Quantification of line-edge roughness of photoresists. II. Scaling and fractal analysis and the best roughness descriptors

Abstract

A search for the best and most complete description of line-edge roughness (LER) is presented. The root mean square (rms) value of the edge (sigma value) does not provide a complete characterization of LER since it cannot give information about its spatial complexity. In order to get this missing information, we analyze the detected line edges as found from scanning electron microscope (SEM) image analysis [see Paper I: G. P. Patsis et al., J. Vac. Sci. Technol. B 21, 1008 (2003)] using scaling and fractal concepts. It is shown that the majority of analyzed experimental edges exhibit a self-affine character and thus the suggested parameters for the description of their roughness should be: (1) the sigma value, (2) the correlation length ξ, and (3) the roughness exponent α. The dependencies of ξ and α on various image recording and analysis parameters (magnification, resolution, threshold value, etc.) are thoroughly examined as well as their implications on the calculation of sigma when it is carried out by averaging over the sigmas of a number of segments of the edge. In particular, ξ is shown to be connected to the minimum segment size for which the average sigma becomes independent of the segment size, whereas α seems to be related to the relative contribution of high frequency fluctuations to LER.