Data augmentation in EUV lithography simulation based on convolutional neural network

Abstract

Data augmentation is a powerful technique in deep learning to increase the number of training data by using limited original data. We apply this technique to EUV lithography simulation based on convolutional neural network (CNN). In previous work, we developed a prototype CNN which reproduces the results of the rigorous electromagnetic (EM) simulations in a small mask area. The prediction time of CNN was 5,000 times faster than the calculation time of EM simulation. We trained the CNN by using 200,000 data which were the results of EM simulation. Although the prediction time of CNN was very short, it took a long time to build a huge amount of the training data. Especially when we enlarge the mask area the calculation time to prepare the training data becomes unacceptably long. The EM calculation time for 1,024 nm X 1,024 nm mask area takes 162 s. It will take a year to calculate 200,000 mask patterns. The training data of our CNN is the diffraction amplitudes of mask patterns. Assuming a periodic boundary condition, the diffraction amplitudes of the shifted or flipped mask pattern can be easily calculated by using the diffraction amplitudes of the original mask pattern. We apply this data augmentation technique to reduce the data preparation time for 1,024 nm X 1,024 nm mask area by a factor of 200. The accuracy of CNN is verified by comparing the CNN predictions with the results of EM simulation. Our CNN successfully reproduces critical dimensions and edge placement errors of line and space patterns.