半导体器件方程混合有限元三步两层网格法

Three-Step Two-Grid Algorithm Based on Mixed Finite Element Method for Semiconductor Device Equations

摘要: 半导体器件数值模拟一直是科学家们关注的重要领域。本文研究半导体器件的非线性方程组，对电子位势方程和两个浓度方程均采用混合有限元法进行离散，并构造了一种有效求解的三步两层网格算法。混合有限元法离散方程可以同时给出未知函数和未知函数通量同等阶数的误差逼近，也具有局部守恒性。三步两层网格算法不仅保持了数值解的可靠性和收敛阶，还大大缩短了计算时间。所以本研究具有重要的理论和实际意义，可为半导体器件的设计优化提供有力支持。

Abstract: Numerical simulation of semiconductor devices has always been an important area of interest for scientists. In this paper, the nonlinear equations of semiconductor device are studied. We use a mixed finite element method to discretize the existing electron potential equation and two concen-tration equations, and construct an effective three-step two-grid algorithm. The mixed finite ele-ment method for discretizing equations can simultaneously provide error approximations of the unknown function itself and its flux of the same order, and also has local conservation. The three-step two-grid algorithm not only maintains the reliability and convergence order of the nu-merical solution, but also greatly reduces computational time. The research has great theoretical and practical significance, providing strong support for the design and optimization of semiconduc-tor device.