Stochastic hotspots in extreme ultraviolet exposed nano-patterns as correlated molecular sub-cluster formation probabilities

Abstract

Stochastic pattern anomalies limit the shrinking of the size of nano-patterns in extreme-ultraviolet lithography at around 10 nm due to the discrete/probabilistic nature of photon–electron-reaction systems. We express the patterns and their anomalies as probability distributions and predict stochastic hotspots where the anomaly generation probabilities rise unexpectedly in arbitrary pattern features. Three-dimensional chemo-physical event distributions in pattern-exposed resist films are calculated by the fully coupled first-principles Monte Carlo simulation combined with the discrete development/etching models. The aggregates of molecular level solubility flipping (sub-cluster) well express spatial correlations in the observed anomalies. Spatial correlation in sub-cluster generation is not scaled and their impact increases with shrinking patterns. The correlation is squeezed near the pattern edge, inducing edge placement error, and it spreads in the areas between edges causing stochastic pattern defects. For materials with sub-cluster size not negligible compared to image size, the stochastic hotspots appear when the correlated area spreads in areas far from the edges adjacent to the higher probability region. Deep neural networks successfully predict the probability distributions of sub-clusters and anomaly generation in arbitrary pattern features without the Monte Carlo method.