Mathematical Sciences: Analysis and Simulation of Energy Models for Semiconductor Transport

本项目涉及两种载体运输模型的数学分析和仿真。它们是：流体力学模型和能量输运模型（RT模型），两者都适用于常规装置。模拟HFET器件，量子流体力学模型，也将进行。该模型提供了非均质结构或化合物半导体中的隧道效应。用于二维模拟的算法基本上是非振荡冲击捕获算法和投影方法。目标是利用过去十年中开发的新算法，在不同数学模型的基础上，对传统半导体器件进行计算机模拟。一种前沿二极管，即所谓的隧道二极管，将根据量子力学模型进行研究。

This project involves mathematical analysis and simulation of two models for carrier transport. These are: the hydrodynamic model and the energy transport model (the RT model,) both for conventional devices. Simulation of HFET devices, a quantum hydrodynamic model, will also be carried out. The model provides for tunneling effects in heterogenous structures, or compound semiconductors. The algorithms to be employed for the two dimensional simulations are the essentially non-oscillatory shock capturing algorithms, and projection methods. The objective is to produce computer simulation of conventional semiconductor devices, based upon different mathematical models, by use of new algorithms developed during the last decade. A cutting edge type of diode, the so-called tunnel diode, will be studied in terms of a quantum mechanical model.