Effect of Cusp Magnetic Fields in Czochralski Silicon Growth

At higher crystal diameters, the role of the natural convection in the melt becomes more critical. That is why horizontal and cusp magnetic fields (MF) are often used in Cz Si to control the flow. Application of MFs changes both heat transfer and convection patterns in the melt. Laminarization of turbulent flow at high MFs results in higher temperature gradients. With vanishing turbulent mixing, it dramatically increases the effect of Marangoni stress tension on the melt free surface. In addition, the effect of the gas shear stress on the melt surface velocity also radically increases. In some cases, it may even govern the global melt flow dynamics in large volumes.

Here we consider the example of cusp magnetic field. Let’s start with the case when no magnetic field is applied (left). Under the considered operating conditions, downward melt motion can be seen under the crystallization front. When cusp MF of low intensity is applied (right), thermal pulsations in the melt are largely suppressed. At the same time, mixing of the melt under the crystallization front remains vigorous.

3D unsteady simulations of Cz Si in CGSim
Time-averaged temperature and velocity distribution in a vertical CS without MF and at Ar flowrate of 5200 slh
3D unsteady simulations of Czochralski Silicon growth
Time-averaged temperature and velocity distribution in a vertical CS at cusp MF of 30 mT and Ar flowrate of 5200 slh

Publications by STR Team and CGSim Users

“Effects of crystal-crucible iso-rotation and a balanced/unbalanced cusp magnetic field on the heat, flow, and oxygen transport in a Czochralski silicon melt” by Thi-Hoai-Thu Nguyen, Jyh-Chen Chen, Chieh Hu, Chun-Hung Chen, J. of Crystal Growth 531 (2020) 125373 https://doi.org/10.1016/j.jcrysgro.2019.125373

Analysis of the effect of symmetric/asymmetric CUSP magnetic fields on melt/crystal interface during Czochralski silicon growth“, Parthiv Daggolu, Jae Woo Ryu, Alex Galyukov, Alexey Kondratyev, J. of Crystal Growth 452 (2016), p. 22-26 https://doi.org/10.1016/j.jcrysgro.2015.12.001

Numerical simulation of oxygen transport during the Czochralski silicon crystal growth with a cusp magnetic field“, J.-C. Chen, P.-C.Guo, C.-H.Chang, Y.-Y.Teng, C.Hsu, H.-M.Wang, C.-C.Liu, J. of Crystal Growth 401 (2014), p. 888-894, https://doi.org/10.1016/j.jcrysgro.2013.10.040

“Use of computer modeling for optimization of Cz Si growth: strategy and examples”, Alex Galyukov, 2009, https://www.slideshare.net/galyukov/cgsim-presentation-cz-si