Size dependence of polaronic effects on an exciton in a spherical quantum dot

The size dependence of polaronic effects (i.e., LO-phonon effects) on an exciton in a spherical quantum dot is studied by using a variational method. Exciton energy, exciton-phonon interaction energy, and virtual phonon number are calculated by taking into account the interaction between an exciton and both bulk-type and interface-type LO phonons in the system. The numerical results for GaAs and CdSe quantum dots clearly show that (i) in the limit of the small dot, polaron effects on an exciton vanish, i.e., an exciton becomes the bare exciton receiving no LO-phonon effect and (ii) with the increase in the dot radius, the polaronic effects increase and then gradually approach the bulk values. The decrease of the polaronic effects for the small dot is due to the cancellation of the polaronic effects owing to the opposite charge of an electron and a hole.