Vacancy and self-interstitial concentration incorporated into growing silicon crystals

Abstract

Comment on "Intrinsic point defect incorporation in silicon single crystals grown from a melt, revisited" [J. Appl.The concentration of vacancies ͑for the growth rate V over the critical value V t ) and of self-interstitials ͑for VϽV t ) 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 V t for the changeover from interstitial to vacancy incorporation is proportional to the near-interface 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 point, 3ϫ10 11 cm Ϫ1 s Ϫ1 , in accord with reported data.

The agglomeration dynamics of self-interstitials in growing Czochralski silicon crystals

“…The published research on the interaction between vacancies and oxygen in CZ crystals to produce particles of silicon oxides near the vicinity of the boundary between the interstitial dominated regions and the vacancy dominated regions, known as the v/i boundary, further validates Voronkov's theory [18][19][20][22][23][24][25][26][27].…”

Numerical Study of the Thermal and Flow Fields during the Growth Process of 800 kg and 1600 kg Silicon Feedstock

“…Figure 5 shows a comparison of V cr /G c for the two cases. As can be seen, this growth parameter was higher than the critical value (0.12 mm 2 /min·K [10]). In the radial direction, as presented in Figure 5a,b, V cr /G c became lower for the 1600 kg case when the central part of the ingot was 50 mm and 250 mm high, respectively.…”

Grown-in defects in silicon produced by agglomeration of vacancies and self-interstitials

“…The incorporated self-interstitial concentration, C Is , increases upon decreasing V/G. The numerically simulated dependence is wellapproximated by a simple analytical expression [12]:…”

“…Vacancies are incorporated if V/G is above some critical value, and self-interstitials are incorporated otherwise. The critical ratio depends on the point defect parameters taken at T m [10,12]:…”