With both LO and SO modes being taken into account, the influence of electron-phonon interaction on QCSE of a bound polaron in a finite quantum well (QW) is investigated by means of the perturbation-variation method. It is found that the presence of an ionized impurity decreases the energy shift and weakens the effect of a finite barrier height. LO and SO mode effects will give significant corrections to the Stark energy shift individually and their influences on the shift just are contrary.
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