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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 11, Iss. 9 — Sep. 1, 1994
  • pp: 2438–2452

Phase-shifting masks for microlithography: automated design and mask requirements

Y. C. Pati and T. Kailath  »View Author Affiliations


JOSA A, Vol. 11, Issue 9, pp. 2438-2452 (1994)
http://dx.doi.org/10.1364/JOSAA.11.002438


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Abstract

The problem of automated design of phase-shifting masks for enhanced-resolution optical lithography is examined. We propose a computationally viable algorithm for the rapid design of phase-shifting masks for arbitrary two-dimensional patterns. Our approach is based on the use of a class of optimal coherent approximations to partially coherent imaging systems described by the Hopkins model. These approximations lead to substantial computational and analytical benefits, and, in addition, the resultant approximation error can be quite small for imaging systems with coherence factor σ ≤ 0.5. These approximate models allow us to reduce the mask-design problem to the classical phase-retrieval problem in optics. A fast iterative algorithm, closely related to the Gerchberg–Saxton algorithm, is then applied to generate (suboptimal) phase-shifting masks. Analytical results related to practical requirements for phase-shifting masks are also presented. These results address questions related to the number of discrete phase levels required for arbitrary patterns and provide some insight into alternative strategies for the use of phase-shifting masks. A number of simulated phase-shifting mask-design examples are provided to illustrate the methods and ideas presented.

© 1994 Optical Society of America

History
Original Manuscript: May 26, 1993
Revised Manuscript: March 9, 1994
Manuscript Accepted: March 10, 1994
Published: September 1, 1994

Citation
Y. C. Pati and T. Kailath, "Phase-shifting masks for microlithography: automated design and mask requirements," J. Opt. Soc. Am. A 11, 2438-2452 (1994)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-9-2438

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