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

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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 $\eta$ decreased with the total number $N_{\text{ALL}}$ of width data points in the same way as that observed in the absence of the image noise. $\eta$ first increased gradually with the image-noise intensity $R$ but markedly when $R$ went beyond the threshold value $R_{\text{th}}$ determined by the ratio of the sampling interval $\Delta y$ to the correlation length $\xi$. The PSDs with these $R_{\text{th}}$'s had the same maximum-to-minimum ratio $\gamma$ (= 10 in this study). The authors approximated $\eta$ by $BN_{\text{ALL}}{}^{-3/4}(\Delta y/\xi)^{-3/8}\ [1+g(R,\Delta y/\xi,\gamma)]$, where $B$ is 49. They also empirically determined the functional form of $g(R,\Delta y/\xi,\gamma)$. Because these functions well fitted massive MC simulation results, they provide guidelines for setting up analysis conditions for securing arbitrarily prescribed accuracy.
2011-01-25