Implications of the Klein tunneling times on high frequency graphene devices using Bohmian trajectories

TL;DR

This paper uses Bohmian trajectories to analyze Klein tunneling times in graphene, revealing insights into high-frequency device behavior and clarifying the relationship between tunneling times and cut-off frequencies.

Contribution

It introduces a trajectory-based Bohmian approach to accurately quantify Klein tunneling times in graphene devices, addressing limitations of previous methods.

Findings

Dwell time roughly equals barrier distance divided by Fermi velocity at zero incident angle.

Transmission coefficient decreases with non-zero incident angles below the critical angle.

High graphene mobility is largely unaffected by Klein tunneling phenomena in the active region.

Abstract

Because of its large Fermi velocity, leading to a great mobility, graphene is expected to play an important role in (small signal) radio frequency electronics. Among other, graphene devices based on Klein tunneling phenomena are already envisioned. The connection between the Klein tunneling times of electrons and cut-off frequencies of graphene devices is not obvious. We argue in this paper that the trajectory-based Bohmian approach gives a very natural framework to quantify Klein tunneling times in linear band graphene devices because of its ability to distinguish, not only between transmitted and reflected electrons, but also between reflected electrons that spend time in the barrier and those that do not. Without such distinction, typical expressions found in the literature to compute dwell times can give unphysical results when applied to predict cut-off frequencies. In particular, we study Klein tunneling times for electrons in a two-terminal graphene device constituted by a potential barrier between two metallic contacts. We show that for a zero incident angle (and positive or negative kinetic energy), the transmission coefficient is equal to one, and the dwell time is roughly equal to the barrier distance divided by the Fermi velocity. For electrons incident with a non-zero angle smaller than the critical angle, the transmission coefficient decreases and dwell time can still be easily predicted in the Bohmian framework. The main conclusion of this work is that, contrary to tunneling devices with parabolic bands, the high graphene mobility is roughly independent of the presence of Klein tunneling phenomena in the active device region.