C incorporation in epitaxial Ge1-yCy layers grown on Ge(001):: An ab initio study

Ab initio density-functional calculations, employing the generalized-gradient approximation, have been used to determine formation energies U and the strain associated with different C lattice site configurations in fully coherent Ge1-yCy layers grown on Ge(001). Calculations using strained 64-atom supercells show that substitutional C, for which U=2.40 eV, is the most stable configuration involving only one C atom per configuration. The bond-centered interstitial and the Ge-C split interstitial configurations have formation energies which are 2.9 and 1.78 eV higher, respectively. However, [001]-oriented C pairs and C triplets are even more stable than substitutional C, by 0.17 and 0.80 eV per C atom, indicating a strong tendency for C atoms to cluster during Ge1-yCy growth. Calculated C-induced strain coefficients provide insight for interpreting Ge1-yCy x-ray diffraction results and macroscopic strain measurements.