Size dependence of electron-phonon coupling in semiconductor nanospheres: The case of CdSe

We study electron-phonon coupling in the case of Fröhlich or polar interaction, with special emphasis on the size dependence of the coupling strength for semiconductor nanospheres exhibiting quantum confinement of the carriers. We first derive the expression of the vibrational LO (longitudinal optic) and SO (surface optic) eigenfunctions for a sphere in the continuum approximation. After having quantized the vibrational eigenmodes, we give the electron-phonon interaction Hamiltonian. Using a model electronic charge distribution, we then show that the coupling strength is size independent when the typical dimensions of the electron charge distribution scale as the sphere radius. These theoretical considerations are then compared with experimental results obtained using resonant Raman scattering by CdSe-doped glasses with particles of various sizes. The experiments confirm the size independence of the coupling strength and also show the existence of surface modes.