3D EUV mask simulator based on physics-informed neural networks: effects of polarization and illumination

Abstract

Background: To enable the manufacturing of advanced semiconductor devices, EUV lithography has been continuously shrinking the lateral dimensions of the mask and features. Resulting complex diffraction, polarization, and oblique illumination effects require rigorous modeling of EUV light diffracted from the mask. Traditional electromagnetic field (EMF) solvers are inefficient for large field-of-view simulations, while deep neural networks rely on a huge amount of expensive rigorously simulated or measured data. [1] Aim: Building upon our prior research [2], which revealed the PINN's potential and enabled sufficient aerial image simulation of small features, this study aims to broaden the scope of PINN's applications. Specifically, we extend this work towards the investigation of polarization effects and variable illumination settings.Approach: The established PINN model [2] was employed for EUV mask simulations under various illumination directions to investigate the orientation dependence of lithographic patterning. Expressing the residual of 3D Maxwell's equations, we effectively decoupled the transverse electric (TE) and transverse magnetic (TM) modes of EUV light. Employing a vectorial formulation of the wave equation, we investigated the ability of the PINN approach to predict the generation of additional electric field components resulting from the scattering at the absorber edges.Results: PINN accurately predicts the polarization effects that are relatively small, but still notable close to the absorber edges and inside the multilayer. The generalized PINN-based solver, adapted for arbitrary illumination settings, demonstrates the significant impact of the illumination direction and exposure wavelength on the reflected EUV light. PINN captures asymmetries in the near field caused by off-axis illumination and the significant drop in the intensity of the reflected light for larger incidence angles.Conclusions: By pushing the application limits of the existing PINN approach, we demonstrated its capability to accurately model oblique illumination effects, polychromatic effects, and even the weak polarization effects in the EUV spectral range. Different from numerical solvers, a universal PINN-based mask solver can simulate light scattering response in several milliseconds for arbitrary mask geometries and illumination settings without re-training.