Theory of excitonic exchange splitting and optical Stokes shift in silicon nanocrystallites: Application to porous silicon

Abstract

Binding energies and radiative lifetimes of excitons in crystallites are calculated with respect to size and temperature by using a tight-binding configuration-interaction technique. We discuss the recent proposal that, for porous silicon, the exchange splitting could be at the origin of the peculiar behavior of the lifetime and luminescence intensity with temperature, as well as the existence of an onset in selectively excited luminescence. We show that the exchange splitting has no influence on the luminescence lifetime of spherical- or cubic-silicon crystallites because of the spin-orbit and valley-orbit couplings. In contrast, in asymmetrical crystallites, we predict that the spin-orbit and valley-orbit couplings are quenched so that the influence of the exchange splitting can be detected. However, we calculate exchange splittings smaller than the onsets observed in the spectra of the selectively excited luminescence of porous silicon. We show that the Stokes shift induced by the lattice relaxation in the excitonic state is significant and may explain at least partially this decrepancy. We confirm that the direct radiative recombinations are not responsible for the observed decay of the luminescence in porous silicon. © 1994 The American Physical Society.