CZ法生長大尺寸藍寶石單晶之熱流場與溶質數值模擬研究

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陳旻聰(Ming-tsung Chen) 查詢紙本館藏

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機械工程學系

論文名稱

CZ法生長大尺寸藍寶石單晶之熱流場與溶質數值模擬研究
(Numerical Simulation of the Flow, Temperature, and Solute Fields for Growing the Larger Sapphire Crystal in Czochralski System)

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摘要(中)

對晶體產業而言，柴式提拉法(Czochralski)是一項重要的關鍵技術。在近年工業的發展中，這項技術已經成為應用於生長大尺寸藍寶石晶體的方法之一。為了提升藍寶石單晶的生長品質，我們有必要深入了解長晶爐內部的整體熱傳與熔湯流動行為。然而這種生長較大尺寸晶體方法，受限於爐體內的高溫使我們無法直接去做實驗量測；除此之外，在長晶過程中容易產生化學雜質，使生長出的藍寶石單晶摻雜許多氣泡，進而影響晶體的光學性質與品質。在業界通常以調整長晶參數的方式進行製程優化，但是需花費許多人為控制時間，因此，我們必須用更有效的方式來獲得長晶參數與條件。本文運用有限元素法，且以準穩態的方式模擬藍寶石生長過程的熱場和流場的耦合行為、熔湯內部溶質流動的傳輸機制，進而去推論其與晶體內氣泡間的關係。
本研究結果發現，溫度場中的等溫線會受到強烈的浮力渦流扭曲變形，而渦流強度亦會隨熱源強度下降而減低；固液界面形狀會隨晶體長度增加而愈凸向熔湯，熔湯內部只存在一個浮力渦流。在非固定支承高度系統中，爐內輸入的熱源和晶體內溫度梯度會較固定支承系統的結果來得高，對長出晶體的完整度會有不良影響。當系統坩堝底部的形狀呈圓形，或在上爐室加裝由石墨碳纖製成的熱遮罩，會使整體晶體凸出率下降。當底部支承材料為氧化鋯球時，較不易發生坩堝底部晶體固化的結果，並使晶體界面較為平坦。
在CZ長晶系統中的溶質場模擬結果顯示，各階段熔湯內溶質濃度最大值位於坩堝側表面，並且發現溶質的分布明顯受到熔湯的流動所影響。另外，在固液界面附近的溶質濃度於靠近晶體中心軸有局部最大值，這表示著熔湯內雜質在中心軸附近堆積程度比起其他位置來得高。一般而言，當固液界面愈不穩定，氣泡愈容易摻入到晶體內部；而固液界面不穩定性與溶質在界面的組成過冷程度是呈正向關係，亦即當組成過冷程度愈大，會使固液界面愈不穩定。
本文模擬結果顯示，當系統內溶質濃度和晶體提拉速度愈大，界面產生溶質組成過冷的機會愈高，並且在中心軸附近的組成過冷程度較大，模擬得到的結果與實驗文獻結果相似。除此之外，長晶爐內部的溫度會影響生成雜質的多寡，故需要非常小心的控制，不宜太高。

摘要(英)

The Czochralski method is one of important technologies for the crystal industry. For recently, it had been mainly applied for industrial larger size sapphire crystal growth. The thermal and flow transport play significant roles in CZ crystal growth, and it is hard to directly observed in experiments. Moreover, the grown sapphire single crystal is commonly accompanied by small bubbles which might affect the optical properties. Manual control for the amount and distribution of this kind chemical defects strongly depends on the trial experiences. Therefore, we must use a more efficient way to obtain growth parameters or conditions. This thesis is numerically investigated on both thermal-flow and solute transport phenomenon using the finite element method and quasi-steady approximation.
The results presented in this study show the effect of different positions of support, heat shield devices, different upper furnace chambers, different support materials, and different crucible bottom shapes. Strong buoyant flow distorts the isotherms in the melt, and the strength decreases when the power supply decreases. The deflection height of the melt-crystal interface increases, as the melt level goes down. The power supply and temperature gradient inside solid crystal increase, when the support is lifted up. This is not good for crystal quality. Besides, the crystal convexity decreases, when the crucible bottom shape is round or the heat shield device made by carbon fiber is adopted. Furthermore, it is more likely grow more flat crystal and no solidified crystal touched at the crucible bottom, as the ZrO2 bubble insulator of support is used.
Then, we used the solutions of thermal-flow field to discuss its influence on the solute field in CZ system. The results show that the maximum value solute concentration locates at the crucible sidewall and solute distribution strongly depends on the flow motion of molten melt. Besides, solutes are inclined to gather near the melt-crystal interface, and the local-maximum value located at the center sites. The gas bubbles are easily incorporated into solid crystal, as the melt-interface is not stable. The instability of crystallization front is proportional to the solute constitutional supercooling.
The results show the chance of constitutional supercooling increases, when the solute concentration in molten melt increases or pulling rate of system is larger. In addition, the degree of constitutional supercooling is larger particularly near the center sites. These computational results are consistent with the experimental results done by foreign researchers. The temperature degrees in the furnace also should be controlled carefully and we concluded that the heat shield system is better than the others. Based on these results, the crystal quality of sapphire is expected to be improved.

關鍵字(中)

★ 柴式晶體生長
★ 藍寶石單晶
★ 氣泡
★ 數值模擬

關鍵字(英)

★ Czochralski
★ crystal growth
★ sapphire
★ bubble
★ numerical simulation

論文目次

摘要 I
Abstracts III
誌謝 V
Table of Contents VI
List of Figures VIII
List of Tables XIII
Nomenclature XV
Chapter I Introduction 1
1-1 Aluminum Oxide Single Crystals (Al2O3) 1
1-2 Czochralski Growth Technology 2
1-3 Literature Review 3
1-3-1 Numerical Simulation of Sapphire Single Crystal 3
1-3-2 Transport and Distribution of Bubble Impurities 7
1-4 Motivation and Objectives 12
Chapter II Physical Model and Mathematical Formulations 20
2-1 Physical Model and Assumptions 20
2-2 Mathematical Formulations 21
2-3 Bubble Nucleation Mechanism 30
2-4 Segregation Process, Equilibrium Temperature, Solute Boundary Theory, and Constitutional Supercooling Criterion 31
Chapter III Numerical Solutions 41
3-1 Parameters Analysis 41
3-2 Quasi-Steady State Examination 42
3-3 Finite Element Method, Grid and Tolerance Test 43
3-3-1 Finite Element Method (FEM) 43
3-3-2 Grid and Tolerance Test 44
3-4 Solidification Analysis 45
3-5 Solving Steps 45
Chapter IV Results and Discussion 51
4-1 Analysis of Thermal-Flow Field with Different Growth Process in CZ System 51
4-2 Comparison of Different Growth Parameters and Conditions 54
4-2-1 Difference between Moved/ Fixed Support System 54
4-2-2 Difference between Heat Shield/ No Shield System 55
4-2-3 Difference between Vacuum and Argon System 56
4-2-4 Influence of Support Material 57
4-2-5 Influence of Crucible Bottom Shape 58
4-2-6 Difference between Surface/ Non Surface Tension System 60
4-3 Analysis of Solute Field of Different Growth Stages in CZ System 60
4-4 Analysis of Solute Field for Different Growth Conditions 62
4-4-1 Different Pulling Rate Systems 63
4-4-2 Influence of Different Furnace Temperature 63
Chapter V Conclusions and Future Works 109
Appendix 111

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指導教授

陳志臣(Jyh-chen Chen)

審核日期

2014-7-29

推文