Stochasticity in extreme-ultraviolet lithography predicted by principal component analysis of Monte Carlo simulated event distributions in resist films

Abstract

Extremely low probability stochastic defects are becoming a major concern in extreme-ultraviolet (EUV) lithography due to the discrete/probabilistic nature of photons, photo- and secondary electrons, reactions, and (macro-) molecular dissolutions. We introduce minimum complete models for stochasticity in EUV exposed resist films and predict the ultimate resolution of EUV lithography from a stochasticity viewpoint. Principal component analysis (PCA) is applied to three-dimensional chemo-physical event distributions in pattern-exposed resist films calculated by a fully coupled Monte Carlo simulation combined with discrete development/etching models. It expresses variabilities in the event distributions as linear combinations of the principal components (eigen-distributions), each of which reflects correlated reactions and clustering of (macro-) molecules. It successfully explains the fluctuations in local pattern edges and their material/process dependencies. Large size event distribution data are generated using the principal components, and stochastic defects are detected in the generated data. This virtual defect generation and inspection explains the observed probabilities and structures of stochastic defects. Thus, PCA provides general and universal representations for reaction stochasticity in resist films exposed by EUV lithography. It predicts that the ultimate resolution of EUV lithography in terms of stochasticity is limited by photoelectron/secondary electron scattering/diffusion or by photo-reaction density around the optical limit of 8 nm.