柴式法生長氧化鋁單晶過程晶體內部輻射對於固液界面及熱應力之分析

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姓名

陳恆超(Heng-chao Chen) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

柴式法生長氧化鋁單晶過程晶體內部輻射對於固液界面及熱應力之分析
(Effect of internal radiation on thermal stress fields and interface shape in Czochralski crystal growth of sapphire)

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摘要(中)

柴式長晶法生長氧化鋁單晶過程中，為了提升氧化鋁單晶的生長品質，必須了解柴式長晶爐內部的熱傳與熔湯流動情形。由於單晶生長過程無法直接觀察熔湯內的熱流場分佈，所以本研究使用有限體積法之CGSim軟體模擬二維軸對稱氧化鋁單晶生長過程之電磁場、熱場與流場。求解的方式先從RF線圈產生電磁場，感應坩堝計算出熱通量分佈之後，在以此為邊界條件來修正並同時解出整個爐體的熱場與流場，以此溫度場再對晶體、熔湯、坩堝、以及長晶區域上爐室內之氣體來做更進一步的深入計算，最後將晶體的溫度分佈數據匯入至COMSOL做三維非等向熱應力分析。
本研究主要模擬柴式法生長氧化鋁單晶的生長過程，探討生長過程中晶體內部熱輻射對於熱流場、固液界面形狀與熱應力分佈之影響。為了做出更理想的長晶模擬，本研究加入了氬氣的流動、熔湯表面張力、考慮熔湯為紊流模式以及晶體內部熱輻射的影響，並針對表面張力、晶體內部輻射與等效熱傳導係數對於熱流場分佈之影響作分析。最後計算出熱應力的分佈用來分析生長c軸與a軸之氧化鋁單晶的缺陷分佈情形。

摘要(英)

The thermal and flow transport in a Czochralski crystal growth furnace plays an important role to effect the single crystal growth quality of sapphire. However, the thermal and flow fields in the melt of the single crystal growth process are difficult to observe in experimental study. This thesis has numerically investigated the thermal and flow transport phenomenons using the finite volume method via CGSim software. The electromagnetic, thermal, and fluid fields during the sapphire single crystal growth process have been investigated. The temperature and flow fields inside the furnace are coupled with the heat generation in the Iridium crucible which is generated by the electromagnetic field using the RF coil.
For different stages of Czochralski crystal growth of sapphire, the configuration usually used in a real Czochralski crystal growth process consists of a crucible, induction coil, insulation, crystal, melt and gas. At first the volumetric distribution of heat generation inside the metal crucible is calculated. Using this heat distribution as a source the fluid flow and temperature fields in the whole system are computed. After that, thermal analysis is computed only in the crystallization zone, including the crystal, melt, crucible, and a gas region around the crystal. The computation in the crystallization zone involves the turbulent flow of the sapphire melt, the laminar gas flow, and radiative heat exchange in the semitransparent crystal.
Then using the temperature distribution in a single crystal to calculate thermal stress via COMSOL software. The anisotropy of elastic constants and thermal expansion coefficients are considered in the problem. The analyses are performed both for the pulling directions of a-axis and c-axis.

關鍵字(中)

★ 熱應力
★ 晶體內部輻射
★ 氧化鋁單晶
★ 柴式法

關鍵字(英)

★ sapphire
★ thermal stress
★ internal radiation
★ Czochralski method

論文目次

摘要…………………………………………………………………………...………..Ι
Abstract……………………………………………………………………….………II
誌謝…………………………………………………………………..…………........III
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(Sapphire)簡介…………………………………………………….…..1
1.2柴式長晶法(CZ)介紹…………………………………………………………...….2
1.3文獻回顧…………………………………………………………...……………….3
1.4研究目的…………………………………………………………...……………….8
第二章系統描述與數學模式………………………………………………….…12
2.1物理系統與假設…………………………………………………………….....….12
2.2數學模式…………………………………………………………...……………...12
2.2.1電磁感應加熱計算方式…………………………………………………….13
2.2.2統御方程式…………………………………………………….………...….13
2.2.3邊界條件…………………………………………………………….…...….15
2.2.4紊流計算方式……………………………………………………….…...….16
2.2.5晶體內部熱輻射計算方式………………………………………………….17
2.2.6晶體生長速度與潛熱計算………………………………………………….17
2.2.7熱應力計算方式……………………………………………………….……17
第三章求解方法與分析步驟………………………………………………….…21
3.1求解方法……………..……………………………………………...………….…21
3.1.1固化計算方式……………………………………………………...……….21
3.1.2判別流場型態…………………………………………………….……...…22
3.2長晶模擬求解流程……………………………………………………..……...…23
3.2.1 CGSim分析步驟…………………………………………………...………24
3.2.2 Flow Module分析步驟 ……………………………………………………24
3.2.3 COMSOL分析步驟……………………………………………………...…25
3.2.4網格測試…………………………………………………………...……….25
第四章結果與討論………………………………………………………….…….32
4.1實際長晶參數生長過程模擬分析………………………………………..………32
4.1.1實際長晶製程參數…………………………………………...……………..32
4.1.2實際長晶過程模擬分析………………………………………….…………32
4.2不同條件下長晶過程之熱流場分析………………………………………..……34
4.2.1考慮表面張力對於熱流場之影響……………………………………….…34
4.2.2晶體熱傳遞機制對於熱流場之影響…………………………….…………35
4.3不同條件之氧化鋁單晶熱應力分佈情形……..…………………………………36
4.3.1晶體內部輻射對於熱應力分佈之影響………………………….…………36
4.3.2生長不同軸向氧化鋁單晶之三維熱應力分析…………………….………37
4.3.3改變晶體轉速與拉速對於熱應力分佈之影響…………………….………37
第五章結論………………………………………………………...………………59
參考文獻……………………………………………………………………..………61

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指導教授

陳志臣(Jyh-Chen Chen)

審核日期

2009-7-23

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