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.

翻译：本文研究了一种含有单层材料活性区的半导体器件。其中，用于自洽计算的电静势泊松方程由表面粒子密度和单层周围区域的离面介电常数共同表征。为避免对该区域进行网格细化，我们基于物理器件提供的自然区域分解，提出了一个界面问题。讨论了两种不同的界面连续性条件。随后，我们编写了相应的变分公式，采用了所谓的区域分解三场公式，并使用适当的有限元方法进行近似。最后，通过数值实验展示了该界面方法的一些特定特性。