Analysis of an inverse problem arising in photolithography

Luca Rondi, Fadil Santosa

Research output: Contribution to journalReview articlepeer-review

1 Scopus citations


We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship between the target shape and the unknown is modeled through diffractive optics. We develop a variational formulation that is well-posed and propose an approximation that can be shown to have convergence properties. The approximate problem can serve as a foundation to numerical methods, much like the AmbrosioTortorelli's approximation of the MumfordShah functional in image processing.

Original languageEnglish (US)
Article number1150026
JournalMathematical Models and Methods in Applied Sciences
Issue number5
StatePublished - May 2012

Bibliographical note

Funding Information:
The authors learned about the inverse problem of photolithography from Apo Sezginer who gave a seminar on this topic at the Institute for Mathematics and its Applications in 2004. We thank Dr. Sezginer for helpful discussions. L.R. is partially supported by GNAMPA under 2008 and 2009 projects. Part of this work was done while L.R. was visiting the School of Mathematics at the University of Minnesota, Minneapolis, USA, whose support and hospitality is gratefully acknowledged. F.S.’s research is supported in part by NSF award DMS0807856.


  • Photolithograpy
  • sets of finite perimeter
  • shape optimization
  • Γ-convergence


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