Excitonic states in spherical layered quantum dots

TL;DR

This paper investigates excitonic states in spherical layered quantum dots using the $oldsymbol{k}oldsymbol{ullet}oldsymbol{p}$ method, revealing complex behaviors of exciton binding energies influenced by core size and material interfaces.

Contribution

It introduces a detailed numerical approach to study excitons in layered quantum dots, highlighting the impact of multilayer structures on excitonic properties.

Findings

Exciton binding energy varies non-linearly with core radius.

Large steep changes in binding energy occur in double-well quantum dots.

Interface polarization charges significantly affect excitonic spectra.

Abstract

he properties of excitons formed in spherical quantum dots are studied using the $\mathbf{k}\cdot\mathbf{p}$ method within the Hartree approximation. The spherical quantum dots considered have a central core and several concentric layers of different semiconductor materials that are modeled as a succession of potential wells and barriers. The $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian and the Coulomb equations for the electron-hole pair are solved using a self-consistent iterative method. The calculation of the spectrum of the empty quantum dot and the electron-hole pair is performed by means of a very accurate numerical approximation. It is found that the exciton binding energy as a function of the core radius of the quantum dot shows a strong non-linear behaviour. In particular, for quantum dots with two potential wells, the binding energy presents a large steep change. This last behaviour is explained in terms of the polarization charges at the interfaces between different materials and the matching conditions for the eigenfunctions.