Calculation of electronic energy states of a spherical quantum dots inside magnetic field

In this study, in existence and absence of an external magnetic field, the electronic properties of a spherical quantum dot were investigated. The quantum dot (QD) is assumed to have a finite and an infinite confining potential well. 1s, 2p, 3d and 4f energy levels and the wave functions of a hydrogenic impurity in GaAs/AlxGa1-xAs spherical quantum dot with radius R are calculated by the Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothan (HFR) method. Based on the wave functions and energy states, the binding energy of the spherical QD is carried out as a function of dot radius and aluminium concentration ratio. In addition, we report a detailed theoretical investigation of the effect of an external magnetic field on the energy states and binding energies of a spherical quantum dot. The Linear Zeeman and quadratic Zeeman transition energies between subbands were computed as a function of dot radius and magnetic field. The results show that the magnetic field, impurity charge, dot radius and aluminium concentration ratio have a strong influence on the energy states and the Zeeman transitions. Besides, the results present that, in large dot radius, the external magnetic field affects strongly the optical transitions between Zeeman states. In the strong spatial confinement cases, energy level is relatively insensitive to the magnetic field, and electron spatial confinement prevails over magnetic confinement.