Binding energy of the complex (${\mathit{D}}^{+}$-X) with Γ-X mixing in GaAs/AlAs quantum wells

The binding energy of excitons to ionized shallow donors in a GaAs/AlAs quantum well in the vicinity of the type-I to type-II transition is obtained for impurities lying anywhere in the structure. We include the Γ-X hybridization in the Brillouin zone, which comes into play when the energies of the conduction subband minima in the two materials become closer. The calculation is performed variationally using a three parameters trial function similar to the one describing a singly ionized molecule. The same model allows the calculation of the binding energies of the neutral impurity and of the free exciton. We obtain that a ratio between the binding energy of the exciton to an ionized donor and that of the neutral donor equals 0.95±0.005, for all values of well widths explored, and independent of the impurity position inside the well. The joint density of states for the transition from free to bound exciton is obtained, and a discussion is presented on the role played by the doping and the compensation on the exciton dynamics. © 1996 The American Physical Society.