Singlet-triplet radiative transitions in silicon nanocrystals with shallow donors

Within the framework of the envelope function approximation, the rates of intraband radiative transitions in silicon nanocrystals with donors are calculated. It is shown that for nanocrystals of sufficiently small sizes (about two nanometers in diameter), the singlet level splitting off from the rest of the spectrum in the conduction band, arising due to the short-range potential of the donor ion, can be sufficiently strong (more than eV for a bismuth atom), which makes emission in the visible range possible. The rates of radiative transitions turn out to be on the order of inverse microseconds. At the same time, in the case of intraband transitions, Auger recombination can be completely eliminated and, thereby, the quantum efficiency of the luminescence process is significantly increased.