Electronic resistances of multilayered two-dimensional crystal junctions

We carry out a layer-by-layer investigation to understand electron transport across metal-insulator-metal junctions. Interfacial structures of junctions were studied and characterized using first-principles density functional theory within the generalized gradient approximation. We found that as a function of the number of crystal layers the calculated transmission coefficients of multilayer silicene junctions decay much slower than for BN-based junctions We revisited the semiclassical Boltzmann theory of electronic transport and applied to multilayer silicene and BN-based junctions. The calculated resistance in the high-transmission regime is smaller than that provided by the Landauer formula. As the thickness of the barrier increases, results from the Boltzmann and the Landauer formulae converge. We provide a upper limit in the transmission coefficient below which, the Landauer method becomes valid. Quantitatively, when the transmission coefficient is lower than $ \sim 0.05 $ per channel, the error introduced by the Landauer formula for calculating the resistance is negligible. In addition, we found that the resistance of a junction is not entirely determined by the averaged transmission, but also by the distribution of the transmission over the first Brillouin zone.