Investigation of quantum confinement within the tunneling-percolation transition for ultrathin bismuth films

We investigate conduction phenomena in ultrathin bismuth (Bi) films that are thermally evaporated onto flat quartz. Critical points in the conductance as a function of deposition time are identified and used to scale the data from time dependence to coverage dependence. The resulting nonlinear coverage scaling equation is verified independently via analysis done on transmission electron microscope images of the evaporated films. The scaled data yields critical exponents in very good agreement with classical percolation theory, and clearly shows the transition from the tunneling regime into percolation. Surprisingly, no noticeable signatures of size-quantization effects in the nucleation sites as a function of deposition time is observed in either regime. We discuss our findings in light of Boltzmann transport modeling of 1D conduction as an approximation to the narrow percolative paths that form at the onset of percolation. Our results suggest that lack of a preferred crystallite orientation in the nucleation process may indeed cause quantum-confinement to be too smeared out to be observable in the tunneling to percolation transition.