Development of Numerical Methods for Semiconductor Device Simulation and Electron Microscopy

University Of Massachusetts, Dartmouth, North Dartmouth MA

Investigators

Abstract

This study will focus on two numerical techniques for discontinuous problems and their physical applications. Particular attention will be paid to the development of a numerical method and its impact on refining the mathematical model of the physical system. Sharp gradients and discontinuities are characteristic of semiconductor device simulations. While numerical methods have been developed to handle these characteristics, these methods need to be refined and tailored to capture the features exhibited by carrier flow in semiconductor device simulations. On the other hand, the mathematical models that are used to describe carrier transport in semiconductors are constantly evaluated and changed. Steady-state weighted essentially non oscillatory methods will be refined and used to determine the validity of macroscopic models of current transport and deposition in semiconductor devices. Discontinuities are also a problem in the determination of protein structure by electron microscopy. The inherently discontinuous nature of physical structures, and the assumption that repetition of the structure in a gridlike formation is a periodic function leads to slow decay of the Fourier coefficients. Fourier coefficient extrapolation and Gegenbauer polynomial methods will be further developed and applied to the field of electron microscopy to achieve better resolution protein structures. This has the potential to be added to any electron microscopy software as a postprocessing step, and provide better resolution structures. Numerical methods for semiconductor device simulation models allow efficient and inexpensive simulation of the processes involved in semiconductor device production. However, these processes have many discontinuities that require sensitive numerical methods to capture the sharp changes in density and pressure without smearing them. Such methods, known as Weighted Essentially Non-Oscillatory methods, have been developed for use in similar problems, but are not efficient for the long time scales necessary for semiconductor simulations. The aim of this project is to further develop these numerical methods, and make them efficient for semiconductor device simulation on computers. Efficient numerical methods will also serve to compare different models, which attempt to describe the physical problem, and to evaluate which models best compare to reality. Another aspect of this project deals with the effects of discontinuities in protein structures studied by electron microscopy. Mathematical methods have been recently developed to solve the underlying problem by adding a smoothing step, which smoothes away numerical artifacts while keeping the real discontinuities. These methods have never been used on protein structures, and need to be tailored to it. These methods may improve the resolution of protein structures determined by electron microscopy.