The concentrations of vacancies in growing crystals (for growth rates above the critical value) and of self-interstitials (at rates below the critical value) were predicted numerically by solving the axial diffusion problem for fast-recombining point defects. An analytical solution was obtained for the important near-critical case. It was found that the critical growth rate for the transition from interstitial to vacancy incorporation was proportional to the near-interface temperature gradient; even if the axial profile of the gradient was quite non-uniform. The experimental critical velocity/gradient ratio, together with the observed numbers of vacancies in voids, provided an estimate, for the interstitial self-diffusion product at the melting point: 3 x 1011/cms, which was in agreement with reported data.

Vacancy and Self-Interstitial Concentration Incorporated into Growing Silicon Crystals V.V.Voronkov, R.Falster: Journal of Applied Physics, 1999, 86[11], 5975-82