Image-Noise Effect on Discrete Power Spectrum of Line-Edge and Line-Width Roughness

Abstract

The authors investigated the effect of scanning-electron-microscope image noise on the accuracy of line-edge-roughness and line-width-roughness (LER/LWR) statistics extracted from power spectral densities (PSDs). To do this, they numerically prepared pseudo-experimental PSDs of LWR using the Monte Carlo (MC) method. The estimation error η decreased with the total number N ALL of width data points in the same way as that observed in the absence of the image noise. η first increased gradually with the image-noise intensity R but markedly when R went beyond the threshold value R th determined by the ratio of the sampling interval Δy to the correlation length ξ. The PSDs with these R th's had the same maximum-to-minimum ratio γ (= 10 in this study). The authors approximated η by B N ALL -3/4(Δy/ξ)-3/8 [1+g(R,Δy/ξ,γ)], where B is 49. They also empirically determined the functional form of g(R,Δy/ξ,γ). Because these functions well fitted massive MC simulation results, they provide guidelines for setting up analysis conditions for securing arbitrarily prescribed accuracy.

Power Spectrum of Smoothed Line-Edge and Line-Width Roughness

“…9, would be masked by the LWR component induced by image noise, which certainly reduces the accuracy of LWR analyses. 31) On the contrary, the differences still exist, and of the three smoothing functions the exponential one yields the best fit, as shown in Fig. 15.…”