KY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

莊效存(Hsiao-Tsun Chuang) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

KY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 during the Kyropoulos Process)

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摘要(中)

泡生法(Kyropoulos method, KY)是目前工業長晶中最大量被使用的長晶方法，因為其生長出來的晶體，溫度梯度較其他長晶法低，也因此較適合拿來生長較大尺寸的晶體；受限於KY爐體的設計，而無法直接觀察生長晶體的完整過程，且直接進行實驗量測，將會耗費許多時間及金錢，因此本研究使用以有限元素法(FEM)為基礎的套裝模擬軟體COMSOL Multiphysics，針對藍寶石晶體生長，模擬分析整個長晶過程的熱流場以及熱應力的分佈。
本研究結果顯示，隨著晶體生長，最大熱應力的發展分為三階段，第一階段為晶冠生長時期，在這個階段，最大熱應力會隨著晶冠的尺寸擴大而增加，第二階段則是晶體增長時期，在這個階段最大熱應力則是隨著晶體長度增加而下降，最後一階段，因為晶體的生長，逐漸靠近坩堝底部，而在這階段，最大熱應力則是隨著越靠進鍋底而增大。
此外透過調整不同加熱器功率下降速度可以發現，若加熱器功率下降速度較快的話，其晶冠外型將會生長的叫為平坦，且其最大熱應力也會跟著變大:反之，若加熱器功率下降的較慢的話，其晶冠外型則會相對陡峭，而熱應力也會相對變小。
另外本研究也透過修改坩堝外型以及輻射熱遮罩面積，來探討這些結構的修改對熱應力所造成的影響，結果顯示有導圓角的坩堝外型將更有助於提升晶體生長的品質；而隨著晶體表面積的增加，輻射熱遮到對於晶體熱應力的影響會越小。

摘要(英)

The Kyropoulos method (KY) is the most common crystal growth method used in the industrial manufacturing large size crystal, because the crystal with this method has lower temperature gradient, and therefore it is more suitable for the larger size crystal growth. It is not easy to observe the complete process of crystal growth directly because of the design of KY furnace. Moreover, experimental measurement will spend a lot of time and money, so this study uses COMSOL Multiphysics which is the finite element software based on the theories of thermal and fluid dynamics. With this software, we tried to simulate the whole process of sapphire crystal growth, and analysis the phenomenon of crystal growth.
The results show that with the growth of crystal, the maximum thermal stress can be divided into three stages: crown stage, body stage and tail stage. At crown stage, the maximum thermal stress increases as the length of crystal increases. And at body stage, the maximum thermal stress decreases as the length of crystal increases. The last stage, because the crystal is closer to the bottom of the crucible, so at tail stage, the maximum thermal stress increases as the length of crystal increase.
By adjusting the speed of different heater power, it can be found that if the heater power decreases faster, the crystal crown shape will be flat, and the maximum thermal stress will be larger. On the other hand, if the heating power decreases slower, the crystal crown shape will be relatively steep, and thermal stress will be relatively smaller.
The study also explored the effect of the different furnace structures, such as different size thermal shield and different crucible shape, which also effect the quality of crystal .

關鍵字(中)

★ 泡生法
★ 藍寶石長晶
★ 數值模擬

關鍵字(英)

論文目次

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(氧化鋁單晶)簡介 1
1-2 泡生法介紹 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 11
2-1 物理系統與假設 11
2-2 數學模式 12
2-2-1 熱流場方程式 12
2-2-2低雷諾數k-ɛ紊流模式 16
2-2-3熱應力場方程式 18
第三章數值方法 23
3-1 無因次參數分析 23
3-2 離散座標法 24
3-3 固化理論及晶體外型繪製 24
3-4 網格測試與收斂測試 25
3-5求解步驟 26
第四章結果與討論 32
4-1 KY法生長大尺寸晶體熱流場分析 32
4-2 Rosseland radiation model & Discrete Ordinates method 35
4-3 KY 法生長過程之熱應力分析 37
4-4 不同 Power history 對晶體外形影響 38
4-5 不同 Power history 對熱應力影響 39
4-6 輻射熱遮罩對熱應力的影響 41
4-7 坩堝外形對熱應力之影響 42
第五章結論與未來研究方向 71
參考文獻 73

參考文獻

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指導教授

陳志臣

審核日期

2017-8-16

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