This paper investigates the morphological stability of epitaxial films growing heteroepitaxially on ultra-thin substrates. The misfitting strain model is incorporated into the quasi-static mechanical equilibrium system. The interfacial evolution equation between the vapour and film phases is used to solve the film evolution. The perturbation method of normal modes is used to derive the analytical form of the normal-mode growth rate. Additionally, this paper investigates the dynamic behaviour of the vapour-film interface. The results of the study show that a decrease in substrate thickness tends to stabilize the system regardless of whether the stiffness ratio, ρ (i.e: the ratio of film stiffness to substrate stiffness) is less than, equal to or greater than unity. Furthermore, it is found that the effects of a finite substrate thickness on the stability behaviour of the system are quite profound, and that this is particularly true when the film thickness is close to hc with values of stiffness ratio greater than unity.
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