Calibration of Compact Resist Model Through CNN Training

We notice that the compact resist model can be mapped to a simple CNN (convolutional neural network): convolutional layer corresponds to convolutions between input images and resist kernels, and a fully connected layer can model the formation of weighted sum of convolutions followed by the comparison to threshold to determine the development. Resist kernels correspond to convolution filters, so they can be obtained through CNN training, which is a key motivation. A number of challenges are identified and solutions are proposed: (1) We demonstrate a CNN structure that can be mapped to a resist model. (2) Convolution filters are large images and cannot be trained with standard methods. Adaptive learning rate and gradient clipping are applied. (3) Convolution filters may easily be overfitted if training data is not enough. We apply gradient descent for fast initialization of filters. (4) CNN is trained with printability of image pixels rather than CD values. Extraction of pixels and their sampling are addressed. The number of kernels and the number of convolutions can greatly be reduced through the proposed method: 22 standard kernel functions are reduced to only 4 optimized ones, which contributes to 44% faster lithography simulation yet accuracy is improved by 10%.