johan pohl STRUCTURE AND PROPERTIES OF DEFECTS IN PHOTOVOLTAIC ABSORBER ...

210 Pages·2013·20.27 MB·English

johan pohl
STRUCTURE AND PROPERTIES OF DEFECTS IN
PHOTOVOLTAIC ABSORBER MATERIALS: ATOMIC SCALE
COMPUTER SIMULATIONS OF Si AND Cu(In,Ga)Se
2
Zur Erlangung des akademischen Grades des Doktors der
Ingenieurwissenschaften (Dr.-Ing.) genehmigte Dissertation
vorgelegt von Dipl.-Phys. Johan Pohl
geboren in Friedberg
Fachgebiet Materialmodellierung
Fachbereich Material- und Geowissenschaften
Technische Universität Darmstadt
Hochschulkennziffer: D17
Referent: Prof. Dr. Karsten Albe,
Technische Universität Darmstadt
Korreferent: Prof. Dr. Hans-Werner Schock,
Helmholtz-Zentrum Berlin
Tag der Einreichung: 20. November 2012
Tag der Prüfung: 23. Januar 2013
Erscheinungsort: Darmstadt
Erscheinungsjahr: 2013

STRUCTURE AND PROPERTIES OF DEFECTS IN PHOTOVOLTAIC
ABSORBER MATERIALS: ATOMIC SCALE COMPUTER
SIMULATIONS OF Si AND Cu(In,Ga)Se
2
johan pohl
Dissertation
2013
On the cover: Twin boundaries originating at a grain boundary during silicon
growth from the melt. Obtained from molecular dynamics simulations and vi-
sualized with OVITO. This image was awarded the second prize in the category
Digitallymodifiedimagesatthe17thAmericanConferenceforCrystalGrowthand
Epitaxy, Lake Geneva, USA.
CONTENTS
List of Abbreviations ix
Abstract xiii
Motivation xv
I introduction 1
1 solar cells: principles and concepts 5
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 The p-n homojunction . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 A p-n heterojunction: band diagram of Cu(In,Ga)Se cells . . . . . 8
2
1.5 Optimizing photovoltaic devices: Sources of efficiency losses . . . 11
1.5.1 Efficiency limits and optimal gaps . . . . . . . . . . . . . . . 11
1.5.2 Photocarrier recombination via defect states . . . . . . . . . 11
1.5.3 Band offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5.4 Lattice mismatch . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5.5 Inhomogeneities and potential fluctuations . . . . . . . . . . 13
1.6 Real high-efficiency devices: Silicon versus Cu(In,Ga)Se . . . . . . 14
2
2 cu(in,ga)se : intrinsic point defects, phase diagram and
2
diffusion 17
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Intrinsic point defects . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 Copper diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5 Open questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 silicon: crystal growth, interface kinetics and extended
defects 29
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Crystal growth methods . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Interface growth kinetics . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 Twin boundaries and stacking faults . . . . . . . . . . . . . . . . . . 31
3.5 Void formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.6 Open questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
II methods 35
4 atomic-scale simulation methods 39
4.1 The fundamental picture . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Methods for total energies . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.1 Density functional theory (DFT) . . . . . . . . . . . . . . . . 43
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contents
4.2.1.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.1.2 Basis Sets . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.1.3 Functionals for Exchange and Correlation . . . . . 44
4.2.2 Quantum Monte Carlo . . . . . . . . . . . . . . . . . . . . . . 46
4.2.3 Classical interatomic potentials . . . . . . . . . . . . . . . . . 48
4.2.4 Lattice Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . 51
4.3 Methods for time evolution and sampling equilibrium . . . . . . . 52
4.3.1 Molecular dynamics . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.2 Metropolis Monte Carlo . . . . . . . . . . . . . . . . . . . . . 53
4.3.3 Kinetic Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . 54
4.4 Methods for saddle point search . . . . . . . . . . . . . . . . . . . . 55
4.4.1 Nudged-elastic band method . . . . . . . . . . . . . . . . . . 55
4.5 Methodological considerations for the topics of this thesis . . . . . 56
5 ab-initio characterization of point defects 57
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 Thermodynamics of Point Defects . . . . . . . . . . . . . . . . . . . 58
5.3 Formation Energies from Ab-Initio Calculations . . . . . . . . . . . 64
5.4 Correction schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
III intrinsic point defect physics in cu(in,ga)se 67
2
6 screened-exchange hybrid density functional theory cal-
culations for chalcopyrites 71
6.1 HSE06: Exchange screening vs. fraction of exact exchange . . . . . 71
6.2 Bulk properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.3 Setup for bulk and defect calculations . . . . . . . . . . . . . . . . . 75
7 copper vacancies in cuinse , cugase , cuins and cugas 77
2 2 2 2
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.2 Defect formation energies . . . . . . . . . . . . . . . . . . . . . . . . 78
7.3 Fermi-level pinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.4 Migration barriers and diffusion . . . . . . . . . . . . . . . . . . . . 80
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
8 copper interstitials in cuinse 85
2
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
8.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
8.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
9 antisite traps and metastable point defects in cuinse and
2
cugase 91
2
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
9.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
9.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 92
9.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
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10 the complete intrinsic point defect physics of cuinse and
2
cugase 101
2
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
10.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
10.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
10.3.1 Stability diagrams . . . . . . . . . . . . . . . . . . . . . . . . 102
10.3.2 Point defect formation energies . . . . . . . . . . . . . . . . . 105
10.3.3 Charge transition levels . . . . . . . . . . . . . . . . . . . . . 108
10.3.4 Defect states . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
10.4 Discussion of Individual Point Defects . . . . . . . . . . . . . . . . . 111
10.4.1 Cation antisites . . . . . . . . . . . . . . . . . . . . . . . . . . 111
10.4.2 Cation vacancies . . . . . . . . . . . . . . . . . . . . . . . . . 112
10.4.3 Interstitials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
10.4.4 Metastable point defects . . . . . . . . . . . . . . . . . . . . . 113
10.5 Is metastability caused by point defects? . . . . . . . . . . . . . . . 114
10.6 Complexes with copper vacancies . . . . . . . . . . . . . . . . . . . 115
10.7 Comparison to the literature: Theory . . . . . . . . . . . . . . . . . 118
10.8 Comparison to the literature: Experiment . . . . . . . . . . . . . . . 119
10.9 Implications for device optimization . . . . . . . . . . . . . . . . . . 120
10.10 Connection to defects in other materials: ZnO and kesterites . . . 121
10.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
IV twin boundary, stacking fault and void formation in
melt-grown silicon 125
11 the twin formation mechanism in melt-grown silicon 129
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
11.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
11.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
11.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
12 void formation from grown-in faulted dislocation loops 137
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
12.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
12.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 138
12.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
13 a lattice monte carlo model for silicon growth includ-
ing twin boundaries 143
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
13.2 Lattice Monte Carlo models for crystal growth . . . . . . . . . . . . 143
13.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
13.3.1 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . 147
13.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 152
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contents
13.4.1 Qualitative assessment of the growth kinetics at the Si(111)
solid-liquid interface . . . . . . . . . . . . . . . . . . . . . . . 152
13.4.2 Interface growth velocities . . . . . . . . . . . . . . . . . . . . 154
13.4.3 Roughening transition . . . . . . . . . . . . . . . . . . . . . . 158
13.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Summary 165
Contributions 169
Erklärung – Disclaimer 171
Danksagung – Acknowledgments 173
Bibliography 177
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contents
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