Ab initio calculations and rate equation simulations for vacancy and vacancy-oxygen clustering in silicon

Formation energies of vacancy clusters Vn with (1≤n≤11) in crystalline Si and of their complexes VnOm (1≤m≤14) with oxygen were computed by ab initio density functional theory (DFT) within the generalized gradient approximation (GGA) and used to simulate the process of vacancy agglomeration after rapid thermal annealing (RTA) and also the formation of bulk microdefects (BMDs) in Si. Rate equation modeling of vacancy agglomeration after RTA and subsequent annealing below 1000 °C was carried out and the results were compared for binding energies obtained with different cell size. In Czochralski silicon, the interaction between vacancies and interstitial oxygen has to be taken into account. The BMD formation in Czochralski silicon was modeled by a continuum model comprised of a large system of rate equations, which accounts for the free energy of BMDs as a function of BMD size and shape, temperature and point defect concentrations.