Continuum percolation with tunneling

Classical percolation theory ignores the possibility of quantum tunneling, which is important for transport on the nanoscale. Here we show that the electrical conductance of a two-dimensional percolating-tunneling system exhibits an exponential dependence on surface coverage, which is in contrast to the classically expected power law, and that there is no evidence for an intrinsic threshold for tunneling conduction. We then show that the percolating-tunneling system is identical to that of an equivalent system of point defects, hence creating a link between continuum percolation and the theory of hopping conduction in semiconductors.