Dipolar vibrational modes in spherical semiconductor quantum dots

Abstract

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 Fro¨hlich 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.