A detailed investigation of the electronic properties of a double electron in a core/shell/well/shell quantum dot heterostructure has been systematically studied for cases with and without an on-center donor impurity. For this purpose, the Poisson-Schrodinger equations have been solved self-consistently in the frame of the single band effective mass approximation and Hartree treatment. The variation of the binding energies of negatively charged donor impurity (D-) have been examined for different core radii, shell thicknesses, and well widths. The results obtained have been presented comparatively as a function of layer thicknesses and probable physical reasons behind in their behavior have been discussed. (C) 2013 AIP Publishing LLC.