Modeling and Numerical Methods for Device Simulations

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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. ***