Wannier excitons in semiconductor quantum wells with small valence-band offsets: A generalized variational approach

The ground-state and binding energy of a Wannier exciton in a quantum well with a small valence-band offset are calculated by generalizing the variational approach normally used to study excitons in GaAs/${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells. The central issue is to properly include the additional confinement of the hole caused by the electron-hole Coulomb interaction in the direction perpendicular to the quantum-well interface. In addition to the relative motion part of the exciton wave function, the envelope function of the hole in that direction is also determined variationally. The application of this method to II-VI–compound semiconductor quantum wells studied in recent experiments is discussed.