Coupled-oscillator model for hybridized optical phonon modes in contacting nanosize particles and quantum dot molecules

Abstract

Modification of optical phonon spectra in contacting nonpolar nanoparticles compared to single particles is studied. Optical phonons in dielectric and semiconducting particles obey the Euclidean metric Klein-Fock-Gordon equation with Dirichlet boundary conditions. This equation is supposed to be solved numerically for manifolds of cojoined spheres. It is proposed to replace this problem with the simpler-to-solve coupled-oscillator model (COM), where an oscillator is attributed to each phonon mode of a particle and the particle overlap leads to the appearance of additional couplings for these oscillators with the magnitude proportional to the overlap volume. For not too big overlaps, this model describes solutions of the original eigenvalue problem with a quantitative level of accuracy. In particular, it works beyond isotropic s modes in dimers, which has been demonstrated for p modes in dimers and for tetramers. It is proposed to apply the 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 dynamical matrix method is also 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. The proposed COM paves a way towards the description of propagation of vibrational modes in the ensembles of particles in contact including tight agglomerates, nanocrystal solids, and porous media.