Effects of crystal rotation on 6-inch SiC crystal growth by top-seeded solution growth method

YANG Yao; LI Zaoyang; GAO Junhao; QI Chongchong; LI Dengnian; WU Guanghui; LIU Lijun

doi:10.7498/aps.74.20250595

Abstract

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.

Keywords:

Authors and contacts

School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Corresponding author: LI Zaoyang, lizaoyang@mail.xjtu.edu.cn

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References

[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 物理学报 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
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[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

Cited By

图 1 溶液法SiC单晶生长炉结构示意图

Figure 1. Structural configuration of the TSSG furnace.

DownLoad: Full-Size Img PowerPoint

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

Figure 2. Power and temperature distribution in the TSSG furnace (4 kHz, 700 A): (a) Power density and temperature distribution; (b) power distribution.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 10 溶液-坩埚交界面的碳浓度梯度

Figure 10. Carbon concentration gradient distribution at the solution-crucible interface.

DownLoad: Full-Size Img PowerPoint

表 1 主要材料的物理特性^[13,16,18]

Table 1. Physical properties of the main materials^[13,16,18].

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	—

DownLoad: CSV

[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 物理学报 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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