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:在本文中, 我们考虑一个半导体装置, 其活性区域由单层材料组成。 相关的静电潜能值 Poisson 等方程式( 为了进行自相兼容的计算, 需要解决) 的特征是, 在单层周围的区域, 表面粒子密度和飞机外电流允许性。 为了避免在这样的区域进行网状改进, 我们根据物理设备建议的自然域分解, 提出一个界面问题 。 讨论了两个不同的界面连续性条件 。 然后, 我们写出相应的变异配方, 调整所谓的三野配方以进行域分解, 我们用适当的有限元素方法来比较这些配方。 最后, 进行数字实验, 以说明这种界面方法的某些具体特征 。