基于混合本征模匹配的光刻掩膜分析方法研究

doi:10.12305/j.issn.1001-506X.2023.11.02

系统工程与电子技术 ›› 2023, Vol. 45 ›› Issue (11): 3374-3381.doi: 10.12305/j.issn.1001-506X.2023.11.02

基于混合本征模匹配的光刻掩膜分析方法研究

刘佳¹^,*, 苏珉², 徐群玉³

1. 北京航空航天大学前沿科学技术创新研究院, 北京 100191
2. 广西师范大学电子与信息工程学院, 广西桂林 541004
3. 中国民航科学技术研究院民航法规与标准化研究所, 北京 100028

收稿日期:2022-04-25 出版日期:2023-10-25 发布日期:2023-10-31
通讯作者: 刘佳
作者简介:刘佳(1985—), 男, 副研究员, 博士, 主要研究方向为雷达目标特性建模、雷达目标识别算法、计算电磁学
苏珉(1985—), 男, 讲师, 博士, 主要研究方向为目标散射特性建模与分析、雷达目标识别、计算电磁学
徐群玉(1985—), 女, 助理研究员, 博士, 主要研究方向为机场安全监视、目标检测与识别、民航标准化体系与技术研究
基金资助:
国家自然科学基金(62371018);北航卓越百人计划专项基金(KG21000501);广西自然科学基金(2020GXNSFBA297119);广西科技基地和人才专项(桂科AD20238025)

Research on hybrid eigenmode restoration and mode matching algorithm for computational lithography problems

Jia LIU¹^,*, Min SU², Qunyu XU³

1. Research Institute for Frontier Science, Beihang University, Beijing 100191, China
2. School of Electronic and Information Engineering, Guangxi Normal University, Guilin 541004, China
3. Research Institute of Civil Aviation Law, China Academy of Civil Aviation Science and Technology, Beijing 100028, China

Received:2022-04-25 Online:2023-10-25 Published:2023-10-31
Contact: Jia LIU

摘要/Abstract

摘要：

隐式模式匹配是分析波导结构电磁特性常用的数值方法。分析了现有隐式模式匹配方法在解决计算光刻问题上存在的局限性, 以该方法为基础, 提出了基于Krylov子空间理论的混合本征模重构以及显式模式匹配方法。修正了隐式模式匹配方法中采用的非严格迭代策略导致的本征模精度不足问题, 算法计算复杂度保持在O(N^1.5)。采用典型波导及周期结构对所提算法的精度及效率进行了验证。通过对高复杂度光刻掩膜结构进行仿真, 将计算结果与高频结构仿真器软件以及严格耦合波分析(rigorous coupled wave analysis, RCWA)算法结果进行了对比, 验证了本文所提方法在分析高复杂度光刻问题中的应用价值和效率优势。

关键词: 计算电磁学, 模式匹配, 计算光刻

Abstract:

Implicit mode matching is a popular analyzing method for waveguide structures in computational electromagnetic. This paper discusses the limitation of conventional implicit mode matching method for solving computational lithography problems. Based on the existing implicit mode matching method, a hybrid eigenmode restoration algorithm based on Krylov subspace theory and a explicit mode matching method are proposed. The eigenmode accuracy loss caused by Lanczos method and other problems are solved while preserving the O(N^1.5) complexity. Benchmark cases for representative waveguide and periodic structures verify the restored eigenmode accuracy and efficiency characters of the proposed method. A simulation case for highly complicated lithography mask structure is presented, and results compared with high frequency structure simulator (HFSS) software and rigorous coupled wave analysis (RCWA) method indicate the application significance of the proposed method in solving highly complicated computational lithography problems.

Key words: computational electromagnetics, mode matching, computational lithography

中图分类号:

O436.1

刘佳, 苏珉, 徐群玉. 基于混合本征模匹配的光刻掩膜分析方法研究[J]. 系统工程与电子技术, 2023, 45(11): 3374-3381.

Jia LIU, Min SU, Qunyu XU. Research on hybrid eigenmode restoration and mode matching algorithm for computational lithography problems[J]. Systems Engineering and Electronics, 2023, 45(11): 3374-3381.

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参考文献 30

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数值算法及参数	TE极化		TM极化
迭代步数	200	300	200	300
隐式模式匹配	0.07	0.04	0.08	0.03
显式模式匹配	0.03	0.009	0.05	0.008

数值算法	传输系数	相位
RCWA	0.042	0.033
隐式模式匹配	0.056	0.029
显式模式匹配	0.040	0.031

数值算法	193 nm	217 nm
RCWA/s	0.042	0.033
隐式模式匹配/s	0.056	0.029
显式模式匹配/s	0.040	0.031

数值算法	193 nm	217 nm
RCWA/MB	1 424	1 233
隐式模式匹配/MB	470	411
显式模式匹配/MB	859	792

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[2]	姬金祖, 刘战合, 黄沛霖, 李洁. 反射张量在射线追踪法中的应用[J]. Journal of Systems Engineering and Electronics, 2011, 33(8): 1685-1689.

基于混合本征模匹配的光刻掩膜分析方法研究

Research on hybrid eigenmode restoration and mode matching algorithm for computational lithography problems

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