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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 12 — Jun. 16, 2014
  • pp: 14180–14198

Inverse lithography source optimization via compressive sensing

Zhiyang Song, Xu Ma, Jie Gao, Jie Wang, Yanqiu Li, and Gonzalo R. Arce  »View Author Affiliations

Optics Express, Vol. 22, Issue 12, pp. 14180-14198 (2014)

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Source optimization (SO) has emerged as a key technique for improving lithographic imaging over a range of process variations. Current SO approaches are pixel-based, where the source pattern is designed by solving a quadratic optimization problem using gradient-based algorithms or solving a linear programming problem. Most of these methods, however, are either computational intensive or result in a process window (PW) that may be further extended. This paper applies the rich theory of compressive sensing (CS) to develop an efficient and robust SO method. In order to accelerate the SO design, the source optimization is formulated as an underdetermined linear problem, where the number of equations can be much less than the source variables. Assuming the source pattern is a sparse pattern on a certain basis, the SO problem is transformed into a l1-norm image reconstruction problem based on CS theory. The linearized Bregman algorithm is applied to synthesize the sparse optimal source pattern on a representation basis, which effectively improves the source manufacturability. It is shown that the proposed linear SO formulation is more effective for improving the contrast of the aerial image than the traditional quadratic formulation. The proposed SO method shows that sparse-regularization in inverse lithography can indeed extend the PW of lithography systems. A set of simulations and analysis demonstrate the superiority of the proposed SO method over the traditional approaches.

© 2014 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(110.5220) Imaging systems : Photolithography
(110.1758) Imaging systems : Computational imaging
(110.2945) Imaging systems : Illumination design

ToC Category:
Geometric Optics

Original Manuscript: February 6, 2014
Revised Manuscript: April 19, 2014
Manuscript Accepted: May 9, 2014
Published: June 3, 2014

Zhiyang Song, Xu Ma, Jie Gao, Jie Wang, Yanqiu Li, and Gonzalo R. Arce, "Inverse lithography source optimization via compressive sensing," Opt. Express 22, 14180-14198 (2014)

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