1 Introduction
 1.1 Need for TCAD in electronics
 1.2 Overview of carrier transport models
  1.2.1 Classification of transport models
  1.2.2 Poisson equation
  1.2.3 Semi-classical models
  1.2.4 Quantum models
  1.2.5 Summary
 1.3 Motivation for Wigner formalism based simulation
  1.3.1 Classical analogies
  1.3.2 Decoherence and scattering
  1.3.3 Transient capability
  1.3.4 Suitable problems
 1.4 Outline of dissertation
2 Wigner Formalism of Quantum Mechanics
 2.1 Wigner equation
  2.1.1 History and derivation
  2.1.2 Properties
 2.2 Wigner-Boltzmann equation
  2.2.1 Derivation
 2.3 Discretization of momentum space
  2.3.1 Semi-discrete Wigner equation
 2.4 Transport problems
  2.4.1 Boundary and initial conditions
  2.4.2 Stationary
  2.4.3 Transient
 2.5 Overview of existing solvers
  2.5.1 Deterministic methods
  2.5.2 Stochastic methods
3 Signed-Particle Method
 3.1 Background
 3.2 Outline
 3.3 Integral formulation
  3.3.1 Fredholm integral form
  3.3.2 Adjoint equation
 3.4 Neumann series
 3.5 Monte Carlo integration
 3.6 Computational task
  3.6.1 Wigner potential as a scattering mechanism
 3.7 Algorithm
  3.7.1 Structure
  3.7.2 Discretization
  3.7.3 Particle initialization
  3.7.4 Free-flight
  3.7.5 Scattering
  3.7.6 Annihilation process
  3.7.7 Implementation
4 Optimized Algorithms for the Signed-Particle Method
 4.1 Wigner potential
  4.1.1 Full discretization
  4.1.2 Efficient calculation of two-dimensional Wigner potential
  4.1.3 Choice of coherence length
  4.1.4 Tapering window
 4.2 Generation process
 4.3 Annihilation process
  4.3.1 Numerical diffusion
  4.3.2 Spatial scaling
  4.3.3 Ensemble sorting
  4.3.4 Particle growth prediction
 4.4 Validation
5 Parallelization of the Wigner Monte Carlo Simulator
 5.1 Background
  5.1.1 Shared memory
  5.1.2 Distributed memory
  5.1.3 Hybrid systems
  5.1.4 Accelerator cards
 5.2 Parallelization approaches for Monte Carlo simulation
  5.2.1 Shared-memory
  5.2.2 Distributed-memory
 5.3 Domain decomposition for Wigner Monte Carlo simulator
  5.3.1 Domain decomposition
  5.3.2 Localized annihilation
 5.4 Algorithm
  5.4.1 MPI topology
  5.4.2 Initialization
  5.4.3 Time loop
 5.5 Evaluation
  5.5.1 Validation
  5.5.2 Performance
  5.5.3 Summary
6 Applications
 6.1 Electrostatic lenses
  6.1.1 Introduction
  6.1.2 Law of refraction
  6.1.3 Converging lens
  6.1.4 Wavepacket control
 6.2 Drive-current enhancement
  6.2.1 Geometry
  6.2.2 Steady-state current
  6.2.3 Results
7 Summary and Evaluation
 7.1 Summary of content
 7.2 Summary of contributions
 7.3 Conclusion
 7.4 Outlook
A Phonon Scattering Models
B Scattering in Discretized k-Space
C Modelling of Surface Roughness
 Journals
 Book Contributions
 Conference Contributions (Full Proceedings)
 Conference Contributions (Book of Abstracts)