Band Gap Of Graphene Nanoribbons Research Articles

Doping-induced bandgap tuning in armchair graphene nanoribbons and its impact on electron transport properties on ZAPn – A DFT study

Graphene, sp2 hybridised-2D material has been widely reviewed for its fabulous structural, electronic, magnetic and optical properties. However, its employment in energy-related devices are controlled due to its semi-metallic nature. A quasi one-dimensional structure of graphene is called as graphene nanoribbon (GNR). Tuning the band gap of GNR based on its width can be achieved via doping. The present work envisages, the doping performance on the electronic properties of armchair graphene nanoribbon AGNR (N9) doped with Boron (B), Nitrogen (N) and Phosphorus (P) in a Z-shape. The effect of B, N, and P dopants in AGNR(N9) systems were analysed by varying the concentration from 0.75 % to 3.03 %. Our results predicts that the band gap has been reduced by the impact of dopants, and also ZAPn systems shows better results in lower concentration of dopants than ZABn and ZANn systems. Further, it is observed that, with the increase in the concentration of P dopants, their electronic structure is transformed from n-type to p-type. Transport calculations were performed for ZAPn systems, and their properties were analyzed with the help of transmission spectrum, device density of states (DDOS), and I-V characteristics. All the doped as well as the pristine two-probe device structures established non-linear current vs. voltage characteristics. The ZAP3 doped system achieved a maximum current of 60 µA. The present study will be established to construct AGNR(N9) based nano-electronic devices.

Graphene Nanoribbon Grids of Sub-10 nm Widths with High Electrical Connectivity.

Quasi-one-dimensional (1D) graphene nanoribbons (GNRs) have finite band gaps and active edge states and therefore can be useful for advanced chemical and electronic devices. Here, we present the formation of GNR grids via seed-assisted chemical vapor deposition on Ge(100) substrates. Nucleation seeds, provided by unzipped C60, initiated growth of the GNRs. The GNRs grew toward two orthogonal directions in an anisotropic manner, templated by the single crystalline substrate, thereby forming grids that had lateral stitching over centimeter scales. The spatially uniform grid can be transferred and patterned for batch fabrication of devices. The GNR grids showed percolative conduction with a high electrical sheet conductance of ∼2 μS·sq and field-effect mobility of ∼5 cm2/(V·s) in the macroscopic channels, which confirm excellent lateral stitching between domains. From transconductance measurements, the intrinsic band gap of GNRs with sub-10 nm widths was estimated as ∼80 meV, similar to theoretical expectation. Our method presents a scalable way to fabricate atomically thin elements with 1D characteristics for integration with various nanodevices.

Strain-inducing photochemical chlorination of graphene nanoribbons on SiC (0001)

As different low-dimensional materials are sought to be incorporated into microelectronic devices, graphene integration is dependent on the development of band gap opening strategies. Amidst the different methods currently investigated, application of strain and use of electronic quantum confinement have shown promising results. In the present work, epitaxial graphene nanoribbons (GNR), formed by surface graphitization of SiC (0001) on crystalline step edges, were submitted to photochemical chlorination. The incorporation of Cl into the buffer layer underlying graphene increased the compressive uniaxial strain in the ribbons. Such method is a promising tool for tuning the band gap of GNRs.

A variation-aware design for storage cells using Schottky-barrier-type GNRFETs

Graphene nanoribbons (GNRs) are a good replacement material for silicon to overcome short-channel effects in nanoscale devices. However, with continuous technology scaling, the variability of device parameters also increases. Indeed, process, voltage, and temperature (PVT) variations affect the performance of GNR devices because of their small size. Moreover, the bandgap of GNRs is strongly affected by the number of carbon atoms across the channel width. This paper accurately evaluates the impact of such PVT variations on the performance of circuits based on Schottky barrier (SB)-type GNR field-effect transistors (SB-GNRFETs) in terms of their timing parameters, power, and energy–delay product (EDP). Extensive simulations and stability analysis are performed on both flip-flop and conventional six-transistor static random-access memory (6T SRAM) cells made using SB-GNRFETs under these variations. A statistical analysis of the impact of the PVT variations on the SB-GNRFET-based flip-flop is also performed using Monte Carlo simulations, considering the variation of one or all of the parameters, with or without line-edge roughness effects.

Chevron-type graphene nanoribbons with a reduced energy band gap: Solution synthesis, scanning tunneling microscopy and electrical characterization

Graphene nanoribbons (GNRs) attract a growing interest due to their tunable physical properties and promise for device applications. A variety of atomically precise GNRs have recently been synthesized by on-surface and solution approaches. While on-surface GNRs can be conveniently visualized by scanning tunneling microscopy (STM), and their electronic structure can be probed by scanning tunneling spectroscopy (STS), such characterization remains a great challenge for the solution-synthesized GNRs. Here, we report solution synthesis and detailed STM/STS characterization of atomically precise GNRs with a meandering shape that are structurally related to chevron GNRs but have a reduced energy band gap. The ribbons were synthesized by Ni0-mediated Yamamoto polymerization of specially designed molecular precursors using triflates as the leaving groups and oxidative cyclodehydrogenation of the resulting polymers using Scholl reaction. The ribbons were deposited onto III-V semiconducting InAs(110) substrates by a dry contact transfer technique. High-resolution STM/STS characterization not only confirmed the GNR geometry, but also revealed details of electronic structure including energy states, electronic band gap, as well as the spatial distribution of the local density of states. The experimental STS band gap of GNRs is about 2 eV, which is very close to 2.35 eV predicted by the density functional theory simulations with GW correction, indicating a weak screening effect of InAs(110) substrate. Furthermore, several aspects of GNR-InAs(110) substrate interactions were also probed and analyzed, including GNR tunable transparency, alignment to the substrate, and manipulations of GNR position by the STM tip. The weak interaction between the GNRs and the InAs(110) surface makes InAs(110) an ideal substrate for investigating the intrinsic properties of GNRs. Because of the reduced energy band gap of these ribbons, the GNR thin films exhibit appreciably high electrical conductivity and on/off ratios of about 10 in field-effect transistor measurements, suggesting their promise for device applications.

Engineering Edge States of Graphene Nanoribbons for Narrow-Band Photoluminescence.

Solid-state narrow-band light emitters are on-demand for quantum optoelectronics. Current approaches based on defect engineering in low-dimensional materials usually introduce a broad range of emission centers. Here, we report narrow-band light emission from covalent heterostructures fused to the edges of graphene nanoribbons (GNRs) by controllable on-surface reactions from molecular precursors. Two types of heterojunction (HJ) states are realized by sequentially synthesizing GNRs and graphene nanodots (GNDs) and then coupling them together. HJs between armchair GNDs and armchair edges of the GNR are coherent and give rise to narrow-band photoluminescence. In contrast, HJs between the armchair GNDs and the zigzag ends of GNRs are defective and give rise to nonradiative states near the Fermi level. At low temperatures, sharp photoluminescence emissions with peak energy range from 2.03 to 2.08 eV and line widths of 2-5 meV are observed. The radiative HJ states are uniform, and the optical transition energy is controlled by the band gaps of GNRs and GNDs. As these HJs can be synthesized in a large quantity with atomic precision, this finding highlights a route to programmable and deterministic creation of quantum light emitters.

Electronic properties of graphene nanoribbons doped with zinc, cadmium, mercury atoms

The effect of substitutional impurities as Zinc (Zn), Cadmium (Cd) and Mercury (Hg) on electronic properties of graphene nanoribbons (GNRs) was investigated by using Density Functional Theory (DFT). A substantial change in the electronic properties of GNR structures was observed while changing the position of dopant atom from the edge to the center of armchair graphene nanoribbons (AGNRs) and zigzag graphene nanoribbons (ZGNRs). The calculations are shown that the electronic band gap of GNRs can be controlled depending on the position of dopant atoms. The calculated electronic band structures for both AGNRs and ZGNRs show spin-dependent metallic or semiconductor behavior according to the position of dopant atoms. From the Density of States (DOS) information, quasi-zero-dimensional (Q0D) and quasi-one-dimensional (Q1D) type behaviors are observed. It is shown that because the doped ZGNRs had the lowest total energies, ZGNRs are energetically more stable than AGNRs.

Effect of ribbon width on electrical transport properties of graphene nanoribbons

There has been growing interest in developing nanoelectronic devices based on graphene because of its superior electrical properties. In particular, patterning graphene into a nanoribbon can open a bandgap that can be tuned by changing the ribbon width, imparting semiconducting properties. In this study, we report the effect of ribbon width on electrical transport properties of graphene nanoribbons (GNRs). Monolayer graphene sheets and Si nanowires (NWs) were prepared by chemical vapor deposition and a combination of nanosphere lithography and metal-assisted electroless etching from a Si wafer, respectively. Back-gated GNR field-effect transistors were fabricated on a heavily p-doped Si substrate coated with a 300 nm-thick SiO2 layer, by O2 reactive ion etching of graphene sheets using etch masks based on Si NWs aligned on the graphene between the two electrodes by a dielectrophoresis method. This resulted in GNRs with various widths in a highly controllable manner, where the on/off current ratio was inversely proportional to ribbon width. The field-effect mobility decreased with decreasing GNR widths due to carrier scattering at the GNR edges. These results demonstrate the formation of a bandgap in GNRs due to enhanced carrier confinement in the transverse direction and edge effects when the GNR width is reduced.

Exciton and phonon dynamics in highly aligned 7-atom wide armchair graphene nanoribbons as seen by time-resolved spontaneous Raman scattering.

The opening of a band gap in graphene nanoribbons induces novel optical and electronic properties, strongly enhancing their application potential in nanoscale devices. Knowledge of the optical excitations and associated relaxation dynamics are essential for developing and optimizing device designs and functionality. Here we report on the optical excitations and associated relaxation dynamics in surface aligned 7-atom wide armchair graphene nanoribbons as seen by time-resolved spontaneous Stokes and anti-Stokes Raman scattering spectroscopy. On the anti-Stokes side we observe an optically induced increase of the scattering intensity of the Raman active optical phonons which we assign to changes in the optical phonon populations. The optical phonon population decays with a lifetime of ∼2 ps, indicating an efficient optical-acoustic phonon cooling mechanism. On the Stokes side we observe a substantial decrease of the phonon peak intensities which we relate to the dynamics of the optically induced exciton population. The exciton population shows a multi-exponential relaxation on the hundreds of ps time scale and is independent of the excitation intensity, indicating that exciton-exciton annihilation processes are not important and the exsistence of dark and trapped exciton states. Our results shed light on the optically induced phonon and exciton dynamics in surface aligned armchair graphene nanoribbons and demonstrate that time-resolved spontaneous Raman scattering spectroscopy is a powerful method for exploring quasi-particle dynamics in low dimensional materials.

Graphene Nanoribbon Heterojunctions with Dbtp Precursors on Ag(111)

The observed width (and edge) dependence of the electronic structure and band gap of graphene nanoribbons has generated a vivid interest in the possibility to generate optically active, graphene-based quantum dots that can play a role in optically driven solid state devices for quantum information. We describe a bottom-up approach to generate armchair graphene nanoribbons (AGNRs) of well defined width and atomically perfect edges on Ag(111) surfaces under UHV conditions by debromination of DBTP precursors, covalent reaction along 1D metal-organic structures and subsequent covalent lateral reaction with neighbouring wires, giving rise to 6-12 AGNRs. The resulting graphene nanoribbons are examined in situ by STM and STS revealing the electronic structure of wires, heterojunctions and quantum dots at the atomic scale. Figure 1

Fabrication and electrical engineering of graphene nanoribbons

Graphene, as a typical representative of advanced materials, exhibits excellent electronical properties due to its unique and unusual crystal structure. The valence band and conduction band of pristine graphene meet at the corners of the Brillouin zone, leading to a half-metal material with zero bandgap. However, although the extraordinary electronical properties make graphene possess excellent electrical conductivity, it also restricts its applications in electronic devices, which usually needs an appropriate bandgap. Therefore, opening and tuning the bandgap of graphene has aroused great scientific interest. To date, many efforts have been made to open the bandgap of graphene, including defects, strain, doping, surface adsorptions, structure tunning, etc. Among these methods, graphene nanoribbon, the quasi-one-dimensional strips of graphene with finite width ( 10 nm) and high aspect ratios, possesses a band gap opening at the Dirac point due to the quantum confinement effects. Thus, graphene nanoribbon has been considered as one of the most promising candidates for the future electronic devices due to its unique electronic and magnetic properties. Specifically, the band gap of graphene nanoribbons is strongly dependent on the lateral size and the edge geometry, which has attracted tremendous attention. Furthermore, it has been reported that armchair graphene nanoribbons possess gaps inversely proportional to their width, and numerous efforts have been devoted to fabricating the graphene nanoribbons with different widths by top-down or bottom-up approaches. Moreover, based on the on-surface reaction, the bottom-up approach shows the capability of controlling the width and edge structures, and it is almost contamination-free processing, which is suitable to performing further characterizations. Ultra-high-vacuum scanning tunneling microscope is a valid tool to fabricate and characterize the graphene nanorribons, and it can also obtain the band structure information when combined with the scanning tunneling spectroscopy. Taking the advantage of the bottom-up synthetic technique, the nearly perfect graphene nanoribbons can be fabricated based on the organic molecule reaction on surface, which is a promising strategy to study the original electronic properties. To precisely tuning the band engineering of graphene nanoribbons, the researchers have adopted various effective methods, such as changing the widths and topological morphologies of graphene nanoribbons, doping the graphene nanoribbons with heteroatoms, fabricating the heterojunctions under a controlable condition. The precise control of graphene synthesis is therefore crucial for probing their fundamental physical properties. Here we highlight the methods of fabricating the graphene nanoribbons and the precise tuning of graphene bandgap structure in order to provide a feasible way to put them into application.

A comparative and a systematic study on the effects of B, N doping and C-atom vacancies on the band gap in narrow zig-zag graphene nanoribbons via quantum transport calculations

Density functional theory(DFT) coupled to non-equilibrium green’s function has been performed to explore avenues to open band gap in graphene nanoribbons in order to reach a high current on/off ratio for their potential applications in transistors and futuristic nanodevices. Introduction of defects such as C-atom vacancies and doping with elements lying on either side of carbon in the periodic table have been invoked to engineer the band gap in narrow zig-zag nanoribbons. By varying the concentration of B and N dopants in zig-zag nanoribbon (ZGNR), their electronic structure is transformed to that of p-type and n-type semiconductor. A maximum band gap of 0.98eV, 0.88eV and 0.89eV is achieved upon incorporating carbon-atom vacancies, boron doping and nitrogen doping respectively. Transport properties have been analyzed through the calculation of transmission spectrum and I–V characteristics. Doped and defective ZGNRs reported herewith show non-linearity in the current-voltage characteristics. The highest current value achieved by doping and defect is 16.5,39μA for boron dopant, 18, 27μA for nitrogen and 25.5, 30.2μA for defects.

Effects of Position and Shape of Atomic Defects on the Band Gap of Graphene Nano Ribbon Superlattices

In this work, we study the behavior of introducing atomic size vacancy in a graphene nanoribbon superlattice. Our investigations are based on the density functional theory (DFT) with the Local Density Approximation in Atomistix Toolkit (ATK). We show that, in addition to its shape, the position of vacancy has a major impact on the electrical properties of a graphene nanoribbon superlattice. We show that the band gap of an armchair graphene nanoribbon may be tuned by introducing an appropriate periodic pattern of vacancies. The band gap changes in a zig-zag manner similar to the variation of band gap of a graphene nanoribbon by changing its width. Keywords—Antidot, Atomistix ToolKit, Superlattice, Vacancy.

Edge-modified zigzag-shaped graphene nanoribbons: Structure and electronic properties

Control of the band gap of graphene nanoribbons is an important problem for the fabrication of effective radiation detectors and transducers operating in different frequency ranges. The periodic edge-modified zigzag-shaped graphene nanoribbon (GNR) provides two additional parameters for controlling the band gap of these structures, i.e., two GNR arms. The dependence of the band gap E g on these parameters is investigated using the π-electron tight-binding method. For the considered nanoribbons, oscillations of the band gap E g as a function of the nanoribbon width are observed not only in the case of armchair-edge graphene nanoribbons (as for conventional graphene nanoribbons) but also for zigzag GNR edges. It is shown that the change in the band gap E g due to the variation in the length of one GNR arm is several times smaller than that due to the variation in the nanoribbon width, which provides the possibility for a smooth tuning of the band gap in the energy spectrum of the considered graphene nanoribbons.

Effective Mass versus Band Gap in Graphene Nanoribbons: Influence of H-Passivation and Uniaxial Strain

A simple model which combines tight-binding (TB) approximation with parameters derived from first principle calculations is developed for studying the influence of edge passivation and uniaxial strain on electron effective mass of armchair graphene nanoribbons (AGNRs). We show that these effects can be described within the same model Hamiltonian by simply modifying the model parameters i.e., the hopping integrals and onsite energies. Our model reveals a linear dependence of effective mass on band gap for H-passivated AGNRs for small band gaps. For large band gap, the effective mass dependence on band gap is parabolic and analytic fits were derived for AGNRs belonging to different families. Both band gap and effective mass exhibit a nearly periodic zigzag variation under strain, indicating that the effective mass remains proportional to the band gap even when strain is applied. Our calculations could be used for studying carrier mobility in intrinsic AGNRs semiconductors where carrier scattering by phonons is the dominant scattering mechanism.

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.

Aligning the Band Gap of Graphene Nanoribbons by Monomer Doping

Eine Frage der Dotierung: Graphen-Nanobänder (GNRs) wurden auf einer Oberfläche in einer Bottom-up-Synthese hergestellt und selektiv an den Ecken durch Einführen von Stickstoffatomen in den Vorstufen dotiert. Während die Bandlückengröße von 2.8 eV durch die N-Substitution beinahe unverändert bleibt, wird eine lineare Verschiebung der Bandstruktur beobachtet, die einer n-Dotierung entspricht (siehe Bild; CB=Leitungsband, VB=Valenzband).

Aligning the Band Gap of Graphene Nanoribbons by Monomer Doping

Silicon-based field-effect transistors (FETs) are the building blocks of modern digital logic circuitry and therefore part of virtually every electronic device available today. Over the past decades, continuous downscaling of existing designs has met the rising performance requirements, but as the size of FETs approaches the regime of atomic structures, new concepts are required to maintain the current pace at which microelectronics is developing. At small gate channel lengths, the applicability of quantum mechanical principles results in several so-called short-channel effects (e.g. reduced carrier mobility). Since its experimental realization in 2004, graphene has been discussed intensively as a substitute for doped silicon in FETs because of its high charge carrier mobility and its unsurpassably low thickness. Graphene transistors have even been realized but cannot be put into the “off” state because of the lack of a band gap. However, there are concepts available for opening a band gap, for example, applying strain along the sheet or biasing bilayers of graphene. Also, lateral confinement in quasione-dimensional graphene nanoribbons (GNRs) leads to a band gap, which furthermore is highly sensitive to the width and edge shape of the GNR, thus opening possibilities to tailor the electronic properties of a device. Indeed, FETs built from nanoribbons show much higher on/off-ratios than graphene transistors, which makes them more suitable for integration into logic devices. However, the ability to control the electronic properties is essential: while the size of the gap can be engineered by varying the nanoribbon widths, the alignment of the GNR band structure with respect to the Fermi level of a metal electrode is equally important. Such a shifting of the entire band structure is observed both in two-dimensional graphene as well as in chemically synthesized or lithographically patterned GNRs upon doping, particularly with nitrogen atoms. Using present doping techniques, the distribution of dopant atoms will not be well-defined on the nanoscale and the band gap shift upon nitrogen doping depends on the site of the N atom, that is, the bonding configuration to neighboring carbon atoms. Generally, for doped and pristine GNRs, fabrication remains a challenge as well-established top-down approaches using lithography or unzipping of carbon nanotubes yield relatively wide ribbons with an undetermined edge structure. Particularly for small widths on the order of a few nanometers (where the band gap reaches a technologically relevant size) atomically precise edges are necessary and can be realized using Br-substituted precursor molecules, which are thermally activated on a surface and—in a bottom-up synthesis— covalently assemble to a specific nanostructure. In this study, we employed the latter approach to prepare GNRs with an atomically precise edge structure and doping pattern through polymerization of specific monomers directly on the Au(111) surface and studied the position and size of the band gap of these GNRs with surface-sensitive electron spectroscopies. Besides straight armchair edge GNRs, another type of chevron-shaped nanoribbons has previously been fabricated using an on-surface reaction. In this process adsorption of several layers of 6,11-dibromo-1,2,3,4-tetraphenyl-triphenylene (monomer 1 in Scheme 1) on Au(111) and heating at 250 8C leads to desorption of the second and higher layers as well as halogen dissociation and coupling of the resulting activated biradical monomers, yielding a sterically crowded and hence twisted polyphenylene. In a second heating step at 440 8C, this polymer undergoes a subsequent cyclodehydrogenation reaction providing access to the desired chevronshaped GNR with armchair edges. Selective substitution of the parent monomer 1 with either one or two N atoms provided monomers 2 and 3, respectively, which were used to generate GNRs with different doping levels (exemplarily shown for the doubly N doped GNR 5 in Scheme 1) and accordingly with potentially different electronic structure properties. Synthesis of the new monomers 2 and 3 was accomplished by Diels–Alder reactions of an appropriate cyclopentadienone with either mixed phenylpyridyl-acetylene or bispyridylacetylene, followed by immediate cheletropic CO extrusion (for details see the Supporting Information). [*] C. Bronner, S. Stremlau, A. Haase, Prof. Dr. P. Tegeder Fachbereich Physik, Freie Universit t Berlin Arnimallee 14, 14195 Berlin (Germany) E-mail: bronner@zedat.fu-berlin.de petra.tegeder@physik.fu-berlin.de

Tuning aromaticity patterns and electronic properties of armchair graphene nanoribbons with chemical edge functionalisation

Tuning the band gap of graphene nanoribbons by chemical edge functionalisation is a promising approach towards future electronic devices based on graphene. The band gap is closely related to the aromaticity distribution and therefore tailoring the aromaticity patterns is a rational way for controlling the band gap. In the present work, it is shown how the three distinct classes of aromaticity patterns already found for armchair graphene nanoribbons can be rationally tuned by chemical edge functionalisation to modify their electronic arrangement and band gap. The electronic structure and the aromaticity distribution are studied using DFT calculations and through a series of delocalisation and geometry analysis methods, like the six-centre index (SCI) and the mean bond length (MBL) geometry descriptor. Novel aromaticity patterns are found for fluorine and nitrogen functionalisation characterised as inverted incomplete-Clar, and broken-Kekulé classes, while oxygen and nitrogen functionalisation is found to cut and extend the aromatic system, respectively. All these different arrangements of aromatic rings along the structure of graphene nanoribbons are explained using Clar's sextet theory, and a mesomeric effect mechanism for fluorine and nitrogen. In all cases, the changes in the aromaticity patterns are related to changes in the band gap. The energy and stability of the different edge functionalised graphene nanoribbons are also studied. An overall picture of edge effects, aromaticity patterns, and band gap tuning is provided.

ELECTRONIC, MAGNETIC, AND MECHANICAL PROPERTIES OF LINE-DEFECT EMBEDDED GRAPHENE NANORIBBONS: A FIRST-PRINCIPLES STUDY

We use first-principles method to investigate the electronic, magnetic, and mechanical properties of graphene nanoribbons (GNRs) with extended line defect. Particular attention has been placed on zigzag GNR with 5-8-5 line defect and armchair GNR with 4-8 line defect. The results show that the band gaps of GNRs can be effectively tuned by line defect, which depend on both their widths and the position of defect. The line-defect embedded GNRs are either metals or semiconductor with markedly reduced band gap. The band-gap reduction is attributed to the defect-induced impurity states. In particular, the metallic line-defect embedded zigzag GNRs are ferromagnetic at ground state, while those semiconducting ones are antiferromagnetic. Upon the line-defect embedded armchair GNRs, the band gaps vary periodically with the increasing widths. Our results imply the potential applications of line-defect embedded GNRs at nanoscale electronics.