Diffusion of point defects in silicon crystals during melt-growth. III: Two diffusor model

In this paper, the phenomenological diffusion equations which describe the diffusion of point defects in silicon single crystals during melt-growth and include the effect of the annihilation reaction between self interstitials and vacancies are developed. The macroscopic structure of the OSF-ring in CZ-crystals, and the swirl and D-defects in FZ-crystals, and their changes dependent on the crystal growth rate were correctly and consistently interpreted by these equations assuming that these grown-in crystal defects are generated by an agglomeration of point defects frozen into the crystals. It is shown that vacancies not only diffuse faster than self interstitials but also exist in higher concentration than self interstitials at the high temperature present in the silicon crystal during melt-growth.