Probability prediction of EUV process failure due to resist-exposure stochastic: applications of Gaussian random fields excursions and Rice's formula

The methods to calculate the probability of success/failure of EUV lithography (EUVL) processes are presented. The success of an EUVL process is defined as a complete removal of the resist material within one set of designated volumes and a complete retention of the resist material within another set of designated volumes in the resist film. We demonstrate that, under certain assumptions, the probability calculation reduces to the well-known problem of calculation of probability of excursion of a certain Gaussian random field. The methods to calculate the probability of success/failure of a lithographic process are presented, including the Monte-Carlo methods, methods based on factorization of a covariance matrix, methods based on Mahalanobis distance, and the methods using Rice's formula and its variations. A particular attention is paid to the methods applicable to full chip OPC and OPC verification. The results from the proposed methods are tested in simulations and by comparison with experimental data.