A fast approach to Discontinuous Galerkin solvers for Boltzmann-Poisson transport systems for full electronic bands and phonon scattering

摘要

The present work is motivated by the development of a fast DG baseddeterministic solver for the extension of the BTE to a system of transportBoltzmann equations for full electronic multi-band transport with intra-bandscattering mechanisms. Our proposed method allows to find scattering effects ofhigh complexity, such as anisotropic electronic bands or full bandcomputations, by simply using the standard routines of a suitable Monte Carloapproach only once. In this short paper, we restrict our presentation to thesingle band problem as it will be also valid in the multi-band system as well.We present preliminary numerical tests of this method using the Kane energyband model, for a 1-D 400nm $n^{+}-n-n^{+}$ silicon channel diode, showingmoments at $t=0.5$ps and $t=3.0$ps.