Strongly out-of-equilibrium simulations for electron Boltzmann transport equation using modal discontinuous Galerkina approach

Abstract

In this study, we present simulations of strongly out-of-equilibrium conditions for the one-dimensional electron Boltzmann transport equation (BTE) in semiconductor devices. An explicit modal discontinuous Galerkin method is employed to solve the electron BTE along with the simplest collisional model–relaxation time approximation. The electron BTE system is discretized in momentum and time, and applied to the description of the dynamics of non-linear electron transport under a strong static electric field. A third-order explicit SSP-RK scheme is adopted for the temporal discretization of the resulting semi-discrete ODE. For the steady-state electron BTE, the analytical solutions are derived at low and high electric fields which are used to validate the numerical approach. The computed solution show a good agreement with derived analytic solution in wide range of tested parameters and regimes. An extensive range of numerical simulations has also been performed to investigate the impact of exploited flow parameters on the electron BTE solutions. Ultimately, these results predict that the modal DG approach is particularly effective in treating the strongly out-of-equilibrium regimes encountered like in ultrafast transport dynamics.