Rough semiconductor electrode: A new percolation problem

We show that current flow through a rough interface with an exhaustion layer of controllable width can be idealized into a novel percolation problem. For an infinitely rough interface between two perfect conductors and a layer of finite conductivity separating the two, there exists a thickness t* such that the normalized resistance R=0 for t<t*, R(t-t*)s for tt*, and Rt for tt*, where s is a universal constant that will vary only with the topology of the interface. We formulate the scaling relations for a real interface and for the practical situation where the separating layer is an exhaustion layer of a semiconductor and where t can be controlled by an applied voltage.