Model-based assist feature generation

We optimize a continuous-tone photomask to meet a set of edge-placement tolerances and 2-D image fidelity requirements, for a set of dose and defocus values. The resulting continuous tone mask, although not realizable, indicates where to place assist features and their polarity. This algorithm derives assist features from first principles: when the mask is optimized for best focus, the optimal continuous-tone photomask does not have any features that resemble assist features. When the mask is optimized for best focus and a defocus condition, the optimal continuoustone photomask spontaneously grows assist features. The continuous-tone photomask also has features that can be identified as phase windows. Polygonal, quantized assist features are extracted from the optimal continuous-tone photomask.