Polaronic effects on the energy levels of a double donor impurity in quantum wells in the presence of a magnetic field

In the presence of a magnetic field the Hamiltonian of the single or double polaron bound to a helium-type donor impurity in semiconductor quantum wel ls (QWs) are given in the case of positively charged donor center and neutr al donor center. Thf couplings of an electron and the impurity with various phonon modes are considered. The binding energy of the single and double b ound polaron in Al-xi Ga1-xi As/GaAs/Al-xr Ga1-xr As QWs are calculated. Th e results show that for a thin well the cumulative effects of the electron- phonon coupling and the impurity-phonon coupling can contribute appreciably to the binding energy in the case of ionized donor. In the case of neutral donor the contribution of polaronic effects are not very important, howeve r the magnetic field significantly modifies the binding energy of the doubl e donor. The comparison between the binding energies in the case of the imp urity placed at the quantum well center and at the quantum well edge is als o given.