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Because of the elastic nature of the PDMS substrate, stress can be easily transmitted between the Ti film and the substrate. The magnitude of the stress determines the cracking pattern and crack spacing (direction and size). This is due to the difference in the elastic moduli of the Ti film and the PDMS substrate [24, 25]. For a Ti film deposited on a PDMS substrate, the stress exerted on the Ti film from the substrate depends on the state of the PDMS substrate. When the PDMS substrate is in a relaxed state, the stress is small and the cracks are straight vertical without buckling. With increasing strain, the PDMS substrate is deformed and the stress is increased. For a 180-nm Ti film, at a strain of 30% the stress is approximately 0.8 MPa and the crack spacing is approximately 1.1 m. This corresponds to the average crack pattern in Figure 2g,h. At a strain of 50%, the stress is approximately 1.7 MPa and the crack spacing is approximately 0.7 m. The average crack pattern in Figure 2h corresponds to this state. For a 250-nm Ti film, at a strain of 30% the stress is approximately 0.8 MPa and the crack spacing is approximately 1.1 m. At a strain of 50%, the stress is approximately 1.7 MPa and the crack spacing is approximately 0.7 m. The average crack pattern in Figure 2i corresponds to this state. The strain-dependent stress caused the variation in crack pattern and crack spacing. Therefore, crack patterns and crack spacings of cracked Ti films on PDMS substrates were dependent on the strain, which lead to the strain-dependent resistance change (Figure 3). The crack pattern and crack spacing were observed and measured using a scanning electron microscope (SEM; Hitachi S-4800) equipped with an energy dispersive X-ray spectroscopy (EDX) system. All the SEM images were processed using the software Photoshop 7.0. The details of crack patterns and crack spacings are given in the Supplementary Information.
The thickness dependence of cracking in Ti films was examined for the case of a 300-nm-thick Ti film on a PDMS substrate. Here, the 300-nm-thick Ti film was simply prepared by RF sputter deposition. The LSM images are presented in Figure 4a,b,c. The cracks are observed to spread at a nearly constant speed, and they eventually intersect with the vertical cracks at a strain of approximately 50%. This can be explained by the c in Equation 1.
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