Summary

An overview of the latest computational materials science methods on an atomic scale.
The authors present the physical and mathematical background in sufficient detail for this highly current and important topic, but without unnecessary complications. They focus on approaches with industrial relevance, covering real-life applications taken from concrete projects that range from tribology modeling to performance optimization of integrated circuits.
Following an introduction to the fundamentals, the book describes the most relevant approaches, covering such classical simulation methods as simple and reactive force field methods, as well as highly accurate quantum-mechanical methods ranging from density-functional theory to Hartree-Fock and beyond. A review of the increasingly important multiscale approaches rounds off this section. The last section demonstrates and illustrates the capabilities of the methods previously described using recent real-life examples of industrial applications. As a result, readers gain a heightened user awareness, since the authors clearly state the conditions of applicability for the respective modeling methods so as to avoid fatal mistakes.

Author Biography

Roman Leitsmann is project leader at GWT-TUD, a leading company for knowledge and technology transfer, in Chemnitz, Germany. After having obtained his PhD in physics from the University of Jena, he changed to GWT-TUD where he is responsible for several research and development projects with industrial partners. In 2011 he received the Nanoscience Award commissioned by the Working Group of the Centers of Competence of Nanotechnology in Germany.

Philipp Plänitz is CEO of AQcomputare, a company focusing on the calculation of materials properties with ab-initio methods as a service for industrial companies. He received the Diploma and PhD degrees in physics from the Chemnitz University of Technology in 2004 and 2009, respectively. In 2009 he founded AQcomputare, a GWT-TUD spin-off company. His research interests include industrial applications of atomic scale methods for calculating a wide range of material properties.

Michael Schreiber is Full Professor of Physics at Chemnitz University of Technology since 1993. After his PhD in physics, obtained from the Technical University of Dortmund, he moved to Tokyo University for two years. He obtained his first professorship in theoretical chemistry from the University of Mainz in 1990 and was Dean of the Faculty of Science from 1998 to 2001. Michael Schreiber has authored or co-authored more than 330 refereed scientific publications, edited 15 books and contributed to more than 100 books and proceedings.

Preface IX

Part I Basic Physical and Mathematical Principles 1

1 Introduction 3

2 Newtonian Mechanics and Thermodynamics 5

2.1 Equation of Motion 5

2.2 Energy Conservation 7

2.3 Many Body Systems 10

2.4 Thermodynamics 11

3 Operators and Fourier Transformations 17

3.1 Complex Numbers 17

3.2 Operators 18

3.3 Fourier Transformation 20

4 Quantum Mechanical Concepts 25

4.1 Heuristic Derivation 25

4.2 Stationary Schrödinger Equation 27

4.3 Expectation Value and Uncertainty Principle 28

5 Chemical Properties and Quantum Theory 33

5.1 Atomic Model 33

5.2 Molecular OrbitalTheory 39

6 Crystal Symmetry and Bravais Lattice 47

6.1 Symmetry in Nature 47

6.2 Symmetry in Molecules 47

6.3 Symmetry in Crystals 49

6.4 Bloch Theorem and Band Structure 53

Part II ComputationalMethods 57

7 Introduction 59

8 Classical SimulationMethods 65

8.1 Molecular Mechanics 65

8.2 Simple Force-Field Approach 68

8.3 Reactive Force-Field Approach 71

9 Quantum Mechanical Simulation Methods 77

9.1 Born–Oppenheimer Approximation and Pseudopotentials 77

9.2 Hartree–Fock Method 80

9.3 Density Functional Theory 83

9.4 Meaning of the Single-Electron Energies within DFT and HF 85

9.5 Approximations for the Exchange–Correlation Functional EXC 88

9.5.1 Local Density Approximation 88

9.5.2 Generalized Gradient Approximation 89

9.5.3 Hybrid Functionals 90

9.6 Wave Function Representations 91

9.6.1 Real-Space Representation 91

9.6.2 PlaneWave Representation 92

9.6.3 Local Basis Sets 93

9.6.4 Combined Basis Sets 95

9.7 Concepts Beyond HF and DFT 96

9.7.1 Quasiparticle Shift and the GWApproximation 97

9.7.2 Scissors Shift 99

9.7.3 Excitonic Effects 100

9.7.4 TDDFT 100

9.7.5 Post-Hartree–Fock Methods 101

9.7.5.1 Configuration Interaction (CI) 102

9.7.5.2 Coupled Cluster (CC) 102

9.7.5.3 Møller–Plesset PerturbationTheory (MPn) 103

10 Multiscale Approaches 105

10.1 Coarse-Grained Approaches 105

10.2 QM/MM Approaches 108

11 Chemical Reactions 111

11.1 Transition State Theory 111

11.2 Nudged Elastic Band Method 114

Part III Industrial Applications 117

12 Introduction 119

13 Microelectronic CMOS Technology 121

13.1 Introduction 121

13.2 Work Function Tunability in High-k Gate Stacks 127

13.2.1 Concrete Problem and Goal 127

13.2.2 Simulation Approach 129

13.2.3 Modeling of the Bulk Materials 129

13.2.4 Construction of the HKMG Stack Model 132

13.2.5 Calculation of the Band Alignment 136

13.2.6 Simulation Results and Practical Impact 138

13.3 Influence of Defect States in High-k Gate Stacks 141

13.3.1 Concrete Problem and Goal 141

13.3.2 Simulation Approach and Model System 144

13.3.3 Calculation of the Charge Transition Level 145

13.3.4 Simulation Results and Practical Impact 146

13.4 Ultra-Low-k Materials in the Back-End-of-Line 149

13.4.1 Concrete Problem and Goal 149

13.4.2 Simulation Approach 151

13.4.3 The Silylation Process: Preliminary Considerations 153

13.4.4 Simulation Results and Practical Impact 155

14 Modeling of Chemical Processes 159

14.1 Introduction 159

14.2 GaN Crystal Growth 163

14.2.1 Concrete Problem and Goal 163

14.2.2 Simulation Approach 165

14.2.3 ReaxFF Parameter Training Scheme 166

14.2.4 Set of Training Structures: ab initio Modeling 168

14.2.5 Model System for the Growth Simulations 170

14.2.6 Results and Practical Impact 172

14.3 Intercalation of Ions into Cathode Materials 174

14.3.1 Concrete Problem and Goal 174

14.3.2 Simulation Approach 176

14.3.3 Calculation of the Cell Voltage 178

14.3.4 Obtained Structural Properties of LixV2O5 178

14.3.5 Results for the Cell Voltage 181

15 Properties of Nanostructured Materials 183

15.1 Introduction 183

15.2 Embedded PbTe Quantum Dots 187

15.2.1 Concrete Problem and Goal 187

15.2.2 Simulation Approach 188

15.2.3 Equilibrium Crystal Shape andWulff Construction 190

15.2.4 Modeling of the Embedded PbTe Quantum Dots 191

15.2.5 Obtained Structural Properties 194

15.2.6 Internal Electric Fields and the Quantum Confined Stark Effect 195

15.3 Nanomagnetism 199

15.3.1 Concrete Problem and Goal 199

15.3.2 Construction of the Silicon Quantum Dots 200

15.3.3 Ab initio Simulation Approach 203

15.3.4 Calculation of the Formation Energy 204

15.3.5 Resulting Stability Properties 205

15.3.6 Obtained Magnetic Properties 206

References 211

Index 221

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