Donor states in a multi-layered quantum dot

Abstract

The ground and excited state energies of a hydrogenic impurity located at the centre of a multi-layered quantum dot (MLQD) are calculated in the framework 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-xAlyAs). We solve the Schrodinger equation exactly. The eigenfunctions of the impurity are expressed in terms of Whittaker function and Coulomb wavefunction. The state energies are expressed in terms of the shell thickness, core radius, total dot radius and the potential heights. Our calculation shows that, as the dot radius approaches infinity, the state energies of an impurity located at the centre of a multi-layered or a single-layered QD approach -1/n(2) Ry, where n is the principal quantum number, Ry = mue(4)/2 epsilon (2)h(2), mu and epsilon are the electronic effective mass and the dielectric constant of GaAs material. Thus it behaves like a three-dimensional free hydrogen atom. For very small dot radius, however, the state energy of the hydrogenic impurity of a MLQD behaves very differently from that of a single-layered QD. For a multi-layered QD with finite shell and bulk potential barrier heights, the state energies of the impurity are found to be dependent on the difference of the shell potential (V-2) and the bulk potential (V-3).