Inter-ribbon tunneling in graphene: an atomistic Bardeen approach

TL;DR

This paper investigates inter-ribbon tunneling in graphene nanoribbons using an atomistic Bardeen approach, revealing resonance and stepwise current features influenced by quantum confinement and doping, with implications for nanoscale electronic devices.

Contribution

It introduces an atomistic Bardeen transfer Hamiltonian method to analyze tunneling in crossed graphene nanoribbons, highlighting the effects of quantum confinement and doping on tunneling characteristics.

Findings

Resonance and stepwise current increases due to density-of-states alignment.

Doping modulates the onset voltage and magnitude of tunneling effects.

Method applicable to various two-dimensional materials beyond graphene.

Abstract

A weakly coupled system of two crossed graphene nanoribbons exhibits direct tunneling due to the overlap of the wavefunctions of both ribbons. We apply the Bardeen transfer Hamiltonian formalism, using atomistic band structure calculations to account for the effect of the atomic structure on the tunneling process. The strong quantum-size confinement of the nanoribbons is mirrored by the one-dimensional character of the electronic structure, resulting in properties that differ significantly from the case of inter-layer tunneling, where tunneling occurs between bulk two-dimensional graphene sheets. The current-voltage characteristics of the inter-ribbon tunneling structures exhibit resonance, as well as stepwise increases in current. Both features are caused by the energetic alignment of one-dimensional peaks in the density-of-states of the ribbons. Resonant tunneling occurs if the sign of the curvature of the coupled energy bands is equal, whereas a step-like increase of the current occurs if the signs are opposite. Changing the doping modulates the onset- voltage of the effects as well as their magnitude. Doping through electrostatic gating makes these structures promising for application towards steep slope switching devices. Using the atomistic Bardeen transfer Hamiltonian method, inter-ribbon tunneling can be studied for the whole range of two-dimensional materials, such as transition metal dichalcogenides. The effects of resonance and of step-like increases of the current, observed in graphene ribbons, are also expected in ribbons made from these alternative two-dimensional materials, because these effects are manifestations of the one-dimensional character of the density-of-states.