Line-edge and linewidth roughness (LER and LWR) is mostly characterized using the edge position data obtained by detecting edges in scanning electron microscope (SEM) images. In order to reduce data errors caused by SEM-image noise, image pixels are usually averaged along or across pattern edges (longitudinal or crosswise averaging) before the edge detection. In the case of the longitudinal averaging, it not only reduces the image-noise-induced additional LWR, but smoothes the real LWR. Because of this smoothing effect, the power spectral density (PSD) of the LWR decreases more markedly at larger wave numbers. A distinct feature of this PSD is oscillatory structures, which depend on the number of averaged pixels. It is difficult to formulate these modifications of PSD in the cases of any LWRs under arbitrary measurement and analysis conditions. By contrast, the crosswise averaging of the image pixels reduces only the image-noise effect without affecting the real LWR, enabling to enjoy the benefits of the methodology developed so far. Accordingly, the authors propose to apply only the crosswise averaging to SEM-image pixels before the edge detection.
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