Kinetic model for thin film stress including the effect of grain growth

Source abstract

Residual stress during thin film deposition is affected by the evolution of the microstructure. This can occur because subsurface grain growth directly induces stress in the film and because changing the grain size at the surface affects the stress in new layers as they are deposited. We describe a new model for stress evolution that includes both of these effects. It is used to explain stress in films that grow with extensive grain growth (referred to as zone II) so that the grain size changes throughout the thickness of the layer as the film grows. Equations are derived for different cases of high or low atomic mobility where different assumptions are used to describe the diffusion of atoms that are incorporated into the grain boundary. The model is applied to measurements of stress and grain growth in evaporated Ni films. A single set of model parameters is able to explain stress evolution in films grown at multiple temperatures and growth rates. The model explains why the slope of the curvature measurements changes continuously with thickness and attributes it to the effect of grain size on new layers deposited on the film.