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List of Figures

1.1 Overview of microscopic transport models
3.1 Flowchart of a Monte Carlo algorithm to solve the Wigner-Boltzmann equation
3.2 Illustration of the pair-wise annihilation of particles in a cell of the phase space
4.1 Coherence box in a discretized, two-dimensional domain
4.2 Depiction of steps to calculate a two-dimensional discrete Fourier transform
4.3 Sequence of steps to apply Box discrete Fourier transform to calculate Wigner potential
4.4 Benchmark results of box discrete Fourier transform
4.5 Difference of the Wigner potential for different boundary treatments
4.6 Analytical potential profiles used to characterize computed Wigner potential
4.7 Wigner potential exhibiting values which do not correspond to the physical potential
4.8 Tukey window function for different tapering values
4.9 Comparison of the Wigner potential with and without the application of a tapering window
4.10 Improved physical simulation results of transistor with use of tapering window
4.11 Illustration of statistical biasing for particle generation with single sampling
4.12 Illustration of numerical diffusion caused by the particle regeneration process
4.13 Numerical diffusion mitigated by regeneration using a uniform distribution
4.14 Numerical diffusion mitigated by regeneration using a Gaussian distribution
4.15 Annihilation of particles on an enlarged spatial cell
4.16 Comparison of regeneration using uniform and Gaussian distributions on an enlarged spatial cell
4.17 Flow-chart of annihilation algorithm based on ensemble sorting
4.18 Validation of simulated density with exact solution for a potential barrier showing reflection and transmission
4.19 Validation of simulated k-distribution with exact solution for a potential barrier showing reflection and transmission
4.20 Validation of simulated density with exact solution for a potential barrier showing strong reflection
4.21 Validation of simulated k-distribution with exact solution for a potential barrier showing strong reflection
4.22 Validation of simulated density with a time-dependent potential using an exact solution for limiting cases
4.23 Validation of simulated k-distribution with a time-dependent potential using an exact solution for limiting cases
5.1 Comparison of decomposition approaches for a two-dimensional domain showing communication links
5.2 Flowchart of the parallelized Wigner Monte Carlo code
5.3 Validation of results obtained by the parallelized Wigner Monte Carlo code
5.4 Parallel speed-up and efficiency of the parallelized Wigner Monte Carlo code for single-barrier problem
5.5 Distribution of particles (computational load) amongst processes at two time-instants for single-barrier problem
5.6 Distribution of particles amongst processes over time for single-barrier problem
5.7 Parallel speed-up and efficiency of the parallelized Wigner Monte Carlo code for a double-barrier problem
5.8 Distribution of particles amongst processes over time for single-barrier problem
5.9 Potential profile and generation rate for a distribution of dopants
5.10 Comparison of the execution times between slab- and block-decomposition
5.11 Comparison of the load balance amongst processes between the slab- and block-decomposition approaches
6.1 Conceptual illustration of experimental structure to realize an electrostatic lens
6.2 Representation of the refractive law for electron optics
6.3 Shape and focussing effect of a double-concave electrostatic lens
6.4 Comparison between a wavepacket evolving freely and traversing a converging lens
6.5 Effect of different potential energy values for converging electrostatic lens
6.6 Potential profile (shape) and associated generation rate for a rhomboid-like lens for wave packet splitting
6.7 Rhomboid-like lens showing different effect on wavepacket based on potential energy value
6.8 Scanning electron microscope image of nanowire and its approximated geometry for simulations
6.9 Converging lens placed in front of nanoscaled channel
6.10 Comparison between the density with and without a converging lens placed in the source region
6.11 Difference in the k-distribution with and without a converging lens placed in the source region
6.12 Comparison of current through channel with and without a converging lens
C.1 Channel between oxide layers with modelled surface roughness

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