Information theoretical computational lithography based on pattern density statistics

Computational lithography is an important technology to improve the image resolution and fidelity of the optical lithography process. Recently, information theoretical models were introduced to explore the physical limit of image fidelity that can be achieved by different computational lithography methods. However, the existing models were derived based on a simple and idealized assumption of uniform pattern density, thus rendering a loose lower bound on the lithography imaging error. This work improves the accuracy of the information theoretical model by introducing a statistical approach of pattern density. In particular, a density classification rule (DCR) of mask and print image is established based on a number of randomly generated layout samples. The information transfer function between the mask and print image is formulated under the DCR constraint. Then, the optimal information transfer (OIT) and the theoretical limit of lithography image fidelity are derived using a numerical optimization algorithm with mask manufacturing regularization. It has been proved analytically and experimentally that our proposed model provides a much more accurate theoretical limit of lithography image fidelity than the conventional approach.