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研究生： 朱信旗
Hsin-chi Chu
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
指導教授： 陳志臣
Jyh-chen Chen
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
畢業學年度： 96
語文別： 中文
論文頁數： 85
中文關鍵詞： 柴氏法 、晶體生長 、氧化鋁單晶 、數值模擬
外文關鍵詞： Czochralski, crystal growth, sapphire, Numerical simulation
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    • 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。

    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.

    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

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