Vibrations of the Interstitial Oxygen Pairs in Silicon

First-principles methods are used to calculate the structures and local vibrational modes of interstitial oxygen pairs in silicon. The staggered ${\mathrm{O}}_i-\mathrm{Si}-{\mathrm{O}}_i$ and skewed ${\mathrm{O}}_i-\mathrm{Si}-\mathrm{Si}-{\mathrm{O}}_i$ structures are nearly degenerate in energy. The calculated local vibration frequencies and their pure and mixed ${}^{18}\mathrm{O}{\to }^{16}\mathrm{O}$ isotopic shifts agree closely with experiments: the highest frequency is assigned to the skewed and the four lower ones to the staggered structure. This result may clear up the controversy of oxygen dimers in silicon, and also suggests a mechanism for fast oxygen diffusion.