Fast lithographic source pupil optimization using difference of convex functions algorithm for transformed L1 penalty

Yiyu Sun; Yanqiu Li; Guanghui Liao; Miao Yuan; Yang Liu; Yaning Li; Lulu Zou; Lihui Liu

doi:10.1117/12.2604052

1 November 2021 Fast lithographic source pupil optimization using difference of convex functions algorithm for transformed L₁ penalty

Yiyu Sun, Yanqiu Li, Guanghui Liao, Miao Yuan, Yang Liu, Yaning Li, Lulu Zou, Lihui Liu

Author Affiliations +

Proceedings Volume 12057, Twelfth International Conference on Information Optics and Photonics; 120570I (2021) https://doi.org/10.1117/12.2604052
Event: Twelfth International Conference on Information Optics and Photonics, 2021, Xi'an, China

Abstract

Fast source pupil optimization (SO) has appeared as an important technique for improving lithographic imaging fidelity and process window (PW) in holistic lithography at 7-5nm node. Gradient-based methods are generally used in current SO. However, most of these methods are time-consuming. In our previous work, compressive sensing (CS) theory is applied to accelerate the SO procedure, where the SO is formulated as an underdetermined linear problem by randomly sampling monitoring pixels on mask features. CS-SO theory assumes that the source pattern is a sparse pattern on a certain basis, then the SO is transformed into a L₁-norm or L_p-norm (0<p<1) image reconstruction problem. However, above methods are relaxation approaches of L₀-norm method for convenient achievement. In this paper, to our best knowledge, transformed L1 penalty (TL1) and the difference of convex functions algorithm (DCA) for TL1 (DCATL1) are first developed to solve this inverse lithography SO problem in advantages. The source pattern is optimized by minimizing cost function pattern error with TL1 penalty. The DCATL1 method decomposes this cost function into the difference of two convex functions. By linearizing one convex function, the SO procedure can be transformed into a sequence of strongly convex minimization sub-problems, which can be accurately and efficiently solved by the Fast Alternating Direction Method of Multipliers (Fast ADMM) algorithm. Compared to previous methods, DCATL1 method can simultaneous realize fast and robust SO.

Citation Download Citation

Yiyu Sun, Yanqiu Li, Guanghui Liao, Miao Yuan, Yang Liu, Yaning Li, Lulu Zou, and Lihui Liu "Fast lithographic source pupil optimization using difference of convex functions algorithm for transformed L₁ penalty", Proc. SPIE 12057, Twelfth International Conference on Information Optics and Photonics, 120570I (1 November 2021); https://doi.org/10.1117/12.2604052

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KEYWORDS

Lithography

Algorithm development

Optimization (mathematics)

Imaging systems

Compressed sensing

Zernike polynomials

Lithium

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