Energy spectra of donors in GaAs-Ga I - xAixAs quantum well structures in the effective mass approximation

We present the results of a study of the energy spectrum of the ground state for shallow donors in quantum well structures, consisting of a single slab of GaAs sandwiched between two semiinfinite layers of Ga1 _ x Alx As. The effect of the position of the impurity atom within the central GaAs slab is investigated for different slab thicknesses and alloy compositions. Two limiting cases are presented: One in which the impurity atom is located at the center of the quantum well (oncenter impurity), the other in which the impurity atom is located at the edge of the quantum well (on-edge impurity). Both the on-center and the on-edge donor ground state are bound for all values of GaAs slab thicknesses and alloy compositions. The alloy composition x is varied between 0.1 and 0.4. In this composition range, Ga1 _ x Alx As is direct and the single-valley effective mass theory is a valid technique for treating shallow donor states. Calculations are carried out in the case of finite potential barriers determined by realistic conduction band offsets.