The polaron effect on the energies of low_lying states of a negatively donor center( D -) confined in a disk_like quantum dot has been studied by using the method of few_body physics. The dependence of the binding energy of the D ˉ ground state on the quantum dot radius is obtained. A considerable enhancement of the binding is found for the D ˉ ground state, which results from the confinement of electrons and electron_phonon coupling.