Cascadic multigrid algorithm for robust inverse mask synthesis in optical lithography

Wen Lv; Edmund Y. Lam; Haiqing Wei; Shiyuan Liu

doi:10.1117/1.JMM.13.2.023003

28 April 2014 Cascadic multigrid algorithm for robust inverse mask synthesis in optical lithography

Wen Lv, Edmund Y. Lam, Haiqing Wei, Shiyuan Liu

Journal of Micro/Nanolithography, MEMS, and MOEMS, Vol. 13, Issue 2, 023003 (April 2014). https://doi.org/10.1117/1.JMM.13.2.023003

Abstract

Robust inverse mask synthesis is computationally intensive, and its turnaround time continues to rise hand-in-hand with the ever-shrinking integrated circuit feature size. We report the development of a cascadic multigrid (CMG) algorithm for robust inverse mask synthesis, which starts from a relatively coarse mask grid and refines it iteratively in stages, so as to achieve significant speedup without compromising numerical accuracy. Since the CMG algorithm entails frequent changes of the computational grid size, we need to intentionally introduce an analytical circle-sampling technique for modeling the forward lithography imaging and employ an edge distance error as metric to guide mask synthesis. These two techniques work nicely with variable grid sizes and are well suited for our CMG algorithm. As a result, our algorithm achieves more than four times speedup over conventional methods that synthesize a mask on a fixed fine grid. Numerical results are presented to demonstrate the validity and efficiency of the proposed method.

CC BY: © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Wen Lv, Edmund Y. Lam, Haiqing Wei, and Shiyuan Liu "Cascadic multigrid algorithm for robust inverse mask synthesis in optical lithography," Journal of Micro/Nanolithography, MEMS, and MOEMS 13(2), 023003 (28 April 2014). https://doi.org/10.1117/1.JMM.13.2.023003

Published: 28 April 2014

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KEYWORDS

Photomasks

Lithography

Optical lithography

Semiconducting wafers

Algorithm development

Imaging systems

SRAF

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