On the Treatment of the Collision Operator for Hydrodynamic Models

Abstract

In this work we study an alternative treatment for the collision operator for hydrodynamic models. We start with a trial displaced Maxwellian function for the electron distribution function and by explicit integration of the collision term, we obtain a hydrodynamic model. The model includes the Drift-Diffusion equations, in the low electric field limit. However, it does not include any heat transfer.

We present numerical results obtained from these equations for a simple N ⁺ - N - N ⁺ structure. We include the interaction of electrons with acoustic and optical phonons and discuss the possibility of including non-parabolic bands and intervalley scattering. The simulations seem to indicate that the lack of heat transfer results in a non-physical decrease in temperature at the entrance of the N-middle region. They also indicate that it is necessary to include the non-parabolicity of the band structure to properly predict the saturation velocity.