Cobalt-mediated crystallographic etching of graphite from defects

Herein is reported a study of Co-assisted crystallographic etching of graphite in hydrogen environment at temperatures above 750 °C. Unlike nanoparticle etching of graphite surface that leaves trenches, the Co could fill the hexagonal or triangular etch-pits that progressively enlarge, before finally balling-up, leaving well-defined etched pits enclosed by edges oriented at 60° or 120° relative to each other. The morphology and chirality of the etched edges have been carefully studied by transmission electron microscopy and Raman analysis, the latter indicating zigzag edges. By introducing defects to the graphite using an oxygen plasma or by utilizing the edges of graphene/graphite flakes (which are considered as defects), an ability to define the position of the etched edges is demonstrated. Based on these results, graphite strips are successfully etched from the edges and graphitic ribbons are fabricated which are enclosed by purely zigzag edges. These fabricated graphitic ribbons could potentially be isolated layer-by-layer and transferred to a device substrate for further processing into graphene nanoribbon transistors.     

Strain-engineering of band gaps in piezoelectric boron nitride nanoribbons

Two-dimensional atomic sheets such as graphene and boron nitride monolayers represent a new class of nanostructured materials for a variety of applications. However, the intrinsic electronic structure of graphene and h-BN atomic sheets limits their direct application in electronic devices. By first-principles density functional theory calculations we demonstrate that band gap of zigzag BN nanoribbons can be significantly tuned under uniaxial tensile strain. The unexpected sensitivity of band gap results from reduced orbital hybridization upon elastic strain. Furthermore, sizable dipole moment and piezoelectric effect are found in these ribbons owing to structural asymmetry and hydrogen passivation. This will offer new opportunities to optimize two-dimensional nanoribbons for applications such as electronic, piezoelectric, photovoltaic, and opto-electronic devices.     

Electronic structure and stability of semiconducting graphene nanoribbons

We present a systematic density functional theory study of the electronic properties, optical spectra, and relative thermodynamic stability of semiconducting graphene nanoribbons. We consider ribbons with different edge nature including bare and hydrogen-terminated ribbons, several crystallographic orientations, and widths up to 3 nm. Our results can be extrapolated to wider ribbons providing a qualitative way of determining the electronic properties of ribbons with widths of practical significance. We predict that in order to produce materials with band gaps similar to Ge or InN, the width of the ribbons must be between 2 and 3 nm. If larger bang gap ribbons are needed (like Si, InP, or GaAs), their width must be reduced to 1-2 nm. According to the extrapolated inverse power law obtained in this work, armchair carbon nanoribbons of widths larger than 8 nm will present a maximum band gap of 0.3 eV, while for ribbons with a width of 80 nm the maximum possible band gap is 0.05 eV. For chiral nanoribbons the band gap oscillations rapidly vanish as a function of the chiral angle indicating that a careful design of their crystallographic nature is an essential ingredient for controlling their electronic properties. Optical excitations show important differences between ribbons with and without hydrogen termination and are found to be sensitive to the carbon nanoribbon width. This should provide a practical way of revealing information on their size and the nature of their edges.     

Direct imaging of graphene edges: atomic structure and electronic scattering

We report an atomically resolved scanning tunneling microscopy investigation of the edges of graphene grains synthesized on Cu foils by chemical vapor deposition. Most of the edges are macroscopically parallel to the zigzag directions of graphene lattice. These edges have microscopic roughness that is found to also follow zigzag directions at atomic scale, displaying many ～120° turns. A prominent standing wave pattern with periodicity ～3a/4 (a being the graphene lattice constant) is observed near a rare-occurring armchair-oriented edge. Observed features of this wave pattern are consistent with the electronic intervalley backscattering predicted to occur at armchair edges but not at zigzag edges.     

First-principles study of heat transport properties of graphene nanoribbons

We use density-functional theory and the nonequilibrium Green's function method as well as phonon dispersion calculations to study the thermal conductance of graphene nanoribbons with armchair and zigzag edges, with and without hydrogen passivation. We find that low-frequency phonon bands of the zigzag ribbons are more dispersive than those of the armchair ribbons and that this difference accounts for the anisotropy in the thermal conductance of graphene nanoribbons. Comparing our results with data on large-area graphene, edge effects are shown to contribute to thermal conductance, enhance the anisotropy in thermal conductance of graphene nanoribbons, and increase thermal conductance per unit width. The edges with and without hydrogen passivation modify the atomic structure and ultimately influence the phonon thermal transport differently for the two ribbon types.     

Raman scattering at pure graphene zigzag edges

Theory has predicted rich and very distinct physics for graphene devices with boundaries that follow either the armchair or the zigzag crystallographic directions. A prerequisite to disclose this physics in experiment is to be able to produce devices with boundaries of pure chirality. Exfoliated flakes frequently exhibit corners with an odd multiple of 30°, which raised expectations that their boundaries follow pure zigzag and armchair directions. The predicted Raman behavior at such crystallographic edges however failed to confirm pure edge chirality. Here, we perform confocal Raman spectroscopy on hexagonal holes obtained after the anisotropic etching of prepatterned pits using carbothermal decomposition of SiO(2). The boundaries of the hexagonal holes are aligned along the zigzag crystallographic direction and leave hardly any signature in the Raman map indicating unprecedented purity of the edge chirality. This work offers the first opportunity to experimentally confirm the validity of the Raman theory for graphene edges.     

Graphene edge lithography

Fabrication of graphene nanostructures is of importance for both investigating their intrinsic physical properties and applying them into various functional devices. In this paper, we report a scalable fabrication approach for graphene nanostructures. Compared with conventional lithographic fabrication techniques, this new approach uses graphene edges as the templates or masks and offers advantage in technological simplicity and capability of creating small features below 10 nm scale. Moreover, mask layers used in the fabrication process could be simultaneously used as the dielectric layers for top-gated devices. The as-fabricated graphene nanoribbons (GNRs) are of high quality with the carrier mobility ～400 cm(2)/(V s) for typical 15 nm wide ribbons. Our technique allows easy and reproducible fabrication of various graphene nanostructures, such as ribbons and rings, and can be potentially extended to other materials and systems by use of their edges or facets as templates.     

Prediction of very large values of magnetoresistance in a graphene nanoribbon device

Graphene has emerged as a versatile material with outstanding electronic properties that could prove useful in many device applications. Recently, the demonstration of spin injection into graphene and the observation of long spin relaxation times and lengths have suggested that graphene could play a role in 'spintronic' devices that manipulate electron spin rather than charge. In particular it has been found that zigzag graphene nanoribbons have magnetic (or spin) states at their edges, and that these states can be either antiparallel or parallel. Here we report the results of first-principles simulations that predict that spin-valve devices based on graphene nanoribbons will exhibit magnetoresistance values that are thousands of times higher than previously reported experimental values. These remarkable values can be linked to the unique symmetry of the band structure in the nanoribbons. We also show that it is possible to manipulate the band structure of the nanoribbons to generate highly spin-polarized currents.     

Electronic and magnetic properties and structural stability of BeO sheet and nanoribbons

The novel electronic and magnetic properties of BeO nanoribbons (BeO NRs) as well as their stability are investigated through extensive density functional theory calculations. Different from semiconducting graphene nanoribbons and insulating BN ribbons, all zigzag edged BeO NRs are revealed to display ferromagnetic and metallic natures independent of the ribbon width and edge passivation. The polarized electron spins in H-passivated zigzag BeO NRs are from the unpaired electrons around the weakly formed Be-H bonds, while those of bare zigzag BeO NRs are due to the 2p states of edge O atoms. In sharp contrast, all armchair BeO NRs are nonmagnetic insulators regardless of the edge passivation. In particular, all bare armchair BeO NRs have a nearly constant band gap due to a peculiar edge localization effect. Interestingly, the band gaps of all armchair BeO NRs can be markedly reduced by an applied transverse electric field and even completely closed at a critical field. The critical electric field required for gap closing decreases with increasing ribbon width, thus the results have practical importance. Further stability analysis shows that bare BeO NRs are more stable than H-passivated BeO NRs of similar ribbon widths and bare armchair BeO NRs are energetically the most favorable among all the nanoribbons.     

Electronic states of graphene nanoribbons and analytical solutions

Abstract

Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of π-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber. The quantization rule of electronic conductance as well as the magnetic instability of edge states due to the electron–electron interaction are briefly discussed.     

Energy gaps and stark effect in boron nitride nanoribbons

A first-principles investigation of the electronic properties of boron nitride nanoribbons (BNNRs) having either armchair or zigzag shaped edges passivated by hydrogen with widths up to 10 nm is presented. Band gaps of armchair BNNRs exhibit family dependent oscillations as the width increases and, for ribbons wider than 3 nm, converge to a constant value that is 0.02 eV smaller than the bulk band gap of a boron nitride sheet owing to the existence of very weak edge states. The band gap of zigzag BNNRs monotonically decreases and converges to a gap that is 0.7 eV smaller than the bulk gap due to the presence of strong edge states. When a transverse electric field is applied, the band gaps of armchair BNNRs decrease monotonically with the field strength. For the zigzag BNNRs, however, the band gaps and the carrier effective masses either increase or decrease depending on the direction and the strength of the field.     

Nonlocal exchange interaction removes half-metallicity in graphene nanoribbons

Band gap studies of zigzag-edge graphene ribbons are presented. While earlier calculations at LDA level show that zigzag-edge graphene ribbons become half-metallic when cross-ribbon electric fields are applied, our calculations with hybrid density functional demonstrate that finite graphene ribbons behave as half-semiconductors. The spin-dependent band gap can be changed in a wide range, making possible many applications in spintronics.     

Chemical sensitivity of graphene edges decorated with metal nanoparticles

Graphene is a novel two-dimensional nanomaterial that holds great potential in electronic and sensor applications. By etching the edges to form nanoribbons or introducing defects on the basal plane, it has been demonstrated that the physical and chemical properties of graphene can be drastically altered. However, the lithographic or chemical techniques required to reliably produce such nanoribbons remain challenging. Here, we report the fabrication of nanosensors based on holey reduced graphene oxide (hRGO), which can be visualized as interconnected graphene nanoribbons. In our method, enzymatic oxidation generated holes within the basal plane of graphene oxide, and after reduction with hydrazine, hRGO was formed. When decorated with Pt nanoparticles, hRGO exhibited a large and selective electronic response toward hydrogen gas. By combining experimental results and theoretical modeling, we propose that the increased edge-to-plane ratio, oxygen moieties, and Pt nanoparticle decoration were responsible for the observed gas sensing with hRGO nanostructures.     

Sawtooth-like graphene nanoribbon

Motivated by recent successful synthesize of segmented graphene nanoribbons (GNRs) with junctions, we explore electronic properties of a novel form of GNR with sawtooth-like structure using the density-functional theory method. It is found that the unique edge structures of the sawtooth-like GNR induce richer band-gap features than the straight GNR counterpart with either armchair or zigzag edges. The effect of external electric field on the electronic properties of the sawtooth-like GNR is also studied. The theoretical results may be useful for designing GNR-based fi eld-effect transistors.     

Enhanced half-metallicity in edge-oxidized zigzag graphene nanoribbons

We present a comprehensive theoretical study of the electronic properties and relative stabilities of edge-oxidized zigzag graphene nanoribbons. The oxidation schemes considered include hydroxyl, lactone, ketone, and ether groups. Using screened exchange density functional theory, we show that these oxidized ribbons are more stable than hydrogen-terminated nanoribbons except for the case of the etheric groups. The stable oxidized configurations maintain a spin-polarized ground state with antiferromagnetic ordering localized at the edges, similar to the fully hydrogenated counterparts. More important, edge oxidation is found to lower the onset electric field required to induce half-metallic behavior and extend the overall field range at which the systems remain half-metallic. Once the half-metallic state is reached, further increase of the external electric field intensity produces a rapid decrease in the spin magnetization up to a point where the magnetization is quenched completely. Finally, we find that oxygen-containing edge groups have a minor effect on the energy difference between the antiferromagnetic ground state and the above-lying ferromagnetic state.     

A facile method for fabrication of large area graphene nanostructures

In this study, we introduce a novel method to produce large area interconnected graphene nanostructures. A single layer CVD (Chemical Vapor Deposition) grown graphene was nanostructured by employing dewetted Ni thin film as an etching mask for the underlying graphene. As a result, a network of graphene nanostructures with irregular shapes and widths down to 10 nm is obtained. The FET (field effect transistor) devices fabricated employing the nanostructured graphene as channel material exhibit increased on/off current ratio compared to pristine graphene indicating a slight band gap opening due to the quantum confinement effect in such narrow graphene nanostructures. This technique can be useful for the large scale fabrication of graphene based electronic devices such as FETs and sensors.     

Edge stability of boron nitride nanoribbons and its application in designing hybrid BNC structures

First-principles investigations of the edge energies and edge stresses of single-layer hexagonal boron nitride (BN) are presented. The armchair edges of BN nanoribbons (BNNRs) are more stable in energy than zigzag ones. Armchair BNNRs are under compressive edge stress while zigzag BNNRs are under tensile edge stress, due to the edge reconstruction effect and edge coulomb repulsion effect. The intrinsic spin-polarization and edge saturation play important roles in modulating the edge stability of BNNRs. The edge energy difference between BN and graphene can be used to guide the design of specific hybrid BNC structures as the hybrid BNC systems prefer the low-energy edge configurations: In an armchair BNC nanoribbon (BNCNR), BN domains are expected to grow outside of C domains, while the opposite occurs in a zigzag BNCNR. More importantly, armchair BNCNRs can reproduce unique electronic properties of armchair graphene nanoribbons (GNRs), which are expected to be robust against edge functionalization or disorder. Within a certain range of C/BN ratios, zigzag BNCNRs may exhibit intrinsic half-metallicity without any external constraints. These diverse electronic properties of BNCNRs may offer unique opportunities to develop nanoscale electronics and spintronics beyond individual graphene and BN. More generally, these principles for designing BNC can also be extended to other hybrid nanostructures.      

The half-metallicity of zigzag graphene nanoribbons with asymmetric edge terminations

The spin-polarized electronic structure and half-metallicity of zigzag graphene nanoribbons (ZGNRs) with asymmetric edge terminations are investigated by using first-principles calculations. It is found that compared with symmetric hydrogen-terminated counterparts, such ZGNRs maintain a spin-polarized ground state with the anti-ferromagnetic configuration at opposite edges, but their energy bands are no longer spin degenerate. In particular, the energy gap of one spin orientation decreases remarkably. Consequently, the ground state of such ZGNRs is very close to half-metallic state, and thus a smaller critical electric field is required for the systems to achieve the half-metallic state. Moreover, two kinds of studied ZGNRs present massless Dirac-fermion band structure when they behave like half-metals.     

Optical control of edge chirality in graphene

We performed optical annealing experiments at the edges of nanopatterned graphene to study the resultant edge reconstruction. The lithographic patterning direction was orthogonal to a zigzag edge. μ-Raman spectroscopy shows an increase in the polarization contrast of the G band as a function of annealing time. Furthermore, transport measurements reveal a 50% increase of the GNR energy gap after optical exposure, consistent with an increased percentage of armchair segments. These results suggest that edge chirality of graphene devices can be optically purified post electron beam lithography, thereby enabling the realization of chiral graphene nanoribbons and heterostructures.     

Coupling of surface and lowest Landau level states in a rectangular graphene dot

A rectangular graphene dot with two zigzag edges and two armchair edges have electronic states in the presence of a magnetic field that are localized on the zigzag edges with non zero values of the wavefunction inside the dot. We have investigated the dependence of these wavefunctions on the size of the dot, and explain the physical origin of them in terms of surface and the lowest Landau level (LLL) states of infinitely long nanoribbons. We find that the armchair edges play a crucial role by coupling the surface and LLL states.