Comparison of effective medium approximation and Rayleigh-Rice theory concerning ellipsometric characterization of rough surfaces

In this paper, the theoretical analysis of the correctness of applying the effective medium approximation (EMA) at the ellipsometric studies of rough surfaces is presented. Within this analysis the Rayleigh-Rice theory (RRT) is used to calculate the simulated ellipsometric data of various slightly randomly rough surfaces. This simulated data are treated using the least-squares method for finding the values of the parameters characterizing the rough surfaces within the EMA, i.e., the values of thickness and packing density factor describing a fictitious (effective) thin films replacing these surfaces within the EMA. It is shown that the EMA could be used to interprete the ellipsometric data of the rough surfaces in a correct way if their roughness only contains the high spatial frequencies. For the low spatial frequencies it is shown that the influence of the surface roughness on the ellipsometric quantities is small in contrast to its influence on the reflectance. Moreover, it is shown that the EMA must be used carefully for optical characterizing rough surfaces and that it is more reasonable to use the RRT for this purpose. It is also presented that in general it is impossible to expect a good agreement between the thickness values determined using EMA within the ellipsometric analysis and the rms values of the heights of the irregularities evaluated by atomic force microscopy (AFM) for the same rough surfaces.