A Hybrid Kinetic-Quantum Model for Stationary Electron Transport

Abstract

Interface conditions between a classical transport model described by the Boltzmann equation and a quantum model described by a set of Schrodinger equations are presented in the one-dimensional stationary setting. These interface conditions, derived thanks to an asymptotic analysis of the Wigner transform, are shown to be flux-preserving and are used to build a hybrid model consisting of a quantum zone surrounded by two classical ones. The hybrid model is shown to be well posed when the potential is either prescribed or computed self-consistently, and the semiclassical limit of the problem is shown to give the right interface conditions between two kinetic regions (the electrostatic potential being fixed). This model can be used to describe far-from-equilibrium electron transport in a resonant tunneling diode.