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Coupled Thermal Solidification Process Simulation of Sapphire Growth

  • Thematic Section: 7th World Congress on Integrated Computational Materials Engineering
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Abstract

Thermal distribution during the sapphire growth process determines to a great extent the thermal stresses and dislocation density in sapphire. In this work, thermal and defect simulations of sapphire growth in a simplified single-boule furnace are presented. The heat transfer in the furnace is modeled via ANSYS Fluent® by considering conduction, convection and radiation effects. A dislocation density-based crystal plasticity model is applied for the numerical simulation of dislocation evolution during the crystal growth of sapphire. The physical models are validated by using a temporal series of measurements in the real furnace geometry, which capture the crystal–melt interface position during the technological growth process. The growth rate and the shape of the crystal growth front are analyzed for different side and top heater powers which result in different thermal distributions in the furnace. It is found that the cooling flux at the crucible bottom wall determines to a great extent the growth profile in the first half of the growth stage. Only toward the end of the growth stage, different top and side power distributions induce different growth front shapes. The effect of the convexity of the growth surface on the generation of dislocation defects is investigated by the crystal plasticity model. The results of simulations show that the convexity of the growth surface has a significant effect on the generation of dislocations.

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Notes

  1. It shall be noted that a concave interface shape might not be practical in industrial applications because of some crystallographic problems such as the formation of low angle grain boundaries.

References

  1. Bruni F (2015) Crystal growth of sapphire for substrates for high-brightness, light emitting diodes. Crys Res Technol 50(1):133–142

    Article  CAS  Google Scholar 

  2. Bruni F (2013) Will Czochralski growth of sapphire once again prevail? Acta Phys Polon A 124:213–218

    Article  ADS  CAS  Google Scholar 

  3. Xu C (2007) Thermal stresses and cracks during the growth of large-sized sapphire with SAPMAC method. Chin J Aeron 20:475–480

    Article  Google Scholar 

  4. Kurlov V (2016) Sapphire: properties, growth and applications: In: Materials science and materials engineering. Oxford, Elsevier, pp 1–11

  5. Demina S (2008) Use of numerical simulation for growing high-quality sapphire crystals by the Kyropoulos method. J Crys Growth 310:1443–1447

    Article  ADS  CAS  Google Scholar 

  6. Ma W (2014) Numerical study of heat transfer during sapphire crystal growth by heat exchanger method. Int J Heat Mass Transf 72:425–460

    Article  Google Scholar 

  7. Lu C-W (2001) Numerical computation of sapphire crystal growth using heat exchanger method. J Crys Growth 225:274–281

    Article  ADS  CAS  Google Scholar 

  8. Zhang N (2013) Simulation of heat transfer and convection during sapphire crystal growth. J Crys Growth 367:27–34

    Article  ADS  CAS  Google Scholar 

  9. Ma W (2017) Role of internal radiation in oxyde crystal growth by heat exchanger method. Crystals 7:18

    Article  Google Scholar 

  10. Fang H (2013) Role of internal radiation at the different growth stages of sapphire by Kyropoulos method. Int J Heat Mass Trans 67:967–973

    Article  CAS  Google Scholar 

  11. Yu QH (2012) Local design of the hot-zone in an industrial seeded directional solidification furnace for quasi-single crystalline silicon ingots. J Crys Growth 358:5–11

    Article  ADS  CAS  Google Scholar 

  12. Chengai X (2007) Thermal stresses and cracks during the growth of large-sized sapphire with SAPMAC method. Chin J Aeron 20:475–480

    Article  Google Scholar 

  13. Wu M (2016) Effect of crucible location on heat transfer in sapphire crystal growth by Heat Exchanger Method. Heat Transf Eng 37(3–4):332–340

    Article  ADS  CAS  Google Scholar 

  14. Chen J (2004) Influence of the crucible geometry on the shape of the melt-crystal interface during growth of sapphire crystal using heat exchanger method. J Crys Growth 266:239–245

    Article  ADS  CAS  Google Scholar 

  15. Ma A, Roters F, Raabe D (2006) A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations. Acta Mater 54(8):2169–2179

    Article  ADS  CAS  Google Scholar 

  16. Lu P (2007) 3D simulation of the effects of growth parameters on the growth of sapphire crystals using heat exchanger method. Crys Res Technol 42:1259–1265

    Article  CAS  Google Scholar 

  17. Voller V (1987) A fixed-grid numerical modeling methodology for convection-diffusion mushy region phase-change problems. Int J Heat Mass Transf 30:1709–1720

    Article  CAS  Google Scholar 

  18. Qi X (2021) "Effect of internal radiation on heat transfer during ti:sapphire crystal growth process by heat exchanger method. Int J Heat Mass Transf 170:121000

    Article  CAS  Google Scholar 

  19. Ma W (2017) Investigation of heat transfer and thermal stress during sapphire crystal. J Crys Growth 468:909–913

    Article  ADS  CAS  Google Scholar 

  20. Chien (1952) https://de.wikipedia.org/wiki/Faustformelverfahren_(Automatisierungstechnik), [Online]

  21. Roters F, Diehl M, Shanthraj P, Eisenlohr P, Reuber C, Wong SL, Maiti T, Ebrahimi A, Hochrainer T, Fabritius H-O (2019) DAMASK–the Düsseldorf advanced material simulation kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Comput Mater Sci 158:420–478

    Article  CAS  Google Scholar 

  22. Kronberg M (1962) Dynamical flow properties of single crystals of sapphire, I. J Am Ceram Soc 45(6):274–279

    Article  CAS  Google Scholar 

  23. Sistaninia M, et al. (2024) Determination of the constitutive parameters of temperature and strain-rate dependent dislocation-density-based crystal plasticity model for single-crystalline sapphire

  24. Gottstein G (2004) Physical foundations of materials science. Springer, Berlin

    Book  Google Scholar 

  25. Dobrovinskaya ER, Lytvynov LA, Pishchik V (2009) Properties of sapphire. Sapphire: material, manufacturing, applications. Springer, Boston, pp 55–176

    Chapter  Google Scholar 

Download references

Acknowledgements

This project receives funding from FAMETEC GmbH and the Austrian Research Promotion Agency FFG.

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Correspondence to R. A. Trasca.

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Trasca, R.A., Sistaninia, M., Reiss, G. et al. Coupled Thermal Solidification Process Simulation of Sapphire Growth. Integr Mater Manuf Innov 13, 1–13 (2024). https://doi.org/10.1007/s40192-023-00321-7

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  • DOI: https://doi.org/10.1007/s40192-023-00321-7

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