Interface fracture toughness from buckled lines Buckling was observed for niobium films on sapphire substrate in the patterned line forms, with interfacial silver levels range from 2.5 monolayer to 7.6 monolayer. Figure 4a shows a representative micrograph of the buckles. The buckles indicate that the residual stress in the niobium film must be compressive. The buckle height and length for buckled lines were measured from the photo. The stress in the niobium film can be determined using the analysis of buckle height given by Hutchinson and Suo [11]. The values of the film stress and the interface fracture toughness for lines that delaminated in the form of buckles ranges from 1.17 GPa to 5.57 GPa in compression, and the interface fracture toughness ranges between 0.62 J/m2 and 13.6J/m2. Given a 3% error in the measurement of the buckle height, the error in the film stress and interface fracture toughness is less than 5%. tilt angle 40Þ tilt angle 40Þ (a) (b) Figure 4: SEM pictures of (a) buckled niobium lines on sapphire substrate (PVD, 3.0 monolayers of silver), and (b) curled photoresist/niobium bilayer lines on a sapphire substrate with lines detached from the substrate at the niobium/sapphire interface (PVD, 2.1 monolayers of silver). The arrows point to buckles. While the magnitude of the stress is not unreasonable for niobium films given hardness measurement of 6 GPa [12], the reason that these films are in compression is unknown. A possible explanation for the formation of the buckles that does not require compressive residual stress in niobium is that the buckles formed at an earlier stage under external force induced by processing or an interface defect (e.g. gas bubble at the interface), causing the niobium to yield. However, optical inspection of the sample showed no observable defects before the photoresist was stripped off. Interface fracture toughness from curled lines Figure 4b is a SEM micrograph of the PVD sample with 2.1 monolayers of silver at the niobium/sapphire interface . The photo was taken after the dry etch step when lines were first observed to detach from the substrate. The final step of the photolithography process (stripping the photoresist) was omitted from this sample. Therefore the sample is a bilayer with a 1.35 µm thick photoresist layer on top of a 0.1 µm thick niobium film, deposited on a sapphire substrate which was pre-deposited with silver. As shown in Fig. 4b, the lines were detached from the substrate at one end. The detached portion of the bilayer (photoresist and niobium) curled up, indicating that there was a stress gradient in the bilayer system in which the stress in the photoresist is tensile relative to the niobium film. The observation of buckles next to the curled ends indicates that the stress in the niobium film must be compressive. Given the radius of the curvature, R, of the curls, and the niobium film stress of -1.32 GPa determined from the buckling analysis on a sample with similar deposition condition , the stress in the photoresist is estimated to be 38 MPa in tension. The fracture toughness of the interface, determined using the analysis in ref. [11], is 0.95 J/m2. As shown in Fig. 4b, both buckling and curling occurred on the same sample. This can be explained by the stress states in
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