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研究生： 阮陳富
Tran-Phu Nguyen
論文名稱： 數值模擬柴氏法生長大尺寸藍寶石晶體
Numerical simulation for large size sapphire crystal growth during Czochralski method
指導教授： 陳志臣
Jyh-Chen Chen
口試委員:
學位類別： 博士
Doctor
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2018
畢業學年度： 107
語文別： 英文
論文頁數： 86
中文關鍵詞： 數值模擬 、藍寶石晶體 、柴氏法生長
外文關鍵詞： Solute concentration, Crucible and crystal rotations
相關次數： 點閱：9  下載：0 
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    • 藍寶石由於其特殊的光學和機械性能，已經成為現代光學電子技術應用的重要材料，特別是應用於發光二極體磊晶的基板用途。柴氏(Czochralski)長晶技術在當今藍寶石的工業發展中起著重要作用。然而，製造藍寶石基板所面臨的主要挑戰是產生大尺寸、低氣泡缺陷和低熱應力晶體。在本研究中，採用數值模擬研究了在大尺寸（8英寸）藍寶石晶體生長過程中，熔體中的熱和流動傳輸以及溶質濃度分布。從這項研究中，以期找到最佳的坩堝和晶體旋轉速度，在界面處具有較低的凸度和較低的熱應力，以獲得較低的溶質濃度，應用於生長c軸取向的大尺寸藍寶石晶體。特別是沿著晶體/熔體界面區域，這可以改善晶體品質並取得更好地材料利用性。
    由計算研究結果顯示，晶體的凸出率很大程度上取決於坩堝和晶體的旋轉速率。與沒有坩堝旋轉或晶體旋轉的情況相比，坩堝和晶體之間的反向旋轉導致更平坦的晶體/ 熔體界面和更低的凸度。此外，在晶體/熔體界面附近發現高的von Mises應力集中，並且與晶體表面的較高曲率有關。應用反向旋轉導致沿晶體/ 熔體界面的徑方向上有較低溫度梯度以及晶體內部較低的熱應力。對於熔體中溶質濃度的大小和分佈受到對流和熱分佈的強烈影響，當坩堝旋轉速率固定在1rpm並且沒有晶體旋轉時，獲得沿晶體/ 熔體界面的最低和最均勻的溶質分佈。

    Sapphire has become an important material for applications in modern optic-electronic technology because of its special optical, mechanical properties and the demand for sapphire substrates has increased significantly been enlarged in recent years. The Czochralski (CZ) technique plays an important role in the industrial growth of sapphire nowadays. However, the primary challenges faced in the manufacturing of sapphire substrates are to produce large size, low bubble defect and low thermal stress crystal. In this study, the thermal and flow transport and the solute concentration in the melt during the growth process in a large size (8 inch) sapphire crystal have been numerically investigated. From this study, it is expected to find the optimal crucible and crystal rotation for growing c-axis oriented large size sapphire crystal with lower convexity at the interface and lower thermal stress. The optimal crucible and crystal rotation rates in order to obtain the lower solute concentration, especially along the crystal-melt interface region is also obtained. This could lead to an improvement of crystal quality and make it possible to obtain better utilization of the material.
    The computational results show that the convexity of the crystal is strongly dependent on the crucible and crystal rotation rates. Counter rotation between the crucible and the crystal results in a flatter crystal-melt interface and lower convexity, compared to the case with no crucible rotation or crystal rotation. Besides, high concentrations of von Mises stress are found close to the crystal-melt interface and are associated with higher curvature of the crystal surface. Applying counter rotation results in a lower temperature gradient in the radial direction along the crystal-melt interface as well as a lower thermal stress inside crystal. For the solute field, the magnitude and distribution of the solute concentration in the melt are strongly influenced by the convective flow and the thermal distribution. The lowest and most uniform solute distribution along the crystal-melt interface is obtained when the crucible rotation rate fixed at 1 rpm and there is no crystal rotation.

    Abstract i 摘要 iii Acknowledgements iv Table of Contents vi List of Figures viii List of Tables xii Nomenclature xiii Chapter 1: Introduction 1 1.1 Introduction 1 1.2 Czochralski growth technology 2 1.3 Literature review 4 1.3.1 Numerical simulation of sapphire Czochralski crystal growth 4 1.3.2 Internal radiation 6 1.3.3 Bubble in sapphire crystal 7 1.4 Motivation and objective 9 Chapter 2: Physical Model and Mathematical Formulations 13 2.1 Physical Model and assumptions 13 2.2 Mathematical Formulations 15 2.2.1 Governing equations 15 2.2.2 Boundary conditions 18 2.3 Numerical procedure 24 2.3.1 Dimensionless parameters 24 2.3.2 Mesh test 26 2.3.3 Solving step 30 Chapter 3: Results and discussion 33 3.1 The thermal and flow fields during the CZ process 33 3.2 The thermal stress during the CZ process 36 3.2.1 Assessment of the radiative heat transfer models 36 3.2.2 The thermal stress for crystals with different lengths during the CZ process 37 3.3 The solute concentration in the CZ system 39 3.4 Effect of the crystal and crucible rotation on the thermal and flow fields during the CZ process 42 3.5 Effect of the crystal and crucible rotation on the thermal stress during the CZ process 51 3.6 Effect of the crystal and crucible rotation on the solute concentration during the CZ process 54 Chapter 4: Conclusions and future works 75 References 77 Appendix A 81 Appendix B 84 Appendix C 86

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