A Resistivity Model for Ultrathin Films and Sensors

Gas sensors have been demonstrated based on the conductivity changes in ultrathin films. These sensors operate in a regime where three different physical phenomena determine the total resistivity of the film; quantum mechanical coupling between metallic islands, bulk material conductivity of the islands, and network resistivity. We present a lumped parameter model that simulates thin-film growth and calculates the total film resistance during the growth process accounting for these three phenomena. The model contains four free parameters and yields a good agreement with experimental data presented for palladium, titanium, and gold. The primary benefit of this model is that it shows the relative contribution of each source of conductivity during the growth process providing insight into the operation of ultrathin films as gas sensors. We then model an ultrathin-film palladium-based hydrogen sensor and show that the sensing mechanism is primarily due to variations in quantum tunneling.