Line edge roughness and critical dimension variation: Fractal characterization and comparison using model functions

Line edge (or width) roughness (LER or LWR) of photoresists lines constitutes a serious issue in shrinking the critical dimensions (CD) of the gates to dimensions of a few tens of nanometers. In this article, we address the problem of the reliable LER characterization as well as the association of LWR with the CD variations. The complete LER characterization requires more parameters than the rms value sigma since the latter neglects the spatial aspects of LER and does not predict the dependence on the length of the measured line. The further spatial LER descriptors may be the correlation length xi and the roughness exponent alpha, which can be estimated through various methods. One aim of the present work is to perform a systematic comparative study of these methods using model edges generated by a roughness algorithm, in order to show their advantages and disadvantages for a reliable and accurate determination of the spatial LER parameters. In particular, we compare the results from (a) the study of the height-height correlation function (HHCF), (b) the Fourier [or power spectrum (PS)] analysis, and (c) the variation of rms value sigma with measured line edge L [ sigma(L) curve]. It is found that the HHCF can be considered approximately a rescaled version of sigma(L) and that the value of sigma becomes almost independent of the measured edge length for lengths larger than ten times the correlation length. As regards the PS, it is shown that the finite length of the edge may harmfully affect the reliable estimation of alpha and xi. Finally, we confirm theoretically and generalize an experimental observation [Leunissen et al., Microelectron. Eng. (to be published)] regarding the relationship between LWR and the sigma of the CD variations within a die of a wafer. It is shown that they behave in a complimentary way as line length increases so that the sum of their squares remains constant and equal to the square of the LWR sigma of the infinite line. (C) 2004 American Vacuum Society.