Meniscus dynamics and melt solidification in the EFG silicon tube growth process

The effect of the pressure on the static meniscus shape in the case of tube growth by edge-defined film-fed growth (E.F.G.) method

“…The calculus was made for the outer and inner static menisci in silicon case using R gi ¼ 42 Â 10 À4 m; R ge ¼ 48 Â 10 À4 m and a e c ¼ a i c ¼ 301. The values for R gi , R ge are those which have been used by Erris et al [1] and the value of the contact angle (301) is the smallest admissible value for silicon according to Yang et al [18]. The numerical values of the pressure limit, given by the above-established formula is p e oÀ3309 Pa the outer meniscus is convex and the growth angle is achieved on it at a point which belongs to the interval (45 Â 10 À4 ; 48 Â 10 À4 ) m. À3309op e o75 Pa the outer meniscus is convex at R ge ¼ 48 Â 10 À4 m. 75op e o197.84 Pa the outer meniscus is concave at R ge ¼ 48 Â 10 À4 m. 197.84op e [Pa] the outer meniscus is concave and the growth angle is not achieved on it p i oÀ3477 Pa, the inner meniscus is convex and the growth angle is achieved on it at a point which belongs to the interval [42 Â 10 À4 ; 45 Â 10 À4 ) m. À3477op i o 85.7 Pa the inner meniscus is convex at R gi ¼ 42 Â 10 À4 m. À85.7op i o209.27 Pa the inner meniscus is concave at R gi ¼ 42 Â 10 À4 m. 209.27op i [Pa] the inner meniscus is concave and the growth angle is not achieved on it.…”

“…For such an inner gas pressure p g i the limitation of the contact angle a i c X301 revealed in Ref. [18] for silicon does not require other restrictions. 2.…”

“…The majority of the conditions established in Refs. [14][15][16][17][18][19] are obtained in this way and are necessary conditions. A necessary condition which can be established using Lagrange theorem is the following: Statement 2.…”

“…Finally, in Ref. [18] the authors present theoretical and numerical study of meniscus dynamics under symmetric and asymmetric configurations. A meniscus dynamics model is developed to consider meniscus shape and its dynamics, heat and mass transfer around the die top and meniscus.…”

Model based, pulling rate, thermal and capillary conditions setting for silicon tube growth

“…For the growth process of a silicon tube with convex profile curves the following numerical data will be used: r 1 ¼ 2.5 Â 10 3 kg/m 3 ; r 2 ¼ 2.3 Â 10 3 kg/m 3 ; l 1 ¼60 W/m K; l 2 ¼21.6 W/m K; L¼1.81 Â 10 6 J/kg; c 1 ¼913 J/kg K [6]; c 2 ¼703 J/kg K [5]; Bi¼0.567; w 1 ¼ l 1 =c 1 r 1 ; w 2 ¼ l 2 =c 2 r 2 ; R c i ¼ 4:339 Â 10 À3 m; R c e ¼ 4:66 Â 10 À3 m;…”