Source optimization incorporating margin image average with conjugate gradient method

Jue Chin Yu, Peichen Yu*, Hsueh Yung Chao

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


Source optimization (SO) becomes increasingly important to resolution enhancement in sub-32 nm lithography nodes because the dense pattern configurations significantly limit the capability of mask correction. A key step in SO is the image formation by Abbe's method, which is a linear operation of integrating all source points' images incoherently to form aerial images. However, the aerial images are usually converted to resist images through the nonlinear sigmoid function. Such operation loses the merit of linearity in optimization and leads to slow convergence and time-consuming calculation. In this paper we propose a threshold-based linear resist model to replace the sigmoid model in SO. The effectiveness of our proposed model can be clearly seen from mathematical analysis. We also compare results based on linear and sigmoid models. Highly similar optimal sources are obtained, but the linear model has a significant advantage over the sigmoid in terms of convergence rate and simulation time. Furthermore, the process variations characterized by exposure-defocus (E-D) windows are still in similar trends for optimal sources based on two different resist models.

Original languageEnglish
Title of host publicationOptical Microlithography XXV
StatePublished - 31 May 2012
EventOptical Microlithography XXV - San Jose, CA, United States
Duration: 13 Feb 201216 Feb 2012

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


ConferenceOptical Microlithography XXV
CountryUnited States
CitySan Jose, CA


  • Computational imaging
  • Inverse problems
  • Microlithography
  • SMO
  • Source optimization

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