柴氏生長單晶矽應用晶體坩堝同向與反向旋轉 之碳雜質傳輸數値分析

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邱琮祐(Chung-Yu Chiu) 查詢紙本館藏

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機械工程學系

論文名稱

柴氏生長單晶矽應用晶體坩堝同向與反向旋轉之碳雜質傳輸數値分析
(Numerical simulation of Carbon transport during Czochralski silicon crystal growth under the application of crystal-crucible counter- and iso-rotations)

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摘要(中)

Czochralski法是生長高品質矽單晶的重要技術。其中矽晶片的電阻率和差排密度與晶棒中雜質有很重要關係，特別是氧和碳的濃度。因此雜質控制便成為Czochralski法製造單晶矽中的重要問題，然而矽晶棒中的碳濃度流動與設定參數之間的關係在現存文獻中尚未確立，在這項研究中，軸對稱數值模型用於研究Cz過程中碳的質量傳遞現象，考慮晶體和坩堝的不同轉速和方向，研究不同流動模式下的質量傳遞現象。
我們研究晶體和坩堝旋轉的哪種組合具有較低的碳濃度，並分別進行晶體坩堝同向與反向旋轉，找到造成碳濃度降低的物理機制。我們發現晶體旋轉10 rpm和反向坩堝旋轉3 rpm具有最低的碳濃度。而碳傳輸的行為與熔融矽中的對流和晶體下方的速度有關，介面的溫度、熔湯氧濃度也會影響碳雜質溶入熔湯的多寡。其中有三個重要的渦流，首先是Taylor-Proudman cell在晶體 - 熔體界面下，它是碳濃度重要的來源。其次，浮力渦流將碳帶入熔體，熔湯的自由表面的範圍成為一個重要因素。這是因為碳在浮力渦流中也會再透過自由液面蒸發，如果被其他渦流抑制，碳便不會在一開始時蒸發而直接流入下個渦流。第三，二次渦流位於Taylor-Proudman cell和浮力渦流之間，適當大小的二次渦流能使碳滯流於此渦流，使碳有更多機會流回到浮力渦流讓碳蒸發。

摘要(英)

Czochralski (Cz) method is widely used for the production of high quality silicon single crystal. Under high temperature condition of growth process, the undesirable impurities, such as oxygen and carbon, enter the silicon melt and their content strongly affects the resistivity and the dislocation density of the silicon wafer. A precise control of these impurities at a low concentration and uniform distribution, therefore, has played an important role for improving the quality of silicon crystals, especially large-sized crystals. To our best knowledge, there are few publications showing the effects of the operation parameters of CZ growth process on carbon concentration. In this study, a 2D axisymmetric numerical model is used to study the heat and carbon transport during the growth of a 6 inch-diameter silicon ingot. Different rotation speed and direction of the seed and crucible are considered to investigate their effects on the variation of heat, flow, and carbon characteristics.
The numerical simulations show that the carbon concentration gets lowest when the counter rotation rates of seed and crucible are 10 rpm and -3rpm, respectively. The behavior of carbon movement is related to the melt convection and the velocity under crystal-melt interface. While the temperature on free melt surface and oxygen in the melt will affect the quantity of carbon. The flow structure is included three main vortices: Taylor-Proudman cell (1), under the crystal-melt interface, buoyancy driven cell near the crucible wall (3), and the secondary cell (2) between (1) and (3). It was found that the carbon atoms are carried by cell (3) into the silicon melt. The carbon atoms are got out of the melt from the free melt surface. The larger effective evaporation area may reduce the carbon content in the melt due to the larger evaporation rate of carbon. Moreover, the secondary vortex (2) also affects the carbon transportation. Appropriate cell (2) may keep the carbon atoms stay longer in the melt and buoyancy cell (3) is easier to bring them to the free melt surface.

關鍵字(中)

★ 單晶矽
★ 柴式法
★ 碳濃度
★ 數值模擬

關鍵字(英)

★ Single crystalline-silicon
★ CZ
★ Carbon concentration
★ numerical simulation

論文目次

摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VI
表目錄 IX
符號說明 X
第一章緒論 1
1-1前言 1
1-2 柴式長晶法(Cz)介紹 1
1-3文獻回顧 4
1-4研究目的與動機 5
第二章物理模型與系統描述 10
2-1物理系統 10
2-2基本假設 10
2-3數學模型與邊界條件 11
2-3-1統御方程式 11
2-3-2熱場邊界條件 12
2-3-3流場邊界條件 13
2-3-3 碳氧雜質邊界層 14
2-4紊流模型 16
2-5無因次參數式 17
第三章研究方法 23
3-1數值方法 23
3-2雜質濃度求解 23
3-3網格測試 23
3-4收斂性測試 24
3-5數值與實驗結果驗證 25
第四章結果與討論 31
4-1固定晶轉10rpm與堝轉反向旋轉搭配 31
4-1-1 反向固定晶轉10rpm流場與碳濃度之關係 32
4-1-2反向固定晶轉10rpm速度場與熱場對碳濃度之影響 32
4-1-3反向固定晶轉10rpm轉速搭配整體小結 32
4-2固定堝轉-3rpm與晶轉反向旋轉搭配 33
4-2-1 反向固定堝轉-3rpm流場與碳濃度之關係 33
4-2-2反向固定堝轉-3rpm速度場與熱場對碳濃度之影響 34
4-2-3反向固定堝轉-3rpm轉速搭配整體小結 34
4-3固定晶轉5rpm與堝轉同向旋轉搭配 34
4-3-1 同向固定晶轉5rpm流場與碳濃度之關係 35
4-3-2同向固定晶轉5rpm速度場與熱場對碳濃度之影響 35
4-3-3同向固定晶轉5rpm轉速搭配整體小結 35
4-4固定堝轉3rpm與堝轉同向旋轉搭配 36
4-4-1 同向固定晶轉3rpm流場與碳濃度之關係 36
4-4-2同向固定晶轉3rpm速度場與熱場對碳濃度之影響 36
4-4-3同向固定晶轉3rpm轉速搭配整體小結 37
4-5同向旋轉與反向旋轉最低碳濃度比較 37
第五章結論與未來研究方向 64
參考文獻 65

參考文獻

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指導教授

陳志臣(Jyh-Chen Chen)

審核日期

2019-8-12

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