Cluster of correlated reactions as a cause for various types of stochastic defects in extreme ultraviolet lithography

Abstract

Stochastic defects are becoming major concern in the future EUV lithography as their probability P_d exponentially increases with decreasing feature size and is highly sensitive to variations in process/mask conditions. Photon shot noises and discrete/probabilistic nature of materials have been blamed as their causes. We introduce models for relating P_d to photon and resist statistics under various exposure and material conditions and analyze their impact in future EUV lithography. Three-dimensional reaction distributions are calculated by a fully-coupled Monte Carlo simulation including discrete photon, photoelectron scattering, and resist stochastics. Then, probability models predict _Pdfrom statistical data extracted from Monte Carlo results. Stochastic defect generation is enhanced by cascade and/or cluster of correlated reactions among nearby polymers/molecules due to secondary electrons (SE)/acid diffusion and SEs generated along scattered photoelectron trajectories. P_ddecreases with increasing reaction density, suppressing effective image blur, and introducing quenchers, where reaction density is limited by SE, PAG and reaction site. Defect probability increases with decreasing target size for the same k1-factor, while strongly dependent on image slope and defocus. Our analyses suggest that applying EUV lithography to smaller target requires careful material choice, extremely precise process control, and further EUV power enhancement.