Oxygen and dioxygen centers in Si and Ge: Density-functional calculations

Ab initio density-functional calculations using Gaussian orbitals are carried out on large Si and Ge supercells containing oxygen defects. The formation energies, local vibrational modes, and diffusion or reorientation energies of ${\mathrm{O}}_i,$ ${\mathrm{O}}_{2i},$ $V\mathrm{O},$ $V\mathrm{OH},$ and $V{\mathrm{O}}_2$ are investigated. The piezospectroscopic tensors for ${\mathrm{O}}_i,$ $V\mathrm{O},$ and $V{\mathrm{O}}_2$ are also evaluated. The vibrational modes of ${\mathrm{O}}_i$ in Si are consistent with the view that the defect has effective $D_{3d}$ symmetry at low hydrostatic pressures but adopts a buckled structure for large pressures. The anomalous temperature dependence of the modes of ${\mathrm{O}}_{2i}$ is attributed to an increased buckling of Si-O-Si when the lattice contracts. The diffusion energy of the dimer is around 0.8 eV lower than that of ${\mathrm{O}}_i$ in Si and 0.6 eV in Ge. The dimer is stable against $V\mathrm{O}$ or $V{\mathrm{O}}_2$ formation and the latter defect has modes close to the reported $894-{\mathrm{cm}}^{-1}$ band. The reorientation energies for O and H in $V\mathrm{O}$ and $V\mathrm{OH}$ defects are found to be a few tenths of an eV and are greater when the defect has trapped an electron.