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姓名 吳東頤(Tung-Yi Wu)  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之數值模擬分析
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摘要(中) KY法在眾多長晶法中是最適合生長大尺寸晶體的長晶法。但在大尺寸坩堝生長藍寶石單晶時,因為爐內高溫無法直接觀察內部熱流場。因此需以模擬軟體計算生長過程,以求提升長晶良率,減少長晶成本。本研究中模擬KY法生長90公斤的藍寶石單晶。為避免高溫梯、爐體熔化與熱源浪費的現象,我們採用多重區段加熱KY爐。
本研究中採用有限元素法COMSOL軟體模擬藍寶石晶體長晶過程。本研究中模擬三種功率配比的長晶過程,而所使用的三種功率配比主要差別在上加熱器與中加熱器的相對大小,分別是0.8:1.0:0.4 (CASE1)、1.0:1.0:0.4 (CASE2)和1.2:1.0:0.4 (CASE3)。結果顯示上加熱器的大小影響上渦流的強度,當上渦流效應強大,會藉由流動使晶體往徑向生長且抑制軸向生長,所以產生了不同的固液界面。隨著熔湯減少使上渦流效應減弱,加速晶體軸向生長而減慢徑向生長,使晶體徑長小於晶肩徑長。在KY法生長大尺寸藍寶石晶體時,上加熱器的功率大小可有效控制生長晶體外型。在研究中比較了固液界面溫梯、所需總功率跟晶體形狀,發現加熱比例為1.2:1:0.4有較佳的長晶結果,但其中出現固化現象。因此修正加熱功率配比,以CASE3為初始值,僅調低上加熱器直到其值與中加熱器相同時,再將上加熱器與中加熱器維持同功率往下降。模擬結果不僅有好的溫梯與較低的加熱總功率,且晶體外型徑長也近似等徑長。
我們亦將各CASE的長晶階段模擬熱應力場分布,以確認在大尺寸藍寶石單晶生長過程中的熱應力變化,經過比較後發現在晶體生長過程中其晶體內熱應力值皆小於藍寶石晶體能承受的最大抗張強度(414MPa)。
摘要(英) In crystal growth, Kyrupoulos method applies to grow large size crystal. During the large size sapphire crystal growth, it’s hard to observe temperature and flow inside the high temperature furnace. According to this reason, we need numerical simulation to calculate crystal growth, to improve the yield and to cost down. The thesis simulates 90kg large size sapphire crystal growth by Kyrupoulos method. In Kyrupoulos furnace, we use three heaters to avoid the high temperature gradient in crystal, crucible melting and thermal waste.
This study uses the COMSOL Multiphysics software to simulate large size sapphire crystal. We simulate three types of heater power ratios, 0.8:1.0:0.4(case1), 1.0:1.0:0.4(case2), 1.2:1.0:0.4(case3), differ from top and middle heater relative magnitude. The result shows top heater power effect the strength of cell. The strong cell makes crystal grow in radial direction and suppress its axial direction growth. Then produce different interface shape.
With melt reduce, upper cell gets weak. It accelerates crystal growth in axial direction, and the crystal diameter is less than crystal shoulder length. In the KY method growth large sapphire crystal, top heater power can control crystal shape effectively. We compare interface temperature gradient, total power and crystal shape. We find that heater power ratio 1.2:1:0.4 has better result, though it has solidification phenomena. We use case3 be the initial value to modify heater power ratio. Decreasing top heater power to be the same with middle heater power, then decrease top and middle heater power at the same time. The simulation result has good temperature gradient, lower total power and crystal ingot grow in same diameter. We also simulate thermal stress field distribution of every crystal growth stage. And get thermal stress variation in large sapphire crystal growth process. The result shows that the thermal stress of crystal is smaller than the maximum tensile strength of sapphire crystal (414MPa).
關鍵字(中) ★ 藍寶石
★ KY法
★ 大尺寸長晶
關鍵字(英) ★ Sapphire
★ Kyropoulos
★ Large crystal growth
論文目次 目錄
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 KY法(Kyrupoulos Method) 2
1-3 文獻回顧 3
1-4 研究動機與目的 7
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熱流場統御方程式 12
2-2-2紊流模式與統御方程式 13
2-2-3熱應力場方程式 16
第三章 數值模型 19
3-1 求解方法 20
3-2 網格選用與收斂測試 20
3-3 固化理論分析 21
3-4 KY爐之生長大尺寸晶體之參數分析 22
3-5 求解分析步驟 23
第四章 結果與討論 27
4-1 KY爐之大尺寸晶體熱流場分析 27
4-2 分段式加熱KY爐之晶體生長分析 29
4-3 晶體等向應力分析 32
第五章 結論與未來研究方向 55
5-1 結論 55
5-2 未來研究方向 56
參考文獻 57
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指導教授 陳志臣(Jyh-Chen Chen) 審核日期 2013-7-26
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