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 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.

About the author

Devashish Pandey received his Bachelor of Technology in Electronics and communication engineering in 2010 from KEC Dwarahat, India. Later he graduated from National Institute of Technology, Silchar, India in 2014 with a Master in Technology with specialization in Microelectronics and VLSI. Currently he is pursuing Ph.D in the Electronics department, Universitat Autónoma de Barcelona. His research interests include quantum transport in 2D materials and study of heterojunctions.

About the author

Matteo Villani got his B. sc. in Physical Engineering and his M. sc. in Nanotechnologies for ICTs at Politecnico di Torino, Italy, respectively in 2015 and 2017. With a final project on electrical characterization of Graphene-based nanostructures, in collaboration with LTM-CEA in Grenoble, France. He is currently pursuing a PhD thesis with the Departament d’Enginyeria Electrònica,Universitat Autònoma de Barcelona, Spain. His current research consists in electron transport simulations in nanoelectronics devices.

About the author

Enrique Colomés was born in Madrid, Spain, in 1989. He received the B.S. degree in physics from the Universidad Complutense de Madrid, Madrid, Spain, in 2013, and the M.S. degree in nanotechnology and materials science from the Universitat Autònoma de Barcelona, Barcelona, Spain, in 2014, where he also obtained his Ph.D. degree in 2018 in electronic engineering. His current research interests include the study of electron devices within the quantum Bohmian mechanics theory.

About the author

Zhen Zhan received the B.S. degree in materials physics from Northwestern Polytechnical University, Xi’an, China, in 2010, the M.S. degree in condensed matter physics from Jinan University, Guangzhou, China, in 2013, and the Ph.D. degree in electronic engineering from the Universitat Autònoma de Barcelona, Barcelona, Spain, in 2017. She is now a postdoc in the School of physics and Technology, Wuhan University. Her current research interests include simulation of the electronic, transport and optical properties of various systems, including graphene and its derivatives, semiconducting 2D materials by using the tight-binding method, and simulation of nanoscale electron devices based on 2D materials by using the Monte Carlo method.

About the author

Xavier Oriols received his BS and MS in Physics from the Universitat Autónoma de Barcelona (UAB) in 1993 and 1994 respectively. During 1997, he worked at the Institute d’ Electronique, Microelectronics and Nanotechnology in Lille (France). He received his doctoral degree in Electronic Engineering from UAB (Spain) in 1999 with an extraordinary doctoral award and the Diploma of Advanced Studies in Signal Theory and Communications from the Universitat Politècnica de Catalunya in 2001. During 2001 and 2002 he was a visiting professor at the State University of New York (USA).

He has authored or co-authored more than 150 contributions to scientific journals and conferences in the fields of electron device physics and foundations of quantum mechanics. He is author of the book “Applied Bohmian Mechanics: from nanoscale system to cosmology” and he has developed the electron transport simulator BITLLES . In 2008, he received the prize for young researchers in the framework of the Spanish I3 Program and the prize for research excellence in 2008 and 2010.

The research activity of Dr. Oriols combines both his practical interest in quantum nanodevices, and his interest in the foundations of quantum mechanics, in general, and in Bohmian mechanics, in particular. His research covers a wide spectrum, from fundamental issues of physics to practical engineering.


Pandey, D., Villani, M., Colomés, E., Zhan, Z., & Oriols, X. (2019). Implications of the Klein tunneling times on high frequency graphene devices using Bohmian trajectories. Semiconductor Science and Technology, 34(3), 034002.

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