Theory of interstitial oxygen in silicon and germanium

The interstitial oxygen centers in silicon and germanium are reconsidered and compared in an analysis based on the first-principles total-energy determination of the potential-energy surface of the centers, and a calculation of their respective low energy excitations and infrared absorption spectra. The total-energy calculations reveal unambiguously that interstitial oxygen is quantum delocalized, the delocalization being essentially different in silicon and in germanium. Oxygen in silicon lies at the bond center site in a highly anharmonic potential well, whereas in germanium it is found to rotate almost freely around the original Ge-Ge bond it breaks. This different delocalization is the origin of the important differences in the low energy excitation spectra: there is a clear decoupling in rotation and vibration excitations in germanium, giving different energy scales (1 cm$^{-1}$ for the rotation, 200 cm$^{-1}$ for the $\nu_2$ mode), whereas both motions are non-trivially mixed in silicon, in a common energy scale of around 30 cm$^{-1}$. The calculation of the vibrational spectra of the defect reveals the existence of vibrational modes (related to the $\nu_1$ mode) never been experimentally observed due to their weak infrared activity. It is found that the combination of these modes with the well established $\nu_3$ asymmetric stretching ones is the origin of the experimentally well characterized modes at frequencies above the $\nu_3$ mode frequency.