A Deterministic Solver for the 1D Non-Stationary Boltzmann-Poisson System for GaAs Devices: Bulk GaAs and GaAs n +-n i -n + Diode

We present a deterministic method for describing the electron transport in spatially one-dimensional gallium arsenide devices. This numerical procedure is based on the combination of kinetic Boltzmann-type equations for a two-valley model of the GaAs conduction band and the Poisson equation in order to consider the electrostatic potential self-consistently. All of the important intra- and intervalley scattering mechanisms for GaAs are taken into account. The dependence of the electron distribution functions on the electron wave vector is treated by means of the multigroup approach, whereas their spatial dependences are handled by a weighted essentially non-oscillatory (WENO) scheme. Numerical results are given for the main transport quantities as functions of time, position and electric field in bulk material and in a n⁺-n_i-n⁺ diode. In addition, the proposed numerical method is validated by comparing the results with those of Monte Carlo calculations and the influence of the discretization used in the numerical procedure is discussed.