Atomic and electronic structures of an interface between silicon and β-cristobalite

We have explored atomic and electronic structures of the interface consisting of crystalline Si and β-cristobalite ${\mathrm{SiO}}_2$ by performing first-principles total-energy electronic-structure calculations within the local-density-functional formalism. A stable atomic geometry has been attained by relaxing the atoms near the interface, according to the calculated forces on the atoms, toward the total-energy-optimized configuration. It is found that the epitaxial bond configuration of the β-cristobalite on Si(100) is stable after relaxation of the atoms on the first and second layers from the interface. In particular, the angle of the Si-O-Si bond near the interface is found to change upon relaxation from 180°, the value in β-cristobalite, to 144°, commonly observed in α-quartz. In the resulting stable atomic geometry, there occur interface states in the Si energy-band gap, originating from the dangling-bond states of the twofold-coordinated interface Si atoms. Contrary to a prevailing picture that an electron is accommodated in each dangling bond, however, the calculated interface states split into two inequivalent states and thus one of the two is unoccupied and the other is occupied with electrons. This semiconducting character is shown to be a consequence of the electrostatic field caused by electron transfer from Si to oxygen through the interface.