Vibrations of free and embedded anisotropic elastic spheres: Application to low-frequency Raman scattering of silicon nanoparticles in silica

TL;DR

This paper models vibrational modes of anisotropic elastic spheres embedded in a medium, revealing the importance of anisotropy and matrix effects in interpreting low-frequency Raman scattering data of silicon nanoparticles.

Contribution

It introduces a method to calculate vibrational modes considering anisotropy and embedding effects, improving understanding of nanoparticle Raman spectra.

Findings

Anisotropy causes significant frequency shifts in vibrational modes.

Matrix effects are essential for accurate Raman spectrum interpretation.

Libration dominates over vibration in low-frequency Raman scattering of silicon nanoparticles.

Abstract

Vibrational mode frequencies and damping are calculated for an elastic sphere embedded in an infinite, homogeneous, isotropic elastic medium. Anisotropic elasticity of the sphere significantly shifts the frequencies in comparison to simplified calculations that assume isotropy. New low frequency Raman light scattering data are presented for silicon spheres grown in a SiO2 glass matrix. Principal features of the Raman spectrum are not correctly described by a simple model of the nanoparticle as a free, isotropic sphere, but require both matrix effects and the anisotropy of the silicon to be taken into account. Libration, not vibration, is the dominant mechanism.