Influence of the image charge effect on the hydrogen-like impurity-bound polaron in a spherical quantum dot in the presence of an electric field

Highlights: • Image charges reduce the binding energies of 1s-, 2s-like states. • Image charges don't allow the occurrence of 2p-like bound states. • Phonon contribution in ground energy is 36.9% at $F=5\mathrm{kV}/\mathrm{cm}$, $ħ{\omega }_0=5\mathrm{meV}.$ We have investigated the influence of an external electric field on the binding energies and polaronic shifts of the ground and some first few excited states of a hydrogenic impurity in a spherical quantum dot by taking into account the image charge effect. By using Landau–Pekar variational method the general analytical expression is obtained for the impurity bound-polaron energies. It has been numerically identified the conditions (electric field, nominal radius of quantum dot, etc.) in which the bound-polaron states can be existence in GaAs quantum dot. We have shown that the polaronic shifts in the binding energy of 1s-like state are the same in cases with and without image charge effect while they for 2s-like state are not coincide and have different monotonic behavior versus confinement potential. Electron–phonon interaction lifts the degeneracy of the 2px-, 2py-, and 2pz-like states of a donor impurity and reduces their binding energies.