Vacancy and self-interstitial concentration incorporated into growing silicon crystals

The concentration of vacancies (for the growth rate V over the critical value Vt) and of self-interstitials (for V<Vt) incorporated into growing silicon crystals is obtained numerically by solving the axial diffusion problem for fast-recombining point defects. An analytical solution is obtained for the important near-critical case. A simple but quite precise interpolation expression is found. The critical growth rate Vt for the changeover from interstitial to vacancy incorporation is proportional to the near-interface temperature gradient G0 even if the axial profile of the gradient, G(z), is of considerable nonuniformity. The experimental critical ratio V/G0, together with the observed amount of vacancies in voids, provides a good estimate for the interstitial self-diffusional product at the melting point, 3×1011 cm−1 s−1, in accord with reported data.