Phase-field modeling of ATG instability in Allen–Cahn framework

The phenomenon of Asaro–Tiller–Grinfeld (ATG) instability is common in the molecular beam epitaxy (MBE) process. In order to investigate the ATG instability, a two-dimensional mathematical model is established, which considers elastic stress. The phase-field method is utilized to simulate the interface evolution and the stress distribution. Furthermore, the Allen–Cahn approach, coupled with the motion of the interface,
is used to investigate the morphology evolution. The results show that the thin film becomes unstable when it reaches a critical value. The
critical thickness of the thin film is about 5.08 nm. The interface breaks into several parts due to the effect of elastic stress. The validity and correctness of the model are verified by the relevant theoretical results. Moreover, the numerical model can provide the basis for optimizing the ATG instability phenomenon in the MBE process.