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Article information
2021 , Volume 26, ¹ 1, p.21-32
Kislitsyn S.A., Mitin K.A., Berdnikov V.S.
Numerical simulation of heat transfer processes during single crystal growth by the Bridgman -Stockbarger method in fixed and rotating crucibles
The dependence of both spatial shape and intensity of the convective flow of silicon melt during the growth of a silicon ingot by the Bridgman — Stockbarger method was studied numerically by the finite element method. Stationary and uniformly rotating graphite crucible in conjugate convective heat transfer regines were examined. The simulation was carried out on the basis of dimensionless system of equations for the thermogravitational convection in the Boussinesq approximation using the bipolar approach. In the mixed convection regine, the system of equations was augmented by an equation for the azimuthal velocity. Adaptive grids on triangles were used to track the position of the crystal-melt interface at each time step. The calculations were carried out at a constant rate of lowering the crucible from the hot to the cold zone, equal to 2.81 cm/h, and at a constant temperature gradient equal to 35 K/cm. Lowering the crucible was simulated by moving the inflection point in the temperature distribution on the outside of the crucible walls. The range of angular velocities of crucible rotation from 0 to 10 rpm is considered. It is shown that as the angular velocity of crucible rotation in the axial region increases, both the velocity of the downward flow arising in the regines of thermogravitational convection gradually and the convective heat flux to the crystal-melt interface decrease. As a result, in the range of angular velocities from 2 to 10 rpm, the shape of the crystal-melt interface gradually approaches to the one typical for the thermal conductivity regime. It is shown that at the initial stage of the process at an angular velocity of 10 rpm in the axial region of the cooled crucible bottom, the nucleation of a single crystal is possible.
[full text]
Keywords: Bridgman - Stockbarger method,crystallization, silicon, conjugate heat transfer,numerical simulation, FEM
doi: 10.25743/ICT.2021.26.1.002
Author(s):
Kislitsyn Stepan Aleksandrovich
Position: engineer
Office: Institute of Thermophysics SB RAS
Address: 630073, Russia, Novosibirsk
Mitin Konstantin Aleksandrovich
PhD.
Position: engineer
Office: Institute of Thermophysics SB RAS
Address: 630073, Russia, Novosibirsk
E-mail: mitin@ngs.ru
SPIN-code: 8383-9699Berdnikov Vladimir Stepanovich
Dr.
Position: Senior Research Scientist
Office: Institute of Thermophysics SB RAS
Address: 630073, Russia, Novosibirsk
E-mail: berdnikov@itp.nsc.ru
SPIN-code: 5385-8498 References:
1. Verozubova G.A., Okunev A.O., Gribenyukov A.I. et al. Newton solution of inviscid and viscous problems growth and defect structure of ZnGeP2 crystals. Journal of Crystal Growth. 2010; 312:1122–1126.
2. Guo Y., Zhou Y., Lin X., Chen W., Ye N. Growth and characterizations of BaGa4S7 crystal. Optical Materials. 2014; 36:2007–2011.
3. Ben Sassi M., Kaddeche S., Lappa M. et al. On the effect of thermodiffusion on solute segregation during the growth of semiconductor materials by the vertical Bridgman method. Journal of Crystal Growth. 2017; 458:154–165.
4. Meier D., Lukin G., Thieme N. et al. Design of model experiments for melt flow and solidification in a square container under time-dependent magnetic fields. Journal of Crystal Growth. 2017; 461:30–37.
5. Antonov P.V., Berdnikov V.S. Dependences of the shape of the crystallization front and growth rate of a silicon ingot on the heat transfer mode in the Bridgman – Stockbarger method. Journal of Applied Mechanics and Technical Physics. 2012; 53(6):860–870.
6. Nepomnyshchikh A.I., Presnyakov R.V., Antonov P.V., Berdnikov V.S. Effect of crucible rotation rate on the growth and macrostructure of multicrystalline silicon. Inorganic Materials. 2014; 50(12):1185–1190.
7. Mitin K.A., Berdnikov V.S., Kislitsin S.A. The dependence of the crystallization front shape on the heat exchange regime in the Bridgman – Stockbarger method. Computational Mechanics of Continua. 2019; 12(1):106–116.
8. Anfimov I.M., Berdnikov V.S., Vygovskaya Ye.A. et al. The homogeneity of the distribution of electrical resistivity in single-crystal silicon grown by the Czochralski method. Izv. Universities. Materials Electron. Technology. 2007; (4):40–44.
9. Berdnikov V.S., Vinokurov V.A., Vinokurov V.V. Effect of nonstationary regimes of the natural and mixed convection of melts on heat transfer and the forms of crystallization fronts in the Czochralski method. Bulletin of the Russian Academy of Sciences: Physics. 2017; 81(10):1257–1262.
10. Samarskij A.A., Vabishchevich P.N. Vychislitel’naya teploperedacha [Computational heat transfer]. Moscow: Editorial URSS; 2003: 784. (In Russ.)
11. Skvortsov A.V. Triangulyatsiya Delone i ee primenenie [Delaunay triangulation and its application]. Tomsk: Izdatel’stvo Tomskogo universiteta; 2002: 128. (In Russ.)
12. Berdnikov V.S., Filippova M.V., Krasin B.A., Nepomnyashchikh A.I. Numerical simulation of thermal-physical processes accompanying multisilicon crystal growing by the method of Bridgman – Stockbarger. Thermophysics and Aeromechanics. 2006; 13(2):257–274.
13. Antonov P.V., Berdnikov V.S. Influence of the crucible bottom shape on conjugate convective heat transfer in the Bridgman method. Izvestiya VUZov. Materialy Elektronnoi Tekhniki. 2011; (4):21–28. (In Russ.)
14. Muhlbauer A., Muiznikes A., Virbulis J., Luedge A., Riemann H. Interface shape, heat transfer and fluid flow in the floating zone growth of large silicon crystals with the needleeye technique. Journal of Crystal Growth. 1995; 151:66–79.
15. Yaws C.L., Dickens L.L., Lutwak R., Hsu G. Semiconductor industry silicon: Physical and thermodynamic properties. Solid State Technologies. 1981; 24(1):87–92.
16. Stankus S.V., Khairulin R.A., Tyagel’skii P.V. The thermal properties of germanium and silicon in condensed state. High Temperature. 1999; 37:529–534.
17. Stankus S.V., Savchenko I.V., Agadzhanov A.S., Yatsuk O.S., Zhmurikov E.I. Thermophysical properties of MPG-6 graphite. High Temperature. 2013; 51:179–182.
18. Raskatov V.M. (ed.) Mashinostroitel’nyye materialy: Kratkiy spravochnik [Engineering materials: Quick reference]. Moscow: Mashinostroyeniye; 1980: 511.
Bibliography link:
Kislitsyn S.A., Mitin K.A., Berdnikov V.S. Numerical simulation of heat transfer processes during single crystal growth by the Bridgman -Stockbarger method in fixed and rotating crucibles // Computational technologies. 2021. V. 26. ¹ 1. P. 21-32
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