The energy of the ground and the excited states for the exciton and the binding energy of the acceptor - donor exciton complexes and as a function of the radius for an impurity position located in the center in the spherical ZnO quantum dots (QDs) embedded in a SiO2 matrix are calculated using the effective mass approximation under the diagonalzation matrix technique, including a three-dimensional confinement of carrier in the QD and assuming a finite depth. Numerical results show that the binding energy of the acceptor- donor exciton complexes is very sensitive to the quantum dot size. These results could be particularly helpful since they are closely related to experiments performed on such nanoparticles. This may allow us to improve the stability and efficiency of the semiconductor quantum dot luminescence which is, in fact, considered critical.