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For Si and Ge nanocrystals (NCs) embedded in wide band-gap matrices, Augerrecombination (AR) and carrier multiplication (CM) lifetimes are computedexactly in a three-dimensional real space grid using empirical pseudopotentialwave functions. Our results in support of recent experimental data offer newpredictions. We extract simple Auger constants valid for NCs. We show that bothSi and Ge NCs can benefit from photovoltaic efficiency improvement via CM dueto the fact that under an optical excitation exceeding twice the band gapenergy, the electrons gain lion's share from the total excess energy and cancause a CM. We predict that CM becomes especially efficient for hot electronswith an excess energy of about 1 eV above the CM threshold.

Auger recombination and carrier multiplication in embedded silicon and germanium nanocrystals