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This work introduces a physics-informed neural operator (PINO) that leverages pseudo-spectral frequency-domain (PSFD) equations to efficiently tackle electromagnetic scattering in extreme ultraviolet (EUV) lithography. By factorizing the Fourier neural operator into lateral and axial branches and employing background decomposition, the method retains full-vector coupling without relying on finite-order Born approximations, significantly reducing computational costs. The PINO model, trained on a diverse set of approximately 16,000 mask designs, achieves a mean absolute error of about $7 \times 10^{-3}$ in predicting scattered intensity, while also accelerating the PSFD solver for finer discretizations through warm-start initialization.
Achieving a mean absolute error of just $7 \times 10^{-3}$, this neural operator revolutionizes how we simulate EUV lithography by drastically cutting computational costs and enhancing accuracy.
We present a physics-informed neural operator (PINO) trained with pseudo-spectral frequency-domain (PSFD) equations for electromagnetic (EM) scattering problems in EUV lithography. The Fourier neural operator is factorized into a two-dimensional lateral ($xy$) branch and a one-dimensional axial ($z$) branch and is trained self-consistently with background decomposition.Thus, the full-vector coupling between the mask and the multilayer response is retained without invoking a finite-order Born approximation. In this way, the computational domain size is significantly reduced, thereby lowering the computational cost. The PINO is trained on approximately 16,000 mask designs from the LithoBench library sampled randomly at each training iteration without using precomputed EM field solutions. The PINO surrogate model yields predictions with a mean absolute error of about $7 \times 10^{-3}$ for the scattered intensity of held-out mask patterns relative to the reference PSFD solution. Combined with spectral damping, the PINO warm-start initialization accelerates the background-decomposed PSFD solver on finer discretizations.
