Impurity Donor in a Quantum Disk

The donor binding energy of a hydrogenic donor impurity located in the center of a GaAs-AlxGa1-xAs circular quantum dot is calculated by solving analytically the Schrödinger equation. The electron wave functions and the impurity energy levels are determined in the standard manner through the solution of the transcendental equations obtained from the boundary conditions imposed at the interfaces of the quantum disk. The roots of the transcendental equations were numerically found for quantum disks with finite height of the confinement potential.