Multi-material Corner Singularity in Electronic Packaging: Avoiding Mesh Dependence in Analyzing Stress

Multi-material corners occur at interfaces in electronic packaging. They are ubiquitous in chip dielectric stacks and in interposers. These corners are locations of stress concentration (singular according to elasticity theory). This paper introduces a practical approach for analyzing singularities in multi-material corners with application to the mechanical analysis of microelectronic interconnect structures. The results of finite element analysis are mesh refinement-dependent, inaccurate, and often yield overly conservative prediction due to stress singularities near corners. The primary objective of this study is to establish a correlation between corner singularities, stress levels, and failure risk, considering material properties and wedge angles. The influence of material behavior and wedge angle on the order of singularity is analyzed using planar elasticity theory. To address the mesh sensitivity issue and provide a robust metric for evaluating failure risk, we propose a generalized stress intensity factor, which remains constant within a defined range near the corner and can be easily integrated into finite element analysis as a post-processing step. This approach offers a mesh-independent solution for assessing designs prone to stress overshooting caused by singularities and a robust metric to evaluate failure risk at multi-material corner.