Surface dynamics and breakdown patterns of a random solid subject to a biased 3D etching

We propose a selective disaggregation model in three dimensions with a mixed Brownian-deterministic motion of the etchant particle driven by a tuning parameter taking into account the presence of an external field. The width of the surface sites in saturation is described by the Edwards-Wilkinson scaling law as in a ballistic selective decay process. Besides, we consider the surfaces resulting when the solid substrate is completely eroded up to the electrical breakdown. In this situation, we analyse the effects of the etchant particle motion on the topology and conductivity of the residual substrate and we compare the relevant patterns with the ones related to the classical percolation theory. These results may interpret some recent experimental findings in electrochemical nanotechnology.