| Abstract Scope |
Thin gold film electrodes on polydimethylsiloxane(PDMS) substrates can be reversibly stretched up to 80% without losing their electrical conductance. The resistance increases nearly linearly with increasing mechanical strain. With improving fabrication techniques the correlation between resistance and strain has become more and more reproducible. Practical application requires a predictive model for this correlation, but no model exists that captures it. We describe a current percolation model that starts with the image analysis of scanning electron micrographs as the basis for the finite element modeling of the electrical potential distribution in the film.The samples are made by electron beam depositing 75nm thick gold films on PDMS and glass control substrates. The films on PDMS are patterned into 100μm wide and 5mm long electrodes. The baseline resistivity of the film is measured on the control sample.15μmx15μm fields of 8-bit grayscale SEM micrographs of the cracked gold film are processed for illumination correction and noise reduction and then converted to binary images–each pixel either representing conducting gold or non-conducting cracks. The potential distribution in the field is calculated from solving for each pixel Gauss’s law under current conservation. From the calculated potential distribution we calculate the current density and the equivalent resistivity for each field selected from the SEM micrograph.We first studied unstrained electrodes. Their surface morphology was imaged by SEM and analyzed by the model we built. 15μmx15μm large fields of the micrograph are analyzed and averaged, resulting in a resistivity of (3.05±0.14)x10<SUP>-5</SUP>Ohmcm. Applying this value to the 100μm wide and 5mm long electrode resulted in a simulated resistance of 211Ohms, which agrees well with the measured value of 215Ohms. Potential distribution maps of the 15μmx15μm fields show that the potential drops are most pronounced (i.e.,local resistances are highest) across cracks that are longer than 1μm, while they are small across smaller cracks. This indicates that cracks over 1μm in size contribute most to the excess resistance, above that of the gold film on glass.To study strained electrodes, samples were 1-D stretched to a precise strain value, and the resistance under strain was measured. Then the strained electrode was fixed by gluing it to a sample holder, and was imaged by SEM. As observed earlier, longer cracks formed with orientation mainly perpendicularly to the stretching direction. Locally some gold film also delaminates at the edge of cracks. Both crack lengthening (which is reversible)and film delamination contribute to the increase in resistance under strain. Applying the same approach as for the unstrained electrode above, the simulated resistance of an electrode strained by 15% is 834Ohms, again agreeing well with the measured resistance of 860Ohms. We will compare experiment with simulation, and describe our progress toward a predictive model. |