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

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.Comment: 11 pages, 10 figure

Localized and extended collective optical phonon modes in regular and random arrays of contacting nanoparticles: escape from phonon confinement

In the present paper, we utilize the coupled-oscillator model describing the hybridization of optical phonons in touching and/or overlapping particles in order to study the Raman spectra of nanoparticles organized into various types of regular and random arrays including nanosolids, porous media, and agglomerates with tightly bonded particles. For the nanocrystal solids, we demonstrate that the ratio of the size variance to the coupling strength allows us to judge the character (localized or propagating) of the optical phonon modes which left the particles of their origin and spread throughout an array. The relation between the shift and the broadening of the Raman peak and the coupling strength and the disorder is established for nanocrystal solids, agglomerates, and porous media providing us with information about the array structure, the structure of its constituents, and the properties of optical phonons.Comment: 13 pages, 11 figure