Analytical approximations were derived, for the distributions of vacancies and self-interstitials in crystals, by using a one-dimensional point defect model. Upon assuming an unlimited high recombination rate, it was found that the results depended only upon the growth parameter, V/G, where V was the growth rate and G was the temperature gradient at the melt/solid interface. At the critical value of the growth parameter, which separated vacancy-dominated regions from interstitial-dominated regions, the familiar Voronkov relationship was retrieved. This relationship, and a first correction to the critical growth parameter, were in excellent agreement with recent experimental results. In the case of a limited recombination rate, the transport equations were first solved by neglecting diffusion. This solution was adjusted by using small corrective terms; using a special series expansion which depended upon the diffusivities. Important features, such as the effects of recombination and cooling rate upon the distributions of intrinsic point defects could be analyzed.

Analytical Approximations for the Distributions of Intrinsic Point Defects in Grown Silicon Crystals H.Lemke, W.Sudkamp: Physica Status Solidi A, 1999, 176[2], 843-65