A tight-binding representation of electron-hole exchange interaction in semiconductors

The electron-hole exchange interaction in semiconductors is analyzed in the framework of the empirical tight-binding method. It is demonstrated that intra-atomic and interatomic contributions to the long-range exchange interaction enter in an inequivalent way. In particular, for the Γ6×Γ7 exciton in a spherical nanocrystal with a cubic lattice, the dipole-dipole contribution associated only with the intra-atomic (or intra-site) transitions does not lead to singlet-triplet splitting of the exciton level. The interatomic transitions, for example, anion-to-cation transitions between the nearest neighbors in binary semiconductor compounds, determine the so-called monopole-monopole contribution to the exchange splitting of the Γ6×Γ7 exciton, and this contribution does not vanish in a spherical nanocrystal.