Defect dynamics were modelled by using a diffusion-reaction theory in which defect types were represented as chemical species and had concentrations that were governed by conservation laws, chemical thermodynamics and kinetics. Self-consistent values were used for the equilibrium, transport and kinetic parameters of point defects and impurities. It was demonstrated that this approach led to a wide range of predictions that were consistent with experiment. The results which were presented here focussed upon the 2-dimensional predictions for micro-defect structures that were grown under conditions where both voids (clusters of vacancies) and self-interstitial aggregates were seen in regions of the crystal that were separated by an oxidation-induced stacking fault ring. The location and structure of the oxidation-induced stacking fault ring was predicted in terms of point defect dynamics near to the melt/crystal interface. This resulted in an annular region with almost balanced point-defect concentrations, and a peak in the residual vacancy concentration, following cluster formation. This residual vacancy concentration facilitated oxide precipitation during crystal growth, and seeded stacking-fault formation during oxidation. The calculations showed that the distribution and peak of the vacancy concentration depended upon V/G, where V was the crystal pulling rate and G was the axial temperature gradient at the melt/crystal interface. An annulus just outside of the oxidation-induced stacking fault ring was identified within which almost no micro-defects were present. This then identified the temperature field that led to almost perfect samples.

Engineering Analysis of Microdefect Formation during Silicon Crystal Growth. R.A.Brown, Z.Wang, T.Mori: Journal of Crystal Growth, 2001, 225[2-4], 97-109