Past Event: Oden Institute Seminar

DG Schemes for Collisional Electron Transport with Insulating Conditions on Rough Boundaries

Jose Morales Escalante, Technical University of Vienna, Austria

Abstract

We consider the mathematical and numerical modeling of reflective boundary conditions, including diffusive reflection in addition to specularity, in the context of collisional electron transport in semiconductors, and their implementation in Discontinuous Galerkin (DG) schemes that solve the related Boltzmann kinetic model. We study the specular, diffusive and mixed (specular plus diffusive) reflection BC on physical boundaries of the problem. We develop a numerical approximation to model an insulating boundary condition, or equivalently, a zero flux mathematical condition for the electron transport equation. This condition balances the incident and reflective momentum flux at the microscopic level pointwise at the boundary, for the case of a more general mixed reflection with momentum dependent specularity probability. We compare the computational prediction of physical observables given by the numerical implementation of these different reflection conditions in our DG scheme for the Boltzmann model, and observe the influence of the diffusive condition in the kinetic moments over the position domain.