CZ法生長大尺寸氧化鋁單晶過程之數值模擬分析

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姓名

謝耀德(Yao-Te Hsieh) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

CZ法生長大尺寸氧化鋁單晶過程之數值模擬分析
(Numerical Simulation of Large-Size Sapphire Crystal Growth with the Czochralski Process)

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摘要(中)

柴式長晶法(Czochralski method, CZ)是目前常用來生長高品質單晶的方法之一，在近年來，這項晶體生長技術已經應用於大尺寸藍寶石單晶生長。為了確保晶體生長品質，我們必須深入了解CZ長晶爐內熔湯的流動行為與熱傳機制。
對於大尺寸晶體生長，受限於爐體溫度過高，無法以實驗直接進行量測，且過於費時，因此我們使用數值模擬的方式，更有效率的來對長晶參數進行製程改善，以減少實驗所耗費的時間與成本。本研究運用以有限元素法(FEM)為基礎的套裝軟體COMSOL Multiphysics，針對大尺寸藍寶石晶體生長之熱流場、固液界面形狀以及熱應力分佈，進行深入研究。
本研究結果發現，熔湯的流場型態由浮力渦流所主導，溫度場中的等溫線會受到強烈的浮力對流影響而扭曲變形，其強度隨著加熱器功率調降而降低；固液界面形狀會隨著晶身長度越長而越凸向熔湯；坩堝的旋轉會增強浮力渦旋的強度，加強熱對流的傳遞；晶體的旋轉會使固液界面下方熔湯受離心力作用，產生一強制渦流，將更多的熱量傳輸至固液界面。坩堝與晶體的反向旋轉，能降低晶體凸出率，使固液介面較為平坦。坩堝與晶體之間，在不同晶體的生長階段時，有著最佳的轉速配合。在熱應力方面，晶體內的熱應力會隨著晶體生長的尺寸增加而上升，增加長晶的困難度。此外，當固液界面越為平坦時，其徑向溫度梯度越低，因此晶體內的熱應力隨著凸出率越低而有顯著的下降。

摘要(英)

The Czochralski method is one of the major technologies used for high quality single crystal growth. Recently, this technology has been applied for industrial larger size sapphire crystal growth. In order to ensure the quality of the crystal growth, we must gain further insight into the flow behavior of the molten melt and heat transfer mechanisms in Czochralski furnace.
During the large size sapphire crystal growth, the temperature of furnace is too high to be observed in experiments directly. Therefore, numerical simulation is necessary in order to reduce the cost and time of experiments. The purpose of this thesis is to numerically investigate on thermal flow field, shape of the crystal-melt interface and thermal stress for larger sapphire crystal growth using the COMSOL Multiphysics software base on the finite element method.
The results show that the flow field is dominated by a buoyant vortex and the isotherms are distorted by the strong buoyancy force. The intensity of the vortex decreases when the power supply reduces. The crystal-melt interface would be more convex to the molten melt when the crystal grows. The crucible rotation increase the transfer of heat convection due to the enhancement of the buoyant vortex. The crystal rotation results in a forced vortex below crystal-melt interface caused by centrifugal force, more heat is transferred to crystallization front. The counter rotation between the crucible and the crystal results in the flatter crystal-melt interface and the lower crystal’s convexity. There is an optimal combination of the crystal and crucible rotation rates for each crystal growth length. The thermal stress would increase when the size of the crystal growth increase. Moreover, the thermal stress significantly decreases for the lower convexity of the crystal-melt interface due to the reduction of temperature gradient in the radial direction along the interface.

關鍵字(中)

★ 柴式長晶
★ 藍寶石晶體生長
★ 數值模擬

關鍵字(英)

★ Czochralski
★ sapphire crystal growth
★ numerical simulation

論文目次

摘要 I
Abstract II
目錄 IV
圖目錄 VI
表目錄 VIII
符號說明 IX
第一章緒論 1
1-1 氧化鋁單晶簡介 1
1-2 柴氏長晶法介紹 2
1-3 文獻回顧 3
1-4 研究動機與目的 6
第二章系統描述與數學模式 9
2-1物理統與假設 9
2-2數學模式 10
2-2-1熱流場方程式 10
2-2-2低雷諾數k-ɛ紊流模式 13
2-2-3熱應力場方程式 15
第三章數值方法 18
3-1無因次參數分析 18
3-2離散座標法 19
3-3反應曲面法 19
3-4固化理論分析 20
3-5網格測試與收斂測試 20
3-6求解分析步驟 21
第四章結果與討論 26
4-1 CZ法生長大尺寸晶體熱流場分析 26
4-2 坩堝旋轉對熱流場之影響 28
4-3 晶體旋轉對熱流場之影響 28
4-4 晶體與坩堝反向旋轉對熱流場之影響 29
4-5 轉速最佳化分析 30
4-6 熱應力分析 31
第五章結論與未來研究方向 57
參考文獻 59

參考文獻

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指導教授

陳志臣(Jyh-Chen Chen)

審核日期

2015-7-29

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