Fast source optimization by clustering algorithm based on lithography properties

Masashi Tawada, Takaki Hashimoto, Keishi Sakanushi, Shigeki Nojima, Toshiya Kotani, Masao Yanagisawa, Nozomu Togawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


Lithography is a technology to make circuit patterns on a wafer. UV light diffracted by a photomask forms optical images on a photoresist. Then, a photoresist is melt by an amount of exposed UV light exceeding the threshold. The UV light diffracted by a photomask through lens exposes the photoresist on the wafer. Its lightness and darkness generate patterns on the photoresist. As the technology node advances, the feature sizes on photoresist becomes much smaller. Diffracted UV light is dispersed on the wafer, and then exposing photoresists has become more difficult. Exposure source optimization, SO in short, techniques for optimizing illumination shape have been studied. Although exposure source has hundreds of grid-points, all of previous works deal with them one by one. Then they consume too much running time and that increases design time extremely. How to reduce the parameters to be optimized in SO is the key to decrease source optimization time. In this paper, we propose a variation-resilient and high-speed cluster-based exposure source optimization algorithm. We focus on image log slope (ILS) and use it for generating clusters. When an optical image formed by a source shape has a small ILS value at an EPE (Edge placement error) evaluation point, dose/focus variation much affects the EPE values. When an optical image formed by a source shape has a large ILS value at an evaluation point, dose/focus variation less affects the EPE value. In our algorithm, we cluster several grid-points with similar ILS values and reduce the number of parameters to be simultaneously optimized in SO. Our clustering algorithm is composed of two STEPs: In STEP 1, we cluster grid-points into four groups based on ILS values of grid-points at each evaluation point. In STEP 2, we generate super clusters from the clusters generated in STEP 1. We consider a set of grid-points in each cluster to be a single light source element. As a result, we can optimize the SO problem very fast. Experimental results demonstrate that our algorithm runs speed-up compared to a conventional algorithm with keeping the EPE values.

Original languageEnglish
Title of host publicationDesign-Process-Technology Co-Optimization for Manufacturability IX
EditorsJohn L. Sturtevant, Luigi Capodieci
ISBN (Electronic)9781628415292
Publication statusPublished - 2015
EventDesign-Process-Technology Co-Optimization for Manufacturability IX - San Jose, United States
Duration: 2015 Feb 252015 Feb 26

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


OtherDesign-Process-Technology Co-Optimization for Manufacturability IX
Country/TerritoryUnited States
CitySan Jose


  • Image Log Slope (ILS)
  • Lithography
  • Source Optimization (SO)

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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