Quantum-confined Stark effects on a GaAs cluster embedded in AlxGa

Quantum-confined Stark effects on the electronic structure of a GaAs microcluster with 63.5-A\r{} (120-a.u.) radius embedded in the ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As bulk crystal were investigated, within the effective-mass approximation, based on the Weyl-Titchmarsh theory. This approach provides both point and continuous spectral functions for the problem. Numerical calculations were performed on a continuous energy spectrum under an electric field for single-particle states of electron and heavy hole, and for an exciton state, using a 57:43 split of the band-gap discontinuity between the conduction and valence bands. The spherical-heterojunction potential barrier effects on the exciton state are discussed with regard to both exciton binding energy and exciton stability. The exciton Coulomb binding energy for the confined exciton in a cluster was found to be much larger than that in a one-dimensional superlattice system. Also, the Coulomb interaction brings about still longer exciton lifetimes compared with the external electrostatic field. Field ionization of the exciton is inhibited by the strong confined effects caused by the existence of the spherical quantum well.