Using a variational approach within the effective mass approximation, we ca
lculated the binding energy of a bound polaron to shallow donor impurity in
spherical Quantum Dots (QD), where a weak electric field is applied in the
z-direction. The interactions of carrier charges (electron and ion) with t
he longitudinal optical phonons as well as the surface optical phonons are
considered. Calculations are made using a finite confinement potential. Res
ults are obtained as a function of the dot size and the donor impurity posi
tion for different electric field strengths. It is found that the binding e
nergy is very sensitive to the polaronic effect, the confinement, and the e
lectric field.