[1] [1] OKUMURA H. Present status and future prospect of widegap semiconductor high-power devices［J］. Japanese Journal of Applied Physics, 2006, 45(10R): 7565.

[2] [2] BIELA J, SCHWEIZER M, WAFFLER S, et al. SiC versus Si—evaluation of potentials for performance improvement of inverter and DC-DC converter systems by SiC power semiconductors［J］. IEEE Transactions on Industrial Electronics, 2011, 58(7): 2872-2882.

[3] [3] MATSUNAMI H, KIMOTO T. Step-controlled epitaxial growth of SiC: high quality homoepitaxy［J］. Materials Science and Engineering: R: Reports, 1997, 20(3): 125-166.

[5] [5] LIU Y L. Recent progress on single-crystal growth and epitaxial growth of 4H silicon carbide［J］. Solid State Phenomena, 2022, 332: 73-84.

[6] [6] YU Y J, BYEON D S, SHIN Y J, et al. Residual stress analysis of 4H-SiC crystals obtained by a top-seeded solution growth method［J］. CrystEngComm, 2017, 19(45): 6731-6735.

[7] [7] LI J J, YANG G, LIU X S, et al. Dislocations in 4H silicon carbide［J］. Journal of Physics D: Applied Physics, 2022, 55(46): 463001.

[8] [8] HYUN K, KIM S J, TAISHI T. Effect of cobalt addition to Si-Cr solvent in top-seeded solution growth［J］. Applied Surface Science, 2020, 513: 145798.

[10] [10] UJIHARA T, MAEKAWA R, TANAKA R, et al. Solution growth of high-quality 3C-SiC crystals［J］. Journal of Crystal Growth, 2008, 310(7/8/9): 1438-1442.

[12] [12] CARTER C H Jr, TSVETKOV V F, GLASS R C, et al. Progress in SiC: from material growth to commercial device development［J］. Materials Science and Engineering: B, 1999, 61/62: 1-8.

[13] [13] HALDEN F A. Growth of silicon carbide crystals from solution in molten metal alloys［J］. Silicon Carbide: A High Temperature Semiconductor, 1959: 115.

[14] [14] YAKIMOVA R T, YANCHEV I Y. On the transport kinetics of silicon carbide in the silicon-scandium-carbon system［J］. Journal of Crystal Growth, 1981, 51(2): 223-226.

[15] [15] IVANTSOV V, DMITRIEV V. Dissolution and growth of silicon carbide crystals in melt-solutions［J］. Materials Science Forum, 1998, 264/265/266/267/268: 73-76.

[16] [16] NASIR KHAN M, NISHIZAWA S I, BAHNG W, et al. Liquid-phase epitaxy on 6H-SiC Acheson seed crystals in closed vessel［J］. Journal of Crystal Growth, 2000, 220(1/2): 75-81.

[17] [17] DUDLEY M, HUANG X R, HUANG W, et al. The mechanism of micropipe nucleation at inclusions in silicon carbide［J］. Applied Physics Letters, 1999, 75(6): 784-786.

[18] [18] KIMOTO T. Bulk and epitaxial growth of silicon carbide［J］. Progress in Crystal Growth and Characterization of Materials, 2016, 62(2): 329-351.

[19] [19] KATSUNO T, WATANABE Y, FUJIWARA H, et al. Analysis of surface morphology at leakage current sources of 4H-SiC Schottky barrier diodes［J］. Applied Physics Letters, 2011, 98(22): 222111.

[20] [20] YAMAMOTO K, NAGAYA M, WATANABE H, et al. Influence of threading dislocations on lifetime of gate thermal oxide［J］. Materials Science Forum, 2012, 717/718/719/720: 477-480.

[21] [21] KIMOTO T. Material science and device physics in SiC technology for high-voltage power devices［J］. Japanese Journal of Applied Physics, 2015, 54(4): 040103.

[22] [22] YAMAMOTO Y, HARADA S, SEKI K, et al. Low-dislocation-density 4H-SiC crystal growth utilizing dislocation conversion during solution method［J］. Applied Physics Express, 2014, 7(6): 065501.

[23] [23] YAMAMOTO Y, HARADA S, SEKI K, et al. High-efficiency conversion of threading screw dislocations in 4H-SiC by solution growth［J］. Applied Physics Express, 2012, 5(11): 115501.

[24] [24] MURAYAMA K, HORI T, HARADA S, et al. Two-step SiC solution growth for dislocation reduction［J］. Journal of Crystal Growth, 2017, 468: 874-878.

[25] [25] KAMEI K, KUSUNOKI K, YASHIRO N, et al. Solution growth of single crystalline 6H, 4H-SiC using Si-Ti-C melt［J］. Journal of Crystal Growth, 2009, 311(3): 855-858.

[26] [26] YASHIRO N, KUSUNOKI K, KAMEI K, et al. Solution growth and crystallinity characterization of bulk 6H-SiC［J］. Materials Science Forum, 2010, 645/646/647/648: 33-36.

[27] [27] KUSUNOKI K, YASHIRO N, OKADA N, et al. Growth of large diameter 4H-SiC by TSSG technique［J］. Materials Science Forum, 2013, 740/741/742: 65-68.

[28] [28] KUSUNOKI K, KAMEI K, OKADA N, et al. Top-seeded solution growth of 3 inch diameter 4H-SiC bulk crystal using metal solvents［J］. Materials Science Forum, 2014, 778/779/780: 79-82.

[29] [29] ZHANG Z S, CHEN L, DENG J, et al. Intrinsic ferromagnetism in 4H-SiC single crystal induced by Al-doping［J］. Applied Physics A, 2020, 126(9): 729.

[30] [30] WELLMANN P J. Review of SiC crystal growth technology［J］. Semiconductor Science and Technology, 2018, 33(10): 103001.

[31] [31] MERCIER F, DEDULLE J M, CHAUSSENDE D, et al. Coupled heat transfer and fluid dynamics modeling of high-temperature SiC solution growth［J］. Journal of Crystal Growth, 2010, 312(2): 155-163.

[32] [32] KUSUNOKI K, OKADA N, KAMEI K, et al. Top-seeded solution growth of three-inch-diameter 4H-SiC using convection control technique［J］. Journal of Crystal Growth, 2014, 395: 68-73.

[33] [33] UMEZAKI T, KOIKE D, HARADA S, et al. Analysis of the carbon transport near the growth interface with respect to the rotational speed of the seed crystal during top-seeded solution growth of SiC［J］. Japanese Journal of Applied Physics, 2016, 55(12): 125601.

[34] [34] HA M T, SHIN Y J, LEE M H, et al. Effects of the temperature gradient near the crystal-melt interface in top seeded solution growth of SiC crystal［J］. Physica Status Solidi (a), 2018, 215(20): 1701017.

[35] [35] MUKAIYAMA Y, IIZUKA M, VOROB’EV A, et al. Numerical investigation of the effect of shape change in graphite crucible during top-seeded solution growth of SiC［J］. Journal of Crystal Growth, 2017, 475: 178-185.

[36] [36] CHOI S H, KIM Y G, SHIN Y J, et al. The effect of stepped wall of the graphite crucible in top seeded solution growth of SiC crystal［J］. Materials Science Forum, 2018, 924: 27-30.

[37] [37] HORIUCHI T, WANG L, SEKIMOTO A, et al. The effect of crucible rotation and crucible size in top-seeded solution growth of single-crystal silicon carbide［J］. Crystal Research and Technology, 2019, 54(5): 1900014.

[38] [38] WANG L, SEKIMOTO A, TAKEHARA Y, et al. Optimal control of SiC crystal growth in the RF-TSSG system using reinforcement learning［J］. Crystals, 2020, 10(9): 791.

[39] [39] YU W C, ZHU C, TSUNOOKA Y, et al. Geometrical design of a crystal growth system guided by a machine learning algorithm［J］. CrystEngComm, 2021, 23(14): 2695-2702.

[41] [41] SCACE R I, SLACK G A. Solubility of carbon in silicon and germanium［J］. The Journal of Chemical Physics, 1959, 30(6): 1551-1555.

[42] [42] MITANI T, KOMATSU N, TAKAHASHI T, et al. Effect of aluminum addition on the surface step morphology of 4H-SiC grown from Si-Cr-C solution［J］. Journal of Crystal Growth, 2015, 423: 45-49.

[43] [43] MITANI T, KOMATSU N, TAKAHASHI T, et al. Growth rate and surface morphology of 4H-SiC crystals grown from Si-Cr-C and Si-Cr-Al-C solutions under various temperature gradient conditions［J］. Journal of Crystal Growth, 2014, 401: 681-685.

[44] [44] ZIENKIEWICZ O C, TAYLOR R L, ZHU J Z. The finite element method: its basis and fundamentals (Seventh Edition)［M］. Butterworth-Heinemann, 2013.

[45] [45] YAMAMOTO T, OKANO Y, UJIHARA T, et al. Global simulation of the induction heating TSSG process of SiC for the effects of Marangoni convection, free surface deformation and seed rotation［J］. Journal of Crystal Growth, 2017, 470: 75-88.

[46] [46] PARK T Y, SHIN Y J, HA M T, et al. Effect of radiation heat transfer on the control of temperature gradient in the induction heating furnace for growing single crystals［J］. Journal of the Korean Institute of Electrical and Electronic Material Engineers, 2019, 32(6): 522-527.

[47] [47] MERCIER F, NISHIZAWA S I. Comparative numerical study of the effects of rotating and traveling magnetic fields on the carbon transport in the solution growth of SiC crystals［J］. Journal of Crystal Growth, 2013, 362: 99-102.

[48] [48] WANG L, HORIUCHI T, SEKIMOTO A, et al. Three-dimensional numerical analysis of Marangoni convection occurring during the growth process of SiC by the RF-TSSG method［J］. Journal of Crystal Growth, 2019, 520: 72-81.

[49] [49] LEFEBURE J, DEDULLE J M, OUISSE T, et al. Modeling of the growth rate during top seeded solution growth of SiC using pure silicon as a solvent［J］. Crystal Growth & Design, 2012, 12(2): 909-913.

[50] [50] TAKEHARA Y, SEKIMOTO A, OKANO Y, et al. Bayesian optimization for a high- and uniform-crystal growth rate in the top-seeded solution growth process of silicon carbide under applied magnetic field and seed rotation［J］. Journal of Crystal Growth, 2020, 532: 125437.

[51] [51] BAUMGARTL J, BUDWEISER W, MLLER G, et al. Studies of bouyancy driven convection in a vertical cylinder with parabolic temperature profile［J］. Journal of Crystal Growth, 1989, 97(1): 9-17.

[52] [52] HAYASHI Y, MITANI T, KOMATSU N, et al. Control of temperature distribution to suppress macro-defects in solution growth of 4H-SiC crystals［J］. Journal of Crystal Growth, 2019, 523: 125151.

[53] [53] LEFEBURE J, DEDULLE J M, OUISSE T, et al. Growth rate prediction in SiC solution growth using silicon as solvent［J］. Materials Science Forum, 2012, 717/718/719/720: 69-72.

[54] [54] HA M T, SHIN Y J, BAE S Y, et al. Effect of hot-zone aperture on the growth behavior of SiC single crystal produced via top-seeded solution growth method［J］. Journal of the Korean Ceramic Society, 2019, 56(6): 589-595.

[55] [55] KOIKE D, UMEZAKI T, MURAYAMA K, et al. Control of interface shape by non-axisymmetric solution convection in top-seeded solution growth of SiC crystal［J］. Materials Science Forum, 2015, 821/822/823: 18-21.

[56] [56] LIU B T, YU Y, TANG X, et al. Optimization of crucible and heating model for large-sized silicon carbide ingot growth in top-seeded solution growth［J］. Journal of Crystal Growth, 2020, 533: 125406.

[57] [57] YOON J Y, LEE M H, KIM Y, et al. Enhancement in the rate of the top seeded solution growth of SiC crystals via a roughening of the graphite surface［J］. Japanese Journal of Applied Physics, 2017, 56(6): 065501.

[58] [58] BRICE J C, CAPPER P, JONES C L, et al. ACRT: a review of models［J］. Progress in Crystal Growth and Characterization, 1986, 13(3): 197-229.

[59] [59] SCHEEL H J, SCHULZ-DUBOIS E O. Flux growth of large crystals by accelerated crucible-rotation technique［J］. Journal of Crystal Growth, 1971, 8(3): 304-306.

[60] [60] KUSUNOKI K, KAMEI K, OKADA N, et al. Solution growth of SiC crystal with high growth rate using accelerated crucible rotation technique［J］. Materials Science Forum, 2006, 527/528/529: 119-122.

[61] [61] DAIKOKU H, KADO M, SEKI A, et al. Solution growth on concave surface of 4H-SiC crystal［J］. Crystal Growth & Design, 2016, 16(3): 1256-1260.

[62] [62] SCRIVEN L E, STERNLING C V. The Marangoni effects［J］. Nature, 1960, 187(4733): 186-188.

[63] [63] STERNLING C V, SCRIVEN L E. Interfacial turbulence: hydrodynamic instability and the Marangoni effect［J］. AIChE Journal, 1959, 5(4): 514-523.

[64] [64] MERCIER F, NISHIZAWA S I. Solution growth of SiC from silicon melts: influence of the alternative magnetic field on fluid dynamics［J］. Journal of Crystal Growth, 2011, 318(1): 385-388.

[65] [65] MERCIER F, NISHIZAWA S I. Numerical investigation of the growth rate enhancement of SiC crystal growth from silicon melts［J］. Japanese Journal of Applied Physics, 2011, 50(3R): 035603.

[66] [66] ARIYAWONG K, DEDULLE J M, CHAUSSENDE D. Electromagnetic enhancement of carbon transport in SiC solution growth process: a numerical modeling approach［J］. Materials Science Forum, 2014, 778/779/780: 71-74.

[67] [67] 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, 498: 140-147.

[68] [68] WANG L, TAKEHARA Y, SEKIMOTO A, et al. Numerical study of three-dimensional melt flows during the TSSG process of SiC crystal for the influence of input parameters of RF-coils and an external rotating magnetic field［J］. Crystals, 2020, 10(2): 111.

[69] [69] DURAND F, DUBY J C. Carbon solubility in solid and liquid silicon—a review with reference to eutectic equilibrium［J］. Journal of Phase Equilibria, 1999, 20(1): 61-63.

[70] [70] DAIKOKU H, KADO M, SAKAMOTO H, et al. Top-seeded solution growth of 4H-SiC bulk crystal using Si-Cr based melt［J］. Materials Science Forum, 2012, 717/718/719/720: 61-64.

[71] [71] GILLESSEN K, VON MNCH W. Growth of silicon carbide from liquid silicon by a travelling heater method［J］. Journal of Crystal Growth, 1973, 19(4): 263-268.

[72] [72] KADO M, DAIKOKU H, SAKAMOTO H, et al. High-speed growth of 4H-SiC single crystal using Si-Cr based melt［J］. Materials Science Forum, 2013, 740/741/742: 73-76.

[73] [73] KUSUNOKI K, KAMEI K, SEKI K, et al. Nitrogen doping of 4H-SiC by the top-seeded solution growth technique using Si-Ti solvent［J］. Journal of Crystal Growth, 2014, 392: 60-65.

[74] [74] JORDAN M I, MITCHELL T M. Machine learning: trends, perspectives, and prospects［J］. Science, 2015, 349(6245): 255-260.

[75] [75] ALZUBI J, NAYYAR A, KUMAR A. Machine learning from theory to algorithms: an overview［J］. Journal of Physics: Conference Series, 2018, 1142: 012012.

[76] [76] MAHESH B. Machine learning algorithms-a review［J］. International Journal of Science and Research (IJSR), 2020, 9: 381-386.

[77] [77] ARULKUMARAN K, DEISENROTH M P, BRUNDAGE M, et al. Deep reinforcement learning: a brief survey［J］. IEEE Signal Processing Magazine, 2017, 34(6): 26-38.

[79] [79] TSUNOOKA Y, KOKUBO N, HATASA G, et al. High-speed prediction of computational fluid dynamics simulation in crystal growth［J］. CrystEngComm, 2018, 20(41): 6546-6550.

[80] [80] DANG Y F, ZHU C, IKUMI M, et al. Adaptive process control for crystal growth using machine learning for high-speed prediction: application to SiC solution growth［J］. CrystEngComm, 2021, 23(9): 1982-1990.

[81] [81] TAKEHARA Y, SEKIMOTO A, OKANO Y, et al. Explainable machine learning for the analysis of transport phenomena in top-seeded solution growth of SiC single crystal［J］. Journal of Thermal Science and Technology, 2021, 16(1): JTST0009.