Interfacial Thermal Stresses in Layered Structures: The Stepped Edge Problem

Abstract

The intense, localized stress field produced by a temperature load in a multilayered structure may be significantly affected by the local geometry of the free edge. We examine here the stepped edge problem associated with bonding an elastic layer (silicon chip) to a single or multilayer substrate with a slightly larger length. Stress functions are introduced in various rectangular regions and the continuity of tractions are enforced across all inter-region boundaries. Furthermore, continuity of displacements is enforced across the junction of the two segments of the base laminate. The analysis results indicate that even a minute protrusion of the edge of the base laminate relative to the attached chip may cause significant changes in the peeling and shearing stresses in the end region of the interface.