A HYBRID KINETIC-QUANTUM MODEL FOR STATIONARY ELECTRON-TRANSPORT

Interface conditions between a classical transport model described by the Boltzmann equation and a quantum model described by a set of Schro dinger equations are presented in the one-dimensional stationary setti ng. These interface conditions, derived thanks to an asymptotic analys is of the Wigner transform, are shown to be flux-preserving and are us ed 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 th e potential is either prescribed or computed self-consistently, and th e semiclassical limit of the problem is shown to give the right interf ace conditions between two kinetic regions (the electrostatic potentia l being fixed). This model can be used to describe far-from-equilibriu m electron transport in a resonant tunneling diode.