Analysis of process dependent mechanical properties of sintered copper nanoparticle pillars for the plating-free bumping by finite element method

Previous studies of sintered copper nanoparticles used in the plating-free bumping by injection molded solder (IMS) have shown that their microstructural features depend on the sintering conditions such as temperature and gas atmosphere. The other study has shown that the elastic modulus and yield of sintered Cu nanoparticles (NPs) also depend on the sintering temperature. In this report, the relationships between the morphological features and elastic modulus of sintered Cu nanoparticles is studied by nanoindentation and by finite element method (FEM). Mechanical testing by nanoindentation revealed that the elastic modulus of sintered Cu nanoparticles depends not only on the sintering temperature, but also on the sintering gas atmosphere. The results together with the previous study on the microstructures indicate that the Cu NPs processed in nitrogen and those processed in formic acid are at the different stages of coalescence and void growth dynamics. Young’s modulus values of sintered Cu nanoparticles processed in formic acid were higher than those processed in nitrogen for the same sintering temperatures. The values of Young’s modulus for the sintering temperatures of 150, 200 and 250°C were 66, 71 and 86 GPa for the nitrogen case and 82, 100 and 99 GPa for the formic acid case, respectively. The reference value for the plated copper was 138 GPa. To elucidate the relationship between the morphological features and the mechanical properties, Young’s modulus and yield were calculated by numerical testing of representative volume elements constructed with morphological features using FEM. Morphological features used for the analyses were neck width and the void ratio which are associated with the particle coalescence and the void growth respectively. The calculation showed that an increase in the neck width results in an increase of Young’s modulus and yield whereas an increase in void ratio results in a decrease of Young’s modulus and yield. Evolution of Young’s modulus with sintering temperature was compared with that obtained by nanoindentation. For the formic acid case, the variation of Young’s modulus was best described by a hierarchical model incorporating both the neck width and the void ratio suggesting that both the particle coalescence and the void growth are important dynamics determining the mechanical properties for this system. Statistical analysis was also performed on the Young’s modulus data randomly generated by FEM to determine the relative influence of the morphological features on elastic modulus.