Multilayer thin films/substrate system with variable film thickness subjected to non-uniform misfit strains

Current methodologies used to infer thin-film stress from curvature measurements are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to a single thin film of non-uniform thickness deposited on a substrate and subjected to the non-uniform misfit strain. Such methodologies are extended to multilayer thin films of non-uniform thickness deposited on a substrate in the present study. Each thin film may have its own non-uniform misfit strain and non-uniform thickness. We obtain the film stresses and system curvatures in terms of the misfit strains and thickness in thin films. We derive the film stresses and interface shear stresses in terms of system curvatures and film thicknesses. They all feature a “non-local” dependence on curvatures, which make full-field measurement a necessity for the experimental inference of such stresses.