Memory efficient constrained optimization of scanning-beam lithography.

Area of Science:

• Computational Science
• Materials Science
• Electrical Engineering

Background:

• Scanning-beam lithography requires solving large-scale optimization problems to determine exposure patterns.
• Millions or billions of variables (pixels) pose significant computational challenges in practical applications.
• Existing methods face limitations in memory efficiency for these complex problems.

Purpose of the Study:

• To develop a memory-efficient method for solving large-scale optimization problems in scanning-beam lithography planning.
• To reduce the computational resources required for identifying optimal exposure patterns.
• To enable more efficient planning of advanced lithography processes.

Main Methods:

• The proposed method divides the problem domain into smaller, overlapping subdomains.
• Constrained boundary conditions are applied, and subdomains are solved sequentially using a constrained gradient search (L-BFGS-B).
• Exploits problem sparsity and uses the fast Fourier transform for efficient gradient calculation.

Main Results:

• Reduces memory requirements by approximately the number of subdomains used.
• Achieved a 67% reduction in memory for a 30 million variable problem.
• Increases computation time by 27% for the same problem, offering a different trade-off.

Conclusions:

• The developed method offers a significant memory reduction for large-scale optimization in lithography.
• This approach provides a flexible trade-off between memory usage and computational time.
• Expected to be applicable to scanning laser lithography, scanning electron beam lithography, and focused ion beam deposition planning.