A theoretical study of stability, electronic, and optical properties of GeC and SnC

We present the results of a first principles study on the ordered $Ge0.50C0.50$ and $Sn0.50C0.50$ cubic alloys. A linear combination of atomic orbitals approach in the framework of density functional theory is employed for total energy calculations in the zincblende phase. A fitting of the energy surface to the equation of state yields the lattice constant of 4.61 and 5.17 Å and the bulk modulus of 181 and 119 GPa for GeC and SnC, respectively. Analysis of band structure suggests a crossover of the nature of the band gap from indirect to direct in going from SiC to GeC to SnC. Although both alloys predicted to be unstable with respect to their elemental components at zero pressure and temperature, GeC appears to become stable at higher pressure. It appears that both the lattice constant and bulk modulus of the ordered alloys do not follow Végard’s linear rule, though the calculated dielectric constant of the cubic alloys is approximately the average of the dielectric constant of their elemental components.