Stability of J-integral calculation in the crack growth of copper/low-K stacked structures

As the technology of the semiconductor process continues to move forward, the next generation IC chip with copper/low-k stacked structures is being developed for reducing the RC delay in order to obtain high-speed signal communication. However, there is a high potential that in doing so it may contribute to interfacial cracks occurring or propagating between the copper interconnections and the low-k material as a result of poor adhesion and lower fracture toughness of the low-k material when temperature loads are applied during the wafer level and the packaging level stages. This fracturing problem is one of the most urgent issues for the thermo-mechanical reliability of a copper/low-k damascene module, and it needs to be resolved urgently. With the simulation of an interfacial fracture based on J-integral value estimation, the interfacial crack growth can be modeled using a finite element analysis (FEA) and compared it to Jc, which is interfacial fracture toughness that must be determined experimentally. Therefore, the stability of the J-integral value obtained from the FEA is crucial so as to avoid a misunderstanding of the cracking energy. In order to discuss the mesh density affecting the convergence of the J-value, various paths with an integral contour surrounding the crack tip are considered in this research. The interfacial crack is constructed using the element birth and death technique to suppose that an actual crack developed between copper/low-k interfaces. The analytic results show that the J-value will converge toward unity when a rectangular contour with a proper ratio of length/width, and multi-layers of element close to the delaminating surfaces are applied to reduce the loss of numerical analysis in precise. It should be noted that the crack tip must be at the center of the integral contour. The long side of the rectangular contour needs to be parallel to the direction of the fracture propagation. On the other hand, the curve of the J-value versus the increase of the crack length calculated from the model with the actual crack embedded shows good agreement with the simulated results with the virtual crack by means of the element birth and death technique