ABSTRACT
A small amplitude perturbation analysis is used to determine the conditions under which a solid film several hundred ångströms thick on a substrate will rupture. If the perturbation grows with time the film is unstable and rupture may occur, whereas if the perturbation decays the film is stable. Film rupture is caused essentially by diffusion of atoms along the free interface of the film which can, under certain conditions, amplify a perturbation applied to the film-gas interface. This surface diffusion is generated by a gradient of the chemical potential along the free interface. The chemical potential is affected by the curvature of the interface, by the pre-existing internal stresses normally found in thin films (they generate a strain energy term in the chemical potential) and by interaction forces between the atoms at the gas-solid interface with those of the film and substrate. The thin film is assumed to behave like an elastic body. The difference in the forces which act on a volume element in a film thinner than the range of interaction forces between the atoms of the film and substrate and the forces in a bulk solid is accounted for by introducing a body force into the equations of displacement of an elastic solid. Because of the difficulties in writing boundary conditions at the film-substrate interface, two limiting situations are considered: (1) a thin film on a rigid substrate and (2) a thin free film. A critical internal stress necessary for rupture is identified. The time of rupture is estimated from the inverse of the maximum growth coefficient of the perturbation. The dominant wavelength corresponding to the maximum growth coefficient gives an idea as to the size of the islands formed through rupture.
