CZ法生長藍寶石單晶之熱應力數值模擬分析

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姓名

吳宜達(YI-TA WU) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

CZ法生長藍寶石單晶之熱應力數值模擬分析
(Numerical Simulation of Thermal Stress for Growing Sapphire Crystal in the Czochralski Process)

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摘要(中)

生長藍寶石的方法最主要為柴式長晶法(Czochralski method,CZ)與凱氏長晶法(Kyropoulos method,KY)兩種為主，而本研究以探討柴式長晶法生長藍寶石之情形，為了提高生長品質，我們需要理解藍寶石在爐體內之熱傳與熔湯流動之機制。
由於柴式長晶法生長藍寶石之爐體內部溫度過高，實驗無法有效觀察其熱流場在爐體內之情形，本研究以套裝軟體COMSOL Multiphysics運用有限元素法來對內部熱流場進行分析，進而降低實驗所花費之時間與耗材成本，探討藍寶石內部熱流場之固液界面熱應力、晶肩熱應力之分佈，進行研究。
研究結果，發現熔湯之流場由浮力渦流為主，浮力渦流之強度會隨著加熱器功率調降而下降；固液界面形狀受到熔湯之浮力渦流與加熱器功率之影響，晶體長度越長則越凸向熔湯；修改熱遮罩位置與形狀以降低熱應力的產生，熱遮罩材質以鉬(molybdenum)與碳(Carbon Fiber)兩種進行研究，在鉬熱遮罩的情況下，因熱擴散較好，使鉬遮罩能有效降低加熱器功率，並且在晶肩熱應力能得到良好的均勻性，而碳因隔熱效果明顯，在熱遮罩低於晶肩時，晶肩應力大幅下降，防止晶肩應力過高造成晶肩破裂的狀況，使用下加熱器，在坩堝底部能有效防止溫度低於熔點而造成晶體固化，使坩堝底部發生損壞的狀況，也能有效降低側邊加熱器功率，降低晶肩熱應力與固液界面熱應力，達到節能與減少成本的效果。

摘要(英)

The method of growing sapphire is mainly Czochralski method (CZ) and Kyropoulos method (KY). In order to improve the growth quality, we need to understand the mechanism of sapphire heat transfer and melting flow in the furnace.
Due to the high temperature inside the sapphire furnace, the experiment can not effectively observe the heat flow field in the furnace. In this study, the finite element method was used to analyze the internal heat flow field by COMSOL Multiphysics. And thus reduce the time spent on the experiment and supplies costs. The thermal stress of the solid - liquid interface and the crystal shoulder should be studied.
The results show that the flow of melt is mainly composed of buoyancy vortex. The buoyancy vortex intensity will decrease with the heater power down. The solid-liquid interface shape is affected by the buoyancy vortex of the melt and the heater power. When the crystal length is longer, the crystal will more convex to the melt. Modify the thermal mask position and shape to reduce the generation of thermal stress, thermal mask material to molybdenum and Carbon Fiber two kinds of research. In the case of molybdenum thermal mask, the thermal diffusion is better, so that the molybdenum mask can effectively reduce the heater power, and in the crystal shoulder thermal stress can get a good uniformity. Carbon fiber insulation effect is obvious, in the thermal mask below the crystal shoulder, the crystal shoulder thermal stress dropped significantly. To prevent the crystal shoulder stress caused by excessive crystal shoulder rupture. The use of the bottom heater, the bottom of the crucible can effectively prevent the temperature below the melting point caused by crystal curing. So that the bottom of the crucible damage. It can also effectively reduce the side heater power. Reduce the thermal stress of the crystal shoulder and the solid-liquid interface. To achieve energy saving and reduce the cost of the effect.

關鍵字(中)

★ 柴氏藍寶石長晶
★ 數值模擬
★ 熱應力分析

關鍵字(英)

★ Growing sapphire crystal in the Czochralski Process
★ Numerical simulation
★ Thermal stress

論文目次

目錄
摘要 I
Abstract II
目錄 IV
圖目錄 VI
表目錄 IX
符號說明 X
第一章緒論 1
1-1 藍寶石晶體簡介 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 5
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熱應力方程式 14
2-2-3熱應力方程式 16
第三章數值方法 19
3-1無因次參數分析 19
3-2準穩態測試 20
3-3固化理論分析 20
3-4網格收斂測試 21
3-5求解分析步驟 22
第四章結果與討論 26
4-1 調整熱遮罩之60mm晶體熱應力分析 27
4-2調整熱遮罩之90mm晶體熱應力分析 29
4-3調整熱遮罩之120mm晶體熱應力分析 30
4-4使用下加熱器60mm、90mm與120mm晶體之熱應力分析 31
第五章結論與未來研究方向 67
參考文獻 68

參考文獻

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指導教授

陳志臣(Jyh-Chen Chen)

審核日期

2017-8-23

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