Roughness of surface decorated with randomly distributed pillars

Abstract

We have presented a quantitative analysis of roughness of planar surfaces decorated with randomly distributed, cylindrical pillars, disks, or cavities. We have described the roughness in terms of the surface power spectral density (PSD). First, we have derived a general equation for the PSD of such surfaces. Then, we have found the PSD for the special case of statistically isotropic, circular areas. We have demonstrated that the PSD provides quantitative information on the radius of the circular area, dimensions of the pillar, and surface coverage. We have also discussed the numerical method of extracting the parameters from experimental PSD data obtained from discrete Fourier transform of surface scanning measurements.

Power Spectral Density Analysis for Optimizing SERS Structures

“…Shoulders or even peaks in PSD functions are typical for the monodisperse ensembles [48]. One can see in Figure 4b, that Raman signal increases with the average radius.…”