不同Cusp磁場條件之柴式與連續柴氏矽單晶生長之熱場與氧濃度數值模擬

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：80

、訪客IP：18.221.101.3

姓名

吳庭宜(Ting I Wu) 查詢紙本館藏

畢業系所

能源工程研究所

論文名稱

不同Cusp磁場條件之柴式與連續柴氏矽單晶生長之熱場與氧濃度數值模擬
(Numerical Simulation of Temperature and Oxygen Concentration under Different Cusp Magnetic Conditions during Czochralski and Continuous Czochralski Silicon Crystal Growths)

相關論文

★ 發光二極體電極設計與電流分佈模擬分析	★ 外加水平式磁場柴氏長晶法生長矽單晶之熱流場數值模擬研究
★ 外加cusp磁場柴氏法生長單晶矽之熱流場及氧雜質傳輸數值分析	★ MOCVD垂直式腔體中氮化鎵薄膜生長之模擬分析
★ 考量氣體分子吸附性質之 MOCVD垂直反應腔體模擬分析	★ Phosphor Packaging Design of white LED with Optical-Thermal-Electrical Coupling
★ 水平式MOCVD腔體中使用氣體脈衝方法生長氮化鋁薄膜之數值模擬與分析	★ 外加Cusp磁場下柴氏法生長單晶矽之不同晶堝轉影響熱流場及氧傳輸數值分析
★ 水解二乙基鋅於近耦合噴淋式反對稱腔體之MOCVD模擬設計分析	★ MOCVD水平式腔體中氮化鎵薄膜製程碳濃度之模擬與傳輸現象分析
★ MOCVD 行星式腔體之模型建立與傳輸現象分析	★ 柴氏法生長6~8吋矽單晶之高溫梯爐體與製程設計模擬
★ 300mm矽晶圓片於平坦度10奈米以下磊晶製程之數值模擬分析	★ 以陽極處理法生長二氧化鈦奈米管於玻璃基板上之研究
★ 二段陽極處理法應用於鈦薄膜成長之研究	★ 交流電發光二極體之接面溫度與熱阻量測研究

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

至系統瀏覽論文 (2025-7-31以後開放)

摘要(中)

連續柴氏長晶法（Continuous Czochralski crystal growth, CCz）在傳統柴氏長晶法（Czochralski crystal growth, Cz）基礎上進行改進，以提高生產效率。CCz 方法通過連續加入多晶矽至坩堝中，使熔體保持一定的液面高度和穩定的化學組成。然而，為了避免尚未熔化完全的多晶矽影響晶體生成，研究中加入一石英隔板，阻隔進料區與晶體生長區。但此也使得氧雜質增加以及熔湯流動和熱傳改變。因此，本研究針對連續柴氏雙坩堝長晶中的氧濃度上升及熔湯流動不穩定問題，通過數值模擬分析在有無cusp磁場(CMF)、不同磁場強度大小、不同晶體坩堝旋轉方向、平衡與不平衡磁場條件與不同磁場強度比（Magnetic Ratio, MR)下對流動型態、溫度分布、氧濃度與固液界面高度造成的影響，並比較Cz與CCz之間的差別。
研究結果顯示，在坩堝和晶體反向旋轉時施加磁場，因磁場產生的勞倫茲力會改變二次渦漩的大小，進而影響熔湯內的流動結構，這對固液界面（晶體-熔湯）處的氧雜質濃度具有關鍵影響。此外，不平衡磁場能使熔湯升溫，促使單晶矽更完全地熔化，並且相比於平衡磁場下，能降低氧雜質濃度。然而，在同向旋轉的情況下，會使得固液界面下方渦漩增強，雖然可以減少氧雜質濃度，但這也會導致界面高度增加。

摘要(英)

The Continuous Czochralski crystal growth (CCz) method is an improvement based on the traditional Czochralski crystal growth (Cz) technique, aimed at enhancing production efficiency. The CCz method continuously adds polycrystalline silicon to the crucible, maintaining a consistent melt level and stable chemical composition. However, to prevent incompletely melted polycrystalline silicon from affecting crystal growth, a partition is added in the study to separate the feed area from the crystal growth area. But this also results in an increase in oxygen concentration and altered melt flow and heat transfer.
Therefore, this study addresses the issues of rising oxygen concentration and unstable melt flow in continuous Czochralski double-crucible growth through numerical simulations to analyzes the effects of various factors on flow patterns, temperature distribution, oxygen concentration, and the height of the crystal-melt interface, including the presence or absence of a cusp magnetic field, different magnetic field densities, different crystal and crucible rotation directions, balanced versus unbalanced magnetic field conditions, and different magnetic ratios (MR). The differences between Cz and CCz methods are also compared.
Research results show that when a magnetic field is applied during the counter-rotation of the crucible and crystal, the Lorentz force generated by the magnetic field alters the size of secondary vortices. Thereby influencing the flow structure within the melt. This has a critical impact on the oxygen concentration at the crystal-melt interface. In addition, an unbalanced magnetic field can increase the temperature of the melt, allowing the silicon to melt more thoroughly. Compared to the balanced magnetic field, it reduces the oxygen concentration. However, in the case of co-rotation, the vortex below the solid-liquid interface is enhanced. While this can reduce the oxygen impurity concentration, it also leads to an increase in the interface height.

關鍵字(中)

★ 柴氏長晶法
★ 連續柴氏長晶法
★ 磁控柴氏長晶法
★ cusp磁場

關鍵字(英)

★ Cz
★ CCz
★ MCz
★ CMF

論文目次

摘要 i
Abstract ii
誌謝 iv
目錄 v
圖目錄 viii
表目錄 xvi
符號說明 xvii
第一章緒論 1
1-1 研究背景 1
1-2 文獻回顧 3
1-3 研究動機及目的 9
第二章物理模型與系統描述 11
2-1 物理模型 11
2-2 基本假設 17
2-3 數學模型及邊界條件 17
2-3-1 統御方程式 17
2-3-2 邊界條件 19
第三章研究方法 27
3-1 數值方法 27
3-2 網格測試 29
3-3 公差收斂性測試 31
第四章結果與討論 33
4-1 坩堝晶體反向旋轉下不同CUSP磁場大小比較 33
4-1-1 Cz單坩堝 33
4-1-2 CCz雙坩堝 37
4-1-3 Cz單坩堝與CCz雙坩堝比較 40
4-2 坩堝晶體同向旋轉下不同CUSP磁場大小比較 47
4-2-1 Cz單坩堝 47
4-2-2 CCz雙坩堝 49
4-2-3 Cz單坩堝與CCz雙坩堝比較 52
4-3 不同磁場強度下坩堝晶體同向旋轉與反向旋轉比較 58
4-4 平衡磁場與不平衡磁場比較 61
4-4-1 Cz單坩堝 62
4-4-2 CCz雙坩堝 64
4-4-3 Cz單坩堝CCz雙坩堝比較 66
4-5不同MR比較 74
4-5-1 Cz單坩堝 74
4-5-2 CCz雙坩堝 77
4-5-3 Cz單坩堝CCz雙坩堝比較 79
第五章結論與未來方向 86
參考文獻 89

參考文獻

[1] SEMI. "SEMI: Global silicon wafer shipments will see a growth rebound in 2024." https://www.semi.org/zh/global_wafer_output?__cf_chl_tk=Q6m8D3mLHttBPyFMOD0MolqThQwBhEnHNKIaMRfPdXY-1714158985-0.0.1.1-1322 (accessed April 27, 2024).
[2] 陳洋元 and 陳正龍, "熱電於再生能源之運用," 物理雙月刊　vol. 202004, pp. 5-18, 2020.
[3] J. Czochralski, "Ein neues verfahren zur messung der kristallisationsgeschwindigkeit der metalle," Zeitschrift für physikalische Chemie, vol. 92, pp. 219-221, 1918.
[4] G. K. Teal, M. Sparks, and E. Buehler, "Growth of germanium single crystals containing p− n junctions," Physical Review, vol. 81, p. 637, 1951.
[5] G. K. Teal and E. Buehler, "Growth of silicon single crystals and of single crystal silicon pn junctions," Phys. Rev, vol. 87, 190, 1952.
[6] O. Anttila, "Czochralski growth of silicon crystals," in Handbook of Silicon Based MEMS Materials and Technologies: Elsevier, pp. 19-60, 2020.
[7] G. W. Rusler, "Crystal growing procedure," Patent Appl. US2892739A, 1959.
[8] R. E. Lorenzini, A. Iwata, and K. Lorenz, "Continuous crystal growing furnace," Patent Appl. US4036595A, 1975.
[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, pp. 247-264, 1993.
[10] A. P. Anselmo, Solid-pellets feed continuous Czochralski growth of silicon single crystals. Columbia University, 1994.
[11] N. Ono, M. Kida, Y. Arai, and K. Sahira, "Thermal Analysis of the Double‐Crucible Method in Continuous Silicon Czochralski Processing: II. Numerical Analysis," Journal of the Electrochemical Society, vol. 140, 2106, 1993.
[12] N. Ono, M. Kida, Y. Arai, and K. Sahira, "Thermal Analysis of the Double‐Crucible Method in Continuous Silicon Czochralski Processing: I. Experimental Analysis," Journal of the Electrochemical Society, vol. 140, 2101, 1993.
[13] 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, 126546, 2022.
[14] T.-H.-T. Nguyen, J.-C. Chen, and C.-C. Chen, "Effects of different crucible shapes on heat and oxygen transport during continuous Czochralski silicon crystal growth," Journal of Crystal Growth, vol. 626, 127474, 2024.
[15] J. Friedrich, "Methods for bulk growth of inorganic crystals: crystal growth," 2016.
[16] M. Sankar, M. Venkatachalappa, and Y. Do, "Effect of magnetic field on the buoyancy and thermocapillary driven convection of an electrically conducting fluid in an annular enclosure," International Journal of Heat and Fluid Flow, vol. 32, pp. 402-412, 2011.
[17] P. Ravishankar, T. Braggins, and R. Thomas, "Impurities in commercial-scale magnetic Czochralski silicon: axial versus transverse magnetic fields," Journal of crystal growth, vol. 104, pp. 617-628, 1990.
[18] J.-C. Chen et al., "Three-dimensional numerical simulation of flow, thermal and oxygen distributions for a Czochralski silicon growth with in a transverse magnetic field," Journal of crystal growth, vol. 401, pp. 813-819, 2014.
[19] J. Ding, Y. Li, and L. Liu, "Effect of cusp magnetic field on the turbulent melt flow and crystal/melt interface during large-size Czochralski silicon crystal growth," International Journal of Thermal Sciences, vol. 170, 107137, 2021.
[20] X. Liu, L. Liu, Z. Li, and Y. Wang, "Effects of cusp-shaped magnetic field on melt convection and oxygen transport in an industrial CZ-Si crystal growth," Journal of Crystal Growth, vol. 354, pp. 101-108, 2012.
[21] Y.-H. Hong, B.-C. Sim, and K.-B. Shim, "Effect of zero-Gauss plane and magnetic intensity on oxygen concentration in cusp-magnetic CZ crystals," Journal of crystal growth, vol. 295, pp. 141-147, 2006.
[22] T.-H.-T. Nguyen and 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, 105758, 2021.
[23] H. Hirata and K. Hoshikawa, "Oxygen solubility and its temperature dependence in a silicon melt in equilibrium with solid silica," Journal of crystal growth, vol. 106, pp. 657-664, 1990.
[24] A. Smirnov and V. Kalaev, "Development of oxygen transport model in Czochralski growth of silicon crystals," Journal of Crystal Growth, vol. 310, pp. 2970-2976, 2008.
[25] T.-H.-T. Nguyen and 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, 105758, 2021.
[26] Y. C. Won, K. Kakimoto, and H. Ozoe, "Transient three-dimensional numerical computation for unsteady oxygen concentration in a silicon melt during a Czochralski process under a cusp-shaped magnetic field," Journal of crystal growth, vol. 233, pp. 622-630, 2001.
[27] 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, 125334, 2020.
[28] J. Friedrich, T. Jung, M. Trempa, C. Reimann, A. Denisov, and A. Muehe, "Considerations on the limitations of the growth rate during pulling of silicon crystals by the Czochralski technique for PV applications," Journal of Crystal Growth, vol. 524, 125168, 2019.
[29] J. Ding and Y. Li, "Three-dimensional characteristics of turbulent flow and heat transfer in Czochralski silicon melt with different cusp magnetic field configurations," Physics of Fluids, vol. 34, 025117, 2022.

指導教授

陳志臣(Jyh-chen Chen)

審核日期

2024-7-11

推文