Influence of structure and thermodynamic stability on electronic properties of two-dimensional SiC, SiGe, and GeC alloys

The energetics and thermodynamic properties of two-dimensional binary graphene-like alloys made from graphene, silicene, or germanene are investigated by combining first-principles total energy calculations, and a statistical approach to account for disorder and composition effects. For the electronic properties the calculations are performed within the GGA-1/2 approach for an approximate quasiparticle bands. We derive lattice constants, first-neighbor distances, and buckling parameters as a function of composition $x$. The ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ system is the only stable random alloy at usual growth temperatures. For ${\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{C}}_{x}$, we observe strong distortions of the lattice making the random configurations less favorable and leading to a pronounced tendency for phase separation. The situation for ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{C}}_{x}$ alloys is completely different. An ordered structure with composition $x=0.5$ is stable up to $T\ensuremath{\approx}1000$ K, while intermediate compositions are mainly realized by silicongraphene and graphene or silicene. The ordering and decomposition effects have a strong influence on the average fundamental energy gap versus composition. Whereas large gaps appear for ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{C}}_{x}$ systems they almost vanish for ${\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{Si}}_{x}$ and ${\mathrm{Ge}}_{1\ensuremath{-}x}{\mathrm{C}}_{x}$. Moreover, the dependence of the ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{C}}_{x}$ energy gap on growth temperature is also obtained. The results can be very useful for chemical vapor deposition growth of these materials.