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Volume 16, Issue 3
An Alternating Direction Method of Multipliers for Inverse Lithography Problem

Junqing Chen & Haibo Liu

DOI: 10.4208/nmtma.OA-2022-0151

Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 820-846.

Published online: 2023-08

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  • 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.

  • Keywords

Inverse lithography techniques, ADMM framework, total variation regularization.

  • AMS Subject Headings

78A46, 78M50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-16-820, author = {Chen , Junqing and Liu , Haibo}, title = {An Alternating Direction Method of Multipliers for Inverse Lithography Problem}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2023}, volume = {16}, number = {3}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2022-0151}, url = {http://global-sci.org/intro/article_detail/nmtma/21968.html} }
TY - JOUR T1 - An Alternating Direction Method of Multipliers for Inverse Lithography Problem AU - Chen , Junqing AU - Liu , Haibo JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 820 EP - 846 PY - 2023 DA - 2023/08 SN - 16 DO - http://doi.org/10.4208/nmtma.OA-2022-0151 UR - https://global-sci.org/intro/article_detail/nmtma/21968.html KW - Inverse lithography techniques, ADMM framework, total variation regularization. AB -

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.

Chen , Junqing and Liu , Haibo. (2023). An Alternating Direction Method of Multipliers for Inverse Lithography Problem. Numerical Mathematics: Theory, Methods and Applications. 16 (3). 820-846. doi:10.4208/nmtma.OA-2022-0151
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