[1] [1] Teng R, Li Y, Cui B, et al. Experiment and numerical simulation of melt convection and oxygen distribution in 400 mm Czochralski silicon crystal growth[J].Rare Metals,2017,36(2):134-141.

[3] [3] Chen J C, Chiang P Y, Nguyen T H T, et al. Numerical simulation of the oxygen concentration distribution in silicon melt for different crystal lengths during Czochralski growth with a transverse magnetic field[J].Journal of Crystal Growth,2016,22(452):6-11.

[4] [4] Li P T, Ren S Q, Jiang D C, et al. Effect of alternating magnetic field on the removal of metal impurities in silicon ingot by directional solidification[J].Journal of Crystal Growth,2016,22(437):14-19.

[6] [6] Wang L, Horiuchi T, Sekimoto A， et al. Numerical investigation of the effect of static magnetic field on the TSSG growth of SiC[J].Journal of Crystal Growth,2018,5(498):140-147.

[7] [7] Zhang J, Ren J C, Liu D. Effect of crucible rotation and crystal rotation on the oxygen distribution at the solid-liquid interface during the growth of Czochralski monocrystalline silicon under superconducting horizontal magnetic field[J].Results in Physics,2019,13.

[8] [8] Guan X J, Zhang X Y. Simulation of V/G During Φ450 mm Czochralski grown silicon single crystal growth under the different crystal and crucible rotation rates[J].International Symposium on Materials Application and Engineering,2016,67:02002.

[9] [9] Zheng Z, Seto T, Kim S, et al. A first-principle model of 300 mm Czochralski single-crystal Si production process for predicting crystal radius and crystal growth rate[J].Journal of Crystal Growth,2018,3(492):105-113.

[10] [10] Su W, Zuo R, Lu J, et al. Numerical and experimental studies on the black periphery wafer in CZ Si growth[J].Journal of Crystal Growth,2014,388:42-47.

[11] [11] Atia A, Ghernaout B, Bouabdallah S, et al. Three-dimensional oscillatory mixed convection in a Czochralski silicon melt under the axial magnetic field[J].Applied Thermal Engineering,2016,7(105):704-715.

[12] [12] Grants I, Pal J, Gerbeth G. Physical modelling of Czochralski crystal growth in horizontal magnetic field[J].Journal of Crystal Growth,2017,470(22):71-78.

[13] [13] Zhang J, Liu D, Zhao Y, et al. Impact of heat shield structure in the growth process of czochralski silicon derived from numerical simulation[J].Chinese Journal of Mechanical Engineering,2014,27(3):504-510.

[14] [14] Jung T, Seebeck J, Friedrich J. Combined global 2D-local 3D modeling of the industrial Czochralski silicon crystal growth process[J].Journal of Crystal Growth,2013,10(368):72-80.

[16] [16] Zhang N, Liu D. Numerical simulation of MHD oscillatory mixed convection in CZ crystal growth by Lattice Boltzmann method[J].Results in Physics,2018(10):882-890.