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

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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.