Mathematical Analysis of a Nonparabolic Two-Band Schrödinger-Poisson Problem

A mathematical model for the quantum transport of a two-band semiconductor that includes the self-consistent electrostatic potential is analyzed. Corrections beyond the usual effective mass approximation are considered. Transparent boundary conditions are derived for the multiband envelope Schrodinger model. The existence of a solution¨ of the nonlinear system is proved by using an asymptotic procedure. Some numerical examples are included. They illustrate the behavior of the scattering and the resonant states