Theory of fine-structure splittings for donor-bound excitons in indirect materials

Abstract

We present a theory for the fine structures in the electronic excitation spectra for excitons bound to various donors in Si and Ge. These fine structures are produced by the mixing of Hartree-Fock solutions through the interparticle interactions. We have calculated excitation energies for the low-lying electronic excited states in the Hartree-Fock approximation, and estimated the fine-structure splitting using the first-order degenerate perturbation theory. The energy separations between these states and the ground state are in good agreement with the experimental data. The fine-structure terms are found to be small relative to the separation between states from different configurations for most donors in Si and Ge, thus allowing an interpretation of the spectra in terms of a shell model.