Electronic structure of a-quartz, the [10 1 0] surface and perfect stoichiometric dislocations

An ab initio calculation of the energy levels of α-quartz is made using a basis of Gaussian-type orbitals and an ionic potential fitted to sums of exponential-type functions. Two [1010] surfaces are considered, one consisting of a plane of Si and O atoms with dangling bonds and the other having a plane of non-bridging oxygen atoms only. Both ideal surfaces have states in the fundamental gap but the second can be relaxed to eliminate these levels. Perfect stoichiometric dislocations largely have no states in the gap, but structures in which oxygen atoms are allowed to come into close proximity give rise to a multitude of partially filled gap states.