物理氣相傳輸法(Physical vapor transport method)為製備碳化矽塊材之主要方式，本研究以數值方法針對其高溫石墨長晶爐內部進行熱場及流場之模擬分析，採用有限差分法建立模擬系統，包含電磁、熱傳、質傳模組及成核能計算。本研究觀察及分析數值模擬之結果，由此對製程進行改善。
由熱場模擬結果發現：為避免熱應力產生，在晶種尺寸增大時，徑向溫度分佈均勻化是改善重點。
由流場模擬結果可知：反應氣氛由粉末晶源高溫區分解產生後，部分被低溫區之再結晶反應消耗，而沒有傳輸至晶種表面，且隨著高溫區孔隙度上升，對反應氣氛流動有加速作用；相對地，低溫區因再結晶而形成一緻密區塊阻擋氣氛流動，低溫區過大將降低粉末利用率且不利反應氣氛傳輸。
由成核自由能之計算結果發現：碳化矽晶體的成核模式與晶種表面過飽和度及表面自由能狀態有關，且存在一臨界過飽和度為二維與三維成核的轉變點。碳化矽生長過程中，晶種表面與粉末晶源間之軸向溫度梯度越小，晶種表面過飽和度越低，碳化矽不同多型間之成核能差越大，較不易發生多型混雜生成的狀況。但是，當晶體厚度增加，晶種與晶體間的晶格失配可能使界面能提高，並在低於臨界過飽和度時產生三維核島，易造成不規則排列。
綜合以上，本研究提出一加熱線圈集中於長晶前端與粉末晶源的線圈非等距設計，兼顧粉末晶源之充分加熱及縮小軸向和徑向溫度梯度，並且在晶體厚度增加後可藉由降低填充氬氣壓均勻調整過飽和度，藉此避免三維核島因晶格失配而出現，避免異質介在物和缺陷在晶體中產生。

Physical vapor transport method (PVT) is the major process for silicon carbide bulk production. In this study, thermal and flow numerical simulation system for high-temperature PVT crucible is built by finite element method (FDM), including electromagnetic induction heating module, heat transport module, mass transport module and nucleation energy calculation. Simulation results are checked and analyzed and some process improvements are brought up according to them.
From thermal simulation results, it is a key point to reduce the radial temperature gradient on seed surface for avoiding thermal stress, when seed size enlarged.
From species transport simulation results, it is found that reaction species are not produced from powder source surface but mainly come from hotter zone of powder source. Powders in hotter zone sublimate to reaction species and the flow accelerates because of increasing porosity. However, parts of reaction species are consumed in cooler zone instead of reaching seed surface. Recrystallization occurs in cooler zone and makes powders denser to block gas flow.
From calculation of nucleation energy, it found that the nucleation mode of silicon carbide crystal is related to supersaturation ratio and surface energy status of seed surface. Furthermore, there is a transition from 2D to 3D nucleation mode and it is called critical supersaturation ratio. The 3D islands may bring about arrangement disorder and be the origin of defects. In growth process, the lower supersaturation ratio is proper for single-polytype crystal growth because of larger nucleation energy difference between polytypes, but it should not be lower than critical supersaturation to avoid 3D islands. With crystal thickness increasing, the interfacial energy may rise because of accumulating crystal mismatch and result in 3D islands occurring.
Furthermore, the supersaturation ratio is in a positive correlation with axial temperature gradient between seed and powder source. Therefore, the supersaturation ratio can be adjusted by crucible temperature distribution.
To sum up, a non-equidistant heating coils design is brought up to look after both the proper powder source utilization and temperature gradient reduction. In this improved design, the coils are separated to two groups and respectively center around seed surface (or crystal front) and powder source. Moreover, to avoid 3D nucleation islands occurring, the supersaturation should be risen above critical supersaturation ratio by reducing inner argon pressure with crystal thickening.

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