Modeling of Near-and Far-Field Diffraction from EUV Absorbers Using Physics-Informed Neural Networks

Extreme ultraviolet (EUV) light with a wavelength of about 13.5 nm is used in modern semiconductor technology for the lithographic fabrication and optical characterization of nanostructures. The predictive simulation of the use of EUV light for these applications requires the accurate modeling of light scattering from small objects, such as absorbers on masks for EUV lithography. Various electromagnetic field solvers [1]–[3] have been adapted and used for the modeling of scattering of EUV light but are inappropriate to address large-scale technology problems with sufficient efficiency. In recent years, deep neural networks have been used to support rigorous simulations with better initial values, to replace single iteration steps, or even the entire simulation [4]. However, these data-driven networks require a large amount of rigorously simulated or measured data [5]. To address these limitations, we explore the potential of physics-informed neural networks (PINN) to simulate the diffraction of EUV light from typical absorber patterns on EUV masks. The developed method solves Maxwell's equations without any training data, so incorporating only the physical knowledge to the loss function. The application of PINNs to electromagnetic scattering and imaging problems requires the implementation of the specific incident field and boundary conditions (BC), including perfectly matched layers (PML), and periodic BCs. The obtained solutions are evaluated in the near field (intensity and phase) and the far field (diffraction efficiency and phase difference between diffraction orders) and are compared to that of the rigorous numerical solver based on the Waveguide method [2]. Our simulation results demonstrate that PINN can approximate the diffracted light in the vicinity of EUV absorbers with high accuracy and significant speed-up compared to conventional electromagnetic field solvers.