Lattice parameter of Si1-x-yGexCy alloys

The introduction of carbon into silicon-germanium-based heterostructures offers increased flexibility in tailoring their strain state and electronic properties. Still, however, fundamental physical properties such as the lattice parameter and the elastic properties of Si1-x-yGexCy random alloys are not precisely known. In this paper, we present a quantitative study of the effect of carbon on the lattice parameter of Si1-x-yGexCy alloys in the technologically relevant range of Ge and C compositions. A strong deviation from Vegard's rule is experimentally and theoretically derived. The influence of the correlation between Ge and C on the lattice parameter is discussed. The results allow us to establish the compensation ratio v of Ge to C concentrations (where the Si1-x-yGexCy epilayer is lattice matched to Si), for which we find a value of v = 12.