Density functional theory studies of interactions of graphene with its environment: Substrate,gate dielectric and edge effects

This paper reviews the theoretical work undertaken using density functional theory (DFT) to explore graphene's interactions with its surroundings. We look at the impact of substrates, gate dielectrics and edge effects on the properties of graphene. In particular, we focus on graphene-on-quartz and graphene-on-alumina systems, exploring their energy spectrum and charge distribution. Silicon-terminated quartz is found to not perturb the linear graphene spectrum. On the other hand, oxygen-terminated quartz and both terminations of alumina bond with graphene, leading to the opening of a band gap. Significant charge transfer is seen between the graphene layer and the oxide in the latter cases. Additionally, we review the work of others regarding the effect of various substrates on the electronic properties of graphene. Confining graphene to form nanoribbons also results in the opening of a band gap. The value of the gap is dependent on the edge properties as well as width of the nanoribbon.     

Tuning of electronic properties and dynamical stability of graphene oxide with different functional groups

The structural, electronic and vibrational properties of graphene oxide (GO) with varying proportion of epoxy and hydroxyl functional groups have been studied using density functional theory. The functional groups and oxygen density have an obvious influence on the electronic and vibrational properties. The dependence of band gap on associated functional groups and oxygen density shows a possibility of tuning the band gap of graphene by varying the functional groups as well as oxidation level. The absorption of high oxygen content in graphene leads to the gap opening and resulting in a transition from semimetal to semiconductor. Phonon dispersion curves show no imaginary frequency or no softening of any phonon mode throughout the Brillouin zone which confirms the dynamical stability of all considered GO models. Different groups and different oxygen density result into the varying characteristics of phonon modes. The computed results show good agreement with the experimental observations. Our results present interesting possibilities for engineering the electronic properties of graphene and GO and impact the fabrication of new electronics.     

Integrating functional oxides with graphene

Graphene–oxide hybrid structures offer the opportunity to combine the versatile functionalities of oxides with the excellent electronic transport in graphene. Understanding and controlling how the dielectric environment affects the intrinsic properties of graphene is also critical to fundamental studies and technological development of graphene. Here we review our recent effort on understanding the transport properties of graphene interfaced with ferroelectric Pb(Zr,Ti)O₃ (PZT) and high-κ HfO₂. Graphene field effect devices prepared on high-quality single crystal PZT substrates exhibit up to tenfold increases in mobility compared to SiO₂-gated devices. An unusual and robust resistance hysteresis is observed in these samples, which is attributed to the complex surface chemistry of the ferroelectric. Surface polar optical phonons of oxides in graphene transistors play an important role in the device performance. We review their effects on mobility and the high source-drain bias saturation current of graphene, which are crucial for developing graphene-based room temperature high-speed amplifiers. Oxides also introduce scattering sources that limit the low temperature electron mobility in graphene. We present a comprehensive study of the transport and quantum scattering times to differentiate various scattering scenarios and quantitatively evaluate the density and distribution of charged impurities and the effect of dielectric screening. Our results can facilitate the design of multifunctional nano-devices utilizing graphene–oxide hybrid structures.     

Electronic structures for armchair-edge graphene nanoribbons under a small uniaxial strain

We theoretically investigate the electronic structures for armchair-edge graphene nanoribbons (AGNRs) under a small in-plane uniaxial strain along armchair (longitudinal) and zigzag (transversal) direction, respectively. We demonstrate that, by both the tight-binding calculation and first-principles study, the applying of a small asymmetrical strain results in variation of energy subband spacing, which opens a band gap for metallic AGNRs and modifies the band gaps for semiconducting AGNRs near the Fermi level. It is believed that these results are of importance in the band gap engineering and electromechanical applications of graphene-nanoribbon-based devices.     

First principles calculations of armchair graphene nanoribbons interacting with Cu atoms

We have investigated the electronic properties of bare, H-terminated, Cu-terminated and Cu-doped armchair graphene nanoribbons (AGNRs) using ab-initio approach. We found that H-termination enhances the stability and band gap whereas H extraction introduces dangling bands and lowers the band gap making bare ribbons indirect band gap semiconductors. The calculations revealed that strong hybridization between Cu atoms and AGNRs, lessen the band gap for Cu-terminated ribbons and gives rise to metallicity in Cu-doped AGNRs irrespective of their widths. Formation energy of considered ribbons yield that H-terminated AGNRs with lowest formation energy are most energetically favored, next are one edge Cu-terminated ribbons followed by bare ones whereas both edges Cu-doped ribbons are least energetically plausible. We predict that presence of Cu atoms in GNRs, significantly alter the band gap and can be used in band gap engineering of nanoribbons.     

Mutual influence of uniaxial tensile strain and point defect pattern on electronic states in graphene

The study deals with electronic properties of uniaxially stressed mono- and multi-layer graphene sheets with various kinds of imperfection: point defects modelled as resonant (neutral) adsorbed atoms or molecules, vacancies, charged impurities, and local distortions. The presence of randomly distributed defects in a strained graphene counteract the band-gap opening and even can suppress the gap occurs when they are absent. However, impurity ordering contributes to the band gap appearance and thereby re-opens the gap being suppressed by random dopants in graphene stretched along zigzag-edge direction. The band gap is found to be non-monotonic with strain in case of mutual action of defect ordering and zigzag deformation. Herewith, the minimal tensile strain required for the band-gap opening (≈12.5%) is smaller than that for defect-free graphene (≈23%), and band gap energy reaches the value predicted for maximal nondestructive strains in the pristine graphene. Effective manipulating the band gap in graphene requires balanced content of ordered dopants: their concentration should be sufficient for a significant sublattice asymmetry effect, but not so much that they may suppress the band gap or transform it into the “quasi- (or pseudo-) gap”.     

石墨烯纳米带的制备与电学特性调控

石墨烯由于其独特的晶体结构展现出了特殊的电学特性,其导带与价带相交于第一布里渊区的六个顶点处,形成带隙为零的半金属材料,具有优异的电子传输特性的同时也限制了其在电子学器件中的使用.因而科研人员尝试各种方法来打开其带隙并调控其能带特性,主要有利用缺陷、应力、掺杂、表面吸附、结构调控等手段.其中石墨烯纳米带由于量子边界效应和限制效应,存在带隙.本综述主要介绍了制备各类石墨烯纳米带的方法,并通过精确调控其细微结构,从而对其进行精确的能带调控,改变其电学特性,为其在电子学器件中的应用提供一些可行的方向.     

石墨烯纳米结构的制备及带隙调控研究

石墨烯在未来微电子学领域有极大的应用前景,但是其零带隙的特点阻碍了石墨烯在半导体领域的应用.研究发现,打开室温下可用的石墨烯带隙所需要的石墨烯纳米结构尺度在10 nm以下,这一尺度的纳米结构一方面制备比较困难,另一方面器件可承载的驱动电流较小.因此,如何实现亚10 nm石墨烯纳米结构的有效加工以及如何在有效调控带隙的基础上增大石墨烯器件可承载的驱动电流,还需要进一步的研究.本文首先研究了利用聚甲基丙烯酸甲酯/铬(PMMA/Cr)双层结构工艺,通过刻蚀时间的控制,利用电子束曝光及刻蚀工艺实现了亚10 nm石墨烯纳米结构的可控制备.同时设计并制备了单排孔石墨烯条带结构,该结构打开的带隙远大于相同特征宽度石墨烯纳米带所能打开带隙的大小.该结构在有效打开石墨烯带隙的同时,增加了石墨烯纳米结构可以承载的驱动电流,有利于石墨烯在未来微电子领域的应用.     

Superlattice based on graphene on a strip substrate

A graphene-based superlattice formed due to the periodic modulation of the band gap has been investigated. Such a modulation is possible in graphene deposited on a strip substrate made of silicon oxide and hexagonal boron nitride. The advantages and some possible problems in the superlattice under consideration are discussed. A model describing such a superlattice is proposed and the dispersion relation between the energy and momentum of carriers has been obtained using the transfer matrix method within this model.     

Simultaneous reduction and sulfonation of graphene oxide for efficient hole selectivity in polymer solar cells

We developed sulfonated, reduced graphene oxide (S-RGO) through fuming/concentrated sulfuric acid treatment of graphene oxide (GO) in ambient conditions. It was demonstrated that the optical band gap and electrical conductivity of S-RGO are easily tunable, and depend on the level of reduction and sulfonation of GO. Whereas, reduction and sulfonation were found dependent on SO₃ content, acid strength, and gas tightness of the reaction mixture. It's actually the water content of oleum that determines the nature of the final product. The easily adjustable band gap and electrical conductivity suggest that S-RGO can be employed as a potential hole extraction layer (HEL) material for several donor-acceptor systems. For P3HT:PC₆₁BM based inverted polymer solar cells, it was observed that the shape of the J–V curve is tailorable with the choice of HEL. Compared to a 2.75% power conversion efficiency (PCE) attained with PEDOT:PSS, a PCE of 2.80% was achieved with tuned S-RGO. Our results imply that an S-RGO of sufficiently high band gap and conductivity can replace some of the state of the art HEL materials for a host of device applications.     

Optimizing long-range order, band gap, and group velocities for graphene on close-packed metal surfaces

We compare different growth methods with the aim of optimizing the long-range order of a graphene layer grown on Ru(0001). Combining chemical vapor deposition with carbon loading and segregation of the surface layer leads to autocorrelation lengths of 240 ?. We present several routes to band gap and charge carrier mobility engineering for the example of graphene on Ir(111). Ir cluster superlattices self-assembled onto the graphene moiré pattern produce a strong renormalization of the electron group velocity close to the Dirac point, leading to highly anisotropic Dirac cones and the enlargement of the gap from 140 to 340 meV. This gap can further be enhanced to 740 meV by Na co-adsorption onto the Ir cluster superlattice at room temperature. This value is close to that of Ge, and the high group velocity of the charge carriers is fully preserved. We also present data for Na adsorbed without the Ir clusters. In both cases we find that the Na is on top of the graphene layer.     

Manipulation of resonant tunneling by substrate-induced inhomogeneous energy band gaps in graphene with square superlattice potentials

We investigate the resonant transmission of Dirac electrons through inhomogeneous band gap graphene with square superlattice potentials by transfer matrix method. The effects of the incident angle of the electrons, Fermi energy and substrate-induced Dirac gaps on the transmission are considered. It is found that the Dirac gap of graphene adds another degree of freedom with respect to the incident angle, the Fermi energy and the parameters of periodic superlattice potentials (i.e., the number, width and height of the barriers) for the transmission. In particular, the inhomogeneous Dirac gap induced by staggered substrates can be used to manipulate the transmission. The properties of the conductance and Fano factor at the resonant peaks are found to be affected by the gaps significantly. The results may be helpful for the practical application of graphene-based electronic devices.     

Inhomogenous electronic structure, transport gap, and percolation threshold in disordered bilayer graphene

The inhomogenous real-space electronic structure of gapless and gapped disordered bilayer graphene is calculated in the presence of quenched charge impurities. For gapped bilayer graphene, we find that for current experimental conditions the amplitude of the fluctuations of the screened disorder potential is of the order of (or often larger than) the intrinsic gap Δ induced by the application of a perpendicular electric field. We calculate the crossover chemical potential Δ(cr), separating the insulating regime from a percolative regime in which less than half of the area of the bilayer graphene sample is insulating. We find that most of the current experiments are in the percolative regime with Δ(cr)?Δ. The huge suppression of Δ(cr) compared with Δ provides a possible explanation for the large difference between the theoretical band gap Δ and the experimentally extracted transport gap.     

Third-order nonlinear optical properties of graphene composites: A review

Graphene has excellent thirdorder nonlinear optical (NLO) properties due to its unique electronic band structure and wideband gap tunability. This paper focuses on the research progress of graphene and its composite materials in nonlinear optics in recent years. In this review, recent results on graphene (or graphene oxide)-metal nanoparticles (G-MNPs), graphene-metal-oxide nanoparticles (G-MONPs), graphene-metal sulfide nanoparticles (G-MSNPs), and graphene-organic molecular composites (G-OM) have been discussed. In addition, the enhancement mechanism of nonlinear absorption (NLA) and optical limiting (OL) have also been covered.     

Magnetoplasmons in gapped graphene in a periodically modulated magnetic field

Motivated by recent experiments on long‐lived magnetoplasmons in the presence of a perpendicular magnetic field, we investigate the dynamical dielectric response function of graphene in contact with a substrate using the random phase approximation. We add a periodically modulated magnetic field within the graphene plane and address both the inter and intra Landau band magnetoplasmons. Verification of the predicted magnetic modulation effects is possible by experiments analogous to those for the zero gap limit.     

Formation of a quasi-free-standing graphene with a band gap at the dirac point by Pb atoms intercalation under graphene on Re(0001)

The control of the graphene electronic structure is one of the most important problems in modern condensed matter physics. The graphene monolayer synthesized on the Re(0001) surface and then subjected to the intercalation of Pb atoms is studied by angle-resolved photoelectron spectroscopy and low-energy electron diffraction. The intercalation of Pb atoms under graphene takes place when the substrate is annealed above 500°C. As a result of the intercalation of Pb atoms, graphene becomes quasi-free-standing and a local band gap appears at the Dirac point. The band gap changes with the substrate temperature during the formation of the graphene/Pb/Re(0001) system. The band gap is 0.3 eV at an annealing temperature of 620°C and it increases up to 0.4 eV upon annealing at 830°C. Based on our data, we conclude that the band gap is mainly caused by the hybridization of the graphene π state with the rhenium 5d states located near the Dirac point of the graphene π state.     

Edge-modified zigzag-shaped graphene nanoribbons: Structure and electronic properties

Control of the band gap of graphene nanoribbons is an important problem for the fabrication of effective radiation detectors and transducers operating in different frequency ranges. The periodic edge-modified zigzag-shaped graphene nanoribbon (GNR) provides two additional parameters for controlling the band gap of these structures, i.e., two GNR arms. The dependence of the band gap E _g on these parameters is investigated using the π-electron tight-binding method. For the considered nanoribbons, oscillations of the band gap E _g as a function of the nanoribbon width are observed not only in the case of armchair-edge graphene nanoribbons (as for conventional graphene nanoribbons) but also for zigzag GNR edges. It is shown that the change in the band gap E _g due to the variation in the length of one GNR arm is several times smaller than that due to the variation in the nanoribbon width, which provides the possibility for a smooth tuning of the band gap in the energy spectrum of the considered graphene nanoribbons.     

Energy band-gap engineering of graphene nanoribbons

We investigate electronic transport in lithographically patterned graphene ribbon structures where the lateral confinement of charge carriers creates an energy gap near the charge neutrality point. Individual graphene layers are contacted with metal electrodes and patterned into ribbons of varying widths and different crystallographic orientations. The temperature dependent conductance measurements show larger energy gaps opening for narrower ribbons. The sizes of these energy gaps are investigated by measuring the conductance in the nonlinear response regime at low temperatures. We find that the energy gap scales inversely with the ribbon width, thus demonstrating the ability to engineer the band gap of graphene nanostructures by lithographic processes.     

Electric field effect in ultrathin zigzag graphene nanoribbons

The electric field effect in ultrathin zigzag graphene nanoribbons containing only three or four zigzag carbon chains is studied by first-principles calculations, and the change of conducting mechanism is observed with increasing in-plane electric field perpendicular to the ribbon. Wider zigzag graphene nanoribbons have been predicted to be spin-splitted for both valence band maximum(VBM) and conduction band minimum(CBM) with an applied electric field and become half-metal due to the vanishing band gap of one spin with increasing applied field. The change of VBM for the ultrathin zigzag graphene nanoribbons is similar to that for the wider ones when an electric field is applied. However, in the ultrathin zigzag graphene nanoribbons, there are two kinds of CBMs, one is spin-degenerate and the other is spin-splitted, and both are tunable by the electric field. Moreover, the two CBMs are spatially separated in momentum space. The conducting mechanism changes from spin-degenerate CBM to spin-splitted CBM with increasing applied electric field. Our results are confirmed by density functional calculations with both LDA and GGA functionals, in which the LDA always underestimates the band gap while the GGA normally produces a bigger band gap than the LDA.     

Zigzag graphene nanoribbons: bandgap and midgap state modulation

We study zigzag graphene nanoribbons with periodic edge roughness and report significant band gap opening. Interestingly, such nanoribbons have a near-midgap state with a small band width. We extensively study the electronic structure and the electric-field modulation of the conduction/valence bands and the near-midgap state. We summarize the important electronic-structure features like the band gap, the band width and the effective mass. We show that by applying an external electric field in the width direction, the band width of the near-midgap state varies linearly due to the edge localization, whereas the band gap remains almost constant. Additionally, the effective mass of these states can switch polarity from negative (hole-like) to positive (carrier-like) at the Γ-point with the field modulation.