Electronic resistances of multilayered two-dimensional crystal junctions

TL;DR

This study investigates electron transport in multilayered 2D crystal junctions, comparing first-principles calculations with semiclassical models, revealing how resistance depends on layer number, transmission distribution, and the validity range of theoretical approaches.

Contribution

It provides a detailed analysis of electron transport in multilayered 2D crystal junctions, establishing the conditions under which the Landauer formula accurately predicts resistance.

Findings

Transmission coefficients decay slower in silicene than BN with increasing layers

Boltzmann theory yields smaller resistance estimates than Landauer in high-transmission regimes

Landauer formula becomes accurate when transmission per channel drops below ~0.05

Abstract

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.