Donor impurity energy levels in GaAs/AlxGa1−xAs circular quantum dots

In this work we calculate the donor binding energy of a hydrogenic donor impurity located in the center of a GaAs–AlxGa1−xAs circular quantum dot. The electron wave functions are obtained analytically by solving the Schrödinger equation and the impurity energy levels are determined through the solution of the transcendental equations obtained from the boundary conditions imposed at the interfaces of the quantum dot. We find numerically the roots of the transcendental equations for circular quantum dots, with finite height of the confinement potential. Our analytical results for circular quantum dot are compared with that obtained via variational method. Results for spherical quantum dots are also included for the sake of comparison.