Pixel-based learning method for an optimized photomask in optical lithography

Circuit design is driven to the physical limit, and thus patterns on a wafer suffer from serious distortion due to the optical proximity effect. Advanced computational methods have been recommended for photomask optimization to solve this problem. However, this entails extremely high computational costs leading to problems including lengthy run time and complex set-up processes. This study proposes a pixel-based learning method for an optimized photomask that can be used as an optimized mask predictor. Optimized masks are prepared by a commercial tool, and the feature vectors and target label values are extracted. Feature vectors are composed of partial signals that are also used in simulation and observed at the center of the pixels. The target label values are determined by the existence of mask polygons at the pixel locations. A single-hidden-layer artificial neural network (ANN) is trained to learn the optimized masks. A stochastic gradient method is adopted for training to handle about 2 million samples. The masks that are predicted by an ANN show averaged edge placement error of 1.3 nm, exceeding that of an optimized mask by 1.0 nm, and averaged process variation band of 4.8 nm, which is lower than that of the optimized mask by 0.1 nm.