Method and system for calculating printed area metric indicative of stochastic variations of the lithographic process

Systems and methods for calculating a printed area metric indicative of stochastic variations of the lithographic process are disclosed. Lithography is a process that uses light to transfer a geometric pattern from a photomask, based on a layout design, to a resist on a substrate. The lithographic process is subject to random stochastic phenomena, with the resulting stochastic randomness potentially becoming a major challenge. To characterize the stochastic phenomena, a printed area metric may be generated analytically (rather than via simulations) and comprise one or more defined moments for a printed area distribution associated with the printed area that are indicative of one or more aspects associated with printing. For example, the printed area metric may be indicative of the likelihood of printing within the printed area or the variance of printing within the printed area due to stochastic randomness in one or both of exposure or resist process.