Shallow-donor states in spherical quantum dots with parabolic confinement

Abstract

The evidence of a parabolic potential well in quantum wires and dots was reported in the literature, and a parabolic potential is often considered to be a good representation of the "barrier" potential in semiconductor quantum dots. In the present work, the variational and fractionaldimensional space approaches are used in a thorough study of the binding energy of on-center shallow donors in spherical GaAs-GalxAlxAs quantum dots with potential barriers taken either as rectangular [Vb (eV) = 1.247 x for r > R ] or parabolic [ Vb (r) = p3 2 r 2 1 isotropic barriers. We define the parabolic potential with a fl parameter chosen so that it results in the same E 0 groundstate energy as for the spherical quantum dot of radius R and rectangular potential in the absence of the impurity. Calculations using either the variational or fractional-dimensional approaches both for rectangular and parabolic potential result in essentially the same on-center binding energies provided the dot radius is not too small. This indicates that both potentials are alike representations of the quantum-dot barrier potential for a radius R quantum dot provided the parabolic potential is defined with fl chosen as mentioned above.

Hydrogenic Donor in a Spherical Quantum Dot with Different Confinements

“…Strictly speaking as 𝑅 → ∞ all these energies should approach zero which is the free particle energy at 𝑘 = 0. Researchers [13,14] have found that the values of binding energies for cubic and spherical quantum dots are very close provided that the dots have similar volumes, which are in good agreement with our results.…”

Diamagnetic Susceptibility of a Confined Donor in a Quantum Dot with Different Confinements

“…We have compared the rectangular confinement with other confinements such as spherical and parabolic potentials as done in Ref. [16] in which the effect of diamagnetic susceptibility is not included. We have computed and compared the susceptibility for a hydrogenic donor in a spherical confinement, harmonic oscillator-like and rectangular well-like potentials for a finite QD and observe a strong influence of the shape of confining potential and geometry of the dot on the susceptibility.…”