Diffusion Approximation and Homogenization of the Semiconductor Boltzmann Equation
نویسندگان
چکیده
Abstract. The paper deals with the diffusion approximation of the Boltzmann equation for semiconductors in the presence of spatially oscillating electrostatic potential. When the oscillation period is of the same order of magnitude as the mean free path, the asymptotics leads to the Drift-Diffusion equation with a homogenized electrostatic potential and a diffusion matrix involving the small scale information. The convergence is proven rigorously for Boltzmann statistics, while it is incomplete for Fermi-Dirac statistics.
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عنوان ژورنال:
- Multiscale Modeling & Simulation
دوره 4 شماره
صفحات -
تاریخ انتشار 2005