Compositional Dependence of Residual and Interfacial Stresses in Thin Film Systems with Substantial Thermal Mismatch Characteristics

Abstract

We present an analysis of residual and interface stresses, caused by a change in external temperature field, due to mismatch in thermal and elastic characteristics in a dissimilar system of a thin film and a flexible substrate. A representative volume element of the system is defined as a heterogeneous two-phase layered element bonded at an interface in a sense of coherent bi-layer, where each phase possesses distinct elastic and thermal characteristics. We use a spatial averaging technique with particular form of strain field that satisfies compatibility equations in the bulk and at the interface. Derived special rule of mixtures yields rigorous estimates for residual stress distribution through thickness of the representative volume element. Corresponding distributions of stress fields are calculated for distinct magnitudes of compositional parameter representing the volumetric fraction of the film.