Local rigidity and physical trends in embedded Si nanocrystals

Abstract

We investigate the problem of local rigidity of Si nanocrystals embedded in amorphous silica. By analyzing the elastic (bulk) modulus field into atomic contributions, we show that it is highly inhomogeneous. It consists of a hard region in the interior of the nanocrystals, with moduli $\ensuremath{\sim}105$ GPa, compared to 98 GPa for bulk Si, and of ``superhard'' ($\ensuremath{\sim}120$ GPa) and ``supersoft'' ($\ensuremath{\sim}80$ GPa) regions in the outer parts. Overall, the nanocrystal bulk modulus is significantly enhanced compared to the bulk, and its variation with size accurately follows a power-law dependence on the average bond length. The bulk modulus of the oxide matrix and of the interface region is nearly constant with size, with values 60 and 70 GPa, respectively. The average optical (homopolar) gap is directly linked to the elastic and bond-length variations.