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E-raamat: Advanced Calculations for Defects in Materials: Electronic Structure Methods

Edited by (EPFL, Switzerland), Edited by (BCCMS, Germany), Edited by (UC Santa Barbara, USA), Edited by (EPFL, Switzerland), Edited by (MPI for Iron Research, Germany)
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  • Ilmumisaeg: 16-May-2011
  • Kirjastus: Blackwell Verlag GmbH
  • Keel: eng
  • ISBN-13: 9783527638536
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Advanced Calculations for Defects in Materials: Electronic Structure MethodsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 16-May-2011
  • Kirjastus: Blackwell Verlag GmbH
  • Keel: eng
  • ISBN-13: 9783527638536
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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.
List of Contributors
xiii
1 Advances in Electronic Structure Methods for Defects and Impurities in Solids
1(16)
Chris G. Van de Walk
Anderson Janotti
1.1 Introduction
1(2)
1.2 Formalism and Computational Approach
3(3)
1.2.1 Defect Formation Energies and Concentrations
3(1)
1.2.2 Transition Levels or Ionization Energies
4(1)
1.2.3 Practical Aspects
5(1)
1.3 The DFT-LDA/GGA Band-Gap Problem and Possible Approaches to Overcome It
6(7)
1.3.1 LDA+U for Materials with Semicore States
6(3)
1.3.2 Hybrid Functionals
9(3)
1.3.3 Many-Body Perturbation Theory in the GW Approximation
12(1)
1.3.4 Modified Pseudopotentials
12(1)
1.4 Summary
13(4)
References
14(3)
2 Accuracy of Quantum Monte Carlo Methods for Point Defects in Solids
17(16)
William D. Parker
John W. Wilkins
Richard C. Hennig
2.1 Introduction
17(1)
2.2 Quantum Monte Carlo Method
18(5)
2.2.1 Controlled Approximations
20(1)
2.2.1.1 Time Step
20(1)
2.2.1.2 Configuration Population
20(1)
2.2.1.3 Basis Set
20(1)
2.2.1.4 Simulation Cell
21(1)
2.2.2 Uncontrolled Approximations
22(1)
2.2.2.1 Fixed-Node Approximation
22(1)
2.2.2.2 Pseudopotential
22(1)
2.2.2.3 Pseudopotential Locality
23(1)
2.3 Review of Previous DM C Defect Calculations
23(2)
2.3.1 Diamond Vacancy
23(2)
2.3.2 MgO Schottky Defect
25(1)
2.3.3 Si Interstitial Defects
25(1)
2.4 Results
25(4)
2.4.1 Time Step
26(1)
2.4.2 Pseudopotential
26(1)
2.4.3 Fixed-Node Approximation
26(3)
2.5 Conclusion
29(4)
References
29(4)
3 Electronic Properties of Interfaces and Defects from Many-body Perturbation Theory. Recent Developments and Applications
33(28)
Matteo Giantomassi
Martin Stankovski
Riad Shaltaf
Myrta Gruning
Fabien Bruneval
Patrick Rinke
Gian-Marco Rignanese
3.1 Introduction
33(1)
3.2 Many-Body Perturbation Theory
34(4)
3.2.1 Hedin's Equations
34(2)
3.2.2 GW Approximation
36(1)
3.2.3 Beyond the GW Approximation
37(1)
3.3 Practical Implementation of GW and Recent Developments Beyond
38(10)
3.3.1 Perturbative Approach
38(2)
3.3.2 QP Self-Consistent GW
40(1)
3.3.3 Plasmon Pole Models Versus Direct Calculation of the Frequency Integral
41(3)
3.3.4 The Extrapolar Method
44(1)
3.3.4.1 Polarizability with a Limited Number of Empty States
45(1)
3.3.4.2 Self-Energy with a Limited Number of Empty States
46(1)
3.3.5 MBPT in the PAW Framework
46(2)
3.4 QP Corrections to the BOs at Interfaces
48(6)
3.5 QP Corrections for Defects
54(3)
3.6 Conclusions and Prospects
57(4)
References
58(3)
4 Accelerating GW Calculations with Optimal Polarizability Basis
61(18)
Paolo Umari
Xiaofeng Qian
Nicola Marzari
Geoffrey Stenuit
Luigi Giacomazzi
Stefano Baroni
4.1 Introduction
61(1)
4.2 The GW Approximation
62(2)
4.3 The Method: Optimal Polarizability Basis
64(4)
4.4 Implementation and Validation
68(4)
4.4.1 Benzene
69(1)
4.4.2 Bulk Si
70(1)
4.4.3 Vitreous Silica
70(2)
4.5 Example: Point Defects in a-Si3N4
72(5)
4.5.1 Model Generation
72(1)
4.5.2 Model Structure
73(1)
4.5.3 Electronic Structure
74(3)
4.6 Conclusions
77(2)
References
77(2)
5 Calculation of Semiconductor Band Structures and Defects by the Screened Exchange Density Functional
79(18)
S. J. Clark
John Robertson
5.1 Introduction
79(1)
5.2 Screened Exchange Functional
80(2)
5.3 Bulk Band Structures and Defects
82(11)
5.3.1 Band Structure of ZnO
83(2)
5.3.2 Defects of ZnO
85(4)
5.3.3 Band Structure of MgO
89(1)
5.3.4 Band Structures of SnO2 and CdO
90(1)
5.3.5 Band Structure and Defects of HfO2
91(1)
5.3.6 BiFeO3
92(1)
5.4 Summary
93(4)
References
94(3)
6 Accurate Treatment of Solids with the HSE Screened Hybrid
97(14)
Thomas M. Henderson
Joachim Paler
Gustavo E. Scuseria
6.1 Introduction and Basics of Density Functional Theory
97(3)
6.2 Band Gaps
100(3)
6.3 Screened Exchange
103(1)
6.4 Applications
104(3)
6.5 Conclusions
107(4)
References
108(3)
7 Defect Levels Through Hybrid Density Functionals: Insights and Applications
111(28)
Audrius Alkauskas
Peter Broqvist
Alfredo Pasquarello
7.1 Introduction
111(1)
7.2 Computational Toolbox
112(5)
7.2.1 Defect Formation Energies and Charge Transition Levels
113(1)
7.2.2 Hybrid Density Functionals
114(1)
7.2.2.1 Integrable Divergence
115(2)
7.3 General Results from Hybrid Functional Calculations
117(8)
7.3.1 Alignment of Bulk Band Structures
118(2)
7.3.2 Alignment of Defect Levels
120(2)
7.3.3 Effect of Alignment on Defect Formation Energies
122(2)
7.3.4 "The Band-Edge Problem"
124(1)
7.4 Hybrid Functionals with Empirically Adjusted Parameters
125(4)
7.5 Representative Case Studies
129(3)
7.5.1 Si Dangling Bond
129(2)
7.5.2 Charge State of O2 During Silicon Oxidation
131(1)
7.6 Conclusion
132(7)
References
134(5)
8 Accurate Gap Levels and Their Role in the Reliability of Other Calculated Defect Properties
139(16)
Peter Deak
Adam Gali
Balint Aradi
Thomas Frauenheim
8.1 Introduction
139(2)
8.2 Empirical Correction Schemes for the KS Levels
141(2)
8.3 The Role of the Gap Level Positions in the Relative Energies of Various Defect Configurations
143(3)
8.4 Correction of the Total Energy Based on the Corrected Gap Level Positions
146(2)
8.5 Accurate Gap Levels and Total Energy Differences by Screened Hybrid Functionals
148(3)
8.6 Summary
151(4)
References
152(3)
9 LDA + U and Hybrid Functional Calculations for Defects in ZnO, SnO2, and TiOz
155(10)
Anderson Janotti
Chris G. Van de Walle
9.1 Introduction
155(1)
9.2 Methods
156(7)
9.2.1 ZnO
158(2)
9.2.2 SnO2
160(1)
9.2.3 TiO2
161(2)
9.3 Summary
163(2)
References
163(2)
10 Critical Evaluation of the LDA + U Approach for Band Gap Corrections in Point Defect Calculations: The Oxygen Vacancy in ZnO Case Study
165(18)
Adisak Boonchun
Walter R. L. Lambrecht
10.1 Introduction
165(1)
10.2 LDA+ U Basics
166(2)
10.3 LDA + L7 Band Structures Compared to GW
168(2)
10.4 Improved LDA + U Model
170(2)
10.5 Finite Size Corrections
172(1)
10.6 The Alignment Issue
173(1)
10.7 Results for New LDA + U
174(2)
10.8 Comparison with Other Results
176(2)
10.9 Discussion of Experimental Results
178(1)
10.10 Conclusions
179(4)
References
180(3)
11 Predicting Polaronic Defect States by Means of Generalized Koopmans Density Functional Calculations
183(18)
Stephan Lany
11.1 Introduction
183(2)
11.2 The Generalized Koopmans Condition
185(2)
11.3 Adjusting the Koopmans Condition using Parameterized On-Site Functionals
187(2)
11.4 Koopmans Behavior in Hybrid-functionals: The Nitrogen Acceptor in ZnO
189(4)
11.5 The Balance Between Localization and Delocalization
193(3)
11.6 Conclusions
196(5)
References
197(4)
12 SiO2 in Density Functional Theory and Beyond
201(12)
L. Martin-Samos
G. Bussi
A. Ruini
E. Molinari
M.J. Caldas
12.1 Introduction
201(1)
12.2 The Band Gap Problem
202(2)
12.3 Which Gap?
204(3)
12.4 Deep Defect States
207(2)
12.5 Conclusions
209(4)
References
210(3)
13 Overcoming Bipolar Doping Difficulty in Wide Gap Semiconductors
213(28)
Su-Huai Wei
Yanfa Yan
13.1 Introduction
213(1)
13.2 Method of Calculation
214(3)
13.3 Symmetry and Occupation of Defect Levels
217(1)
13.4 Origins of Doping Difficulty and the Doping Limit Rule
218(2)
13.5 Approaches to Overcome the Doping Limit
220(17)
13.5.1 Optimization of Chemical Potentials
220(1)
13.5.1.1 Chemical Potential of Host Elements
220(2)
13.5.1.2 Chemical Potential of Dopant Sources
222(1)
13.5.2 H-Assisted Doping
223(1)
13.5.3 Surfactant Enhanced Doping
224(2)
13.5.4 Appropriate Selection of Dopants
226(3)
13.5.5 Reduction of Transition Energy Levels
229(3)
13.5.6 Universal Approaches Through Impurity-Band Doping
232(5)
13.6 Summary
237(4)
References
238(3)
14 Electrostatic Interactions between Charged Defects in Supercelis
241(18)
Christoph Freysoldt
Jorg Neugebauer
Chris G. Van de Walle
14.1 Introduction
241(2)
14.2 Electrostatics in Real Materials
243(7)
14.2.1 Potential-based Formulation of Electrostatics
245(1)
14.2.2 Derivation of the Correction Scheme
246(3)
14.2.3 Dielectric Constants
249(1)
14.3 Practical Examples
250(4)
14.3.1 Ga Vacancy in GaAs
250(2)
14.3.2 Vacancy in Diamond
252(2)
14.4 Conclusions
254(5)
References
257(2)
15 Formation Energies of Point Defects at Finite Temperatures
259(26)
Blazej Grabowski
Tilmann Hickel
Jorg Neugebauer
15.1 Introduction
259(2)
15.2 Methodology
261(17)
15.2.1 Analysis of Approaches to Correct for the Spurious Elastic Interaction in a Supercell Approach
261(1)
15.2.1.1 The Volume Optimized Aapproach to Point Defect Properties
262(2)
15.2.1.2 Derivation of the Constant Pressure and Rescaled Volume Approach
264(2)
15.2.2 Electronic, Quasiharmonic, and Anharmonic Contributions to the Formation Free Energy
266(1)
15.2.2.1 Free Energy Born--Oppenheimer Approximation
266(3)
15.2.2.2 Electronic Excitations
269(2)
15.2.2.3 Quasiharmonic Atomic Excitations
271(1)
15.2.2.4 Anharmonic Atomic Excitations: Thermodynamic Integration
272(2)
15.2.2.5 Anharmonic Atomic Excitations: Beyond the Thermodynamic Integration
274(4)
15.3 Results: Electronic, Quasiharmonic, and Anharmonic Excitations in Vacancy Properties
278(4)
15.4 Conclusions
282(3)
References
282(3)
16 Accurate Kohn--Sham DFT With the Speed of Tight Binding: Current Techniques and Future Directions in Materials Modelling
285(20)
Patrick R. Briddon
Mark J. Rayson
16.1 Introduction
285(1)
16.2 The AIMPRO Kohn--Sham Kernel: Methods and Implementation
286(4)
16.2.1 Gaussian-Type Orbitals
286(2)
16.2.2 The Matrix Build
288(1)
16.2.3 The Energy Kernel: Parallel Diagonalisarion and Iterative Methods
288(1)
16.2.4 Forces and Structural Relaxation
289(1)
16.2.5 Parallelism
289(1)
16.3 Functionality
290(2)
16.3.1 Energetics: Equilibrium and Kinetics
290(1)
16.3.2 Hyperfine Couplings and Dynamic Reorientation
291(1)
16.3.3 D-Tensors
291(1)
16.3.4 Vibrational Modes and Infrared Absorption
291(1)
16.3.5 Piezospectroscopic and Uniaxial Stress Experiments
291(1)
16.3.6 Electron Energy Loss Spectroscopy (EELS)
292(1)
16.4 Filter Diagonalisarion with Localisation Constraints
292(6)
16.4.1 Performance
294(2)
16.4.2 Accuracy
296(2)
16.5 Future Research Directions and Perspectives
298(4)
16.5.1 Types of Calculations
299(1)
16.5.1.1 Thousands of Atoms on a Desktop PC
299(1)
16.5.1.2 One Atom Per Processor
299(1)
16.5.2 Prevailing Application Trends
299(1)
16.5.3 Methodological Developments
300(2)
16.6 Conclusions
302(3)
References
302(3)
17 Ab Initio Green's Function Calculation of Hyperfine Interactions for Shallow Defects in Semiconductors
305(36)
Uwe Gerstmann
17.1 Introduction
305(1)
17.2 From DFT to Hyperfine Interactions
306(5)
17.2.1 DFT and Local Spin Density Approximation
306(2)
17.2.2 Scalar Relativistic Hyperfine Interactions
308(3)
17.3 Modeling Defect Structures
311(8)
17.3.1 The Green's Function Method and Dyson's Equation
311(2)
17.3.2 The Linear Muffin-Tin Orbital (LMTO) Method
313(2)
17.3.3 The Size of The Perturbed Region
315(2)
17.3.4 Lattice Relaxation: The AsGa-Family
317(2)
17.4 Shallow Defects: Effective Mass Approximation (EMA) and Beyond
319(9)
17.4.1 The EMA Formalism
320(2)
17.4.2 Conduction Bands with Several Equivalent Minima
322(1)
17.4.3 Empirical Pseudopotential Extensions to the EMA
322(2)
17.4.4 Ab Initio Green's Function Approach to Shallow Donors
324(4)
17.5 Phosphorus Donors in Highly Strained Silicon
328(4)
17.5.1 Predictions of EMA
329(1)
17.5.2 Ab Initio Treatment via Green's Functions
330(2)
17.6 N-Type Doping of SiC with Phosphorus
332(2)
17.7 Conclusions
334(7)
References
336(5)
18 Time-Dependent Density Functional Study on the Excitation Spectrum of Point Defects in Semiconductors
341(18)
Adam Gali
18.1 Introduction
341(4)
18.1.1 Nitrogen-Vacancy Center in Diamond
342(2)
18.1.2 Divacancy in Silicon Carbide
344(1)
18.2 Method
345(6)
18.2.1 Model, Geometry, and Electronic Structure
345(1)
18.2.2 Time-Dependent Density Functional Theory with Practical Approximations
346(5)
18.3 Results and Discussion
351(5)
18.3.1 Nitrogen-Vacancy Center in Diamond
351(2)
18.3.2 Divacancy in Silicon Carbide
353(3)
18.4 Summary
356(3)
References
356(3)
19 Which Electronic Structure Method for The Study of Defects: A Commentary
359(22)
Walter R. L. Lambrecht
19.1 Introduction: A Historic Perspective
359(3)
19.2 Themes of the Workshop
362(11)
19.2.1 Periodic Boundary Artifacts
362(5)
19.2.2 Band Gap Corrections
367(3)
19.2.3 Self-Interaction Errors
370(2)
19.2.4 Beyond DFT
372(1)
19.3 Conclusions
373(8)
References
375(6)
Index 381
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.
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