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

Advancement in nanotechnology has been of great benefit in various fields of applications. In particular, graphene has been recently identified as a novel and promising electronics material owing to its excellent properties such as high mobility. However, it is more preferable for an analog application rather than digital applications due to lack of bandgap. In a recently published literature, the transmission of electrons in graphene impinging a potential barrier perpendicularly, has been investigated. The exotic tunneling effect, otherwise known as Klein tunneling, contrast to most of the traditional semiconductors whose transmission rely majorly on barrier height and width due to the presence of parabolic bands.

Based on Klein tunneling effects, a possibility of developing graphene-based field-effect transistors for high-frequency applications have been tabled. Unfortunately, the mobility effects of the graphene electrons undergoing Klein tunneling have not been fully understood. Consequently, the effects of the transit time and tunneling have to be taken into account to compute the electron mobility and cut-off frequency, which are of great significance in high-frequency electronics. Therefore, it is crucial to understand the relationship between the cut-off frequencies and the Klein tunneling times of graphene devices. In orthodox quantum mechanics, several approaches have been proposed for an accurate prediction of tunneling times. The commonly used orthodox protocols involve determining the transit times by using clocks as meters, during tunneling, that are not present in the real device.

Recently, Autonomous University of Barcelona scientists: Devashish Pandey (PhD candidate), Matteo Villani (PhD candidate), Dr. Enrique Colomés, and Professor Xavier Oriols in collaboration with Dr. Zhen Zhan from Wuhan University presented an analysis of the Klein tunneling times in graphene structures using the home made simulator BITLLES (available for free at http://europe.uab.es/bitlles). Fundamentally, dwell time for the electrons in two-terminal graphene barriers was investigated. Furthermore, the Bohmian theory was used to accurately define the dynamic paths in terms of Bohmian trajectories for computing the tunneling times and evaluating their relationship with the cut-off frequencies of electron devices. Their main aim was to develop graphene-based field-effect transistors for high-frequency applications based on Klein tunneling phenomenon. The research work is currently published in the research journal, Semiconductor Science and Technology.

The authors successfully distinguished Klein tunneling times from the typical tunneling times in materials with parabolic bands thereby indicating unique features of graphene structures. Also, the trajectory-based Bohmian approach exhibited the ability to distinguish the transmitted and reflected electrons as well as those reflected electrons that lasted in the barrier and those that did not thus quantifying Klein tunneling in linear band graphene devices. Such distinction is not possible in orthodox quantum mechanics since it leads to unphysical conclusions in tunneling time computations. Furthermore, the final result of computing the tunneling time in graphene has a very simple and intuitive explanation in terms of the Bohmian theory which is obtained by dividing the effective barrier width by the Fermi velocity. Considering the ability of Bohmian theory to provide both measured and unmeasured properties for quantum systems, the study provides vital information that will advance the development of graphene-based field-effect transistors for high-frequency applications of electronic devices.