Cracks in thin Cu films on Si substrate - Plasticity influence

The finite element method was used to quantify the change of the crack driving force for mode I crack propagation in thin copper (Cu) films towards the interface with silicon (Si) substrate. Both elastic-elastic and plastic elastic transitions at the Cu-Si interface were considered. The plasticity of the thin Cu film was modelled for different material behavior (elastic-ideal plastic, bi-linear and multi-linear material models). The influence of the crack tip plastic region and its characteristic dimension (related to the thickness of Cu film) on the crack driving force for different crack lengths was quantified for several magnitudes of loading (for models with the same yield stress to simulate different stages of evolution of the crack tip plastic zone). The results then divided these loading stages into several groups from a simple small scale yielding of the composite to fully plastic Cu film with severe plasticity influence. Extreme cases for full scale yielding (with the full thickness of the Cu thin film under plastic deformation) were modelled to show the fully developed plasticity influence on the crack approaching the Cu-Si interface. These findings can lead to better understanding of the crack propagation through thin plastic films on elastic substrates and permit a better lifetime prediction of electronical or electro-mechanical devices.