Void growth drives electrical resistance increase: A physics-based damage model for ductile metallic conductors

This work introduces a novel physics-based model to track and quantify damage-induced degradation in metallic conductors through the increase in electrical resistance. We hypothesize this degradation is driven by the growth of internal porosity, and propose an evolution law for the decrease in material conductivity based on the Voigt–Reuss composite bounds with a single fitting parameter. To relate the local conductivity with the effective resistance of a conductor, a novel homogenization scheme based on power equivalency principles is also introduced. Our model is validated on copper microvias under interconnect stress test conditions for which experimental data are collected. Finite element simulations of 200 complete thermal cycles are performed for both stacked and staggered microvia configurations, with geometries derived from scanning electron microscopy measurements. The proposed model fits the industrial experimental data well, improving upon existing models by over one order of magnitude. The analysis is extended with a crystal plasticity constitutive model informed by electron backscatter diffraction texture data, which revealed highly localized plastic strain hotspots within the grain structure, preferential sites for void nucleation and growth. This provides direct evidence for the mechanism that creates porosity within the microvia, validating the fundamental assumptions of our model.