Exact ground state solution of shallow hydrogenic impurity states of a spherical parabolic GaAs/InAs quantum dot

Abstract

The ground state spin magnetic moment current, binding energy, wave function and diamagnetic susceptibility of a shallow hydrogenic impurity located at the center of a parabolic spherical quantum dot (QD) are calculated analytically as a function of the dot size, interaction strength and confinement frequency. For comparison purposes, the results are discussed in the presence and in the absence of an impurity. Also, the dependence of the spin magnetic moment current on the spherical coordinates are derived, it is found that the spin magnetic moment current exhibits a peak structure and this current has a pronounced maximum for both small dot sizes and in the absence of impurities. Our results show that the impurities’ ground state binding energy enhances as the dot dimension decreases and depends strongly on the interaction strength as the dot size increases and reduces to zero in the bulk limit for large dimensions of the dot. Moreover, the harmonic interaction has a strong influence on the diamagnetic susceptibility when the dot size increases where it decreases sharply in the presence of impurities while in the absence of impurities it decreases smoothly. In addition, the intensity of the magnetic field created by the spin magnetic moment current at the center of the QD has been calculated. It is concluded that there is a critical value for characteristic parameters and the dot size for each type of semiconductor QD to give a specific function that might be important for nanotechnology manufacturing techniques.