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溶液法是生长低缺陷高品质碳化硅(SiC)单晶的重要方法, 针对6英寸溶液法生长SiC单晶系统, 建立了感应加热和热质传递全局数值分析模型, 考虑了洛伦兹力、离心力、热浮力以及表面张力对溶液流动的耦合作用, 研究了晶体旋转对溶液中速度场、温度场、碳浓度场、晶体生长速率以及坩埚壁面碳溶解析出的影响规律. 结果表明, 溶液中洛伦兹力的存在使得低晶体转速下的流场十分复杂, 晶体转速需要控制在合适的范围内, 使得生长界面下方由输运决定的碳浓度分布与生长界面处由温度决定的碳浓度分布相协调, 才能获得均匀且高的SiC单晶生长速率. 晶体转速过小使得SiC单晶生长速率很低, 过大导致生长速率径向均匀性下降, 转速为25 r/min时SiC单晶的平均生长速率较高且沿径向分布均匀性较好. 进一步分析了溶液-坩埚交界面碳组分的溶解和析出, 定位了坩埚壁面溶解较快区域和SiC多晶颗粒生成区域, 并结合速度场预测了多晶颗粒的去向. 研究结果为溶液法生长6英寸SiC单晶提供了科学依据.The top-seeded solution growth (TSSG) method is a critical technique for growing low-defect and high-quality silicon carbide (SiC) single crystals. A comprehensive numerical analysis model including induction heating, heat and mass transfer is developed for growing 6-inch SiC single crystals. The coupling effects of Lorentz force, centrifugal force, thermal buoyancy force and surface tension on the solution flow are considered, and the effects of crystal rotation speed on the velocity field, temperature field, carbon concentration field, crystal growth rate and carbon dissolution and precipitation on the crucible wall are systematically investigated. The results indicate that the Lorentz force in the solution results in a more complex flow field at low crystal rotation speeds. The crystal rotation speed should be controlled within the appropriate range to ensure that the carbon concentration distribution beneath the growth interface determined by the transport mode is coordinated with that at the growth interface determined by the temperature, which is beneficial for the uniform and high growth rate of SiC single crystals. Low rotation speeds reduce the growth rate of SiC single crystals, while high rotation speeds lead radial uniformity of growth rate to decrease. At a rotation speed of 25 r/min, the average growth rate of SiC single crystals is higher and the radial distribution uniformity is better. Further analysis is conducted on the dissolution and precipitation of carbon at the solution-crucible interface, and the regions, where the crucible wall dissolves quickly and SiC polycrystalline particles are generated, are located. The transport directions of polycrystalline particles are predicted based on the velocity field. The research results provide a scientific basis for growing 6-inch SiC single crystals by TSSG method.
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Keywords:
- top-seeded solution growth /
- silicon carbide single crystal /
- crystal rotation /
- numerical simulation
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图 2 SiC单晶炉的功率和温度分布 (a)功率密度和温度分布; (b)功率分配
Fig. 2. Power and temperature distribution in the TSSG furnace (4 kHz, 700 A): (a) Power density and temperature distribution; (b) power distribution.
图 3 溶液中洛伦兹力的大小与方向分布(4 kHz, 700 A). 图中左侧云图表示力的大小; 右侧箭头仅表示力的方向, 与大小无关
Fig. 3. Lorentz force distribution in the solution (4 kHz, 700 A). The left side indicates the magnitude of the force. The right arrow indicates only the direction of the force, independent of the magnitude.
图 4 不考虑洛伦兹力时不同晶体转速下溶液中的温度场(左侧)和速度场(右侧) (a) 0 r/min; (b) 10 r/min; (c) 25 r/min; (d) 55 r/min; (e) 100 r/min; (f) 150 r/min
Fig. 4. Temperature (left: ∆T = 1 K) and velocity fields (right: ∆u = 0.01 m/s) in the solution at different crystal rotation rates without considering Lorentz force: (a) 0 r/min; (b) 10 r/min; (c) 25 r/min; (d) 55 r/min; (e) 100 r/min; (f) 150 r/min.
图 5 考虑洛伦兹力时不同晶体转速下溶液中的温度场(左侧)和速度场(右侧) (a) 0 r/min; (b) 10 r/min; (c) 25 r/min; (d) 55 r/min; (e) 100 r/min; (f) 150 r/min
Fig. 5. Temperature (left: ∆T = 1 K) and velocity fields (right: ∆u = 0.01 m/s) in the solution at different crystal rotation rates considering Lorentz force: (a) 0 r/min; (b) 10 r/min; (c) 25 r/min; (d) 55 r/min; (e) 100 r/min; (f) 150 r/min.
图 6 不同晶体转速下溶液中的碳浓度(左侧)与过饱和度(右侧)分布 (a) 0 r/min; (b) 10 r/min; (c) 25 r/min; (d) 55 r/min; (e) 100 r/min; (f) 150 r/min
Fig. 6. Distribution of carbon concentration (left: $\Delta C$= 5 mol/m3) and supersaturation (right: $\Delta S$= 0.001) in the solution at different crystal rotation rates: (a) 0 r/min; (b) 10 r/min; (c) 25 r/min; (d) 55 r/min; (e) 100 r/min; (f) 150 r/min.
图 7 生长界面附近碳浓度局部分布 (a) 10 r/min; (b) 25 r/min; (c) 100 r/min
Fig. 7. Local distribution of carbon concentration at the growth interface (∆C = 1 mol/m3): (a) 10 r/min; (b) 25 r/min; (c) 100 r/min.
图 8 生长界面SiC单晶生长速率 (a)径向生长速率分布; (b)平均生长速率和生长速率标准差
Fig. 8. SiC single-crystal growth rates at the growth interface: (a) Radial growth rate distribution; (b) average growth rate and standard deviation of growth rate.
图 9 径向温度和碳浓度分布 (a)生长界面径向温度分布; (b)生长界面与相邻第一层网格处的径向碳浓度分布
Fig. 9. Radial temperature and carbon concentration distribution: (a) Radial temperature distribution along the growth interface; (b) radial carbon concentration distribution at the growth interface and the neighboring mesh.
图 10 溶液-坩埚交界面的碳浓度梯度
Fig. 10. Carbon concentration gradient distribution at the solution-crucible interface.
Materials Parameters Value Units Si Density 2550 kg/m3 Viscosity 8×10–4 Pa·s Electrical conductivity 1.2×106 S/m Thermal conductivity 65 W/(m·K) Specific heat 1000 J/(kg·K) Thermal expansion coefficient 0.00014 1/K Surface tension –2.5×10–4 N/m·K Surface emissivity 0.3 — SiC Density 3216 kg/m3 Electrical conductivity 1000 S/m Thermal conductivity 30 W/(m·K) Specific heat 1290 J/(kg·K) Surface emissivity 0.5 — Graphite Electrical conductivity 75400 S/m Thermal conductivity 150×300/T W/(m·K) Surface emissivity 0.9 — Carbon felt Electrical conductivity 430 S/m Thermal conductivity 0.336 W/(m·K) Surface emissivity 0.8 — Copper Electrical conductivity 5.99×107 S/m Thermal conductivity 400 W/(m·K) Surface emissivity 0.5 — 
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[1] Matsunami H, Kimoto T 1997 Mater. Sci. Eng. , R 20 125
Google Scholar
[2] Meyer C, Philip P 2005 Cryst. Growth Des. 5 1145
Google Scholar
[3] 刘东静, 周福, 陈帅阳, 胡志亮 2023 72 157901
Google Scholar
Liu D J, Zhou F, Chen S Y, Hu Z L 2023 Acta Phys. Sin. 72 157901
Google Scholar
[4] Yang N J, Song B, Wang W J, Li H 2022 Crystengcomm 24 3475
Google Scholar
[5] Kimoto T 2016 Prog. Cryst. Growth Charact. Mater. 62 329
Google Scholar
[6] Xiao S Y, Harada S, Murayama K, Ujihara T 2016 Cryst. Growth Des. 16 5136
Google Scholar
[7] Ujihara T, Maekawa R, Tanaka R, Sasaki K, Kuroda K, Takeda Y 2008 J. Cryst. Growth 310 1438
Google Scholar
[8] Wang G B, Sheng D, Li H, et al. 2023 Crystengcomm 25 560
Google Scholar
[9] Umezaki T, Koike D, Horio A, Harada S, Ujihara T 2014 15th International Conference on Silicon Carbide and Related Materials (ICSCRM) Miyazaki, Japan, September 29–October 4, 2014 p63
[10] Dang Y F, Zhu C, Ikumi M, et al. 2021 Crystengcomm 23 1982
Google Scholar
[11] Yamamoto T, Okano Y, Ujihara T, Dost S 2017 J. Cryst. Growth 470 75
Google Scholar
[12] Umezaki T, Koike D, Harada S, Ujihara T 2016 Jpn. J. Appl. Phys. 55 125601
Google Scholar
[13] Mercier F, Dedulle J M, Chaussende D, Pons M 2010 J. Cryst. Growth 312 155
Google Scholar
[14] Ha M T, Shin Y J, Lee M H, Kim C J, Jeong S M 2018 Phys. Status Solidi A 215 1701017
Google Scholar
[15] Kusunoki K, Kishida Y, Seki K 2019 Mater. Sci. Forum (Switzerland) 963 85
Google Scholar
[16] Ha M T, Shin Y J, Bae S Y, Park S Y, Jeong S M 2019 J. Korean Ceram. Soc. 56 589
Google Scholar
[17] Su Hun C, Young Gon K, Yun Ji S, et al. 2018 Mater. Sci. Forum (Switzerland) 924 27
Google Scholar
[18] Liu B T, Yu Y, Tang X, Gao B 2020 J. Cryst. Growth 533 125406
Google Scholar
[19] Yoon J Y, Lee M H, Kim Y, Seo W S, Shul Y G, Lee W J, Jeong S M 2017 Jpn. J. Appl. Phys. 56 065501
Google Scholar
[20] Li F C, He L, Yan Z Y, Qi X F, Ma W C, Chen J L, Xu Y K, Hu Z G 2023 J. Cryst. Growth 607 127112
Google Scholar
[21] Sui Z R, Xu L B, Cui C, Wang R, Pi X D, Yang D R, Han X F 2024 Crystengcomm 26 1022
Google Scholar
[22] Fujii K, Takei K, Aoshima M, et al. 2015 Mater. Sci. Forum (Switzerland) 821–823 35
Google Scholar
[23] Liu Y H, Li M Y, Yan Z Y, et al. 2024 J. Cryst. Growth 643 127801
Google Scholar
[24] Mercier F, Nishizawa S 2011 8th European Conference on Silicon Carbide and Related Materials Oslo, Norway, August 29–September 2, 2011 p32
[25] Ariyawong K, Dedulle J M, Chaussende D 2014 15th International Conference on Silicon Carbide and Related Materials (ICSCRM) Miyazaki, Japan, September 29–October 04, 2014 p71
[26] Mercier F, Nishizawa S 2013 J. Cryst. Growth 362 99
Google Scholar
[27] Wang L, Horiuchi T, Sekimoto A, Okano Y, Ujihara T, Dost S 2018 J. Cryst. Growth 498 140
Google Scholar
[28] Ha M T, Lich L V, Shin Y J, Bae S Y, Lee M H, Jeong S M 2020 Materials 13 651
Google Scholar
[29] Wang L, Takehara Y, Sekimoto A, Okano Y, Ujihara T, Dost S 2020 Crystals 10 111
Google Scholar
[30] Li Z Y, Yang Y, Wang J L, Luo J P, Liu L J 2024 Proceedings of the 11th International Workshop on Modeling in Crystal Growth, ROMANIA, September 22–25, 2024 p573198
[31] Weiss J, Csendes Z J 1982 IEEE Transactions on Power Apparatus and Systems 101 3796
Google Scholar
[32] Tavakoli M H 2008 Cryst. Growth Des. 8 483
Google Scholar
[33] Lefebure J, Dedulle J M, Ouisse T, Chaussende D 2012 Cryst. Growth Des. 12 909
Google Scholar
[34] Liu B T, Yu Y, Tang X, Gao B 2019 J. Cryst. Growth 527 125248
Google Scholar
[35] Hayashi Y, Mitani T, Komatsu N, Kato T, Okumura H 2019 J. Cryst. Growth 523 125151
Google Scholar
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