Strain effect on electronic structures of graphene nanoribbons: A first-principles study

Combined effect of strain and intrinsic spin-orbit coupling on band gap engineering of GNRs: a first-principles study

By employing first-principles calculations, we theoretically investigate the impact of uniaxial strain and intrinsic spin-orbit coupling (SOC) on the electronic properties of zigzag and armchair edge hydrogen (H)-passivated graphene nanoribbons (GNRs). We find that band structure and density of states of 4-zigzag graphene nanoribbon (ZGNR) and 15-armchair graphene nanoribbon (AGNR) are highly sensitive to the combined effect of strain and intrinsic SOC. In the case of H-passivated 4-ZGNR, SOC with a strain>10% increases the energy band by increasing spin-polarized states at the opposite edges. In contrast to 4-ZGNR, the oscillatory behavior of band gap of H-passivated 15-AGNR is preserved in the presence of strain and SOC. Moreover, for both types of GNRs (zigzag and armchair), the presence of strain and intrinsic SOC preserve spin symmetry.

Rich essential properties of silicon-substituted graphene nanoribbons: a comprehensive computational study

The diverse structural, electronic, and magnetic properties of silicon (Si)-substituted armchair and zigzag graphene nanoribbons (AGNRs and ZGNRs) were investigated using spin-polarized density functional theory (DFT) calculations. Pristine AGNRs belong to a nonmagnetic semiconductor with a direct bandgap of 1.63/1.92 eV determined by PBE/HSE06 functionals. Under various Si substitutions, nonmagnetic bandgaps were tuned at 1.49/1.87, 1.06/1.84, 0.81/1.45, 1.04/1.71, 0.89/1.05, and 2.38/3.0 eV (PBE/HSE06) in the single Si edge-, single Si non-edge-, double Si ortho-, double Si meta-, double Si para-, and 100% Si-substituted AGNR configurations, respectively. Meanwhile, pristine ZGNRs displayed antiferromagnetic semiconducting behavior with a spin degenerate bandgap of 0.52/0.81 eV (PBE/HSE06) and becomes a ferromagnetic semimetal in the single Si configurations or an unusual ferromagnetic semiconductor in the 100% Si configuration. Under the developed first-principles theoretical framework, the formation of quasi π (C-2pz and Si-3pz) and quasi σ (C-2s, -2pxy and Si-3s and -3pxy) bands was identified in the Si-substituted configurations. These quasi π and quasi σ bands showed weak separation, resulting in weak quasi sp2 hybridization in Si-C bonds, in which the identified hybridization mechanism was a strong evidence for the formation of stable planar 1D structures in the Si-substituted configurations. Our complete revelation of the essential properties of Si-substituted GNRs can provide a complete understanding of their chemically doped 1D materials for various practical applications.

Quantum Confinement in Epitaxial Armchair Graphene Nanoribbons on SiC Sidewalls

The integration of graphene into devices necessitates large-scale growth and precise nanostructuring. Epitaxial growth of graphene on SiC surfaces offers a solution by enabling both simultaneous and targeted realization of quantum structures. We investigated the impact of local variations in the width and edge termination of armchair graphene nanoribbons (AGNRs) on quantum confinement effects using scanning tunneling microscopy and spectroscopy (STM, STS), along with density-functional tight-binding (DFTB) calculations. AGNRs were grown as an ensemble on refaceted sidewalls of SiC mesas with adjacent AGNRs separated by SiC(0001) terraces hosting a buffer layer seamlessly connected to the AGNRs. Energy band gaps measured by STS at the centers of ribbons of different widths align with theoretical expectations, indicating that hybridization of π-electrons with the SiC substrate mimics sharp electronic edges. However, regardless of the ribbon width, band gaps near the edges of AGNRs are significantly reduced. DFTB calculations successfully replicate this effect by considering the role of edge passivation, while strain or electric fields do not account for the observed effect. Unlike idealized nanoribbons with uniform hydrogen passivation, AGNRs on SiC sidewalls generate additional energy bands with non-pz character and nonuniform distribution across the nanoribbon. In AGNRs terminated with Si, these additional states occur at the conduction band edge and rapidly decay into the bulk of the ribbon. This agrees with our experimental findings, demonstrating that edge passivation is crucial in determining the local electronic properties of epitaxial nanoribbons.

Unveiling and Manipulating Hidden Symmetries in Graphene Nanoribbons

Armchair graphene nanoribbons are a highly promising class of semiconductors for all-carbon nanocircuitry. Here, we present a new perspective on their electronic structure from simple model Hamiltonians and ab initio calculations. We focus on a specific set of nanoribbons of width n=3p+2, where n is the number of carbon atoms across the nanoribbon axis and p is a positive integer. We demonstrate that the energy-gap opening in these nanoribbons originates from the breaking of a previously unidentified hidden symmetry by long-ranged hopping of π electrons and structural distortions occurring at the edges. This hidden symmetry can be restored or manipulated through the application of in-plane lattice strain, which enables continuous energy-gap tuning, the emergence of Dirac points at the Fermi level, and topological quantum phase transitions. Our work establishes an original interpretation of the semiconducting character of armchair graphene nanoribbons and offers guidelines for rationally designing their electronic structure.

Electronic, transport, magnetic and optical properties of graphene nanoribbons review

Low dimensional materials have attracted great research interest from both theoretical and experimental point of view. These materials exhibit novel physical and chemical properties due to the confinement effect in low dimensions. The experimental observations of graphene open a new platform to study the physical properties of materials restricted to two dimensions. This featured article provides a review on the novel properties of quasi one-dimensional (1D) material known as graphene nanoribbon. Graphene nanoribbons can be obtained by unzipping carbon nanotubes (CNTs) or cutting the graphene sheet. Alternatively, it is also called the finite termination of graphene edges. It gives rise different edge geometries namely zigzag and armchair among others. There are various physical and chemical techniques to realize these materials. Depending on the edge type termination, these are called the zigzag and armchair graphene nanoribbons (ZGNR and AGNR). These edges play an important role in controlling the properties of graphene nanoribbons. The present review article provides an overview of the electronic, transport, optical and magnetic properties of graphene nanoribbons. However, there are different ways to tune these properties for device applications. Here, some of them are highlighted such as external perturbations and chemical modifications. Few applications of graphene nanoribbon have and chemical modifications. Few applications of graphene nanoribbon have also been briefly discussed.

Inducing a topological transition in graphene nanoribbon superlattices by external strain

Armchair graphene nanoribbons, when forming a superlattice, can be classified into different topological phases, with or without edge states. By means of tight-binding and classical molecular dynamics (MD) simulations, we studied the electronic and mechanical properties of some of these superlattices. MD shows that fracture in modulated superlattices is brittle, as for unmodulated ribbons, and occurs at the thinner regions, with staggered superlattices achieving a larger fracture strain than inline superlattices. We found a general mechanism to induce a topological transition with strain, related to the electronic properties of each segment of the superlattice, and by studying the sublattice polarization we were able to characterize the transition and the response of these states to the strain. For the cases studied in detail here, the topological transition occurred at ∼3-5% strain, well below the fracture strain. The topological states of the superlattice - if present - are robust to strain even close to fracture. The topological transition was characterized by means of the sublattice polarization of the states.

Graphene as a Piezoresistive Material in Strain Sensing Applications

High accuracy measurement of mechanical strain is critical and broadly practiced in several application areas including structural health monitoring, industrial process control, manufacturing, avionics and the automotive industry, to name a few. Strain sensors, otherwise known as strain gauges, are fueled by various nanomaterials, among which graphene has attracted great interest in recent years, due to its unique electro-mechanical characteristics. Graphene shows not only exceptional physical properties but also has remarkable mechanical properties, such as piezoresistivity, which makes it a perfect candidate for strain sensing applications. In the present review, we provide an in-depth overview of the latest studies focusing on graphene and its strain sensing mechanism along with various applications. We start by providing a description of the fundamental properties, synthesis techniques and characterization methods of graphene, and then build forward to the discussion of numerous types of graphene-based strain sensors with side-by-side tabular comparison in terms of figures-of-merit, including strain range and sensitivity, otherwise referred to as the gauge factor. We demonstrate the material synthesis, device fabrication and integration challenges for researchers to achieve both wide strain range and high sensitivity in graphene-based strain sensors. Last of all, several applications of graphene-based strain sensors for different purposes are described. All in all, the evolutionary process of graphene-based strain sensors in recent years, as well as the upcoming challenges and future directions for emerging studies are highlighted.

Strain effect on electronic structure and transport properties of zigzagα-T3nanoribbons: a mean-field theoretical study

Theα-T₃lattice, a minimal model that presents flat bands, has sparked much interest in research but the finite-size effect and interaction has been rarely involved. Here we theoretically study the electronic structure and transport properties of zigzag-edgeα-T₃nanoribbons (ZαT₃NRs) with and without uniaxial strain, where the exemplary widthsN= 40 and 41 for two series are considered. By adopting the mean-field Hubbard model combined with the nonequilibrium Green's function method, we show that the spin-degenerate dispersionless flat band at the Fermi energy for the pristine ribbons is split into spin-up and -down flat bands under electron-electron Coulomb interaction. Specifically, the two bands are shifted toward in an opposite direction and away from the Fermi energy, which leads to an energy gap opening in the case ofα≠ 1. All three series of ZαT₃NRs with widthN= 3n, 3n+ 1, 3n+ 2 (wherenis a positive integer) exhibit an energy gap. This differs from the simple tight-binding calculations without considering electron-electron Coulomb interaction, for which the gap is always zero in the case ofN= 3n+ 1. Here, the origin of the energy gap forN= 3n+ 1 arises from Coulomb repulsion between electrons. Importantly, the energy gap can be effectively manipulated by an uniaxial strain and Coulomb interaction ifα≠ 1. The gap linearly increases (decreases) when a tensile (compressive) strain increases, and it also monotonously increases as enhancing Coulomb interaction. Interestingly, a ground state of antiferromagnetic to ferromagnetic transition occurs whenαincreases from 0.8 to 1, leading to a semiconductor to metallic transition. Besides, theα-, strain- and interaction-dependent conductance is also explored. The findings here may be of importance in the band gap engineering and electromechanical applications ofα-T₃nanoribbon-based devices.

Materials Science Challenges to Graphene Nanoribbon Electronics

Graphene nanoribbons (GNRs) have recently emerged as promising candidates for channel materials in future nanoelectronic devices due to their exceptional electronic, thermal, and mechanical properties and chemical inertness. However, the adoption of GNRs in commercial technologies is currently hampered by materials science and integration challenges pertaining to synthesis and devices. In this Review, we present an overview of the current status of challenges, recent breakthroughs toward overcoming these challenges, and possible future directions for the field of GNR electronics. We motivate the need for exploration of scalable synthetic techniques that yield atomically precise, placed, registered, and oriented GNRs on CMOS-compatible substrates and stimulate ideas for contact and dielectric engineering to realize experimental performance close to theoretically predicted metrics. We also briefly discuss unconventional device architectures that could be experimentally investigated to harness the maximum potential of GNRs in future spintronic and quantum information technologies.

Gap opening in graphene nanoribbons by application of simple shear strain and in-plane electric field

The effects of shear strain and applied in plane electric field on the electronic properties of monolayer graphene nanoribbons (GNRs) are theoretically investigated. Band structures and the probability densities are calculated within the tight-binding model and the mechanical stresses submitted to the GNRs are taken into account by using the theory of linear elasticity with joint modifications in the elongation of the nearest-neighbor vectors and the modification of the hopping parameters. The energy gaps for specific widths of (semiconducting) armchair nanoribbons are verified also in the presence of either strain or field, whereas zigzag nanoribbons are metallic for any value of strain and exhibit a small gap for any value of field. However, our results demonstrate that when both strain and electric field are combined, a significant energy gap is always observed in the band structure, for any width or edge type of the ribbon. Moreover, the obtained total wave function is asymmetric along the ribbon width due to the applied electric field that pushes the electrons to one side of the ribbon and, under shear strain, a peak at the center of the ribbon in the spatial distribution is also observed owing to the preferable localization around the almost undeformed carbon bonds at ribbon center.

Strain modulated carrier mobility and optical properties of graphene nanowiggles

Recently, synthesized Chevron graphene nanoribbons (CGNRs) and its laterally extended counterpart known as extended CGNRs (ECGNR) are constructed by making alternated regular cuts in pristine graphene nanoribbons (GNRs). First-principles calculations demonstrate that these GNRs are super-ductile and possess width-dependent mechanical properties. The Young's modulus is calculated to be 389.4 GPa and 414.6 GPa for CGNR and ECGNR, respectively. The bandgap of these nanoribbons decreases on the application of tensile strain. The carrier effective masses are found to be highly sensitive towards mechanical strains. The holes (electrons) mobility of ECGNR is calculated to be 7.68 × 10⁴ cm² V^-1 s^-1 (1.69 × 10⁴ cm² V^-1 s^-1), which is higher than that of CGNR can be further enhanced by elongation. The prominent peaks of the imaginary part of dielectric function and electron energy loss spectra show redshift on increasing the tensile strain. The electron energy loss spectra show intense plasmonic structure in low energy spectrum indicating GNRs to be more sensitive to the visible region than ultra violet spectrum. Our results provide insight about the possible applications of GNRs in the fields of high-speed transistors, sensors, photonics, and optoelectronics.

Conductance of Buckled N = 5 Armchair Graphene Nanoribbons

Electromechanical coupling in graphene nanoribbons has been the focus of much basic research. Although ab initio methods have been used to compute the current-voltage characteristics of deformed nanoribbons, analytical models that embody fundamental quantum electron transmission concepts are needed to support the conceptual design of new nanoelectromechanical devices. Numerical analysis of the conduction properties of buckled armchair graphene nanoribbons indicates that, consistent with experiment, the bending effects on current flow in rippled nanoribbons are determined by an integral measure of the total rotation along the conductor, which accounts for scattering effects accumulated along the entire transport path. The modeling results provide the first general description of both length and bending effects on current flow in semiconducting nanowires.

Distortion-Controlled Redshift of Organic Dye Molecules

It is shown, quantum chemically, how structural distortion of an aromatic dye molecule can be leveraged to rationally tune its optoelectronic properties. By using a quantitative Kohn-Sham molecular orbital (KS-MO) approach, in combination with time-dependent DFT (TD-DFT), the influence of various structural and electronic tuning parameters on the HOMO-LUMO gap of a benzenoid model dye have been investigated. These parameters include 1) out-of-plane bending of the aromatic core, 2) bending of the bridge with respect to the core, 3) the nature of the bridge itself, and 4) π-π stacking. The study reveals the coupling of multiple structural distortions as a function of bridge length and number of bridges in benzene to be chiefly responsible for a decreased HOMO-LUMO gap, and consequently, red-shifting of the absorption wavelength associated with the lowest singlet excitation (λ≈560 nm) in the model cyclophane systems. These physical insights together with a rational approach for tuning the oscillator strength were leveraged for the proof-of-concept design of an intense near-infrared (NIR) absorbing cyclophane dye at λ=785 nm. This design may contribute to a new class of distortion-controlled NIR absorbing organic dye molecules.

Emerging chemical strategies for imprinting magnetism in graphene and related 2D materials for spintronic and biomedical applications

Graphene, a single two-dimensional sheet of carbon atoms with an arrangement mimicking the honeycomb hexagonal architecture, has captured immense interest of the scientific community since its isolation in 2004. Besides its extraordinarily high electrical conductivity and surface area, graphene shows a long spin lifetime and limited hyperfine interactions, which favors its potential exploitation in spintronic and biomedical applications, provided it can be made magnetic. However, pristine graphene is diamagnetic in nature due to solely sp2 hybridization. Thus, various attempts have been proposed to imprint magnetic features into graphene. The present review focuses on a systematic classification and physicochemical description of approaches leading to equip graphene with magnetic properties. These include introduction of point and line defects into graphene lattices, spatial confinement and edge engineering, doping of graphene lattice with foreign atoms, and sp3 functionalization. Each magnetism-imprinting strategy is discussed in detail including identification of roles of various internal and external parameters in the induced magnetic regimes, with assessment of their robustness. Moreover, emergence of magnetism in graphene analogues and related 2D materials such as transition metal dichalcogenides, metal halides, metal dinitrides, MXenes, hexagonal boron nitride, and other organic compounds is also reviewed. Since the magnetic features of graphene can be readily masked by the presence of magnetic residues from synthesis itself or sample handling, the issue of magnetic impurities and correct data interpretations is also addressed. Finally, current problems and challenges in magnetism of graphene and related 2D materials and future potential applications are also highlighted.

Interfacial engineering in graphene bandgap

Graphene exhibits superior mechanical strength, high thermal conductivity, strong light-matter interactions, and, in particular, exceptional electronic properties. These merits make graphene an outstanding material for numerous potential applications. However, a graphene-based high-performance transistor, which is the most appealing application, has not yet been produced, which is mainly due to the absence of an intrinsic electronic bandgap in this material. Therefore, bandgap opening in graphene is urgently needed, and great efforts have been made regarding this topic over the past decade. In this review article, we summarise recent theoretical and experimental advances in interfacial engineering to achieve bandgap opening. These developments are divided into two categories: chemical engineering and physical engineering. Chemical engineering is usually destructive to the pristine graphene lattice via chemical functionalization, the introduction of defects, doping, chemical bonds with substrates, and quantum confinement; the latter largely maintains the atomic structure of graphene intact and includes the application of an external field, interactions with substrates, physical adsorption, strain, electron many-body effects and spin-orbit coupling. Although these pioneering works have not met all the requirements for electronic applications of graphene at once, they hold great promise in this direction and may eventually lead to future applications of graphene in semiconductor electronics and beyond.

Bias induced ferromagnetism and half-metallicity in graphene nano-ribbons

Towards spin selective electronics made of three coordinated carbon atoms, here we computationally propose robust and reversibly bias driven evolution of pristine undoped graphene nano-ribbons(GNR) into ferromagnetic-semiconductor, metal or a half metal, irrespective of their edge configurations. The evolution is a result of a rare ferromagnetic(FM) order emerging among nearest neighbouring(n-n) sites, in positively biased regions in their in-homogeneous bias unit-cells, in attempt to cooperatively minimise on-site Coulomb repulsion and kinetic energy, while maximising localization of electrons at the positively biased sites. The phenomenon appears to be a general property of in-homogeneously biased Coulomb correlated bipartite systems. Consequences are particularly rich in zigzag edged graphene nano-ribbons(ZGNR) due to the contest of bias driven n-n FM order and the inter-edge antiferromagnetic order inherent to ZGNRs, leading to systematic closing of gap for one of the spins, amounting to bias controlled unmissable opening of window for FM-semiconducting and half-metallic transport.

Edge-functionalization of armchair graphene nanoribbons with pentagonal-hexagonal edge structures

Using density functional theory calculations, we have studied the edge-functionalization of armchair graphene nanoribbons (AGNRs) with pentagonal-hexagonal edge structures. While the AGNRs with pentagonal-hexagonal edge structures (labeled (5,6)-AGNRs) are metallic, the edge-functionalized (5,6)-AGNRs with substitutional atoms opens a band gap. We find that the band structures of edge-functionalized (5,6)-N-AGNRs by substitution resemble those of defect-free (N-1)-AGNR at the Γ point, whereas those at the X point show the original ones of the defect-free N-AGNR. The overall electronic structures of edge-functionalized (5,6)-AGNRs depend on the number of electrons, supplied by substitutional atoms, at the edges of functionalized (5,6)-AGNRs.

In-Situ Stretching Patterned Graphene Nanoribbons in the Transmission Electron Microscope

The mechanical response of patterned graphene nanoribbons (GNRs) with a width less than 100 nm was studied in-situ using quantitative tensile testing in a transmission electron microscope (TEM). A high degree of crystallinity was confirmed for patterned nanoribbons before and after the in-situ experiment by selected area electron diffraction (SAED) patterns. However, the maximum local true strain of the nanoribbons was determined to be only about 3%. The simultaneously recorded low-loss electron energy loss spectrum (EELS) on the stretched nanoribbons did not reveal any bandgap opening. Density Functional Based Tight Binding (DFTB) simulation was conducted to predict a feasible bandgap opening as a function of width in GNRs at low strain. The bandgap of unstrained armchair graphene nanoribbons (AGNRs) vanished for a width of about 14.75 nm, and this critical width was reduced to 11.21 nm for a strain level of 2.2%. The measured low tensile failure strain may limit the practical capability of tuning the bandgap of patterned graphene nanostructures by strain engineering, and therefore, it should be considered in bandgap design for graphene-based electronic devices by strain engineering.

Coupling effects of the electric field and bending on the electronic and magnetic properties of penta-graphene nanoribbons

The magnetic configuration transitions for P-GNRs vs. critical electric field strength on applying different bending strains.

Modulating the electronic and magnetic properties of graphene

Graphene, an sp²hybridized single sheet of carbon atoms organized in a honeycomb lattice, is a zero band gap semiconductor or semimetal.

Acute mechano-electronic responses in twisted phosphorene nanoribbons

Many different forms of mechanical and structural deformations have been employed to alter the electronic structure of various modern two-dimensional (2D) nanomaterials. Given the recent interest in the new class of 2D nanomaterials - phosphorene, here we investigate how the rotational strain-dependent electronic properties of low-dimensional phosphorene may be exploited for technological gain. Here, using first-principles density-functional theory, we investigate the mechanical stability of twisted one-dimensional phosphorene nanoribbons (TPNR) by measuring their critical twist angle (θc) and shear modulus as a function of the applied mechanical torque. We find a strong anisotropic, chirality-dependent mechano-electronic response in the hydrogen-passivated TPNRs upon vortical deformation, resulting in a striking difference in the change in the carrier effective mass as a function of torque angle (and thus, the corresponding change in carrier mobility) between the zigzag and armchair directions in these TPNRs. The accompanied tunable band-gap energies for the hydrogen-passivated zigzag TPNRs may then be exploited for various key opto-electronic nanodevices.

Super flexibility and stability of graphene nanoribbons under severe twist

The structure and properties of nanostructured materials formed upon deformation are determined to a great extent by the states of stress and strain and the regimes of deformation. The nanostructures and properties of the graphene nanoribbons (GNRs) subjected to severe twist deformation were studied using molecular dynamics (MD) simulations. The GNRs show superflexibility and withstanding severe twisting, which leads to GNR nanostructures transforming from flat to twisted and then getting thoroughly coiled and fail. The appearance of a decreasing Young's moduli of the GNRs was observed with increasing rotation in general. The chirality has little effect on the Young's moduli of flat GNRs, whereas the degree of the GNR aspect ratio does. The severely twisted GNRs follow a similar rule but with slightly decreased Young's moduli (∼0.1 TPa), which demonstrates that the twisted GNRs maintain their stiff nature. The electronic properties of the GNRs under severely twisted conditions also show slight changes studied by density-functional theory (DFT) simulations. The stable mechanical properties and structure changes of GNRs under severely twisted conditions makes them a good candidate in some polymers, enhancing the load transfer and interfacial bonding by adding the twisted GNRs.

Tunable electronic and magnetic properties of two-dimensional materials and their one-dimensional derivatives

Low‐dimensional materials exhibit many exceptional properties and functionalities which can be efficiently tuned by externally applied force or fields. Here we review the current status of research on tuning the electronic and magnetic properties of low‐dimensional carbon, boron nitride, metal‐dichalcogenides, phosphorene nanomaterials by applied engineering strain, external electric field and interaction with substrates, etc, with particular focus on the progress of computational methods and studies. We highlight the similarities and differences of the property modulation among one‐ and two‐dimensional nanomaterials. Recent breakthroughs in experimental demonstration of the tunable functionalities in typical nanostructures are also presented. Finally, prospective and challenges for applying the tunable properties into functional devices are discussed. WIREs Comput Mol Sci 2016, 6:324–350. doi: 10.1002/wcms.1251

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Conflict of interest: The authors have declared no conflicts of interest for this article.

Structural band-gap tuning in g-C3N4

Experimental and theoretical results uncover an almost perfectly linear relationship between the band gap and structural aspects of g-C₃N₄, allowing the tuning of the frequency at which g-C₃N₄ absorbs light.

Analytical performance of 3 m and 3 m +1 armchair graphene nanoribbons under uniaxial strain

The electronic band structure and carrier density of strained armchair graphene nanoribbons (AGNRs) with widths of n =3 m and n =3 m +1 were examined using tight-binding approximation. The current-voltage (I-V) model of uniaxial strained n =3 m AGNRs incorporating quantum confinement effects is also presented in this paper. The derivation originates from energy dispersion throughout the entire Brillouin zone of uniaxial strained AGNRs based on a tight-binding approximation. Our results reveal the modification of the energy bandgap, carrier density, and drain current upon strain. Unlike the two-dimensional graphene, whose bandgap remains near to zero even when a large strain is applied, the bandgap and carrier density of AGNRs are shown to be sensitive to the magnitude of uniaxial strain. Discrepancies between the classical calculation and quantum calculation were also measured. It has been found that as much as 19% of the drive current loss is due to the quantum confinement. These analytical models which agree well with the experimental and numerical results provide physical insights into the characterizations of uniaxial strained AGNRs.

Tuning electronic and magnetic properties of partially hydrogenated graphene by biaxial tensile strain: a computational study

Using density functional theory calculations, we have investigated the effects of biaxial tensile strain on the electronic and magnetic properties of partially hydrogenated graphene (PHG) structures. Our study demonstrates that PHG configuration with hexagon vacancies is more energetically favorable than several other types of PHG configurations. In addition, an appropriate biaxial tensile strain can effectively tune the band gap and magnetism of the hydrogenated graphene. The band gap and magnetism of such configurations can be continuously increased when the magnitude of the biaxial tensile strain is increased. This fact that both the band gap and magnetism of partially hydrogenated graphene can be tuned by applying biaxial tensile strain provides a new pathway for the applications of graphene to electronics and photonics.

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(e(2)/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.

Analytical modeling of uniaxial strain effects on the performance of double-gate graphene nanoribbon field-effect transistors

: The effects of uniaxial tensile strain on the ultimate performance of a dual-gated graphene nanoribbon field-effect transistor (GNR-FET) are studied using a fully analytical model based on effective mass approximation and semiclassical ballistic transport. The model incorporates the effects of edge bond relaxation and third nearest neighbor (3NN) interaction. To calculate the performance metrics of GNR-FETs, analytical expressions are used for the charge density, quantum capacitance, and drain current as functions of both gate and drain voltages. It is found that the current under a fixed bias can change several times with applied uniaxial strain and these changes are strongly related to strain-induced changes in both band gap and effective mass of the GNR. Intrinsic switching delay time, cutoff frequency, and Ion/Ioff ratio are also calculated for various uniaxial strain values. The results indicate that the variation in both cutoff frequency and Ion/Ioff ratio versus applied tensile strain inversely corresponds to that of the band gap and effective mass. Although a significant high frequency and switching performance can be achieved by uniaxial strain engineering, tradeoff issues should be carefully considered.

Spin-semiconducting properties in silicene nanoribbons

Our investigations show that silicene nanoribbons with one sawtooth edge are spin-semiconductors (left). They become spin gapless semiconductors under a suitable electric field (middle) or compressive strain (right).

The effect of uniaxial strain on graphene nanoribbon carrier statistic

: Armchair graphene nanoribbon (AGNR) for n=3m and n=3m+1 family carrier statistic under uniaxial strain is studied by means of an analytical model based on tight binding approximation. The uniaxial strain of AGNR carrier statistic models includes the density of state, carrier concentration, and carrier velocity. From the simulation, it is found that AGNR carrier concentration has not been influenced by the uniaxial strain at low normalized Fermi energy for n=3m and n=3m+1. In addition, the carrier velocity of AGNR is mostly affected by strain at high concentration of n≈3.0×107 and 1.0 × 107 m-1 for n=3m and n=3m+1, respectively. The result obtained gives physical insight into the understanding of uniaxial strain in AGNR.

A review of carbon nanotube- and graphene-based flexible thin-film transistors

Carbon nanotubes (CNTs) and graphene have attracted great attention for numerous applications for future flexible electronics, owing to their supreme properties including exceptionally high electronic conductivity and mechanical strength. Here, the progress of CNT- and graphene-based flexible thin-film transistors from material preparation, device fabrication techniques to transistor performance control is reviewed. State-of-the-art fabrication techniques of thin-film transistors are divided into three categories: solid-phase, liquid-phase, and gas-phase techniques, and possible scale-up approaches to achieve realistic production of flexible nanocarbon-based transistors are discussed. In particular, the recent progress in flexible all-carbon nanomaterial transistor research is highlighted, and this all-carbon strategy opens up a perspective to realize extremely flexible, stretchable, and transparent electronics with a relatively low-cost and fast fabrication technique, compared to traditional rigid silicon, metal and metal oxide electronics.

Strain dependence of the heat transport properties of graphene nanoribbons

Using a combination of accurate density-functional theory and a nonequilibrium Green's function method, we calculate the ballistic thermal conductance characteristics of tensile-strained armchair (AGNR) and zigzag (ZGNR) edge graphene nanoribbons, with widths between 3 and 50 Å. The optimized lateral lattice constants for AGNRs of different widths display a three-family behavior when the ribbons are grouped according to N modulo 3, where N represents the number of carbon atoms across the width of the ribbon. Two lowest-frequency out-of-plane acoustic modes play a decisive role in increasing the thermal conductance of AGNR-N at low temperatures. At high temperatures the effect of tensile strain is to reduce the thermal conductance of AGNR-N and ZGNR-N. These results could be explained by the changes in force constants in the in-plane and out-of-plane directions with the application of strain. This fundamental atomistic understanding of the heat transport in graphene nanoribbons paves a way to effect changes in their thermal properties via strain at various temperatures.

Tuning Magnetism and Electronic Phase Transitions by Strain and Electric Field in Zigzag MoS2 Nanoribbons

Effective modulation of physical properties via external control may open various potential nanoelectronic applications of single-layer MoS2 nanoribbons (MoS2NRs). We show by first-principles calculations that the magnetic and electronic properties of zigzag MoS2NRs exhibit sensitive response to applied strain and electric field. Tensile strain in the zigzag direction produces reversible modulation of magnetic moments and electronic phase transitions among metallic, half-metallic, and semiconducting states, which stem from the energy-level shifts induced by an internal electric polarization and the competing covalent/ionic interactions. A simultaneously applied electric field further enhances or suppresses the strain-induced modulations depending on the direction of the electric field relative to the internal polarization. These findings suggest a robust and efficient approach to modulating the properties of MoS2NRs by a combination of strain engineering and electric field tuning.

Strain-engineering of band gaps in piezoelectric boron nitride nanoribbons

Two-dimensional atomic sheets such as graphene and boron nitride monolayers represent a new class of nanostructured materials for a variety of applications. However, the intrinsic electronic structure of graphene and h-BN atomic sheets limits their direct application in electronic devices. By first-principles density functional theory calculations we demonstrate that band gap of zigzag BN nanoribbons can be significantly tuned under uniaxial tensile strain. The unexpected sensitivity of band gap results from reduced orbital hybridization upon elastic strain. Furthermore, sizable dipole moment and piezoelectric effect are found in these ribbons owing to structural asymmetry and hydrogen passivation. This will offer new opportunities to optimize two-dimensional nanoribbons for applications such as electronic, piezoelectric, photovoltaic, and opto-electronic devices.

Engineering the work function of armchair graphene nanoribbons using strain and functional species: a first principles study

First principles density functional theory calculations were performed to study the effects of strain, edge passivation, and surface functional species on the structural and electronic properties of armchair graphene nanoribbons (AGNRs), with a particular focus on the work function. The work function was found to increase with uniaxial tensile strain and decrease with compression. The variation of the work function under strain is primarily due to the shift of the Fermi energy with strain. In addition, the relationship between the work function variation and the core level shift with strain is discussed. Distinct trends of the core level shift under tensile and compressive strain were discovered. For AGNRs with the edge carbon atoms passivated by oxygen, the work function is higher than for nanoribbons with the edge passivated by hydrogen under a moderate strain. The difference between the work functions in these two edge passivations is enlarged (reduced) under a sufficient tensile (compressive) strain. This has been correlated to a direct-indirect bandgap transition for tensile strains of about 4% and to a structural transformation for large compressive strains at about - 12%. Furthermore, the effect of the surface species decoration, such as H, F, or OH with different covering density, was investigated. It was found that the work function varies with the type and coverage of surface functional species. Decoration with F and OH increases the work function while H decreases it. The surface functional species were decorated on either one side or both sides of AGNRs. The difference in the work functions between one-sided and two-sided decorations was found to be relatively small, which may suggest an introduced surface dipole plays a minor role.

Edges bring new dimension to graphene nanoribbons

Chemistry at the edges of saturated graphene nanoribbons can cause ribbons to leave the plane and form three-dimensional helical structures. Calculations, based on density functional theory and enabled by adopting helical symmetry, show that F-terminated armchair ribbons are intrinsically twisted in helices, unlike flat H-terminated strips. Twisting ribbons of either termination couple the conduction and valence bands, resulting in band gap modulation. This electromechanical response could be exploited in switches and sensor applications.