J. Semicond. > 2013, Volume 34 > Issue 6 > 063005, doi: 10.1088/1674-4926/34/6/063005
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SEMICONDUCTOR MATERIALS

Numerical study of heat transport and fluid flow during the silicon crystal growth process by the Czochralski method

Chaohua Jin

+ Author Affiliations

 Corresponding author: Jin Chaohua, Email:xiamiren01@163.com

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Abstract: A global analysis of heat transfer and fluid flow in a real Czochralski single silicon crystal furnace is developed using the FLUENT package. Good agreement was obtained for comparisons of the power and crystal growth speed between the simulation and experimental data, and the effect of the length of the crystal on heat transfer and fluid flow was analyzed. The results showed that Tmax increases and its location moves downward as the crystal length increases. The flow pattern in the melt does not change until the crystal grows to 900 mm. As the crystal length increases, the flow pattern in the first gas area only changes when the crystal length is less than 700 mm, but the flow pattern in the second area changes throughout the growth process.

Key words: Czochralski crystal growth, silicon, fluid flow, numerical study



[1]
Lipchin A, Brown R A. Comparison of three turbulence models for simulation of melt convection in Czochralski crystal growth of silicon. J Cryst Growth, 1999, 205(1/2):71 http://cat.inist.fr/?aModele=afficheN&cpsidt=1923038
[2]
Lipchin A, Brown R A. Hybrid finite-volume/finite-element simulation of heat transfer and melt turbulence in Czochralski crystal growth of silicon. J Cryst Growth, 2000, 216(1-4):192 doi: 10.1016/S0022-0248(00)00428-0
[3]
Chen Q, Jiang Y, Yan J, et al. Progress in modeling of fluid flows in crystal growth processes. Process in Natural Science, 2008, 18(12):1465 doi: 10.1016/j.pnsc.2008.06.003
[4]
Järvinen J, Nieminen R, Tiihonen T. Time-dependent simulation of Czochralski silicon crystal growth. J Cryst Growth, 1997, 180(3/4):468 http://cat.inist.fr/?aModele=afficheN&cpsidt=2050676
[5]
Ren Bingyan, Zhao Long, Fu Hongbo, et al. Effect of a heat shield on pull speed and oxygen concentration in a Φ 200 mm CZ Si. Chinese Journal of Semiconductors, 2005, 26(9):1764
[6]
Ren Bingyan, Zhang Zhicheng, Liu Caichi, et al. Effect of argon gas flow rate on oxygen and carbon concentration in CZ Si crystals. Chinese Journal of Semiconductors, 2001, 22(11):1416
[7]
Kalaev V V, Evstratov I Y, Makarov Y N. Gas flow effect on global heat transport and melt convection in Czochralski silicon growth. J Cryst Growth, 2003, 249(1/2):87 http://www.sciencedirect.com/science/article/pii/S0022024802021097
[8]
Kalaev V V, Lukanin D P, Zabelin V A, et al. Prediction of bulk defects in CZ Si crystals using 3D unsteady calculations of melt convection. Materials Science in Semiconductor Processing, 2003, 5(4/5):369
[9]
Kalaev V V, Lukanin D P, Zabelin V A, et al. Calculation of bulk defects in CZ Si growth:impact of melt turbulent fluctuations. J Cryst Growth, 2003, 250(1/2):203 https://www.sciencedirect.com/science/article/pii/S0022024802022406
[10]
Evstratov I Y, Kalaev V V, Zhmakin A I, et al. Numerical study of 3D unsteady melt convection during industrial-scale CZ Si-crystal growth. J Cryst Growth, 2002, 237-239(3):1757 http://www.sciencedirect.com/science/article/pii/S0022024801023272
[11]
Ivanov N G, Korsakov A B, Smirnov E M, et al. Analysis of magnetic field effect on 3D melt flow in CZ Si growth. J Cryst Growth, 2003, 250(1/2):183 http://www.sciencedirect.com/science/article/pii/S0022024802022637
[12]
Kalaev V V. Combined effect of DC magnetic field and free surface stresses on the melt flow and crystallization front formation during 400 mm diameter Si Cz crystal growth. J Cryst Growth, 2007, 303(1):203 doi: 10.1016/j.jcrysgro.2006.11.345
[13]
Banerjee J, Muralidhar K. Simulation of transport processes during Czochralski growth of YAG crystals. J Cryst Growth, 2006, 286(2):350 doi: 10.1016/j.jcrysgro.2005.10.114
[14]
Galazka Z, Wilke H. Influence of Marangoni convection on the flow pattern in the melt during growth of Y3Al5O12 single crystals by the Czochralski method. J Cryst Growth, 2000, 216(1-4):389 doi: 10.1016/S0022-0248(00)00426-7
[15]
Tavakoli M H. Numerical study of heat transport and fluid flow during different stages of sapphire Czochralski crystal growth. J Cryst Growth, 2008, 310(12):3107 doi: 10.1016/j.jcrysgro.2008.03.017
[16]
Tavakoli M H, Wike H. Numerical study of heat transport and fluid flow of melt and gas during the seeding process of sapphire Czochralski crystal growth. Crystal Growth and Design, 2007, 7(4):644 doi: 10.1021/cg060383y
[17]
Tavakoli M H, Wike H. Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 1:non-rotating seed. Crystal Research Technology, 2007, 42(6):544 doi: 10.1002/(ISSN)1521-4079
[18]
Tavakoli M H, Wike H. Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 2:rotating seed. Crystal Research Technology, 2007, 42(7):688 doi: 10.1002/(ISSN)1521-4079
[19]
Tavakoli M H, Wike H, Crnogorac N. Influence of the crucible bottom shape on the heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth. Crystal Research Technology, 2007, 42(12):1252 doi: 10.1002/(ISSN)1521-4079
[20]
Li Yourong, Ruan Dengfang, Peng Lan, et al. Global simulation of silicon crystal Czochralski growth:characteristics of heat transfer and fluid flow. Chinese Journal of Materials Research, 2004, 18(2):212
[21]
Que Duanling, Chen Xiuzhi. Silicon material science and technology. Hangzhou:Zhejiang University Press, 2000:119
[22]
Liu L, Kitashima T, Kakimoto K. Global analysis of effects of magnetic field configuration on melt-crystal interface shape and melt flow in CZ-Si crystal growth. J Cryst Growth, 2005, 275(1/2):e2135
[23]
Shao Shufang, Zhang Qingli, Su Jing, et al. Research progress in numerical simulation for crystal growth by Czochralski method. Journal of Synthetic Crystals, 2005, 34(8):687 http://en.cnki.com.cn/Article_en/CJFDTOTAL-RGJT200504025.htm
Fig. 1.  The experimental power and crystal length change with growth time (the red foursquare is the simulation power at different crystal length).

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Fig. 2.  The crystal growth speed and crystal length change with time in the same stage (the red foursquare is the simulation speed).

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Fig. 3.  The temperature distribution (left-hand side) and flow field (right-hand side) when crystal grows to 200 mm.

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Fig. 4.  The temperature distribution (left-hand side) and flow field (right-hand side) when crystal grows to 600 mm.

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Fig. 5.  The temperature distribution (left-hand side) and flow field (right-hand side) when crystal grows to 1000 mm.

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Fig. 6.  The temperature distribution (left-hand side) and flow field (right-hand side) when crystal grows to 1400 mm.

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Fig. 7.  The heat transfer through the crystal-gas surfaces changes as the crystal length increases.

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Fig. 8.  The axial temperature gradient in the melt changes as the crystal length increases.

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Table 1.   $T_{\rm max}$ and its location with different crystal length.
[1]
Lipchin A, Brown R A. Comparison of three turbulence models for simulation of melt convection in Czochralski crystal growth of silicon. J Cryst Growth, 1999, 205(1/2):71 http://cat.inist.fr/?aModele=afficheN&cpsidt=1923038
[2]
Lipchin A, Brown R A. Hybrid finite-volume/finite-element simulation of heat transfer and melt turbulence in Czochralski crystal growth of silicon. J Cryst Growth, 2000, 216(1-4):192 doi: 10.1016/S0022-0248(00)00428-0
[3]
Chen Q, Jiang Y, Yan J, et al. Progress in modeling of fluid flows in crystal growth processes. Process in Natural Science, 2008, 18(12):1465 doi: 10.1016/j.pnsc.2008.06.003
[4]
Järvinen J, Nieminen R, Tiihonen T. Time-dependent simulation of Czochralski silicon crystal growth. J Cryst Growth, 1997, 180(3/4):468 http://cat.inist.fr/?aModele=afficheN&cpsidt=2050676
[5]
Ren Bingyan, Zhao Long, Fu Hongbo, et al. Effect of a heat shield on pull speed and oxygen concentration in a Φ 200 mm CZ Si. Chinese Journal of Semiconductors, 2005, 26(9):1764
[6]
Ren Bingyan, Zhang Zhicheng, Liu Caichi, et al. Effect of argon gas flow rate on oxygen and carbon concentration in CZ Si crystals. Chinese Journal of Semiconductors, 2001, 22(11):1416
[7]
Kalaev V V, Evstratov I Y, Makarov Y N. Gas flow effect on global heat transport and melt convection in Czochralski silicon growth. J Cryst Growth, 2003, 249(1/2):87 http://www.sciencedirect.com/science/article/pii/S0022024802021097
[8]
Kalaev V V, Lukanin D P, Zabelin V A, et al. Prediction of bulk defects in CZ Si crystals using 3D unsteady calculations of melt convection. Materials Science in Semiconductor Processing, 2003, 5(4/5):369
[9]
Kalaev V V, Lukanin D P, Zabelin V A, et al. Calculation of bulk defects in CZ Si growth:impact of melt turbulent fluctuations. J Cryst Growth, 2003, 250(1/2):203 https://www.sciencedirect.com/science/article/pii/S0022024802022406
[10]
Evstratov I Y, Kalaev V V, Zhmakin A I, et al. Numerical study of 3D unsteady melt convection during industrial-scale CZ Si-crystal growth. J Cryst Growth, 2002, 237-239(3):1757 http://www.sciencedirect.com/science/article/pii/S0022024801023272
[11]
Ivanov N G, Korsakov A B, Smirnov E M, et al. Analysis of magnetic field effect on 3D melt flow in CZ Si growth. J Cryst Growth, 2003, 250(1/2):183 http://www.sciencedirect.com/science/article/pii/S0022024802022637
[12]
Kalaev V V. Combined effect of DC magnetic field and free surface stresses on the melt flow and crystallization front formation during 400 mm diameter Si Cz crystal growth. J Cryst Growth, 2007, 303(1):203 doi: 10.1016/j.jcrysgro.2006.11.345
[13]
Banerjee J, Muralidhar K. Simulation of transport processes during Czochralski growth of YAG crystals. J Cryst Growth, 2006, 286(2):350 doi: 10.1016/j.jcrysgro.2005.10.114
[14]
Galazka Z, Wilke H. Influence of Marangoni convection on the flow pattern in the melt during growth of Y3Al5O12 single crystals by the Czochralski method. J Cryst Growth, 2000, 216(1-4):389 doi: 10.1016/S0022-0248(00)00426-7
[15]
Tavakoli M H. Numerical study of heat transport and fluid flow during different stages of sapphire Czochralski crystal growth. J Cryst Growth, 2008, 310(12):3107 doi: 10.1016/j.jcrysgro.2008.03.017
[16]
Tavakoli M H, Wike H. Numerical study of heat transport and fluid flow of melt and gas during the seeding process of sapphire Czochralski crystal growth. Crystal Growth and Design, 2007, 7(4):644 doi: 10.1021/cg060383y
[17]
Tavakoli M H, Wike H. Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 1:non-rotating seed. Crystal Research Technology, 2007, 42(6):544 doi: 10.1002/(ISSN)1521-4079
[18]
Tavakoli M H, Wike H. Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 2:rotating seed. Crystal Research Technology, 2007, 42(7):688 doi: 10.1002/(ISSN)1521-4079
[19]
Tavakoli M H, Wike H, Crnogorac N. Influence of the crucible bottom shape on the heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth. Crystal Research Technology, 2007, 42(12):1252 doi: 10.1002/(ISSN)1521-4079
[20]
Li Yourong, Ruan Dengfang, Peng Lan, et al. Global simulation of silicon crystal Czochralski growth:characteristics of heat transfer and fluid flow. Chinese Journal of Materials Research, 2004, 18(2):212
[21]
Que Duanling, Chen Xiuzhi. Silicon material science and technology. Hangzhou:Zhejiang University Press, 2000:119
[22]
Liu L, Kitashima T, Kakimoto K. Global analysis of effects of magnetic field configuration on melt-crystal interface shape and melt flow in CZ-Si crystal growth. J Cryst Growth, 2005, 275(1/2):e2135
[23]
Shao Shufang, Zhang Qingli, Su Jing, et al. Research progress in numerical simulation for crystal growth by Czochralski method. Journal of Synthetic Crystals, 2005, 34(8):687 http://en.cnki.com.cn/Article_en/CJFDTOTAL-RGJT200504025.htm

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    Received: 11 September 2012 Revised: 17 November 2012 Online: Published: 01 June 2013

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      Article Navigation >  Journal of Semiconductors  > 2013  >  34(6): 063005
      Chaohua Jin. Numerical study of heat transport and fluid flow during the silicon crystal growth process by the Czochralski method[J]. Journal of Semiconductors, 2013, 34(6): 063005. doi: 10.1088/1674-4926/34/6/063005 C H Jin. Numerical study of heat transport and fluid flow during the silicon crystal growth process by the Czochralski method[J]. J. Semicond., 2013, 34(6): 063005. doi: 10.1088/1674-4926/34/6/063005.Export: BibTex EndNote
      Citation:
      Chaohua Jin. Numerical study of heat transport and fluid flow during the silicon crystal growth process by the Czochralski method[J]. Journal of Semiconductors, 2013, 34(6): 063005. doi: 10.1088/1674-4926/34/6/063005

      C H Jin. Numerical study of heat transport and fluid flow during the silicon crystal growth process by the Czochralski method[J]. J. Semicond., 2013, 34(6): 063005. doi: 10.1088/1674-4926/34/6/063005.
      Export: BibTex EndNote
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      Numerical study of heat transport and fluid flow during the silicon crystal growth process by the Czochralski method

      doi: 10.1088/1674-4926/34/6/063005

      • Institute of Refrigeration and Thermal Engineering, School of Mechanical Engineering, Tongji University, Shanghai 200092, China

      Funds:

      the Jiangsu Zhongli PV Technology Co., Ltd 

      Project supported by the Jiangsu Zhongli PV Technology Co., Ltd

      More Information
      • Corresponding author: Jin Chaohua, Email:xiamiren01@163.com
      • Received Date: 2012-09-11
      • Revised Date: 2012-11-17
      • Published Date: 2013-06-01

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