Constitutive Model of Secondary Annealing Behavior of Cu-Cu Joints in Cu/SiO₂ Hybrid Bonding

In this study, the stress-strain constitutive models of Cu-Cu joints in hybrid bonding after primary and secondary annealing were determined using nanoindentation experiments and finite element inverse analysis, and the correlation mechanism between the microstructure and macroscopic mechanical properties in hybrid bonding Cu-Cu joints during secondary annealing was revealed. The 350-400 °C secondary annealing facilitates recrystallization-grain growth, increasing grain size from 0.62 μm after primary annealing to 0.71 μm, accompanied by a 12% reduction in kernel average misorientation (KAM) values. This process enhances interface non-planarization and optimizes bonding quality. Concurrently, the secondary annealed Cu-Cu joints exhibit a softening effect, manifested by decreasing trends in elastic modulus (131.02 → 118.98 GPa), hardness (1.78 → 1.51 GPa), and yield strength (70.52 → 56.12 MPa), primarily attributed to the Hall-Petch effect and residual stress release. Notably, the yield strength of secondary annealed Cu-Cu joints demonstrates 31.0% and 68.5% enhancements compared to TSV-Cu (42.83 MPa) and bulk Cu (33.3 MPa), respectively.