Analytical predictions were made of the behaviour of point defects in growing crystals. It was concluded that the saturation of point defects was governed by 2 factors. One was the ratio of the normalized temperature gradient to the growth rate. The other was the ratio of the differential of the temperature gradient to the product of the temperature gradient and the growth rate. The former condition was same as Voronkov's; except that the temperature gradient was normalized. In the case of zero, or near-zero, growth rates the saturation was determined by only 1 factor. This was the ratio of the differential of the temperature gradient to the square of the temperature gradient. Diffusion equations in which the heat of transfer took negative values of the formation enthalpy were also considered. It was concluded that those equations could not indicate any dependence of the point-defect distribution upon the growth conditions without assuming such large diffusivity values that the transport of point-defects due to Fickian diffusion was not negligible in comparison with that due to crystal pulling.

Factors Determining the Saturation of Point Defects in Growing Silicon Crystals T.Ebe: Journal of Crystal Growth, 1999, 203[3], 387-99