Dipolar vibrational modes in spherical semiconductor quantum dots

Spatially quantized dipolar phonon modes in a spherical quantum dot (QD) made of a polar isotropic material are considered in the framework of a continnum model. Different mechanical boundary conditions are analyzed, which are shown to strongly influence the spectrum of the dipole-active modes. The phonon-related polarizability of a single QD and an average dielectric function of a composite containing QDs are calculated. Numerical results are presented for CdSe and InP dots. A strongly dipole-active gap mode is predicted for InP QDs embedded in a matrix with a defined range of dielectric constant. The effect of increasing QD concentration in ensembles is discussed in terms of the dipole–dipole interaction between the dots, which can result in their bulk-like FIR absorption spectra with a peak at the transverse optical (TO) phonon frequency instead of the Fröhlich frequency. It is suggested that similar effects might occur in individual microcrystals, which can explain their absorbtion of FIR radiation at the TO phonon frequency, despite having a size much smaller than the radiation wavelength.