Coupled oscillators model for hybridized optical phonon modes in contacting nanosized particles and quantum dot molecules

TL;DR

This paper introduces a coupled oscillators model to efficiently approximate optical phonon spectra in contacting nanosized particles and quantum dot molecules, providing a simpler alternative to complex eigenvalue problems.

Contribution

The paper proposes a coupled oscillators model that accurately describes optical phonon modifications in contacting nanoparticles, extending beyond isotropic modes and validated against the dynamical matrix method.

Findings

The COM accurately reproduces phonon spectra for overlapping nanoparticles.

Van der Waals contacts cause minimal phonon spectrum modifications.

Raman spectra can distinguish dimerized particles from size-distributed single particles.

Abstract

Modification of optical phonon spectra in contacting nanoparticles as compared to the single ones is studied. Optical phonons in dielectric and semiconducting particles obey the Euclidean metric Klein-Fock-Gordon equation with Dirichlet boundary conditions. The latter is supposed to be solved numerically for manifolds of interpenetrating spheres. It is proposed to replace this problem with the simpler-to-solve coupled oscillators model (COM), where an oscillator is attributed to each phonon mode of a particle and the particles overlap leads to appearance of additional couplings for these oscillators with the magnitude proportional to the overlapped volume. For not too big overlaps this model describes solutions of the original eigenvalue problem on a good level of accuracy. In particular, it works beyond isotropic s modes, which has been demonstrated for p modes in dimer and also for tetramer. It is proposed to apply COM for the description of recently manufactured dimer nanoparticles and quantum dots. The obtained results are in agreement with the dynamical matrix method for optical phonons in nanodiamonds. The latter is used to demonstrate that the van der Waals contacts between faceted particles lead to very small modifications of the optical phonon spectra, which therefore could be neglected when discussing the propagation of vibrational excitations via a nanopowder. The possibility to distinguish between dimerized and size-distributed single particles from their Raman spectra is also considered.