Doping in silicon nanocrystals

The absorption and, for the first time, the emission spectra of doped silicon nanocrystals have been calculated within a first-principles framework including geometry optimization. Starting from hydrogenated silicon nanocrystals, simultaneous n- and p-type doping with boron and phosphorous impurities have been considered. We found that the B-P co-doping results to be easier than simple B- or P-doping and that the two impurities tend to occupy nearest neighbours sites inside the nanocrystal itself. The co-doped nanocrystals bandstructure presents band edge states that are localized on the impurities and are responsible of the red-shifted absorption threshold with respect to that of pure un-doped nanocrystals in fair agreement with the experimental outcome. The emission spectra show a Stokes shift with respect to the absorption due to the structural relaxation after the creation of the electron-hole pair. Moreover, the absorption and emission spectra have been calculated for a small co-doped nanocrystal beyond the single particle approach by introducing the self-energy correction and solving the Bethe-Salpeter equation scheme. Our procedure shows the important role played by the many-body effects.