本研究為發展新的數學模式來模擬之砷化鎵在布氏爐中之長晶過程。過程中包含之流場、溫度場、濃度場、隨時間變化之固界面的位置與形狀及長晶時於液固界面會釋放出溶質與潛熱，這些都是本文探討的內容。在數值方法上採用有限差分法，對於流場方面則採用SIMPLEC法來計算，溫度場之潛熱效應是採用本文修正之等效比熱法來處理，而濃度場則是提出液固界面加點法來估算液固界面所釋放到液體之溶質。修正等效比熱法和界面加點法與其他解法作比對分析，同時其計算結果與文獻上之正解很吻合。從砷化鎵長晶之分析結果，發現由於液、固態之熱傳導係數差異和潛熱效應來產生自然對流，而自然對流對於溶質再分布有強烈主導性，但在溫度場中其影響則不大。為了減緩界面形狀之撓曲，本文根據液固界面之能量平衡來調整爐壁溫度分佈，近而得到較平坦之界面形狀，並降低流場之強度與改善結晶後軸向和徑向之偏析現象。

This work is to develop a new mathematical model to simulate the crystal growth in a Bridgman furnace. The relationship among the flow, temperature, concentration fields, the released latent heat and the curved solid/liquid interface was investigated. In this paper, the numerical scheme is the finite different method. The SIMPLEC algorithm is used to solve the flow field. The effective specific heat method is modified to handle the release of latent heat. Adding extra nodes at the interface is proposed to deal with the solute release at the solid/liquid interface. The computational results of these two new methods are compared with those of other methods and very consistent with the exact solutions from the literature. From the analysis of the crystal growth, it can be found that the curved solid/liquid interface is caused by the unequality of liquid and solid thermal conductivities and the latent heat. The curved interface induces the natural convection, which has a great effect on the solute redistribution, but not on the temperature field. To ease off the effect of curved interface, a modified temperature profile of furnace wall was applied according to the heat balance at the solid/liquid interface and its results have less curved interfaces, weaker flow fields and lower segregations along either the radial or the axial direction than those of unmodified one. With the modified method, it could be expected to have the better crystal quality, having more uniform distribution of dopant.

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