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

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The principal investigators will study the partial differential equations and integro-differential equations that model semiconductor devices by using analytical and numerical methods. Their work will span the entire range from the actual derivation of the basic equations to the solution of concrete boundary value problems. In particular, the investigators will study the Boltzmann equation and systems derived from it such as the hydrodynamic model and the drift-diffusion model using asymptotic methods. The systems of differential equations that describe the behavior of semiconductor devices are difficult to solve analytically. Even large computers are unable to resolve aspects of the solutions accurately. Thus there is a great need for approximate theories that contain enough of the physics of the devices to be realistic and yet are tractable mathematically. The principal investigators will derive approximate models of semiconductors and study them with asymptotic and numerical methods, in order to understand the workings of actual devices.