Macroscopic model for coupled surface and volume collisions in semiconductor superlattices

Abstract

This paper follows [7], by N. Ben Abdallah, P. Degond, F. Poupaud and the author, in which a diffusion model for semiconductor superlattices was derived. At the starting point of our study, the device consists of a periodic array of localized scatters (the heterojunction between two semiconductor materials), and electron motion is described by the Boltzmann equation. Assuming that both the collisions and the scattering processes preserve the energy of the particles, we prove the convergence of the electron distribution function to the solution of the SHE model equation (for Spherical Harmonics Expansion). Since the device has microscopic periodicity, the proof relies on the recently developed tool of two‐scale convergence.