Advanced Calculations for Defects in Materials

This book investigates the possible ways of improvement by applying more sophisticated electronic structure methods as well as corrections and alternatives to the supercell model. In particular, the merits of hybrid and screened functionals, as well as of the +U methods are assessed in comparison to various perturbative and Quantum Monte Carlo many body theories. The inclusion of excitonic effects is also discussed by way of solving the Bethe-Salpeter equation or by using time-dependent DFT, based on GW or hybrid functional calculations. Particular attention is paid to overcome the side effects connected to finite size modeling.
The editors are well known authorities in this field, and very knowledgeable of past developments as well as current advances. In turn, they have selected respected scientists as chapter authors to provide an expert view of the latest advances.
The result is a clear overview of the connections and boundaries between these methods, as well as the broad criteria determining the choice between them for a given problem. Readers will find various correction schemes for the supercell model, a description of alternatives by applying embedding techniques, as well as algorithmic improvements allowing the treatment of an ever larger number of atoms at a high level of sophistication.

Auteur
Chris G. Van de Walle is Professor at the Materials Department of the University of California in Santa Barbara. Before that he worked at IBM Yorktown Heights, at the Philips Laboratories in New York, as Adjunct Professor at Columbia University, and at the Xerox Palo Alto Research Center. Dr. Van de Walle has published over 200 articles and holds 18 U.S. patents. In 2002, he was awarded the David Adler Award by the APS. Dr. Van de Walle's research focuses on computational physics, defects and impurities in solids, novel electronic materials and device simulations.

Jörg Neugebauer is the Director of the Computational Materials Design Department at the Max-Planck-Institute for Iron Research in Düsseldorf, Germany. Since 2003 he has been the Chair of Theoretical Physics at the University of Paderborn.Before that, he held positions as Honorary Professor and Director of the advanced study group 'Modeling' at the Interdisciplinary Center for Advanced Materials Simulation (ICAMS) at the Ruhr University in Bochum, Germany. His research interests cover surface and defect physics, ab initio scale-bridging computer simulations, ab initio based thermodynamics and kinetics, and the theoretical study of epitaxy, solidification, and microstructures.

Alfredo Pasquarello is Professor of Theoretical Condensed Matter Physics and Chair of Atomic Scale Simulation at EPFL, Switzerland. His research activities focus on the study of atomic-scale phenomena with the aim to provide a realistic description of the mechanisms occurring on the atomic and nanometer scale. Specific research projects concern the study of disordered materials and oxide-semiconductor interfaces, which currently find applications in glass manufacturing and in the microelectronic technology, respectively.

Peter Deák was Professor and Head of the Surface Physics Laboratory at the Budapest University of Technology & Economics and is currently Group Leader at the Center for Computational Materials Science in Bremen, Germany. His research interests cover materials science and the technology of electronic and electric devices, functional coatings and plasma discharges, and atomic scale simulation of electronic materials. Peter Deák has published over 150 papers, eight book chapters, and six textbooks.

Audrius Alkauskas holds a position at the Electron Spectrometry and Microscopy Laboratory of the EPFL, Switzerland. His scientific interests cover computational material science, theoretical solid state spectroscopy and surface and interface science with respect to applications in renewable energy, photovoltaics, energy conversion, and molecular nanotechnology.

Contenu

List of Contributors XIII

1 Advances in Electronic Structure Methods for Defects and Impurities in Solids 1
Chris G. Van de Walle and Anderson Janotti

1.1 Introduction 1

1.2 Formalism and Computational Approach 3

1.2.1 Defect Formation Energies and Concentrations 3

1.2.2 Transition Levels or Ionization Energies 4

1.2.3 Practical Aspects 5

1.3 The DFT-LDA/GGA Band-Gap Problem and Possible Approaches to Overcome It 6

1.3.1 LDAþU for Materials with Semicore States 6

1.3.2 Hybrid Functionals 9

1.3.3 Many-Body Perturbation Theory in the GW Approximation 12

1.3.4 Modified Pseudopotentials 12

1.4 Summary 13

References 14

2 Accuracy of Quantum Monte Carlo Methods for Point Defects in Solids 17
William D. Parker, John W. Wilkins, and Richard G. Hennig

2.1 Introduction 17

2.2 Quantum Monte Carlo Method 18

2.2.1 Controlled Approximations 20

2.2.1.1 Time Step 20

2.2.1.2 Configuration Population 20

2.2.1.3 Basis Set 20

2.2.1.4 Simulation Cell 21

2.2.2 Uncontrolled Approximations 22

2.2.2.1 Fixed-Node Approximation 22

2.2.2.2 Pseudopotential 22

2.2.2.3 Pseudopotential Locality 23

2.3 Review of Previous DMC Defect Calculations 23

2.3.1 Diamond Vacancy 23

2.3.2 MgO Schottky Defect 25

2.3.3 Si Interstitial Defects 25

2.4 Results 25

2.4.1 Time Step 26

2.4.2 Pseudopotential 26

2.4.3 Fixed-Node Approximation 26

2.5 Conclusion 29

References 29

3 Electronic Properties of Interfaces and Defects from Many-body Perturbation Theory: Recent Developments and Applications 33
Matteo Giantomassi, Martin Stankovski, Riad Shaltaf, Myrta Grüning, Fabien Bruneval, Patrick Rinke, and Gian-Marco Rignanese

3.1 Introduction 33

3.2 Many-Body Perturbation Theory 34

3.2.1 Hedin.s Equations 34

3.2.2 GW Approximation 36

3.2.3 Beyond the GW Approximation 37

3.3 Practical Implementation of GW and Recent Developments Beyond 38

3.3.1 Perturbative Approach 38

3.3.2 QP Self-Consistent GW 40

3.3.3 Plasmon Pole Models Versus Direct Calculation of the Frequency Integral 41

3.3.4 The Extrapolar Method 44

3.3.4.1 Polarizability with a Limited Number of Empty States 45

3.3.4.2 Self-Energy with a Limited Number of Empty States 46

3.3.5 MBPT in the PAW Framework 46

3.4 QP Corrections to the BOs at Interfaces 48

3.5 QP Corrections for Defects 54

3.6 Conclusions and Prospects 57

References 58

4 Accelerating GW Calculations with Optimal Polarizability Basis 61
Paolo Umari, Xiaofeng Qian, Nicola Marzari, Geoffrey Stenuit, Luigi Giacomazzi, and Stefano Baroni

4.1 Introduction 61

4.2 The GW Approximation 62

4.3 The Method: Optimal Polarizability Basis 64

4.4 Implementation and Validation 68

4.4.1 Benzene 69

4.4.2 Bulk Si 70

4.4.3 Vitreous Silica 70

4.5 Example: Point Defects in a-Si3N4 72

4.5.1 Model Generation 72

4.5.2 Model Structure 73

4.5.3 Electronic Structure 74

4.6 Conclusions 77

References 77

5 Calculation of Semiconductor Band Structures and Defects by the Screened Exchange Density Functional 79
S. J. Clark and John Robertson

5.1 Introduction 79

5.2 Screened Exchange Functional 80

5.3 Bulk Band Structures and Defects 82

5.3.1 Band Structure of ZnO 83

5.3.2 Defects of ZnO 85

5.3.3 Band Structure of MgO 89

5.3.4 Band Structures of SnO2 and CdO 90

5.3.5 Band Structure and Defects of HfO2 91

5.3.6 BiFeO3 92

5.4 Summary 93 References 94</p...