Simulation of germanium crystal growth by Czochralski method

Document Type : Full length research Paper

Authors

1 Physics. Science faculty. Bu Ali Sina University.Hamedan.Iran

2 Department of Physics, Bu-Ali Sina University, Hamedan, Iran

Abstract

In this article, a set of 2D numerical simulations were performed for different stages of a real Czochralski (Cz) growth of germanium crystal using Finite Element Method. The results of temperature distribution, melt and gas flow field, and crystal-melt interface were obtained numerically using the Reynolds-averaged turbulence modelling approach. The obtained results show that, as the crystal length is increased (i.e., the melt depth is decreased), the constant rotation rates of crystal and crucible increase both the melt Reynolds number and its turbulent kinetic energy, because of transferring constant momentum and energy to the remaining Ge melt. In addition, the computed crystal-melt interface shape for germanium crystal having 9 cm height was in a good agreement with the experimental data and observations in the crystal growth lab.

Keywords

Main Subjects

References

[1] H. Wu, N. Conrad, W. Luo, D.Y. Peide, First experimental demonstration of ge cmos circuits, In 2014 IEEE International Electron Devices Meeting, pages 9–3. IEEE (2014). https://doi.org/10.1109/IEDM.2014.7047016
[2] G.K. Teal, J.B. Little, Growth of germanium single crystals, Physical review 78, American Physical Soc one Physics Ellipse, College Pk, MD 20740-3844 USA (1950) 647–647.
[3] A. Crowley, Mathematical modelling of heat flow in czochralski crystal pulling, IMA Journal of Applied Mathematics 30 (1983) 173–189. https://doi.org/10.1093/imamat/30.2.173
[4] N.V. Bogaert, F. Dupret, Dynamic global simulation of the czochralski process ii. Analysis of the growth of a germanium crystal, Journal of crystal growth 171 (1997) 77–93. https://doi.org/10.1016/S0022-0248(96)00489-7
[5] J.J. Derby, Theoretical modeling of czochralski crystal growth, MRS Bulletin 13 (1988) 29–35. https://doi.org/10.1557/S0883769400064162
[6] K. Abe, T. Kondoh, Y Nagano, A new turbulence model for predicting fluid flow and heat transfer in separating and reattaching flows-i. flow field calculations, International journal of heat and mass transfer 37 (1994) 139–151. https://doi.org/10.1016/0017-9310(94)90168-6
[7] K. Abe, T. Kondoh, Y Nagano, A new turbulence model for predicting fluid flow and heat transfer in separating and reattaching flows—ii. Thermal field calculations, International Journal of Heat and Mass Transfer 38 (1995) 1467–1481. https://doi.org/10.1016/0017-9310(94)00252-Q
[8] M.H. Tavakoli, H. Karbaschi, F. Samavat, Computational modeling of induction heating process, Progress in Electromagnetics Research 11 (2009) 93–102. https://doi.org/10.2528/PIERL09071509
[9] Z. Warhaft, An introduction to thermal-fluid engineering: the engine and the atmosphere, Cambridge University Press (1997).
 [10] F. Moukalled, L. Mangani, M. Darwish, et al, The finite volume method in computational fluid dynamics, Springer 113 (2016).
[11] D.C. Wilcox et al, Turbulence modeling for CFD, volume 2. DCW industries La Canada, CA (1998).
[12] S. Omid, M.H. Tavakoli, K. Mohammadi, Simulation of BGO Single Crystal Growth by Improved Low Thermal Gradient (LTG) Czochralski, Journal of Research on Many-body Systems 10 (2018) 23-33. https://doi.org/10.22055/jrmbs.2018.13962
[13] V.V. Voronkov, B. Dai, M.S. Kulkarni, Fundamentals and engineering of the czochralski growth of semiconductor silicon crystals. Comprehensive Semiconductor Science and Technology (2011) 81–169. https://doi.org/10.1016/B978-0-44-453153-7.00089-4
[14] L. Davidson, An introduction to turbulence models (2015).
[15] V.V. Kalaev, I.Y. Evstratov, Y.N. Makarov, Gas flow effect on global heat transport and melt convection in czochralski silicon growth, Journal of Crystal Growth 249  (2003) 87–99. https://doi.org/10.1016/S0022-0248(02)02109-7
[16] M.H. Tavakoli, E. Kabiri Renani, M. Honarmandnia, M. Ezheiyan, Computational analysis of heat transfer, thermal stress and dislocation density during resistively czochralski growth of germanium single crystal, Journal of Crystal Growth 483 (2018) 125–133. https://doi.org/10.1016/j.jcrysgro.2017.11.021
[17] C.W. Lu, J.C. Chen, Numerical simulation of thermal and mass transport during czochralski crystal growth of sapphire, Crystal Research and Technology: Journal of Experimental and Industrial Crystallography 45 (2010) 371–379. https://doi.org/10.1002/crat.200900528
[18] D.T.J. Hurle, Handbook of crystal growth, Elsevier Science & Technology, (1993).
[19] Y. Kishida, K. Okazawa, Geostrophic turbulence in cz silicon crucible, Journal of crystal growth 198 (1999) 135–140. https://doi.org/10.1016/S0022-0248(98)01123-3
Journal of Research on Many-body Systems
Volume 11, Issue 2 - Serial Number 29
September 2021
Pages 25-35

Files

History

  • Receive Date: 25 February 2021
  • Revise Date: 15 March 2021
  • Accept Date: 04 August 2021

Share

How to cite

Statistics