Study of hydrodynamical limits in a multicollision scale Boltzmann equation for semiconductors

Abstract

We derive in this paper a generalized hydrodynamical model for semiconductors from a multicollision scale Boltzmann equation. We apply a Chapman–Enskog method for two time-scale collisional operators. These two time scales are linked respectively with the elastic part of the electron/lattice scattering term and the electron/electron collision term. Our model has a global entropy function and a symmetric formulation. It is a generalization of the classical hydrodynamical model since we add two terms: a “thermal friction force” and a “friction heat flux.” Moreover, with some changes of parameters we obtain both the energy-transport model and the Euler–Poisson hydrodynamical model.