Energy‐transport model for a nondegenerate semiconductor: Convergence of the Hilbert expansion in the linearized case

Article type: Research Article

Authors: Génieys, S.

Affiliations: Université Paul Sabatier, UMR MIP, 118 rte de Narbonne, 31062 Toulouse Cedex, France

Abstract: This paper is concerned with the derivation of an energy‐transport model from the Boltzmann equation for a nondegenerate semiconductor with a parabolic band structure. Electron–electron collisions and elastic collisions (i.e., impurity scattering and the “elastic part” of phonon collisions) are retained as leading order terms. Then, a Hilbert expansion leads to an energy‐transport model, and a Chapman–Enskog expansion leads to the same energy‐transport model if the electric field vanishes. For the case of the Boltzmann equation linearized about a global equilibrium, the convergence of the Hilbert expansion is shown when the electric field vanishes.

Journal: Asymptotic Analysis, vol. 17, no. 4, pp. 279-308, 1998