Gradient-based inverse lithography for EUV masks via the waveguide method and a physics-informed neural operator

The key novelty is treating the entire mask-to-wafer physics pipeline as differentiable end-to-end, which means mask designers can now compute gradients backward through waveguide simulation itself rather than relying on discrete trial-and-error loops. Prior work either used gradient-free black-box optimization or treated neural networks as pure surrogates; this fuses both.

This connects directly to the black-box optimization unification paper from earlier this month. That work showed how gradient-free methods (Evolution Strategies, consensus-based approaches) differ only in aggregation and scope. This EUV work inverts the problem: by making physics differentiable, it eliminates the need for black-box methods entirely in this domain. The trade-off is now explicit: you gain gradient information but must commit to a specific physics model (waveguide approximation). For practitioners, this means mask optimization moves from the robustness-vs-performance dial that black-box methods offer to a precision-vs-model-fidelity dial instead.

If this framework ships in a commercial mask design tool (ASML, Synopsys, or equivalent) within 18 months and reduces mask iteration cycles from weeks to days on real 3nm or 2nm production runs, the differentiable physics approach has crossed from research to manufacturing. If it remains confined to academic benchmarks or only handles simplified absorber materials, the industrial constraints (thermal stability, process variation) likely remain unsolved.