Energy gaps and stark effect in boron nitride nanoribbons

A first-principles investigation of the electronic properties of boron nitride nanoribbons (BNNRs) having either armchair or zigzag shaped edges passivated by hydrogen with widths up to 10 nm is presented. Band gaps of armchair BNNRs exhibit family dependent oscillations as the width increases and, for ribbons wider than 3 nm, converge to a constant value that is 0.02 eV smaller than the bulk band gap of a boron nitride sheet owing to the existence of very weak edge states. The band gap of zigzag BNNRs monotonically decreases and converges to a gap that is 0.7 eV smaller than the bulk gap due to the presence of strong edge states. When a transverse electric field is applied, the band gaps of armchair BNNRs decrease monotonically with the field strength. For the zigzag BNNRs, however, the band gaps and the carrier effective masses either increase or decrease depending on the direction and the strength of the field.     

First-principles study of heat transport properties of graphene nanoribbons

We use density-functional theory and the nonequilibrium Green's function method as well as phonon dispersion calculations to study the thermal conductance of graphene nanoribbons with armchair and zigzag edges, with and without hydrogen passivation. We find that low-frequency phonon bands of the zigzag ribbons are more dispersive than those of the armchair ribbons and that this difference accounts for the anisotropy in the thermal conductance of graphene nanoribbons. Comparing our results with data on large-area graphene, edge effects are shown to contribute to thermal conductance, enhance the anisotropy in thermal conductance of graphene nanoribbons, and increase thermal conductance per unit width. The edges with and without hydrogen passivation modify the atomic structure and ultimately influence the phonon thermal transport differently for the two ribbon types.     

Computational investigation on structural and physical properties of AIN nanosheets and nanoribbons

Through first-principles computations, we investigated the structural, electronic and magnetic properties of two-dimensional AIN single layer and one-dimensional AIN nanoribbons. AIN single layer and nanoribbons quit the Wurtzite configuration and adopt a graphitic-like structure after geometry optimization. Both hydrogen-terminated zigzag and armchair AIN nanoribbons have a direct band gap, which increases monotonically with increasing ribbon width. Bare zigzag AIN nanoribbons have a spin-polarized ground state and are magnetic semiconductors. The results may promote the experimental preparation of AIN nanosheets and nanoribbons and their applications to nanotechnology.     

Electronic states of graphene nanoribbons and analytical solutions

Abstract

Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of π-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber. The quantization rule of electronic conductance as well as the magnetic instability of edge states due to the electron–electron interaction are briefly discussed.     

First-Principles Study on the Electronic and Magnetic Properties of Zigzag AlN-SiC Nanoribbons

The electronic and magnetic properties of zigzag AlN-SiC nanoribbons are investigated by using the first-principles calculations. The band structures reveal that all the investigated AlN-SiC systems are the magnetic semiconductors, the band gaps of which decrease with the increasing width of the ribbon. The majority spin density is mostly contributed by the edge C atoms with dangling bonds. The total magnetic moments increase with the increasing width of the ribbon and decrease with the increase of the strain. These studies are helpful to the potential applications of the AlN-SiC ribbon in spintronics.     

Electronic structure and stability of semiconducting graphene nanoribbons

We present a systematic density functional theory study of the electronic properties, optical spectra, and relative thermodynamic stability of semiconducting graphene nanoribbons. We consider ribbons with different edge nature including bare and hydrogen-terminated ribbons, several crystallographic orientations, and widths up to 3 nm. Our results can be extrapolated to wider ribbons providing a qualitative way of determining the electronic properties of ribbons with widths of practical significance. We predict that in order to produce materials with band gaps similar to Ge or InN, the width of the ribbons must be between 2 and 3 nm. If larger bang gap ribbons are needed (like Si, InP, or GaAs), their width must be reduced to 1-2 nm. According to the extrapolated inverse power law obtained in this work, armchair carbon nanoribbons of widths larger than 8 nm will present a maximum band gap of 0.3 eV, while for ribbons with a width of 80 nm the maximum possible band gap is 0.05 eV. For chiral nanoribbons the band gap oscillations rapidly vanish as a function of the chiral angle indicating that a careful design of their crystallographic nature is an essential ingredient for controlling their electronic properties. Optical excitations show important differences between ribbons with and without hydrogen termination and are found to be sensitive to the carbon nanoribbon width. This should provide a practical way of revealing information on their size and the nature of their edges.     

First-principles study on electronic properties of SiC nanoribbon

Under the generalized gradient approximation (GGA), the electronic properties are studied for SiC nanoribbon with zigzag edge (ZSiCNR) and armchair edge (ASiCNR) by using the first-principles projector-augmented wave (PAW) potential within the density function theory (DFT) framework. Distinct variation behaviors in band gap are exhibited with increasing ribbon width. The ZSiCNR is metallic except for the thinner ribbons (N _z = 2–4) with small direct band gaps, while the direct band gaps of ASiCNR exhibit sawtooth-like periodic oscillation features and quench to a constant value of 2.359 eV as width N _a increases. The PDOS onto individual atom shows that a sharp peak appeared at the Fermi level for broader ZSiCNR comes from the edge C and Si atoms with H terminations. The charge density contours analysis shows the valence charges are strongly accumulated around C atom, reflecting a significant electron transfer from Si atom to C atom and thus an ionic binding feature. In addition, the Si–H bond is also ionic bond while the C–H bond is covalent bond. The dangling bonds give rise to one (two) flat extra band at the Fermi level for ZSiCNR with either bare C or bare Si edge (for ZSiCNR with bare C and Si edges as well as for ASiCNR with either bare C edge or bare Si edge), except for ASiCNR with bare C and Si edges in which two nearly flat extra bands appear up and below the Fermi level.     

Gate electrostatics and quantum capacitance of graphene nanoribbons

Capacitance-voltage (C-V) characteristics are important for understanding fundamental electronic structures and device applications of nanomaterials. The C-V characteristics of graphene nanoribbons (GNRs) are examined using self-consistent atomistic simulations. The results indicate strong dependence of the GNR C-V characteristics on the edge shape. For zigzag edge GNRs, highly nonuniform charge distribution in the transverse direction due to edge states lowers the gate capacitance considerably, and the self-consistent electrostatic potential significantly alters the band structure and carrier velocity. For an armchair edge GNR, the quantum capacitance is a factor of 2 smaller than its corresponding zigzag carbon nanotube, and a multiple gate geometry is less beneficial for transistor applications. Magnetic field results in pronounced oscillations on C-V characteristics.     

Edge stability of boron nitride nanoribbons and its application in designing hybrid BNC structures

First-principles investigations of the edge energies and edge stresses of single-layer hexagonal boron nitride (BN) are presented. The armchair edges of BN nanoribbons (BNNRs) are more stable in energy than zigzag ones. Armchair BNNRs are under compressive edge stress while zigzag BNNRs are under tensile edge stress, due to the edge reconstruction effect and edge coulomb repulsion effect. The intrinsic spin-polarization and edge saturation play important roles in modulating the edge stability of BNNRs. The edge energy difference between BN and graphene can be used to guide the design of specific hybrid BNC structures as the hybrid BNC systems prefer the low-energy edge configurations: In an armchair BNC nanoribbon (BNCNR), BN domains are expected to grow outside of C domains, while the opposite occurs in a zigzag BNCNR. More importantly, armchair BNCNRs can reproduce unique electronic properties of armchair graphene nanoribbons (GNRs), which are expected to be robust against edge functionalization or disorder. Within a certain range of C/BN ratios, zigzag BNCNRs may exhibit intrinsic half-metallicity without any external constraints. These diverse electronic properties of BNCNRs may offer unique opportunities to develop nanoscale electronics and spintronics beyond individual graphene and BN. More generally, these principles for designing BNC can also be extended to other hybrid nanostructures.      

电场作用下扶手椅型石墨烯纳米带的第一原理计算

本文采用密度泛函理论,研究了边缘氧化扶手椅型石墨烯纳米带(AGNRs)的电子结构和相对稳定性.结果表明,边缘氧化的AGNRs要比边缘氢化的纳米带稳定.由于氧原子比碳原子具有较大的电负性,边缘氧化AG-NRs表现出金属性能带结构.此外,氧饱和AGNRs比氢饱和AGNRs对电场作用更为敏感,这将有助于在带隙工程中实现其电子结构剪裁.     

Effect of the edge type and strain on the structural, electronic and magnetic properties of the BNRs

We present the effect of edge structures on the edge energy and stress of BN nanoribbons. Ab initio density functional calculations show that the armchair edge is lower in energy than the zigzag edge by 0.43 eV/angstrom. Both types of the edges are under the compressive stress. The zigzag edges are mechanically more stable than the armchair edges. Based on the calculated edge energies, the equilibrium shape of the BN flakes are found to be regular hexagonal, and dominated by the armchair edges. The zigzag ribbons are found to be half-metallic, whereas the armchair ribbons are semiconducting.     

Graphene nanoribbons in criss-crossed electric and magnetic fields

Graphene nanoribbons (GNRs) in mutually perpendicular electric and magnetic fields are shown to exhibit dramatic changes in their band structure and electron-transport properties. A strong electric field across the ribbon induces multiple chiral Dirac points, closing the semiconducting gap in armchair GNRs. A perpendicular magnetic field induces partially formed Landau levels as well as dispersive surface-bound states. Each of the applied fields on its own preserves the even symmetry E(k)=E(-k) of the sub-band dispersion. When applied together, they reverse the dispersion parity to be odd, which gives E(e,k)=-E(h,-k), and mix the electron and hole sub-bands within the energy range corresponding to the change in potential across the ribbon. This leads to oscillations of the ballistic conductance within this energy range. The broken time-reversal symmetry provides dichroism in the absorption of the circularly polarized light. As a consequence, one can observe electrically enhanced Faraday rotation, since the edges of the ribbon provide formation of the substantial density of states.     

Magnetic boron nitride nanoribbons with tunable electronic properties

We present theoretical evidence, based on total-energy first-principles calculations, of the existence of spin-polarized states well localized at and extended along the edges of bare zigzag boron nitride nanoribbons. Our calculations predict that all the magnetic configurations studied in this work are thermally accessible at room temperature and present an energy gap. In particular, we show that the high spin state, with a magnetic moment of 1 muB at each edge atom, presents a rich spectrum of electronic behaviors as it can be controlled by applying an external electric field in order to obtain metallic <--> semiconducting <--> half-metallic transitions.     

Optical control of edge chirality in graphene

We performed optical annealing experiments at the edges of nanopatterned graphene to study the resultant edge reconstruction. The lithographic patterning direction was orthogonal to a zigzag edge. μ-Raman spectroscopy shows an increase in the polarization contrast of the G band as a function of annealing time. Furthermore, transport measurements reveal a 50% increase of the GNR energy gap after optical exposure, consistent with an increased percentage of armchair segments. These results suggest that edge chirality of graphene devices can be optically purified post electron beam lithography, thereby enabling the realization of chiral graphene nanoribbons and heterostructures.     

The half-metallicity of zigzag graphene nanoribbons with asymmetric edge terminations

The spin-polarized electronic structure and half-metallicity of zigzag graphene nanoribbons (ZGNRs) with asymmetric edge terminations are investigated by using first-principles calculations. It is found that compared with symmetric hydrogen-terminated counterparts, such ZGNRs maintain a spin-polarized ground state with the anti-ferromagnetic configuration at opposite edges, but their energy bands are no longer spin degenerate. In particular, the energy gap of one spin orientation decreases remarkably. Consequently, the ground state of such ZGNRs is very close to half-metallic state, and thus a smaller critical electric field is required for the systems to achieve the half-metallic state. Moreover, two kinds of studied ZGNRs present massless Dirac-fermion band structure when they behave like half-metals.     

Strain effects in graphene and graphene nanoribbons: The underlying mechanism

A tight-binding analytic framework is combined with first-principles calculations to reveal the mechanism underlying the strain effects on electronic structures of graphene and graphene nanoribbons (GNRs). It provides a unified and precise formulation of the strain effects under various circumstances-including the shift of the Fermi (Dirac) points, the change in band gap of armchair GNRs with uniaxial strain in a zigzag pattern and its insensitivity to shear strain, and the variation of the k-range of edge states in zigzag GNRs under uniaxial and shear strains which determine the gap behavior via the spin polarization interaction.      

Band gap of strained graphene nanoribbons

The band structures of strained graphene nanoribbons (GNRs) are examined using a tight-binding Hamiltonian that is directly related to the type and magnitude of strain. Compared to a two-dimensional graphene whose band gap remains close to zero even if a large strain is applied, the band gap of a graphene nanoribbon (GNR) is sensitive to both uniaxial and shear strains. The effect of strain on the electronic structure of a GNR depends strongly on its edge shape and structural indices. For an armchair GNR, a weak uniaxial strain changes the band gap in a linear fashion, whereas a large strain results in periodic oscillation of the band gap. On the other hand, shear strain always tends to reduce the band gap. For a zigzag GNR, the effect of strain is to change the spin polarization at the edges of GNR, and thereby modulate the band gap. A simple analytical model, which agrees with the numerical results, is proposed to interpret the response of the band gap to strain in armchair GNRs.      

Sawtooth-like graphene nanoribbon

Motivated by recent successful synthesize of segmented graphene nanoribbons (GNRs) with junctions, we explore electronic properties of a novel form of GNR with sawtooth-like structure using the density-functional theory method. It is found that the unique edge structures of the sawtooth-like GNR induce richer band-gap features than the straight GNR counterpart with either armchair or zigzag edges. The effect of external electric field on the electronic properties of the sawtooth-like GNR is also studied. The theoretical results may be useful for designing GNR-based fi eld-effect transistors.     

Crystallographically selective nanopatterning of graphene on SiO<Subscript>2</Subscript>

Graphene has many advantageous properties, but its lack of an electronic band gap makes this two-dimensional material impractical for many nanoelectronic applications, for example, field-effect transistors. This problem can be circumvented by opening up a confinement-induced gap, through the patterning of graphene into ribbons having widths of a few nanometres. The electronic properties of such ribbons depend on both their size and the crystallographic orientation of the ribbon edges. Therefore, etching processes that are able to differentiate between the zigzag and armchair type edge terminations of graphene are highly sought after. In this contribution we show that such an anisotropic, dry etching reaction is possible and we use it to obtain graphene ribbons with zigzag edges. We demonstrate that the starting positions for the carbon removal reaction can be tailored at will with precision.     

Simulation of ripples in single layer graphene sheets and study of their vibrational and elastic properties

We present the results of our theoretical investigation on ripples and elastic properties of single layer graphene sheets in both membrane and ribbon conformations. The formation of ripples in both the systems is simulated and analyzed using two-dimensional vibrating membrane model. We have chosen both square graphene membrane, armchair and zigzag graphene nanoribbons with different sizes. The amplitude of vibrational modes of each system is determined using this model. We observed that the vertical displacement (amplitude of the ripples) reaches a maximum height of about 0.99 nm from the mean plane in both conformations whose lengths are integral multiple of the basic armchair/zigzag units. We have studied the dynamical elastic properties through the calculation of parameters like normalized stiffness, speed parameter, Cauchy number and critical velocity with reference to a new aspect ratio of graphene sheets. We have made correlations between the calculated parameters with the formation of ripples and found that the out-of-plane deformations are spontaneous and significant in square conformation of graphene than the graphene nanoribbons. The vibrational modes obtained for GNRs and membranes are acoustic modes. The results of our study will be very much useful in selecting graphene sheets with suitable conformation and chirality for designing nanoscale devices.