[1] [1] KAKIMOTO K, GAO B, LIU X, et al. Growth of semiconductor silicon crystals［J］. Progress in Crystal Growth and Characterization of Materials, 2016, 62(2): 273-285.

[4] [4] SONG D W, LEE S H, MUN Y H, et al. Oxygen content increasing mechanism in Czochralski (CZ) silicon crystals doped with heavy antimony under a double-typed heat shield［J］. Journal of Crystal Growth, 2011, 325(1): 27-31.

[6] [6] KUMAR M A, SRINIVASAN M, RAMASAMY P. Reduction of carbon and oxygen impurities in mc-silicon ingot using molybdenum gas shield in directional solidification process［J］. Silicon, 2021, 13(12): 4535-4544.

[7] [7] 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.

[9] [9] JANA S, DOST S, KUMAR V, et al. A numerical simulation study for the Czochralski growth process of Si under magnetic field［J］. International Journal of Engineering Science, 2006, 44(8/9): 554-573.

[10] [10] MUKAIYAMA Y, SUEOKA K, MAEDA S, et al. Numerical analysis of effect of thermal stress depending on pulling rate on behavior of intrinsic point defects in large-diameter Si crystal grown by Czochralski method［J］. Journal of Crystal Growth, 2020, 531: 125334.

[17] [17] KALAEV V. Computer modeling of HMCz Si growth［J］. Journal of Crystal Growth, 2020, 532: 125413.

[18] [18] SMIRNOV A D, KALAEV V V. Development of oxygen transport model in Czochralski growth of silicon crystals［J］. Journal of Crystal Growth, 2008, 310(12): 2970-2976.

[20] [20] DING J L, LI Y Q, LIU L J. Effect of cusp magnetic field on the turbulent melt flow and crystal/melt interface during large-size Czochralski silicon crystal growth［J］. International Journal of Thermal Sciences, 2021, 170: 107137.

[21] [21] JOMA M, M′HAMDI M, HU Y, et al. Numerical analysis of oxygen control during growth of Czochralski silicon single crystals［C］//2014 IEEE 40th Photovoltaic Specialist Conference (PVSC). June 8-13, 2014, Denver, CO, USA. IEEE, 2014: 3521-3525.

[22] [22] 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, 452: 6-11.

[23] [23] LIU X, HARADA H, MIYAMURA Y, et al. Transient global modeling for the pulling process of Czochralski silicon crystal growth. II. Investigation on segregation of oxygen and carbon［J］. Journal of Crystal Growth, 2019, 532: 125404.

[24] [24] GENG X, WU X B, GUO Z Y. Numerical simulation of combined flow in Czochralski crystal growth ［J］. Journal of Crystal Growth, 1997, 179(1/2): 309-319.

[25] [25] TENG Y Y, CHEN J C, HUANG C C, et al. Numerical investigation of the effect of heat shield shape on the oxygen impurity distribution at the crystal-melt interface during the process of Czochralski silicon crystal growth ［J］. Journal of Crystal Growth, 2012, 352(1): 167-172.