Special Section on Computational Lithography

On the uniqueness of optical images and solutions of inverse lithographical problems

[+] Author Affiliations
Yuri Granik

Mentor Graphics Corporation, 1001 Ridder Park Drive, San Jose, California 95131

J. Micro/Nanolith. MEMS MOEMS. 8(3), 031405 (July 02, 2009). doi:10.1117/1.3158613
History: Received October 29, 2008; Revised May 13, 2009; Accepted May 18, 2009; Published July 02, 2009
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We analyze the uniqueness of the solutions of inverse lithographical problems, stated as optimization problems, and optical images. By considering a band-limitedness argument, examples of ill-posed problems are constructed with multiple solutions in the domain of real non-negative passive masks. We conclude that the necessary condition for the solution m to be unique is to touch (or to pass infinitely close to) the boundary of the constraint 0m1. In the domain of binary masks, we propose a procedure to construct two nonunique solutions from a possibly unique one. We prove the existence of unique binary solutions in some class of optical systems and suggest a thresholding procedure to generate a unique solution from a possibly nonunique one.

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© 2009 Society of Photo-Optical Instrumentation Engineers

Citation

Yuri Granik
"On the uniqueness of optical images and solutions of inverse lithographical problems", J. Micro/Nanolith. MEMS MOEMS. 8(3), 031405 (July 02, 2009). ; http://dx.doi.org/10.1117/1.3158613


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