A Discontinuous Galerkin Solver for Full-Band Boltzmann-Poisson Models

Abstract

We present new preliminary results of a discontinuous Galerkin (DG) scheme applied to deterministic computations of the transients for the Boltzmann-Poisson (BP) system describing electron transport in semiconductor devices. Very recently in [1], [2], [3], results for one and two dimensional devices were obtained in the case of silicon semiconductor assuming the non-parabolic band approximation. Here, more general band structures are considered. Preliminary benchmark numerical tests on Kane and Brunetti et al. band models are reported.

Positivity-preserving discontinuous Galerkin schemes for linear Vlasov-Boltzmann transport equations

“…and K 1 and R are constants from (13). Regarding Sobolev regularity results for perturbative states from equilibrium, a broad work of C. Mouhot and N. Newman [38] was also done around the same period of Herau's and Ben Abdallah-Tayeb's results from [33,2] on existence and regularity associated with the linear Vlasov-Boltzmann equation (1).…”

“…The discontinuous Galerkin (DG) finite element method, which is well suited for hp-adaptivity and parallel implementation, recently gained much attention in this field [12,10,13].…”

“…Consequently, deterministic methods are more competitive when greater accuracy is required. A comparative study of DSMC and deterministic solvers by WENO [8,9] and DG schemes [11,10,12,13,14] for short base channel models by 1-dimensional electron transport models and 2-dimensional MESFET and MOSFET devices have been carried out. There are important discrepancies between both methods near ohmic contacts and interface layers.…”

“…For more details about the RKDG scheme, one can refer to the survey paper [24] and the references within. Very recently in [11,10,12,13], DG schemes for solving the Boltzmann-Poisson system in semiconductor device modeling are proposed. The scheme shows excellent behavior in terms of quality of the numerical solution and computational efficiency.…”

“…A DG implementation for this system in realistic sub-micron highly heterogeneous structures was developed by the authors in collaboration with A. Majorana and C.W. Shu; see [11,10,12,13].…”