3D mask simulation and lithographic imaging using physics-informed neural networks

Background: The increasing demands on computational lithography and computational imaging in the design and optimization of lithography processes necessitate rigorous modeling of EUV light diffracted from the mask. Traditional electromagnetic field (EMF) solvers are inefficient for large-scale technology problems, while deep neural networks rely on a huge amount of expensive rigorously simulated or measured data. Aim: In order to overcome these constraints, we explore the potential of physics-informed neural networks (PINN) as a promising solution for addressing complex optical problems in the field of EUV lithography. Approach: We extend the existing MaxwellNet to simulate the light diffraction from typical reflective EUV masks. The coupling of the predicted diffraction spectrum with image simulations enables the evaluation of PINN performance in predicting relevant lithographic metrics and typical mask 3D effects. Results: The results of modeling near- and far-field diffraction using PINN showcase a good performance in terms of convergence behavior, stability, accuracy, and a significant speed-up (up to ×10000) compared to the rigorous 3D mask simulation using an established numerical EMF solver. In contrast to other machine learning approaches, PINN is able to accurately simulate the near field, learns the involved physics, and captures the optical and mask-induced 3D effects. PINNs can predict lithographic process windows with sufficient accuracy. Conclusions: Differently from numerical solvers, once trained, generalized PINN can simulate light scattering in several milliseconds without re-training and independently of problem complexity. This opens up the capabilities for partially coherent imaging simulations without the Hopkins approach, source optimization, and fast investigation of mask 3D effects.