Measurement of ultra-thin film fracture by nano-indentation: a numerical study
As the individual layers of interconnect structures decrease in size, it becomes increasingly difficult to determine the fracture toughness, and hence the reliability, of these layers. After a layer is thinner than ~500nm, it becomes difficult to determine the fracture toughness directly with traditional methods. Using nano-indentation, it is possible to extract the cohesive and adhesive fracture energies of these films without elaborate experimental setups. There are, however, several issues with this approach. Nano-indentation creates cracks both within the film (the cohesive cracks) and between the film and the substrate (the adhesive cracks) as well as significant plastic deformation of the film and substrate. Using SIMULA Abaqus Standard, a commercial finite element analysis tool, 2D and 3D models were created to examine the deformation characteristics associated with the nano-indentation process. The models either have pre-existing stationary cracks, or simulated by cohesive zone surfaces to account for crack nucleation and growth. The 2D model is axi-symmetric and only accounts for the adhesive crack. It is used primarily as a test the cohesive zone model and to begin to determine experimental testing limits. The 3D model is a one sixth slice of the area indented. Both cohesive and adhesive cracks are modeled and the interaction between the two cracks is investigated. While there are many parameters controlling the crack initiation and propagation process, several trends were identified. The domain of practical testing should be between one and three film thickness, so as to avoid the confluence of the indenter plastic process zone on the propagating crack front. When excursion on the load-indentation depth happens, the fracture energy is about 20% of the associated work done by the indenter (or the area under the excursion segment). The FEM simulation showed the general role of film thickness, toughness and modulus on the initiation and propagation of both cohesive and adhesive cracks. Though, there remains to be many other geometric attributes of the thin film fracture process that requires additional investigations.