  In this study, we have performed a detailed investigation of the electronic
properties of a core/shell/well/shell multi-layered spherical quantum dot, such
as energy eigenvalues, wave functions, electron probability distribution and
binding energies. The energy eigenvalues and their wave functions of the
considered structure have been calculated for cases with and without an
on-center impurity. For this purpose, the Schr\"{o}dinger equation has been
numerically solved by using the shooting method in the effective mass
approximation for a finite confining potential. The electronic properties have
been examined for different core radii, barrier thickness and well widths in a
certain potential. The results have been analyzed in detail as a function of
the layer thickness and their physical reasons have been interpreted. It has
found that the electronic properties are strongly depending on the layer
thickness.
