Variation and adjustment of the optical gap of small Si nanocrystals by partial substitution of Si with Ge

In order to adjust the optimum region of diameters of Si based nanocrystals, which can emit in the visible region of the spectrum, we have partially substituted in Si nanocrystals layers of Si atoms by similar layers of Ge atoms and calculated the optical and HOMO-LUMO gaps as a function of Ge concentration and of the size of the nanocrystals, up to about 20 Å in diameter. For the calculation of the optical gap of Si_xGe_y:H_z nanocrystals as a function of x , y, and z, we have used the framework of time dependent density functional theory (TDDFT) with the hybrid nonlocal exchange-correlation functional of Becke, Lee and Yang (B3LYP). Our results show that by proper adjustment of x, y and z we can optimize either the range of diameters for a desired gap, or the value of the optical gap for a given diameter.