An analysis of non-uniform stress states in finite thin film/substrate system: The need of full-field curvature measurements

Current methodologies used for the inference of thin film stresses through curvatures are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. In this dissertation, we extend these methodologies to non-uniform stress and curvature states for the single layer of thin film or multi-layer thin film with non-uniform thickness subjected to non-uniform isotropic misfit strain between film and substrate. 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. We also extend the methodologies to the case that of single thin film/substrate subjected to non-uniform anisotropic misfit strain. The film stresses and system curvatures are both obtained in terms of the non-uniform, anisotropic misfit strains. For arbitrarily non-uniform, anisotropic misfit strains, it is shown that a direct relation between film stresses and system curvatures cannot be established. However, such a relation exists for uniform or linear anisotropic misfit strains, or for the average film stresses and average system curvatures when the anisotropic misfit strains are arbitrarily non-uniform.