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

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姓名

吳庭宜(Ting I Wu) 查詢紙本館藏

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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)

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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

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指導教授

陳志臣(Jyh-chen Chen)

審核日期

2024-7-11

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