . . . . . . . . . . . . . . . . . . . . . . 112
9.5. of properties of oxygen molecules and bulk phases . . . . . . . . 114
VII