A variational approach to the inverse photolithography problem

Luca Rondi, Fadil Santosa, Zhu Wang

Research output: Contribution to journalArticlepeer-review


Photolithography is a process in the production of integrated circuits in which a mask is used to create an exposed pattern with a desired geometric shape. In the inverse problem of photolithography, a desired pattern is given and the mask that produces an exposed pattern which is close to the desired one is sought. We propose a variational approach formulation of this shape design problem and introduce a regularization strategy. The main novelty in this work is the regularization term that makes the thresholding operation involved in photolithography stable. The potential of the method is demonstrated in numerical experiments.

Original languageEnglish (US)
Pages (from-to)110-137
Number of pages28
JournalSIAM Journal on Applied Mathematics
Issue number1
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016 Alexandre Munnier and Karim Ramdani.


  • A-convergence
  • Calculus of variations
  • Inverse problem
  • Photolithograpy
  • Sets of finite perimeter
  • Shape optimization


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