Optical properties of confined polaronic excitons in spherical ionic quantum dots

We report the results of a variational calculation of the energy and the oscillator strength of the exciton ground state in a spherical ionic quantum dot as a function of radius, assuming infinite potential barriers. The strong interaction of the exciton with optical phonons is taken into account by using an effective potential between the electron and the hole as derived by Pollmann and Buttner. The values of the exciton ground-state energies calculated using this effective potential are compared with the results of a recent calculation that treats the exciton interaction with confined and interface phonons independently, and excellent agreement is found. Comparisons with two simpler models of excitons reveal that the high degree of confinement in small quantum dots suppresses polaronic corrections in exciton properties. The reduction of the electron-hole correlation in small quantum dots is observed in the behavior of oscillator strength, which becomes less dependent on the form of the effective interaction as the dot size is reduced. A proper definition of exciton transition energy in ionic materials is pointed out, where self-energy renormalization effects are important. The results of our calculation are presented for quantum dots of some ionic materials such as CdSe, GaN, ZnO, and CuCl.