A discontinuous Galerkin solver for Boltzmann Poisson systems in nano devices

TL;DR

This paper introduces a discontinuous Galerkin finite element method for simulating electron transport in nano-scale semiconductor devices, effectively capturing transient behaviors and optical-phonon interactions.

Contribution

It develops a novel DG scheme tailored for Boltzmann-Poisson systems in nano devices, enabling accurate deterministic simulations of hot electron transport.

Findings

The DG method accurately models transient electron transport in silicon devices.

Results compare favorably with high-order WENO and DSMC simulations.

The approach effectively handles complex geometries on unstructured meshes.

Abstract

In this paper, we present results of a discontinuous Galerkin (DG) scheme applied to deterministic computations of the transients for the Boltzmann-Poisson system describing electron transport in semiconductor devices. The collisional term models optical-phonon interactions which become dominant under strong energetic conditions corresponding to nano-scale active regions under applied bias. The proposed numerical technique is a finite element method using discontinuous piecewise polynomials as basis functions on unstructured meshes. It is applied to simulate hot electron transport in bulk silicon, in a silicon $n^+$-$n$-$n^+$ diode and in a double gated 12nm MOSFET. Additionally, the obtained results are compared to those of a high order WENO scheme simulation and DSMC (Discrete Simulation Monte Carlo) solvers.