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Memory efficient constrained optimization of scanning-beam lithography

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posted on 2025-05-09, 03:02 authored by Carl Jidling, Andrew FlemingAndrew Fleming, Adrian WillsAdrian Wills, Thomas B. Schon
This article describes a memory efficient method for solving large-scale optimization problems that arise when planning scanning-beam lithography processes. These processes require the identification of an exposure pattern that minimizes the difference between a desired and predicted output image, subject to constraints. The number of free variables is equal to the number of pixels, which can be on the order of millions or billions in practical applications. The proposed method splits the problem domain into a number of smaller overlapping subdomains with constrained boundary conditions, which are then solved sequentially using a constrained gradient search method (L-BFGS-B). Computational time is reduced by exploiting natural sparsity in the problem and employing the fast Fourier transform for efficient gradient calculation. When it comes to the trade-off between memory usage and computational time we can make a different trade-off compared to previous methods, where the required memory is reduced by approximately the number of subdomains at the cost of more computations. In an example problem with 30 million variables, the proposed method reduces memory requirements by 67% but increases computation time by 27%. Variations of the proposed method are expected to find applications in the planning of processes such as scanning laser lithography, scanning electron beam lithography, and focused ion beam deposition, for example.

Funding

ARC

DP210103383

History

Journal title

Optics Express

Volume

30

Issue

12

Pagination

20564-20579

Publisher

Optica Publishing Group

Language

  • en, English

College/Research Centre

College of Engineering, Science and Environment

School

School of Engineering

Rights statement

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement.

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