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Experimental Investigation of Convective Heat Transfer Between Silicon-Melt and Solidification Front

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Abstract

Convective heat transfer between silicon melt and solidification front during Bridgman-type solidification process in a ceramic crucible has been investigated by means of heat balance analysis of the crucible during the process. The effect of aspect ratio on the Rayleigh and Nusselt numbers has been investigated. For a large crucible size (with inner diameter of about 0.50-m), the dependence correlates well with the empiric formula Nu = 0.303 Ra0.279. For a small crucible size (with inner diameter of about 0.20-m), the dependence correlates well with the empiric formula Nu = 0.181 Ra0.285. The experimental data obtained were compared with the available literature experimental and numerical simulation data.

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References

  1. 1.

    Pimputkar SM, Ostrach S (1981) Convective effects in crystals grown from melt. J Cryst Growth 55(3):614–646, ISSN 0022-0248. https://doi.org/10.1016/0022-0248(81)90121-4

  2. 2.

    Rajendran S, Wilcox WR (1984) Steady state thermal modelling of casting of silicon. J Cryst Growth 69(1):62–72, ISSN 0022-0248. https://doi.org/10.1016/0022-0248(84)90009-5

  3. 3.

    Chang CJ, Brown RA (1984) Natural convection in steady solidification: finite element analysis of a two-phase Rayleigh-Bernard problem. J Comput Phys 53(1):1–27, ISSN 0021-9991. https://doi.org/10.1016/0021-9991(84)90049-4

  4. 4.

    Muller G, Neumann G, Weber W (1984) Natural convection in vertical Bridgman configurations. J Cryst Growth 70(1–2):78–93, ISSN 0022–0248. https://doi.org/10.1016/0022-0248(84)90250-1

  5. 5.

    Seidl A, Muller G, Dornberger E, Tomzig E, Rexer B, Ammon W (1998) Turbulent melt convection and its implication on large diameter silicon Czochralski crystal growth. ECS Proceedings 98(1):417–423

  6. 6.

    Carra S, Masi M, Morbidelli M (1989) Fundamentals of convection in melt growth. J Cryst Growth 97(1):1–8, ISSN 0022-0248. https://doi.org/10.1016/0022-0248(89)90240-6

  7. 7.

    Zhang T, Ladeinde F, Prasag V (1999) Turbulent convection in Czochralski silicon melt. J Heat Transf 121(4):1027–1041. https://doi.org/10.1115/1.2826053

  8. 8.

    Gelfgat AY, Bar-Yosef PZ, Solan A (2000) Axisymmetry breaking instabilities of natural convection in a vertical Bridgman growth configuration. J Cryst Growth 220:316–325

  9. 9.

    Steinbach I, Apel M, Rettelbach T, Franke D (2002) Numerical simulations for silicon crystallization processes – examples from ingot and ribbon casting. Sol. Energy Mater Sol Cells 72(1–4):59–68, ISSN 0927–0248. https://doi.org/10.1016/S0927-0248(01)00150-7

  10. 10.

    Mittal V, Baig MF, Khan BK (2005) Buoyancy-driven convection in liquid metals subjected to transverse magnetic fields. J Indian Inst Sci 85:119–129. journal.iisc.ernet.in/index.php/iisc/article/view/2352

  11. 11.

    Kokh KA, Popov VN, Kokh AE, Krasin BA, Nepomnyaschikh AI (2007) Numerical modeling of melt flows in vertical Bridgman configuration affected by a rotating heat field. J Cryst Growth 303:253–257

  12. 12.

    Chen X, Nakano S, Liu L, Kakimoto K (2008) Numerical investigation of thermal stress and dislocation density in silicon ingot during a solidification process. Reports of Research Institute for Applied Mechanics, Kyushu University 135:45–52

  13. 13.

    Vizman D, Friedrich J, Mueller G (2007) 3D time-dependent numerical study of the influence of the melt flow on the interface shape in a silicon ingot casting process. J Cryst Growth 303(1):231–235

  14. 14.

    Teng YY, Chen JC, Lu CW, Chen CY (2010) The carbon distribution in multi-crystalline silicon ingots grown using the directional solidification process. J Cryst Growth 312:1282–1290

  15. 15.

    Wei J, Zhang H, Zheng L, Wang C, Zhao B (2009) Modelling and improvement of silicon ingot directional solidification for industrial production systems. Sol Energy Mater Sol Cells 93(9):1531–1539, ISSN 0927-0248. https://doi.org/10.1016/j.solmat.2009.04.001

  16. 16.

    Wunderwald U, Dadzis K, Zschorsch M, Jung T, Friedrich J (2009) Influence of traveling magnetic fields on melt convection during Bridgman type solidification of multi-crystalline silicon. 24th European Photovoltaic Solar Energy, Hamburg, Germany, pp 2023–1028

  17. 17.

    Popescu A, Vizman D (2011) Numerical study of the influence of melt convection on the crucible dissolution rate in a silicon directional solidification process. Int J Heat Mass Transf 54(25–26):5540–5544, ISSN 0017-9310. https://doi.org/10.1016/j.ijheatmasstransfer.2011.07.037

  18. 18.

    Lv G, Bao Y, Zhang Y, He Y, Ma W, Lei Y (2018) Effects of electromagnetic directional solidification conditions on the separation of primary silicon from Al-Si alloy with high Si content. Mater Sci Semicond Process 81:139–148, ISSN 1369-8001. https://doi.org/10.1016/j.mssp.2018.03.006

  19. 19.

    Cablea M, Zaidat K, Gagnoud A, Nouri A, Chichignoud G, Delannoy Y (2015) Multi-crystalline silicon solidification under controlled forced convection. J Cryst Growth 417:44–50, ISSN 0022-0248. https://doi.org/10.1016/j.jcrysgro.2014.07.042

  20. 20.

    Popescu A, Vizman D (2017) Numerical study of the influence of forced melt convection on the impurities transport in a silicon directional solidification process. J Cryst Growth 474:55–60, ISSN 0022-0248. https://doi.org/10.1016/j.jcrysgro.2016.11.122

  21. 21.

    He Y, Ma W, Lv G, Zhang Y, Lei Y, Yang X (2018) An efficient method to separate silicon from high-silicon aluminum alloy melts by electromagnetic directional solidification. J Clean Prod 185:389–398, ISSN 0959-6526. https://doi.org/10.1016/j.jclepro.2018.02.039

  22. 22.

    Tan Y, Ren S, Shi S, Wen S, Jiang D, Dong W, Ji M, Sun S (2014) Removal of aluminum and calcium in multi-crystalline silicon by vacuum induction melting and directional solidification. Vacuum 99:272–276, ISSN 0042-207X. https://doi.org/10.1016/j.vacuum.2013.06.015

  23. 23.

    Thomas LC (1980) Fundamentals of heat transfer. Prentice-Hall, Englewood Cliffs, NJ. ISBN-13: 978-0133399035

  24. 24.

    Ahmanache A, Zeraibi N (2013) Numerical study of natural melt convection in cylindrical cavity with hot walls and cold bottom sink. Therm Sci 17:853–864. https://doi.org/10.2298/TSCI110327166A

  25. 25.

    Srinivasan M, Nagarajan SG, Ramasamy P (2015) Computational study of heat transfer on molten silicon during directional solidification for solar cell applications. Procedia Eng 127:1250–1255. https://doi.org/10.1016/j.proeng.2015.11.479

  26. 26.

    Hu C, Chen JC, Thu Nguyen TH, Hou ZZ, Chen CH, Huang YH, Yang M (2018) Optimization of heat transfer during the directional solidification process of 1600 kg silicon feedstock. J Cryst Growth 484:70–77, ISSN 0022-0248. https://doi.org/10.1016/j.jcrysgro.2017.12.042

  27. 27.

    Du Y, Tao W, Liu Y, Jiang J, Huang H (2017) Heat transfer modeling and temperature experiments of crystalline silicon photovoltaic modules. Sol Energy 146:257–263, ISSN 0038-092X. https://doi.org/10.1016/j.solener.2017.02.049

  28. 28.

    Qi X, Zhao W, Liu L, Yang Y, Zhong G, Huang X (2014) Optimization via simulation of a seeded directional solidification process for quasi-single crystalline silicon ingots by insulation partition design. J Cryst Growth 398:5–12, ISSN 0022-0248. https://doi.org/10.1016/j.jcrysgro.2014.04.011

  29. 29.

    Zhao W, Liu L (2017) Control of heat transfer in continuous-feeding Czochralski-silicon crystal growth with a water-cooled jacket. J Cryst Growth 458:31–36, ISSN 0022-0248. https://doi.org/10.1016/j.jcrysgro.2016.10.041

  30. 30.

    Ding J, Liu L, Zhao W (2017) Enhancement of heat transfer in Czochralski growth of silicon crystals with a chemical cooling technique. J Cryst Growth 468:894–898, ISSN 0022-0248. https://doi.org/10.1016/j.jcrysgro.2016.11.036

  31. 31.

    Djambazov G, Bojarevics V, Pericleous K, Forzan M (2016) Numerical modelling of silicon melt purification in induction directional solidification system. International Journal of Applied Electromagnetics and Mechanics Padova, pp 2385–2933. https://doi.org/10.3233/JAE-162248

  32. 32.

    Myrum TA (1990) Natural convection from a heat source in a top-vented enclosure. ASME J Heat Transfer 112(3):632–639. https://doi.org/10.1115/1.2910434

  33. 33.

    Kolev NI (2009) Multiphase flow dynamics 4. nuclear thermal hydraulics. Berlin: Springer, vol 4. https://doi.org/10.1007/978-3-540-92918-5

  34. 34.

    Popov V, Katz-Demyanetz A, Bamberger M (2018) Heat transfer and phase formation through EBM 3D-printing of Ti-6Al-4V cylindrical parts. Defect and Diffusion Forum 383:190–195. https://doi.org/10.4028/www.scientific.net/DDF.383.190

  35. 35.

    JCGM 100:2008 – Evaluation of measurement data – Guide to the expression of uncertainty in measurement. Available [online] https://ncc.nesdis.noaa.gov/documents/documentation/JCGM_100_2008_E.pdf. Accessed 26 Dec 2018

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Acknowledgments

The authors would like to thank LINN HT (Germany) for the equipment design.

This research was supported by GLOBE Specialty Metals (USA).

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Correspondence to Vladimir V. Popov Jr.

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Fleisher, A., Kovalevsky, A., Popov, V.V. et al. Experimental Investigation of Convective Heat Transfer Between Silicon-Melt and Solidification Front. Silicon 12, 621–628 (2020). https://doi.org/10.1007/s12633-019-00141-5

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Keywords

  • Convective heat transfer
  • Direct solidification
  • Solidification front
  • Silicon ingot