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Numerical analysis of thermohydraulic behavior in a directional solidification furnace

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Abstract

In this study, the crystallization process in a directional solidification furnace is studied by using the transient numerical simulation. The flow field in melt silicon in conjunction with different solidification stages is investigated. A separated side-heater design is proposed, showing a pronounced improvement on temperature gradient in axial direction normal to the solidification interface at late period. Result shows that the Voronkov ratio which can reflect the crystal quality is reduced by 16.5–24.8% and the energy consumption can be saved by 6% simultaneously. On the other hand, the airflow management for argon gas in the crucible chamber, which contains advantage to reduce chemical impurity in crystal during solidification process, is also numerically studied. By installing a guiding plate beneath the graphite cover can appreciably lower the oxygen mass fraction in contact with the cover plate and reduce the potential chemical reaction accordingly. The plate diameter and the spacing between the plate and graphite cover are optimized. Compared to the original design, the oxygen mass fraction at the graphite cover can be pronouncedly reduced by 10.6–33.3%, which can be further improved by combining a corner outlet configuration. Meanwhile, under the same volumetric flow rate of argon gas, yet the argon gas could be saved by almost half (e.g., from 40 SLM to 20 SLM) for the same chemical concentration with the optimized configuration.

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Abbreviations

C :

Oxygen concentration, m3 m−3

c p :

Specific heat capacity, J kg−1 K−1

D b :

Diameter of guiding plate, mm

D L :

Concentration diffusivity, dimensionless

G cr :

Crystal thermal gradient, K mm−1

g :

Gravity, m s−2

H b :

Spacing between guiding plate and graphite cover, mm

K :

Isothermal crystallization rate

k :

Conductivity, W m−1 K−1

p :

Pressure, Pa

T :

Temperature, K

t :

Time, s

\(\vec{V}\) :

Velocity vector, m s−1

V cr :

Crystallization rate, mm min−1

α cv :

Oxygen mass fraction in crucible volume

α gc :

Oxygen mass fraction at graphite cover

μ :

Viscosity, Pa s

ρ :

Density, kg m−3

σ :

Emissivity

References

  1. 1.

    Zervos, A. Renewables 2019 Global status report—a comprehensive annual overview of the state of renewable energy. REN21. 2019.

  2. 2.

    Murphy DJ, Hall CAS. Year in review-EROI or energy return on (energy) invested. In: Limburg K, Costanza R, editors. Ecological economics reviews. 2010. p. 102–118.

  3. 3.

    Celik I, Philips AB, Song ZN, Yan YF, Ellingson RJ, Heben MJ, Apul D. Energy payback time (EPBT) and energy return on energy invested (EROI) of perovskite tandem photovoltaic solar cells. IEEE J Photovolt. 2018;8(1):305–9.

  4. 4.

    Bhandari KP, Collier JM, Ellingson RJ, Apul DS. Energy payback time (EPBT) and energy return on energy invested (EROI) of solar photovoltaic systems: a systematic review and meta-analysis. Renew Sust Energy Rev. 2015;47:133–41.

  5. 5.

    Philipps S. Photovoltaics report. Fraunhofer Institute for Solar Energy Systems (ISE). 2019.

  6. 6.

    Jager-Waldau A. European roadmap for PV R&D–R&D for PV products generating clean electricity. Joint Research Center. 2004.

  7. 7.

    Fujiwara K, Obinata Y, Ujihara T, Usami N, Sazaki G, Nakajima K. Grain growth behaviors of polycrystalline silicon during melt growth processes. J Cryst Growth. 2004;266(4):441–8.

  8. 8.

    Steinbach I, Apel M, Rettelbach T, Franke D. Numerical simulations for silicon crystallization processes—examples from ingot and ribbon casting. Sol Energy Mater Sol Cells. 2002;72(1–4):59–68.

  9. 9.

    Ferrazza F. Large size multicrystalline silicon ingots. Sol Energy Mater Sol Cells. 2002;72(1–4):77–81.

  10. 10.

    Franke D, Rettelbach T, Hassler C, Koch W, Muller A. Silicon ingot casting: process development by numerical simulations. Sol Energy Mater Sol Cells. 2002;72(1–4):83–92.

  11. 11.

    Chen XJ, Nakano S, Liu LJ, Kakimoto K. Study on thermal stress in a silicon ingot during a unidirectional solidification process. J Cryst Growth. 2008;310(19):4330–5.

  12. 12.

    Chen W, Wang QZ, Yang DR, Li LD, Yu XG, Wang L, Jin H. Influence of vertical temperature gradients on wafer quality and cell efficiency of seed-assisted high-performance multi-crystalline silicon. J Cryst Growth. 2017;467:65–70.

  13. 13.

    Vizman D, Friedrich J, Mueller G. 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. 2007;303(1):231–5.

  14. 14.

    Yang X, Ma WH, Lv GQ, Wei KX, Luo T, Chen DT. A modified vacuum directional solidification system of multicrystalline silicon based on optimizing for heat transfer. J Cryst Growth. 2014;400:7–14.

  15. 15.

    Ma WC, Zhong GX, Sun L, Yu QH, Huang XM, Liu LJ. Influence of an insulation partition on a seeded directional solidification process for quasi-single crystalline silicon ingot for high-efficiency solar cells. Sol Energy Mater Sol Cells. 2012;100:231–8.

  16. 16.

    Qi XF, Yu QH, Zhao WH, Liang XQ, Zhang J, Liu LJ. Improved seeded directional solidification process for producing high-efficiency multi-crystalline silicon ingots for solar cells. Sol Energy Mater Sol Cells. 2014;130:118–23.

  17. 17.

    Yu QH, Liu LJ, Ma WC, Zhong GX, Huang XM. Local design of the hot-zone in an industrial seeded directional solidification furnace for quasi-single crystalline silicon ingots. J Cryst Growth. 2012;358:5–11.

  18. 18.

    Nguyen THT, Liao SH, Chen JC, Chen CH, Huang YH, Yang CJ, Lin HW, Nguyen HB. Effects of the hot zone design during the growth of large size multi-crystalline silicon ingots by the seeded directional solidification process. J Cryst Growth. 2016;452:27–34.

  19. 19.

    Saitoh T, Wang X, Hashigami H, Abe T, Igarashi T, Glunz S, Rein S, Wettling W, Yamasaki I, Sawai H, Ohtuka H, Warabisako T. Suppression of light degradation of carrier lifetimes in low-resistivity CZ-Si solar cells. Sol Energy Mater Sol Cells. 2001;65(1–4):277–85.

  20. 20.

    Matsuo H, Ganesh RB, Nakano S, Liu LJ, Arafune K, Ohshita Y, Yamaguchi M, Kakimoto K. Analysis of oxygen incorporation in unidirectionally solidified multicrystalline silicon for solar cells. J Cryst Growth. 2008;310(7–9):2204–8.

  21. 21.

    Li ZY, Liu LJ, Liu X, Zhang YF, Xiong JF. Effects of argon flow on melt convection and interface shape in a directional solidification process for an industrial-size solar silicon ingot. J Cryst Growth. 2012;360:87–91.

  22. 22.

    Li ZY, Liu LJ, Ma WC, Kakimoto K. Effects of argon flow on impurities transport in a directional solidification furnace for silicon solar cells. J Cryst Growth. 2011;318(1):304–12.

  23. 23.

    Li ZYY, Liu LJ, Ma WC, Kakimoto K. Effects of argon flow on heat transfer in a directional solidification process for silicon solar cells. J Cryst Growth. 2011;318(1):298–303.

  24. 24.

    COMSOL Multiphysics 5.3a. COMSOL AB, Stockholm, Sweden. www.comsol.com.

  25. 25.

    Brahmia N, Bourgin P, Boutaous M, Garcia D. Numerical simulation with “comsol multiphysics” of crystallization kinetics of semi-crystalline polymer during cooling: application to injection moulding process. In: Proceeding of the conference comsol multiphysics, Nov 2006, Paris, France. 2006.

  26. 26.

    Li ZY, Qi XF, Liu LJ, Zhou GS. Numerical study of melt flow under the influence of heater-generating magnetic field during directional solidification of silicon ingots. J Cryst Growth. 2018;484:78–85.

  27. 27.

    Voronkov VV, Falster R. Vacancy and self-interstitial concentration incorporated into growing silicon crystals. J Appl Phys. 1999;86(11):5975–82.

  28. 28.

    ANSYS lnc. ANSYS FLUENT Release 18.2. 2017. http://www.ansys.com.

  29. 29.

    National Institute of Standards and Technology. 2017. http://webbook.nist.gov/chemistry/fluid.

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Acknowledgements

The author would like to thank for the support from the Ministry of Science and Technology of Taiwan, under contract under Contract Number 108-2221-E-009-058-MY3.

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Correspondence to Chi-Chuan Wang.

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Chu, W., Yang, C. & Wang, C. Numerical analysis of thermohydraulic behavior in a directional solidification furnace. J Therm Anal Calorim (2020). https://doi.org/10.1007/s10973-020-09417-0

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Keywords

  • Directional solidification
  • Numerical simulation
  • Separated heater
  • Airflow management