Material size effects on crack growth along patterned wafer-level Cu–Cu bonds

The role of micron-scale patterning on the interface toughness of bonded Cu-to-Cu nanometer-scale films is analyzed, motivated by experimental studies of Tadepalli, Turner and Thompson. In the experiments 400nm Cu films were deposited in various patterns on Si wafer substrates and then bonded together. Crack growth along the bond interface is here studied numerically using finite element analyses. The experiments have shown that plasticity in the Cu films makes a major contribution to the macroscopic interface toughness. To account for the size dependence of the plastic flow a strain gradient plasticity model is applied here for the metal. A cohesive zone model is applied to represent the crack growth along the bond between the two Cu films. This cohesive zone model incorporates the effect of higher order stresses in the continuum, such that the higher order tractions on the crack faces decay to zero values when the crack separation process takes place. The analyses focus on a pattern of Cu lines orthogonal to the crack growth direction, and the analyses are carried out for plane strain conditions with the assumption of small scale yielding under remote mode I loading. When crack growth over a Cu line initiates at the 90° edge on the Cu substrate the resistance curve shows a high peak before the toughness decays to a rather constant plateau. Later, when the crack tip approaches the 90° edge at the end of the Cu line, the fracture toughness decays below the plateau. It is found that both the toughness peak and the subsequent plateau level are highly sensitive to the value of the characteristic material length. A small material length, relative to the thickness of the Cu film, gives high toughness whereas a length comparable to the film thickness gives much reduced crack growth resistance.