Abstract
Under the dielectric continuum approximation, the confined longitudinal-optical (LO) phonon and interface-optical (IO) phonon modes of a multi-shell spherical nanoheterosystem are discussed. To describe the vibrations of the LO phonons, a proper eigenfunction for LO phonon modes in the core region is adopted and a legitimate eigenfunction for LO modes in the shell region is constructed. To deal with the IO phonon modes, determinant methods are employed, and the determinant deciding the frequencies of IO phonon modes are obtained. The quantized LO and IO phonons fields as well as their corresponding electron-phonon interaction Hamiltonians are also derived.
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