本研究利用數值模擬方法，探討如何在柴氏長晶中過程生產無缺陷矽晶棒，
因此研究不同鍋晶轉速對於 V/G 的影響，並分析不同鍋晶轉下的流場如何影響晶棒的縱向溫度梯度。以往在模擬缺陷時並不會加入熱應力的考量，因為熱應力在矽晶棒半徑小時影響不大，但隨著矽晶圓直徑愈來愈大，且電晶體通道長度持續縮減，因此也考慮了長矽晶時，不同鍋晶轉下，熱應力對缺陷的影響。最後模擬各參雜物濃度在不同向旋轉下，對缺陷團簇濃度和直徑的影響。本研究首先探討鍋晶轉在同向以及反向旋轉時，對徑向 V/G 的影響，並分析矽熔湯內的流場如何影響徑向的縱向溫度梯度，結果顯示為求較均勻的縱向溫度梯度，同向旋轉會優於反向旋轉。並分析同向旋轉下，不同鍋晶轉對於縱向溫度梯度的影響，提升晶轉會提高中心的縱向溫度梯度，降低邊緣的縱向溫度梯度，因此適當提升晶轉可以增加縱向溫度梯度的均勻度，而提升鍋轉則會提高中心的縱向溫度梯度，因此會產生較差的均勻度。而後比較了不同拉速對熱應力分布及大小的影響，可以發現當拉速提升時，壓應力會從中心往兩側分散，而拉應力則會集中於中心，另外同向旋轉下的熱應力與反向旋轉下的熱應力分布截然不同，反向旋轉下的壓應力會較集中於晶棒中心，拉應力則分散於兩側，而同向旋轉下的趨勢則完全相反。另外提升鍋轉與鍋轉對於熱應力的分布也呈現相反趨勢，也可以從固液界面的形狀去推論熱應力分布的情形。最後在參雜不同雜質時，各有不同表現，例如參雜硼會使間隙的團簇濃度下降，並使間隙團簇的大小增加；而參雜磷和銻時，則會使空缺的團簇濃度下降，並使空缺團簇的大小增加。

關鍵字：V/G、鍋晶轉、熱應力、參雜、團簇

Numerical simulation was used in this research in order to study how to manufacture the defect-free silicon crystal in the CZ method. Compare the effect to V/G in different rotation rate of crucible and crystal and analyze how the flow field affect the axial temperature gradient. With the increasing of the diameter of wafer and decreasing of the process node, it also considers the thermal stress effect to defect in different rotation rate of crucible and crystal. In the end, it simulates the doping concentration effect to the concentration and diameter of cluster in different rotation direction.
At first, we discuss the value of V/G in iso-rotation and counter rotation and analyze how the flow filed affect the axial temperature gradient. The simulations show we can get the more uniform value of axial temperature gradient in iso-rotation. This research also compares the axial temperature gradient in different rotation rate of crystal and crucible. We can get the more uniform value of axial temperature gradient by adjusting the rotation rate of crystal. Increasing the rotation rate of crucible will be worse if we want to get a uniform value of axial temperature gradient. On the other hand, the distribution of thermal stress in iso-rotation and counter rotation are totally different. We can observe the thermal stress in different rotation rate of crucible and crystal. The distribution of the thermal stress is opposite. We also can infer the distribution of thermal stress by observing the shape of the interface. In the end, we also can find the relationship between doping concentration, cluster density and cluster diameter.

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