Stability analysis of nanoscale surface patterns in ultrathin film coating

This paper presents a theoretical approach to the analysis of ultrathin film morphological stability under surface diffusion. Based on the simplified Gurtin–Murdoch model the surface elasticity has been taken into account. Due to the lattices mismatch, the film structure is subjected to misfit stress. It is assumed that the free surface can change its shape via mass transfer in order to minimize the total energy. Surface diffusion is considered the main mechanism leading to the morphological instability of the film surface. It is supposed that the atomic flow along the surface is proportional to the gradient of the chemical potential.  The change in surface profile amplitude is described by the linearized evolution equation, which is derived by taking into account the solution of the corresponding plane elasticity problem. Based on the proposed approach, the effect of the physical and geometric parameters on the morphological stability of the ultrathin film surface has been analyzed.