A simplified model for evaluating the electrical resistance of a zirconia substrate with co-planar electrodes

The use of zirconia, both as planar substrate and as conductor of oxygen ions, combined with the flexibility of screen-printing technology enables the construction of planar sensors or oxygen pumps with nearly any shape of the electrodes. Whereas, the evaluation of the electrical resistance of such devices is immediate when identical electrodes are facing each other on both sides of the substrate, the situation is not quite so obvious when the electrodes are located on the same side. The paper presents a simplified model, derived from that used for thin films, which leads to a rough, but straightforward estimation of the electrical resistance of zirconia substrates with co-planar electrodes. The applicability of the model is shown to be better at large oxygen concentrations.