Hydrogenic-Donor Impurity States In Coupled Quantum Disks In The Presence Of A Magnetic Field

We report the binding energies of a hydrogenic-donor impurity in a cylindrically symmetric GaAs/Ga_0.6Al_0.4As coupled quantum disk in the presence of a uniform magnetic field for different disk and barrier thicknesses, disk radii, and donor ion positions within the disk. The calculations were performed using a variational procedure for infinite and finite confinement potentials within the effective-mass approximation. The calculated results show that the binding energy is dependent on the interplay of the spatial confinement and magnetic field confinement: A high magnetic field significantly enhances the binding energy in the case of weak spatial confinement. The binding energy of a hydrogenic-donor impurity in two coupled quantum disks is found to be smaller than that in a corresponding single quantum disk, due to the coupling effect between the disks. For all positions of the donor ion, it is observed that the binding energy increases linearly with the strength of the applied magnetic field. For the case of an infinite potential barrier, the values of the binding energy are slightly larger than in the case of a finite potential barrier. The reason for this behavior is explained in terms of the leakage of the electron wave function, which depends on the spatial confinement and the magnetic field strength. In the limits of a single quantum disk and coupled quantum wells, the results are in good agreement with the previous calculations for the case in which the donor ion is located at the center of the quantum disk.The calculated results show that the binding energy is dependent on the interplay of the spatial confinement and magnetic field confinement: A high magnetic field significantly enhances the binding energy in the case of weak spatial confinement. It is clear that the binding energy increases gradually as the donor ion position goes from the center of the barrier to the edge of the disk. After reaching a maximum value at the center of the right disk, it then decreases. The binding energy with the donor ion located at the disk edge is larger than in the case in which the donor ion is located at the barrier center, due to the stronger confinement of the potential barrier. As can be seen, the peak values of the binding energy always occur at the center of the quantum disk when the applied magnetic field changes. We would like to mention that the electron probability density for the donor ion at the barrier center (solid lines) is moresymmetrically distributed than the case in which for the donor ion is located at the center of the right disk (dashed lines), independent of the applied magnetic field. The obvious difference between the two distributions is that one is symmetrical with two maxima while the other is asymmetric.The study of the behaviors of binding energies and electron probability of such systems under applied magnetic fields will lead to a better understanding of the electronic and optical properties of low-dimensional semiconductor systems.