[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. [2] 刘立军. 晶体生长数值模拟领域的若干研究进展[J]. 中国材料进展, 2019, 38(5): 523-527. LIU L J. Some research progress in the field of numerical simulation of crystal growth[J]. Materials China, 2019, 38(5): 523-527 (in Chinese). [3] 张西亚, 高德东, 王 珊, 等. 热屏下降式单晶炉设计与研究[J]. 人工晶体学报, 2021, 50(6): 987-995. ZHANG X Y, GAO D D, WANG S, et al. Design and research on descended heat shield of the single crystal furnace[J]. Journal of Synthetic Crystals, 2021, 50(6): 987-995 (in Chinese). [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. [5] 滕 冉, 常 青, 吴志强, 等. 热屏结构对大直径单晶硅生长影响的数值分析[J]. 人工晶体学报, 2014, 43(3): 508-512. TENG R, CHANG Q, WU Z Q, et al. Numerical analysis of the effect of heat shield structure on growth of large diameter monocrystalline silicon[J]. Journal of Synthetic Crystals, 2014, 43(3): 508-512 (in Chinese). [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] 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. [8] 李 进, 张洪岩, 高忙忙, 等. 氩气流速对400 mm大直径磁场直拉单晶硅固液界面、热应力及氧含量的影响[J]. 人工晶体学报, 2014, 43(5): 1193-1198+1211. LI J, ZHANG H Y, GAO M M, et al. Influence of argon flow rate on the solid/liquid interface, thermal stress and oxygen concentration in the 400 mm CZ silicon with a magnetic field[J]. Journal of Synthetic Crystals, 2014, 43(5): 1193-1198+1211 (in Chinese). [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] 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. [11] 谭建国. 使用ANSYS6.0进行有限元分析[M]. 北京: 北京大学出版社, 2002. TAN J G. Finite element analysis using ANSYS 6.0[M]. Beijing: Peking University Press, 2002 (in Chinese). [12] 巴特 K J, 威尔逊 E L. 有限元分析中的数值方法[M]. 林公豫, 罗 恩, 译. 北京: 科学出版社, 1985. BATHE K J, WILSON E L. Numerical method in finite element analysis[M]. LIN G Y, LUO E, Transl. Beijing: Science Press, 1985 (in Chinese). [13] 帕斯卡S V. 传热与流体流动的数值计算[M]. 张 政, 译. 北京: 科学出版社, 1984. PATANKAR S V. Numerical Heat Transfer and Fluid Flow[M]. ZHANG Z, Transl. Beijing: Science Press, 1984 (in Chinese). [14] 唐兴伦, 范群波, 张朝辉,等. ANSYS工程应用教程(热与电磁篇)[M]. 北京: 中国铁道出版社, 2003. TANG X L, FAN Q B, ZHANG C H, et al. Application of ANSYS on the engineering of heat and magnetism[M]. Beijing: China Railway Publishing House, 2003 (in Chinese). [15] 俞昌铭. 热传导及其数值分析[M]. 北京: 清华大学出版社, 1981. YU C M. Heat transfer and numerical analysis[M]. Beijing: Tsinghua University Press,1981 (in Chinese). [16] 孔祥谦, 王传溥. 有限元在传热学中的应用[M]. 北京: 科学出版社, 1981. KONG X Q, WANG C P. Application of finite element in heat transfer[M]. Beijing: Science Press, 1981 (in Chinese). [17] KALAEV V. Computer modeling of HMCz Si growth[J]. Journal of Crystal Growth, 2020, 532: 125413. [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. [19] 林明献. 硅晶圆半导体材料技术[M]. 全华图书股份有限公司, 2020. LIN M X. Silicon wafer semiconductor[M]. Chuan Hwa Book Co., Ltd., 2020 (in Chinese). [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] JOMÂA 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] 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] 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] 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] 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. |