Stark effects on Coulomb-bound states in GaAs–(Ga,Al)As quantum wells: virial theorem and scaling properties

The effects of applied electric fields on donor and exciton states confined in GaAs–(Ga,Al)As quantum wells are studied in the effective mass approximation and within the variational and fractional-dimensional space approaches. In the fractional-dimensional scheme, an effective isotropic medium is used to model the anisotropic Coulomb-bound state + quantum well + electric-field system, whereas a hydrogenic-like wave function is used in the variational procedure. Results are obtained for the binding energies, virial-theorem values, and scaling properties of the Coulomb-bound states under growth-direction applied electric fields. We show that a ground-state wave function assumed as a D-dimensional hydrogenic wave function leads to a virial-theorem value of 2 and a hyperbolic scaling for binding energies of Coulomb-bound states versus quantum-confined Bohr radii, in contrast with results using the variational approach. Both methods result in Stark shifts for the exciton-peak energies in good agreement with electroabsorption experiments.