Machine learning for inverse lithography: using stochastic gradient descent for robustphotomask synthesis

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Inverse lithography technology (ILT) synthesizes photomasks by solving an inverse imagingproblem through optimization of an appropriate functional. Much effort on ILT isdedicated to deriving superior masks at a nominal process condition. However, the lowerk1 factor causes the mask to be more sensitive to process variations. Robustness to majorprocess variations, such as focus and dose variations, is desired. In this paper, we considerthe focus variation as a stochastic variable, and treat the mask design as a machinelearning problem. The stochastic gradient descent approach, which is a useful tool inmachine learning, is adopted to train the mask design. Compared with previous work,simulation shows that the proposed algorithm is effective in producing robust masks.