Mathematical Sciences: Analytical and Numerical Studies of Partial Differential Equations of Semiconductor Devices

本项目主要研究半导体器件设计中的问题制定、分析和大规模计算。将回顾经典的漂移扩散方程，并推导更现实的边界条件。将发展定常和非定常情况的计算方法。将考虑MOSFET和双极器件。新的物理模型适用于较小的设备将开发，特别是那些基于玻尔兹曼方程公式。将推导出合适的边界条件和计算方法。

This project is concerned with problem formulation, analysis, and large scale computation in semi-conductor device design. The classical drift-diffusion equations will be reviewed and more realistic boundary conditions derived. Computation methods for steady and unsteady cases will be developed. Both MOSFET and Bipolar devices will be considered. New physical models appropriate for smaller devices will be developed, especially those based on a Boltzmann equation formulation. Suitable boundary conditions and computational methods will be derived.