Excitones confinados en puntos cuánticos esferoidales prolatos

Abstract

The variational method is used to solve in approximately way the Schrödinger's wave equation associated to a Wannier-Mott exciton confined within a spheroidal quantum dot. The confinement effect on the ground-state energy of the electron-hole pair trapped inside a crystallite with this geometry, and with soft or hard walls, is analyzed. The walls can be modeled as finite or infinite potential barriers with suitable border conditions, which will depend on the considered case. The results of this work are compared with those obtained by other authors through more sophisticated methods. A comparison with experimental data of CdS crystallites embedded in materials of different composition is made, too. For a finite potential barrier, a critical size of the crystallite from which the exciton escapes of the quantum dot, is predicted. This is in opposition with the infinite potential barrier model where the exciton never can leave the region where it is confined.