Effect of Compliant Interface on the Curvature and Stress of Micron-Size Film-Substrate Composite Structure

The stress inside the film or substrate can be evaluated by the Stoney's formula and its modified/extended formula, which links the curvature to the stress state inside the composite. However, the Stoney's formula and its modified/extended formula assume the rigid interface, which allows no interfacial slip. The compliance of interface results in an interfacial slip, which can significantly affect the distribution of stress inside the film and substrate. The interface layer with the effect of interfacial slip plays the vital role of stress transfer between the film and substrate. The curvatures of film and substrate are shown to be different in general with the presence of interfacial slip and deviate significantly from that predicated by the models of rigid interface. This could be a serious error source when using the models of rigid interface to evaluate the stress inside the film or substrate, especially when the dimension of the composite is the order of several microns. A model which extends the application of Stoney's formula to the case of composite with interfacial slip is presented.