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三维半导体器件漂移扩散模型的并行有限元方法研究

王芹1,2, 马召灿1,2, 白石阳1,2, 张林波1,2, 卢本卓1,2, 李鸿亮3   

  1. 1 LSEC, 国家数学与交叉科学中心, 中国科学院数学与系统科学研究院, 计算数学与科学工程计算研究所, 北京 100190;
    2 中国科学院大学数学科学学院, 北京 100049;
    3 四川师范大学数学科学学院, 成都 610066
  • 收稿日期:2020-04-02 出版日期:2020-06-15 发布日期:2020-06-15
  • 通讯作者: 李鸿亮,lihongliang@mtrc.ac.cn
  • 基金资助:

    科学挑战专题(TZ2016003),国家重点研发计划(2016YFB0201304),NSFC(11771435).

王芹, 马召灿, 白石阳, 张林波, 卢本卓, 李鸿亮. 三维半导体器件漂移扩散模型的并行有限元方法研究[J]. 数值计算与计算机应用, 2020, 41(2): 85-104.

Wang Qin, Ma Zhaocan, Bai Shiyang, Zhang Linbo, Lu Benzhuo, Li Hongliang. RESEARCH ON PARALLEL FINITE ELEMENT METHODS FOR THE DRIFT-DIFFUSION MODEL IN SEMICONDUCTOR DEVICE SIMULATIONS[J]. Journal of Numerical Methods and Computer Applications, 2020, 41(2): 85-104.

RESEARCH ON PARALLEL FINITE ELEMENT METHODS FOR THE DRIFT-DIFFUSION MODEL IN SEMICONDUCTOR DEVICE SIMULATIONS

Wang Qin1,2, Ma Zhaocan1,2, Bai Shiyang1,2, Zhang Linbo1,2, Lu Benzhuo1,2, Li Hongliang3   

  1. 1 LSEC, NCMIS, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
    2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
    3 Department of Mathematics, Sichuan Normal University, Chengdu 610066, China
  • Received:2020-04-02 Online:2020-06-15 Published:2020-06-15
本文设计了一种新的三维自适应迎风稳定化有限元方法(SUPG-IP),并对比研究了几种半导体器件模拟的并行有限元方法.数值模拟结果表明:稳定化有限元方法适用于大偏压以及高掺杂器件模拟;而经典的Zlamal有限元方法更适用于计算半导体器件的电学响应曲线.我们基于三维并行自适应有限元平台PHG开发了半导体器件漂移扩散模型求解器DevSim,并对几种典型的半导体器件进行了模拟测试.计算结果与商业软件Sentaurus吻合较好,验证了算法的有效性.我们对PN结进行了超大规模网格并行模拟测试,网格达8亿单元并使用2048进程计算,展示了算法良好的并行可扩展性.
In this paper, we propose a novel 3D adaptive upwind stabilized finite element method (SUPG-IP), and perform a study to compare several parallel finite element methods for semiconductor device simulations. Numerical results show that the stabilized finite element methods are applicable to problems with large biases and high doping concentrations, while the classic Zlamal finite element method is more suitable for calculation of electrical characteristics of devices. Based on the three-dimensional parallel adaptive finite element toolbox PHG, a Drift-Diffusion model solver, DevSim, for semiconductor device simulations is developed. It is applied to simulating several typical semiconductor devices. The results are consistent with those of the commercial software Sentaurus, which verifies the effectiveness of the algorithms. A large-scale numerical experiment of PN diode, with 800 million elements and 2048 MPI processes, was carried out, demonstrating good parallel scalability of the algorithms.

MR(2010)主题分类: 

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