Effect of Horizontal Magnetic Field in Czochralski Silicon Growth
Increase in the crystal diameter necessitates the control over the turbulent natural convection in large volumes, which is often achieved with magnetic fields (MF). Application of MFs changes both heat transfer and convection patterns in the melt. So, flow laminarization at high MFs results in higher temperature gradients. Along with vanishing turbulent mixing it, in turn, dramatically increase the effect of Marangoni stress tension on the melt free surface. Besides, the effect of the gas shear stress on the melt surface velocity also significantly increases. In some cases it may even govern the global melt flow dynamics.
MF 30 mT, Ar flowrate 5200 slh
Results of 3D unsteady modeling in CGSim show that at the horizontal MF of 30 mT there is only a small difference between cross-sections positioned along and orthogonal to the magnetic induction vector. The melt over the whole free surface, in this case, is rotating due to the crucible rotation. The temperature distribution is quite symmetric.
MF 300 mT, Ar flowrate 5200 slh
As the horizontal MF increases up to 300 mT, it becomes obvious that strong horizontal MFs nearly completely suppress flow in a cross-section positioned along the induction vector. Thus, high velocity flows are only observed in the CS positioned orthogonal to the magnetic induction vector.
MF 300 mT, Ar flowrate 500 slh
With reduced Ar flow rate, one can also see substantially asymmetric temperature distribution at the melt surface and an upward flow of the melt in the area located under the crystal. This upward motion results from combined action of MFs and Ar flow. Therefore, it can not be reproduced when Ar flow is low or ignored in computations.
Effect on deflection and V/G
Adequate account of the Ar flow is crucial for modelling of large diameter Silicon growth by Czochralski method. It allows one to reproduce and study regimes with upward flow motion under the crystal. These regimes appear to be close to optimal in terms of the crystallization front deflection and distribution of the V/G parameter, see the plots obtained by 3D unsteady modeling with CGSim on the right.
Publications by STR Team and CGSim Users
“Computer modeling of HMCz Si growth“, Vladimir Kalaev, J. of Crystal Growth 532 (2020) 125413, https://doi.org/10.1016/j.jcrysgro.2019.125413
“Effect of numerical parameters on unsteady melt flow features and impurity transport within simplified Cz Si crystal growth process Geometry with effect of Transverse magnetic fields”, Andrey Smirnov, et. al,, ICCGE-19 Proceedings, Keystone, Colorado, USA, 2019
“Melt Flow before Crystal Seeding in Cz Si Growth with Transversal MF”, Masaya Iizuka, Yuji Mukaiyama, S.E.Demina, V.V.Kalaev, J. of Crystal Growth 468 (2017) p. 510-513, http://dx.doi.org/10.1016/j.jcrysgro.2016.11.002
“Numerical simulation of the oxygen concentration distribution in silicon melt for different crystal lengths during Czochralski growth with a transverse magnetic field”, Jyh-Chen Chen, Pei-Yi Chiang, Thi Hoai Thu Nguyen, Chieh Hu, Chun-Hung Chen, Chien-Cheng Liu, J. of Crystal Growth 452 (2016), p. 6-11, http://dx.doi.org/10.1016/j.jcrysgro.2016.03.024
“Effect of numerical parameters on accuracy of the melt flow prediction within a simplified geometry of Cz Si crystal growth process with Transverse Magnetic field”, Andrey Smirnov, et. al, ICCGE-18, Proceedings, Nagoya, Japan, 2016
“Crystal twisting in Cz Si growth“, with Siltronic AG, by Vladimir Kalaev, Andreas Sattler, Lev Kadinski, J. of Crystal Growth 413 (2015), p. 12-16, http://dx.doi.org/10.1016/j.jcrysgro.2014.12.005
“Three-dimensional numerical simulation of flow, thermal and oxygen distributions for a Czochralski silicon growth with in a transverse magnetic field” by Jyh-Chen Chen, Pei-Yi Chiang, Ching-Hsin Chang, Ying-Yang Teng, Cheng-Chuan Huang, Chun-Hung Chen, Chien-Cheng Liu, J. of Crystal Growth 401 (2014), p. 813-819, https://doi.org/10.1016/j.jcrysgro.2014.01.028
“Combined effect of DC magnetic fields and free surface stresses on the melt flow and crystallization front formation during 400 mm diameter Si Cz crystal growth” by V.V. Kalaev, J. of Crystal Growth 303 (2007) p.203-210, https://doi.org/10.1016/j.jcrysgro.2006.11.345