半导体drift-diffusion模型的局部间断Galerkin方法及数值模拟

doi:10.6040/j.issn.1671-9352.0.2021.808

《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (4): 1-7.doi: 10.6040/j.issn.1671-9352.0.2021.808

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半导体drift-diffusion模型的局部间断Galerkin方法及数值模拟

肖红单,刘蕴贤^*

山东大学数学学院, 山东济南 250100

发布日期:2023-03-27
作者简介:肖红单(1995— ),女,硕士研究生,研究方向为偏微分方程数值解. E-mail:xiaohongdan@163.com*通信作者简介:刘蕴贤(1974— ),女,博士,教授,硕士生导师,研究方向为偏微分方程数值解.E-mail:yxliu@sdu.edu.cn
基金资助:
国家自然科学基金资助项目(12071262);山东省自然科学基金资助项目(ZR2020MA048)

Local discontinuous Galerkin method and numerical simulation of semiconductor drift-diffusion model

XIAO Hong-dan, LIU Yun-xian^*

School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Published:2023-03-27

摘要/Abstract

摘要： 考虑半导体drift-diffusion(DD)模型一维和二维问题的局部间断Galerkin(LDG)方法,并进行数值模拟。模拟一维问题时,在浓度变化剧烈的部分采用细网格,在浓度变化平缓的地方采用粗网格,并与均匀网格的数值模拟进行比较,实现了在非均匀剖分下节省空间剖分单元数并加快了运行速度的目的。模拟二维问题时,采用了Dirichlet和Neumann相结合的边界。数值结果验证了LDG方法的稳定性。

关键词: 半导体, drift-diffusion模型, 局部间断Galerkin方法

Abstract: This paper considers the local discontinuous Galerkin(LDG)method for one-dimensional and two-dimensional problems of semiconductor drift-diffusion(DD)model, and performs numerical simulations. When simulating a one-dimensional problem, fine meshes are used in the parts where the concentration changes sharply, and coarse meshes are used in the places where the concentration changes gently, and compared with the numerical simulation of uniform meshes, it realizes the purpose of saving space and dividing the number of elements and speeding up the running speed under non-uniform division. When simulating two-dimensional problems, a combination of Dirichlet and Neumann boundaries is used. Numerical results verify the stability of the LDG method.

Key words: semiconductor, drift-diffusion model, local discontinuous Galerkin method

中图分类号:

O241.82

肖红单,刘蕴贤. 半导体drift-diffusion模型的局部间断Galerkin方法及数值模拟[J]. 《山东大学学报(理学版)》, 2023, 58(4): 1-7.

XIAO Hong-dan, LIU Yun-xian. Local discontinuous Galerkin method and numerical simulation of semiconductor drift-diffusion model[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(4): 1-7.

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半导体drift-diffusion模型的局部间断Galerkin方法及数值模拟

Local discontinuous Galerkin method and numerical simulation of semiconductor drift-diffusion model

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