Investigation of Auger recombination in Ge and Si nanocrystals embedded in SiO2 matrix

We study theoretically the optical properties of embedded Ge and Si nanocrystals (NCs) in wide band-gap matrix and compared the obtained results for both NCs embedded in SiO2 matrix. We calculate the ground and excited electron and hole levels in both Ge and Si nanocrystals (quantum dots) in a multiband effective mass approximation. We use the envelope function approximation taking into account the elliptic symmetry of the bottom of the conduction band and the complex structure of the top of the valence band in both Si and Ge (NCs). The Auger recombination (AR) in both nanocrystals is thoroughly investigated. The excited electron (EE), excited hole (EH) and biexciton AR types are considered. The Auger recombination (AR) lifetime in both NCs has been estimated and compared.