Semiclassical Limit of Quantum Semiconductor Models

摘要

In this contributed paper, we first briefly review some macroscopic quantum semiconductor models and then focus on the semi- classical limit problem of the quantum drift diffusion model and a simplified quantum energy transport model. In the second section, some of the known semiclassical limit results with positive boundary condition and the main technical tools will be reviewed. In the last section, we will introduce an interesting problem, i.e., the semiclassical limit problem with vanishing density on the boundary, which comes from the inversion layer in MOSFET devices.