Reaction-diffusion power spectral density

Abstract

Characterization of a stochastic process in lithography, giving rise to photoresist line-edge roughness (LER), requires elucidation of the power spectral density (PSD) for that process. Thus, any analytical model for LER requires an analytical model for the PSD. Using a previously derived formulation for the reaction-diffusion autocorrelation function, the PSD can be derived from its Fourier transform. The resulting analytical expression for the reaction-diffusion PSD provides an interesting and useful form that will aid modeling work in LER prediction. Numerically calculating the PSD for the stochastic development rate shows that this same analytical expression approximately matches the simulation but with a correlation length that decreases as the amount of development noise increases.