Width Of Graphene Nanoribbons Research Articles

Spectroscopic study of graphene nanoribbons formed by crystallographic etching of highly oriented pyrolytic graphite

We report a scanning tunneling spectroscopy study systematically performed on graphene nanoribbons (GNRs) with various widths and layer numbers. The GNRs are formed on highly oriented pyrolytic graphite (HOPG) by crystallographic etching, as reported by Datta and co-workers [Nano Lett. 8, 1912 (2008)]. Regardless of the width and layer numbers, GNRs having zigzag edges exhibit a peak at the Fermi energy in their local density of states (LDOS) when measured near the edges, whereas no peak appears away from the edges. On the other hand, a depression of the LDOS emerges at the Fermi energy in the case of a GNR having armchair edges with no relation to the measured position in an identical GNR. The energy gap of the LDOS depression monotonically decreases with increasing GNR width, whereas there is no apparent dependence on the layer numbers. By comparison with the band structure calculated by a nearest-neighbor tight-binding method, it is suggested that the overlap of wave functions between the topmost layer and the underlayers is negligible, resulting in an LDOS similar to that on an isolated monolayer GNR even on an HOPG substrate. From the quantitative scaling of energy gaps (Egap) of LDOS depression with respect to GNR widths (W), the relation between the two is obtained as Egap = 1.9 [eV nm]/W.

Band gap opening in zigzag graphene nanoribbon modulated with magnetic atoms

The effects of magnetic atom on the band structure of zigzag-edged graphene nanoribbons are investigated by the density functional theory. The results show that for narrow zigzag-edged graphene nanoribbons, the band gap can be opened duo to the spin-up/spin-down charges being re-enriched on the edge sites. However, for the wide zigzag-edged graphene nanoribbons, a spin-up/spin-down half-metallic property can be observed. Moreover, it is found that the Seebeck coefficients in the narrow zigzag-edged graphene nanoribbons are reversed and enlarged, which provides a way to design novel thermoelectric device.

Tri-Gate Graphene Nanoribbon Transistors With Transverse-Field Bandgap Modulation

The CMOS-compatible double-spacer lithography demonstrates a scalable approach to fabricate the tri-gate graphene nanoribbon (GNR) transistor with self-aligned side gates, controllable GNR width, and reduced variations in line-edge roughness and GNR width. The electrical characteristics show bandgap modulation with transverse fields and ambipolar conduction with perpendicular fields. Bandgap modulation parameters are extracted from various GNR devices, but the experimental results show lower critical fields than those in the theoretical calculation. By integrating the bandgap modulation effect into CMOS device designs, the device switching performance can be improved. The subthreshold region and ON-state characteristics are investigated by simulation with the extracted parameters to purge the parasitic effects in the present fabrication process. The extra side-gate dependence achieves drain current enhancement in both saturation and linear regions, and the decreasing bandgap by the increasing transverse field results in the sharp switching of 37 mV/decade close to the threshold voltage. This FET switching improvement can be directly used for low-power operation without sacrificing ON current. In addition, the low-linear-region resistance makes bandgap modulation a promising concept for power gating devices.

Unified bandgap engineering of graphene nanoribbons

Unified bandgap engineering, valid both for the armchair and zigzag graphene nanoribbons (GNRs), is enunciated. Using the boundary condition appropriate for K–K′ points of the Dirac cones, GNRs are shown to exhibit three distinct semiconducting states SC0, SC1, and SC2 with complete absence of metallic state. The experimental bandgap for 7‐AGNR and 13‐AGNR armchair (A) is found to be in excellent agreement with SC1 state. Similar associations are pointed out for other configurations. Both the experimental data and theoretical results show bandgap and effective mass inversely proportional to the GNR width. The effective mass is directly proportional to the bandgap. The indexing scheme connects chiral index of carbon nanotubes (CNTs) to that used for GNR by making edge corrections for the dangling bonds.

Rectification induced in N2AA-doped armchair graphene nanoribbon device

By using non-equilibrium Green function formalism in combination with density functional theory, we investigated the electronic transport properties of armchair graphene nanoribbon devices in which one lead is undoped and the other is N2AA-doped with two quasi-adjacent substitutional nitrogen atoms incorporating pairs of neighboring carbon atoms in the same sublattice A. Two kinds of N2AA-doped style are considered, for N dopants substitute the center or the edge carbon atoms. Our results show that the rectification behavior with a large rectifying ratio can be found in these devices and the rectifying characteristics can be modulated by changing the width of graphene nanoribbons or the position of the N2AA dopant. The mechanisms are revealed to explain the rectifying behaviors.

Mechanical properties and thermal conductivity of the twisted graphene nanoribbons

Molecular dynamics method was used to simulate the twists of four GNRs (graphene nanoribbons), two AGNRs (armchair GNRs), and two ZGNRs (zigzag GNRs). Thermal conductivity of the length-fixing GNRs under torsion and at high temperature was calculated. It is found that the ZGNRs have better torsional rigidity than the AGNRs; under the torsional deformation of 34.2°/nm local buckling occurs in the length-fixing GNRs, and under the deformation of 22.8°/nm overall buckling occurs in the ones with free-length. In the range of investigated twist-angle and temperature, the thermal conductivity of the length-fixing GNRs decreases with the increase of torsional deformation and temperature. The wider GNRs have better anti-torsion capability and thermal conductivity.

Ballistic thermoelectric properties in double-bend graphene nanoribbons

Abstract Ballistic thermoelectric properties in double-bend graphene nanoribbons (GNRs) are investigated by using the nonequilibrium Green's function. We find that due to the elastic scattering caused by the interface mismatching, the thermal conductance contributed by phonons is greatly reduced, while ballistic transport behaviors for electrons are dramatically demolished, and even some gaps can be opened at antiresonance energies. Near these antiresonance gaps, the maximum value of ZT ( Z T max ) can be observed, much larger than that for straight GNRs. Moreover, this Z T max can be effectively tuned by modulating the length or width of double-bend GNRs.

Magnetism and transport properties of zigzag graphene nanoribbons/hexagonal boron nitride heterostructures

Results of ab initio study of magnetism and transport properties of charge carriers in zigzag graphene nanoribbons (ZGNR) on hexagonal boron nitride (h-BN(0001)) substrate are presented within the density functional theory framework. Peculiarities of the interface band structure and its role in the formation of magnetism and transport properties of the ZGNR/h-BN(0001) heterostructure have been studied using two different density functional approximations. The effect of the substrate and graphene nanoribbons width on the low-energy spectrum of π-electrons, local magnetic moments on atoms of interface, and charge carriers mobility in the ZGNR/h-BN(0001) heterostructures have been established for the first time. The regularity consisting in the charge carrier mobility growth with decrease of dimers number in nanoribbon was also established. It is found that the charge carriers mobility in the N-ZGNR/h-BN(0001) (N—number of carbon (C) dimers) heterostructures is 5% higher than in freestanding ZGNR.

Molecular mobility on graphene nanoribbons

Graphene nanoribbons (GNRs) have been proposed to be used as nanoscale mass-conveyor highways. However, how factors such as edge confinement, edge rippling, ribbon twisting, and thermal fluctuations affect the mobility of admolecules on GNRs for such application remains unknown. Using molecular dynamics (MD) simulations, we address these issues by investigating the surface mobility of a physisorbed C60 admolecule on pristine GNRs. We show that the absorption energy and edge energy barrier of a GNR are able to keep and confine the admolecule motion only on one side of the GNR. The twisting of narrow GNRs in combination with thermal fluctuations causes the admolecule to move in a helical trajectory, and thus markedly affects its mobility. As the GNR width increases, its twisting is gradually inhibited, and the motion of the admolecule becomes planar. A comparison between the results from our MD simulations and those from the confined Langevin model indicates that the distinct behavior of molecular mobility on narrow GNRs is due to their twisting rather than geometrical confinement. These findings shed light on the important factors that control the characteristics of the GNR-based mass transport highways.

Graphene nanoribbon based spaser

A novel type of spaser with the net amplification of surface plasmons (SPs) in doped graphene nanoribbon is proposed. The plasmons in THz region can be generated in a dopped graphene nanoribbon due to nonradiative excitation by emitters like two level quantum dots located along a graphene nanoribbon. The minimal population inversion per unit area, needed for the net amplification of SPs in a doped graphene nanoribbon is obtained. The dependence of the minimal population inversion on the surface plasmon wavevector, graphene nanoribbon width, doping and damping parameters necessary for the amplification of surface plasmons in the armchair graphene nanoribbon is studied.

Edge Effects on the pH Response of Graphene Nanoribbon Field Effect Transistors

We report the pH response enhancement of the electrolyte-gated graphene field effect transistors by controllably introducing edge defects. An average improvement of pH response from 4.2 to 24.6 mV/pH has been observed after downscaling the pristine graphene into graphene nanoribbon arrays with electron beam lithography (EBL) and oxygen plasma. We attribute the improved pH response in graphene nanoribbons to the increased number of hydroxyl groups attached to edge defects as the edge length to surface area ratio increases with decreasing graphene nanoribbon width. Moreover, the shift of the Dirac point in response to the pH change has been found to be reversible, indicating that the hydroxyl ions are binding to the edge defect sites of the graphene nanoribbons through physical adsorption.

Localized vibrational, edges and breathing modes of graphene nanoribbons with topological line defects

Peculiar vibrational modes of graphene nanoribbons (GNRs) with topological line defects were presented. We find that phonon dispersion relations of the topological defective GNRs are more similar to those of perfect armchair-edge GNR than to zigzag-edge GNR in spite of their zigzag edge. All vibrational modes at Γ point are assigned in detail by analyzing their eigenvectors and are presented by video. Three types of characteristic vibrational modes, namely, localized vibrational modes in defect sites, edges, and breathing modes, are observed. Five localized vibrational modes near the defect sites are found to be robust against the width of the topological line-defective GNR. The Raman D’ band just originates from one localized mode, 1622 cm-1. The vibrational mode is sensitive to symmetry. The edge modes are related with structural symmetry but not with widths. Two edge modes are asymmetrical and only one is symmetrical. The breathing modes are inversely proportional to the width for wide-defect GNRs, and inversely proportional to the square root of the width for narrow-defect GNRs. The breathing mode frequencies of defective GNRs are slightly higher than those of perfect GNRs. These vibrational modes may be useful in the manipulation of thermal conductance and implementation of single phonon storage.

Influence of substrate type and quality on carrier mobility in graphene nanoribbons

We report the results of a thorough numerical study on carrier mobility in graphene nanoribbons (GNRs) with the widths from ∼250 nm down to ∼1 nm, with a focus on the influence of substrate type (SiO2, Al2O3, HfO2, and h-BN) and substrate quality (different interface impurity densities) on GNR mobility. We identify the interplay between the contributions of Coulomb and surface optical phonon scattering as the crucial factor that determines the optimum substrate in terms of carrier mobility. In the case of high impurity density (∼1013 cm−2), we find that HfO2 is the optimum substrate irrespective of GNR width. In contrast, for low impurity density (1010 cm−2), h-BN offers the greatest enhancement, except for nanoribbons wider than ∼200 nm for which the mobility is highest on HfO2.

Ballistic phonon thermal conductance in graphene nanoribbons

Phonon dispersions for graphene nanoribbons (GNRs) have been derived from the first-principles calculations, and ballistic phonon thermal conductances have been evaluated using the Landauer theory. The phonon thermal conductance per unit width for GNR is larger than that for graphene and increases with decreasing ribbon width. The normalized thermal conductance with a unit of thermal quantum for the zigzag GNR is higher than that for the single-walled carbon nanotube that has a circumferential length corresponding to the width of GNR.

Quantum capacitance of the armchair-edge graphene nanoribbon

The quantum capacitance, an important parameter in the design of nanoscale devices, is derived for armchair-edge single-layer graphene nanoribbon with semiconducting property. The quantum capacitance oscillations are found and these capacitance oscillations originate from the lateral quantum confinement in graphene nanoribbon. Detailed studies of the capacitance oscillations demonstrate that the local channel electrostatic potential at the capacitance peak, the height and the number of the capacitance peak strongly depend on the width, especially a few nanometres, of the armchair-edge graphene nanoribbon. It implies that the capacitance oscillations observed in the experiments can be utilized to measure the width of graphene nanoribbon. The results also show that the capacitance oscillations are not seen when the width is larger than 30 nm.

Tuning the Band Gap of Graphene Nanoribbons Synthesized from Molecular Precursors

A prerequisite for future graphene nanoribbon (GNR) applications is the ability to fine-tune the electronic band gap of GNRs. Such control requires the development of fabrication tools capable of precisely controlling width and edge geometry of GNRs at the atomic scale. Here we report a technique for modifying GNR band gaps via covalent self-assembly of a new species of molecular precursors that yields n = 13 armchair GNRs, a wider GNR than those previously synthesized using bottom-up molecular techniques. Scanning tunneling microscopy and spectroscopy reveal that these n = 13 armchair GNRs have a band gap of 1.4 eV, 1.2 eV smaller than the gap determined previously for n = 7 armchair GNRs. Furthermore, we observe a localized electronic state near the end of n = 13 armchair GNRs that is associated with hydrogen-terminated sp(2)-hybridized carbon atoms at the zigzag termini.

Elektronni vlastyvosti funktsionalizovanykh hrafenovykh nanostrichok

Distributions of valence electron density in and the electron energy spectrum of graphene nanoribbons covered with hydrogen, fluorine, or oxygen atoms have been calculated ab initio in the framework of the density functional and pseudopotential theories. The emergence of a forbidden gap for graphene nanoribbons with zigzag edges and 9.23 ˚ A in width and its absence in an unconfined graphene plane are shown. The forbidden gap is demonstrated to decrease, as the graphene nanoribbon width increases. For graphene nanoribbons with hydrogen-decorated edges, the energy gap disappears. The interaction between a hydrogen atom and carbon atoms in the graphene nanoribbon plane that are coordinated in accordance with the sp2-hybridization is shown to induce local changes of the hybridization to the sp3 type.

Disorder-induced variability of transport properties of sub-5 nm-wide graphene nanoribbons

Transport properties of sub-5 nm-wide graphene nanoribbons (GNRs) are investigated by using atomistic non-equilibrium Green’s function (NEGF) simulations and semiclassical mobility simulations of large ensembles of randomly generated nanoribbons. Realistic GNRs with dimensions targeting the 12nm CMOS node are investigated by accounting for edge defects, vacancies and potential fluctuations. Effects of disorder on transmission, transport gap, mean free path, density of states and acoustic phonon limited carrier mobility are explored for various disorder strengths and GNR widths in the 1–5nm range. We report the high variability of GNR transport properties that could be a strong limiter for potential nanoelectronics applications of GNRs.

I–V Curves of graphene nanoribbons under uniaxial compressive and tensile strain

Using the non-equilibrium Green’s function method together with the density-functional theory, the current–voltage (I–V) characteristics of armchair and zigzag graphene nanoribbons (GNR) have been evaluated. It is found that the strain effect on the GNRs is periodically changed with the GNR width of 3. The conductivity of GNRs under compressive strain changes a lot, which is associated with the buckled configuration. In addition, the transport properties of elongate GNRs are changed due to the difference in the electronic structures of C atoms.

Thermal transport in graphene nanoribbons supported on SiO2

We present a theoretical model for thermal transport in graphene nanoribbons (GNRs) on SiO${}_{2}$ based on solving the phonon Boltzmann transport equation. Thermal transport in supported GNRs is characterized by a complex interplay between line edge roughness (LER) and internal scattering, as captured through an effective LER scattering rate that depends not only on the surface roughness features, but also on the strength of internal scattering mechanisms (substrate, isotope, and umklapp phonon scattering). Substrate scattering is the dominant internal mechanism, with a mean free path (mfp) of approximately 67 nm. In narrow supported GNRs ($Wl130$ nm, i.e., roughly twice the mfp due to substrate scattering), phonon transport is limited by LER and spatially anisotropic. For intermediate widths ($130\phantom{\rule{0.16em}{0ex}}\mathrm{nm}lWl1$ $\ensuremath{\mu}$m) a competition between LER and substrate scattering governs transport, while thermal transport in wide GNRs ($Wg1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}$m) is dominated by substrate scattering and spatially isotropic. Thermal transport in supported GNRs can be tailored by controlling the ribbon width and edge roughness. We conclude that narrow ribbons act as longitudinal heat conduits while wide ribbons act as good omnidirectional heat spreaders.