Suspended Graphene Nanoribbons Research Articles

In-situ electrical conductance measurement of suspended ultra-narrow graphene nanoribbons observed via transmission electron microscopy

Graphene nanoribbon is an attractive material for nano-electronic devices, as their electrical transport performance can be controlled by their edge structures. However, in most cases, the electrical transport has been investigated only for graphene nanoribbons fabricated on a substrate, which hinders the appearance of intrinsic electrical transport due to screening effects. In this study, we developed special devices based on silicon chips for transmission electron microscopy to observe a monolayer graphene nanoribbon suspended between two gold electrodes. Moreover, with the development of an in-situ transmission electron microscopy holder, the current–voltage characteristics were achieved simultaneously with observing and modifying the structure. We found that the current–voltage characteristics differed between 1.5 nm-wide graphene nanoribbons with armchair and zigzag edge structures. The energy gap of the zigzag edge was more than two-fold larger than that of the armchair edge and exhibited an abrupt jump above a critical bias voltage in the differential conductance curve. Thus, our in-situ transmission electron microscopy method is promising for elucidating the structural dependence of electrical conduction in two-dimensional materials.

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.

Optimal in situ electromechanical sensing of molecular species

We investigate protocols for optimal molecular detection with electromechanical nanoscale sensors under ambient conditions. Our models are representative of suspended graphene nanoribbons, which due to their piezoelectric and electronic properties provide responsive and versatile sensors. In particular, we analytically account for the corrections in the electronic transmission function and signal-to-noise ratio originating in environmental perturbations, such as thermal fluctuations and solvation effects. We also investigate the role of the sampling time in the current statistics. As a result, we formulate a protocol for optimal sensing based on the modulation of the Fermi level at a fixed bias and provide approximate forms for the current, linear susceptibility, and current fluctuations. We show how the algebraic tails in the thermally broadened transmission function affect the behavior of the signal-to-noise ratio and optimal sensing. These results provide further insights into the operation of graphene deflectometers and other techniques for electromechanical sensing.

Enhanced Thermoelectric Performance of As-Grown Suspended Graphene Nanoribbons.

Conventionally, graphene is a poor thermoelectric material with a low figure of merit (ZT) of 10-4-10-3. Although nanostructuring was proposed to improve the thermoelectric performance of graphene, little experimental progress has been accomplished. Here, we carefully fabricated as-grown suspended graphene nanoribbons with quarter-micron length and ∼40 nm width. The ratio of electrical to thermal conductivity was enhanced by 1-2 orders of magnitude, and the Seebeck coefficient was several times larger than bulk graphene, which yielded record-high ZT values up to ∼0.1. Moreover, we observed a record-high electronic contribution of ∼20% to the total thermal conductivity in the nanoribbon. Concurrent phonon Boltzmann transport simulations reveal that the reduction of lattice thermal conductivity is mainly attributed to quasi-ballistic phonon transport. The record-high ratio of electrical to thermal conductivity was enabled by the disparate electron and phonon mean free paths as well as the clean samples, and the enhanced Seebeck coefficient was attributed to the band gap opening. Our work not only demonstrates that electron and phonon transport can be fundamentally tuned and decoupled in graphene but also indicates that graphene with appropriate nanostructures can be very promising thermoelectric materials.

Highly Stable Persistent Photoconductivity with Suspended Graphene Nanoribbons

Graphene nanoribbon (GNR), also known as 1-dimensional graphene, with a non-zero band gap has a huge potential for various electrical and optoelectrical applications because of its high transparency, flexibility, controllable band gap, and unique edge states. Recent advances in the synthesis of GNR enable us to show the possibility of GNRs as future high performance electrical devices. However, the applicability of GNRs to optoelectrical devices is unclear. Here we report that suspended GNR devices can show persistent photoconductivity (PPC) with long decay time (over 72 h) and adequate environmental stability. Repeated non-volatile memory operation is also demonstrated with an integrated PPC device using GNRs. This very stable PPC device can be applied to a wide variety of fields such as ultra-low-power non-volatile memory, nanoscale imaging, and biological sensors. Our results have opened the door to advance the study of GNRs in novel directions such as optoelectrical applications.

Controlled fabrication of electrically contacted carbon nanoscrolls

Carbon nanoscrolls (CNS) with their open ended morphology have recently attracted interest due to the potential application in gas capture, biosensors and interconnects. However, CNS currently suffer from the same issue that have hindered widespread integration of CNTs in sensors and devices: formation is done ex situ, and the tubes have to be placed with precision and reliability—a difficult task with low yield. Here, we demonstrate controlled in situ formation of electrically contacted CNS from suspended graphene nanoribbons with slight tensile stress. Formation probability depends on the length to width aspect ratio. Van der Waals interaction between the overlapping layers fixes the nanoscroll once formed. The stability of these CNSs is investigated by helium nano ion beam assisted in situ cutting. The loose stubs remain rolled and mostly suspended unless subject to a moderate helium dose corresponding to a damage rate of 4%–20%. One CNS stub remaining perfectly straight even after touching the SiO2 substrate allows estimation of the bending moment due to van der Waals force between the CNS and the substrate. The bending moment of 5400 eV is comparable to previous theoretical studies. The cut CNSs show long-term stability when not touching the substrate.

Thermal Conductivity Measurement of Suspended Graphene Nanoribbons of 40nm Width

Thermal Conductivity Measurement of Suspended Graphene Nanoribbons of 40nm Width

Length divergence of the lattice thermal conductivity in suspended graphene nanoribbons

Thermal properties of graphene have attracted much attention, culminating in a recent measurement of its length dependence in ribbons up to 9 $\ensuremath{\mu}\mathrm{m}$ long. In this paper, we use the improved Callaway model to solve the phonon Boltzmann transport equation while capturing both the resistive (umklapp, isotope, and edge roughness) and nonresistive (normal) contributions. We show that for lengths smaller than 100 $\ensuremath{\mu}\mathrm{m}$, scaling the ribbon length while keeping the width constant leads to a logarithmic divergence of thermal conductivity. The length dependence is driven primarily by a ballistic-to-diffusive transition in the in-plane (LA and TA) branches, while in the hydrodynamic regime when $10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}lLl100$ $\ensuremath{\mu}\mathrm{m}$, the contribution from the in-plane branches saturates and the out-of-plane (ZA) branch shows a clear logarithmic trend, driven by the nonresistive normal contribution. We find that thermal conductivity converges beyond $Lg100$ $\ensuremath{\mu}\mathrm{m}$ due to the coupling between in-plane and flexural modes. This coupling leads to renormalization of ZA phonon dispersion in the long-wavelength range, preventing further divergence of thermal conductivity. We also uncover a strong dependence on sample width, which we attribute to the interplay between nonresistive normal and diffusive edge scattering in the Poisseuille flow regime. We conclude that normal processes play a crucial role in the length and width dependence of thermal transport in graphene in the hydrodynamic regime and dictate the relative in-plane (LA+TA) to out-of-plane (ZA) contribution to transport.

Wafer-scale fabrication and growth dynamics of suspended graphene nanoribbon arrays.

Adding a mechanical degree of freedom to the electrical and optical properties of atomically thin materials can provide an excellent platform to investigate various optoelectrical physics and devices with mechanical motion interaction. The large scale fabrication of such atomically thin materials with suspended structures remains a challenge. Here we demonstrate the wafer-scale bottom–up synthesis of suspended graphene nanoribbon arrays (over 1,000,000 graphene nanoribbons in 2 × 2 cm2 substrate) with a very high yield (over 98%). Polarized Raman measurements reveal graphene nanoribbons in the array can have relatively uniform-edge structures with near zigzag orientation dominant. A promising growth model of suspended graphene nanoribbons is also established through a comprehensive study that combined experiments, molecular dynamics simulations and theoretical calculations with a phase-diagram analysis. We believe that our results can contribute to pushing the study of graphene nanoribbons into a new stage related to the optoelectrical physics and industrial applications.

Signatures of single quantum dots in graphene nanoribbons within the quantum Hall regime.

We report on the observation of periodic conductance oscillations near quantum Hall plateaus in suspended graphene nanoribbons. They are attributed to single quantum dots that are formed in the narrowest part of the ribbon, in the valleys and hills of a disorder potential. In a wide flake with two gates, a double-dot system's signature has been observed. Electrostatic confinement is enabled in single-layer graphene due to the gaps that are formed between the Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states.

Thermal transport in a 2D stressed nanostructure with mass gradient

Inspired by some recent molecular dynamics (MD) simulations and experiments on suspended graphene nanoribbons, we study a simplified model where the atoms are disposed in a rectangular lattice coupled by nearest neighbor interactions which are quadratic in the interatomic distance. The system has a mechanical strain, and the border atoms are coupled to Langevin thermal baths. Atom masses vary linearly in the longitudinal direction, modeling an isotope or doping distribution. This asymmetry and tension modify thermal properties. Although the atomic interaction is quadratic, the potential is anharmonic in the coordinates. By direct MD simulations and solving Fokker-Planck equations at low temperatures, we can better understand the role of anharmonicities in thermal rectification. We observe an increasing thermal current with an increasing applied mechanical tension. The temperatures and thermal currents vary along the transverse direction. This effect can be useful to establish which parts of the system are more sensitive to thermal damage. We also study thermal rectification as a function of strain and system size.Received: 20 Novembre 2014, Accepted: 17 April 2015; Edited by: C. A. Condat, G. J. Sibona; DOI: http://dx.doi.org/10.4279/PIP.070008Cite as: R Barreto, M F Carusela, A Mancardo Viotti, A G Monastra, Papers in Physics 7, 070008 (2015)This paper, by R Barreto, M F Carusela, A Mancardo Viotti, A G Monastra, is licensed under the Creative Commons Attribution License 3.0.

Temperature dependent thermal conductivity of a suspended submicron graphene ribbon

Thermophysical characterization of graphene is very important for both fundamental and technological research. While most of the existing thermal conductivity measurements are for graphene sheets with sizes larger than 1 μm, the thermal conductivities for suspended submicron graphene ribbons are still very few, although the thermal conductivity of graphene ribbons at the submicron scale is predicted to be much smaller than large graphene and strongly size dependent for both length and width due to the 2D nature of phonon transport. Here, we report the temperature dependent thermal conductivity of a 169-nm wide and 846-nm long graphene ribbon measured by the electrical self-heating method. The measured thermal conductivities range from (12.7 ± 2.95) W/m/K at 80 K to (932 ± 333) W/m/K at 380 K, being (349 ± 63) W/m/K at 300 K, following a ∼ T2.79 law for the full temperature range of 80 K to 380 K and a ∼ T1.23 law at low temperatures. The comparison of the measured thermal conductance with the ballistic transport limit indicates diffusive transport in this narrow and short ribbon due to phonon-edge as well as phonon-defect scattering. The data were also combined with an empirical model to predict possible width dependence of thermal conductivity for suspended graphene ribbons. These results help understand the 2D phonon transport in suspended submicron graphene ribbons and provide knowledge for controlling thermophysical properties of suspended graphene nanoribbons through size manipulation.

Full-dispersion Monte Carlo simulation of phonon transport in micron-sized graphene nanoribbons

We simulate phonon transport in suspended graphene nanoribbons (GNRs) with real-space edges and experimentally relevant widths and lengths (from submicron to hundreds of microns). The full-dispersion phonon Monte Carlo simulation technique, which we describe in detail, involves a stochastic solution to the phonon Boltzmann transport equation with the relevant scattering mechanisms (edge, three-phonon, isotope, and grain boundary scattering) while accounting for the dispersion of all three acoustic phonon branches, calculated from the fourth-nearest-neighbor dynamical matrix. We accurately reproduce the results of several experimental measurements on pure and isotopically modified samples [S. Chen et al., ACS Nano 5, 321 (2011);S. Chen et al., Nature Mater. 11, 203 (2012); X. Xu et al., Nat. Commun. 5, 3689 (2014)]. We capture the ballistic-to-diffusive crossover in wide GNRs: room-temperature thermal conductivity increases with increasing length up to roughly 100 μm, where it saturates at a value of 5800 W/m K. This finding indicates that most experiments are carried out in the quasiballistic rather than the diffusive regime, and we calculate the diffusive upper-limit thermal conductivities up to 600 K. Furthermore, we demonstrate that calculations with isotropic dispersions overestimate the GNR thermal conductivity. Zigzag GNRs have higher thermal conductivity than same-size armchair GNRs, in agreement with atomistic calculations.

Fabrication of highly regular suspended graphene nanoribbons through a one-step electron beam lithography process

A method to obtain pre-oriented large longitudinal 1-D arrays of identical suspended graphene nanoribbons is presented. Mechanical exfoliation from graphite was done in order to deposit single- and multiple-layered graphene over a Polymethyl-Methacrylate (PMMA) substrate, which is used as a sacrificial material. Electron beam lithography (EBL) is used to define the anchors and the suspended part of the structures. The method allows achieving a high number of graphene suspended nanoribbons with a very regular width and length. The main advantage of the method, from the process point of view, with respect to other standard procedures is that only one EBL step is needed in the whole sequence, so that the overall process is extremely simplified.

Correlating atomic structure and transport in suspended graphene nanoribbons.

Graphene nanoribbons (GNRs) are promising candidates for next generation integrated circuit (IC) components; this fact motivates exploration of the relationship between crystallographic structure and transport of graphene patterned at IC-relevant length scales (<10 nm). We report on the controlled fabrication of pristine, freestanding GNRs with widths as small as 0.7 nm, paired with simultaneous lattice-resolution imaging and electrical transport characterization, all conducted within an aberration-corrected transmission electron microscope. Few-layer GNRs very frequently formed bonded-bilayers and were remarkably robust, sustaining currents in excess of 1.5 μA per carbon bond across a 5 atom-wide ribbon. We found that the intrinsic conductance of a sub-10 nm bonded bilayer GNR scaled with width as GBL(w) ≈ 3/4(e2/h)w, where w is the width in nanometers, while a monolayer GNR was roughly five times less conductive. Nanosculpted, crystalline monolayer GNRs exhibited armchair-terminated edges after current annealing, presenting a pathway for the controlled fabrication of semiconducting GNRs with known edge geometry. Finally, we report on simulations of quantum transport in GNRs that are in qualitative agreement with the observations.

Thermal conductivity of graphene nanoribbons in noble gaseous environments

We investigate the thermal conductivity of suspended graphene nanoribbons in noble gaseous environments using molecular dynamics simulations. It is reported that the thermal conductivity of perfect graphene nanoribbons decreases with the gaseous pressure. The decreasing is more obvious for the noble gas with large atomic number. However, the gaseous pressure cannot change the thermal conductivity of defective graphene nanoribbons apparently. The phonon spectra of graphene nanoribbons are also provided to give corresponding supports.

Coulomb blockade effect of molecularly suspended graphene nanoribbons investigated with scanning tunneling microscopy

We present the study of the quantum tunneling through a vertical two-barrier structure sandwiching a graphene nanoribbon quantum object. Scanning tunneling microscopy measurements of the graphene nanoribbon show staircase I-U characteristics and oscillating dI/dU spectra. To identify the physical origin of the observed effect, we varied the tunneling resistance of the tip-ribbon junction and found a tip-to-ribbon distance dependent oscillating period change. Together with the numerical analysis, we confirm that the resonances in the spectroscopy arise from the Coulomb blockade effect. The study of the Coulomb blockade effect in graphene nanoribbons may be of potential usages for the fabrication of superthin quantum dot devices.

Buckling suspended graphene nanoribbons to harvest energy from noisy vibrations

Most mechanical vibrations in our environment can be classified as noisy vibrations, since they have no preferred frequency and a spectrum that spreads to the low frequency range. Bistable systems have shown to be a solution to the existing frequency mismatch between the energy source and the harvester device. In this work a parametric study is carried out in order to show the dependence of these improvements with the quality factor Q of a vibrating beam and the different responses when driven by different types of model noise. Specifically, we studied Colored Gaussian Noise instead of the much more common White Gaussian Noise, considered as a reference in most studies.

Crossover from Coulomb Blockade to Quantum Hall Effect in Suspended Graphene Nanoribbons

Suspended graphene nanoribbons formed during current annealing of suspended graphene flakes have been investigated experimentally. Transport measurements show the opening of a transport gap around charge neutrality due to the formation of "Coulomb islands", coexisting with quantum Hall conductance plateaus appearing at moderate values of the magnetic field B. Upon increasing B, the transport gap is rapidly suppressed, and is taken over by a much larger energy gap due to electronic correlations. Our observations show that suspended nanoribbons allow the investigation of phenomena that could not so far be accessed in ribbons on SiO(2) substrates.

Substrate effects on the thermal conductivity of epitaxial graphene nanoribbons

We study the effect of SiC substrate on thermal conductivity of epitaxial graphene nanoribbons (GNRs) using the nonequilibrium molecular dynamics method. We show that the substrate has strong interaction with single-layer GNRs during the thermal transport, which largely reduces the thermal conductivity. The high thermal conductivity of suspended GNRs is obtained in the second layers of bilayer GNRs, which has a weak van der Waals interaction with the underlying structures. The out-of-plane phonon mode is found to play a critical role on the thermal conductivity variation of the second GNR layer induced by the underlying structures. The effect of disordered edge defects on thermal conductivity is further investigated. The results show that the disordered edge defects can remarkably decrease thermal conductivity of GNRs weakly interacted with substrate, while the effect becomes minor on GNRs strongly interacted with substrate.