Factors determining the saturation of point defects in growing silicon crystals

An analytical calculation on the behavior of point-defects in growing silic on crystals was performed. The calculation concluded that the saturation of point-defect is determined by only two factors, which are the ratio of the normalized temperature gradient to the growth rate (T'/TV) and the ratio o f the second-order differential of the temperature to the product of the te mperature gradient and the growth rate (T "/T'V). The former is same as Vor onkov's conclusion except that the temperature gradient is normalized and t he latter is newly found in the current calculation. In case of zero or nea r to zero growth rate, the saturation is determined by only one factor, whi ch the ratio of the second-order differential of the temperature to the squ are of the temperature gradient (T "/(T')(2)). In addition, diffusion equat ions where the heat of transfer takes minus values of the formation enthalp y, which were adopted by most of the models proposed so far, are also discu ssed. It was concluded that those equations do not show any dependency of p oint-defect distributions on the growth conditions without assuming such la rge diffusivity that the transport of point-defects due to Fickian diffusio n is not negligible compared with that due to the crystal pulling. (C) 1999 Published by Elsevier Science B.V. All rights reserved.