D I S S E R T A T I O N

Deterministic Numerical Solution
of the
Boltzmann Transport Equation

ausgeführt zum Zwecke der Erlangung des akademischen Grades
eines Doktors der technischen Wissenschaften

eingereicht an der Technischen Universität Wien
Fakultät für Elektrotechnik und Informationstechnik
von

Karl Rupp

Linke Bahnzeile 7/6
A-2486 Pottendorf-Landegg, Österreich

Matr. Nr. 0325941
geboren am 12. Juni 1984 in Bad Radkersburg

Wien, im Dezember 2011      

To Antonia, Thomas, Hubert and Dieter.
Rest in peace.

Kurzfassung
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 H  -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