Electrons Behave Like Light

Illustration of a ballistic electron refracting across a PN junction in high purity grapheme. (Source: C. Dean / Columbia U)

Illustration of a ballistic electron refracting across a PN junction in high purity grapheme. (Source: C. Dean / Columbia U)

A team led by Cory Dean, assistant professor of physics at Columbia Uni­versity, Avik Ghosh, professor of electrical and computer engineering at the University of Virginia, and James Hone, Wang Fong-Jen Professor of Mechanical Engi­neering at Columbia Engi­neering, has directly observed negative refraction for electrons passing across a boundary between two regions in a conducting material. First predicted in 2007, this effect has been difficult to confirm experi­mentally. The researchers were able to observe the effect in graphene, demonstrating that electrons in the atomi­cally thin material behave like light rays, which can be mani­pulated by such optical devices as lenses and prisms. The findings could lead to the deve­lopment of new types of electron switches, based on the principles of optics rather than electronics.

“The ability to mani­pulate electrons in a con­ducting material like light rays opens up entirely new ways of thinking about elec­tronics,” says Dean. “For example, the switches that make up computer chips operate by turning the entire device on or off, and this consumes signi­ficant power. Using lensing to steer an electron beam between electrodes could be drama­tically more efficient, solving one of the critical bottle­necks to achieving faster and more energy efficient elec­tronics.” Dean adds, “These findings could also enable new experi­mental probes. For example, electron lensing could enable on-chip versions of an electron micro­scope, with the ability to perform atomic scale imageing and diag­nostics. Other components inspired by optics, such as beam splitters and inter­ferometers, could addi­tionally enable new studies of the quantum nature of electrons in the solid state.”

While graphene has been widely explored for supporting high electron speed, it is noto­riously hard to turn off the electrons without hurting their mobility. Ghosh says, “The natural follow-up is to see if we can achieve a strong current turn-off in graphene with multiple angled junctions. If that works to our satis­faction, we’ll have on our hands a low-power, ultra-high-speed switching device for both analog (RF) and digital (CMOS) electronics, poten­tially mitigating many of the chal­lenges we face with the high energy cost and thermal budget of present day electronics.”

Hone notes: “Optical metamaterials are enabling exotic and important new techno­logies such as super lenses, which can focus beyond the dif­fraction limit, and optical cloaks, which make objects invisible by bending light around them.”

Electrons travelling through very pure conductors can travel in straight lines like light rays, enabling optics-like phenomena to emerge. In materials, the electron density plays a similar role to the index of re­fraction, and electrons refract when they pass from a region of one density to another. Moreover, current carriers in materials can either behave like they are negatively charged or positively charged, depending on whether they inhabit the conduction or the valence band. In fact, boun­daries between hole-type and electron-type conductors, known as p-n junctions, form the building blocks of electrical devices such as diodes and tran­sistors. “Unlike in optical materials”, says Hone, “where creating a negative index meta­material is a significant engineering challenge, negative electron refraction occurs naturally in solid state materials at any p-n junction.”

The develop­ment of two-dimensional conducting layers in high-purity semiconductors such as Gallium arsenide in the 1980s and 1990s allowed researchers to first demonstrate electron optics including the effects of both refrac­tion and lensing. However, in these materials, electrons travel without scattering only at very low tempe­ratures, limiting techno­logical appli­cations. Further­more, the presence of an energy gap between the conduction and valence band scatters electrons at interfaces and prevents observation of negative refraction in semi­conductor p-n junctions. In this study, the researchers’ use of graphene, a 2D material with unsur­passed performance at room temperature and no energy gap, overcame both of these limi­tations.

The possi­bility of negative refrac­tion at graphene p-n junctions was first proposed in 2007 by theorists working at both the University of Lancaster and Columbia University. However, observation of this effect requires extremely clean devices, such that the electrons can travel ballisti­cally, without scattering, over long distances. Over the past decade, a multi­disciplinary team at Columbia has worked to develop new techniques to construct extremely clean graphene devices. This effort culminated in the 2013 demon­stration of ballistic transport over a length scale in excess of 20 microns. Since then, they have been attempting to develop a Veselago lens, which focuses electrons to a single point using negative refraction. But they were unable to observe such an effect and found their results puzzling.

In 2015, a group at Pohang University of Science and Techno­logy in South Korea reported the first evidence focusing in a Veselago-type device. However, the response was weak, appearing in the signal derivative. The Columbia team decided that to fully understand why the effect was so elusive, they needed to isolate and map the flow of electrons across the junction. They utilized magnetic focusing to inject electrons onto the p-n junction. By measuring trans­mission between elec­trodes on opposite sides of the junction as a function of carrier density they could map the trajectory of electrons on both sides of the p-n junction as the incident angle was changed by tuning the magnetic field.

Crucial to the Columbia effort was the theore­tical support provided by Ghosh’s group at the University of Virginia, who developed detailed simu­lation techniques to model the Columbia team’s measured response. This involved calculating the flow of electrons in graphene under the various electric and magnetic fields, accounting for multiple bounces at edges, and quantum mechanical tunneling at the junction. The theoretical analysis also shed light on why it has been so difficult to measure the predicted Veselago lensing in a robust way, and the group is developing new multi-junction device archi­tectures based on this study. Together the experimental data and theo­retical simulation gave the researchers a visual map of the refraction, and enabled them to be the first to quanti­tatively confirm the relation­ship between the incident and refracted angles, as well as confirmation of the magnitude of the trans­mitted intensity as a function of angle.

“In many ways, this intensity of trans­mission is a more crucial parameter,” says Ghosh, “since it deter­mines the proba­bility that electrons actually make it past the barrier, rather than just their refracted angles. The trans­mission ultimately determines many of the per­formance metrics for devices based on these effects, such as the on-off ratio in a switch, for example.” (Source: Columbia U)

Reference: S. Chen et al.: Electron optics with p-n junctions in ballistic graphene, Science 353, 1522 (2016); DOI: 10.1126/science.aaf5481

Link: Nanoelectronics Lab., Dept. of Physics, Columbia University, New York, USA

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