Confined Neutral Donor States

Abstract

The early calculations on the impurity states in quantum wells were based on the one-band effective mass approximation (EMA), which earlier has been successfully applied on the corresponding shallow impurity states in 3D bulk material. In the original theoretical work for the confined impurity states, Bastard performed calculations on the electronic structure of the impurities in quantum wells assuming a hydrogenic impurity confined in a quantum well with infinite barrier heights [21]. In this approximation, the electronic wave function vanishes in the barrier and the wave function of an impurity at the interface must be a p-like state, whereas the corresponding wave function for an on-center impurity is a s-like state. For the case of an impurity at the interface and in the center in the wide quantum well limit, a binding energy of R ^* _3D/4 and R ^* _3D, respectively, is predicted (with R ^* _3D being the effective Rydberg for a hydrogenic impurity in bulk). Also the calculated binding energies for an on-center impurity was found to increase monotonically from the bulk value, R ^* _3D to R ^* _2D = 4R ^* _3D at vanishing quantum well width, L _z (see Fig. 4.1).