Discontinuous Galerkin finite element methods and applications to Boltzmann-Poisson models in semiconductor device simulation

In modern highly integrated devices, the charge carrier transport can be described by the semiclassical Boltzmann-Poisson (BP) system. While Monte-Carlo method was traditionally used to simulate this system, in recent years, deterministic solvers were proposed because they offer more reliable results without having any statistical noise.

This talk will focus on discontinuous Galerkin (DG) finite element methods and their applications to BP models. I will first review the DG methods with an emphasis on my past research in this area. Then we move on to the introduction of the Boltzmann equation and its application in semiconductor device modeling. Some of our recent work on DG methods for solving the full-band BP models will be discussed. Numerical tests are provided to benchmark the scheme with Monte-Carlo and finite difference solvers. I will conclude with ongoing projects on positivity-preserving DG schemes for linear Boltzmann equations.