Binding energies of core excitons in semiconductors

Abstract

Excitons from core levels in semiconductors are treated by the effective-mass approximation. The problem of the appropriate electron-hole interaction is considered and the electron polaron model which treats valence electrons as quantum oscillators is adapted in order to include dynamical effects. An effective Hamiltonian is obtained, which contains electron and hole polarization self-energies and an electronhole interaction, all terms depending on variational parameters. Because of the large-hole self-energy the best choice of the variational parameters corresponds to free-electron and hole self-energies and to a Coulomb interaction screened by the static dielectric constant. Consideration of dispersive effects preserves the above results, but modifies the self-energies and introduces dispersive screening. The above results are unable to explain the large increase in binding energies of core excitons with respect to valence excitons. It is argued that this effect can be explained by nonlocal screening contributions due to off-diagonal terms in the dielectric matrix coupled to the interference of Bloch functions from equivalent minima at the hole position.