Aberration-balanced initial structure design of extreme ultraviolet lithography objective systems via hybrid optimization

The optimization of extreme ultraviolet lithography (EUVL) objective systems depends on establishing an aberration-balanced and structurally feasible initial structure. This study develops an optical model for the initial structure of EUVL objective systems based on the ray tracing theory and the primary aberration theory. A simulated annealing particle swarm optimization-sequential quadratic programming (SAPSO-SQP) algorithm is proposed to solve this optical model. A comparative analysis with the conventional particle swarm optimization (PSO) algorithm and the simulated annealing-particle swarm optimization (SA-PSO) algorithm indicates that the proposed method attains effective convergence and consistent stability across repeated simulations. Even with a population size of only 20, low-aberration solutions are effectively achieved, indicating low dependence on the initial solutions and strong robustness. With this population size, an EUVL objective system with a numerical aperture of 0.33 is designed using the established model and algorithm, without introducing freeform surfaces. Its root mean square (RMS) wavefront error is less than 0.016λ, and the distortion is less than 0.42 nm. Further tolerance analysis indicates that the RMS wavefront error remains below 0.033λ with 97% probability, demonstrating relaxed tolerance limits. The results validate the effectiveness of the proposed model and algorithm, providing a feasible and efficient hybrid optimization strategy for high-dimensional nonlinear optimization problems, particularly for the initial structural design of EUVL objective systems.