Modeling the dynamics of trapped electrons in quantum dots

TL;DR

This study models the complex electron dynamics in quantum dots, revealing short transient behaviors, electronic correlations, and conditions affecting light emission, with implications for understanding optical properties of nanomaterials.

Contribution

It introduces a simple yet effective numerical model to analyze electron interactions and light emission in quantum dots, highlighting correlation effects and transient dynamics.

Findings

Electron dynamics have short transient phases of tens of femtoseconds.

Strong electronic correlations are observed for negative Coulomb interactions.

Light emission occurs under most conditions, except when the valence band is initially filled with two electrons.

Abstract

We analyze the effects of electron-electron and electron-phonon interactions in the dynamics of a system of two or three electrons that can be trapped to a localized state and detrapped to ab extended band states of a quantum dot using a simple model. In spite of its simplicity the time dependent problem has no analytical solution but a numerically exact one can be found at a relatively low computational cost. Within this model, we study the time evolution of the electron occupancies of conduction and valence bands and the trap state, as well as the statistical factors influencing light emission of different energies. In most of the analyzed cases, the system dynamics has a very short transient determined by the hopping parameters, that can be of tens of femptoseconds,followed by a quasi-stationary regime in which the electron occupancies either oscillate periodically around their time-averaged values or remain nearly constant. We find signatures of strong electronic correlations in the electronic motion for negative values of the effective electron-electron Coulomb interaction that are not translated to the statistical factors for light emission. Our calculations show that light emission of different energies is always possible except in the especial cases in which the valence band is initially filled with two electrons. In these cases the valence band can lose and recover electrons periodically but exciton emission is negligible at any time. We use this fact to attempt to give a possible explanation for the increase in the intensity of exciton emission with the concomitant decrease in the intensity of the green emission lines upon continuous illumination with ultraviolet radiation, experimentally observed for ZnO nanoparticles suspended in an alcohol.