Modeling the dynamics of trapped electrons in quantum dots
Phys. Rev. B 114, 065416 – Published 15 July, 2026
DOI: https://doi.org/10.1103/g6pd-qpd1
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 extended band states of a quantum dot using a simple model in which the valence and conduction bands of the quantum dot are modeled by two single-particle energy levels and the trap is described by one single-particle level within the band gap. 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 femtoseconds, followed by a quasistationary 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. These factors always show fast oscillations associated to electrons hopping back and forth from the conduction band to the trap, irrespective of the motion of the valence band electrons. Our calculations show that light emission of different energies is always possible except in the special 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.
