Tunneling currents between carbon nanotubes inside the 3-dimensional potential of a dielectric matrix

We have examined the tunneling currents between CNTs dispersed in a dielectric matrix as is normally the case in a tensile stress or toxic gas sensors. Due to the randomness of the immersion process the CNTs are at random angles and configurations between them, thus producing a 3-dimensional potential (3-D). We have produced a method that solves the Laplace equation for this type of problem and uses the WKB formulation to calculate the transmission coefficient between CNTs. We have then shown that the tunneling currents between a pair of CNTs depend critically on their relative angle and configuration. In particular we have shown that the tunneling currents do not occur only along a CNT tip to CNT tip configuration but other more efficient paths exist which give a current higher by two orders of magnitude from what a simple 1D theory would give. On the other hand the tunneling current between non-coplanar CNTs is negligible. We conclude that such phenomena cannot be analyzed by a simple 1-dimensional WKB theory and the percolation threshold necessary for conduction may be lower than the one such a theory would predict