Finite Element Approach Based Numerical Framework for Device Simulator

Abstract

In this work, a finite element method (FEM)-based numerical framework is proposed to effectively calculate the drift-diffusion equations and compiled into a parallel computing device simulator. In this framework, a novel upwind FEM is developed to solve the convection dominated continuity equations. In the implementation of the upwind method, the vector basis functions are employed to interpolate the edge streamline upwind (SU) current densities into mesh grid to obtain the spatial current density, and then the scalar FEM is used to construct the element matrix equation. Through comparing the calculating results of a 2-D PN-junction with those obtained by the COMSOL Semiconductor, the accuracy of proposed framework is verified first. Then, through several numerical cases, its advantages in comparison with FBSG-, SU Petrov Galerkin (SUPG)-, or control-volume-finite-element method SUPG-based frameworks in terms of mesh grid adaptivity, computing stability, and efficiency are presented. At last, by combining the proposed framework with a domain decomposition scheme and a fully coupled Newton’s approach, a parallel computing device simulator is developed, including both steady-state and transient solvers. The performance of the in-house simulator is evaluated in terms of calculating accuracy, large-scale problem solution capability, and scalabilities.