連續柴氏長晶法（Continuous-feeding Czochralski crystal growth，CCz）是在傳統柴氏長晶法（Czochralski crystal growth，Cz）上加入隔板(雙坩堝)，並在長晶過程中，不斷的投入和長晶速率相同質量的多晶矽顆粒原物料。藉此生長方法來將長晶過程維持在最佳熔湯縱橫比(aspect ratio)，以降低氧濃度；同時，利用隔板來阻隔未熔化的多晶矽顆粒進入內坩堝熔湯。不過石英隔板的加入，也導致氧雜質的來源增加，同時也影響了熔湯的流動和熱傳。為減少此缺陷，在CCz雙坩堝的熱傳效率提升和降低氧濃度的研究非常重要。因此，本文將使用數值模擬方法(CGSim)進行研究，探討以長晶爐體的幾何設計，坩堝外型、加熱器、絕熱層和熱遮罩，對CCz雙坩堝長晶的缺陷改善，並研究其對於熔湯內流動和熱傳的影響，以及晶體的品質和缺陷。
研究結果顯示，平坦的坩堝底部有利於熔湯內渦旋的產生，加強未熔化顆粒進入內坩堝的效果，同時改善熔湯內的熱傳，降低坩堝壁面溫度，減少氧雜質。接續，調整側加熱器的設置並使熱源向上移動，將熔湯內的高溫區由底部移至側壁靠近自由表面，加強自由表面投料的熔化效率，同時降低坩堝底部的溫度和氧雜質析出，也能降低加熱器的功率。最後，優化後的絕熱層和熱遮罩，大幅度減少熱源向爐體上方散失，同時造成氬氣流速的提升影響熔湯的渦旋大小，使氧雜質流向固液(晶體/熔湯)界面受阻，降低氧濃度。爐體優化後的設計下能使加熱器降低41%的功率，以及降低15%的氧濃度。

The continuous-feeding Czochralski crystal growth method (CCz) is an improvement over the traditional Czochralski crystal growth method (Cz). In CCz crystal growth, the raw material, polycrystalline silicon granules, is added to the free melt surface at the same rate as the crystal puller, maintaining a constant melt height in a lower aspect ratio and reducing oxygen impurities. Additionally, a partition, known as the inner crucible, is placed in the middle of the melt to prevent unmelted granules from flowing into the inner melt and affecting crystallization. However, the partition also acts as a source of oxygen impurities and hampers heat transfer. To minimize the increase in oxygen impurities and improve heat transfer efficiency, this paper investigates the geometric design of the furnace, including the shape of the crucible, heater, heat shield, and insulation, using the numerical simulation method (CGSim software).
The results demonstrate that a flatter crucible bottom generates larger vortexes in the outer melt, keeping unmelted granules in the outer melt and improving heat transfer. This reduces the temperature on the crucible surface and the dissolution of oxygen impurities. By separating the side heaters and increasing the power of the upper side heater, the high temperature region shifts from the crucible bottom to the crucible side wall, enhancing the melting effect on the granules and reducing the temperature at the crucible bottom, which is the primary source of oxygen impurities at the crystal-melt interface. For improved heat efficiency, the optimized heat shield and insulation prevent heat loss from the upper furnace, saving more heater power and increasing the velocity of argon flow. This strengthens the vortex that prevents oxygen flow to the crystal-melt interface. As a result, the temperature on the crucible wall decreases, and the prevention of oxygen flow becomes stronger, reducing the oxygen concentration at the crystal-melt interface. The optimized furnace design reduces CCz crystal defects while saving 41% of heater power and reducing oxygen by 15%.

[1] J.-C. Ren, D. Liu, and Y. Wan, "Modeling and application of Czochralski silicon single crystal growth process using hybrid model of data-driven and mechanism-based methodologies," Journal of Process Control, vol. 104, pp. 74-85, 2021.
[2] C. Wang, H. Zhang, T. Wang, and T. Ciszek, "A continuous Czochralski silicon crystal growth system," Journal of Crystal Growth, vol. 250, no. 1-2, pp. 209-214, 2003.
[3] T.-H.-T. Nguyen, J.-C. Chen and C.-H. Li, "Controlling the heat, flow, and oxygen transport by double-partitions during continuous Czochralski (CCz) silicon crystal growth," Materials Science in Semiconductor Processing, vol. 155, p. 107235, 2023.
[4] W. Zhao and L. Liu, "Control of heat transfer in continuous-feeding Czochralski-silicon crystal growth with a water-cooled jacket," Journal of Crystal Growth, vol. 458, pp. 31-36, 2017.
[5] A. Giannattasio, "A simplified model to predict resistivity profiles in continuous-feeding Cz-silicon crystals," Journal of Crystal Growth, vol. 542, p. 125686, 2020.
[6] T.-H.-T. Nguyen, J.-C. Chen and S.-C. Lo, "Effects of different partition depths on heat and oxygen transport during continuous Czochralski (CCz) silicon crystal growth," Journal of Crystal Growth, vol. 583, p. 126546, 2022.
[7] W. Su, Z. Zhang, J. Li, Z. Guan, J. Li, and J. Liu, "Numerical study on the effects of inner crucible window heights on the growth of silicon in a continuous Czochralski process," Journal of Crystal Growth, vol. 607, p. 127129, 2023.
[8] I. Jafri, V. Prasad, A. Anselmo, and K. Gupta, "Role of crucible partition in improving Czochralski melt conditions," Journal of crystal growth, vol. 154, no. 3-4, pp. 280-292, 1995.
[9] A. Anselmo, V. Prasad, J. Koziol, and K. Gupta, "Numerical and experimental study of a solid pellet feed continuous Czochralski growth process for silicon single crystals," Journal of crystal growth, vol. 131, no. 1-2, pp. 247-264, 1993.
[10] D. Lukanin, V. Kalaev, Y. N. Makarov, T. Wetzel, J. Virbulis, and W. Von Ammon, "Advances in the simulation of heat transfer and prediction of the melt-crystal interface shape in silicon CZ growth," Journal of Crystal Growth, vol. 266, no. 1-3, pp. 20-27, 2004.
[11] O. A. Noghabi, M. Jomâa, and M. M'hamdi, "Analysis of W-shape melt/crystal interface formation in Czochralski silicon crystal growth," Journal of crystal growth, vol. 362, pp. 77-82, 2013.
[12] J.-C. Chen et al., "Numerical simulation of oxygen transport during the CZ silicon crystal growth process," Journal of crystal growth, vol. 318, no. 1, pp. 318-323, 2011.
[13] Y.-Y. Teng, J.-C. Chen, C.-C. Huang, C.-W. Lu, W.-T. Wun, and C.-Y. Chen, "Numerical investigation of the effect of heat shield shape on the oxygen impurity distribution at the crystal–melt interface during the process of Czochralski silicon crystal growth," Journal of crystal growth, vol. 352, no. 1, pp. 167-172, 2012.
[14] W. Su, R. Zuo, K. Mazaev, and V. Kalaev, "Optimization of crystal growth by changes of flow guide, radiation shield and sidewall insulation in Cz Si furnace," Journal of Crystal Growth, vol. 312, no. 4, pp. 495-501, 2010.
[15] S. Baik, A. Jeong, J. M. Kang, Y. Hahn, W.-J. Nam, and W. Nam, "Improved hot-zone for manufacturing low-oxygen silicon ingots for passivated emitter and rear cell," Japanese Journal of Applied Physics, vol. 57, no. 8S3, p. 08RB02, 2018.
[16] B. Zhou, W. Chen, Z. Li, R. Yue, G. Liu, and X. Huang, "Reduction of oxygen concentration by heater design during Czochralski Si growth," Journal of Crystal Growth, vol. 483, pp. 164-168, 2018.
[17] H. Matsuo et al., "Thermodynamical analysis of oxygen incorporation from a quartz crucible during solidification of multicrystalline silicon for solar cell," Journal of Crystal Growth, vol. 310, no. 22, pp. 4666-4671, 2008.
[18] A. Smirnov and V. Kalaev, "Development of oxygen transport model in Czochralski growth of silicon crystals," Journal of Crystal Growth, vol. 310, no. 12, pp. 2970-2976, 2008.
[19] O. Smirnova, N. Durnev, K. Shandrakova, E. Mizitov, and V. Soklakov, "Optimization of furnace design and growth parameters for Si Cz growth, using numerical simulation," Journal of Crystal Growth, vol. 310, no. 7-9, pp. 2185-2191, 2008.
[20] D. Borisov et al., "Advanced approach for oxygen transport and crystallization front calculation in Cz silicon crystal growth," Journal of Crystal Growth, vol. 583, p. 126493, 2022.
[21] J. R. Cost, K. R. Janowski, and R. C. Rossi, "Elastic properties of isotropic graphite," The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics, vol. 17, no. 148, pp. 851-854, 1968.
[22] Y. Mukaiyama, K. Sueoka, S. Maeda, M. Iizuka, and V. M. Mamedov, "Numerical analysis of effect of thermal stress depending on pulling rate on behavior of intrinsic point defects in large-diameter Si crystal grown by Czochralski method," Journal of Crystal Growth, vol. 531, p. 125334, 2020.
[23] J.-C. Chen, "Effects of different cusp magnetic ratios and crucible rotation conditions on oxygen transport and point defect formation during Cz silicon crystal growth," Materials Science in Semiconductor Processing, vol. 128, p. 105758, 2021.