Adaptive Phase Field Modeling of Morphological Instability in Directional Solidification of SiGe Alloy

固化過程中，界面失穩是一個很重要的課題，因界面形態會影響材料品質。一般常見的物質已經有很多研究投入於其中，例如金屬材料NiCu及有機材料SCN-ACT等，但對於高熔點晶體如矽(Si)等，由於其熔點高達1683 K的關係，相關實驗較少。近年來，Fujiwara et al.發表對矽凝固界面形態觀察的研究，於2009年開始，更對單晶矽及矽鍺合金的界面不穩定性現象，發表了一些深入且結構完整的文章，但是相關模擬還是很缺乏‧本文主旨為使用相場模式模擬Fujiwara的實驗並與其結果相比較，開始時選用該實驗所發表參數進行模擬，其中提出實驗溫梯G = 8 K/mm，但模擬的結果並無法得到不穩定行為。於此我們進一步使用熱傳分析及古典理論分析，得到理論溫梯應為G = 1 ~ 2 K/mm，並將此溫梯代入二維的相場模式，可以得到不穩地性的行為。在確認不穩定性參數後，我們也根據實驗所得到的界面形態，討論模擬中一些重要的參數，如凹陷動力學在相場模式中為必要的考量參數，其扮演角色為決定奇異面的形態，而界面能高非均向性強度(ε4)，所扮演的角色為不穩定波長之選擇因子。在矽鍺合金實驗中，實驗觀察出不同鍺濃度下，其臨界長速滿足古典理論預測，另一方面，不同晶向的條件與不穩定行為無關，在此我們的模擬也得到相同的結論。最後，我們模擬出在高濃度著(15 at%)的條件下，和實驗類似的界面形態。In the solidification process, the morphological instability of solidification is a very important problem, people had discussed some metal or organic material such as NiCu and SCN-ACT for this topic very well. But because of the high melting point of silicon, there are few paper discuss the instability phenomenon for silicon growth. From 2002, Fujiwara et al. had published some experiment result for silicon growth, and from 2009, they published more experiment for the instability phenomenon for silicon and silicon –germanium. At first we use the parameter given by Fujiwara, they claim the temperature gradient of the system is 8 K/mm, but we can’t simulate the instability. And then we use the classical theory and heat transfer analysis, we found that the temperature gradient is 1 K/mm, and by using the parameter we can found the instability phenomenon in 2D simulation. We also discuss the impact of some physical parameters, such as the cusp kinetic is the requirement and the role of the surface energy anisotropy is determining the wavelength of instable pattern. In the SiGe system, we found the SiGe instability follow the classical theory and the instability behavior is independent of orientation, both of the two conclusion is the same as Fujiwara et al claim. Finally, we simulate the morphology like experiment result very well for 15 at% Ge