Predictive modelling of the dielectric response of plasmonic substrates: application to the interpretation of ellipsometric spectra

A predictive modelling of plasmonic substrates appropriate to read ellipsometric spectra is presented in this work. We focus on plasmonic substrates containing a single layer of silver nanoparticles (AgNPs) embedded in silica matrices. The model uses the Abeles matrix formalism and is based on the quasistatic approximation of the classical Maxwell-Garnett mixing rule, however accounting for the electronic confinement effect through the damping parameter. It is applied on samples elaborated by: (i) RF-diode sputtering followed by Plasma Enhanced Chemical Vapor Deposition (PECVD) and (ii) Low Energy Ion Beam Synthesis (LE-IBS), and represents situations with increasing degree of complexity that can be accounted for by the model. It allows extraction of the main characteristics of the AgNPs population: average size, volume fraction and distance of the AgNPs layer from the matrix free surface. Model validation is achieved through comparison with results obtained from transmission electron microscopy approving for its applicability. The advantages and limitations of the proposed model are discussed after eccentricity-based statistical analysis along with further developments related to the quality of comparison between the model-generated spectra and the experimentally-recorded ellipsometric spectra.