Fast Mask Optimization Under Process Variation Using Guided Local Search on Quadratic Programming

In advanced optical lithography, it is critical to obtain a mask with high fidelity to a target pattern and strong tolerance to process variation within a short time. This paper formulates the mask optimization problem as a 0-1 convex Quadratically Constrained Quadratic Programming (0-1 QCQP) problem, aiming to maximize tolerance under fidelity constraints. We propose a fast pixel-based mask optimization algorithm, Guided Local Search for Mask Optimization (GLS-MO), which achieves high fidelity and tolerance. GLS-MO relaxes the 0-1 QCQP into a 0-1 convex Quadratic Programming problem by introducing Lagrange multipliers (LMs) that convert constraints into objectives. By dynamically adjusting LMs, GLS-MO balances fidelity and tolerance efficiently. The algorithm iteratively performs local searches until LM changes converge. During each local search, constraints are addressed by updating LMs using Weight Updating, which gradually reduces LM changes. Once a converged solution is found, LM changes are increased to escape local optima. GLS-MO employs Fourier interpolation and the Difference Map to estimate intensity values at evaluation points, minimizing computation time with acceptable error. In each iteration, the Gradient Deciding method determines the 0-1 value of each pixel. Experimental results confirm that GLS-MO achieves high fidelity to the target pattern and strong tolerance to process variation in a short time.