Narrow Graphene Nanoribbons Research Articles

Effective low-energy spin model for narrow zigzag graphene nanoribbons

The magnetic properties of narrow zigzag graphene nanoribbons with periodically embedded atoms of transition metals have been studied in the framework of Heisenberg spin Hamiltonian. We have proposed the simple effective model to give a semi-qualitative description of the peculiarities of magnetization profiles of the systems under consideration. This model can be used for an arbitrary value of spin of the embedded atoms of transition metals. Our analytical and numerical calculations confirm the correctness of the proposed model.

Gate-voltage-driven quantum oscillations in the microwave third-harmonic response of electron-doped graphene nanoribbons

Microwave third-harmonic response of narrow graphene nanoribbons (GNRs) is studied by employing Boltzmann equation techniques. It is assumed that the GNRs are electron-doped by electrostatic gating. We predict gate-voltage-driven periodic quantum oscillations of the microwave third-harmonic output power from such GNRs, resulting from the confinement-induced quantization of the Dirac energy dispersion cones into a set of energy subbands at the bottom of which the electronic density of states exhibits the Van Hove square-root singularities. The oscillations are shown to have a large enough amplitude (∼ several tens of decibel-milliwatts) and should be observable in narrow GNRs of width ∼10 nm even at room temperature.

Optimized Substrates and Measurement Approaches for Raman Spectroscopy of Graphene Nanoribbons

The on‐surface synthesis of graphene nanoribbons (GNRs) allows for the fabrication of atomically precise narrow GNRs. Despite their exceptional properties which can be tuned by ribbon width and edge structure, significant challenges remain for GNR processing and characterization. Herein, Raman spectroscopy is used to characterize different types of GNRs on their growth substrate and track their quality upon substrate transfer. A Raman‐optimized (RO) device substrate and an optimized mapping approach are presented that allow for the acquisition of high‐resolution Raman spectra, achieving enhancement factors as high as 120 with respect to signals measured on standard SiO2/Si substrates. This approach is well suited to routinely monitor the geometry‐dependent low‐frequency modes of GNRs. In particular, the radial breathing‐like mode (RBLM) and the shear‐like mode (SLM) for 5‐, 7‐, and 9‐atom‐wide armchair GNRs (AGNRs) are tracked and their frequencies are compared with first‐principles calculations.

Size-dependent mode contributions to the thermal transport of suspended and supported graphene

Graphene is promising for thermal management applications due to its superior thermal conductivity, but the inherent thermal transport mechanism is not fully understood. In this work, we directly extract the mode contributions to the thermal conductivity of free-standing and supported graphene nanoribbons using nonequilibrium molecular dynamics simulations. With the aid of the mode analyses, it is uncovered that the acoustic contribution increases with respect to the characteristic length in suspended graphene, and such a size-dependency is compromised in supported graphene. In addition, the contribution of optical modes could be more than 25% for heat conduction in narrow graphene nanoribbons because of strong boundary scatterings. Furthermore, the LA and TA modes rather than the ZA modes are dominant heat carriers in suspended and supported graphene owing to their large group velocities and long mean free path. Our results are instructive for understanding the mode thermal transport in free and supported graphene.

Thermosize voltage induced in a ballistic graphene nanoribbon junction

A thermoelectric voltage is induced in a junction, constituted of two dissimilar materials under a temperature gradient. Similarly, a thermosize voltage is expected to be induced in a junction made by the same material but having different sizes, so-called thermosize junction. This is a consequence of dissimilarity in Seebeck coefficients due to differences in classical and/or quantum size effects in the same materials with different sizes. The studies on thermosize effects in the literature are mainly based on semiclassical models under relaxation time approximation or even simpler local equilibrium ones where only very general ideas and results have been discussed without considering quantum transport approaches and specific materials. To make more realistic predictions for a possible experimental verification, here we consider ballistic thermosize junctions made by narrow and wide (n−w) pristine graphene nanoribbons with perfect armchair edges and calculate the electronic contribution to the thermosize voltage, at room temperature, by using the Landauer formalism. The results show that the maximum thermosize voltage can be achieved for semiconducting nanoribbons and it is about an order of magnitude larger than that of metallic nanoribbons. In the semiconducting case, the thermosize voltage forms a characteristic plateau for a finite range of gating conditions. We demonstrate, through numerical calculations, that the induced thermosize voltage per temperature difference can be in the scale of mV/K, which is high enough for experimental measurements. Owing to their high and persistent thermosize voltage values, graphene nanoribbons are expected to be good candidates for device applications of thermosize effects.

Unraveling the Band Gap Trend in the Narrowest Graphene Nanoribbons from the Spin-Adapted Excited-Spectra Reduced Density Matrix Method

Polybenzenes as the narrowest graphene nanoribbons with versatile electronic properties are widely studied both theoretically and technologically. Here, we examine the singlet–triplet band gap as a...

Highly stretchable graphene nanoribbon springs by programmable nanowire lithography

Graphene nanoribbons are ideal candidates to serve as highly conductive, flexible, and transparent interconnections, or the active channels for nanoelectronics. However, patterning narrow graphene nanoribbons to <100 nm wide usually requires inefficient micro/nano fabrication processes, which are hard to implement for large area or flexible electronic and sensory applications. Here, we develop a precise and scalable nanowire lithography technology that enables reliable batch manufacturing of ultra-long graphene nanoribbon arrays with programmable geometry and narrow width down to ~50 nm. The orderly graphene nanoribbons are patterned out of few-layer graphene sheets by using ultra-long silicon nanowires as masks, which are produced via in-plane solid–liquid–solid guided growth and then transferred reliably onto various stiff or flexible substrates. More importantly, the geometry of the graphene nanoribbons can be predesigned and engineered into elastic two-dimensional springs to achieve outstanding stretchability of >30%, while carrying stable and repeatable electronic transport. We suggest that this convenient scalable nanowire lithography technology has great potential to establish a general and efficient strategy to batch-pattern or integrate various two-dimensional materials as active channels and interconnections for emerging flexible electronic applications.

Magnetic Properties of Quasi-One-Dimensional Crystals Formed by Graphene Nanoclusters and Embedded Atoms of the Transition Metals

Using the density-matrix renormalization group method and quantum Monte Carlo simulation, we studied numerically the energy spectrum and thermodynamics of the quantum Heisenberg spin model for narrow graphene nanoribbons and their derivatives with periodically embedded heteroatoms. For several nanoribbon structures we found macroscopic ground state spin, gapless lowest excitation spectra and intermediate magnetization plateaus at low temperatures. We also studied the lowest energy states of frustrated systems formed by triangular graphitic clusters connected by bridged ions of transition metals. On the base of many-body perturbation theory and the exact diagonalization method, we showed the possibility of spin switching for this model due to the change the corresponding coupling parameters.

(Invited) Atomically Precise Graphene Nanoribbons: From Synthesis to Applications

Atomically precise graphene nanoribbons (GNRs) are at the forefront of nanocarbon research and hold great promise for electronic and optoelectronic applications. Theoretical studies have shown that narrow GNRs possess interesting electronic and magnetic properties that strongly depend on the nanoribbon’s width and edge structure. GNRs with different structures can be synthesized with atomic precision and fine-tuned properties by coupling properly designed molecular precursors and planarization of the resulting polymers. In this talk, I will discuss our efforts on designing and synthesizing new atomically precise GNRs for electronic applications. First, I will describe a scalable bottom-up solution approach for atomically precise GNRs that is based on Yamamoto coupling of pre-synthesized molecular precursors followed by cyclodehydrogenation using Scholl reaction. This approch can be applied to the synthesis of a variety of GNRs, including pristine and nitrogen-doped GNRs with the chevron structure. Then, I will demonstrate that the electrical conductivity of atomically precise chevron GNRs can be improved by their lateral extension. Two types of new laterally extended chevron GNRs (eGNRs) were synthesized in solution, and their high structural quality was confirmed by a number of characterization techniques, including high-resolution scanning tunneling microscopy and Raman spectroscopy combined with a computational analysis. Optical spectroscopy and scanning tunneling spectroscopy showed that lateral extension of chevron GNRs resulted in the decrease of their electronic bandgap. We developed a procedure for processing eGNRs into uniform thin films that exhibit improved electrical conductivity compared to similar films of regular chevron GNRs. The eGNR films were employed in gas sensors that showed very high responsivity to low molecular weight alcohols compared to similar sensors based on benchmark graphitic materials, such as graphene and graphene oxide. Finally, we demonstrated the first electronic nose system based on atomically precise GNRs that could reliably recognize analytes of nearly the same chemical nature, such as methanol and ethanol. Overall, this talk will demonstrate the entire path from designing new atomically precise GNRs with improved properties to their bottom-up synthesis, characterization, processing and implementation in electronic devices.

Exciton absorption spectra in narrow armchair graphene nanoribbons in an electric field

We present an analytical investigation of the exciton optical absorption in a narrow armchair graphene nanoribbon (AGNR) in the presence of a longitudinal external electric field directed parallel to the ribbon axis. The two-body 2D Dirac equation for the massless electron and hole subject to the ribbon confinement, Coulomb interaction and electric field is employed. The ribbon confinement is assumed to be much stronger than the internal exciton electric field which in turn considerably exceeds the external electric field. This justifies an adiabatic approximation implying a slow longitudinal and fast transverse electron-hole relative motion governed by the exciton attraction and accompanied by the external electric field and ribbon confinement effects, respectively. In the single subband approximation of the isolated size-quantized subbands induced by the ribbon confinement the exciton electroabsorption coefficient is determined in an explicit form. The pronounced dependencies of the exciton peak positions, widths and intensities on the ribbon width and electric field strength are traced. The electron-hole exciton attraction modifies remarkably the Franz-Keldysh electroabsorption in the frequency region both below and above the edges determined by the size-quantized energy levels. In the double-subband approximation of the interacting ground and first excited subbands the combined effect of the exciton electro- and autoionization caused by the electric field and intersubband coupling, respectively, are explored. Estimates of the expected experimental values for the typically employed AGNR show that for a weak electric field the exciton quasi-discrete states remain sufficiently stable to be observed in optical experiments, while relatively strong fields free the captured carriers to further restore their contribution to the transport.

Surface-Synthesized Graphene Nanoribbons for Room Temperature Switching Devices: Substrate Transfer and ex Situ Characterization

Recent progress in the on-surface synthesis of graphene nanoribbons (GNRs) has given access to atomically precise narrow GNRs with tunable electronic band gaps that makes them excellent candidates for room-temperature switching devices such as field-effect transistors (FET). However, in spite of their exceptional properties, significant challenges remain for GNR processing and characterization. This contribution addresses some of the most important challenges, including GNR fabrication scalability, substrate transfer, long-term stability under ambient conditions and ex situ characterization. We focus on 7- and 9-atom wide armchair graphene nanoribbons (i.e, 7-AGNR; and 9-AGNR) grown on 200 nm Au(111)/mica substrates using a high throughput system. Transfer of both, 7- and 9-AGNRs from their Au growth sub-strate onto various target substrates for additional characterization is accomplished utilizing a polymer-free method that avoids residual contamination. This results in a homogeneous GNR film morphology with very few tears and wrinkles, as examined by atomic force microscopy. Raman spectroscopy indicates no significant degradation of GNR quality upon substrate transfer, and reveals that GNRs have remarkable stability under ambient conditions over a 24-month period. The transferred GNRs are analyzed using multi-wavelength Raman spectroscopy, which provides detailed insight into the wavelength dependence of the width-specific vibrational modes. Finally, we characterize the optical properties of 7- and 9-AGNRs via ultra-violet-visible (UV-Vis) spectroscopy

Interface Coupling as a Crucial Factor for Spatial Localization of Electronic States in a Heterojunction of Graphene Nanoribbons

The heterojunction (HJ) band structures of graphene nanoribbons (GNRs), generated by modulating ribbon width, are currently considered for use in tunnel field-effect transistors and optoelectronic applications, but interfacial states often exist and remove the band offsets. Here first-principles calculations show that these states are induced by C---C bonds at the interfacial edge, and can be eliminated by ``spare'' coupling of wide and narrow GNR segments, which is predicted to be stable at room temperature. Knowing how best to construct GNR HJs naturally will promote the technologies based on them.

Thermoelectric properties of nanostructured systems based on narrow armchair graphene nanoribbons

Thermoelectric properties of hybrid systems composed of graphene nanoribbons (GNRs) coupled to rectangular rings or functionalized with aromatic carbon molecules are theoretically addressed here. Graphene-based nanostructures are designed with the purpose of enhancing thermopower responses compared to the thermal performance of pristine GNRs. The electronic transport is calculated using standard tight binding models and the Landauer transport formalism. We found that both semiconducting and metallic armchair nanoribbons coupled to rings exhibit a pronounced enhancement of the thermoelectric responses with comparable intensities, due to Fano antiresonance and Breit–Wigner-like resonances in the electronic transport. As expected, details of the ring geometry and ribbons are important in determining the precise chemical potential values for optimal performance. Different configurations of attached aromatic molecules (single and double molecules) at the graphene nanoribbon edges are addressed. Our findings show that the presence of a molecule induces a gap formation in the metallic pristine GNRs, and a pronounced peak of the Seebeck coefficient is revealed for low chemical potential values, independent of the molecule length. Other features on the Seebeck spectra are found to depend on the electronic nature of the GNRs and on the molecule length and distribution. We have shown that by playing with them, it is possible to design better thermoelectric devices based on GNRs.

Wafer Scale Growth and Characterization of Edge Specific Graphene Nanoribbons for Nanoelectronics

One of the ways to use graphene in field effect transistors is to introduce a band gap by quantum confinement effect. That is why narrow graphene nanoribbons (GNRs) with width less than 50 nm are c...

Edge-insensitive magnetism and half metallicity in graphene nanoribbons

Realizing magnetism in graphene nanostructures is a decade-long challenge. The magnetic edge state and half metallicity in zigzag graphene nanoribbons are particularly promising (Son et al 2006 Nature 444 347). However, its experimental realization has been hindered by the stringent requirement of the mono-hydrogenated zigzag edge. Using first-principle calculations, we predict that free-carrier doping can overcome this challenge and realize ferromagnetism and half-metallicity in narrow graphene nanoribbons of general types of edge structures. This magnetism exists within the density range of gate-doping experiments (~1013 cm−2) and has large spin polarization energy up to 17 meV per carrier, which induces a Zeeman splitting equivalent to an external magnetic field of a few hundred Tesla. Moreover, we trace the formation of this edge-insensitive magnetism to the quantum confinement of the electronic state near the band edge and reveal the scaling law of magnetism versus the ribbon width. Our findings suggest that combining doping with quantum confinement could be a general tool to realize transition-metal-free magnetism in light-element nanostructures.

Graphene Nanoribbon as Potential On-Chip Interconnect Material—A Review

In recent years, on-chip interconnects have been considered as one of the most challenging areas in ultra-large scale integration. In ultra-small feature size, the interconnect delay becomes more pronounced than the gate delay. The continuous scaling of interconnects introduces significant parasitic effects. The resistivity of interconnects increases because of the grain boundary scattering and side wall scattering of electrons. An increased Joule heating and the low current carrying capability of interconnects in a nano-scale dimension make it unreliable for future technology. The devices resistivity and reliability have become more and more serious problems for choosing the best interconnect materials, like Cu, W, and others. Because of its remarkable electrical and its other properties, graphene becomes a reliable candidate for next-generation interconnects. Graphene is the lowest resistivity material with a high current density, large mean free path, and high electron mobility. For practical implementation, narrow width graphene sheet or graphene nanoribbon (GNR) is the most suitable interconnect material. However, the geometric structure changes the electrical property of GNR to a small extent compared to the ideal behavior of graphene film. In the current article, the structural and electrical properties of single and multilayer GNRs are discussed in detail. Also, the fabrication techniques are discussed so as to pattern the graphene nanoribbons for interconnect application and measurement. A circuit modeling of the resistive-inductive-capacitive distributed network for multilayer GNR interconnects is incorporated in the article, and the corresponding simulated results are compared with the measured data. The performance of GNR interconnects is discussed from the view of the resistivity, resistive-capacitive delay, energy delay product, crosstalk effect, stability analysis, and so on. The performance of GNR interconnects is well compared with the conventional interconnects, like Cu, and other futuristic potential materials, like carbon nanotube and doped GNRs, for different technology nodes of the International Technology Roadmap for Semiconductors (ITRS).

Probing plasmons on the edge of graphene nanoribbons under electric field

By using first principle method, we address the plasmon excitation in narrow zigzag and armchair graphene nanoribbons under the effect of the perpendicular electric field. We observed that the edge plasmons with very high one-dimensional confinement mainly originated from π transition peaks and along with increasing the ribbon width, edges contribute much less than in narrow ribbons. Applying electric field excites and hybrids distinct plasmon modes which indicate, the magnitude, intensity and type of plasmon modes within various momentum transfer range are dependent differently on the gating. The key role of charge polarization at the edge and surface plasmons is discussed in the presence of electric field based on the evolution of the dielectric function. Confined edge and surface plasmon modes change under electric field makes graphene nanoribbons a suitable candidate for new terahertz plasmonic applications.

Braiding of edge states in narrow zigzag graphene nanoribbons: Effects of third-neighbor hopping on transport and magnetic properties

We study narrow zigzag graphene nanoribbons (ZGNRs), employing density functional theory (DFT) simulations and the tight-binding (TB) method. The main result of these calculations is the braiding of the conduction and valence bands, generating Dirac cones for non-commensurate wave vectors $\vec{k}$. Employing a TB Hamiltonian, we show that the braiding is generated by the third-neighbor hopping (N3). We calculate the band structure, the density of states and the conductance, new conductance channels are opened, and the conductance at the Fermi energy assumes integer multiples of the quantum conductance unit $G_{o} = 2e^{2}/h$. We also investigate the satisfaction of the Stoner criterion by these ZGNRs. We calculate the magnetic properties of the fundamental state employing LSDA (spin-unrestricted DFT) and we confirm that ZGNRs with $N=(2,3)$ do not satisfy the Stoner criterion and as such the magnetic order could not be developed at their edges. These results are confirmed by both tight-binding and LSDA calculations.

Symmetrized density matrix renormalization group algorithm for low-lying excited states of conjugated carbon systems: Application to 1,12-benzoperylene and polychrysene

The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry $({C}_{2})$, electron-hole symmetry $(J)$, and parity or spin-flip symmetry $(P)$ in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.

Toward Thiophene-Annulated Graphene Nanoribbons.

Narrow thiophene-edged graphene nanoribbons (GNRs) were prepared from polychlorinated thiophene-containing poly(p-phenylene)s using the photochemical, metal-free cyclodehydrochlorination (CDHC) reaction. 1 H NMR and Raman spectroscopy confirmed the structures of the GNRs. The regioselectivity of the CDHC reaction allows the preparation of both laterally symmetrical and unsymmetrical GNRs and, consequently, the modulation of their optical and electronic properties.