Cascade and cluster of correlated reactions as causes of stochastic defects in extreme ultraviolet lithography

Abstract. Background: Stochastic defects are becoming major concern in the future extreme ultraviolet (EUV) lithography as their probability Pd exponentially increases with decreasing feature size and is highly sensitive to variations in process/mask conditions. Photon shot-noise and discrete/probabilistic nature of materials have been blamed as their causes. Aim: We introduce models for relating Pd to photon and resist statistics under various exposures and material conditions and analyze their impact in future EUV lithography. Approach: Three-dimensional reaction distribution is calculated by a fully coupled Monte Carlo simulation including discrete photon, photoelectron scattering, and resist stochastics. Then probability models predict Pd from statistical data extracted from Monte Carlo results. 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. Pd decreases with increasing reaction density, suppressing effective image blur, and introducing quenchers, where reaction density is limited by SE, photoacid generator, and reaction site. Defect probability increases with decreasing target size for the same k1-factor, while strongly dependent on image slope and defocus. Conclusions: Our analyses suggest that applying EUV lithography to smaller target requires careful material choice, extremely precise process control, and further EUV power enhancement.