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.

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