Modeling the development and relaxation of stresses in films

Abstract

The mechanics for the development and relaxation of stresses in films is briefly reviewed. The discussion initially focuses on how stresses are distributed within a film and substrate, and on the resultant deformations that these stresses induce. Although the particular case of an elastically homogeneous system with a uniform stress within the film is addressed in detail, the modifications that would result from a nonhomogeneous system, or a nonuniform stress, are also outlined. A brief discussion of stress relaxation in epitaxial systems and the glide of dislocations in thin films then follows. In polycrystalline films, diffusion of atoms as well as the motion of dislocations can contribute to the relaxation of stresses. It is possible to use constitutive models for the different relaxation processes to predict the development of stresses during thermal cycling. A comparison of these predictions with experimental observations allows general conclusions about the dominant relaxation mechanisms that operate in particular thin-film systems to be made. An additional mechanism of stress relief is that of cracking and delamination. In this paper, just one mechanism is addressed - that where a brittle film cracks. An energy-balance calculation leads to results for a critical film thickness below which cracking will not occur and for the crack spacing as a function of both film thickness and residual stress.