Negative-Donor in Graded Quantum Well-Wire: Fractal Dimension Approach

Abstract

Ground state energy of a D0 and D— placed at the axis of a GaAs/(Ga,Al)As cylindrical quantum-well-wire (QWW) in the presence of an external magnetic field oriented along the growth axis is calculated within the framework of effective-mass approximation. A model of confinement with a soft-barrier profile produced by a gradual variation of the Al concentration in the transition region of the junctions is considered. The one- and two-particle problems in a homogeneous space with cylindrical symmetry are reduced to similar problems in an effective non-homogeneous isotropic space by using the fractal dimension method. The variable fractal dimension in this space is expressed in terms of the unbounded electron ground state wave function, which we find by using trigonometric sweep method. The D— binding energy as a function of the graded GaAs/Ga0.7Al0.3As QWW radius for different values of the transition region thickness and the magnetic field intensity are calculated by using the Hylleraas procedure. It is found that the D— binding energy increases from 0.055 Ry* up to about 1.230 Ry* as the radius decreases from infinity up to 30 Å. It is shown that the magnetic field and a smoothing confining potential produce a considerable enhancement of negative-donor binding energy, only for radii greater than 100 Å.