Polaronic exciton in a parabolic quantum dot

A calculation of the variations of the energy and oscillator strength of the ground state of an exciton in an ionic quantum dot as a function of the dot size, using a parabolic confining potential and a variational ap-proach, is presented. The strong exciton–phonon interaction is taken into account by using an effective potential between the electron and the hole as derived by Pollmann and Büttner. The values of the exciton binding energies calculated using this potential are compared with those obtained using statically screened Coulomb potential and are found to be considerably larger for all values of the quantum dot size. In small quantum dots, the electron–hole correlation is reduced as the single particle energies scale at a much faster rate than the interaction energy. This is manifested in the behavior of oscillator strength, which be-comes less dependent on the form of the effective interaction as the quantum dot size is reduced.