Skip to main content
SpringerLink
Log in

Time-Dependent Viscoplastic Model for Dislocation Generation During the Cooling Process in the Silicon Ingot

  • Conference paper
Challenges in Mechanics of Time Dependent Materials, Volume 2

Abstract

Silicon growth is a process in which a silicon ingot is solidified from the melted and then cooled to the room temperature through the control of multi-heater. Dislocation densities are generated in the ingot by excessed thermal stresses caused by the nonuniform temperature field in the ingot. The generation of the dislocation density is considered as s a process of viscoplastic deformation. A three dimensional transient finite element model based on the Haasen viscoplastic constitutive model (HAS) is developed to evaluate the dislocation densities generated in silicon ingots grown by directional solidification process. The stress fields and dislocation densities generated in silicon ingots are the two major parameters for the evaluation of ingot quality. These two results calculated by HAS model are compared with those obtained from CRSS model. The result demonstrates that HAS model is more accurate than CRSS model for the calculation of dislocation densities and stresses during the cooling process of silicon ingot because of the consideration of time-dependent viscoplastic deformation in HAS model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A. Poullikkas, G. Kourtis, I. Hadjipaschalis, Parametric analysis for the installation of solar dish technologies in Mediterranean regions. Renew. Sust. Energ. Rev. 14, 2772–2783 (2010)

    Article  Google Scholar 

  2. G.E. Dieter, Mechanical Metallurgy (McGraw-Hill, New York, 1976)

    Google Scholar 

  3. P. Haasen, Zur plastischen verformung von Germanium und InSb. Zeitschrift für Physik 167, 461–467 (1962)

    Article  Google Scholar 

  4. H. Alexander, P. Haasen, Dislocations and plastic flow in the diamond structure. Solid State Phys. 22, 27–158 (1969)

    Google Scholar 

  5. I. Yonenaga, K. Sumino, Dislocation dynamics in the plastic deformation of silicon crystals I. Experiments. Phys. Status Solidi (a) 50, 685–693 (1978)

    Article  Google Scholar 

  6. M. Suezawa, K. Sumino, I. Yonenaga, Dislocation dynamics in the plastic deformation of silicon crystals. II. Theoretical analysis of experimental results. Phys. Status Solidi (a) 51, 217–226 (1979)

    Article  Google Scholar 

  7. I. Yonenaga, K. Sumino, K. Hoshi, Mechanical strength of silicon crystals as a function of the oxygen concentration. J Appl. Phys. 56, 2346–2350 (1984)

    Article  Google Scholar 

  8. K. Sumino, M. Imai, Interaction of dislocations with impurities in silicon crystals studied by in situ X-ray topography. Philos. Mag. A 47, 753–766 (1983)

    Article  Google Scholar 

  9. C. Tsai, O. Dillon, R. De Angelis, The constitutive equation for silicon and its use in crystal growth modeling. J. Eng. Mater. Technol. 112, 183–187 (1990)

    Article  Google Scholar 

  10. J. Moosbrugger, Continuum slip viscoplasticity with the Haasen constitutive model: application to CdTe single crystal inelasticity. Int. J. Plast. 11, 799–826 (1995)

    Article  MATH  Google Scholar 

  11. S. Pendurti, V. Prasad, H. Zhang, Modelling dislocation generation in high pressure Czochralski growth of InP single crystals: part I. Construction of a visco-plastic deformation model. Model. Simul. Mater. Sci. Eng. 13, 249 (2005)

    Article  Google Scholar 

  12. S. Nakano, X. Chen, B. Gao, K. Kakimoto, Numerical analysis of cooling rate dependence on dislocation density in multicrystalline silicon for solar cells. J. Cryst. Growth 318, 280–282 (2011)

    Article  Google Scholar 

  13. X. Chen, S. Nakano, L. Liu, K. Kakimoto, Study on thermal stress in a silicon ingot during a unidirectional solidification process. J. Cryst. Growth 310, 4330–4335 (2008)

    Article  Google Scholar 

  14. X. Chen, S. Nakano, K. Kakimoto, Three-dimensional global analysis of thermal stress and dislocations in a silicon ingot during a unidirectional solidification process with a square crucible. J. Cryst. Growth 312, 3261–3266 (2010)

    Article  Google Scholar 

  15. C. Parfeniuk, F. Weinberg, I. Samarasekera, C. Schvezov, L. Li, Measured critical resolved shear stress and calculated temperature and stress fields during growth of CdZnTe. J. Cryst. Growth 119, 261–270 (1992)

    Article  Google Scholar 

  16. G. Meduoye, D. Bacon, K. Evans, Computer modelling of temperature and stress distributions in LEC-grown GaAs crystals. J. Cryst. Growth 108, 627–636 (1991)

    Article  Google Scholar 

  17. M. Duseaux, Temperature profile and thermal stress calculations in GaAs crystals growing from the melt. J. Cryst. Growth 61, 576–590 (1983)

    Article  Google Scholar 

  18. S. Motakef, A.F. Witt, Thermoelastic analysis of GaAs in LEC growth configuration: I. Effect of liquid encapsulation on thermal stresses. J. Cryst. Growth 80, 37–50 (1987)

    Article  Google Scholar 

  19. W. Rosch, F. Carlson, Computed stress fields in GaAs during vertical Bridgman growth. J. Cryst. Growth 109, 75–81 (1991)

    Article  Google Scholar 

  20. A.S. Jordan, R. Caruso, A. Von Neida, A thermoelastic analysis of dislocation generation in pulled GaAs crystals. J. Bell Syst. Technol. 59, 593–637 (1980)

    Article  Google Scholar 

  21. A. Jordan, A. Von Neida, R. Caruso, The theoretical and experimental fundamentals of decreasing dislocations in melt grown GaAs and InP. J. Cryst. Growth 79, 243–262 (1986)

    Article  Google Scholar 

  22. O. Dillon Jr., C. Tsai, R. De Angelis, Dislocation dynamics during the growth of silicon ribbon. J. Appl. Phys. 60, 1784–1792 (1986)

    Article  Google Scholar 

  23. C. Tsai, M. Yao, A. Chait, Prediction of dislocation generation during Bridgman growth of GaAs crystals. J. Cryst. Growth 125, 69–80 (1992)

    Article  Google Scholar 

  24. C. Tsai, A. Gulluoglu, C. Hartley, A crystallographic methodology for modeling dislocation dynamics in GaAs crystals grown from melt. J. Appl. Phys. 73, 1650–1656 (1993)

    Article  Google Scholar 

  25. K. Sumino, I. Yonenaga, Dislocation dynamics and mechanical behaviour of elemental and compound semiconductors. Phys. Status Solidi (a) 138, 573–581 (1993)

    Article  Google Scholar 

  26. N. Subramanyam, C. Tsai, Dislocation reduction in GaAs crystal grown from the Czochralski process. J. Mater. Process Technol. 55, 278–287 (1995)

    Article  Google Scholar 

  27. X. Chen, S. Nakano, K. Kakimoto, 3D numerical analysis of the influence of material property of a crucible on stress and dislocation in multicrystalline silicon for solar cells. J. Cryst. Growth 318, 259–264 (2011)

    Article  Google Scholar 

  28. N. Zhou, M. Lin, M. Wan, L. Zhou, Lowering dislocation density of directionally grown multicrystalline silicon ingots for solar cells by simplifying their post-solidification processes—a simulation approach. J. Therm. Stresses 38, 146–155 (2015)

    Article  Google Scholar 

  29. N. Zhou, M. Lin, L. Zhou, Q. Hu, H. Fang, S. Wang, A modified cooling process in directional solidification of multicrystalline silicon. J. Cryst. Growth 381, 22–26 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL, 33431, USA

    Maohua Lin, Qingde Chen & C. T. Tsai

Authors
  1. Maohua Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qingde Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. T. Tsai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. T. Tsai .

Editor information

Editors and Affiliations

  1. Sandia National Laboratories, Livermore, California, USA

    Bonnie Antoun

Rights and permissions

Reprints and permissions

Copyright information

© 2016 The Society for Experimental Mechanics, Inc.

About this paper

Cite this paper

Lin, M., Chen, Q., Tsai, C.T. (2016). Time-Dependent Viscoplastic Model for Dislocation Generation During the Cooling Process in the Silicon Ingot. In: Antoun, B. (eds) Challenges in Mechanics of Time Dependent Materials, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-22443-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22443-5_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22442-8

  • Online ISBN: 978-3-319-22443-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation