Mathematical and Numerical Methods for Complex Quantum Systems

Discontinuous Galerkin (DG) Methods for Full Band Boltzmann - Poisson (BP) models of Electronic Transport in Semiconductors using Empirical Pseudopotential Methods (EPM)

Jose Morales Escalante

TU Wien (Technical University of Vienna)


The purpose of our work is to develop Discontinuous Galerkin (DG) based numerical solvers for Boltzmann-Poisson (BP) mathematical models of hot electronic transport in semiconductors, which consider a more realistic picture of the phenomena. The methodology to accomplish it follows several lines. The first one is by incorporating a full electronic band structure, given by Empirical Pseudopotential Methods (EPM), including then in the model the anisotropy of the band far away from the local conduction band minimum, as it is needed for a correct description of hot electronic transport. The second one is to extend the previously developed scheme for one electron conduction band to a multiband BP system for conduction and valence bands that describes electron and hole transport with their respective collision scattering mechanisms. We present results of a DG scheme applied to deterministic computations of the probability density function (pdf) for the BP system describing hot electron transport along the conduction energy band for a n+ ? n ? n+ Silicon diode, with n channel lengths of 400 nm and 50 nm, using a symmetrized radially averaged EPM band, comparing it with traditional analytical band models such as the Parabolic or Kane, which give a simple (usually taken as isotropic) description of the conduction band, valid just close to a local conduction band minimum and for low electric fields. DG formulations related to the electron transport problem with a full band structure and to the multiband BP system for electrons and holes will be discussed. Boundary Conditions related to this phenomena will be discussed as well.