Sensitivity derivatives of dissimilar material junctions in electronic packages

Electronic packages are susceptible to failure initiation due to high thermo-mechanical stresses near the regions of adhesive bond lines forming geometrical corners with other components such as the die or substrate. It is well known that the stress state near such junctions is singular and that the strength of the singularity depends on the junction geometry and the mechanical properties of the materials. In order to reduce the strength of the singularity and/or the magnitude of the peeling and shear stresses, it is essential to evaluate the effect of variations in the material properties and geometric parameters of such junctions under combined mechanical and thermal loadings. Therefore, the sensitivity derivatives of the maximum interfacial peeling or shearing stress and the stress intensity factors are calculated with respect to the material properties and geometric variables. These sensitivity derivatives measure the sensitivity of the maximum interfacial peeling or shearing stress and the stress intensity factors to variations in the material properties and geometric parameters. Their values help in identifying the critical design parameter and lead to an optimum design of dissimilar material junctions. In this study, the sensitivity derivatives associated with the maximum interface stress in the absence of a crack and with the stress intensity factors in the presence of a crack are calculated by using a finite element method that couples a special element with traditional finite elements