Transport properties of composite solid films with rough self-affine surfaces

We develop a method for computing the ac and dc conductivity ${\sigma }_e$ of composite films, composed of two types of particles. The films are grown by integrating the Kardar-Parisi-Zhang and the Ginzburg-Landau equations that govern their height and the order parameter. ${\sigma }_e$ is computed as a function of the film’s thickness, frequency, and several relevant morphological parameters. Simulations indicate that the surface roughness strongly affects the films’ conductivity. In particular, while ${\sigma }_e$ exhibits universality if the films’ surface is smooth, the universality breaks down with a rough surface. The results also indicate the consistency of the trends in the conductivities with the morphological transitions in the films.