Mathematical Sciences: Mathematical Models for Submicron Semiconductor Devices

本研究将考虑描述新型器件结构中半导体输运模型的数学和数值方面。问题的两个方面将同时考虑。首先，不断增加的小型化导致的效应，虽然它们仍然可以用基本半导体方程（BSE）来描述，但本质上是三维的。为了解决这一问题，本研究将开发和分析一种基于渐近分析的解耦过程求解非线性BSE的迭代算法。其次，小型化会导致物理现象，如“热电子”，这是疯牛病没有描述的。因此，本研究也将考虑开发和使用新的模型方程。这项研究可能对半导体器件的设计产生直接影响，并有助于先进技术的发展。

This research will consider mathematical and numerical aspects of models describing semiconductor transport in novel device structures. Two aspects of the problems will be considered in tandem. First, increasing miniaturization results in effects which, while they can still be described by the Basic Semiconductor Equations (BSE), are intrinsically three- dimensional in nature. To address this problem, this research will develop and analyze an iterative algorithm for solution of the nonlinear BSE using a decoupling procedure based on asymptotic analysis. Secondly, miniaturization leads to physical phenomena, such as "hot electrons," which are not described by the BSE. This research will thus also consider the development and use of new model equations. This research could have a direct impact on the design of semiconductor devices and aid in the development of advanced technology.