Accelerating extreme ultraviolet lithography simulation with weakly guiding approximation and source position dependent transmission cross coefficient formula

Abstract

Background: Mask three-dimensional (3D) effects distort diffraction amplitudes from extreme ultraviolet masks. In a previous work, we developed a convolutional neural network (CNN) that predicted distorted diffraction amplitudes very fast from input mask patterns.Aim: In this work, we reduce both the time for preparing the training data and the time for image intensity integration. Approach: We reduce the time for preparing the training data by applying weakly guiding approximation to 3D waveguide model. The model solves Helmholtz type coupled vector wave equations of two polarizations. The approximation decomposes the coupled vector wave equations into two scalar wave equations, reducing the computation time to solve the equations. Regarding the image intensity integration, Abbe's theory has been used in electromagnetic (EM) simulations. The transmission cross coefficient (TCC) formula is known to be faster than Abbe's theory, but the TCC formula cannot be applied to source position dependent diffraction amplitudes in EM simulations. We derive source position dependent TCC (STCC) formula starting from Abbe's theory to reduce the image intensity integration time.Results: Weakly guiding approximation reduces the time of EM simulation by a factor of 5, from 50 to 10 min. STCC formula reduces the time of the image intensity integration by a factor of 140, from 10 to 0.07 s. Conclusions:The total time of the image intensity prediction for 512 nm × 512 nm area on a wafer is ∼0.1 s. A remaining issue is the accuracy of the CNN.