Modeling and Numerical Methods for Device Simulations

9627849舒本项目是美国国家科学基金会资助的ECS-9214488研究的继续。其目的是研究用于半导体器件模拟的建模、数学分析，特别是使用最近发展的、准确和稳定的有限差分和有限元算法的数值近似。重点是模拟流体动力学(HD)模型、能量输运(ET)和量子流体动力学(QHD)模型，并研究它们的物理意义。我们将特别关注与时间相关的问题，如多谷Gunn振子，这就需要在空间和时间上都具有高阶精度的稳健算法。将保持与设备物理学家、设备工程师和应用数学家的合作，从物理、数学和数值角度研究设备模拟问题。***

9627849 Shu This project is a continuation of the research supported by NSF Grant ECS-9214488. The object is to study the modeling, mathematical analysis, and in particular numerical approximations using recently developed, accurate and stable finite difference and finite element algorithms, for semiconductor device simulations. The emphasis is on simulating the hydrodynamic (HD) models, the energy transport (ET), and the quantum hydrodynamic (QHD) models, and investigating their physical implications. Special attention will be paid to time dependent problems, such as the multi-valley Gunn oscillator, which require robust algorithms with high order accuracy both in space and in time. Collaborations with device physicists, device engineers, and applied mathematicians will be maintained, to investigate device simulation problems form both physical, mathematical, and numerical points of view. ***