電磁式感應加熱柴氏法生長氧化鋁單晶過程之數值模擬分析

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：33

、訪客IP：18.221.8.126

姓名

朱信旗(Hsin-chi Chu) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

電磁式感應加熱柴氏法生長氧化鋁單晶過程之數值模擬分析
(Numerical simulation during an inductively heated Czochralski sapphire crystal growth system)

相關論文

★ 鋰鋁矽酸鹽之負熱膨脹陶瓷製程	★ 鋰鋁矽酸鹽摻鈦陶瓷之性質研究
★ 高功率LED之熱場模擬與結構分析	★ 干涉微影之曝光與顯影參數對週期性結構外型之影響
★ 週期性極化反轉鈮酸鋰之結構製作與研究	★ 圖案化藍寶石基板之濕式蝕刻
★ 高功率發光二極體於自然對流環境下之熱流場分析	★ 液珠撞擊熱板之飛濺行為現象分析
★ 柴式法生長氧化鋁單晶過程最佳化熱流場之分析	★ 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
★ 交流電發光二極體之接面溫度量測	★ 柴氏法生長單晶矽過程之氧雜質傳輸控制數值分析
★ 泡生法生長大尺寸氧化鋁單晶降溫過程中晶體熱場及熱應力分析	★ KY法生長大尺寸氧化鋁單晶之數值模擬分析
★ 外加水平式磁場柴氏法生長單晶矽之熱流場及氧雜質傳輸數值分析	★ 大尺寸LED晶片Efficiency Droop之光電熱效應研究

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

柴氏單晶生長法(Czochralski single crystal growth method)又稱提拉法，是目前生長氧化鋁單晶（Sapphire）最經濟也最常使用的方法。為能確保生長sapphire單晶的品質及掌握坩堝內熔湯之生長情況，因此使用有限元素法（FEM）為基礎的COMSOL Multiphysics軟體來進行電磁場、熱場及流場三場耦合之柴氏生長氧化鋁單晶過程的數值分析模擬，以獲得熔湯內之熱流場分佈情形及相關資訊。
本研究主要探討CZ法生長氧化鋁單晶過程中以電磁場感應加熱的方式分析坩堝內的熔湯之熱流場的分佈情形。從未長晶階段到不同長晶過程逐一進行模擬並探討流場內及晶體固液界面形態的變化，包括調整感應電流及加熱線圈位置改變的影響。分析影響熔湯內熱流場分佈的各項製程的重要因素。希望透過完整的分析模擬，將整個長晶過程一一呈現。
模擬結果探討氧化鋁單晶生長過程中調降加熱線圈的電流量，熔湯內部溫度分佈等溫線及速度場會趨於緩和。且因為晶體生長長度增加，晶體會帶走較多的能量，使得固液界面曲率增加會更凸向熔湯。最後探討調整加熱線圈位置的影響，加熱線圈產生的感應磁場中心接近坩堝中間位置時，加熱坩堝內氧化鋁熔湯達適當溫度時所需的能量最小。這些分析結果將可作為柴氏長晶系統生長氧化鋁單晶時之重要參考指標，並可為將來深入研究單晶生長機制的基礎。

摘要(英)

Sapphire single crystals are widely used in variety of modern high- tech applications. Among crystal growth methods, the Czochralski single crystal growth method is a good commercial method for growing the larger, high-optical-quality sapphire crystal. The finite element software COMSOL Multiphysics is employed to simulate the melt temperature and velocity distribution during an inductively heated of sapphire crystal growth process using CZ.
Temperature and velocity field in an inductively heated Czochralski crystal growth furnace is investigated numerically during the different crystal growth stage (from 25 to 125mm). The temperature and flow field inside the furnace was calculated coupled with the heat generation of the Ir crucible that was induced by the electromagnetic field (supported by the RF coil). The heat loss from the free surface and the crystal are due to thermal radiations which are calculated by the emissivity, the Gebhart factor and temperature of the furnace surface.
The results show that the temperature distributions of the melt and crystal are affected by the relative position between crucible and induction coil due to the modification of the electromagnetic field in the CZ furnace. The shape of solid-melt interface is also affected by the radiation of the crystal surface. Therefore, the growth parameters such as the position of RF coil, the growth length of crystal and the surface tension etc.; will be investigated in the present study.

關鍵字(中)

★ 柴氏法
★ 晶體生長
★ 氧化鋁單晶
★ 數值模擬

關鍵字(英)

★ Czochralski
★ crystal growth
★ sapphire
★ Numerical simulation

論文目次

摘要 ……………………………………………………………….……………..Ⅰ
Abstract ………………………………………………………...……………….Ⅱ
誌謝 …………………………………………………………………...…………Ⅲ
目錄 …………………………………………………………………………….. Ⅳ
圖目錄 ……………………………………………………………………….….Ⅶ
表目錄 ………………………………………………………..………………….Ⅸ
符號說明 ……………………………………………………………………….. Ⅹ
第一章、緒論 ………………………………………………….……………..…..1
1.1 前言 …………………………………………….………...…..………..1
1.2 氧化鋁單晶性質與結構 …………………………………...…...……..2
1.3 柴式長晶法簡介 …………………………………...…………….……2
1.4 文獻回顧 …………………………………………………...……....….3
1.5 研究動機與目的 ………………………...…………………….………6
第二章、物理模式與系統描述 ………………………………………….…..…..8
2.1 長晶過程熱傳遞行為 ……………………………...………….………9
2.2 影響長晶熱流場的因素 …………………………...……….…...…….9
2.3 二維軸對稱模型及準穩態系統描述 ……………………………......10
2.3.1 電磁場物理模式 ……………………………………….…......…10
2.3.2 熱場物理模式 ………………………...………………….…...…12
2.3.3 流場物理模式 …………………………………...…….…...……16
2.4 邊界條件 ……………………………………………….…….........…17
2.5 晶體固化理論 …………………………………………………..........17
2.6 判別流場型態 …………………...………………...……….…..…….18
第三章、數值分析與研究方法 ……………………………………………...…20
3.1 有限元素法 …………………………………………………....……..20
3.2 形狀函數 …………………………………………………...……...…21
3.3 收斂條件 ………………………………………………...………...…21
3.4 分析流程 ……………………………………………………......……22
3.4.1 建立模型與繪製幾何圖形 ………………………………..…….22
3.4.2 元素型式、統御域及材料定義 …………………..…………….23
3.4.3 邊界條件設定 …………………………………………….……..23
3.4.4 網格之產生 ………………………………………………..…….23
3.4.5 分析 ………………………………………………………...……24
3.4.6 結果 …………………………………………………………...…24
3.5 模擬項目 ………………………………………………….…...……..25
第四章、結果與討論 ……………………………………………….…………..26
4.1 網格測試 ………………………………………………..……...…….27
4.2 未長晶階段之電磁場及熱流場分佈 ……………………………..…27
4.2.1 未長晶階段之電磁場分佈 ……………………………..……….28
4.2.2 未長晶階段之熱流場分佈 ……………………………...………28
4.3 生長25 mm晶柱之電磁場及熱流場分佈 …………………….….....29
4.3.1 生長25mm晶柱之電磁場分佈 ………………….……...……...29
4.3.2 生長 25mm晶柱之熱流場分佈 …………………………………29
4.4 長晶過程及不同長晶階段之熱流場分析 ……………….……...…..30
4.4.1 不同長晶階段之電磁場分佈 ……………………….…………..30
4.4.2 不同長晶階段之熱流場分佈 ……………………….…………..31
4.4.3 不同長晶階段固液界面形狀之變化 ……………….………..…31
4.5 調整加熱線圈位置對於整體電磁場及熔湯熱流場分佈之影響 …..32
4.5.1 加熱線圈位置與爐體電磁場分佈之影響 ……….………….….32
4.5.2 加熱線圈位置與輸入電流之關係 ………….……………...…...32
4.5.3 加熱線圈位置不同之熱流場分佈 ……………………...………33
4.6 加入表面張力對於氧化鋁熔湯熱流場的影響 ……………...…...…33
第五章、結論 …………………………………………………………………...34
參考文獻 ………………………………………………………………………...36

參考文獻

1. S. K. Hong, B. J. Kim, H. S. Park, Y. Park, S. Y. Yoon and T. I. Kim, “Evaluation of nanopipes in MOCVD grown （0001）GaN/Al2O3 by wet chemical etching,” Journal of Crystal Growth, Vol 191, pp. 275, (1998).
2. S. Nakamura, T. Mukai and M. Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue- light-emitting diodes,” Applied Physsics Letters, Vol 64, pp. 1687, (1994).
3. Brian R. Pamplin ed., Crystal Growth., 2nd edition, Pergamon Press Ltd., 1980.
4. Pawel E. Tomaszewski, “Jan Czochralski-father of the Czochralski method,” Journal of Crystal Growth, Vol 236, pp. 1-4, (2002).
5. Jan Czochralski, “Ein neues Verfahren zur Messung der Kristallisation geschwindigheit der Metalle,” Z. Phys. Chemie, Vol 92, pp. 219, (1918).
6. G. K. Teal and J. B. Little, “Growth of germanium single crystals,” Physical Review, Vol 78, pp. 647, (1950).
7. H. E. Buckley, Crystal Growth., John Wiley and Sons Inc., New York, (1951).
8. H. J. Scheel and T. Fukuda, “The Development of Crystal Growth Technology,” Crystal Growth Technology, pp.3-14, (2003).
9. K. Nassau and L.G. Van Uitert, “Preparation of Large Calcium-Tungstate Crystals Containing Paramagnetic Ions for Maser Applications,” Journal of Applied Physics, Vol 31, pp. 1508, (1960).
10. 張克從和張樂潓，晶體生長，科學出版社，1981。
11. J. J. Derby and R.A. Brown, “Thermal-capillary analysis of Czochralski and liquid encapsulated crystal growth Ⅰ. Simulation,” Journal of Crystal Growth, Vol 74, pp. 605-624, (1986).
12. J. J. Derby and R.A. Brown, “Thermal-capillary analysis of Czochralski and liquid encapsulated crystal growth Ⅱ. Processing strategies,” Journal of Crystal Growth, Vol 75, pp. 227-240, (1986).
13. F. Dupret, Y. Ryckmans, P. Wouters and M. J. Crochet, “Numerical calculation of the global heat transfer in a Czochralski furnace,” Journal of Crystal Growth, Vol 79, pp. 84-91, (1986）.
14. F. Dupret, P. Nicodeme, Y. Ryckmans, P. Wouters and M. J. Crochet, “Global modeling of heat transfer in crystal growth furnaces,” Int. J. Heat Mass Transfer, Vol 33, pp. 1849-1871, (1990).
15. N. Van den Bogaert and F. Dupret, “Dynamic global simulation of the Czochralski process Ⅰ. Principles of the method,” Journal of Crystal Growth, Vol 171, pp. 65-76, (1997).
16. N. Van den Bogaert and F. Dupret, “Dynamic global simulation of the Czochralski process Ⅱ. Analysis of the growth of a germanium crystal,” Journal of Crystal Growth, Vol 171, pp. 77-93, (1997).
17. A. Lipchin and R. A. Brown, “Hybrid finite-volume/finite-element simulation of heat transfer and melt turbulence in Czochralski crystal growth of silicon,” Journal of Crystal Growth, Vol 216, pp. 192-203, (2000).
18. K. Takano, Y. Shiraishi, T. Iida, N. Takase, J. Matsubara, N. Machida, M. Kuramoto and H. Yamagishi, “Numerical simulation for silicon crystal growth of up to 400mm diameter in Czochralski furnaces,” Mater. Sci. and Eng., Vol B73, pp. 30-35, (2000).
19. K. Takano, Y. Shiraishi, T. Iida, N. Takase, J. Matsubara, N. Machida, M. Kuramoto and H. Yamagishi, “Global simulation of the CZ silicon crystal growth up to 400mm in diameter,” Journal of Crystal Growth, Vol 229, pp. 26-30, (2001).
20. M. Li, Y. Li, N. Imaishi and T. Tsukada, “Global simulation of a silicon Czochralski furnace,” Journal of Crystal Growth, Vol 234, pp. 32-46, (2002).
21. T. Tsukada, N. Imaishi and M, Hozawa, “Theoretical Study of the Flow and Temperature Fields in CZ Single Crystal Growth,” Journal of Chemical Engineering, Vol 21, pp. 184-191, (1988).
22. T. Tsukada, M. Hozawa and N. Imaishi, “Global Analysis of Transfer in CZ Crystal Growth of Oxide,” Journal of Chemical Engineering, Vol 27, pp. 25-31, (1994).
23. Kobayashi N., “Hydrodynamics in Czochralski Growth-Computer Analysis and Experiments,” Journal of Crystal Growth, Vol 52, pp. 425-434, (1981).
24. Hurle D. T. J., “Analytical Representation of the Shape of the Meniscus in Czochralski Growth,” Journal of Crystal Growth, Vol 63, pp. 13-17, (1983).
25. Wu X. B., Geng X. and Guo Z. Y., “Fundamental Study of Crystal-Melt Interface Shape Change in Czochralski Crystal Growth,” Journal of Crystal Growth, Vol 169, pp. 786-794 (1996).
26. Geng X., Wu X. B. and Guo Z. Y., “Numerical Simulations of Combined Flow in Czochralski Crystal Growth,” Journal of Crystal Growth, Vol 179, pp. 309-319, (1997).
27. You Rong Li, Deng Fang Ruan, Nobuyuki Imaishi, Shuang Ying Wu, Lan Peng and Dan Ling Zeng, “Global simulation of a silicon Czochralski furnace in an axial magnetic field,” International Journal of Heat and Mass Transfer, Vol 46, pp. 2887–2898, (2003).
28. Akira Hayashi, Masaki Kobayashi, Chengjun Jing, Takao Tsukada and Mitsunori Hozawa, “Numerical simulation of the Czochralski growth process of oxide crystals with a relatively thin optical thickness,” International Journal of Heat and Mass Transfer, Vol 47, pp. 5501–5509, (2004).
29. Jyotirmay Banerjee and Krishnamurthy Muralidhar, “Role of internal radiation during Czochralski growth of YAG and Nd:YAG crystals,” International Journal of Thermal Sciences, Vol 45, pp. 151–167, (2006).
30. M. H. Tavakoli and H. Wilke, “Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 1：non-rotating seed,” Cryst. Res. Techol., Vol 42, No. 6, pp. 544-557, (2007).
31. 陳志勇，“柴式法生長鈮酸鋰塊晶之研究分析”，國立中央大學機械工程研究所，碩士論文， (2004)。

指導教授

陳志臣(Jyh-chen Chen)

審核日期

2008-1-24

推文