A model for the dynamics of intrinsic point defects, vacancies, and self-interstitials in monocrystalline material was analyzed. Computation and asymptotic analysis were used to describe the appearance of oxidation-induced stacking-fault rings which were created during the cooling of crystals during Czochralski growth. The model predicted that the oxidation-induced stacking-fault ring separated an inner region that was supersaturated with vacancies from a self-interstitial rich outer region. The oxidation-induced stacking-fault ring corresponded to a region of no net excess of either type of point defect. Simulations of the dynamics of the oxidation-induced stacking-fault ring, with changes in crystal growth rate, V, and axial temperature gradient at the melt/crystal interface, G, accurately predicted the experimental results for a wide range of growth conditions when point defect thermophysical properties (equilibrium concentrations and diffusivities) were fitted to a single set of experimental data. The point defect properties which were determined in this way were within the range of values that were reported in the literature. Asymptotic analysis of the point defect dynamics model furnished a simple mechanistic picture for the development of point defect supersaturations, and yielded a closed-form expression for the critical value of V/G giving the location of the oxidation-induced stacking-fault ring. This expression was in excellent agreement with the predictions of simulations and with empirical correlations arising from experiment.

T.Sinno, R.A.Brown, W.Von Ammon, E.Dornberger: Journal of the Electrochemical Society, 1998, 145[1], 302-18