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  • UNIVERSITEIT ANTWERPENFaculteit Wetenschappen

    Departement Fysica

    First-principles electronic structure

    calculations of transparent conducting oxide

    materials

    First-principles berekeningen van de

    elektronische structuur van transparante

    geleidende oxide - materialen

    Proefschrift voorgelegd tot het behalen van de graad van doctor in dewetenschappen aan de Universiteit Antwerpen te verdedigen door

    Hemant Dixit

    PromotorenProf. Dr. B. Partoens AntwerpenProf. Dr. D. Lamoen July, 2012

  • Members of the Jury:

    ChairmanProf. Wim Wenseleers, Universiteit Antwerpen, Belgium

    SupervisorsProf. Bart Partoens, Universiteit Antwerpen, BelgiumProf. Dirk Lamoen, Universiteit Antwerpen, Belgium

    MembersProf. Jacques Tempere, Universiteit Antwerpen, BelgiumProf. Nick Van Remortel, Universiteit Antwerpen, BelgiumProf. Stefaan Cottenier, Universiteit Gent, BelgiumProf. Xavier Gonze, Universite Catholique de Louvain, Belgium

    Contact Information

    Hemant DixitG.U. 313Groenenborgerlaan 1712020 AntwerpenBelgiumHemant.Dixit@ua.ac.be

  • Acknowledgement

    On this page I wish to express my sincere gratitude to my promoters Prof. B.Partoens and Prof. D. Lamoen, for their motivation, support and guidanceduring my PhD. They have given me an opportunity and complete freedomto work on interesting research topics during the last four years. This thesisis a result of their consistent encouragement and the fruitful discussions I hadwith them. My special thanks to Dr. Rolando Saniz for working together andhis guidance during early stage of my PhD. My other colleagues in Antwerp:Dr. Ying Xu, Ms. Mozhgan Amini, Dr. Nandan Tandon, Dr. MatsubaraMasahiko, Dr. Fabiana Da Pieve have also helped me and provided a cheerfulatmosphere. I want to thank the people I collaborated with: Prof. X. Gonze,Prof. Gian-Marco Rignanese, Dr. Martin Stankovski, Ms. Anna Miglio andother members of the ABINIT group in Louvain-la-Neuve along with Prof.Stefaan Cottenier at the University of Ghent. Also I would like to thankProf. F. Peeters, my colleagues from the CMT group in Antwerp. Finally,special thanks to my parents, family members and many friends including ateam called Sahyadri Explorers for supporting me during my studies.

  • iv

  • Contents

    List of abbreviations 1

    1 Introduction 3

    1.1 Transparent Conducting Oxides . . . . . . . . . . . . . . . . . 3

    1.2 TCO Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    1.2.1 Alternative materials for TCO applications . . . . . . . 5

    1.3 Basic physics of TCOs . . . . . . . . . . . . . . . . . . . . . . 6

    1.3.1 Electron energy bands in TCOs . . . . . . . . . . . . . 6

    1.3.2 Conductivity in TCOs . . . . . . . . . . . . . . . . . . 8

    1.3.3 Role of defects . . . . . . . . . . . . . . . . . . . . . . 9

    1.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

    1.5 First-principles study of TCOs . . . . . . . . . . . . . . . . . . 12

    1.6 Goal of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . 14

    2 Electronic structure with Density Functional Theory 17

    2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    2.1.1 Born-Oppenheimer approximation . . . . . . . . . . . . 18

    2.1.2 The Hartree approximation . . . . . . . . . . . . . . . 19

    2.1.3 The Hartree-Fock approximation . . . . . . . . . . . . 19

    2.1.4 The correlation energy . . . . . . . . . . . . . . . . . . 20

    2.2 The fundamentals of density functional theory . . . . . . . . . 21

    2.2.1 The Hohenberg-Kohn theorems . . . . . . . . . . . . . 21

    2.2.2 The Kohn-Sham equations . . . . . . . . . . . . . . . . 22

    2.2.3 The exchange-correlation approximations . . . . . . . . 23

    2.3 Computation on solids: electronic band structure . . . . . . . 26

    2.4 Methods for electronic structure calculations . . . . . . . . . . 27

    2.4.1 Plane wave pseudopotential method . . . . . . . . . . . 27

    2.4.2 All-electron methods . . . . . . . . . . . . . . . . . . . 28

    2.4.3 Projector augmented wave method . . . . . . . . . . . 31

    2.5 The band gap problem in DFT . . . . . . . . . . . . . . . . . 32

  • vi CONTENTS

    3 Electronic band structure of prototype TCOs with DFT 353.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

    3.1.1 Computational details . . . . . . . . . . . . . . . . . . 363.2 Zinc oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3 Cadmium oxide . . . . . . . . . . . . . . . . . . . . . . . . . . 383.4 Tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.5 Indium oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

    3.6.1 Structural properties . . . . . . . . . . . . . . . . . . . 413.6.2 Electronic properties . . . . . . . . . . . . . . . . . . . 42

    4 GW approximation: an introduction 454.1 Photoelectron spectroscopy . . . . . . . . . . . . . . . . . . . 454.2 Greens Function . . . . . . . . . . . . . . . . . . . . . . . . . 46

    4.2.1 The Lehmann representation . . . . . . . . . . . . . . . 474.3 Feynman diagrams . . . . . . . . . . . . . . . . . . . . . . . . 484.4 The Dyson equation and concept of self-energy . . . . . . . . . 494.5 Hedins equations . . . . . . . . . . . . . . . . . . . . . . . . . 52

    4.5.1 The GW approximation . . . . . . . . . . . . . . . . . 584.6 The GW approximation in practice . . . . . . . . . . . . . . . 62

    5 ZnO: quasiparticle corrections to the band gap 675.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.2 Computational details . . . . . . . . . . . . . . . . . . . . . . 685.3 Result and discussion . . . . . . . . . . . . . . . . . . . . . . . 695.4 Details of 20-electron PP . . . . . . . . . . . . . . . . . . . . . 775.5 Effect of plasmon-pole model . . . . . . . . . . . . . . . . . . . 785.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

    6 Quasiparticle band structure of SnO2 and CdO 836.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 836.2 Computational details . . . . . . . . . . . . . . . . . . . . . . 846.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 84

    6.3.1 SnO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856.3.2 CdO . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

    7 TCOs based on ZnX2O4 (X=Al,Ga and In) spinel structure 957.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957.2 Computational details . . . . . . . . . . . . . . . . . . . . . . 97

    7.2.1 Pseudopotentials . . . . . . . . . . . . . . . . . . . . . 977.2.2 DFT, GW and TB-mBJ . . . . . . . . . . . . . . . . . 97

  • CONTENTS vii

    7.3 Result and discussion . . . . . . . . . . . . . . . . . . . . . . . 987.3.1 Structural properties and electronic band structure us-

    ing DFT . . . . . . . . . . . . . . . . . . . . . . . . . . 987.3.2 GW and TB-mBJ band gaps . . . . . . . . . . . . . . . 1027.3.3 Formation enthalpy . . . . . . . . . . . . . . . . . . . . 105

    7.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

    8 Electronic structure with TB-mBJ scheme 1078.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1078.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1098.3 Computational details . . . . . . . . . . . . . . . . . . . . . . 1108.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

    8.4.1 n-type binary oxides . . . . . . . . . . . . . . . . . . . 1108.4.2 p-type ternary oxides . . . . . . . . . . . . . . . . . . . 116

    8.5 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . 121

    9 Formation energy of native defects in ZnAl2O4 spinel 1239.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1239.2 Method and Computational Details . . . . . . . . . . . . . . . 1249.3 Result and discussion . . . . . . . . . . . . . . . . . . . . . . . 128

    9.3.1 Electronic band structure with HSE06 . . . . . . . . . 1289.3.2 Formation energy with GGA and GGA+U . . . . . . . 1299.3.3 Formation energy with HSE06 . . . . . . . . . . . . . . 130

    9.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

    Summary 133

    Samenvatting 137

    Appendices 141

    List of publications 159

    Curriculum Vitae 161

    Bibliography 163

  • viii CONTENTS

  • List of abbreviations

    TCO Transparent conducting oxidesDFT Density functional theoryLDA Local density approximationGGA Generalized gradient approximationPPM Plasmon-pole modelPP PseudopotentialTB-mBJ Tran-Blaha modified Becke Johnson potentialAPW Augmented plane wave methodLAPW Linearized Augmented Plane WaveAPW+lo Augmented plane wave method + local orbitalsPAW Projector augmented wave methodZB, RS, WZ zincblende, rocksalt, wurtzite

  • 2 CONTENTS

  • Chapter 1

    Introduction

    1.1 Transparent Conducting Oxides

    Transparent conducting oxides (TCO) constitute a unique class of materialswhich combine two physical properties together - high optical transparencyand high electrical conductivity. These properties are generally consideredto be mutually exclusive of each other since high conductivity is a propertypossessed by metals while insulators are optically transparent. This peculiarcombination of physical properties is achieved by generating free electronor hole carriers in a material having a sufficiently large energy band gap(i.e., >3.1 eV) so that it is non absorbing or transparent to visible light.The charge carriers are usually generated by doping the insulator with suit-able dopan