We examine the strain-composition relation and band gap/deep-level properties of ${\mathrm{Si}}_{1-x-y}{\mathrm{Ge}}_x{\mathrm{C}}_y$ alloys using a local-orbital density-functional scheme. For purely substitutional carbon, a strong nonlinearity in the dependence of the bulk-alloy lattice constant on the concentration is found. In the linear regime of small carbon concentrations, this leads to a much more rapid decrease of the lattice constant with carbon concentration than predicted by Vegard’s law. A comparison of our dependence of the lattice constants in ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ and ${\mathrm{Si}}_{1-y}{\mathrm{C}}_y$ alloys on the concentrations suggests a germanium-carbon strain compensation ratio of $(15\mathrm{}\pm 3)$:1. This ratio is found to decrease when interstitial carbon is present. These results are compared with recent experiments, where the strain as well as the fraction of interstitial carbon have been measured. We also examine the band structure of ${\mathrm{Si}}_{1-y}{\mathrm{C}}_y$ alloys in the technically interesting concentration range of a few percent carbon. We find that the carbon-induced states are highly localized, and can form a deep level in the band gap of silicon. We show that these findings are an important step toward an understanding of recent experimental photoluminescence spectra.

• Received 22 May 1997

DOI:https://doi.org/10.1103/PhysRevB.57.2431