利用物理氣相傳輸法(Physical vapor transport method)生長大尺寸(4吋以上)的單晶碳化矽為目前最常見的方式，本研究以數值方法分析4吋單晶碳化矽在高溫石墨長晶爐內生長時的溫度場、流場和應力場之間的相互影響，以有限差分法作為數值分析基礎。
由溫度場模擬結果顯示，坩堝構形會對溫度場分佈有很大的影響，本研究討論坩堝蓋與坩堝壁厚度對溫度場之影響，坩堝蓋厚度增加可以減少徑向溫度梯度，而坩堝壁厚度增加則會同時增加軸向溫度梯度與徑向溫度梯度。長晶速度會隨著軸向溫度差增加而上升，而徑向溫度則是會改變熱應力分佈，進而影響缺陷的產生。為了提升晶體生長的速度與品質，同時維持高軸向溫度差和低徑向溫度差的溫度分佈為改善生長晶體品質的重點。
流場的模擬結果顯示坩堝內部構形會改變流場的分佈，對晶體生長速度會造成影響，適當的坩堝構型設計，可以在提升長晶速度的同時，避免造成長晶速度不均勻的分佈而增加缺陷產生的機會。在粉末晶源區的溫度分佈也會影響流場的分佈，其中反應氣氛主要由高溫區產生，在低溫區反應氣氛則會再結晶阻礙反應氣氛流動，保持粉末晶源區之溫度平均分佈為改善粉末晶源使用效率之重要因素。
應力場模擬結果也顯示了晶體形貌對熱應力影響，較平坦的晶體表面會有較低的熱應力，預期可以減少缺陷產生的機率，其中最大應力會集中在晶體中心位置，可以預測晶體中心是比較容易產生缺陷的位置。
本研究藉由上述的模擬結果，提出坩堝構型的改進方向，在提升長晶速度的同時維持晶體平坦的生長面，預期可以減少熱應力造成的缺陷，達到改善晶體品質之目的。

Physical vapor transport (PVT) method is the major used method in growing large size single crystal silicon carbide (SiC) bulk. In this study, temperature, flow and thermal stress field is analyzed in numerical system by finite difference method.
From the simulation result of temperature field, the effect of different crucible lid thickness and crucible wall thickness is discussed in this study. The increasing of crucible lid thickness increases the axial temperature gradient, and the increasing of crucible wall thickness increases both axial and radial temperature gradient. The higher radial temperature gradient lead to higher crystal growth rate. The axial temperature gradient change may affect the formation of defects.
Proper crucible design can increase the crystal growth rate and avoid large growth rate distribution which may increase the formation of defects. In the powder source region, temperature distribution also influence the species flow distribution. The reaction species is produced mainly from the hotter zone, and will be consumed in the cooler zone in the powder source region which will block the species transport. Maintaining the average temperature distribution in the powder source region is the key to ameliorate powder source usage efficiency.
The thermal stress simulation results showed the relationship between thermal stress and crystal shapes. Crystal with flat surface shape have lower thermal stress distribution, and crystal with convex surface have higher thermal stress distribution.
To sum up, a modified crucible design guide is brought up to improve the crystal growth quality and productivity by increasing growth rate and avoiding thermal stress defects.

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