Stability of large vacancy clusters in silicon

Using a density-functional-based tight-binding method we investigate the stability of various vacancy clusters up to a size of 17 vacancies. Additionally, we compute the positron lifetimes for the most stable structures to compare them to experimental data. A simple bond-counting model is extended to take into account the formation of new bonds. This yields a very good agreement with the explicitly calculated formation energies of the relaxed structures for $V_6$ to $V_{14}.$ The structures, where the vacancies form closed rings, such as $V_6$ and $V_{10},$ are especially stable against dissociation. For these structures, the calculated dissociation energies are in agreement with experimentally determined annealing temperatures and the calculated positron lifetimes are consistent with measurements.