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

Two-Dimensional Wigner Monte Carlo Simulation for Time-Resolved
Quantum Transport with Scattering

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

Paul Ellinghaus

Meiselstraße 27/20
A-1150 Wien, Österreich

geboren am 22. Mai 1986 in Johannesburg, Südafrika

Wien, im Februar 2016

Kurzfassung
Abstract
Acknowledgements
Contents
Nomenclature
List of Tables
List of Figures
1 Introduction
 1.1 Need for TCAD in electronics
 1.2 Overview of carrier transport models
 1.3 Motivation for Wigner formalism based simulation
 1.4 Outline of dissertation
2 Wigner Formalism of Quantum Mechanics
 2.1 Wigner equation
 2.2 Wigner-Boltzmann equation
 2.3 Discretization of momentum space
 2.4 Transport problems
 2.5 Overview of existing solvers
3 Signed-Particle Method
 3.1 Background
 3.2 Outline
 3.3 Integral formulation
 3.4 Neumann series
 3.5 Monte Carlo integration
 3.6 Computational task
 3.7 Algorithm
4 Optimized Algorithms for the Signed-Particle Method
 4.1 Wigner potential
 4.2 Generation process
 4.3 Annihilation process
 4.4 Validation
5 Parallelization of the Wigner Monte Carlo Simulator
 5.1 Background
 5.2 Parallelization approaches for Monte Carlo simulation
 5.3 Domain decomposition for Wigner Monte Carlo simulator
 5.4 Algorithm
 5.5 Evaluation
6 Applications
 6.1 Electrostatic lenses
 6.2 Drive-current enhancement
7 Summary and Evaluation
 7.1 Summary of content
 7.2 Summary of contributions
 7.3 Conclusion
 7.4 Outlook
A Phonon Scattering Models
 Intravalley scattering
 Intervalley scattering
B Scattering in Discretized k-Space
 Elastic scattering
 Inelastic scattering
 Magnitude of discretization error
C Modelling of Surface Roughness
Bibliography
Own Publications
 Journals
 Book Contributions
 Conference Contributions (Full Proceedings)
 Conference Contributions (Book of Abstracts)
Curriculum Vitae