Length Of Graphene Nanoribbons Research Articles

Growth Optimization and Device Integration of Narrow‐Bandgap Graphene Nanoribbons

The electronic, optical, and magnetic properties of graphene nanoribbons (GNRs) can be engineered by controlling their edge structure and width with atomic precision through bottom-up fabrication based on molecular precursors. This approach offers a unique platform for all-carbon electronic devices but requires careful optimization of the growth conditions to match structural requirements for successful device integration, with GNR length being the most critical parameter. In this work, the growth, characterization, and device integration of 5-atom wide armchair GNRs (5-AGNRs) are studied, which are expected to have an optimal bandgap as active material in switching devices. 5-AGNRs are obtained via on-surface synthesis under ultrahigh vacuum conditions from Br- and I-substituted precursors. It is shown that the use of I-substituted precursors and the optimization of the initial precursor coverage quintupled the average 5-AGNR length. This significant length increase allowed the integration of 5-AGNRs into devices and the realization ofthe first field-effect transistor based on narrow bandgap AGNRs that shows switching behavior at room temperature. The study highlights that the optimized growth protocols can successfully bridge between the sub-nanometer scale, where atomic precision is needed to control the electronic properties, and the scale of tens of nanometers relevant for successful device integration of GNRs.

Origin of nonlinear current-voltage curves for suspended zigzag edge graphene nanoribbons

The structure-dependent electronic properties of suspended graphene nanoribbon (GNR) have still been important issues. However, these properties have been rarely investigated experimentally due to technical difficulties to produce high-quality suspended GNRs and the identification of atomic structures. Here, we report the electronic properties of suspended GNRs by in situ transmission electron microscopy observations to simultaneously obtain the structural information while measuring the current-voltage (I-V) curves. The suspended GNRs could be obtained by convergent electron beam nanosculpting after careful cleaning by current annealing. The I-V curves were measured for GNRs with a mixture of both zigzag and armchair edges (MGNR) with widths of 3.7 to 1.9 nm and also zigzag edge GNRs (ZGNR) with widths of 1.7 to 1.2 nm. The I-V curves for the ZGNRs were different from those of the MGNRs, as follows. (1) The ZGNRs showed a sharp increase at the threshold voltage in differential conductance-voltage curves. (2) The band gaps measured for ZGNRs were smaller than the band gaps calculated using the GW approximation. (3) The threshold voltage increased with the GNR length. These findings support magnetic-insulator and nonmagnetic-metal nonequilibrium phase transitions as theoretically predicted. Narrow and short ZGNR represents the potential for further nanosized switching devices.

Charge transport mechanism in networks of armchair graphene nanoribbons

In graphene nanoribbons (GNRs), the lateral confinement of charge carriers opens a band gap, the key feature that enables novel graphene-based electronics. Despite great progress, reliable and reproducible fabrication of single-ribbon field-effect transistors (FETs) is still a challenge, impeding the understanding of the charge transport. Here, we present reproducible fabrication of armchair GNR-FETs based on networks of nanoribbons and analyze the charge transport mechanism using nine-atom wide and, in particular, five-atom-wide GNRs with large conductivity. We show formation of reliable Ohmic contacts and a yield of functional FETs close to unity by lamination of GNRs to electrodes. Modeling the charge transport in the networks reveals that transport is governed by inter-ribbon hopping mediated by nuclear tunneling, with a hopping length comparable to the physical GNR length. Overcoming the challenge of low-yield single-ribbon transistors by the networks and identifying the corresponding charge transport mechanism is a key step forward for functionalization of GNRs.

A Universal Length-Dependent Vibrational Mode in Graphene Nanoribbons

Graphene nanoribbons (GNRs) have attracted considerable interest, as their atomically tunable structure makes them promising candidates for future electronic devices. However, obtaining detailed information about the length of GNRs has been challenging and typically relies on low-temperature scanning tunneling microscopy. Such methods are ill-suited for practical device application and characterization. In contrast, Raman spectroscopy is a sensitive method for the characterization of GNRs, in particular for investigating their width and structure. Here, we report on a length-dependent, Raman-active low-energy vibrational mode that is present in atomically precise, bottom-up-synthesized armchair graphene nanoribbons (AGNRs). Our Raman study demonstrates that this mode is present in all families of AGNRs and provides information on their length. Our spectroscopic findings are corroborated by scanning tunneling microscopy images and supported by first-principles calculations that allow us to attribute this mode to a longitudinal acoustic phonon. Finally, we show that this mode is a sensitive probe for the overall structural integrity of the ribbons and their interaction with technologically relevant substrates.

Conductance through the armchair graphene nanoribbons 9-AGNR: Strong dependence on contact to leads

The successful use of graphene nanoribbons (GNRs) in a variety of applications in nanoelectronics depends not only on reliable control of their forbidden gaps, but also on the understanding of the effects that contacts to leads may have on their conductance $G$. By combining Landauer's formalism and a simplified version of the embedded cluster method, $G$ through suspended 9-AGNR has been calculated as a function of energy (sample bias) and the strength of the contact between the ribbon and leads attached to both zigzag edges. Green's functions of contacted ribbons have been derived from HF nonspin polarized solutions of the Pariser-Parr-Pople Hamiltonian. It is shown that the G associated with the two quasidegenerate states around the Fermi level, which are strongly localized at the zigzag edges, equals a conductance quantum ${G}_{0}$ for very weak leads-ribbon coupling, decreasing to zero as that coupling increases. At the Fermi level $G$ is zero for small coupling, increasing up to ${G}_{0}$ for a value of coupling that depends on the GNR length, and, finally, decreasing to zero for large coupling. Conductance through other energies, starting at $G=0$ for no coupling, increases with coupling to the electrodes up to near one quantum at a pace that may appreciably depend on the particular molecular orbital. These results illustrate the difficulties that may be found in exploring practical uses of GNRs.

Optoelectronic application of graphene nanoribbon for mid-infrared bandpass filtering.

In this study, an ultra-compact optoelectronic bandpass filter is proposed. A single piece of graphene nanoribbon (GNR) is placed between two input-output GNRs to form a Fabry-Perot-like cavity. The GNR, as a mid-infrared surface waveguide, enhances the compatibility with complementary metal oxide-semiconductor processing technologies. The transmission characteristics of the bandpass filter are tuned by the modulation of surface charge carrier density simply through changing the bias voltage applied on the GNR cavity, and thus a tunable filter at room temperature is achieved. It is found that increasing the gate voltage and the silica substrate thickness or middle GNR width alters the max peak of transmission spectra of the filter toward smaller wavelengths. In contrast, increasing the middle GNR length redshifts max peak of the filter toward longer wavelengths. The finite different time domain (FDTD) inhouse code has been employed to verify the designs.

Graphene nanoribbons on gold: understanding superlubricity and edge effects

We address the atomistic nature of the longitudinal static friction against sliding of graphene nanoribbons (GNRs) deposited on gold, a system whose structural and mechanical properties have been recently the subject of intense experimental investigation. By means of numerical simulations and modeling we show that the GNR interior is structurally lubric (‘superlubric’) so that the static friction is dominated by the front/tail regions of the GNR, where the residual uncompensated lateral forces arising from the interaction with the underneath gold surface opposes the free sliding. As a result of this edge pinning the static friction does not grow with the GNR length, but oscillates around a fairly constant mean value. These friction oscillations are explained in terms of the GNR-Au(111) lattice mismatch: at certain GNR lengths close to an integer number of the beat (or moiré) length there is good force compensation and superlubric sliding; whereas close to half odd-integer periods there is significant pinning of the edge with larger friction. These results make qualitative contact with recent state-of-the-art atomic force microscopy experiment, as well as with the sliding of other different incommensurate systems.

Unraveling mechanics of armchair and zigzag graphene nanoribbons

The unraveling process of armchair and zigzag graphene nanoribbons (GNRs) was studied with molecular dynamics simulations using the Adaptive Intermolecular Reactive Empirical Bond Order Potential for carbon–carbon bond. Simulations were performed at 300°K, with GNR length and width varying from 2.5 nm to 15 nm in 2.5 nm increments. In these simulations, the unraveling of the GNRs was started from two positions; the corner or the middle of the top side. Force–displacement relationship was analyzed for the terminal atom of the unraveling chains. For armchair GNRs (AGNRs) that were unraveled from the corner, the force required for the onset of the unraveling is in the range of 4.279–5.045 eV/Å, and the observed failure force in the carbon chain is in the range of 5.553–5.963 eV/Å. Unraveling will not happen when AGNRs are unraveled from the middle, and zigzag GNRs (ZGNRs) are unraveled either from corner or middle. For the latter cases, the bond between the terminal atom and GNR sheet breaks under the stretching force, and only one carbon atom can be pulled out from the GNR sheet. The size effect of width and length on the unraveling process was also studied. Simulations show that size has a trivial effect on unraveling. Comparison between unraveling of AGNRs and ZGNRs indicates that AGNRs are perfect structure to produce Monatomic Carbon Chains, while ZGNRs are more stable and are good candidate for graphene nanodevices that are free from unraveling disintegration.

Aspect ratio effect on shear modulus and ultimate shear strength of graphene nanoribbons

This paper focuses on shear modulus and shear deformation behavior of Graphene Nano Ribbons (GNR) post-wrinkling taking into account size effect. Atomistic modeling of armchair and zigzag GNR were performed at 300°K for GNR with a constant 10nm width and lengths ranging from 2.5nm to 25nm. Results show that ridge formation is oriented at 45 degrees for GNR with an aspect ratio less than one and that the number of ridges is equal to the reciprocal of the aspect ratio, while for aspect ratios higher than one, the ridge formation direction coincides with the diagonal direction of the GNR and only one ridge is formed. Once the diagonal tension reached its ultimate elastic level, three major stress-relaxing phenomena are reported. Results show that the average slope of the stress-strain curve beyond the ultimate elastic stress decreases with increasing GNR length. Moreover, the slope of the shear stress-strain curve in that region is always greater in armchair GNR than in Zigzag GNR. GNR can sustain very high plastic shear strains beyond 400% before failure for wide GNR. It is observed that the shear modulus is inversely proportional to the aspect ratio of the GNR.

Molecular Dynamics Studies on Ballistic Thermal Resistance of Graphene Nano-Junctions* *Supported by the National Natural Science Foundation of China under Grant Nos. 51322603, 51136001, 51356001, Science Fund for Creative Research Groups (No. 51321002), the Program for New Century Excellent Talents in University, Tsinghua University Initiative Scientific Research Program, the Tsinghua National Laboratory for Information Science and Technology of China

Ballistic thermal resistance of graphene nano-junctions is investigated using non-equilibrium molecular dynamics simulation. The simulation system is consisted of two symmetrical trapezoidal or rectangular graphene nano-ribbons (GNRs) and a connecting nanoscale constriction in between. From the simulated temperature profile, a big temperature jump resulted from the constriction is found, which is proportional to the heat current and corresponds to a local ballistic thermal resistance. Fixing the constriction width and the length of GNRs, this ballistic thermal resistance is independent of the width of the GNRs bottom layer, i.e., the convex angle. But interestingly, this thermal resistance has obvious size effect. It is inversely proportional to the constriction width and will disappear with the constriction being wider. Moreover, based on the phonon dynamics theory, a theoretical model of the ballistic thermal resistance in two-dimensional nano-systems is developed, which gives a good explanation on microcosmic level and agrees well with the simulation result quantitatively and qualitatively.

Coherent Electron Transmission across Nanographenes Tethered to Gold Electrodes: Influence of Linker Topology, Ribbon Width, and Length

The conductance of several well-defined and experimentally accessible graphene nanoribbons (GNRs) linked to gold electrodes by thiol groups to form single-molecule junctions is investigated within the nonequilibrium Green’s function formalism coupled to density functional theory. We focus on the change in conduction as a function of the width and length of the ribbons as well as the number and position of the linking groups. The calculations illustrate that the position of the linkers is a key parameter controlling the conductance through the GNRs investigated here, as can be anticipated from their Clar sextet representations. The increase in width yields higher conductance only if accompanied by an increasing number of linkers due to the opening of additional pathways. The decay of transmission with GNR length is close to exponential, with rather low attenuation factors (0.06–0.11 Å–1) that depend on the ribbon topology.

IN SITU UNZIPPING OF CARBON NANOTUBES TO FORM GRAPHENE NANORIBBONS

We report the one step facile synthesis of graphene nanoribbons (GNRs) by unzipping carbon nanotubes (CNTs) from glucose ( C 6 H 12 O 6) precursor, using a simple chemical vapor deposition method. Some nanotubes are partially cut resulting in a GNR–CNT hybrid whereas others are fully cut to form GNRs. The average length of GNRs achieved by this method is typically in the range of 1–10 μm. The formation of GNRs is ascribed to the in situ oxygen-driven unzipping of CNTs. The process is free from aggressive oxidants and utilizes the in situ unzipping. This method offers an alternative approach for making GNRs, compared to previously used techniques to synthesize GNRs.

Analytical modeling of trilayer graphene nanoribbon Schottky-barrier FET for high-speed switching applications

Recent development of trilayer graphene nanoribbon Schottky-barrier field-effect transistors (FETs) will be governed by transistor electrostatics and quantum effects that impose scaling limits like those of Si metal-oxide-semiconductor field-effect transistors. The current–voltage characteristic of a Schottky-barrier FET has been studied as a function of physical parameters such as effective mass, graphene nanoribbon length, gate insulator thickness, and electrical parameters such as Schottky barrier height and applied bias voltage. In this paper, the scaling behaviors of a Schottky-barrier FET using trilayer graphene nanoribbon are studied and analytically modeled. A novel analytical method is also presented for describing a switch in a Schottky-contact double-gate trilayer graphene nanoribbon FET. In the proposed model, different stacking arrangements of trilayer graphene nanoribbon are assumed as metal and semiconductor contacts to form a Schottky transistor. Based on this assumption, an analytical model and numerical solution of the junction current–voltage are presented in which the applied bias voltage and channel length dependence characteristics are highlighted. The model is then compared with other types of transistors. The developed model can assist in comprehending experiments involving graphene nanoribbon Schottky-barrier FETs. It is demonstrated that the proposed structure exhibits negligible short-channel effects, an improved on-current, realistic threshold voltage, and opposite subthreshold slope and meets the International Technology Roadmap for Semiconductors near-term guidelines. Finally, the results showed that there is a fast transient between on-off states. In other words, the suggested model can be used as a high-speed switch where the value of subthreshold slope is small and thus leads to less power consumption.

Dimension Dependence of Negative Differential Thermal Resistance in Graphene Nanoribbons

Negative differential thermal resistance (NDTR) in approximate graphene nanoribbons (GNRs) is investigated from one dimension to three dimensions by using classical molecular dynamics method. For single-layer GNRs, NDTR can not be observed for very narrow GNRs (one dimension), NDTR appears when the width of GNRs increases (two dimensions). However, NDTR disappears gradually on further increasing the width. For multiple-layer GNRs, when the number of the layers increases, GNRs becomes from two-dimensional system to three-dimensional system, NDTR regime reduces and eventually disappears. In addition, when the length of GNRs increases, NDTR regime also reduces and vanishes in the thermodynamic limit. These effects may be useful for designing thermal devices where NDTR plays an important role.

Tunable thermal rectification in graphene nanoribbons through defect engineering: A molecular dynamics study

Using non-equilibrium molecular dynamics, we show that asymmetrically defected graphene nanoribbons (GNR) are promising thermal rectifiers. The optimum conditions for thermal rectification (TR) include low temperature, high temperature bias, ∼1% concentration of single-vacancy or substitutional silicon defects, and a moderate partition of the pristine and defected regions. TR ratio of ∼80% is found in a 14-nm long and 4-nm wide GNR at a temperature of 200 K and bias of 90 K, where heat conduction is in the ballistic regime since the bulk effective phonon mean-free-path is around 775 nm. As the GNR length increases towards the diffusive regime, the TR ratio decreases and eventually stabilizes at a length-independent value of about 3%–5%. This work extends defect engineering to 2D materials for achieving TR.

Electronic transport through side-contacted graphene nanoribbons: effects of overlap,aspect ratio and orientation

We numerically calculate the conductance and shot noise Fano factor of graphenenanoribbons (GNRs) side-contacted to metallic leads. A tight-binding model andLandauer’s formalism are used in combination with a modified recursion method forGreen’s functions. The interfaces are modeled as a contact region between aninfinite metallic electrode and a segment of the GNR put on top of it. The keyquestion to answer in this study is how the size and orientation of the GNR and theGNR/electrode interface area influence the transport properties. It turns out that ingeneral the transport characteristics depend strongly on overlap, meant as theratio between the electrode-supported GNR length and the unsupported one.Moreover, a speed of convergence (with the overlap length) depends on both thetransport direction and the aspect ratio of the GNR. It is shown that a shortoverlap interface is often, but not always, advantageous in nanoelectronics. Thesefindings reconcile some seemingly conflicting opinions reported in the literature.

Simulation of thermal conductance across dimensionally mismatched graphene interfaces

This paper considers phonon transport behavior in graphene nanoribbons (GNRs) that bridge semi-infinite graphene contacts. The work employs an atomistic Green’s function (AGF) method to investigate phonon wave effects in GNRs with both zigzag and armchair edges. Thermal conductances are found to be sensitive to the edge shape of the ribbons; a sandwiched zigzag GNR structure has almost twice the thermal conductance of the corresponding armchair structure. Results show that the graphene/GNR interface moderately reduces phonon conductance compared to a freestanding GNR. At fixed device lengths, conductance increases with the width of GNR. On the other hand, conductance decreases with GNR length. The zigzag ribbons show smaller reduction upon increasing of GNR length than armchair ribbons; the conductances of both ribbons converge to a length-independent value. For very short devices, thermal conductance can exceed that of a single graphene-GNR interface.