長晶實驗是一項昂貴的實驗程序，尤其是類似熱交換器長晶法(HEM)這種生長大型晶體的方法。對於這種問題的解決之道，是使用數值模擬的方式先期獲得一些基本的資料，再反覆推知所需的生長條件以減少實驗所費的時間。由於熱交換器長晶法(HEM)主要是控制溫度梯度來控制整個晶體生長的過程，因此加熱爐所提供的整體熱場設計、熱交換器取熱方式的設計等熱流控制問題對於生長品質優良之氧化鋁單晶來說相當重要。 為了確保生長sapphire單晶的品質我們須掌握坩堝內之生長情況；因此使用模擬的方法對坩堝內之情形加以分析，以獲得各項熱流場情形資訊。本研究我們選用以有限元素法（FEM）為基礎的套裝軟體FIDAP，進行模擬分析工作。在模擬研究的初期，我們使用準穩態的方式針對不同生長變數如爐體內環境溫度及熱傳係數、熱交換器內之溫度、熱傳係數及取熱區大小，對生長氧化鋁單晶過程之熱流場及固液界面形狀的影響作深入的研究，各種模擬的結果與過去的實驗比較是吻合的。之後我們亦分析有關溫度梯度大小、不同坩堝形狀等因素，對生長氧化鋁單晶過程之熱流場及固液界面形狀的影響，結果發現愈高的正向溫度梯度對HEM長晶愈有利。另由於高溫狀況下生長材料之熱傳導係數值一般均無法確知，所以我們也對此進行分析比較，發現較小的熱傳導係數值會有較大的固液界面凸出率；最後我們也針對非等向性材料性質之影響，使用ANSYS套裝軟體進行三維模擬相關之研究，發現不同軸向的熱傳導係數值會影響生長的凸出率。 這些分析結果將可作為HEM系統單晶生長進行時之重要參考指標，並可為將來深入研究HEM單晶生長機制的基礎。未來的研究方向則可依據真實的生長情形推定相關參數值後，再針對合於實際狀態的長晶情形加以分析，同時藉由模擬結果與實驗比對的過程，希望未來能對整個HEM長晶系統作出細部的改善，以期能得到更佳之系統穩定性，而使長晶過程更順利，而能生長出高純度、大尺寸氧化鋁單晶。 Sapphire single crystals are widely used in variety of modern high-tech applications. Among crystal growth methods, the heat exchanger method (HEM) is a good commercial method for growing the larger, high-optical-quality sapphire. The finite element software FIDAP is employed to study the temperature and velocity distribution and the interface shape during sapphire crystal growth process using HEM. In the present study, the energy input to the crucible by the radiation and convection inside the furnace and the energy output through the heat exchanger is modeled by the convection boundary conditions. The associations of the various parameters are studied. It is found that the contact angle is obtuse before the solid-melt interface touches the sidewall of the crucible. Therefore, hot spots always appear in this process. The maximum convexity decreases significantly when the cooling-zone radius (RC) increases. The maximum convexity also decreases significantly as the combined convection coefficient inside the furnace (hI) decreases. In the second part, the effects of the thermal distribution in a HEM crystal growth system on the convexity of the melt-crystal interface and the rate of crystal size increase have been performed to investigate. A higher environmental temperature generates higher maximum convexity. During the environmental temperature reduction process, the crystal quickly enlarges in size as the environmental temperature approaches the melting point of the growing crystal. Therefore, decreases in the environmental temperature must be slow to obtain a constant rate of crystal size increase. An upward temperature gradient decreases the convexity of the melt-crystal interface and the hot spot area. An upward temperature gradient case is more adapted to the maintenance of a constant increase in the crystal size during a decreased in the furnace temperature to near the melting point of the growing crystal. The influences of crucible wall and the conductivity of the sapphire on the growth process have been also investigated in the present study,. We found that a lower conductivity of sapphire generates higher maximum convexity. The finite element software ANSYS is also employed to study the effects of sapphire’s anistropic conductivity. These results will be the important index of the HEM crystal growth process and for further study.
