The low lying state binding energies of hydrogenic impurity located at the center of a GaAs-A1xGa1-xAs-A1yGa1-yAs multi-layer quantum dot (MLQD) are calculated with different effective mass and dielectric constant parameter combinations. The MLQD consists of a spherical core (GaAs) and a coated spherical shell (A1xGa1-xAs). The whole dot is embedded inside a bulk material (A1yGa1-yAs). The eigenfunctions of the impurity can be expressed in terms of Whittaker functions and Coulomb wave functions. The ground state and low lying state binding energies are expressed in terms of the dot radius, core radius, and oncentration of A1 with ifferent parameter ombinations. Our result hows the low lying state binding nergies is approximate for low concentration of A1 and large dot radius. As the oncentration of A1 increases the difference of binding energy increases. We must consider the difference of the effective mass and dielectric constant between the GaAs and A1xGa1-xAs region for the small dot radius calculations. Our results also show the effective mass is more important than ielectric constant for low lying state binding energy. PACS Number: 63. 20. Kr; 71. 38 +i
