Macroscopic model for coupled surface and volume collisions in semiconductor superlattices

Article type: Research Article

Authors: Mellet, A.

Affiliations: Mathématiques pour l'Industrie et la Physique, UMR CNRS 5640, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex, France E‐mail: mellet@mip.ups‐tlse.fr

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.

Keywords: Boltzmann equation, Spherical Harmonics Expansion model, semiconductor superlattices, diffusion approximation, homogenization, interface operators, two‐scale limit

Journal: Asymptotic Analysis, vol. 33, no. 3-4, pp. 337-361, 2003