Size Effects and the Problem with Percolation in Nanostructured Transparent Conductors

Much research is underway at present to develop nanostructured transparent conductors for use as electrodes. Transparent electrodes typically require high visible transmittances, T > 90%, and so must be very thin. We show that for most nanostructured films thin enough to display T > 90%, the conduction can be described by percolation theory. This means DC conductivities are lower than in bulk, giving correspondingly higher sheet resistances, Rs. To improve our understanding of the consequences of this, we develop a model which relates T to Rs in the percolation regime. We define a percolative figure of merit, Π, for which high values result in high T and low Rs. High values of Π are achieved for high DC conductivity and low optical conductivity. In addition, the film thickness, tmin, where the DC conductivity first deviates from its bulk value and the percolation exponent, n, must both be as low as possible. We find that this model fits extremely well to much of the data in the literature. We demonstrate ...