Quantum properties of spherical semiconductor quantum dots

TL;DR

This paper enhances the theoretical modeling of semiconductor quantum dots by introducing an effective pseudo-potential, enabling more accurate predictions of their quantum properties and potential applications like QD-LASERs.

Contribution

It proposes a new pseudo-potential within the effective mass approximation, improving analytic calculations and aligning better with experimental data for quantum dot properties.

Findings

Predicted observable Lamb shift for specific semiconductors and radii.

Derived ground state energy, Stark, and Lamb shifts as functions of QD radius.

Evaluated Purcell factor indicating potential for visible light QD-LASERs.

Abstract

Quantum effects at the nanometric level have been observed in many confined structures, and particularly in semiconductor quantum dots (QDs). In this work, we propose a theoretical improvement of the so-called effective mass approximation with the introduction of an effective pseudo-potential. This advantageously allows analytic calculations to a large extent, and leads to a better agreement with experimental data. We have obtained, as a function of the QD radius, in precise domains of validity, the QD ground state energy, its Stark and Lamb shifts. An observable Lamb shift is notably predicted for judiciously chosen semiconductor and radius. Despite the intrinsic non-degeneracy of the QD energy spectrum, we propose a Gedankenexperiment based on the use of the Casimir effect to test its observability. Finally, the effect of an electromagnetic cavity on semiconductor QDs is also considered, and its Purcell factor evaluated. This last result raises the possibility of having a QD-LASER emitting in the range of visible light.