Reliability study of hybrid bonded structures based on flux divergence method

Purpose The purpose of this study is to reveal the electromigration-induced failure mechanisms in Cu–Cu hybrid bonding structures and to identify the key factors governing failure location and lifetime under multiphysics coupling conditions. Design/methodology/approach A multiphysics coupled simulation model based on the atomic flux divergence method is developed to analyze electromigration behavior in Cu–Cu hybrid bonding structures. The effects of current density, temperature, equivalent stress and alignment offset on failure evolution are systematically investigated. Simulation results are further validated through comparison with reported experimental observations. Findings The results indicate that although electromigration, thermomigration and stress migration influence the failure process, electromigration dominates failure in Cu–Cu hybrid bonding structures due to limited temperature and stress gradients from small feature sizes and high thermal conductivity. Alignment offset is a critical factor determining device lifetime and failure location, with a transition in failure mode when the offset exceeds 90 nm. The extrema of the current density gradient accurately predict failure locations and reflect failure severity. An optimized bonding structure with a modified Cu pad etch angle is proposed, effectively reducing current density gradient extrema and improving reliability. Research limitations/implications This study is primarily based on numerical simulations and relies on previously reported experimental data for validation. Future work investigation via in situ experimental characterization would further strengthen the generality of the conclusions. Practical implications The findings provide practical design guidelines for improving the reliability of Cu–Cu hybrid bonding structures by controlling geometric parameters to mitigate current density gradients. The proposed structural optimization offers a feasible approach for extending device lifetime in advanced interconnect technologies. Originality/value This work establishes a comprehensive multiphysics framework for analyzing electromigration in Cu–Cu hybrid bonding structures and identifies the current density gradient as a key indicator of failure location and severity. The study further demonstrates a geometry-based optimization strategy to suppress electromigration-driven failure, offering valuable insights for the design of reliable hybrid bonding interconnects.