Effect of the type-I to type-II transition on the binding energy of shallow donors in GaAs/AlAs quantum wells

The binding energy of electrons to shallow donors in GaAs/AlAs quantum wells in the vicinity of the type-I to type-II transition is obtained for impurities lying inside the GaAs layer. The calculation is performed variationally using a two-parameter trial function, the same for both type-I and type-II structures. The transition occurs for a GaAs layer width near 37 Å. For widths smaller than 37 Å we obtain the binding energy for the X electrons in a GaAs/AlAs double well, where the impurity lies inside the GaAs middle barrier. For widths larger than 37 Å the binding energy is calculated using a single well for the Γ electrons. A change of symmetry from s-like to p-like is obtained as the transition occurs, for the Γ and for the X electron, respectively.