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

Gregory Kopnov, Sudhansu Sekhar Das, Alexander Gerber

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number2409
Issue number5
StatePublished - Mar 2023


  • hydrogen sensor
  • palladium
  • percolation
  • thin film sensors

All Science Journal Classification (ASJC) codes

  • Analytical Chemistry
  • Information Systems
  • Biochemistry
  • Atomic and Molecular Physics, and Optics
  • Instrumentation
  • Electrical and Electronic Engineering


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