The oxygen vacancy in α-quartz has been studied in various charge states using the molecular-orbital techniques modified intermediate neglect of differential overlap (MINDO/3) and its open-shell version (MOPN). The solid containing the defect is simulated by a cluster of 30 to 40 atoms, including hydrogen terminators. In the case of the neutral O vacancy the neighboring silicon atoms are predicted to relax significantly, forming a strong Si—Si bond which is comparable to that in bulk Si. We find that the positively charged (+1) oxygen vacancy relaxes asymmetrically, consistent with most aspects of published electron paramagnetic resonance (EPR) spectroscopy data on the $E_1^{\mathcal{’}}$ center. Our calculations support the model of Feigl et al., as opposed to the divacancy model of Jani et al. which had been proposed in response to controversies over the two weak hyperfine interactions of the $E_1^{\mathcal{’}}$ center. Our calculations, furthermore, reveal that the long-bond-side silicon which, in the model of Feigl et al., relaxes into the plane of its three backbonded oxygens (we call this configuration the planar $E_1^{\mathcal{’}}$ configuration), in fact relaxes through the plane of the oxygens, emerging on the other side of the vacancy in a puckered configuration. The latter is calculated to be more stable by about 0.3 eV than the planar configuration, and it agrees even better with EPR data. Our study also shows that the O vacancy introduces two levels (0/+ and +/2+), and possibly a third (-/0) into the band gap of silicon dioxide.

• Received 21 November 1986

DOI:https://doi.org/10.1103/PhysRevB.35.8223