The relationship between thin film fragmentation and buckle formation: Synchrotron-based in situ studies and two-dimensional stress analysis

Fragmentation and buckling of Ta layers with thicknesses of 50, 100, and 200 nm on polyimide substrates was studied by in situ light microscopy and synchrotron analysis. Buckling indicates the presence of compressive stress, which cannot be explained exclusively by a Poisson ratio mismatch. We extended the classical shear lag model and derived a rigorous analytical solution for the biaxial stress field in a single fragment attached to a uniaxially loaded substrate. The presence of cracks not only gives rise to tensile stress relaxation, but also induces compressive stress in the perpendicular direction, which eventually leads to film buckling. The validity of the model has been confirmed using a synchrotron-based technique for the in situ determination of the biaxial coating stress during uniaxial tensile testing. Taking into account the mean crack distance as a function of the applied strain, the model is utilized to determine the residual stress and fracture toughness of thin films.