Auger recombination and carrier multiplication in embedded silicon and germanium nanocrystals

For Si and Ge nanocrystals (NCs) embedded in wide band-gap matrices, the Auger recombination and carrier multiplication (CM) lifetimes are computed exactly in a three-dimensional real space grid using empirical pseudopotential wave functions. Our results in support of recent experimental data offer other predictions. We extract simple Auger constants valid for NCs. We show that both Si and Ge NCs can benefit from photovoltaic efficiency improvement via CM due to the fact that under an optical excitation exceeding twice the band-gap energy, the electrons gain lion's share from the total excess energy and can cause a CM. We predict that CM becomes especially efficient for hot electrons with an excess energy of about 1 eV above the CM threshold.