Effect of Fractal Topology on the Resistivity Response of Thin Film Sensors

We discuss the effect of topological inhomogeneity of very thin metallic conductometric sensors on their response to external stimuli, such as pressure, intercalation, or gas absorption, that modify the material's bulk conductivity. The classical percolation model was extended to the case in which several independent scattering mechanisms contribute to resistivity. The magnitude of each scattering term was predicted to grow with the total resistivity and diverge at the percolation threshold. We tested the model experimentally using thin films of hydrogenated palladium and CoPd alloys where absorbed hydrogen atoms occupying the interstitial lattice sites enhance the electron scattering. The hydrogen scattering resistivity was found to grow linearly with the total resistivity in the fractal topology range in agreement with the model. Enhancement of the absolute magnitude of the resistivity response in the fractal range thin film sensors can be particularly useful when the respective bulk material response is too small for reliable detection.