This document contains a proposal for the creation of a simulator that can accurately model the interaction of electromagnetic (EM) and semiconductor effects for modern wireless devices including nonlinear and/or active devices. The proposed simulator couples the balanced semiconductor equations (charge, momentum, kinetic energy) with a FDTD full-wave Yee-based electromagnetic (EM) simulator. The resultant CAD tool is able to model the response of one semiconductor device to both small signal and DC bias based on the process parameters (material, charge distribution and doping) without any a-priori knowledge of the device performance characteristics, thus making it extremely useful in modeling and integrating novel devices in RF and Wireless topologies. As a proof of concept an n+--i--n+ diode will be simulated. In the future, more complicated structures, such as MODFETs, will be modeled as well.

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The two-dimensional electronic systems (2DESs) have kept surprising physicists for the last few decades. Examples include the integer and fractional quantum Hall effects, cuprate superconductivity, and graphene. This thesis is intended to develop suitable theoretical tools which can be generalized to study new types of 2DESs with strong correlation feature. The first part of this thesis describes the investigation of heterostructures made by Mott insulators. This work is mostly motivated by the significant improvement of techniques for layer-by-layer growth of transition metal oxides in the last few years. We construct a toy model based on generalized Hubbard model complemented with long-ranged Coulomb interaction, and we study it by Hartree-Fock theory, dynamical mean-field theory, and Thomas-Fermi theory. We argue that interesting 2D strongly correlated electronic systems can be created in such heterostructures under several conditions. Since these 2D systems are formed entirely due to the gap generated by electron-electron interaction, they are not addiabatically connected to a noninteracting electron states. This feature makes these 2D systems distinguish from the ones created in semiconductor heterostructures, and they may be potential systems having non-Fermi liquid behaviors. The second part of this thesis is devoted to the study of collective excitations in high-temperature superconductors. One important achievement in this work is to develop a time-dependent mean-field theory for t-U-J-V model, an effective low energy model for cuprates. The time-dependent mean-field theory is proven to be identical to the generalized random-phase approximation (GRPA) which includes both the bubble and ladder diagrams. We propose that the famous 41 meV magnetic resonance mode observed in the inelastic neutron scattering measurements is a collective mode arising from a conjugation relation, which has been overlooked in previous work, between the antiferromagnetic fluctuation and the phase fluctuation of the d-wave superconducting order parameter near momentum ([pi, pi]). Furthermore, we find that this collective mode signals the strength of the antiferromagnetic fluctuations which are responsible for the suppression of the superfluid density in the underdoped cuprates even at zero temperature. Finally, we perform a complete analysis on an effective model with parameters fitted by experimental data of Bi2212 within the GRPA scheme and conclude that the short-range antiferromagnetic interactions which are a remnant of the parent Mott-insulator are more likely the pairing mechanism of the High-T[subscript c] cuprates. / text

The parallelization and vectorization of Monte Carlo algorithms for modelling charge transport in semiconductor devices are considered. The standard ensemble Monte Carlo simulation of a three parabolic band model for GaAs is first presented as partial verification of the simulation. The model includes scattering due to acoustic, polar-optical and intervalley phonons. This ensemble simulation is extended to a full device simulation by the addition of real-space positions, and solution for the electrostatic potential from the charge density distribution using Poisson's equation. Poisson's equation was solved using the cloud-in-cell scheme for charge assignment, finite differences for spatial discretization, and simultaneous over-relaxation for solution. The particle movement (acceleration and scattering) and the solution of Poisson's are both separately parallelized. The parallelization techniques used in both parts are based on the use of semaphores for the protection of shared resources and processor synchronization. The speed increase results for parallelization with and without vectorization on the Ardent Titan II are presented. The results show saturation due to memory access limitations at a speed increase of approximately 3.3 times the serial case when four processors are used. Vectorization alone provides a speed increase of approximately 1.6 times when compared with the nonvectorized serial case. It is concluded that the speed increase achieved with the Titan II is limited by memory access considerations and that this limitation is likely to plague shared memory machines for the forseeable future. For the program presented here, vectorization is concluded to provide a better speed increase per day of development time than parallelization. However, when vectorization is used in conjunction with parallelization, the speed increase due to vectorization is negligible. / Graduation date: 1993