The novel non-linear dc response of Ag thin films deposited on porous silicon: a fractal model explanation

We have observed a novel non-linear dc resistivity of Ag thin films deposited on porous silicon (PS) surfaces. We also found that as the porous silicon is oxidized in a HNO3 solution, the dc resistivities of the Ag thin films become two orders of magnitude smaller, and behave linearly but are divided into three different regions. Each region exhibits different resistivities which drops abruptly at the thresholds. The resistivity decreases as the current increasing into a higher current region. The atomic force microscopy (AFM) image shows a self-affine structure of the PS surface with wires, hillocks and voids on various scales. After oxidation, the rough surface is smoothed down to simpler fractal hillock clusters. The silver clusters are deposited on the glazed surface in a fractal-like size distribution. A branched Koch curve fractal model is proposed in this study to model the tunneling between fractal-like silver clusters. It explains the stepwise linear fractal-like resistivity behavior.