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

The present work is motivated by the development of a fast DG based deterministic solver for the extension of the BTE to a system of transport Boltzmann equations for full electronic multi-band transport with intra-band scattering mechanisms. Our proposed method allows to find scattering effects of high complexity, such as anisotropic electronic bands or full band computations, by simply using the standard routines of a suitable Monte Carlo approach only once. In this short paper, we restrict our presentation to the single 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 energy band model, for a 1-D 400nm $n^{+}-n-n^{+}$ silicon channel diode, showing moments at $t=0.5$ps and $t=3.0$ps.