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

Abstract

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's 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.

Light scattering from coupled plasmonic nanospheres on a substrate

“…By comparing our results with the corresponding experimental data with only a few fitting parameters, we can determine rather uniquely the size, average spacing, and fraction of nanoparticle clusters in a given sample. A similar comparison was reported in a previous paper [8], in which the nanoparticle clusters are resembled by pancakes with various sizes. Here, we include the realistic effects of clusters of coupled nanospheres and find more truthful description of the experimental results.…”

“…To observe the plasmonic coupling of aggregated nanoparticles, it is more convenient to place them on a substrate. Nanoparticle clusters can also be found in a random distribution of metallic nanoparticles on a glass substrate which was formed by dipping a chemically treated glass plate in a solution containing metallic nanoparticles of similar size, and the plasmonic effect of these nanoparticle clusters can be measured experimentally via conventional ellipsometry setup [7][8]. There were several theoretical investigations of this subject.…”

Efficient Simulation for Light Scattering from Plasmonic Core-Shell Nanospheres on a Substrate for Biosensing

“…[25] For example, if the shape of nanoparticles is spherical, we choose the products of spherical harmonics and spherical Bessel functions as the basis functions. [26,27] This significantly reduces the number of basis functions needed to describe the localized nature of the electromagnetic field for frequencies near the plasmonic resonance. [26] Using this geometry-adopted basis, we have analyzed the effect of clustering features on the ellipsometry spectra of glass substrates covered with a random distribution of Au nanoparticles (AuNPs) and determined the structure information of the sample, including average sizes, separations of nanoparticles and fractional area covered by clusters of AuNPs.…”

“…[26,27] This significantly reduces the number of basis functions needed to describe the localized nature of the electromagnetic field for frequencies near the plasmonic resonance. [26] Using this geometry-adopted basis, we have analyzed the effect of clustering features on the ellipsometry spectra of glass substrates covered with a random distribution of Au nanoparticles (AuNPs) and determined the structure information of the sample, including average sizes, separations of nanoparticles and fractional area covered by clusters of AuNPs. [27] In this paper, we first construct the theoretical formulation for light scattering from an isolated nanoparticle first fully and next partially covered by a shell, using Green's function (GF) method with spherical harmonic basis functions.…”

“…same for all sites). For a random distribution of nanoparticles, we may approximate for sites j other than i, where f denotes a similarity factor [26,27]. For a completely random and uniform distribution, every nanoparticle "sees" the same environment.…”