Charge transport in polycrystalline graphene: challenges and opportunities

Graphene-based chemiresistive gas sensors

Gas sensors allow the monitoring of the chemical environment of humans, which is often crucial for their wellbeing or even survival. Miniaturization, reversibility, and selectivity are some of the key challenges for serial use of chemical sensors. This tutorial review describes critical aspects when using nanomaterials as sensing substrates for the application in chemiresistive gas sensors. Graphene has been shown to be a promising candidate, as it allows gas sensors to be operated at room temperature, possibly saving large amounts of energy. In this review, an overview is given on the general mechanisms for gas-sensitive semiconducting materials and the implications of doping and functionalization on the sensing parameters of chemiresistive devices. It shows in detail how different challenges, like sensitivity, response time, reversibility and selectivity have been approached by material development and operation modes. In addition, perspectives from the area of data analysis and intelligent algorithms are presented, which can further enhance these sensors' usability in the field.

Domain Growth in Polycrystalline Graphene

Graphene is a two-dimensional carbon allotrope which exhibits exceptional properties, making it highly suitable for a wide range of applications. Practical graphene fabrication often yields a polycrystalline structure with many inherent defects, which significantly influence its performance. In this study, we utilize a Monte Carlo approach based on the optimized Wooten, Winer and Weaire (WWW) algorithm to simulate the crystalline domain coarsening process of polycrystalline graphene. Our sample configurations show excellent agreement with experimental data. We conduct statistical analyses of the bond and angle distribution, temporal evolution of the defect distribution, and spatial correlation of the lattice orientation that follows a stretched exponential distribution. Furthermore, we thoroughly investigate the diffusion behavior of defects and find that the changes in domain size follow a power-law distribution. We briefly discuss the possible connections of these results to (and differences from) domain growth processes in other statistical models, such as the Ising dynamics. We also examine the impact of buckling of polycrystalline graphene on the crystallization rate under substrate effects. Our findings may offer valuable guidance and insights for both theoretical investigations and experimental advancements.

Graphene Spin Valves for Spin Logic Devices

An alternative to charge-based electronics identifies the spin degree of freedom for information communication and processing. The long spin-diffusion length in graphene at room temperature demonstrates its ability for highly scalable spintronics. The development of the graphene spin valve (SV) has inspired spin devices in graphene including spin field-effect transistors and spin majority logic gates. A comprehensive picture of spin transport in graphene SVs is required for further development of spin logic. This review examines the advances in graphene SVs and their role in the development of spin logic devices. Different transport and scattering mechanisms in charge and spin are discussed. Furthermore, the on/off switching energy between graphene SVs and charge-based FETs is compared to highlight their prospects for low-power devices. The challenges and perspectives that need to be addressed for the future development of spin logic devices are then outlined.

Grain Size Engineering of CVD-Grown Large-Area Graphene Films

Graphene, a single atomic layer of graphitic carbon, has attracted much attention because of its outstanding properties hold great promise for a wide range of technological applications. Large-area graphene films (GFs) grown by chemical vapor deposition (CVD) are highly desirable for both investigating their intrinsic properties and realizing their practical applications. However, the presence of grain boundaries (GBs) has significant impacts on their properties and related applications. According to the different grain sizes, GFs can be divided into polycrystalline, single-crystal, and nanocrystalline films. In the past decade, considerable progress has been made in engineering the grain sizes of GFs by modifying the CVD processes or developing some new growth approaches. The key strategies involve controlling the nucleation density, growth rate, and grain orientation. This review aims to provide a comprehensive description of grain size engineering research of GFs. The main strategies and underlying growth mechanisms of CVD-grown large-area GFs with nanocrystalline, polycrystalline, and single-crystal structures are summarized, in which the advantages and limitations are highlighted. In addition, the scaling law of physical properties in electricity, mechanics, and thermology as a function of grain sizes are briefly discussed. Finally, the perspectives for challenges and future development in this area are also presented.

Corrugations in Free-Standing Graphene

Although both the tendency of 2D materials to bend out of plane as well as its effect on materials' properties are well known, the factors influencing this phenomenon have not been extensively studied. Graphene, the one-atom-thick membrane of carbon atoms, is both arguably the best known 2D material, as well as the most prone to spontaneous corrugations. Here, we use electron diffraction to systematically study the factors influencing corrugations in graphene, including the size of the free-standing area, the preparation method, the amount of surface contamination, and electron-beam-induced structural disorder. We find that mechanically exfoliated graphene is less corrugated than graphene grown via chemical vapor deposition (corrugation amplitude of (0.83±0.10) Å compared to (1.33±0.20) Å for a free-standing area with a diameter of 1.7μm). Similarly, corrugation amplitude grows by more than a factor of two when the diameter of the free- standing area is increased from 1.7μm to ca. 3.0μm. Electron beam irradiation affects the corrugation in two ways, firstly by removing the hydrocarbon contamination, which decreases corrugation, and secondly by creating increasing amounts of disorder into the material, which again increases corrugation. Overall, our results show that control over the sample during both initial preparation and post-preparation treatment allows for a change in the amount of corrugation in free-standing 2D materials, which may lead to new advances in their use in applications.

Electrical resistivity of polycrystalline graphene: effect of grain-boundary-induced strain fields

We have revealed the decisive role of grain-boundary-induced strain fields in electron scattering in polycrystalline graphene. To this end, we have formulated the model based on Boltzmann transport theory which properly takes into account the microscopic structure of grain boundaries (GB) as a repeated sequence of heptagon–pentagon pairs. We show that at naturally low GB charges the strain field scattering dominates and leads to physically reasonable and, what is important, experimentally observable values of the electrical resistivity. It ranges from 0.1 to 10 k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega$$\end{document}Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu m$$\end{document}μm for different types of symmetric GBs with a size of 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu$$\end{document}μm and has a strong dependence on misorientation angle. For low-angle highly charged GBs, two scattering mechanisms may compete. The resistivity increases markedly with decreasing GB size and reaches values of 60 k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega$$\end{document}Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu$$\end{document}μm and more. It is also very sensitive to the presence of irregularities modeled by embedding of partial disclination dipoles. With significant distortion, we found an increase in resistance by more than an order of magnitude, which is directly related to the destruction of diffraction on the GB. Our findings may be of interest both in the interpretation of experimental data and in the design of electronic devices based on poly- and nanocrystalline graphene.

Insights and Implications of Intricate Surface Charge Transfer and sp3-Defects in Graphene/Metal Oxide Interfaces

Adherence of metal oxides to graphene is of fundamental significance to graphene nanoelectronic and spintronic interfaces. Titanium oxide and aluminum oxide are two widely used tunnel barriers in such devices, which offer optimum interface resistance and distinct interface conditions that govern transport parameters and device performance. Here, we reveal a fundamental difference in how these metal oxides interface with graphene through electrical transport measurements and Raman and photoelectron spectroscopies, combined with ab initio electronic structure calculations of such interfaces. While both oxide layers cause surface charge transfer induced p-type doping in graphene, in sharp contrast to TiO_x, the AlO_x/graphene interface shows the presence of appreciable sp³ defects. Electronic structure calculations disclose that significant p-type doping occurs due to a combination of sp³ bonds formed between C and O atoms at the interface and possible slightly off-stoichiometric defects of the aluminum oxide layer. Furthermore, the sp³ hybridization at the AlO_x/graphene interface leads to distinct magnetic moments of unsaturated bonds, which not only explicates the widely observed low spin-lifetimes in AlO_x barrier graphene spintronic devices but also suggests possibilities for new hybrid resistive switching and spin valves.

Multi-scale electronics transport properties in non-ideal CVD graphene sheet

In this work, we benchmark non-idealities and variations in the two-dimensional graphene sheet. We have simulated more than two hundred graphene-based devices structure. We have simulated distorted graphene sheets and have included random, inhomogeneous, asymmetric out-of-plane surface corrugation and in-plane deformation corrugation in the sheet through autocorrelation function in the non-equilibrium Green's function (NEGF) framework to introduce random distortion in flat graphene. These corrugation effects inevitably appear in the graphene sheet due to background substrate roughness or the passivation encapsulation material morphology in the transfer step. We have examined the variation in density of state, propagating density of transmission modes, electronic band structure, electronic density, and hole density in those device structures. We have observed that the surface corrugation increases the electronic and hole density distribution variation across the device and creates electron-hole charge puddles in the sheet. This redistribution of microscopic charge in the sheet is due to the lattice fields' quantum fluctuation and symmetry breaking. Furthermore, to understand the impact of scattered charge distribution on the sheet, we simulated various impurity effects within the NEGF framework. The study's objective is to numerically simulate and benchmark numerous device design morphology with different background materials compositions to elucidate the electrical property of the sheet device.

Construction and physical properties of low-dimensional structures for nanoscale electronic devices

Over the past decades, construction of nanoscale electronic devices with novel functionalities based on low-dimensional structures, such as single molecules and two-dimensional (2D) materials, has been rapidly developed. To investigate their intrinsic properties for versatile functionalities of nanoscale electronic devices, it is crucial to precisely control the structures and understand the physical properties of low-dimensional structures at the single atomic level. In this review, we provide a comprehensive overview of the construction of nanoelectronic devices based on single molecules and 2D materials and the investigation of their physical properties. For single molecules, we focus on the construction of single-molecule devices, such as molecular motors and molecular switches, by precisely controlling their self-assembled structures on metal substrates and charge transport properties. For 2D materials, we emphasize their spin-related electrical transport properties for spintronic device applications and the role that interfaces among 2D semiconductors, contact electrodes, and dielectric substrates play in the electrical performance of electronic, optoelectronic, and memory devices. Finally, we discuss the future research direction in this field, where we can expect a scientific breakthrough.

Valleytronics in two-dimensional materials with line defect

The concept of valley originates from two degenerate but nonequivalent energy bands at the local minimum in the conduction band or local maximum in the valence band. Manipulating the valley states for information storage and processing develops a brand-new electronics-valleytronics. Broken inversion symmetry is a necessary condition to produce pure valley currents. The polycrystalline two-dimensional materials (graphene, silicene, monolayer group-VI transition metal dichalcogenides, etc) with pristine grains stitched together by disordered grain boundaries (GBs) are the natural inversion-symmetry-broken systems and the candidates in the field of valleytronics. Different from their pristine forms, the Dirac valleys on both sides of GBs are mismatched in the momentum space and induce peculiar valley transport properties across the GBs. In this review, we systematically demonstrate the fundamental properties of valley degree of freedom across mostly studied and experimentally feasible polycrystalline structure-the line defect, and the manipulation strategies with electrical, magnetic and mechanical methods to realize the valley polarization. We also introduce an effective numerical method, the non-equilibrium Green's function technique, to tackle the valley transport issues in the line defect systems. The present challenges and the perspective on the further investigations of the line defect in valleytronics are also summarized.

Scanning probe analysis of twisted graphene grown on a graphene/silicon carbide template

Overlayer growth of graphene on an epitaxial graphene/silicon carbide (SiC) as a solid template by ethanol chemical vapor deposition is performed over a wide growth temperature range from 900 °C to 1450 °C. Structural analysis using atomic force and scanning tunneling microscopies reveal that graphene islands grown at 1300 °C form hexagonal twisted bilayer graphene as a single crystal. When the growth temperature exceeds 1400 °C, the grown graphene islands show a circular shape. Moreover, moiré patterns with different periods are observed in a single graphene island. This means that the graphene islands grown at high temperature are composed of several graphene domains with different twist angles. From these results, we conclude that graphene overlayer growth on the epitaxial graphene/SiC solid at 1300 °C effectively synthesizes the twisted few-layer graphene with a high crystallinity.

Simultaneous Extraction of the Grain Size, Single-Crystalline Grain Sheet Resistance, and Grain Boundary Resistivity of Polycrystalline Monolayer Graphene

The electrical properties of polycrystalline graphene grown by chemical vapor deposition (CVD) are determined by grain-related parameters-average grain size, single-crystalline grain sheet resistance, and grain boundary (GB) resistivity. However, extracting these parameters still remains challenging because of the difficulty in observing graphene GBs and decoupling the grain sheet resistance and GB resistivity. In this work, we developed an electrical characterization method that can extract the average grain size, single-crystalline grain sheet resistance, and GB resistivity simultaneously. We observed that the material property, graphene sheet resistance, could depend on the device dimension and developed an analytical resistance model based on the cumulative distribution function of the gamma distribution, explaining the effect of the GB density and distribution in the graphene channel. We applied this model to CVD-grown monolayer graphene by characterizing transmission-line model patterns and simultaneously extracted the average grain size (~5.95 μm), single-crystalline grain sheet resistance (~321 Ω/sq), and GB resistivity (~18.16 kΩ-μm) of the CVD-graphene layer. The extracted values agreed well with those obtained from scanning electron microscopy images of ultraviolet/ozone-treated GBs and the electrical characterization of graphene devices with sub-micrometer channel lengths.

Recent trends in covalent functionalization of 2D materials

Covalent functionalization of the surface is more crucial in 2D materials than in conventional bulk materials because of their atomic thinness, large surface-to-volume ratio, and uniform surface chemical potential. Because...

Quantum Hall Effect across Graphene Grain Boundary

Charge carrier scattering at grain boundaries (GBs) in a chemical vapor deposition (CVD) graphene reduces the carrier mobility and degrades the performance of the graphene device, which is expected to affect the quantum Hall effect (QHE). This study investigated the influence of individual GBs on the QH state at different stitching angles of the GB in a monolayer CVD graphene. The measured voltage probes of the equipotential line in the QH state showed that the longitudinal resistance (R_xx) was affected by the scattering of the GB only in the low carrier concentration region, and the standard QHE of a monolayer graphene was observed regardless of the stitching angle of the GB. In addition, a controlled device with an added metal bar placed in the middle of the Hall bar configuration was introduced. Despite the fact that the equipotential lines in the controlled device were broken by the additional metal bar, only the R_xx was affected by nonzero resistance, whereas the Hall resistance (R_xy) revealed the well-quantized plateaus in the QH state. Thus, our study clarifies the effect of individual GBs on the QH states of graphenes.

Kinetically Determined Shapes of Grain Boundaries in Graphene

A large-scale chemical synthesis of graphene produces a polycrystalline material with grain boundaries (GBs) that disturb the lattice structure and drastically affect material properties. An uncontrollable formation of GB can be detrimental, yet precise GB engineering can impart added functionalities onto graphene-and its noncarbon two-dimensional "cousins." While the importance of growth kinetics in shaping single-crystalline graphene islands has lately been appreciated, kinetics' role in determining a GB structure remains unaddressed. Here we report on the analysis of the GB formation as captured by kinetic Monte Carlo simulations in contrast with global minimum guided GB structures considered previously. We identified a key parameter-edge misorientation angle-that describes the initial geometry of merging grains and unambiguously defines the resulting GB structure, while a commonly used lattice tilt angle corresponds to several qualitatively different GB structures. A provided systematic analysis of GB structures formed from a full range of edge misorientation angles reveals conditions that result in straight and periodic GBs as well as conditions responsible for meandering and disordered GBs. Additionally, we address the special case of translational GBs, where lattices of merging grains are aligned but shifted compared to each other. Collected data can be used for deliberate GB structural engineering, for example, by a three-dimensional patterning of the substrate surface to introduce disclinations creating a graphene lattice tilt.

The effect of catalytic copper pretreatments on CVD graphene growth at different stages

The controllable synthesis of high-quality and large-area graphene by chemical vapor deposition (CVD) remains a challenge nowadays. The massive grain boundaries in graphene grown on polycrystalline Cu by CVD significantly reduce its carrier mobility, limiting its application in high-performance electronic devices. Here, we confirm that the synergetic pretreatment of Cu with electropolishing and surface oxidation is a more efficient way to further suppress the graphene nucleation density (GND) and to accelerate the growth rate of the graphene domain by CVD. With increasing the growth time, we found that the increasing amount of GND and growth rate of the graphene domain were both decreasing during the whole CVD process when the Cu surface was not oxidized. By contrast, they kept growing over time when the Cu surface was pre-oxidized, which suggested that the change trends of the effects on the GND and growth rate between the Cu surface morphology and oxygen were opposite in the CVD process. In addition, not only the domain shape, but the number of graphene domain layers were impacted as well, and a large number of irregular ellipse graphene wafers with dendritic multilayer emerged when the Cu surface was oxidized.

Growth and in situ characterization of 2D materials by chemical vapour deposition on liquid metal catalysts: a review

2D materials (2DMs) have now been established as unique and attractive alternatives to replace current technological materials in a number of applications. Chemical vapour deposition (CVD), is undoubtedly the most renowned technique for thin film synthesis and meets all requirements for automated large-scale production of 2DMs. Currently most CVD methods employ solid metal catalysts (SMCat) for the growth of 2DMs however their use has been found to induce structural defects such as wrinkles, fissures, and grain boundaries among others. On the other hand, liquid metal catalysts (LMCat), constitute a possible alternative for the production of defect-free 2DMs albeit with a small temperature penalty. This review is a comprehensive report of past attempts to employ LMCat for the production of 2DMs with emphasis on graphene growth. Special attention is paid to the underlying mechanisms that govern crystal growth and/or grain consolidation and film coverage. Finally, the advent of online metrology which is particularly effective for monitoring the chemical processes under LMCat conditions is also reviewed and certain directions for future development are drawn.

Electronic Transport and Corrosion Mechanisms of Graphite-Like Nanocrystalline Carbon Films Used on Metallic Bipolar Plates in Proton-Exchange Membrane Fuel Cells

Nanocrystalline carbon films, which consist of graphite-like nanocrystals within an amorphous carbon matrix, have recently attracted extensive theoretical and experimental attention. Understanding the electronic transport and corrosion mechanisms of graphite-like nanocrystalline carbon films (GNCFs) is essential for their application in proton-exchange membrane fuel cells (PEMFCs). So far, limited progress has been made on the electronic or atomistic understanding of how the degree of structural order and grain boundaries affect the electronic transport and corrosion behaviors of GNCFs. In this work, using the Landauer-Büttiker formula merged with first-principles density functional theory, the conductance of GNCFs is presented as a function of their crystallinity. As the crystallinity decreases, the electron states around the Fermi level are found to be more spatially localized, thus hindering the electronic transport of GNCFs. Additionally, a systemic picture of the chemical reactivity of nanostructured surface in GNCFs toward typical particles existing in PEMFCs is drawn by ab initio molecular dynamics simulations. Systemic experimental investigations on the corrosion mechanisms of GNCFs used in PEMFCs have been conducted in this work. Compared with pure amorphous carbon films, the GNCFs exhibit higher corrosion current densities due to the preferential corrosion in the larger slit pores at the grain boundaries, but their stability in interfacial contact resistance is significantly improved by the embedded graphite-like nanocrystals, which have high levels of resistance to oxygen chemical adsorptions and act as high-speed ways to transport electrons.

Hydrogen-Assisted Fast Growth of Large Graphene Grains by Recrystallization of Nanograins

Chemical vapor deposition has been highlighted as a promising tool for facile graphene growth in a large area. However, grain boundaries impose detrimental effects on the mechanical strength or electrical mobility of graphene. Here, we demonstrate that high-pressure hydrogen treatment in the preannealing step plays a key role in fast and large grain growth and leads to the successful synthesis of large grain graphene in 10 s. Large single grains with a maximum size of ∼160 μm grow by recrystallization of nanograins, but ∼1% areal coverage of nanograins remains with 28-30° misorientation angles. Our findings will provide insights into mass production of high-quality graphene.

Robust Spin Interconnect with Isotropic Spin Dynamics in Chemical Vapor Deposited Graphene Layers and Boundaries

The utilization of large-area graphene grown by chemical vapor deposition (CVD) is crucial for the development of scalable spin interconnects in all-spin-based memory and logic circuits. However, the fundamental influence of the presence of multilayer graphene patches and their boundaries on spin dynamics has not been addressed yet, which is necessary for basic understanding and application of robust spin interconnects. Here, we report universal spin transport and dynamic properties in specially devised single layer, bilayer, and trilayer graphene channels and their layer boundaries and folds that are usually present in CVD graphene samples. We observe uniform spin lifetime with isotropic spin relaxation for spins with different orientations in graphene layers and their boundaries at room temperature. In all of the inhomogeneous graphene channels, the spin lifetime anisotropy ratios for spins polarized out-of-plane and in-plane are measured to be close to unity. Our analysis shows the importance of both Elliott-Yafet and D'yakonov-Perel' mechanisms with an increasing role of the latter mechanism in multilayer channels. These results of universal and isotropic spin transport on large-area inhomogeneous CVD graphene with multilayer patches and their boundaries and folds at room temperature prove its outstanding spin interconnect functionality, which is beneficial for the development of scalable spintronic circuits.

Exploration of mechanical, thermal conductivity and electromechanical properties of graphene nanoribbon springs

Recent experimental advances [Liu et al., npj 2D Mater. Appl., 2019, 3, 23] propose the design of graphene nanoribbon springs (GNRSs) to substantially enhance the stretchability of pristine graphene. A GNRS is a periodic undulating graphene nanoribbon, where undulations are of sinus or half-circle or horseshoe shapes. Besides this, the GNRS geometry depends on design parameters, like the pitch's length and amplitude, thickness and joining angle. Because of the fact that parametric influence on the resulting physical properties is expensive and complicated to examine experimentally, we explore the mechanical, thermal and electromechanical properties of GNRSs using molecular dynamics simulations. Our results demonstrate that the horseshoe shape design GNRS (GNRH) can distinctly outperform the graphene kirigami design concerning the stretchability. The thermal conductivity of GNRSs was also examined by developing a multiscale modeling, which suggests that the thermal transport along these nanostructures can be effectively tuned. We found that however, the tensile stretching of the GNRS and GNRH does not yield any piezoelectric polarization. The bending induced hybridization change results in a flexoelectric polarization, where the corresponding flexoelectric coefficient is 25% higher than that of graphene. Our results provide a comprehensive vision of the critical physical properties of GNRSs and may help to employ the outstanding physics of graphene to design novel stretchable nanodevices.

Controllable valley filter in graphene topological line defect with magnetic field

The extended line defect of graphene is an extraordinary candidate in valleytronics while the high valley polarization can only occur for electrons with high incidence angles which brings about tremendous challenges to experimental realization. In this paper, we propose a novel quantum mechanism to filter one conical valley state in the line defect of graphene by applying a local magnetic field. It is found that due to the movement of the Dirac points, the transmission profiles of the two valleys are shifted along the injection-angle axis at the same pace, resulting in the peak transmission of one valley state being reduced drastically while remaining unaffected for the other valley state, which induces nearly perfect valley polarization. The valley polarization effect can occur for all the incident angle and plays a key role in graphene valleytronics.

Computational Atomistic Modeling in Carbon Flatland and Other 2D Nanomaterials

As in many countries, the rise of nanosciences in Belgium has been triggered in the eighties in the one hand, by the development of scanning tunneling and atomic force microscopes offering an unprecedented possibility to visualize and manipulate the atoms, and in the other hand, by the synthesis of nano-objects in particular carbon nanostructures such as fullerene and nanotubes. Concomitantly, the increasing calculating power and the emergence of computing facilities together with the development of DFT-based ab initio softwares have brought to nanosciences field powerful simulation tools to analyse and predict properties of nano-objects. Starting with 0D and 1D nanostructures, the floor is now occupied by the 2D materials with graphene being the bow of this 2D ship. In this review article, some specific examples of 2D systems has been chosen to illustrate how not only density functional theory (DFT) but also tight-binding (TB) techniques can be daily used to investigate theoretically the electronic, phononic, magnetic, and transport properties of these atomically thin layered materials.

Aharonov-Bohm interferences in polycrystalline graphene

Aharonov-Bohm (AB) interferences in the quantum Hall regime can be achieved, provided that electrons are able to transmit between two edge channels in nanostructures. Pioneering approaches include quantum point contacts in 2DEG systems, bipolar graphene p-n junctions, and magnetic field heterostructures. In this work, defect scattering is proposed as an alternative mechanism to achieve AB interferences in polycrystalline graphene. Indeed, due to such scattering, the extended defects across the sample can act as tunneling paths connecting quantum Hall edge channels. Consequently, strong AB oscillations in the conductance are predicted in polycrystalline graphene systems with two parallel grain boundaries. In addition, this general approach is demonstrated to be applicable to nano-systems containing two graphene barriers with functional impurities and perspectively, can also be extended to similar systems of 2D materials beyond graphene.

A Strategy To Prepare High-Quality Monocrystalline Graphene: Inducing Graphene Growth with Seeding Chemical Vapor Deposition and Its Mechanism

High-quality monocrystalline graphene has gained considerable attention in fundamental physics, materials science, and nanoelectronics. However, the performance of the graphene obtained by chemical synthesis methods is currently significantly restricted by the crystal quality. Herein, a seeding chemical vapor deposition (SCVD) method is designed to cultivate high-quality monocrystalline graphene on a Cu(111) substrate with hexagonal boron nitride (h-BN) as the seed crystal. Combining the experimental and theoretical research, the nucleation behavior of the growth-induced graphene on the h-BN seed crystal is investigated, and the induced growth mechanism on the Cu(111) substrate is studied. The results show that the h-BN seed crystal can dramatically reduce the adsorption energy of active carbon atoms and the energy barrier for C-C aggregation at the BN/Cu(111) step, thus promoting graphene growth around the h-BN seed. Large monocrystalline graphene domains are obtained by the proposed SCVD method. Further study shows that the growth-induced graphene has good crystal quality and could maintain high structural integrity. This new strategy can be applied for growing high-quality graphene and other two-dimensional materials.

Ultrafast growth of nanocrystalline graphene films by quenching and grain-size-dependent strength and bandgap opening

Nanocrystallization is a well-known strategy to dramatically tune the properties of materials; however, the grain-size effect of graphene at the nanometer scale remains unknown experimentally because of the lack of nanocrystalline samples. Here we report an ultrafast growth of graphene films within a few seconds by quenching a hot metal foil in liquid carbon source. Using Pt foil and ethanol as examples, four kinds of nanocrystalline graphene films with average grain size of ~3.6, 5.8, 8.0, and 10.3 nm are synthesized. It is found that the effect of grain boundary becomes more pronounced at the nanometer scale. In comparison with pristine graphene, the 3.6 nm-grained film retains high strength (101 GPa) and Young's modulus (576 GPa), whereas the electrical conductivity is declined by over 100 times, showing semiconducting behavior with a bandgap of ~50 meV. This liquid-phase precursor quenching method opens possibilities for ultrafast synthesis of typical graphene materials and other two-dimensional nanocrystalline materials.

Green function, quasi-classical Langevin and Kubo-Greenwood methods in quantum thermal transport

With the advances in fabrication of materials with feature sizes at the order of nanometers, it has been possible to alter their thermal transport properties dramatically. Miniaturization of device size increases the power density in general, hence faster electronics require better thermal transport, whereas better thermoelectric applications require the opposite. Such diverse needs bring new challenges for material design. Shrinkage of length scales has also changed the experimental and theoretical methods to study thermal transport. Unsurprisingly, novel approaches have emerged to control phonon flow. Besides, ever increasing computational power is another driving force for developing new computational methods. In this review, we discuss three methods developed for computing vibrational thermal transport properties of nano-structured systems, namely Green function, quasi-classical Langevin, and Kubo-Green methods. The Green function methods are explained using both nonequilibrium expressions and the Landauer-type formula. The partitioning scheme, decimation techniques and surface Green functions are reviewed, and a simple model for reservoir Green functions is shown. The expressions for the Kubo-Greenwood method are derived, and Lanczos tridiagonalization, continued fraction and Chebyshev polynomial expansion methods are discussed. Additionally, the quasi-classical Langevin approach, which is useful for incorporating phonon-phonon and other scatterings is summarized.

Controllable Growth of Graphene on Liquid Surfaces

Controllable fabrication of graphene is necessary for its practical application. Chemical vapor deposition (CVD) approaches based on solid metal substrates with morphology-rich surfaces, such as copper (Cu) and nickel (Ni), suffer from the drawbacks of inhomogeneous nucleation and uncontrollable carbon precipitation. Liquid substrates offer a quasiatomically smooth surface, which enables the growth of uniform graphene layers. The fast surface diffusion rates also lead to unique growth and etching kinetics for achieving graphene grains with novel morphologies. The rheological surface endows the graphene grains with self-adjusted rotation, alignment, and movement that are driven by specific interactions. The intermediary-free transfer or the direct growth of graphene on insulated substrates is demonstrated using liquid metals. Here, the controllable growth process of graphene on a liquid surface to promote the development of attractive liquid CVD strategies is in focus. The exciting progress in controlled growth, etching, self-assembly, and delivery of graphene on a liquid surface is presented and discussed in depth. In addition, prospects and further developments in these exciting fields of graphene growth on a liquid surface are discussed.

Graphene Nucleation Preference at CuO Defects Rather Than Cu2O on Cu(111): A Combination of DFT Calculation and Experiment

It is well-known that reducing the nucleation density is an effective way to enhance the growth quality of graphene. In this work, we explore the mechanism of graphene nucleation and growth around CuO defects on a Cu(111) substrate by using density functional theory combined with the nudged elastic band method. The defect formation mechanism at the initial nucleation stage is also studied. Our calculation results of the C adsorption energy and the reaction barrier of C-C dimer formation illustrate that the initial nucleation of graphene could be promoted by artificially introducing CuO defects on a Cu(111) surface and the nucleation on the clean Cu(111) substrate could thus be suppressed. These conclusions have been verified by graphene growth experiments using a chemical vapor deposition method. Further studies showed that graphene grown around CuO "seed crystals" could maintain its structural integrity without significantly producing defective carbon rings. This work provides a fundamental understanding and theoretical guidance for the controllable preparation of large-dimension and high-quality graphene by artificially introducing CuO seeds.

Tailoring the Grain Size of Bi-Layer Graphene by Pulsed Laser Deposition

Improving the thermoelectric efficiency of a material requires a suitable ratio between electrical and thermal conductivity. Nanostructured graphene provides a possible route to improving thermoelectric efficiency. Bi-layer graphene was successfully prepared using pulsed laser deposition in this study. The size of graphene grains was controlled by adjusting the number of pulses. Raman spectra indicated that the graphene was bi-layer. Scanning electron microscopy (SEM) images clearly show that graphene changes from nanostructured to continuous films when more pulses are used during fabrication. Those results indicate that the size of the grains can be controlled between 39 and 182 nm. A detailed analysis of X-ray photoelectron spectra reveals that the sp² hybrid state is the main chemical state in carbon. The mobility is significantly affected by the grain size in graphene, and there exists a relatively stable region between 500 and 800 pulses. The observed phenomena originate from competition between decreasing resistance and increasing carrier concentration. These studies should be valuable for regulating grains sizes for thermoelectric applications of graphene.

Scattering Theory of Graphene Grain Boundaries

The implementation of graphene-based electronics requires fabrication processes that are able to cover large device areas, since the exfoliation method is not compatible with industrial applications. The chemical vapor deposition of large-area graphene represents a suitable solution; however, it has an important drawback of producing polycrystalline graphene with the formation of grain boundaries, which are responsible for the limitation of the device's performance. With these motivations, we formulate a theoretical model of a single-layer graphene grain boundary by generalizing the graphene Dirac Hamiltonian model. The model only includes the long-wavelength regime of the charge carrier transport, which provides the main contribution to the device conductance. Using symmetry-based arguments deduced from the current conservation law, we derive unconventional boundary conditions characterizing the grain boundary physics and analyze their implications on the transport properties of the system. Angle resolved quantities, such as the transmission probability, are studied within the scattering matrix approach. The conditions for the existence of preferential transmission directions are studied in relation with the grain boundary properties. The proposed theory provides a phenomenological model to study grain boundary physics within the scattering approach, and represents per se an important enrichment of the scattering theory of polycrystalline graphene. Moreover, the outcomes of the theory can contribute to understanding and limiting the detrimental effects of graphene grain boundaries, while also providing a benchmark for more elaborate techniques.

Extracting the Energy Sensitivity of Charge Carrier Transport and Scattering

It is a challenge to extract the energy sensitivity of charge carriers’ transport and scattering from experimental data, although a theoretical estimation in which the existing scattering mechanism(s) are preliminarily assumed can be easily done. To tackle this problem, we have developed a method to experimentally determine the energy sensitivities, which can then serve as an important statistical measurement to further understand the collective behaviors of multi-carrier transport systems. This method is validated using a graphene system at different temperatures. Further, we demonstrate the application of this method to other two-dimensional (2D) materials as a guide for future experimental work on the optimization of materials performance for electronic components, Peltier coolers, thermoelectricity generators, thermocouples, thermopiles, electrical converters and other conductivity and/or Seebeck-effect-related sensors.

Ab initio quantum transport in polycrystalline graphene

Synthesis techniques such as chemical vapor deposition yield graphene in polycrystalline flakes where single-crystal domains are separated by grain boundaries (GBs) of irregular shape. These structural defects are mostly made up of pentagon-heptagon pairs and represent an important source of scattering, thus strongly affecting electronic mobilities in polycrystalline graphene (PG). In the present article, first-principles simulations are performed to explore charge transport through a GB in PG using the Landauer-Büttiker formalism implemented within the Green's function approach. In ideal GB configurations, electronic transport is found to depend on their topology as already suggested in the literature. However, more realistic GBs constructed out of various carbon rings and with more complex periodicities are also considered, possibly inducing leakage currents. Finally, additional realistic disorder such as vacancies, a larger inter-connectivity region and out-of plane buckling is investigated. For specific energies, charge redistribution effects related to the detailed GB topology are found to substantially alter the transmissions. Altogether, the transport gap is predicted to be inversely proportional to the smallest significant periodic pattern and nearly independent of the interface configuration.

Scale-invariant large nonlocality in polycrystalline graphene

The observation of large nonlocal resistances near the Dirac point in graphene has been related to a variety of intrinsic Hall effects, where the spin or valley degrees of freedom are controlled by symmetry breaking mechanisms. Engineering strong spin or valley Hall signals on scalable graphene devices could stimulate further practical developments of spin- and valleytronics. Here we report on scale-invariant nonlocal transport in large-scale chemical vapor deposition graphene under an applied external magnetic field. Contrary to previously reported Zeeman spin Hall effect, our results are explained by field-induced spin-filtered edge states whose sensitivity to grain boundaries manifests in the nonlocal resistance. This phenomenon, related to the emergence of the quantum Hall regime, persists up to the millimeter scale, showing that polycrystalline morphology can be imprinted in nonlocal transport. This suggests that topological Hall effects in large-scale graphene materials are highly sensitive to the underlying structural morphology, limiting practical realizations.

Spatially resolved Raman spectroscopy of defects, strains, and strain fluctuations in domain structures of monolayer graphene

We report spatially resolved Raman scattering results of polycrystalline monolayer graphene films to study the effects of defects, strains, and strain fluctuations on the electrical performance of graphene. Two-dimensional Raman images of the integrated intensities of the G and D peaks (I_G and I_D) were used to identify the graphene domain boundaries. The domain boundaries were also identified using Raman images of I_D/I_G and I_2D/I_G ratios and 2D spectral widths. Interestingly, the I_D maps showed that the defects within individual domains significantly increased for the graphene with large domain size. The correlation analysis between the G and 2D peak energies showed that biaxial tensile strain was more developed in the graphene with large domain size than in the graphene with small domain size. Furthermore, spatial variations in the spectral widths of the 2D peaks over the graphene layer showed that strain fluctuations were more pronounced in the graphene with large domain size. It was observed that the mobility (sheet resistance) was decreased (increased) for the graphene with large domain size. The degradation of the electrical transport properties of the graphene with large domain size is mainly due to the defects, tensile strains, and local strain fluctuations within the individual domains.

Thermal and electronic transport characteristics of highly stretchable graphene kirigami

For centuries, cutting and folding papers with special patterns have been used to build beautiful, flexible and complex three-dimensional structures. Inspired by the old idea of kirigami (paper cutting), and the outstanding properties of graphene, recently graphene kirigami structures were fabricated to enhance the stretchability of graphene. However, the possibility of further tuning the electronic and thermal transport along the 2D kirigami structures has remained original to investigate. We therefore performed extensive atomistic simulations to explore the electronic, heat and load transfer along various graphene kirigami structures. The mechanical response and thermal transport were explored using classical molecular dynamics simulations. We then used a real-space Kubo-Greenwood formalism to investigate the charge transport characteristics in graphene kirigami. Our results reveal that graphene kirigami structures present highly anisotropic thermal and electrical transport. Interestingly, we show the possibility of tuning the thermal conductivity of graphene by four orders of magnitude. Moreover, we discuss the engineering of kirigami patterns to further enhance their stretchability by more than 10 times as compared with pristine graphene. Our study not only provides a general understanding concerning the engineering of electronic, thermal and mechanical response of graphene, but more importantly can also be useful to guide future studies with respect to the synthesis of other 2D material kirigami structures, to reach highly flexible and stretchable nanostructures with finely tunable electronic and thermal properties.

Bimodal Grain-Size Scaling of Thermal Transport in Polycrystalline Graphene from Large-Scale Molecular Dynamics Simulations

Grain boundaries in graphene are inherent in wafer-scale samples prepared by chemical vapor deposition. They can strongly influence the mechanical properties and electronic and heat transport in graphene. In this work, we employ extensive molecular dynamics simulations to study thermal transport in large suspended polycrystalline graphene samples. Samples of different controlled grain sizes are prepared by a recently developed efficient multiscale approach based on the phase field crystal model. In contrast to previous works, our results show that the scaling of the thermal conductivity with the grain size implies bimodal behavior with two effective Kapitza lengths. The scaling is dominated by the out-of-plane (flexural) phonons with a Kapitza length that is an order of magnitude larger than that of the in-plane phonons. We also show that, to get quantitative agreement with the most recent experiments, quantum corrections need to be applied to both the Kapitza conductance of grain boundaries and the thermal conductivity of pristine graphene, and the corresponding Kapitza lengths must be renormalized accordingly.

Direct Four-Probe Measurement of Grain-Boundary Resistivity and Mobility in Millimeter-Sized Graphene

Grain boundaries (GBs) in polycrystalline graphene scatter charge carriers, which reduces carrier mobility and limits graphene applications in high-speed electronics. Here we report the extraction of the resistivity of GBs and the effect of GBs on carrier mobility by direct four-probe measurements on millimeter-sized graphene bicrystals grown by chemical vapor deposition (CVD). To extract the GB resistivity and carrier mobility from direct four-probe intragrain and intergrain measurements, an electronically equivalent extended 2D GB region is defined based on Ohm's law. Measurements on seven representative GBs find that the maximum resistivities are in the range of several kΩ·μm to more than 100 kΩ·μm. Furthermore, the mobility in these defective regions is reduced to 0.4-5.9‰ of the mobility of single-crystal, pristine graphene. Similarly, the effect of wrinkles on carrier transport can also be derived. The present approach provides a reliable way to directly probe charge-carrier scattering at GBs and can be further applied to evaluate the GB effect of other two-dimensional polycrystalline materials, such as transition-metal dichalcogenides (TMDCs).

Controlled Chemical Synthesis in CVD Graphene

Due to the unique properties of graphene, single layer, bilayer or even few layer graphene peeled off from bulk graphite cannot meet the need of practical applications. Large size graphene with quality comparable to mechanically exfoliated graphene has been synthesized by chemical vapor deposition (CVD). The main development and the key issues in controllable chemical vapor deposition of graphene has been briefly discussed in this chapter. Various strategies for graphene layer number and stacking control, large size single crystal graphene domains on copper, graphene direct growth on dielectric substrates, and doping of graphene have been demonstrated. The methods summarized here will provide guidance on how to synthesize other two-dimensional materials beyond graphene.

The integration of graphene into microelectronic devices

Since 2004 the field of graphene research has attracted increasing interest worldwide. Especially the integration of graphene into microelectronic devices has the potential for numerous applications. Therefore, we summarize the current knowledge on this aspect. Surveys show that considerable progress was made in the field of graphene synthesis. However, the central issue consists of the availability of techniques suitable for production for the deposition of graphene on dielectric substrates. Besides, the encapsulation of graphene for further processing while maintaining its properties poses a challenge. Regarding the graphene/metal contact intensive research was done and recently substantial advancements were made towards contact resistances applicable for electronic devices. Generally speaking the crucial issues for graphene integration are identified today and the corresponding research tasks can be clearly defined.

Electrical and Thermal Transport in Coplanar Polycrystalline Graphene-hBN Heterostructures

We present a theoretical study of electronic and thermal transport in polycrystalline heterostructures combining graphene (G) and hexagonal boron nitride (hBN) grains of varying size and distribution. By increasing the hBN grain density from a few percent to 100%, the system evolves from a good conductor to an insulator, with the mobility dropping by orders of magnitude and the sheet resistance reaching the MΩ regime. The Seebeck coefficient is suppressed above 40% mixing, while the thermal conductivity of polycrystalline hBN is found to be on the order of 30-120 Wm^-1 K^-1. These results, agreeing with available experimental data, provide guidelines for tuning G-hBN properties in the context of two-dimensional materials engineering. In particular, while we proved that both electrical and thermal properties are largely affected by morphological features (e.g., by the grain size and composition), we find in all cases that nanometer-sized polycrystalline G-hBN heterostructures are not good thermoelectric materials.

Tailoring the thermal and electrical transport properties of graphene films by grain size engineering

Understanding the influence of grain boundaries (GBs) on the electrical and thermal transport properties of graphene films is essentially important for electronic, optoelectronic and thermoelectric applications. Here we report a segregation-adsorption chemical vapour deposition method to grow well-stitched high-quality monolayer graphene films with a tunable uniform grain size from ∼200 nm to ∼1 μm, by using a Pt substrate with medium carbon solubility, which enables the determination of the scaling laws of thermal and electrical conductivities as a function of grain size. We found that the thermal conductivity of graphene films dramatically decreases with decreasing grain size by a small thermal boundary conductance of ∼3.8 × 10⁹ W m^-2 K^-1, while the electrical conductivity slowly decreases with an extraordinarily small GB transport gap of ∼0.01 eV and resistivity of ∼0.3 kΩ μm. Moreover, the changes in both the thermal and electrical conductivities with grain size change are greater than those of typical semiconducting thermoelectric materials.

Valley Filtering and Electronic Optics Using Polycrystalline Graphene

In this Letter, both the manipulation of valley-polarized currents and the optical-like behaviors of Dirac fermions are theoretically explored in polycrystalline graphene. When strain is applied, the misorientation between two graphene domains separated by a grain boundary can result in a mismatch of their electronic structures. Such a discrepancy manifests itself in a strong breaking of the inversion symmetry, leading to perfect valley polarization in a wide range of transmission directions. In addition, these graphene domains act as different media for electron waves, offering the possibility to modulate and obtain negative refraction indexes.

Valley filtering by a line-defect in graphene: quantum interference and inversion of the filter effect

Valley filters are crucial to any device exploiting the valley degree of freedom. By using an atomistic model, we analyze the mechanism leading to the valley filtering produced by a line-defect in graphene and show how it can be inverted by external means. Thanks to a mode decomposition applied to a tight-binding model we can resolve the different transport channels in k-space while keeping a simple but accurate description of the band structure, both close and further away from the Dirac point. This allows the understanding of a destructive interference effect, specifically a Fano resonance or antiresonance located on the p-side of the Dirac point leading to a reduced conductance. We show that in the neighborhood of this feature the valley filtering can be reversed by changing the occupations with a gate voltage, the mechanism is explained in terms of a valley-dependent Fano resonance splitting. Our results open the door for enhanced control of valley transport in graphene-based devices.

Site-Specific Chemical Surface Functionalization and Electronic Patterning of Graphene by Electrooxidative Lithography

The combination of different properties being manipulated on nanomaterials is one of the challenges in nanotechnology research. In particular, the possibility to tailor the electronic and chemical properties offers promising possibilities for the design of functional nanostructures. Herein, we report an approach that permits control of these properties on the basis of electrooxidative lithography to structure reduced graphene oxide functionalized with a self-assembled monolayer of n-octadecyltrichlorosilane. The electrochemical oxidation process first induces the formation of polar acid groups on the monolayer, which can be used to covalently bind nanoparticles and molecules and, secondly, also allows the reoxidation of the underlying reduced graphene oxide. As such, the chemical signature as well as the electronic properties of the substrate can be tailored on the micro- and nanometer scale. Details on the oxidation of the monolayer as well as thorough characterization of the electronic properties will be presented. Finally, the approach is used to demonstrate the fabrication of a sensitive glucose sensor device.

Nanoscale Mechanics of Graphene and Graphene Oxide in Composites: A Scientific and Technological Perspective

Graphene shows considerable promise in structural composite applications thanks to its unique combination of high tensile strength, Young's modulus and structural flexibility which arise due to its maximal chemical bond strength and minimal atomic thickness. However, the ultimate performance of graphene composites will depend, in addition to the properties of the matrix and interface, on the morphology of the graphene used, including the size and shape of the sheets and the number of chemical defects present. For example, whilst oxidized sp(3) carbon atoms and vacancies in a graphene sheet can degrade its mechanical strength, they can also increase its interaction with other materials such as the polymer matrix of a composite, thus maximizing stress transfer and leading to more efficient mechanical reinforcement. Herein, we present an overview of some recently published work on graphene mechanical properties and discuss a list of challenges that need to be overcome (notwithstanding the strong hype existing on this material) for the development of graphene-based materials into a successful technology.

Transport properties through graphene grain boundaries: strain effects versus lattice symmetry

As most materials available at the macroscopic scale, graphene samples usually appear in a polycrystalline form and thus contain grain boundaries. In the present work, the effect of uniaxial strain on the electronic transport properties through graphene grain boundaries is investigated using atomistic simulations. A systematic picture of transport properties with respect to the strain and lattice symmetry of graphene domains on both sides of the boundary is provided. In particular, it is shown that strain engineering can be used to open a finite transport gap in all graphene systems where the two domains are arranged in different orientations. This gap value is found to depend on the strain magnitude, on the strain direction and on the lattice symmetry of graphene domains. By choosing appropriately the strain direction, a large transport gap of a few hundred meV can be achieved when applying a small strain of only a few percents. For a specific class of graphene grain boundary systems, strain engineering can also be used to reduce the scattering on defects and thus to significantly enhance the conductance. With a large strain-induced gap, these graphene heterostructures are proposed to be promising candidates for highly sensitive strain sensors, flexible electronic devices and p-n junctions with non-linear I-V characteristics.

Oxidative-Etching-Assisted Synthesis of Centimeter-Sized Single-Crystalline Graphene

Centimeter-sized single-crystalline graphene is obtained by an oxidative-etching-assisted chemical vapor deposition (CVD) method. Gaseous oxidants are found to be highly responsible for graphene etching. By diminishing the uncertain amount of H2 O vapor in commercial H2 and precisely introducing additional O2 , the graphene nucleation density can be well controlled.