David Kirkpatrick

August 11, 2010

Better understanding graphene

Yes, graphene is something of a miracle material (hit this link for my extensive graphene blogging), and yes it’s proving to be very vexing material as well. There’s a whole lot of promise, but not so much practice because graphene is proving to be a very fickle material. Research like this from the Georgia Institute of Technology is particularly important because unlocking the secret life of graphene will allow for increasing practical applications. Better understanding will lead to better utilization.

The release:

Study of electron orbits in multilayer graphene finds unexpected energy gaps

Electron transport

IMAGE: Stacking of graphene sheets creates regions where the moiré alignment is of type AA (all atoms have neighbors in the layer below), AB (only A atoms have neighbors) or BA…

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Researchers have taken one more step toward understanding the unique and often unexpected properties of graphene, a two-dimensional carbon material that has attracted interest because of its potential applications in future generations of electronic devices.

In the Aug. 8 advance online edition of the journal Nature Physics, researchers from the Georgia Institute of Technology and the National Institute of Standards and Technology (NIST) describe for the first time how the orbits of electrons are distributed spatially by magnetic fields applied to layers of epitaxial graphene.

The research team also found that these electron orbits can interact with the substrate on which the graphene is grown, creating energy gaps that affect how electron waves move through the multilayer material. These energy gaps could have implications for the designers of certain graphene-based electronic devices.

“The regular pattern of energy gaps in the graphene surface creates regions where electron transport is not allowed,” said Phillip N. First, a professor in the Georgia Tech School of Physics and one of the paper’s co-authors. “Electron waves would have to go around these regions, requiring new patterns of electron wave interference. Understanding such interference will be important for bi-layer graphene devices that have been proposed, and may be important for other lattice-matched substrates used to support graphene and graphene devices.”

In a magnetic field, an electron moves in a circular trajectory – known as a cyclotron orbit – whose radius depends on the size of the magnetic field and the energy of electron. For a constant magnetic field, that’s a little like rolling a marble around in a large bowl, First said.

“At high energy, the marble orbits high in the bowl, while for lower energies, the orbit size is smaller and lower in the bowl,” he explained. “The cyclotron orbits in graphene also depend on the electron energy and the local electron potential – corresponding to the bowl – but until now, the orbits hadn’t been imaged directly.”

Placed in a magnetic field, these orbits normally drift along lines of nearly constant electric potential. But when a graphene sample has small fluctuations in the potential, these “drift states” can become trapped at a hill or valley in the material that has closed constant potential contours. Such trapping of charge carriers is important for the quantum Hall effect, in which precisely quantized resistance results from charge conduction solely through the orbits that skip along the edges of the material.

IMAGE: This graphic shows electrons that move along an equipotential, while those that follow closed equipotentials (as in a potential-energy valley) become localized (right). The arrows denote the magnetic field,…

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The study focused on one particular electron orbit: a zero-energy orbit that is unique to graphene. Because electrons are matter waves, interference within a material affects how their energy relates to the velocity of the wave – and reflected waves added to an incoming wave can combine to produce a slower composite wave. Electrons moving through the unique “chicken-wire” arrangement of carbon-carbon bonds in the graphene interfere in a way that leaves the wave velocity the same for all energy levels.

In addition to finding that energy states follow contours of constant electric potential, the researchers discovered specific areas on the graphene surface where the orbital energy of the electrons changes from one atom to the next. That creates an energy gap within isolated patches on the surface.

“By examining their distribution over the surface for different magnetic fields, we determined that the energy gap is due to a subtle interaction with the substrate, which consists of multilayer graphene grown on a silicon carbide wafer,” First explained.

In multilayer epitaxial graphene, each layer’s symmetrical sublattice is rotated slightly with respect to the next. In prior studies, researchers found that the rotations served to decouple the electronic properties of each graphene layer.

“Our findings hold the first indications of a small position-dependent interaction between the layers,” said David L. Miller, the paper’s first author and a graduate student in First’s laboratory. “This interaction occurs only when the size of a cyclotron orbit – which shrinks as the magnetic field is increased – becomes smaller than the size of the observed patches.”

The origin of the position dependent interaction is believed to be the “moiré pattern” of atomic alignments between two adjacent layers of graphene. In some regions, atoms of one layer lie atop atoms of the layer below, while in other regions, none of the atoms align with the atoms in the layer below. In still other regions, half of the atoms have neighbors in the underlayer, an instance in which the symmetry of the carbon atoms is broken and the Landau level – discrete energy level of the electrons – splits into two different energies.

Experimentally, the researchers examined a sample of epitaxial graphene grown at Georgia Tech in the laboratory of Professor Walt de Heer, using techniques developed by his research team over the past several years.

They used the tip of a custom-built scanning-tunneling microscope (STM) to probe the atomic-scale electronic structure of the graphene in a technique known as scanning tunneling spectroscopy. The tip was moved across the surface of a 100-square nanometer section of graphene, and spectroscopic data was acquired every 0.4 nanometers.

The measurements were done at 4.3 degrees Kelvin to take advantage of the fact that energy resolution is proportional to the temperature. The scanning-tunneling microscope, designed and built by Joseph Stroscio at NIST’s Center for Nanoscale Science and Technology, used a superconducting magnet to provide the magnetic fields needed to study the orbits.

According to First, the study raises a number of questions for future research, including how the energy gaps will affect electron transport properties, how the observed effects may impact proposed bi-layer graphene coherent devices – and whether the new phenomenon can be controlled.

“This study is really a stepping stone in long path to understanding the subtleties of graphene’s interesting properties,” he said. “This material is different from anything we have worked with before in electronics.”


In addition to those already mentioned, the study also included Walt de Heer, Kevin D. Kubista, Ming Ruan, and Markus Kinderman from Georgia Tech and Gregory M. Rutter from NIST. The research was supported by the National Science Foundation, the Semiconductor Research Corporation and the W.M. Keck Foundation. Additional assistance was provided by Georgia Tech’s Materials Research Science and Engineering Center (MRSEC)

June 5, 2009

Graphene beats copper in IC connections

It’s been a while since I’ve had the chance to blog about graphene, but here is the latest on the carbon nanomaterial.  (Be sure to hit the second link for images.)

The release:

Graphene May Have Advantages Over Copper for Future IC Interconnects

New Material May Replace Traditional Metal at Nanoscale Widths

Atlanta (June 4, 2009) —The unique properties of thin layers of graphite—known as graphene—make the material attractive for a wide range of potential electronic devices. Researchers have now experimentally demonstrated the potential for another graphene application: replacing copper for interconnects in future generations of integrated circuits.

In a paper published in the June 2009 issue of the IEEE journal Electron Device Letters, researchers at the Georgia Institute of Technology report detailed analysis of resistivity in graphene nanoribbon interconnects as narrow as 18 nanometers.

The results suggest that graphene could out-perform copper for use as on-chip interconnects—tiny wires that are used to connect transistors and other devices on integrated circuits. Use of graphene for these interconnects could help extend the long run of performance improvements for silicon-based integrated circuit technology.

“As you make copper interconnects narrower and narrower, the resistivity increases as the true nanoscale properties of the material become apparent,” said Raghunath Murali, a research engineer in Georgia Tech’s Microelectronics Research Center and the School of Electrical and Computer Engineering. “Our experimental demonstration of graphene nanowire interconnects on the scale of 20 nanometers shows that their performance is comparable to even the most optimistic projections for copper interconnects at that scale. Under real-world conditions, our graphene interconnects probably already out-perform copper at this size scale.”

Beyond resistivity improvement, graphene interconnects would offer higher electron mobility, better thermal conductivity, higher mechanical strength and reduced capacitance coupling between adjacent wires.

“Resistivity is normally independent of the dimension—a property inherent to the material,” Murali noted. “But as you get into the nanometer-scale domain, the grain sizes of the copper become important and conductance is affected by scattering at the grain boundaries and at the side walls. These add up to increased resistivity, which nearly doubles as the interconnect sizes shrink to 30 nanometers.”

The research was supported by the Interconnect Focus Center, which is one of the Semiconductor Research Corporation/DARPA Focus Centers, and the Nanoelectronics Research Initiative through the INDEX Center.

Murali and collaborators Kevin Brenner, Yinxiao Yang, Thomas Beck and James Meindl studied the electrical properties of graphene layers that had been taken from a block of pure graphite. They believe the attractive properties will ultimately also be measured in graphene fabricated using other techniques, such as growth on silicon carbide, which now produces graphene of lower quality but has the potential for achieving higher quality.

Because graphene can be patterned using conventional microelectronics processes, the transition from copper could be made without integrating a new manufacturing technique into circuit fabrication.

“We are optimistic about being able to use graphene in manufactured systems because researchers can already grow layers of it in the lab,” Murali noted. “There will be challenges in integrating graphene with silicon, but those will be overcome. Except for using a different material, everything we would need to produce graphene interconnects is already well known and established.”

Experimentally, the researchers began with flakes of multi-layered graphene removed from a graphite block and placed onto an oxidized silicon substrate. They used electron beam lithography to construct four electrode contacts on the graphene, then used lithography to fabricate devices consisting of parallel nanoribbons of widths ranging between 18 and 52 nanometers. The three-dimensional resistivity of the nanoribbons on 18 different devices was then measured using standard analytical techniques at room temperature.

The best of the graphene nanoribbons showed conductivity equal to that predicted for copper interconnects of the same size. Because the comparisons were between non-optimized graphene and optimistic estimates for copper, they suggest that performance of the new material will ultimately surpass that of the traditional interconnect material, Murali said.

“Even graphene samples of moderate quality show excellent properties,” he explained. “We are not using very high levels of optimization or especially clean processes. With our straightforward processing, we are getting graphene interconnects that are essentially comparable to copper. If we do this more optimally, the performance should surpass copper.”

Though one of graphene’s key properties is reported to be ballistic transport—meaning electrons can flow through it without resistance—the material’s actual conductance is limited by factors that include scattering from impurities, line-edge roughness and from substrate phonons—vibrations in the substrate lattice.

Use of graphene interconnects could help facilitate continuing increases in integrated circuit performance once features sizes drop to approximately 20 nanometers, which could happen in the next five years, Murali said. At that scale, the increased resistance of copper interconnects could offset performance increases, meaning that without other improvements, higher density wouldn’t produce faster integrated circuits.

“This is not a roadblock to achieving scaling from one generation to the next, but it is a roadblock to achieving increased performance,” he said. “Dimensional scaling could continue, but because we would be giving up so much in terms of resistivity, we wouldn’t get a performance advantage from that. That’s the problem we hope to solve by switching to a different materials system for interconnects.”