A kinetic model for stress generation in thin films grown from energetic vapor fluxes

Abstract

We have developed a kinetic model for residual stress generation in thin films grown from energetic vapor fluxes, encountered, e.g., during sputter deposition. The new analytical model considers sub-surface point defects created by atomic peening, along with processes treated in already existing stress models for non-energetic deposition, i.e., thermally activated diffusion processes at the surface and the grain boundary. According to the new model, ballistically induced sub-surface defects can get incorporated as excess atoms at the grain boundary, remain trapped in the bulk, or annihilate at the free surface, resulting in a complex dependence of the steady-state stress on the grain size, the growth rate, as well as the energetics of the incoming particle flux. We compare calculations from the model with in situ stress measurements performed on a series of Mo films sputter-deposited at different conditions and having different grain sizes. The model is able to reproduce the observed increase of compressive stress with increasing growth rate, behavior that is the opposite of what is typically seen under non-energetic growth conditions. On a grander scale, this study is a step towards obtaining a comprehensive understanding of stress generation and evolution in vapor deposited polycrystalline thin films.