Excitons Bound to Ionized Impurities: Calculation of the Binding Energies of Exciton—Ionized-Donor Complexes

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Abstract
The method given by Pekeris for the helium atom and generalized recently by Frost for the three-particle system has been developed extensively to apply to complexes of excitons bound to ionized impurities in semiconductors. Haken's exciton potential is generalized for the complex, and the dielectric constant between the different particles is a function of the interparticle distances. This potential is different from that given by Schroder and Birman, where the ionic polarizability has been neglected. An elaborate general recursion relation is obtained. The application of this relation to the case of ionized donors shows the importance of the corrections introduced due to the polarizability of the potential between the particles. The calculations also show that the critical mass ratio below which the system is stable depends not only on the wave function, but also on the distances between the particles as well as on the fundamental constants: the optical and static dielectric constants, the effective masses of the electron and the hole, and the longitudinal vibrational frequency of the lattice. The results for exciton—ionized-donor complexes in CdS, CdTe, ZnSe, ZnTe, and ZnO give better agreement with experiment than those reported by the previous authors where the polarizabilility has been neglected. The calculations also confirm the existence of such a complex for 6H SiC. The exciton binding energies calculated for TlCl and TlBr are in better agreement with experiment than those given previously.