Influence of the local microstructure on the macroscopic properties of Si _1-x-yGe _xC _y alloys

We performed a theoretical study of the microscopic arrangement of the C atoms in Si _1×x-yGe _xC _y alloys using the Sankey local-orbital density-functional formalism. Our first-principles calculations show that in the dilute limit, the lattice constant in Si _1-yC _y alloys decreases much more (by about 2/3) with concentration than predicted by Vegard's law. We show that this result is consistent with Raman and infrared experiments and with previous empirical calculations. As the C concentration increases, the interactions between the C atoms become important: Interstitial C becomes more abundant and increases the lattice constant, and the substitutional C atoms array under appropriate growth conditions. The effect of this ordering on the lattice constant is small, but it can be seen in the Raman spectra of layer-by-layer grown samples.