Determination of the optical properties and size dispersion of Si nanoparticles within a dielectric matrix by spectroscopic ellipsometry

We report on a comparative study between dielectric functions of Si nanoparticles (Si-NPs) obtained from Bruggeman effective medium approximation (BEMA), Maxwell-Garnett (MG), and a modified Maxwell-Garnett (MMG) models. Unlike BEMA and MG, a size-distribution dependent dielectric function of Si-NPs is considered in the introduced MMG model. We show that the standard deviation σ of a size distribution can be evaluated by analyzing the imaginary part of the dielectric functions of Si-NPs extracted from BEMA and MMG. In order to demonstrate this, several samples composed of Si-NPs embedded in silicon-rich silicon nitride are investigated by spectroscopic ellipsometry over the photon energy range varying between 2 and 4 eV. Assuming a lognormal size distribution of the Si nanoparticles, it is evidenced that the parameter σ ranges between 1.15 and 1.35. The values of size dispersion deduced by this methodology are in good agreement with TEM observations.