本研究以生長直徑 8 吋單晶矽之 CZ長晶法為對象，建立二維軸對 稱準穩態模型，利用 COMSOL 模擬長晶過程中的溫度場與速度場，並 採用 k-ε 紊流雙方程模型描述熔湯紊流行為；同時結合 MATLAB 進行 固液界面迭代計算，以求得穩定界面形狀。為驗證模型之適用性，並將 COMSOL 結果與專業長晶模擬軟體 CGSim 進行比較，探討不同晶體長 度與旋轉條件下之溫度場、速度場與界面變化。結果顯示，在無旋轉條 件下，隨晶體長度增加，晶體軸向導熱效應增強，使熔湯最高溫度下降、 界面附近溫度分佈趨於均勻，自然對流強度減弱，速度場逐漸穩定；固 液界面整體呈現中心較低、外側較高之形狀。比較兩套軟體結果可知， 兩者在溫度場與速度場整體趨勢上具有相似性，但在不同晶體長度造成 之界面相對高低排序上仍存在差異。在旋轉條件下，隨晶體轉速提高， 強制對流增強，使溫度場更均勻，且 COMSOL 與 CGSim 之預測結果 更為接近。此外，兩套軟體於相同操作條件下所需之加熱器功率並不完 全相似，顯示其在熱傳輸分配與整體能量平衡預測上仍存在差異。整體 而言，COMSOL 可有效模擬 CZ 長晶過程中溫度場、速度場與固液界 面之變化，具備作為製程分析與操作條件評估工具之潛力。;In this study， a two-dimensional axisymmetric quasi-steady-state model was established to investigate the CZ growth process of 8-inch single-crystal silicon. COMSOL was used to simulate the temperature and velocity fields during crystal growth， while the turbulent behavior of the silicon melt was described by the standard k-ε two-equation turbulence model. MATLAB was further coupled with the simulation to iteratively determine the solid–liquid interface until a stable interface shape was obtained. To assess the applicability of the model， the simulation results obtained from COMSOL were compared with those predicted by the specialized crystal growth simulation software CGSim under different crystal lengths and rotation conditions. The simulation results show that， under the non-rotating condition， increasing crystal length strengthens axial heat conduction in the crystal， thereby reducing the maximum melt temperature， making the temperature distribution near the interface more uniform， weakening natural convection， and stabilizing the flow structure. The solid–liquid interface generally exhibits a lower center and a higher outer region. Comparisons between COMSOL and CGSim indicate that the two tools show similar overall trends in the temperature and velocity fields， although discrepancies remain in the relative interface-height distribution for different crystal lengths. Under rotating conditions， increasing crystal rotation speed enhances forced convection， resulting in a more uniform temperature field and closer ii agreement between the predictions of COMSOL and CGSim. Overall， the results demonstrate that COMSOL is capable of effectively describing the thermal flow behavior and solid–liquid interface evolution during the CZ crystal growth process， and thus has considerable potential as a tool for process analysis and operating-condition evaluation.
