Substitutional carbon in germanium

Carbon impurities implanted into single-crystalline germanium are studied with infrared absorption spectroscopy and ion channeling. After implantation of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{+}{}_{}{}^{}$ at room temperature and subsequent annealing at 350 °C, a sharp infrared absorption line is observed at 531 ${\mathrm{cm}}^{\mathrm{-}1}$. When ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{+}{}_{}{}^{}$ is substituted by ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}_{}^{+}{}_{}{}^{}$, the line shifts down in frequency to 512 ${\mathrm{cm}}^{\mathrm{-}1}$ and co-implantation of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{+}{}_{}{}^{}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}_{}^{+}{}_{}{}^{}$ does not give rise to additional lines. Therefore, the 531-${\mathrm{cm}}^{\mathrm{-}1}$ line represents a local vibrational mode of a defect containing a single carbon atom. Channeling measurements are carried out around the 〈100〉, 〈110〉, and 〈111〉 axes in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{+}{}_{}{}^{}$-implanted samples annealed at 450 °C. The analysis of the data shows that 31±3 % of the carbon atoms are located at substitutional sites, while the remaining carbon atoms appear to be located randomly. The population of the substitutional site and the intensity of the 531-${\mathrm{cm}}^{\mathrm{-}1}$ mode have identical temperature dependencies. It is concluded that the 531-${\mathrm{cm}}^{\mathrm{-}1}$ mode is the three-dimensional ${\mathrm{T}}_2$ stretch mode of substitutional carbon. The effective charge of the mode is determined to be (3.4±0.5)e.mAb initio local density functional cluster theory is applied to calculate the structure and the local vibrational modes of substitutional carbon in germanium. The calculated frequencies and isotope shifts for the ${\mathrm{T}}_2$ stretch mode are in good agreement with the observations.