Analytical waveguide model for EUV masks: insights and comparison with RCWA

Rigorous modeling of extreme-ultraviolet (EUV) masks—using techniques such as rigorous coupled-wave analysis (RCWA)—is critical for advancing semiconductor manufacturing, as it accurately captures the complex electromagnetic interactions within multilayer and absorber structures. While these numerical methods are indispensable for quantitative predictions, they often provide limited physical insight into the underlying optical phenomena. To address this, Mesilhy et al. introduced an analytical waveguide-based model that treats the vacuum gap between absorbers as an isolated waveguide, offering a more intuitive understanding of modal behavior. In this work, we build on that model by automating the detection of all supported modes and quantifying their individual contributions to the total field using overlap integrals. We further extend the model to periodic line-space masks using grating theory, capturing lateral mode coupling and Bloch-periodic field behavior. This extended formulation captures the modulation of diffraction efficiencies with absorber thickness and reveals how refractive index contrast governs energy redistribution among diffraction orders. Comparisons with RCWA show excellent agreement, particularly for thin absorbers, demonstrating the improved accuracy of the extended model and establishing the analytical approach as a complementary tool to rigorous methods for fast mask evaluation and design exploration.