On Composite Discontinuous Galerkin Method for simulations of electric properties of semiconductor devices

TL;DR

This paper introduces a Composite Discontinuous Galerkin Method based on SIPG for simulating electric properties of semiconductor devices, effectively handling interface irregularities and providing error estimates and numerical validation.

Contribution

It develops a novel discretization approach for the van Roosbroeck equations using a Composite Discontinuous Galerkin Method tailored for semiconductor device interfaces.

Findings

The method is well-defined and yields unique solutions.

Error estimates are rigorously derived.

Numerical simulations confirm the method's effectiveness.

Abstract

In this paper, a variant of discretization of the van Roosbroeck equations in the equilibrium state with the Composite Discontinuous Galerkin Method for the rectangular domain is discussed. It is based on Symmetric Interior Penalty Galerkin (SIPG) method. The proposed method accounts for lower regularity of the solution on the interfaces of devices' layers. It is shown that the discrete problem is well-defined and that discrete solution is unique. Error estimates are derived. Finally, numerical simulations are presented.