外加水平式磁場柴氏長晶法生長矽單晶之熱流場數值模擬研究

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黃正權(Cheng-chuan Huang) 查詢紙本館藏

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能源工程研究所

論文名稱

外加水平式磁場柴氏長晶法生長矽單晶之熱流場數值模擬研究

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摘要(中)

本研究利用數值模擬方法，在柴式晶體生長過程外加水平式磁場，探討水平磁場對熔湯流場及溫場分布之影響。分析熔湯溫度分布與速度分布在無磁場與水平式磁場下之變化，並比較不同晶體拉速對其之影響。水平式磁場的熔湯流動流動型態受羅倫茲作用呈現三維流動分布，在平行磁場與垂直磁場兩方向形成不同的渦流流動型態，其平行磁場方向剖面之熔湯流動大多為往堝底流，而在垂直磁場方向之流動則保留完整的渦流型態，而熔湯中固液界面下方會形成一個流速較快的盤旋渦流，此渦流使的水平式磁場中固液界面形狀較無磁場時平坦。其兩剖面之熔湯對流的差異會影響會其熔湯內的熱量傳遞，因此熔湯內溫度分布在兩剖面產生不同分布曲線，其堝壁最高溫亦不相同。水平式磁場之堝壁溫度比無磁場作用時之堝壁溫度高，因此熔湯內之溫度梯度較大，且其固液界面上之溫度梯度亦較大。熔湯流速在水平式磁場中小於無磁場，且熔湯內之速度分布不同，其熔湯中大部分區域之流速緩慢，僅在靠近三相點附近流速較快，比較兩這之自由表面熔湯流速，水平式磁場下之熔湯自由表面流速大幅降低。不同晶體拉速下，水平式磁場固液界面形狀變化相對大於無磁場，在無磁場與水平式磁中，堝壁最高溫會隨著晶體拉速的提高而減少，但是其固液界面上之溫度梯度隨著晶體拉速提高而增加，熔湯速度場受晶體拉速影響不大，熔湯內速度分布保持相似，且自由表面附近之熔湯流速變化極小。

摘要(英)

In this study, the numerical simulation has been performed in order to clear the effect of transverse magnetic field during crystal growth that compared the flow of melt, temperature distribution and velocity distribution in the melt between transverse magnetic field and no magnetic field, and also compared in different crystal pulling rate. The Lorentz force induced by transverse magnetic field strongly affected the melt flow. Melt flow was Three-dimensional, so there were two different flow patterns on plane along and crossing transverse magnetic field, separately. Melt flow went down to the bottom of crucible on the plane along magnetic field. By contrast, melt flow maintained with full vortex on the plane crossing magnetic field. A stronger spiral vortex motion is formed under the crystal-melt interface that makes the interface in transverse magnetic field was more uniform in no magnetic field. Heat transfer was influenced by these two different flow patterns in two directions. Thus, both temperature distribution and the highest temperature were different in two perpendicular directions. Temperature of crucible with transverse magnetic field is higher than that without magnetic field. So, not only the temperature gradient but also the temperature gradient on melt-crystal interface with transverse magnetic field was higher than that without magnetic field. Melt flow velocity with transverse magnetic field was lower than without magnetic field and there were different velocity distributions in transverse magnetic field and without magnetic field. With transverse magnetic field, most parts of melt flow were slow, but velocity increased near the triple point. At the melt-free surface, flow velocity with transverse magnetic field was strongly lower than that without magnetic field. This paper also discussed about melt flow patterns, temperature field, and velocity field using different crystal growth rates with transverse magnetic field and without magnetic field. With increasing crystal growth rate, the melt-crystal interface of transverse magnetic field was more convex toward crystal than one without magnetic field. Melt temperature field is similar to each other with different crystal growth rates, but the highest point decreased with increasing crystal growth rate. However, the temperature gradient on melt-crystal interface increased with increasing crystal growth rate. Melt velocity field was little affected by changing crystal growth rate, and velocity field was similar to each other, and so as near melt-free surface the velocity changed slightly.

關鍵字(中)

★ 磁場
★ 氧
★ 柴氏長晶法
★ 矽單晶

關鍵字(英)

★ oxygen
★ Czochralski (CZ)
★ transverse magnetic field
★ single crystalline-silicon (sc-si)

論文目次

摘要...................................................i
Abstract...............................................ii
誌謝...................................................iv
目錄...................................................v
圖目錄.................................................vii
表目錄.................................................x
符號說明...............................................xi
第一章緒論............................................1
1-1 前言...............................................1
1-2 文獻回顧...........................................1
1-3 研究動機與目的.....................................4
第二章研究方法........................................7
2-1 物理系統...........................................7
2-2 基本假設...........................................7
2-3 數學模式...........................................8
2-3-1 統御方程式...................................8
2-3-2紊流計算方式..................................9
2-3-3 邊界條件.....................................9
2-4 無因次參數.........................................11
2-5 數值方法與網格、收斂條件測試.......................14
2-5-1 數值方法.....................................14
2-5-2 網格與收斂條件測試...........................14
第三章結果與討論......................................22
3-1外加磁場對柴氏長晶法之影響機制......................22
3-1-1 磁場對熔湯之機制.............................22
3-1-2 水平式磁場下晶體旋轉與坩堝旋轉之機制.........23
3-2 水平式磁場之熔湯流場、熱場與速度場分析.............24
3-2-1 熔湯流場分析.................................24
3-2-2 熔湯熱場分析.................................26
3-2-3 熔湯速度分析.................................27
3-3 水平式磁場下不同晶體拉速之影響.....................28
3-3-1 不同晶體拉速之熔湯流場分析...................28
3-3-2 不同晶體拉速之熔湯流場分析...................29
3-3-3不同晶體拉速之熔湯速度場分析..................29
第四章結論與未來研究方向..............................62
4-1 結論...............................................62
4-2 未來研究方向.......................................63
參考文獻...............................................64

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指導教授

陳志臣(Jyh-chen Chen)

審核日期

2012-1-30

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