Physics-Informed Neural Operator Accelerates 3D EUV Mask Simulation

Researchers have developed a physics-informed neural operator (PINO) for electromagnetic scattering problems in extreme ultraviolet (EUV) lithography. The model, trained with pseudo-spectral frequency-domain (PSFD) equations, uses a Fourier neural operator factorized into a two-dimensional lateral branch and a one-dimensional axial branch. It is trained self-consistently with background decomposition, retaining full-vector coupling between the mask and multilayer response without invoking a finite-order Born approximation. This reduces computational domain size and cost. The PINO was trained on approximately 16,000 mask designs from the LithoBench library, sampled randomly at each iteration without precomputed EM field solutions. It achieves a mean absolute error of about 7×10⁻³ for scattered intensity of held-out mask patterns. The work, published on arXiv (2607.25330), enables scalable 3D EUV mask simulation.