Microstructure effects on the response of gas-sensitive resistors based on semiconducting oxides

A simple numerical method to describe the effects of microstructure on the response of gas-sensitive resistors is presented. The model material is constructed as a random assembly of spheres with a Poisson distribution of radius, each sphere being built from elementary cubes of side δ, the Debye length. The key scaling variable is thus the ratio of the mean sphere radius to the Debye length. The gas is considered to change the conductance of only those elementary cubes which contact the void space. The model is a simple ohmic one, and does not take into account any effects of variation of potential within the particles induced by the surface charge which in practise exists. However, it usefully reproduces the observed effects of microstructure on response, showing that the agglomeration of small sensor crystallites into larger masses within the fabricated device is a key phenomenon which leads to gross variation of the apparent power-law-response exponent.