晶體生長是一項重要的技術，尤其是泡生法(Kyropoulos)這種主要應用在工業上生長大型晶體的低溫度梯度法。對於這種生長大尺寸晶體，且處於高溫無法直接觀測的生長法，必須使用數值模擬的方式獲得初始的基本資料，以減少實驗所耗費的時間與成本。因為泡生法主要是調整加熱功率與取熱大小來控制整個晶體生長的過程，因此晶體生長爐所提供的加熱器設計、熱場設計與通水取熱方式的設計等熱流控制問題對於生長品質優良之藍寶石單晶來說相當重要。為了確保生長藍寶石單晶的品質，本文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，以獲得各項熱流場分佈情形資訊。本研究本文選用以有限元素法(FEM)為基礎的套裝軟體 COMSOL Multiphysics，進行模擬分析工作。在模擬研究的初期，本文使用準穩態的方式針對鳥籠式加熱器系統生長氧化鋁單晶過程之熱流場、固液界面形狀與晶體外形分佈作深入的研究。結果發現晶體生長過程中，溫度場會受到浮力作用影響而扭曲變形；熔湯內經過設計只有一個渦漩；固液界面形狀會越來越凸向熔湯，待固液界面尾端接近坩堝底部時，因為固液界面形狀變平坦而使凸出長度開始下降，模擬完成之晶體與工業上實際長晶之梨子狀相似。之後本文亦針對分段加熱器的調整對晶體形狀、固液界面形狀、固液界面溫度梯度與晶體熱流場分佈的影響，而針對結果做了修正，得到當加熱器的加熱功率比率為1.3:1:0.8為初始時，亦即上加熱器比中加熱器功率高，固定其他兩個加熱器只調降上加熱器，可獲得比較接近等直徑的晶體，且晶體的溫度梯度最小。並且分析了晶體內部非等向熱應力分佈情況，在本文所模擬的低溫梯系統中，熱應力分佈會呈現幾乎軸對稱的效果，而非等向的效果並不顯著。本研究針對複雜之KY法藍寶石晶體生長系統簡化分析，可提供模擬之數值結果供實際長晶做為參考。The Kyropoulos method is the low temperature gradient technology and mainly used in industrial growth of large size sapphire crystals. During the large size sapphire crystal growth, the Kyropoulos (KY) furnace has high temperature and can not be directly observed. It must use the numerical simulations to obtain the growth data and conditions to reduce the cost and paste of experiments. The Kyropoulos method must reduce the power history and control the water cooling rate to get the high quality sapphire single crystal. In this study, the governing equations are solved numerically using the COMSOL Multiphysics software based on the finite-element method and the quasi-steady state approximation in the present study. The results show that the isotherms are distorted by the strong buoyancy force and it has only one vortex in the melt and higher convexity of crystal-melt interface. The convexity decreases when the crystal-melt interface is closed to the bottom of the crucible since the interface shape becomes flattened. The crystal shape is pear-liked as the industrial experiment. Then we have used the different power arrangements in a three-zone resistance heated KY furnace to calculate the crystal shape, solid-liquid interface shape, temperature gradient and heat and flow distributions. The power ratio was maintained at a constant during the growth process. The power ratio of zone A: zone B: zone C equal to 1.3:1:0.8 has a lower power and temperature gradient along the crystallization front, but the remelting phenomenon may occur in the middle stages during the growth process. Then this case is selected, and the power of zone A decreases with the power of zone B and zone C being fixed during the growth. The results show that it has the lowest temperature gradient along the crystallization front and the crystal diameter after crown growth is almost constant. The thermal stress distribution during the growth has been computed. It is almost axisymmetric. Therefore, the effect of anisotropic structure of the sapphire crystal on the thermal stress distribution may be insignificant due to the lower temperature gradient inside the sapphire single crystal.
