Effects of Γ-X mixing on the binding energy of a shallow donor in an AlAs/GaAs quantum well

The effects of mixing between the Γ and χ valleys of the conduction band on the binding energy of a shallow donor in a thin type-I AlAs/GaAs quantum well are investigated. The multivalley effective-mass equations are solved variationally, with a separable hydrogenlike trial function. The binding energy, as a function of well width, is found to be almost the same as in the zero-mixing case, except in the vicinity of the type I–to–type II crossover, where mixing leads to a fundamentally different behavior, namely, instead of decreasing monotonically with increasing well width, the binding energy presents a peak close to the crossover. Using a renormalized effective mass for the Γ point in the AlAs layers, the interaction with the valence band is estimated to the first order and shown to be quite important.