Power spectrum of smoothed line-edge and line-width roughness

Line-edge and line-width roughness (LER and LWR) is a challenge for device variability control, especially in future devices. Actual device patterns have LER/LWR that is smoothed from the original photoresist patterns used as etching masks. In this study, the LER/LWR of these actual patterns was assumed to have a modified exponential autocorrelation function, which was smoothed by another exponential function. An analytical formula of the discrete power spectral density (PSD) of this LER/LWR was derived on the basis of the previous formula for nonsmoothed LER/LWR, for use in a PSD fitting method. The PSDs calculated using this formula excellently fit the experimental PSDs of both types of polycrystalline-silicon lines without and with sidewall spacers. Through these fittings, it was found that the actual LER/LWR is accurately characterized using the variance and correlation length of the original non-smoothed LER/LWR simply by introducing a third parameter that characterizes the smoothing effect.