Micro-defect distributions in Czochralski-type single-crystals, and their response to the crystal growth conditions, were analyzed in terms of self-consistent quantitative models of point-defect transport, recombination and aggregation during crystal growth. A convenient defect system to consider was the oxidation-induced stacking-fault ring, as a function of crystal growth-rate and thermal conditions. It was known that the radial position of the oxidation-induced stacking-fault ring correlated well with a constant value, (0.00134cm2/minK) of the ratio of the crystal growth rate to the axial temperature gradient at the melt/solid interface, at the radial location of the oxidation-induced stacking-fault ring. The present model reproduced the experimental results, and provided a closed-form expression for the above ratio as a function of the point-defect thermophysical properties at the melting point.

T.Sinno, R.A.Brown: Solid State Phenomena, 1997, 57-58, 343-8