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.37566066