Constraint-Aware Robustness and Multi-Objective Synthesis of Multi-Layer DUV Interference Coatings

The evolution of 193 nm deep-ultraviolet (DUV) lithography toward high numerical aperture (NA > 1.35) presents challenges approaching physical limits for antireflective (AR) coatings on strongly curved lens elements. In this study, a full-stack multi-objective optimization framework is developed by coupling the Non-dominated Sorting Genetic Algorithm II (NSGA-II) with the Transfer Matrix Method (TMM) to optimize a 7-layer LaF3/MgF2 system on strongly curved substrates (R=150 mm). The model integrates material dispersion, thermo-optic effects, deposition flux deviations, and manufacturing thickness constraints. Following 1500 generations of optimization and TOPSIS-based decision-making, the selected Pareto optimal solution achieves a full-aperture average reflectance of 1.3633% and a radial uniformity of 9.5037%. The design further exhibits high environmental robustness with a thermal drift of 0.0019% and a residual stress of 39.23 MPa. These results demonstrate that the proposed method overcomes the critical process bottleneck of achieving full-aperture uniformity below 10% on strongly curved optics. This framework provides a general paradigm for the robust design of next-generation ultra-precision DUV optical systems, effectively balancing theoretical depth with engineering feasibility.