Vacancy and self-interstitial concentration incorporated into growing silicon crystals

The concentration of vacancies (for the growth rate V over the critical val ue V-t) and of self-interstitials (for V < V-t) incorporated into growing s ilicon crystals is obtained numerically by solving the axial diffusion prob lem for fast-recombining point defects. An analytical solution is obtained for the important near-critical case. A simple but quite precise interpolat ion expression is found. The critical growth rate V-t for the changeover fr om interstitial to vacancy incorporation is proportional to the near-interf ace temperature gradient G(0) even if the axial profile of the gradient, G( z), is of considerable nonuniformity. The experimental critical ratio V/G(0 ), together with the observed amount of vacancies in voids, provides a good estimate for the interstitial self-diffusional product at the melting poin t, 3 x 10(11) cm(-1) s(-1), in accord with reported data. (C) 1999 American Institute of Physics. [S0021-8979(99)01123-8].