Modeling stochastic effects of exposure/diffusion and dissolution on missing contacts

An algebraic model and simulation with the Multivariate Poisson Propagation Model (MPPM) are used to investigate the formation and extrapolation with dose of missing contact defects due to inherent inhomogeneity in on-average uniform resist component densities. A Poisson model of both local roadblocks as well global initial clearing of contacts is derived. When fit to the 2019 experimental data from Maslow et al. this model becomes nearly Gaussian and with 400 equivalent effective dissolution aiding events N_Eff. A dose 9% higher than the central Bossong process window dose reduces the error rate to 10^-13. Fitting revealed that the asymptotic scaling behavior is present at error rates of 10^-1 and thus measuring less than a million contacts at doses of 80% to 95% of normal is likely adequate. An algebraic expression to interpret N_Eff is derived in terms of the averages and variances of exposure, acid generation, base, and deprotection in the Post-Exposure Bake (PEB) process. The model assumes concentration independent Poisson generation rates and greatly simplifies when averages are substituted for Poisson variances. The variance in EUV exposure dominates as it is inherited by acid and deprotection neither of which is Poisson. The large N_Eff is attributed to regional sharing due to acid movement. MPPM simulations of the PEB time-evolution include the behavior of averages and variations of species with saturation or their disappearance with depletion, the volumetric reduction of variance by acid motion, and the mitigation of a local programmed doubling of the quencher base.