Hydrogenic donor states in quantum dots in the presence of a magnetic field

We report a calculation of the binding energy of the ground state of a hydrogenic donor in a quantum dot, assumed to be in the form of a disk, in the presence of a uniform magnetic field applied parallel to the disk axis. We assume that the impurity ion is located at the center of the disk. The quantum disk is assumed to consist of a finite length cylinder of GaAs material surrounded by ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As. The calculations have been performed by using a suitable variational wave function for infinite confinement potential at all surfaces. The binding energy of a donor impurity located at the center of the disk depends on the radius and length of the disk. The three-dimensional confinement of the quantum disk results in a larger binding energy for the hydrogenic donor than in the corresponding quantum well and quantum wire structures. In addition for a given set of values of the radius and the length of the disk, the binding energy increases as a function of the magnetic field. We recover two- and three-dimensional limits for the binding energy for various combinations of disk radius and length.