Hydrogenic impurity states in GaAs-Ga_1-xAl_xAs quantum well structures

The authors report the results of a variational calculation for the energy spectrum of the ground state and the low-lying excited states of hydrogenic impurities in quantum well structures consisting of a single slab of GaAs sandwiched between two semi-infinite slabs of Ga_1-xAl_xAs. The binding energies of donor levels are calculated as a function of GaAs slab thickness and the impurity position. Two alloy compositions x=0.1 and 0.4 are studied. Calculations are carried out for the cases of finite potential barriers determined by realistic conduction band offsets at the interface. The results of the present calculation are compared with some previous papers. It is shown that the binding energy correction is substantial when the well thickness L<50 AA, for the case when the impurity atom is located at the centre of the quantum well and x=0.4. The peak value correction exceeds 15%, so that the result resembles Bastard's infinite-barrier model. As expected, the lifting of the degeneracy for the energy levels on the impurity position is not as remarkable as that of the latter. Furthermore, the influence of the different effective masses of GaAs and Ga_1-xAl_xAs on the ground-state binding energy is investigated. It is found that this influence enhances with the decrease of well width. In order to depict the spreading of the wavefunctions and the shape of the peak, they have plotted wavefunctions for some typical GaAs well widths.