柴氏長晶法是最常用於生長大尺寸單晶矽的方法，而生長單晶矽的過程中，由於爐體內的溫度相當高無法直接觀察到矽熔湯內的熱流場情形，因此使用數值模擬方法來掌控爐體內的情況，以減少實驗所耗費的成本和時間。
本研究使用以有限元素法基礎的COMSOL Multiphysics軟體對柴氏長晶法爐體內的熱流場做模擬分析，以獲得爐體內的熱流場情形與相關資料。主要模擬矽晶棒在各階段生長過程中熱流場和濃度的分佈情形，從尚未長晶至不同長晶過程中觀察矽熔湯內的熱流場及液固界面形狀變化。包括坩堝及晶軸旋轉對矽熔湯的影響、裝設輻射隔絕器對爐體內的熱流場及濃度場的影響。
模擬結果發現矽晶棒生長過程中，矽熔湯內的流場主要受到自然對流影響導致溫度分佈不均，藉由坩堝及晶軸旋轉能抑制自然對流，改善矽熔湯內的熱流場，而液固界面形狀會受到拉速的影響導致有不同的形狀產生，也會影響到晶棒內部缺陷形態，裝設輻射隔絕器能有效的引導氬氣流動會對濃度場造成影響和降低加熱器的使用功率。透過本研究的模擬結果提供生長單晶矽的參考依據。

Czochralski method is the most commonly used to grow large single crystals of silicon. In the growth process of silicon single crystal, due to the furnace body of very high temperature, the thermal flow within the melt pool cannot be observed directly. Consequently, the numerical simulation is employed to control the situation in the furnace, which could help to reduce the cost and time of crystal-growth experiments.
The study is to use COMSOL Multiphysics software to simulate the thermal flow in the furnace of Czochralski method during the crystal growth. It is expected to obtain the temperature and velocity fields and the relevant data in the furnace. It is mainly based on the different growth stages of the silicon ingot to simulate the temperature, velocity and concentration fields and the shape variation of the crystal/melt interface. In the simulation, the crucible and crystal rotations and the radiation shield are considered to analyse their effects on the heat flow and concentration fields and the interface shape.
From the simulation results of the silicon crystal growth, the natural convection, caused by the coupled effect of temperature and flow fields, could make the temperature distribution of the melt pool uneven. By using the rotation of the crucible and the crystal, the natural convection could be suppressed and the thermal flow field would be modified. Consequently, the impact of pulling rate could not make the crystal/melt interface produce different shapes and affect the internal defects. The installation of the radiation shield could effectively guide the gas flow and reduce the input heater power.

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