本研究採用的碳化矽晶體材料之生產製程為物理氣相轉移法（Physical vapor transport, PVT），但物理氣相傳輸法之坩堝為密閉狀態，且長晶腔內的溫度及氣流分佈難以經由直接測量而得到，在操作與控制製程條件上有其難度，有鑑於此，需要利用電腦輔助工程VR-STR作為分析爐體的工具。
本研究目標在於開發一碳化矽長晶模擬系統，系統現象包含電磁加熱，熱場之分佈，碳化矽顆粒分解氣化，氣流的流動，[Si]、 [SiC2]、[Si2C]的壓力分佈，粉末之石墨化以及在晶種上的長晶情形。藉由數值模擬方法了解碳化矽生長製程中的溫度場及流場之分佈情形，並分析石墨坩堝內部之物理行為變化，包含熱流、質傳、粉末石墨化、晶體成長速率，晶體形貌預測等。
電磁感應加熱主要是集中在坩堝表面中間的位置，所感應到之電流最大值為5.1×10-4 W/m3，接著利用感應在坩堝上之電流轉換成加熱功率，其加熱功率在坩堝上之最大值為2.5×107 W/m3。加熱功率經由轉換成熱能後，熱會藉由熱傳導、熱輻射以及熱對流的方式，把熱傳遞至整個系統，成功計算出爐子升溫過程及成長之溫度分佈，在加熱後期，溫度已經達到穩定的狀態，在坩堝蓋上之溫度為2423 K與實驗測量結果2424 K非常吻合。
石墨化與反應氣氛分佈行為變化之模擬結果顯示，在不同成長時間下，粉末被氣化分解後之石墨化、反應氣氛壓力和流動分佈之變化行為。反應氣氛壓力分佈和流場之演變情況說明在靠近高溫狀態之粉末會優先分解氣化成 Si，Si2C，SiC2三種反應氣氛。在成長初期，反應氣氛在高溫處的粉末表面開始分解氣化生成，被氣化之氣體會藉由粉末的孔隙流動傳輸到成長室中，再流動到晶體表面，部分氣氛流動到晶體表面，另一部分回流至較低溫之粉末表面。而未被氣化的碳原子殘留在原處造成粉末石墨化的現象產生。隨著粉末不斷被分解氣化，石墨化蔓延至粉末中部，反應氣氛從氣化介面生成，此外反應氣氛之回流現象也降低，因此更多的氣氛流向晶體表面。當成長時間160小時後，在上半部之碳化矽粉末完全被分解氣化成反應氣氛，而底部的粉末因處於低溫區，因此仍殘留在底部。
成長速率與形貌模擬結果顯示，在成長初期0至14小時，被分解氣化的氣氛部分回流到低溫的粉末表面，因此粉末表面發生凝結的現象導致成長速率下降。當晶體成長14小時後，因粉末與晶體間之溫度梯度為上升和凝結區域成為一新的反應氣氛來源，導致成長速率為大幅回升。直至成長時間為155至160小時，因為提供氣氛之碳化矽粉末已經續漸消耗完畢，成長速率急劇下降。經過160小時成長後，碳化矽晶體形貌呈現為凸形，其成長晶體之總厚度為30.082 mm，與實驗成長之晶體厚度30 mm大致相符。

Physical vapor transport (PVT) method is the major used method in growing single crystal silicon carbide bulk with large size. It is hard to directly measure the temperature and flow distribution due to the closed furnace. Hence, it is necessary to use the simulation to help us analyze the procedure for silicon carbide crystal growth. The purpose of this project is to develop a system to simulate the procedure for silicon carbide crystal growth, and by using the simulation process to understand more about its temperature field, fluid flow distribution and also analyze the physical behavior such as, thermal field, mass transport, inside of the crucible. This project is expected to improve the productivity of silicon carbide, improving its crystal growth rate and the crystal quality of silicon carbide, and with its improvement in productivity, the device performance could also be improved.

[1] Carter Jr, C.H., Tsvetkov, V.F., Glass, R.C., Henshall, D., Brady, M., St G, M., Kordina, O., Irvine, K., Edmond, J.A., Kong, H.S. and Singh, R., “Progress in SiC: from material growth to commercial device development,” Materials Science and Engineering: B, vol. 61, pp. 1-8, 1999.
[2] Siergiej, R.R., Clarke, R.C., Sriram, S., Agarwal, A.K., Bojko, R.J., Morse, A.W., Balakrishna, V., MacMillan, M.F., Burk Jr, A.A. and Brandt, C.D., “Advances in SiC materials and devices: an industrial point of view,” Materials Science and Engineering: B, vol. 61, pp. 9-17, 1999.
[3] Lambrecht, W.R., Limpijumnong, S., Rashkeev, S.N. and Segall, B., “Electronic band structure of SiC polytypes: a discussion of theory and experiment,” Physica Status Solidi (B), vol. 202, pp. 5-33, 1997.
[4] Bechstedt, F., Käckell, P., Zywietz, A., Karch, K., Adolph, B., Tenelsen, K. and Furthmüller, J, “Polytypism and properties of silicon carbide,” Physica Status Solidi (B), vol. 202, pp. 35-62, 1997.
[5] Råback P., “Modeling of the sublimation growth of silicon carbide crystals,” Center for Scientific Computing, Finland, 1999.
[6] Tatsumi, M., Hosokawa, Y., Iwasaki, T., Toyoda, N. and Fujita, K., “Growth and characterization of III–V materials grown by vapor-pressure-controlled Czochralski method: comparison with standard liquid-encapsulated Czochralski materials,” Materials Science and Engineering: B, vol. 28, pp. 65-71, 1994.
[7] Kordina, O., Irvine, K.G., Sumakeris, J.J., Kong, H.S., Paisley, M.J. and Carter Jr, C.H., “Growth of thick epitaxial 4H-SiC layers by chemical vapor deposition,” vol. 264, pp. 107-110, 1998.
[8] Tairov, Y. M., “Growth of bulk SiC,” Materials Science and Engineering: B, vol. 29, pp. 83-89, 1995.
[9] Lilov, S.K., "Thermodynamic analysis of the gas phase at the dissociative evaporation of silicon carbide," Computational Materials Science, vol. 1, pp. 363-368, 1993.
[10] Dudley, M., Huang, X.R., Huang, W., Powell, A., Wang, S., Neudeck, P. and Skowronski, M., “The mechanism of micropipe nucleation at inclusions in silicon carbide,” Applied Physics Letters, vol. 75, pp. 784-786, 1999.
[11] Li, H., Chen, X.L., Ni, D.Q. and Wu, X., “An analysis of seed graphitization for sublimation growth of SiC bulk crystal,” Diamond and Related Materials, vol. 13, pp. 151-156, 2004.
[12] Liu, J., Gao, J., Cheng, J., Yang, J. and Qiao, G., “Effects of graphitization degree of crucible on SiC single crystal growth process,” Diamond and Related Materials, vol. 15, pp. 117-120, 2006.
[13] Herro, Z.G., Epelbaum, B.M., Bickermann, M., Masri, P. and Winnacker, A., “Effective increase of single-crystalline yield during PVT growth of SiC by tailoring of temperature gradient,” Journal of Crystal Growth, vol. 262, pp. 105-112, 2004.
[14] Selder, M., Kadinski, L., Durst, F. and Hofmann, D., “Global modeling of the SiC sublimation growth process: prediction of thermoelastic stress and control of growth conditions,” Journal of Crystal Growth, vol. 226, pp. 501-510, 2001.
[15] Zhang, Z., Lu, J., Chen, Q. and Prasad, V., “Thermoelastic stresses in SiC single crystals grown by the physical vapor transport method,” Acta Mechanica Sinica, vol. 22, pp. 40-45, 2006.
[16] Ma, R., Zhang, H., Prasad, V. and Dudley, M., “Growth kinetics and thermal stress in the sublimation growth of silicon carbide,” Crystal Growth & Design, vol. 2, pp. 213-220, 2002.
[17] Zhmakin, I.A., Kulik, A.V., Karpov, S.Y., Demina, S.E., Ramm, M.S. and Makarov, Y.N., “Evolution of thermoelastic strain and dislocation density during sublimation growth of silicon carbide,” Diamond and Related Materials, vol. 9, pp. 446-451, 2000.
[18] Yan, J.Y., Chen, Q.S., Jiang, Y.N. and Zhang, H., “Improvement of the thermal design in the SiC PVT growth process,” Journal of Crystal Growth, vol. 385, pp. 34-37, 2014.
[19] Lu, J., Zhang, Z.B. and Chen, Q.S., “Numerical simulation of the flow field and concentration distribution in the bulk growth of silicon carbide crystals,” Journal of Crystal Growth, vol. 292, no. 2, pp. 519-522, 2006.
[20] Su, J., Chen, X. and Li, Y., “Numerical design of induction heating in the PVT growth of SiC crystal,” Journal of Crystal Growth, vol. 401, pp. 128-132, 2014.
[21] Liu, X., Chen, B.Y., Song, L.X., Shi, E.W. and Chen, Z.Z., “The behavior of powder sublimation in the long-term PVT growth of SiC crystals,” Journal of Crystal Growth, vol. 312, pp. 1486-1490, 2010.
[22] Liu, X., Shi, E.W., Song, L.X. and Chen, Z.Z., “Effects of graphitization of the crucible on silicon carbide crystal growth,” Journal of Crystal Growth, vol. 310, pp. 4314-4318, 2008.
[23] Chen, K.L., Ciou, J. J., “The Simulation of SiC Single Crystal Growth by PVT Method,” J. China Uni. Sci. Tech, vol. 53, pp. 91-104, 2012.
[24] Matukov, I.D., Kalinin, D.S., Bogdanov, M.V., Karpov, S.Y., Ofengeim, D.K., Ramm, M.S., Barash, J.S., Mokhov, E.N., Roenkov, A.D., Vodakov, Y.A. and Ramm, M.G., “Modeling of facet formation in SiC bulk crystal growth,” Journal of Crystal Growth, vol. 266, pp. 313-319, 2004.
[25] Reitz, J.R., Milford, F.J. and Christy, R.W., "Foundations of electromagnetic theory: Addison-Wesley" Reading, MA, pp. 105, 2008.
[26] Wang, K.F., Chandrasekar, S. and Yang, H.T., “Finite-element simulation of induction heat treatment,” Journal of Materials Engineering and Performance, vol. 1, pp. 97-112, 1992.
[27] Chen, Q.S., Gao, P. and Hu, W.R., “Effects of induction heating on temperature distribution and growth rate in large-size SiC growth system,” Journal of Crystal Growth, vol. 266, pp. 320-326, 2004.
[28] Gresho, P.M. and Derby, J.J., “A finite element model for induction heating of a metal crucible,” Journal of Crystal Growth, vol. 85, pp. 40-48, 1987.
[29] Chen, Q.S., Yan, J.Y., Prasad, V., and V. Prasad, “Application of flow-kinetics model to the PVT growth of SiC crystals,” Journal of Crystal Growth, vol. 303, pp. 357-361, 2007.
[30] Ergun S., “Fluid flow through packed columns,” Chem. Eng. Prog., vol. 48, pp. 89-94, 1952.
[31] Karpov, S.Y., Prokofyev, V.G., Yakovlev, E.V., Talalaev, R.A. and Makarov, Y.N., “Novel approach to simulation of group-III nitrides growth by MOVPE,” MRS Internet Journal of Nitride Semiconductor Research, vol. 4, pp. e4, 1999.
[32] Gurvich, L.V. and Veyts, I. eds., “Thermodynamic Properties of Individual Substances: Elements and Compounds,” CRC press, Indiana, vol. 2, 1990.
[33] T. Kaneko, “Growth rates of vapor grown filaments,” Journal of Crystal Growth, vol. 69, pp. 1-9, 1984.
[34] Kaneko T., “Growth kinetics of vapor-grown SiC,” Journal of Crystal Growth, vol. 128, pp. 354-357, 1993.
[35] Chen, Q.S., Zhang, H., Prasad, V., Balkas, C.M., Yushin, N.K. and Wang, S., “Kinetics and modeling of sublimation growth of silicon carbide bulk crystal,” Journal of Crystal Growth, vol. 224, pp. 101-110, 2001.
[36] Chen, X.J., Liu, L.J., Tezuka, H., Usuki, Y. and Kakimoto, K., “Optimization of the design of a crucible for a SiC sublimation growth system using a global model,” Journal of Crystal Growth, vol. 310, pp. 1810-1814, 2008.
[37] Lilov, S.K., “Study of the equilibrium processes in the gas phase during silicon carbide sublimation,” Materials Science and Engineering: B, vol. 21, pp. 65-69, 1993.
[38] Wellmann, P.J., Herro, Z.G., Sakwe, S.A., Masri, P.M., Bogdanov, M.V., Karpov, S.Y., Kulik, A.V., Ramm, M.S. and Makarov, Y.N., "Analysis of graphitization during physical vapor transport growth of silicon carbide," Materials Science Forum, vol. 457, pp. 55-58, 2004.
[39] Wellmann, P.J., Bickermann, M., Hofmann, D., Kadinski, L., Selder, M., Straubinger, T.L. and Winnacker, A., “In situ visualization and analysis of silicon carbide physical vapor transport growth using digital X-ray imaging,” Journal of Crystal Growth, vol. 216, no. 1, pp. 263-272, 2000.
[40] Gao, B. and Kakimoto, K., “Optimization of power control in the reduction of basal plane dislocations during PVT growth of 4H-SiC single crystals,” Journal of Crystal Growth, vol. 392, pp. 92-97, 2014.
[41] Bogdanov, M.V., Demina, S.E., Karpov, S.Y., Kulik, A.V., Ofengeim, D.K., Ramm, M.S., Mokhov, E.N., Roenkov, A.D., Vodakov, Y.A., Makarov, Y.A. and Helava, H., “Modeling analysis of free-spreading sublimation growth of SiC crystals, ” MRS Proceedings, vol. 742, pp. 1-3, 2002.