Modeling of Copper Hybrid Bonding Anneal

This work incorporates surface diffusion, which is generally outside of commercial solid mechanics software, in the modeling of copper bond formation. The surface diffusion is driven by the curvature of the copper surface and the surface diffusion coefficient. The surface diffusion coefficient is itself a function of temperature. The governing equations were adapted to a phase field model. A finite element simulation was used to determine the bulge out behavior and estimate the required recess for bonding through pitch, temperature, and time. Voids where the dielectric meets the copper are simulated using a sharp interface model incorporating stress and strain under thermal expansion. The bulge out from the phase field model was used to approximate the stress relaxation in the copper. Predictions were verified experimentally by bonding coupons at various conditions and measuring with transmission electron microscopy (TEM) imaging. A key result is that the observed bulge out and contact is likely determined, in part, by thermal expansion in larger features, but mostly by surface diffusion in smaller features. The relative importance of the surface composition, therefore, increases with shrinking pitch. The final condition of the void depends on the stress of all materials in the design, including the surrounding silicon over a given temperature profile through time, and the local morphology / shape of the dielectric near the copper recess after CMP.