We calculate spin-dependent excitation energies of Ge and Si nanocrystals by means of a $\Delta$-self-consistent-field method that considers the excitation of an electron-hole pair and thus includes the electron-hole Coulomb interaction. The method is based on local-density and local-spin-density calculations and yet reproduces the respective time-dependent local-density approximation results well. In addition, lattice contributions to the luminescence Stokes shift and the radiative lifetimes of the electron-hole pairs are calculated. All quantities are discussed in terms of their confinement dependence as well as with respect to the different behavior of Ge and Si crystallites. A detailed comparison to experimental work and to other theoretical results is presented.

• Received 11 June 2003

DOI:https://doi.org/10.1103/PhysRevB.69.115310