  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.
