Towards a complete description of line width roughness: A comparison of different methods for vertical and spatial LER and LWR analysis and CD variation

Line edge (or width) roughness (LER or LWR) of photoresists lines consists a serious issue in shrinking the CDs of the gates to dimensions of a few tens of nanometers. in this paper, we address he 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 xi of the measured fine. The further spatial LER descriptors may be the correlation length and the roughness exponent alpha, which can be estimated through various methods(1). 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 thew 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 a with measured line edge L (sigma(L) curve). It is found that the HHCF can be considered approximately a resealed version of sigma(L) and that the value of sigma becomes almost independent on 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 affect harmfully the reliable estimation of alpha and xi. Finally, we confirm theoretically and generalize an experimental observation(2) 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 Hue length increases so that the sum of their squares remains constant and equal to the. square of the LWR sigma of the infinite line.