Two-component density functional theory calculations of positron lifetimes for small vacancy clusters in silicon

The positron lifetimes for various vacancy clusters in silicon are calculated within the framework of the two-component electron-positron density functional theory. The effect of the trapped positron on the electron density and on the relaxation of the structure is investigated. Our calculations show that, contrary to the usual assumption, the positron-induced forces do not compensate in general for electronic inward forces. Thus, geometry optimization is required in order to determine positron lifetime accurately. For the monovacancy and the divacancy, the results of our calculations are in good agreement with the experimental positron lifetimes, suggesting that this approach gives good estimates of positron lifetimes for larger vacancy clusters, required for their correct identification with positron annihilation spectroscopy. As an application, our calculations show that fourfold trivacancies and symmetric fourfold tetravacancies have positron lifetimes similar to monovacancies and divacancies, respectively, and can thus be confused in the interpretation of positron annihilation experiments.