讲座论坛
荔园数学讲坛: A positivity-preserving finite element method for quantum drift-diffusion model
发布时间:2022-04-22 17:25:17 2258


内容摘要: 

We propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion model. The model consists of five nonlinear elliptic equations, and two of them describe quantum corrections for quasi-Fermi levels. We propose an interpolated-exponential finite element (IEFE) method for solving the two quantum-correction equations. The IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction equations. Moreover, we solve the two continuity equations with the edge-averaged finite element (EAFE) method to reduce numerical oscillations of quasi-Fermi levels. The Poisson equation of electrical potential is solved with standard Lagrangian finite elements. We prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional. A Newton method is proposed to solve the nonlinear discrete problem. Numerical experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V.

主讲人简介: 

郑伟英,中国科学院数学与系统科学研究院研究员。1996、1999年于郑州大学数学系分别获学士和硕士学位;2002年博士毕业于北京大学数学科学学院。主要从事电磁场和半导体器件的计算方法和理论研究。2017年获得国家杰出青年科学基金资助,2021年获冯康科学计算奖。

腾讯会议号:365-937-845

会议链接:https://meeting.tencent.com/dm/ljBi1U9ANiQ4