氧化鎵（Ga2O3）作為寬能隙氧化物半導體，由於其優異的材料性質，在化合物半導體產業中引起了高度興趣。β-Ga2O3可由液相生長，由於柴氏Czochralski（Cz）長晶技術具有較高的生長速度與品質控制，因此本研究中以數值模擬方法探討柴氏生長氧化鎵晶體過程之輸送現象。然而由於Ga2O3在高溫容易氧分解、晶體結構具有強烈劈裂面，及不同摻雜晶體下自由載子的熱輻射吸收性都將成為生長高品質氧化鎵晶體需克服的挑戰。目前生長高品質Ga2O3晶體仍待突破，對生長技術發最有助益的數值模擬技術仍在起步階段，所以本研究將延伸過去本實驗室對半透明氧化物晶體的模擬經驗，至使用Cz生長Ga2O3晶體的熱流輸送現象。
本研究就吸收係數、晶轉轉速、反向堝轉轉速、拉伸速度進行模擬並分析熱場、流場、固液界面形狀及晶體內熱輻射的現象。從研究中發現晶體內部輻射主要受吸收係數的影響，吸收係數越高晶體由體輻射轉為表輻射與其他部件進行熱交換，並使固液界面由凸向熔湯轉為凹向熔湯。晶轉及堝轉轉速增加造成熔湯內流場型態改變使熱場分部不均勻，固液界面上升凸率下降，同時使加熱器功率上升。拉伸速度的提升同樣影響熔湯內流場型態，固液界面上升凸率下降。固液界面的形狀將影響晶體內部熱應力的分部，凹向熔湯的界面形狀雖有較低的晶體熱應力，但此形狀容易造成生長過程不穩甚至產生螺旋型生長，減少晶體的可使用量。

Gallium oxide (Ga2O3), as a wide Band-gap oxide semiconductor, has aroused high attention in the compound semiconductor industry as its excellent material properties. β-Ga2O3 crystal could be grown from liquid phase. Due to a high growth rate and quality control, numerical simulation methods are used to investigate the Cz growth Ga2O3 crystal heat transfer phenomenon in this study. Ga2O3 is easily decomposed by oxygen at high temperature, the crystal structure has a strong crack surface, and the thermal radiation absorption of free carriers under different doped crystals. The growth of high-quality Ga2O3 crystals is still to breakthrough, and the most useful numerical simulation technology for growth technology is still in its infancy. This research will extend the laboratory’s simulation experience of semi-transparent oxide crystals to the Cz growth Ga2O3 crystal heat transfer phenomenon.
Different absorption coefficient; crystal and crucible rotation speed; and pulling rate are considered to investigate their effects on the variation of heat, flow, and interface shape. The numerical simulations show that the internal radiation of the crystal is mainly affected by absorption coefficient. The higher the absorption coefficient, the crystal radiate from bulk radiation to surface radiation, and the solid-liquid interface change from convex to concave. The increase of the crystal rotation and crucible rotation speed causes the change of the flow field pattern in the melt to make the thermal field uneven, which decreases the convexity of the interface and increases the heater power. The increase of the pulling rate also affects the flow field pattern in the melt and decreases the convexity of the interface. The shape of the solid-liquid interface will affect the division of the thermal stress inside the crystal. Although the shape of the interface of the concave to the melt has lower thermal stress of the crystal, this shape is easy to cause unstable growth process or even spiral growth, reducing the crystal Usage amount.

[1] M. A. Mastro, A. Kuratama, J. Calkins, J. Kim, F. Ren, S. J. Pearton, Opportunities and Future Directions for Ga2O3, ECS Journal of Solid State Science and Technology, Vol. 6, pp. 356 - 359, 2017.
[2] M. Higashiwaki, K. Sasaki, A. Kuramata, T. Masui, S. Yamakoshi, Gallium oxide (Ga2O3) metal-semiconductor field-effect transistors on single-crystal β-Ga2O3 (010) substrates, Applied Physics Letters, Vol. 100, 2012
[3] M. Baldini, Z. Galazkz, G. Wagner, Recent progress in the growth of β-Ga2O3 for power electronics applications, Materials Science in Semiconductor Processing, Vol. 78, pp. 132 – 146, 2018.
[4] Y. Tomm, P. Reiche, D. Klimm, T. Fukuda, Czochralski grown Ga2O3 crystals, Journal of Crystal Growth, Vol. 220, pp. 510-514, 2000.
[5] Z. Galazka, R. Uecker, K, Irmscher, M. Albrecht, D. Klimm, M. Pietsch, M. Brützam, R. Bertram, S. Ganschow, and R. Fornari, Czochralski growth and characterization of β-Ga2O3 single crystals, Crystal Research and Technology, Vol. 45, pp. 1299 – 1236, 2010.
[6] Z. Galazka, K. Irmscher, R. Uecker, R. Bertram, M. Pietsch, A. Kwasniewski, M. Naumann, T. Schulz, R. Schewski, D. Klimm, M. Bickermann, On the bulk β-Ga2O3 single crystals grown by the Czochralski method, Journal of Crystal Growth, Vol. 404, pp. 184 – 191, 2014.
[7] D. Schwabe, R. Uecker, M. Bernhagen, Z. Galazka, An analysis of and a model for spiral growth of Czochralski-grown oxide crystals with high melting point, Journal of Crystal Growth, Vol. 335, pp. 138 – 147, 2011.
[8] Z. Yuan, A. Anopchenko, N. Daldosso, R. Guider, D. N. Urrios, A. Pitanti, R. Spano, L. Pavesi, Silicon Nanocrystals as an Enabling Material for Silicon Photonics, Proceedings of the IEEE, Vol. 97, pp. 1250-1268, 2009.
[9] W. Miller, K. Bottcher, Z. Galazka, J. Schreuer, Numerical Modelling of the Czochralski Growth of β-Ga2O3, Crystals, pp. 26-40, 2017.
[10] C.-W. Lu and J.-C. Chen, Numerical computation of sapphire crystal growth using heat exchanger method, Journal of Crystal Growth, Vol. 225, pp. 274-281, 2001.
[11] C.-W. Lu, J.-C. Chen, L.-J. Hu, A numerical investigation of the thermal distribution effects in a heat-exchanger-method crystal growth system, Modelling and Simulation in Materials Science and Engineering, Vol. 10, pp. 147-162, 2002.
[12] J.-C. Chen and C.-W. Lu, Influence of the crucible geometry on the shape of the melt-crystal interface during growth of sapphire crystal using a heat-exchanger-method, Journal of Crystal Growth, Vol. 266, pp. 239-245, 2004.
[13] C.-W. Lu and J.-C. Chen, Influence of thermal conductivity on interface shape during growth of sapphire crystal using a heat-exchanger-method, Journal of Rare Earths, Vol. 24, pp. 222-227, 2006.
[14] T. P. Nguyen, Y. T. Hsieh, J.-C. Chen, C. Hu, H. B. Nguyen, Effect of crucible and crystal rotations on the convexity and the thermal stress in large size sapphire crystals during Czochralski growth, Journal of Crystal Growth, Vol. 468, pp. 514-525, 2017.
[15] T. P. Nguyen, H.-T. Chuang, J.-C. Chen, C. Hu, Effect of power history on the shape and the thermal stress of a large sapphire crystal during the Kyropoulos process, Journal of Crystal Growth, Vol. 484, pp. 43-49, 2018.
[16] Z. Galazka, Growth Measures to Achieve Bulk Single Crystals of Transparent Semiconducting and Conducting Oxides Chap.6, Handbook of Crystal Growth 2nd edition, pp. 209-218, 2015.
[17] D. B. Dingwell, Density of Ga2O3 Liquid, Journal of the American Cecamic Society, Vol. 75, pp.1656-1657, 1992.
[18] Xin Liu, Bing Gao, Koichi Kakimoto, Numerical investigation of carbon contamination during the melting process of Czochralski silicon crystal growth, Journal of Crystal Growth, Vol. 417, pp. 56-64, 2014