Speaker: Dr. Hengbin An (安恒斌研究员)

Time: 12:10-13:10, 13 October 2022 (Thursday) (Beijing time)

Venue: A103, Lijiao Building

Tencent Meeting ID: 532-263-431

Abstract

The drift-diffusion equations are a class of nonlinear systems in the application of semiconductor devices. High efficient solution methods for solving these equations play a significant role in numerical simulations. Some nonlinear iterative methods, including Newton method and Gummel method, are usually used to solve the discretized drift-diffusion equations. Therefore, a nonlinear initial iterate should be given. The nonlinear initial iterate has a strong influence on the solution method. Typically, the related physical values in the equilibrium state, including the potential, the electron concentration, and the hole concentration, are used as the initial iterate for solving the equations with a given bias voltage. Due to the strong nonlinearity, by using the typical initial iterate, the nonlinear iterative methods converge slowly or even diverge when the given bias voltage is large. In this paper, an efficient initial iterate is constructed by exploiting the application features of the drift-diffusion equations. The key idea is to construct an approximate equation of the drift-diffusion equations by neglecting the recombination effect and casting the effects of the bias voltage on carriers' quasi-Fermi potential. And the initial iterate is obtained by solving the approximate equation. Some physical interpretations and theoretical analyses for the proposed method are given. Numerical results show that the proposed initial iterate is effective, and the number of nonlinear iterations can be reduced by about 90\% at most compared to the typical initial iterate. In some cases, the nonlinear iteration does not converge when the typical initial iterate is used, while the iteration converges if the new initial iterate is used.

About Dr. An

安恒斌，北京应用物理与计算数学研究所研究员，博士生导师，中物院高性能数值模拟软件中心首席专家，中物院高性能数值模拟软件中心数值团队负责人。2004年毕业于中科院数学与系统科学研究院，获博士学位；2004年至2006年在北京应用物理与计算数学研究所从事博士后科研工作；2006年博士后出站并留所工作。主要从事大规模线性与非线性代数方程组并行求解算法研究与软件研制。曾获应用数值代数奖、军队科技进步一等奖、中国博士后科学基金一等资助等。主持国家自然科学基金、国家重点研发计划、军口973项目以及国防基础科研核科学挑战专题等项目多项。