Weak solutions to one-dimensional quantum drift-diffusion equations for semiconductors

摘要

The weak solutions to the stationary quantum drift-diffusion equations (QDD) for semiconductor devices are investigated in one space dimension. The proofs are based on a reformulation of the system as a fourth-order elliptic boundary value problem by using an exponential variable transformation. The techniques of a priori estimates and Leray-Schauder's fixed-point theorem are employed to prove the existence. Furthermore, the uniqueness of solutions and the semiclassical limit δ → 0 from QDD to the classical drift-diffusion (DD) model are studied.