The mechanism of swirl defects formation in silicon

The observed influence of growth rate V and temperature gradient G0 on swirl defects leads to the conclusion: the first stage of defect formation is recombination and diffusion of vacancies and self-interstitials in the vicinity of the crystallization front. The equilibrium concentrations Cv0 and Ci0 and the diffusion coefficients Dv and Di of these points defects are determined from the experimental data; Cv0 is slightly higher than Ci0 but DvCv0 is lower than DiCi0. The type and concent ration of point defects that remain in the crystal after the recombination, depends on the ratio V/G0 (vacancies if V/G0>ξt, interstitials if V /G0<ξt where ξt is a certain constant). Typical growth conditions correspond to the interstitial case V/G0<ξt. The subsequent process consists of several successive stages: diffusion of interstitials to the crystal surface, nucleation of primary interstitial clusters, cluster growth, conversion of clusters into other forms (particularly dislocation loops). The quantitative results of the theory are in a fairly good agreement with the growth-stop and growth-quench experiments and the data on concentration and size of microdefects.