Table of Contents

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

About the Author

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 Planitz 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.