The energy states of a hydrogenic impurity, located at the center of a multilayered spherical quantum dot, are calculated as functions of the barrier thickness and the inner dot thickness by using a fourth-order Runge-Kutta method. It is shown that the method is able to calculate all the energy states for any potential pro. le in the dot. Also, the binding energies show dramatic changes in comparison with those of single spherical quantum dots. (C) 2009 Elsevier B.V. All rights reserved.