Energy Models for One-Carrier Transport in Semiconductor Devices

Moment models of carrier transport, derived from the Boltzmann equation, made possible the simulation of certain key effects through such realistic assumptions as energy dependent mobility functions. This type of global dependence permits the observation of velocity overshoot in the vicinity of device junctions, not discerned via classical drift-diffusion models, which are primarily local in nature. It was found that a critical role is played in the hydrodynamic model by the heat conduction term. When ignored, the overshoot is inappropriately damped. When the standard choice of the Wiedemann-Franz law is made for the conductivity, spurious overshoot is observed. Agreement with Monte-Carlo simulation in this regime required empirical modification of this law, or nonstandard choices. Simulations of the hydrodynamic model in one and two dimensions, as well as simulations of a newly developed energy model, the RT model, are presented. The RT model, intermediate between the hydrodynamic and drift-diffusion model, was developed to eliminate the parabolic energy band and Maxwellian distribution assumptions, and to reduce the spurious overshoot with physically consistent assumptions. The algorithms employed for both models are the essentially non-oscillatory shock capturing algorithms. Some mathematical results are presented and contrasted with the highly developed state of the drift-diffusion model

WENO schemes applied to the quasi-relativistic Vlasov--Maxwell model for laser-plasma interaction

In this paper we focus on WENO-based methods for the simulation of the 1D Quasi-Relativistic Vlasov--Maxwell (QRVM) model used to describe how a laser wave interacts with and heats a plasma by penetrating into it. We propose several non-oscillatory methods based on either Runge--Kutta (explicit) or Time-Splitting (implicit) time discretizations. We then show preliminary numerical experiments

Multiscale Modeling and Simulation of Organic Solar Cells

In this article, we continue our mathematical study of organic solar cells (OSCs) and propose a two-scale (micro- and macro-scale) model of heterojunction OSCs with interface geometries characterized by an arbitrarily complex morphology. The microscale model consists of a system of partial and ordinary differential equations in an heterogeneous domain, that provides a full description of excitation/transport phenomena occurring in the bulk regions and dissociation/recombination processes occurring in a thin material slab across the interface. The macroscale model is obtained by a micro-to-macro scale transition that consists of averaging the mass balance equations in the normal direction across the interface thickness, giving rise to nonlinear transmission conditions that are parametrized by the interfacial width. These conditions account in a lumped manner for the volumetric dissociation/recombination phenomena occurring in the thin slab and depend locally on the electric field magnitude and orientation. Using the macroscale model in two spatial dimensions, device structures with complex interface morphologies, for which existing data are available, are numerically investigated showing that, if the electric field orientation relative to the interface is taken into due account, the device performance is determined not only by the total interface length but also by its shape

Electro-thermal-mechanical modeling of GaN HFETs and MOSHFETs

High power Gallium Nitride (GaN) based field effect transistors are used in many high power applications from RADARs to communications. These devices dissipate a large amount of power and sustain high electric fields during operation. High power dissipation occurs in the form of heat generation through Joule heating which also results in localized hot spot formation that induces thermal stresses. In addition, because GaN is strongly piezoelectric, high electric fields result in large inverse piezoelectric stresses. Combined with residual stresses due to growth conditions, these effects are believed to lead to device degradation and reliability issues. This work focuses on studying these effects in detail through modeling of Heterostructure Field Effect Transistors (HFETs) and metal oxide semiconductor hetero-structure field effect transistor (MOSHFETs) under various operational conditions. The goal is to develop a thorough understanding of device operation in order to better predict device failure and eventually aid in device design through modeling. The first portion of this work covers the development of a continuum scale model which couples temperature and thermal stress to find peak temperatures and stresses in the device. The second portion of this work focuses on development of a micro-scale model which captures phonon-interactions at the device scale and can resolve local perturbations in phonon population due to electron-phonon interactions combined with ballistic transport. This portion also includes development of phonon relaxation times for GaN. The model provides a framework to understand the ballistic diffusive phonon transport near the hotspot in GaN transistors which leads to thermally related degradation in these devices.M.S.Committee Chair: Graham, Samuel; Committee Member: Cola, Baratunde; Committee Member: Joshi, Yogendr

An Anlaysis of Methods for Modeling Advective-Dominated Transport

Finite element modeling of sharp front advective-dispersive-reactive transport is not accurate for highly advective or reactive problems. Two techniques were studied with the goal of accurately modeling these problems: an h-adaptive method that adjusted element lengths, and Petrov-Galerkin upwinding which used weighting functions of higher polynomial order than that of the basis functions. Finite element models were constructed using linear and quadratic basis functions in one spatial dimension. The h-adaptive method was shown to give good results with linear and quadratic basis functions. Petrov-Galerkin upwinding also yielded excellent results. This method was implemented for both classes of basis functions, but was studied only for the linear case. The benefits of Petrov-Galerkin upwinding depend on user defined parameters that regulate the amount of upwinding applied to the solution. Taylor series and Fourier analyses of the finite element truncation error as well as numerical experimentation were performed to define optimal upwinding parameters. Published results by other investigators were reproduced, and an automated method of deriving optimal upwinding parameters was developed. Analysis and operation of the Petrov-Galerkin models indicated that optimal levels of upwinding are a function of the gradient across each element. This observation led to a new upwinding scheme that adjusts the upwinding condition at each element as a function of the local gradient. Significantly better results were obtained with the new method relative to existing Petrov-Galerkin formulations. The utility of this technique will be greatly enhanced when optimal upwinding conditions are described as a function of dimensionless model parameters such as Peclet, Courant, and Damkohler numbers, and the method is generalized to multiple spatial dimensions.Master of Science in Environmental Engineerin

On adaptive grid refinement in the presence of internal or boundary layers

We propose an anisotropic refinement strategy which is specially designed for the efficient numerical resulution of internal and boundary layers. This strategy is based on the directed refinement of single triangles together with adaptive multilevel grid orientation. Compared to usual methods, the new anisotropic refinement ends up in more stable and more accurate solutions at much less computational cost. This is demonstrated by several numerical examples

Simulation of neutron radiation damage in silicon semiconductor devices.

A code, Charon, is described which simulates the effects that neutron damage has on silicon semiconductor devices. The code uses a stabilized, finite-element discretization of the semiconductor drift-diffusion equations. The mathematical model used to simulate semiconductor devices in both normal and radiation environments will be described. Modeling of defect complexes is accomplished by adding an additional drift-diffusion equation for each of the defect species. Additionally, details are given describing how Charon can efficiently solve very large problems using modern parallel computers. Comparison between Charon and experiment will be given, as well as comparison with results from commercially-available TCAD codes

Activities of the Research Institute for Advanced Computer Science

The Research Institute for Advanced Computer Science (RIACS) was established by the Universities Space Research Association (USRA) at the NASA Ames Research Center (ARC) on June 6, 1983. RIACS is privately operated by USRA, a consortium of universities with research programs in the aerospace sciences, under contract with NASA. The primary mission of RIACS is to provide research and expertise in computer science and scientific computing to support the scientific missions of NASA ARC. The research carried out at RIACS must change its emphasis from year to year in response to NASA ARC's changing needs and technological opportunities. Research at RIACS is currently being done in the following areas: (1) parallel computing; (2) advanced methods for scientific computing; (3) high performance networks; and (4) learning systems. RIACS technical reports are usually preprints of manuscripts that have been submitted to research journals or conference proceedings. A list of these reports for the period January 1, 1994 through December 31, 1994 is in the Reports and Abstracts section of this report