One of the ways of countering the ever increasing computational requirements in the simulation and modeling of electrical and electromagnetic devices and phenomena, is the development of simulation and modeling tools on parallel computing platforms. In this thesis, a previously developed Monte Carlo parallel device simulator is utilized, enhanced, and evolved, to render it applicable to the modeling and simulation of certain key applications. A three-dimensional Monte Carlo simulation of GaAs MESFETs is first presented to study small-geometry effects. Then, a finite-difference time-domain numerical solution of Maxwell's equations is developed and coupled to Monte Carlo particle simulation, to illustrate a photoconductive switching experiment. As the third and major application of the Monte Carlo code, high-field electron transport simulations of the ZnS phosphor of AC thin film electroluminescent devices are presented. A full band structure (of ZnS) computed using a nonlocal empirical pseudopotential technique is included in the Monte Carlo simulation. The band structure is computed using a set of form factors, that were tuned to fit experimentally measured critical point transitions in ZnS. The Monte Carlo algorithms pertaining to the full band model are developed. Most of the scattering mechanisms, pertinent to ZnS are included to model the electron kinetics. The hot electron distributions are computed as a function of the electric field in the ZnS phosphor layer, to estimate the percentage of hot electrons that could potentially contribute to excitation of luminescent impurity centers in the ZnS phosphor layer. Impact excitation, a key process in electroluminescence, is included in the Monte Carlo simulation to estimate the quantum yield of the devices. Preliminary results based on the full band k-space model exhibit experimentally observed trends.

This volume presents the application of the Monte Carlo method to the simulation of semiconductor devices, reviewing the physics of transport in semiconductors, followed by an introduction to the physics of semiconductor devices.

We consider the parallelization of Monte Carlo algorithms for analyzing numerical models of charge transport used in semiconductor device physics. Parallel algorithms for the standard k-space Monte Carlo simulation of a three band model of bulk GaAs on hypercube multicomputers are first presented. This Monte Carlo model includes scattering due to polar-optical, intervalley, and acoustic phonons, as well as electron-electron scattering. The k-space Monte Carlo program, excluding electron-electron scattering, is then extended to simulate a semiconductor device by the addition of the real space position of each simulated particle and the assignment of particle charge, using a cloud in cell scheme, to solve the Poisson's equation with particle dynamics. Techniques for effectively partitioning this device so as to balance the computational load while minimizing the communication overhead are discussed. Approaches for improving the efficiency of the parallel algorithm, either by dynamically balancing of load or by employing the usual techniques for enhancing rare events in Monte Carlo simulations are also considered. The parallel algorithms were implemented on a 64-node NCUBE multiprocessor and test results were generated to validate the parallel k-space, as well as the device simulation programs. Timing measurements were also made to study the variation of speedups as both the problem size and number of processors are varied. The effective exploitation of the computational power of message passing multiprocessors requires the efficient mapping of parallel programs onto processors so as to balance the computational load while minimizing the communication overhead between processors. A lower bound for this communication volume when mapping arbitrary task graphs onto distributed processor systems is derived. For a K processor system this lower bound can be computed from the K (possibly) largest eigenvalues of the adjacency matrix of the task graph and the eigenvalues of the adjacency matrix of the processor graph. We also derive the eigenvalues of the adjacency matrix of the processor graph for a hypercube and give test results comparing the lower bound for the communication volume with the values given by a heuristic algorithm for a number of task graphs.

The Monte Carlo method is inherently parallel and the extensive and rapid development in parallel computers, computational clusters and grids has resulted in renewed and increasing interest in this method. At the same time there has been an expansion in the application areas and the method is now widely used in many important areas of science including nuclear and semiconductor physics, statistical mechanics and heat and mass transfer. This book attempts to bridge the gap between theory and practice concentrating on modern algorithmic implementation on parallel architecture machines. Although a suitable text for final year postgraduate mathematicians and computational scientists it is principally aimed at the applied scientists: only a small amount of mathematical knowledge is assumed and theorem proving is kept to a minimum, with the main focus being on parallel algorithms development often to applied industrial problems. A selection of algorithms developed both for serial and parallel machines are provided. Sample Chapter(s). Chapter 1: Introduction (231 KB). Contents: Basic Results of Monte Carlo Integration; Optimal Monte Carlo Method for Multidimensional Integrals of Smooth Functions; Iterative Monte Carlo Methods for Linear Equations; Markov Chain Monte Carlo Methods for Eigenvalue Problems; Monte Carlo Methods for Boundary-Value Problems (BVP); Superconvergent Monte Carlo for Density Function Simulation by B-Splines; Solving Non-Linear Equations; Algorithmic Effciency for Different Computer Models; Applications for Transport Modeling in Semiconductors and Nanowires. Readership: Applied scientists and mathematicians.

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These proceedings present recent advances in the Monte Carlo methods, covering theoretical aspects, a wide range of applications in solving problems, and parallel algorithms for Monte Carlo computations.