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

Abstract

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.

A direct multigroup-WENO solver for the 2D non-stationary Boltzmann–Poisson system for GaAs devices: GaAs-MESFET

“…3, we find values which exceed the maximum drift velocity of bulk GaAs (about 1.8 · 10 5 m s À1 at room temperature [9]) significantly. Thus, ballistic transport plays an important role in the considered device.…”

“…On the other hand, the charge accumulation, which is formed around the drain n-n + interface, is not found in the corresponding silicon device. As discussed in [9,17] for the GaAs n + -nÀn + diode, this enhanced electron density near the drain results from the backscattering of carriers into the active region after having already entered the high doping drain region. Due to this typical multi-valley effect, the anode contact cannot be simply treated as a drain for the electrons in the designing of submicron GaAs devices, since this region has a strong influence on the distribution of electrons in the active zone.…”

“…However, schemes which allow the investigation of the carrier transport in III-V compound semiconductor devices are still rare in the literature. As very recent examples, we refer to the WENO solver for the BP system of Cáceres et al [8] considering the electron transport in one-dimensional GaAs-diodes and to Galler and Schürrer [9] who study these devices with the help of a multigroup-WENO solver.…”

“…Therefore, we follow the main ideas proposed in [9] for simulating a 1D GaAs-diode and in [10], where a multigroup-WENO solver for 2D silicon devices is presented. We regard the multi-valley regime typical for polar semiconductors and take into account the anisotropy of some of the main scattering mechanisms of GaAs.…”