Graphene nanoribbon

Graphene nanoribbons are strips of graphene with width less than 100 nm. Graphene ribbons were introduced as a theoretical model by Mitsutaka Fujita and coauthors to examine the edge and nanoscale size effect in graphene. Some earlier studies of graphitic ribbons within the area of conductive polymers in the field of synthetic metals include works by Kazuyoshi Tanaka, Tokio Yamabe and co-authors, Steven Kivelson and Douglas J. Klein. While Tanaka, Yamabe and Kivelson studied so-called zigzag and armchair edges of graphite, Klein introduced a different edge geometry that is frequently referred to as a bearded edge.

Production

Nanotomy

Large quantities of width-controlled GNRs can be produced via graphite nanotomy, where applying a sharp diamond knife on graphite produces graphite nanoblocks, which can then be exfoliated to produce GNRs as shown by Vikas Berry. GNRs can also be produced by "unzipping" or axially cutting nanotubes. In one such method multi-walled carbon nanotubes were unzipped in solution by action of potassium permanganate and sulfuric acid. In another method GNRs were produced by plasma etching of nanotubes partly embedded in a polymer film. More recently, graphene nanoribbons were grown onto silicon carbide substrates using ion implantation followed by vacuum or laser annealing. The latter technique allows any pattern to be written on SiC substrates with 5 nm precision.

Epitaxy

GNRs were grown on the edges of three-dimensional structures etched into silicon carbide wafers. When the wafers are heated to approximately, silicon is preferentially driven off along the edges, forming nanoribbons whose structure is determined by the pattern of the three-dimensional surface. The ribbons had perfectly smooth edges, annealed by the fabrication process. Electron mobility measurements surpassing one million correspond to a sheet resistance of one ohm per square — two orders of magnitude lower than in two-dimensional graphene.

Chemical vapor deposition

Nanoribbons narrower than 10 nm grown on a germanium wafer act like semiconductors, exhibiting a band gap. Inside a reaction chamber, using chemical vapor deposition, methane is used to deposit hydrocarbons on the wafer surface, where they react with each other to produce long, smooth-edged ribbons. The ribbons were used to create prototype transistors. At a very slow growth rate, the graphene crystals naturally grow into long nanoribbons on a specific germanium crystal facet. By controlling the growth rate and growth time, the researchers achieved control over the nanoribbon width.
Recently, researchers from SIMIT reported on a strategy to grow graphene nanoribbons with controlled widths and smooth edges directly onto dielectric hexagonal boron nitride substrates. The team use nickel nanoparticles to etch monolayer-deep, nanometre-wide trenches into h-BN, and subsequently fill them with graphene using chemical vapour deposition. Modifying the etching parameters allows the width of the trench to be tuned to less than 10 nm, and the resulting sub-10-nm ribbons display bandgaps of almost 0.5 eV. Integrating these nanoribbons into field effect transistor devices reveals on–off ratios of greater than 10⁴ at room temperature, as well as high carrier mobilities of ~750 cm² V⁻¹ s⁻¹.

Multistep nanoribbon synthesis

A bottom-up approach was investigated. In 2017 dry contact transfer was used to press a fiberglass applicator coated with a powder of atomically precise graphene nanoribbons on a hydrogen-passivated Si surface under vacuum. 80 of 115 GNRs visibly obscured the substrate lattice with an average apparent height of 0.30 nm. The GNRs do not align to the Si lattice, indicating a weak coupling. The average bandgap over 21 GNRs was 2.85 eV with a standard deviation of 0.13 eV.
The method unintentionally overlapped some nanoribbons, allowing the study of multilayer GNRs. Such overlaps could be formed deliberately by manipulation with a scanning tunneling microscope. Hydrogen depassivation left no band-gap. Covalent bonds between the Si surface and the GNR leads to metallic behavior. The Si surface atoms move outward, and the GNR changes from flat to distorted, with some C atoms moving in toward the Si surface.

Electronic structure

The electronic states of GNRs largely depend on the edge structures. In zigzag edges each successive edge segment is at the opposite angle to the previous. In armchair edges, each pair of segments is a 120/-120 degree rotation of the prior pair. The animation below provides a visualization explanation of both. Zigzag edges provide the edge localized state with non-bonding molecular orbitals near the Fermi energy. They are expected to have large changes in optical and electronic properties from quantization.
Calculations based on tight binding theory predict that zigzag GNRs are always metallic while armchairs can be either metallic or semiconducting, depending on their width. However, density functional theory calculations show that armchair nanoribbons are semiconducting with an energy gap scaling with the inverse of the GNR width. Experiments verified that energy gaps increase with decreasing GNR width. Graphene nanoribbons with controlled edge orientation have been fabricated by scanning tunneling microscope lithography. Energy gaps up to 0.5 eV in a 2.5 nm wide armchair ribbon were reported.
Armchair nanoribbons are metallic or semiconducting and present spin polarized edges. Their gap opens thanks to an unusual antiferromagnetic coupling between the magnetic moments at opposite edge carbon atoms. This gap size is inversely proportional to the ribbon width and its behavior can be traced back to the spatial distribution properties of edge-state wave functions, and the mostly local character of the exchange interaction that originates the spin polarization. Therefore, the quantum confinement, inter-edge superexchange, and intra-edge direct exchange interactions in zigzag GNR are important for its magnetism and band gap. The edge magnetic moment and band gap of zigzag GNR are reversely proportional to the electron/hole concentration and they can be controlled by alkaline adatoms.
Their 2D structure, high electrical and thermal conductivity and low noise also make GNRs a possible alternative to copper for integrated circuit interconnects. Research is exploring the creation of quantum dots by changing the width of GNRs at select points along the ribbon, creating quantum confinement. Heterojunctions inside single graphene nanoribbons have been realized, among which structures that have been shown to function as tunnel barriers.
Graphene nanoribbons possess semiconductive properties and may be a technological alternative to silicon semiconductors capable of sustaining microprocessor clock speeds in the vicinity of 1 THz field-effect transistors less than 10 nm wide have been created with GNR – "GNRFETs" – with an I_on/I_off ratio >10⁶ at room temperature.

Electronic structure in external fields

The electronic properties in external field such as static electric or magnetic field have been extensively studied. The various levels of the tight-binding model as well as first principles calculations have been employed for such studies.
For for zigzag nanoribbons the most interesting effect under an external electric field is inducing of half-metallicity. In a simple tight-binding model the effect of the external in-plane field applied across the ribbon width is the band gap opening between the edge states. However, the first principles spin-polarized calculations demonstrate that the spin up and down species behave differently. One spin projection closes the band gap whereas another increases. As a result, at some critical value of field, the ribbon turns into a metallic for one spin projection and an insulating for another spin. In this way, half-metallicity that may be useful for spintronics applications is induced.
Armchair ribbons behave differently from their zigzag siblings. They usually feature a band gap that closes under an external in-plane electric field. At some critical value of the field the gap fully closes forming a Dirac cone linear crossing, see Fig. 9d in Ref. This intriguing result have been corroborated by the density functional theory calculations and explained in a simplified tight-binding model. It does not depend on the chemical composition of the ribbon edges, for example both fluorine and chorine atoms can be used for the ribbon edge passivation instead of a usual hydrogen. Also this effect can be induced by chemical co-doping, i.e. by placing nitrogen and boron atoms atop the ribbon at its opposite sides. Modelwise the effect can be explained by a pair of cis-polyacetylene chains placed at a distance corresponding to the ribbon width and subjected to the different gate potentials.
Bearded ribbons with Klen-type edges behave in the tight-binding model approximation similar to zigzag ribbons. Namely, the band gap opens between the edge states. Due to chemical instability of this type of the edge configuration, such ribbons are normally excluded from the publications. Whether they can at least hypothetically exhibit half-metallicity in external in-plane fields similar to zigzag nanoribbons is not yet clear.
A vast family of cousins of the above ribbons with both similar edges is the class of ribbons combining non-equivalent edge geometries in a single ribbon. One of the simplest examples can be a half-bearded nanoribbon. Such ribbons, in principle, could be more stable than nanoribbons with two bearded edges because they could be realized via asymmetric hydrogenation of zigzag ribbons. In the nearest neighbor tight-binding model and in non-spin-polarized density functional theory calculations such ribbons exhibit chiral anomaly structure. The fully flat band of a pristine half-bearded nanoribbon subjected to the in-plane external electric field demonstrates unidirectional linear dispersions with group velocities of opposite directions around each of the two Dirac points. At high fields, the linear bands around the Dirac points transform into a wiggly cubic-like dispersions. This nontrivial behavior is favorable for the field-tunable dissipationless transport. The drastic transformation from fully flat to linear and then cubic-like band allows for a continuum model description based on the Dirac equation. The Dirac equation supplemented with the suitable boundary conditions breaking the inversion/mirror symmetry and a single field strength parameter admits an analytic solution in terms of Airy-like special functions.