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

Area of Science:

• Computational lithography
• Semiconductor manufacturing processes
• Numerical optimization techniques

Background:

• Source mask optimization (SMO) is crucial for process stability in advanced optical lithography (22 nm and beyond).
• Existing SMO algorithms are computationally intensive due to nonlinear optimization challenges.

Purpose of the Study:

• To develop a fast algorithm for solving source mask optimization (SMO) problems.
• To improve computational efficiency and convergence speed for SMO.
• To enhance pattern fidelity and process stability in optical lithography.

Main Methods:

• Developed a novel algorithm based on augmented Lagrangian methods (ALMs) for SMO.
• Utilized variable splitting to convert the optimization problem into a constrained form.
• Employed alternating minimization and quasi-Newton methods for efficient sub-problem solving and accelerated convergence.

Main Results:

• The proposed ALM-based algorithm significantly accelerates SMO convergence.
• Demonstrated improved pattern fidelity compared to existing methods.
• The method provides a straightforward implementation for practical application.

Conclusions:

• The fast ALM algorithm offers an effective solution for computationally intensive SMO problems.
• This approach enhances process stability and pattern fidelity in advanced optical lithography.
• The developed method contributes to overcoming challenges in next-generation semiconductor manufacturing.