Classical and quantum energy-transport models for semiconductors: modeling, analysis and numerical approximation

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Due to the increasing miniaturization of semiconductor devices the existing, classical semiconductor models have to be refined, since temperature and quantum effects become more and more important. The main goals of this project are to understand the influence of the electron temperature on the particle current, the heating of the semiconductor crystal, and the interplay of the temperature with quantum effects. More precisely, we plan to analyze the classical and quantum energy-transport models mathematically, perform an asymptotic expansion around the state of constant temperature, and solve the model equations with appropriate boundary and initial conditions in up to three space dimensions using mixed finite-element techniques. Furthermore, ultrasmall field-effect transistors (MOSFET, HEMT) are numerically simulated. We expect that our results will help in the understanding of highly nonlinear cross-diffusion systems and of heat and quantum transport in semiconductor devices.