基于梯度的源掩模和混合Hopkins-Abbe模型的极化优化

IF 1.5 2区 物理与天体物理 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC
M. Ding, Zhiyuan Niu, Fang Zhang, Linglin Zhu, Weijie Shi, Aijun Zeng, Huijie Huang
{"title":"基于梯度的源掩模和混合Hopkins-Abbe模型的极化优化","authors":"M. Ding, Zhiyuan Niu, Fang Zhang, Linglin Zhu, Weijie Shi, Aijun Zeng, Huijie Huang","doi":"10.1117/1.JMM.19.3.033201","DOIUrl":null,"url":null,"abstract":"Abstract. Source mask and polarization optimization (SMPO) is a promising extension of the widely used resolution enhancement technology, source mask optimization (SMO), to further enhance chip manufacturability beyond 28-nm node. Our work is aimed to develop an efficient gradient-based SMPO method by employing the hybrid Hopkins–Abbe imaging model to fulfill the goal. In addition to source and mask variables, the model is adapted to also include polarization variables to realize the optimization. Compact formulas for forward and backward model application are derived. The computation benefits from precomputed transmission cross coefficients and features high efficiency. Validity of the method is confirmed by case studies. For dense array pattern case, the optimal source and polarization can be found analytically. SMPO optimized results match well with the theoretical expectations. In addition, process window, mask error enhancement factor, and normalized image log-slope for the studied cases all get improved over the counterpart SMO results, which employ commonly used polarization. Runtime analysis shows the method is computationally efficient. Our work provides a valid way to optimize polarization together with source and mask.","PeriodicalId":16522,"journal":{"name":"Journal of Micro/Nanolithography, MEMS, and MOEMS","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Gradient-based source mask and polarization optimization with the hybrid Hopkins–Abbe model\",\"authors\":\"M. Ding, Zhiyuan Niu, Fang Zhang, Linglin Zhu, Weijie Shi, Aijun Zeng, Huijie Huang\",\"doi\":\"10.1117/1.JMM.19.3.033201\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. Source mask and polarization optimization (SMPO) is a promising extension of the widely used resolution enhancement technology, source mask optimization (SMO), to further enhance chip manufacturability beyond 28-nm node. Our work is aimed to develop an efficient gradient-based SMPO method by employing the hybrid Hopkins–Abbe imaging model to fulfill the goal. In addition to source and mask variables, the model is adapted to also include polarization variables to realize the optimization. Compact formulas for forward and backward model application are derived. The computation benefits from precomputed transmission cross coefficients and features high efficiency. Validity of the method is confirmed by case studies. For dense array pattern case, the optimal source and polarization can be found analytically. SMPO optimized results match well with the theoretical expectations. In addition, process window, mask error enhancement factor, and normalized image log-slope for the studied cases all get improved over the counterpart SMO results, which employ commonly used polarization. Runtime analysis shows the method is computationally efficient. Our work provides a valid way to optimize polarization together with source and mask.\",\"PeriodicalId\":16522,\"journal\":{\"name\":\"Journal of Micro/Nanolithography, MEMS, and MOEMS\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2020-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Micro/Nanolithography, MEMS, and MOEMS\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1117/1.JMM.19.3.033201\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Micro/Nanolithography, MEMS, and MOEMS","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1117/1.JMM.19.3.033201","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 2

摘要

摘要源掩膜和偏振优化(SMPO)是广泛应用的分辨率增强技术——源掩膜优化(SMO)的一个有前途的扩展,可以进一步提高芯片在28nm节点以上的可制造性。我们的工作旨在开发一种有效的基于梯度的SMPO方法,采用混合霍普金斯-阿贝成像模型来实现这一目标。除了源和掩模变量外,该模型还适应了极化变量以实现优化。推导了正向和反向模型应用的简洁公式。计算得益于预先计算的传输交叉系数,具有较高的效率。通过实例验证了该方法的有效性。在密集阵图情况下,可以解析找到最优的源和极化。SMPO优化结果与理论预期吻合较好。此外,在处理窗口、掩模误差增强因子、归一化图像对数斜率等方面均比采用常用偏振的SMO结果有所改善。运行时分析表明,该方法计算效率高。我们的工作提供了一种有效的方法来优化偏振与源和掩模。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Gradient-based source mask and polarization optimization with the hybrid Hopkins–Abbe model
Abstract. Source mask and polarization optimization (SMPO) is a promising extension of the widely used resolution enhancement technology, source mask optimization (SMO), to further enhance chip manufacturability beyond 28-nm node. Our work is aimed to develop an efficient gradient-based SMPO method by employing the hybrid Hopkins–Abbe imaging model to fulfill the goal. In addition to source and mask variables, the model is adapted to also include polarization variables to realize the optimization. Compact formulas for forward and backward model application are derived. The computation benefits from precomputed transmission cross coefficients and features high efficiency. Validity of the method is confirmed by case studies. For dense array pattern case, the optimal source and polarization can be found analytically. SMPO optimized results match well with the theoretical expectations. In addition, process window, mask error enhancement factor, and normalized image log-slope for the studied cases all get improved over the counterpart SMO results, which employ commonly used polarization. Runtime analysis shows the method is computationally efficient. Our work provides a valid way to optimize polarization together with source and mask.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
3.40
自引率
30.40%
发文量
0
审稿时长
6-12 weeks
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信