Understanding doping in silicon nanostructures

The effects of both single doping and simultaneous codoping on the structural, electronic, and optical properties of Si nanocrystals are calculated by the first-principles method. We show that the amount of the nanocrystal relaxation around the impurity is directly related to the impurity valence. Moreover, both the neutral impurity formation energies and the impurity activation energies scale with the reciprocal radius. Interestingly, no significant variation of the activation energy on the impurity species is found, and the cluster relaxation gives a minor contribution to it. The role of the impurity position within the nanocrystal has also been elucidated showing that the subsurface positions are the most stable ones. We show that, if the carriers in the Si nanocrystals are perfectly compensated by simultaneous doping with the n- and p-type impurities, the nanocrystals undergo a minor structural distortion around the impurities. The formation energies are always smaller than that for the corresponding single-doped cases. Moreover, in the case of codoping, the bandgap is strongly reduced with respect to the gap of the pure crystals showing the possibility of an impurity-based engineering of the photoluminescence properties of the Si nanocrystals.