Calculation of Binding Energies of the Ground and Excited States of a Donor in GaAs-AlxGa1-xAs Step Quantum Wells11The project supported by National Natural Science Foundation of China.

Abstract

In this paper we present for the first time completely analytical variational expressions for calculating the binding energies of the low-lying bound states of a hydrogenic donor in a quantum well (QW). These expressions can be used for the problem of the binding energy of an impurity in a general manner, e.g. for calculating the binding energies of a donor associated with subband states of any order in the QW with any arbitrary potential profile. To demonstrate the utilization of these expressions we have theoretically studied the binding energies for the ground and a few low-lying excited states of a hydrogenic donor in a stepped quantam well (SQW). The variations of the binding energies for these donor etates with impurity positions are investigated for different heights of the step potential. The numerical calculation results show that the binding-energy curves in the SQW, in contrast to the case of the flat quantum wells (FQW's), exhibit a non-symmetrical structure relative to the center of the QW and depend on the sub-barrier potential. The peak position in the binding energy curves shifts away from the region occupied by the sub-barrier as increasing sub-barrier height. The maximum in the binding energies increases as the step potential increaaes. These effects can be interpreted by referring to the variation of the electron probability-density distribution and of the lowest subband in the SQW. The shape of the binding-energy curves related to the 2p0like state is different from the other states. It is associated with the particular feature of the wave function of the 2p0 state in the QW.