Energy spectra of donors in GaAs-Ga_(1-x)Al_(x)As quantum well structures in the effective mass approximation

We present the results of a study of the energy spectrum of the ground state and the low-lying excited states for shallow donors in quantum well structures consisting of a single slab of GaAs sandwiched between two semi-infinite layers of Ga_(1-x)Al_(x)As. The effect of the position of the impurity atom within 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 (on-center 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, Ga_(1-x)Al_(x)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