Effect of clustering on ellipsometric spectra of randomly distributed gold nanoparticles on a substrate

We present a theoretical model for describing light scattering from randomly distributed Au nanoparticles on a substrate, including the clustering effect. By using the finite-element Green function method and spherical harmonic basis functions, we are able to calculate the polarization-dependent reflectivity spectra of the system (modeled by randomly distributed nanoparticles coupled with clusters) efficiently and accurately. The calculated ellipsometric spectra of the system with clusters can adequately describe the experimental data for the whole frequency range. We find that the clustering effect leads to some prominent features in the low frequency range of the ellipsometric spectra, which are attributed to plasmonic resonances associated with the coupling of Au nanoparticles and clusters.