A simple equivalent circuit model to represent microstructure effects on the response of semiconducting oxide-based gas sensors

We show that the effects of microstructure on the response of gas-sensitive resistors based on semiconducting oxides can be understood in a pragmatic and practically useful way using a simple three-element resistance network, in which only one of the elements is gas-sensitive. This model, with the gas-sensitive resistance showing a simple form of response consistent with surface reaction models, displays the power-law response to variation of gas concentration (P-g) shown by practical devices: G = A(g)P(g)(beta), where G is (R - R-0)/R-0 for resistance increase or (sigma - sigma(0))/sigma(0) for conductance increase. The observations that beta varies widely between preparations, is different for different gases on the same sensor, and changes with change of the relative humidity of the gas, are simply explained as being due to changes in the relative values of the resistors in the network, related to the microstructure. The model predicts that, for a range of sensor preparations responding to a given gas, A(g) and beta should be correlated. The predictions are confirmed by measurements of the response of a wide range of microstructures of sensors of both tin dioxide and chromium titanium oxide to toluene, ethanol and carbon monoxide in atmospheres of varying relative humidity. We show that the correlation of A(g) and beta is a powerful tool for discovering subtle effects on the sensor response. These include: effects due to gas concentration gradients within the sensing layer, effects of variation in microstructure throughout the sensing layer, the extent of sintering of the material in the finished sensor, and whether water vapour acts on the sensor surface synergistically or independently of the reactive gas being measured.