The binding energies of hydrogenic impurity located at the center of a multi-layer quantum dot (MLQD) are studied within the framewokr of the effective-mass approximation. The MLQD consists of a spherical core (e.g.GaAs) and a coated spherical shell (e.g. Ga1-xAlxAS). The whole dot is then embedded inside a bulk material (e.g.Ga1-yAlyAs). The eigenfunctions of the impurity can be expressed in terms of Whittaker functions and Coulomb wave functions. For illustration, the ground state energy and binding energies are calculated as functions of the shell thickness, core radius, total dot radius and the potential heights. Our calculation shows that , as the dot radius approaches infinity, the ground state binding energy of a multi-layer or a single layer QD approaches 1Ry and behaves like that in a 3-dimensional free hydrogen atom. For very small dot radius, the ground state binding energy of the hydrogenic impurity located at the center of a MLQD behaves very different from that of a single layer QD. In contrast with 1Ry for a single layer QD with finite potential height, the ground state binding energy of the impurity located at the center of a MLQD with finite shell and bulk potential barrier height approaches different limiting values from zero to 1Ry depending on the difference of the shell potential (V2) and the bulk potential (V3). For V2-1≧V3, the electron tunnels to the bulk region and behaves like a free electron, and the ground state binding energy approaches zero for very small dot radius. For V2≦V3, the electron tunnels to the shell region and the impurity atom behaves like a free hydrogen atom and the binding energy is equals to 1Ry. For 0<(V2-V3)<1, the electron is able to stay either in the shell or in the bulk region and the binding energy is 1-(V2-V3). PACS Number:63.20.kr;71.38.+i
