Efficient source and mask optimization with augmented Lagrangian methods in optical lithography.

Source mask optimization (SMO) is a powerful and effective technique to obtain sufficient process stability in optical lithography, particularly in view of the challenges associated with 22 nm process technology and beyond. However, SMO algorithms generally involve computation-intensive nonlinear optimization. In this work, a fast algorithm based on augmented Lagrangian methods (ALMs) is developed for solving SMO. We first convert the optimization to an equivalent problem with constraints using variable splitting, and then apply an alternating minimization method which gives a straightforward implementation of the algorithm. We also use the quasi-Newton method to tackle the sub-problem so as to accelerate convergence, and a tentative penalty parameter schedule for adjustment and control. Simulation results demonstrate that the proposed method leads to faster convergence and better pattern fidelity.