Luminescence polarization of silicon nanocrystals

We consider theoretically the polarization of the luminescence of Si nanocrystals that ru-ises from the anisotropy of the optical moments. No-phonon and phonon-assisted optical transitions are calculated in tight binding and interpreted using effective-mass theory. In contrast to direct-gap semiconductors, we show that simple selection rules cannot be established in Si nanocrystals because the degree of linear polarization presents large oscillations with respect to the size of the clusters. This effect is due to the indirect nature of the Si band gap that leads to a dependence of the optical matrix elements on the oscillatory overlaps between electron and hole states in momentum space. However, in a statistical ensemble of crystallites elongated in a given direction and with size larger than 2-3 nm, we obtain that the light is in average polarized along this direction, in agreement with the experiments.