Abstract
Preface and Acknowledgement
Contents
Notation
Symbols
Abbreviations
1 Introduction
1.1 Semiclassical Carrier Transport
1.2 Requirements of Modern TCAD
1.3 Outline
2 The SHE Equations
2.1 Historical Overview
2.2 Derivation of the SHE Equations
2.3
-Transform and MEDS
2.4 Self-Consistency with Poisson’s Equation
2.5 Compatibility with Modern TCAD
3 Physical Modeling
3.1 Spherically Symmetric Energy Band Models
3.2 Incorporation of Full-Band Effects
3.3 Linear Scattering Operators
3.4 Nonlinear Scattering Operators
4 Structural Properties
4.1 Sparse Coupling for Spherical Energy Bands
4.2 Coupling for Nonspherical Energy Bands
4.3 Stabilization Schemes
4.4 Boundary Conditions
4.5 Solution of the Linear System
4.6 Results
5 SHE on Unstructured Grids
5.1 The Box Integration Scheme
5.2 Construction of Boxes
5.3 Box Integration for SHE
5.4 Results
6 Adaptive Variable-Order SHE
6.1 Variable-Order SHE
6.2 Adaptive Control of the SHE Order
6.3 Results
7 Parallelization
7.1 Energy Couplings Revisited
7.2 Symmetrization of the System Matrix
7.3 A Parallel Preconditioning Scheme
7.4 Results
8 Numerical Results
8.1 MOSFET
8.2 FinFET
9 Outlook and Conclusion
9.1 Possible Further Improvements of the SHE Method
9.2 Conclusion
A Mathematical Tools
A.1 The Kronecker Product
A.2 Wigner 3jm Symbols
Bibliography
Own Publications
Journal Articles
Contributions to Books
Conference Contributions
Software
Curriculum Vitae