An interface formulation for the Poisson equation in the presence of a semiconducting single-layer material

TL;DR

This paper introduces an interface formulation for solving the Poisson equation in devices with single-layer semiconducting materials, enabling efficient numerical simulations without mesh refinement in the active region.

Contribution

It proposes a novel interface problem and variational formulation for the Poisson equation tailored to single-layer materials, improving computational efficiency.

Findings

Effective interface approach demonstrated through numerical experiments

Avoids mesh refinement in the active layer region

Adapts three-fields formulation for domain decomposition

Abstract

In this paper, we consider a semiconducting device with an active zone made of a single-layer material. The associated Poisson equation for the electrostatic potential (to be solved in order to perform self-consistent computations) is characterized by a surface particle density and an out-of-plane dielectric permittivity in the region surrounding the single-layer. To avoid mesh refinements in such a region, we propose an interface problem based on the natural domain decomposition suggested by the physical device. Two different interface continuity conditions are discussed. Then, we write the corresponding variational formulations adapting the so called three-fields formulation for domain decomposition and we approximate them using a proper finite element method. Finally, numerical experiments are performed to illustrate some specific features of this interface approach.