Distribution of grown-in crystal defects in silicon crystals formed by point defect diffusion during melt-growth: Disappearance of the oxidation induced stacking faults-ring

A set of requirements for the diffusion coefficients and the equilibrium densities of self-interstitials and vacancies in a silicon crystal were derived from macroscopic experimental quantities. It was shown that the combination of the diffusion coefficients and the equilibrium densities which satisfy the derived requirements and the phenomenological diffusion equations proposed previously by the present authors can give the diffusion profiles of self interstitials and vacancies which agree well with the distribution of the grown-in crystal defects observed in a dislocation free, Czochralski (CZ)-silicon single crystal. The calculated results are able to explain the movement of the oxidation induced stacking faults (OSF)-ring depending upon crystal growth rate and formation of the radial distribution of the micro-defects in a CZ-wafer reported previously.