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研究生:謝豐仰
研究生(外文):Feng-Yang Xie
論文名稱:砷化鎵長晶之熱與質量傳遞分析
論文名稱(外文):Analysis of Heat and Mass Transfer For Crystal Growth of GaAs
指導教授:趙隆山
指導教授(外文):Long-Sun Chao
學位類別:碩士
校院名稱:國立成功大學
系所名稱:工程科學系碩博士班
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:116
中文關鍵詞:砷化鎵長晶
外文關鍵詞:mass transferGaAs
相關次數:
  • 被引用被引用:2
  • 點閱點閱:548
  • 評分評分:
  • 下載下載:102
  • 收藏至我的研究室書目清單書目收藏:0
摘 要
半導體材料砷化鎵於長晶的過程中,包含了溫度場、流場、濃度場的互相耦合、液固相變化的潛熱效應、液固界面之移動與界面形狀變化、長晶時的濃度再分佈等,是一個複雜的問題,其中,濃度場中的溶質偏析現象,特別受到關注。
本文以軸對稱的模式來模擬砷化鎵在布氏爐中的長晶過程。數值方法在流場方面是使用SIMPLEST演算法來求解,以等效比熱-熱焓法來處理凝固時發生之潛熱效應,使用控制體積推導的方式去處理濃度場在液固界面的效應。本文以此模式來探討在不同工作條件(潛熱、雷利數)下,溫度場、液固界面形狀、流場強度及濃度再分佈間的相互關係。
研究發現,撓曲的液固界面是造成自然對流的主因,而自然對流對於溶質在分佈有強烈的主導性。潛熱釋放時,使俓向溫度梯度加大,造成更撓曲的液固界面的形狀及更強的流場,使得液固界面溶質偏析的現象增大,藉由調整爐壁溫度分佈發現,可得到較平坦的液固界面,進提昇界面之溶質分佈均勻度,來改善長晶之偏析現象。最後我們也使用控制體積修正的方式將界面附近的流線崎嶇現象,加以改善。
ABSTRACT
The crystal growth of GaAs includes the coupling of flow, temperature and concentration fields, the release of latent heat, the movement and the shape variation of solid/liquid interface, and the solute redistribution of dopant. This is a very complicated problem, in which especially the solute segregation obtains a great attention. In this paper, an axi-symmetric model was built to simulate the crystal growth of GaAs in a Bridgman furnace. The numerical scheme was the finite difference method. The SIMPLEST algorithm was used to solve the flow field and the specific heat/enthalpy method was applied to handle the release of latent heat. A special control-volume treatment of concentration field at the solid/liquid interface was utilized to derive the finite difference equations there. The proposed model was used to investigate the relationship among the flow and temperature fields, the shape of solid/liquid interface, and the solute redistribution under different working conditions (different thermal boundary conditions, Rayleigh numbers, and Stefan numbers). From the computing results, it can be found the natural convection is primarily induced by the curved solid/liquid interface, which is caused by the release of latent heat and the difference between solid and liquid thermal conductivities. The curved interface makes the segregation problem worse than the less curved one. The flow field induced by natural convection has little effect on the temperature field, but a great effect on the concentration field. Modifying the temperature distribution along the furnace wall can make the solid/interface flatter (less curved) and the natural convection weaker, which could improve the condition of solute segregation.
目錄
摘要………………………………………………….………. I
英文摘要…………………………………………….………. II
誌謝………………………………………………………….. III
目錄………………………………………………….………. Ⅳ
表目錄………………………………………………….……. Ⅶ
圖目錄………………………………………………….……. Ⅷ
符號說明…………………………………………….………. XII
第一章 緒論………………………………………………… 1
1-1研究動機…………………………………………... 1
1-1-1半導體材料…………………………………. 2
1-1-2半導體材料長晶方法之概述………………. 2
1-2文獻回顧…………………………………………... 4
1-3研究目的與方法…………………………………… 7
第二章 理論分析…………………………………………… 9
2-1問題描述………………………………………….. 9
2-2基本假設………………………………………….. 9
2-3統御方程式……………………………………….. 10
2-4起始條件與邊界條件…………………………….. 11
2-5無因次變數與參數……………………………….. 14
2-6無因次統御方程式……………………………….. 15
2-7無因次化後起始條件與邊界條件……………….. 16
第三章 數值方法…………………………………………… 18
3-1交錯網格與控制體積示………………………….. 18
3-2差分方程式與解法……………………………….. 19
3-3溫度場數值分析………………………………….. 20
3-4流場數值分析…………………………………….. 25
3-4-1 SIMPLE 演算法…………………….……… 25
3-4-2 SIMPLE法與SIMPLEST法之比較………. 27
3-5流場差分方程式之液固界面效應修正…………... 28
3-6 濃度場之液固界面的效應……………………….. 30
3-7收斂條件…………………………………………... 32
3-8求解的流程………………………………………... 33
第四章 實例測試與討論…………………………………… 34
4-1濃度場數值解測試……………………………….. 34
4-1-1統御方程式、初始條件及邊界條件….….. 35
4-1-2無因次化…………………………………… 36
4-1-3測試結果討論……………………………… 36
4-2速度場與溫度場數值測試……………………….. 38
第五章 結果與討論………………………………………… 39
5-1潛熱對流場、溫度場及濃度場的影響………….. 39
5-1-1不考慮潛熱……………………………………... 39
5-1-2 考慮潛熱………………………………….......... 41
5-2調整熱邊界條件………………………………….. 43
5-3 流場差分方程式之液固界面效應修正…………. 44
第六章 結論………………………………………………… 46
參考文獻…………………………………………………….. 47
附錄A……………………………………………………….. 104
附錄B……………………………………………………….. 108
附錄C……………………………………………………….. 110
附錄D……………………………………………………….. 114
自述
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