Noise-free estimation of spatial line edge/width roughness parameters

At present, the most widely used technique for Line Edge and Width Roughness (LER/LWR) measurement is based on the analysis of top-down CD-SEM images. However, the presence of noise on these affects importantly the obtained edge morphologies leading to biased LER/LWR measurements. In the last few years, significant progress has been made towards the acquisition of noise-free LER/LWR metrics. The output of all proposed methods is the noise-free rms value Rq estimated using lines with sufficiently long lengths. Nevertheless, one of the recent advances in LER/LWR metrology is the realization that a single Rq value does not provide a complete description of LER and a three parameter model has been introduced including the Rq value at infinite line length, the correlation length ξ and the roughness exponent α. The latter two parameters describe the spatial fluctuations of edge morphology and can be calculated by the height height correlation function G(r) or the dependence of rms value Rq on line length Rq(L). In this paper, a methodology for noise free estimation of G(r) and Rq(L) is proposed. Following Villarrubia et al. [Proc.SPIE5752, 480 (2005)], we obtain a formula for the noise free estimation of G(r) and assess its predictions by implementing and applying a modeling approach. Also, we extend appropriately the methodology of Yamagutchi et al. [Proc.SPIE6152, 61522D (2006)] to a large range of line lengths and show that it can provide a reliable noise free estimation of the whole Rq(L) curve.