Landau quantization of a circular Quantum Dot using the BenDaniel-Duke boundary condition

TL;DR

This paper derives and analyzes the energy levels of a circular quantum dot under magnetic fields using the BenDaniel-Duke boundary condition, showing strong influence on charge densities and energies with good experimental agreement.

Contribution

It introduces a novel application of the BenDaniel-Duke boundary condition to quantum dot energy level calculations, including analytical approximations and experimental validation.

Findings

Numerical results agree with experimental data on GaAs-InGaAs quantum dots.

The BDD significantly affects charge densities and transition energies.

Analytical approximations converge well for larger quantum dots.

Abstract

We derive the energy levels of a circular Quantum Dot (QD) under a transverse magnetic field, incorporating the Ben-Daniel Duke boundary condition (BDD). The parameters in our model are the confinement barrier height, the size of the QD, the magnetic field strength, and a mass ratio highlighting the effect of using BDD. Charge densities, transition energies, and the dependence of energies on magnetic field has been calculated to show the strong influence of BDD. We find that our numerical calculations agree well with experimental results on the GaAs-InGaAs Quantum Dot and can be used further. We also provide an insightful analytical approximation to our numerical results, which converges well for larger values of size and confinement.