Point defect dynamics and the oxidation-induced stacking-fault ring in Czochralski-grown silicon crystals

A model is presented and analyzed for the dynamics of intrinsic point defects, vacancies, and self-interstitials, in single-crystal silicon. Computations and asymptotic analysis are used to describe the appearance of the oxidation-induced stacking-fault ring (OSF ring) created during the cooling of silicon crystals in the Czochralski growth process. The model predicts that the OSF ring separates an inner region supersaturated with vacancies from a self-interstitial rich outer region. The OSF ring corresponds to a region of no net excess of either point defect. Simulations of the dynamics of the OSF ring with changes in the crystal growth rate (V) and the axial temperature gradient at the melt/crystal interface (G) accurately predict experimental data for a wide range of growth conditions when point defect thermophysical properties (equilibrium concentrations and diffusivities) are fit to a single set of experimental data. The paint defect properties determined this way are within the range of values reported in the literature. Asymptotic analysis of the point defect dynamics model gives a simple mechanistic picture for the development of the point defect supersaturations and yields a closed-form expression for the critical value of (V/G) for the location of the OSF ring. This expression is in excellent agreement with the predictions of simulation and with the empirical correlation determined from experiments.