Model of partitioning of point defect species during precipitation of a misfitting compound in Czochralski silicon

Abstract

The partitioning of point defect species during diffusion controlled precipitation of a misfitting compound in Czochralski silicon is studied using the principle of maximum degradation rate of the total system free energy. The degradation rate of the system free energy is obtained from the entropy production due to mass diffusion in the matrix. The results are then compared with those obtained using the principle of maximum growth rate. It is shown that, for a precipitation process involving more than one chemical or structural component species with their concentrations deviating from the appropriate thermal equilibrium values, the maximum growth rate description does not generally correspond to that of the maximum degradation rate of the system free energy. The results are then applied to oxygen precipitation in silicon, showing some equilibrium characteristics pertinent to a multicomponent system with intrinsic point defects acting as pseudocomponents. It is also shown that, depending on the intrinsic point defect concentrations at the far field of diffusion, the oxide precipitate can grow either by emitting or by absorbing both vacancies and Si self-interstitials.