Effect of Dimension on Thermal Expansion of Cu Pads in SiO2 Vias for 3D IC Fine-pitch Hybrid Bonding

In this study, the effect of dimension on thermal expansion of $\mathbf{C u}$ pads was investigated. $\mathbf{C u}$ pad diameters ranging from $1 \mu ~\mathrm{m}$ to $5 \mu ~\mathrm{m}$ were fabricated. The results revealed that as the temperature increased, the Cu pads protruded accordingly, but the extent of expansion varied with via size. Specifically, the smallest vias ($1 \mu ~\mathrm{m}$ in diameter) exhibited a protrusion of approximately 2.1 nm, while the largest vias ($5 \mu ~\mathrm{m}$ in diameter) expanded by around 5.1 nm in average. This finding indicates that the thermal expansion of Cu pads is highly dependent on via size, suggesting that the coefficient of thermal expansion is influenced by geometric constraints at small scales. Additionally, we compared our experimental thermal expansion values with theoretical predictions and observed discrepancies, indicating additional factors-such as aspect ratio and via diameters-may influence the expansion behavior.