Year: 2023
Author: Junqing Chen, Haibo Liu
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 3 : pp. 820–846
Abstract
We propose an alternating direction method of multipliers (ADMM) to solve an optimization problem stemming from inverse lithography. The objective functional of the optimization problem includes three terms: the misfit between the imaging on wafer and the target pattern, the penalty term which ensures the mask is binary and the total variation regularization term. By variable splitting, we introduce an augmented Lagrangian for the original objective functional. In the framework of ADMM method, the optimization problem is divided into several subproblems. Each of the subproblems can be solved efficiently. We give the convergence analysis of the proposed method. Specially, instead of solving the subproblem concerning sigmoid, we solve directly the threshold truncation imaging function which can be solved analytically. We also provide many numerical examples to illustrate the effectiveness of the method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0151
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 3 : pp. 820–846
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Inverse lithography techniques ADMM framework total variation regularization.