Charge Transport in Polycrystalline Graphene: Challenges and Opportunities

Graphene has attracted significant interest both for exploring fundamental science and for a wide range of technological applications. Chemical vapor deposition (CVD) is currently the only working approach to grow graphene at wafer scale, which is required for industrial applications. Unfortunately, CVD graphene is intrinsically polycrystalline, with pristine graphene grains stitched together by disordered grain boundaries, which can be either a blessing or a curse. On the one hand, grain boundaries are expected to degrade the electrical and mechanical properties of polycrystalline graphene, rendering the material undesirable for many applications. On the other hand, they exhibit an increased chemical reactivity, suggesting their potential application to sensing or as templates for synthesis of one‐dimensional materials. Therefore, it is important to gain a deeper understanding of the structure and properties of graphene grain boundaries. Here, we review experimental progress on identification and electrical and chemical characterization of graphene grain boundaries. We use numerical simulations and transport measurements to demonstrate that electrical properties and chemical modification of graphene grain boundaries are strongly correlated. This not only provides guidelines for the improvement of graphene devices, but also opens a new research area of engineering graphene grain boundaries for highly sensitive electro‐biochemical devices.     

Surface crystallographic structure insensitive growth of oriented graphene domains on Cu substrates

Cu-based chemical vapor deposition method can produce large-area graphene films, usually polycrystalline films with grain boundaries as the main defects. One way to reduce grain boundaries is to grow oriented graphene domains (OGDs), which can ultimately perfectly integrate. In contrast to previously reported methods of limiting OGD growth on Cu (1 1 1), we find that OGDs can grow on Cu substrates with a large surface crystallographic structure tolerance. Density functional theory calculations show that this is due to the single lowest energy state of graphene nucleation. The growth temperature is crucial. It must be high enough (1045 °C) to suppress mis-OGD nucleation, but not too high (1055 °C) to deteriorate OGD growth. Mis-OGD nucleation can also be caused by C impurity in Cu grains, which can be depleted by thermal pretreatment of the substrate in an oxidizing atmosphere. On the other hand, OGD growth is not sensitive to the atmosphere at growth stage within the range that we have tested.     

Rapid growth of angle-confined large-domain graphene bicrystals

In the chemical vapor deposition growth of large-area graphene polycrystalline thin films,the coalescence of randomly oriented graphene domains results in a high density of uncertain grain boundaries (GBs).The structures and properties of various GBs are highly dependent on the misorientation angles between the graphene domains,which can significantly affect the performance of the graphene films and impede their industrial applications.Graphene bicrystals with a specific type of GB can be synthesized via the controllable growth of graphene domains with a predefined lattice orientation.Although the bicrystal has been widely investigated for traditional bulk materials,no successful synthesis strategy has been presented for growing two-dimensional graphene bicrystals.In this study, we demonstrate a simple approach for growing well-aligned large-domain graphene bicrystals with a confined tilt angle of 30° on a facilely recrystallized single-crystal Cu (100) substrate.Control of the density of the GBs with a misorientation angle of 30° was realized via the controllable rapid growth of subcentimeter graphene domains with the assistance of a cooperative catalytic surface-passivation treatment.The large-area production of graphene bicrystals consisting of the sole specific GBs with a tunable density provides a new material platform for fundamental studies and practical applications.     

Chemical vapor deposition-derived graphene with electrical performance of exfoliated graphene

While chemical vapor deposition (CVD) promises a scalable method to produce large-area graphene, CVD-grown graphene has heretofore exhibited inferior electronic properties in comparison with exfoliated samples. Here we test the electrical transport properties of CVD-grown graphene in which two important sources of disorder, namely grain boundaries and processing-induced contamination, are substantially reduced. We grow CVD graphene with grain sizes up to 250 μm to abate grain boundaries, and we transfer graphene utilizing a novel, dry-transfer method to minimize chemical contamination. We fabricate devices on both silicon dioxide and hexagonal boron nitride (h-BN) dielectrics to probe the effects of substrate-induced disorder. On both substrate types, the large-grain CVD graphene samples are comparable in quality to the best reported exfoliated samples, as determined by low-temperature electrical transport and magnetotransport measurements. Small-grain samples exhibit much greater variation in quality and inferior performance by multiple measures, even in samples exhibiting high field-effect mobility. These results confirm the possibility of achieving high-performance graphene devices based on a scalable synthesis process.     

Effects of polycrystalline cu substrate on graphene growth by chemical vapor deposition

Chemical vapor deposition of graphene on Cu often employs polycrystalline Cu substrates with diverse facets, grain boundaries (GBs), annealing twins, and rough sites. Using scanning electron microscopy (SEM), electron-backscatter diffraction (EBSD), and Raman spectroscopy on graphene and Cu, we find that Cu substrate crystallography affects graphene growth more than facet roughness. We determine that (111) containing facets produce pristine monolayer graphene with higher growth rate than (100) containing facets, especially Cu(100). The number of graphene defects and nucleation sites appears Cu facet invariant at growth temperatures above 900 °C. Engineering Cu to have (111) surfaces will cause monolayer, uniform graphene growth.     

Hybrid molecular dynamics–finite element simulations of the elastic behavior of polycrystalline graphene

In this paper, we develop an efficient multiscale molecular dynamics (MD)–finite element (FE) modeling scheme capable of determining the elastic and fracture properties of polycrystalline graphene. The local elastic properties of a grain boundary (GB) connecting two adjacent graphene grains, with different lattice orientations, were first determined using MD simulations. In a two-dimensional medium, randomly distributed grains connected with GBs were then created using the Voronoi tessellation method. The constructed Voronoi diagrams were used to create FE models of the polycrystalline graphene, where the GBs were represented by interphase regions with their local properties determined using MD. The grains were modeled as pristine graphene and the accuracy of the polycrystalline FE model was validated with MD simulations of a geometrically identical polycrystalline graphene. The results reveal good agreement between MD and FE simulations. They further show that the elastic and fracture properties of polycrystalline graphene are greatly influenced by the grain size and the misorientation angle. They also indicate that the predicted elastic properties are in agreement with earlier reported experimental and MD results. We believe that this newly proposed multiscale scheme could be easily integrated into current design software to model graphene based nano- and micro-devices.     

Synthesis of hexagonal graphene on polycrystalline Cu foil from solid camphor by atmospheric pressure chemical vapor deposition

Understanding of graphene nucleation and growth on a metal substrate in chemical vapor deposition (CVD) process is critical to obtain high-quality single crystal graphene. Here, we report synthesis of individual hexagonal graphene and their large cluster on Cu foil using solid camphor as a carbon precursor in the atmospheric pressure CVD (AP-CVD) process. Optical and scanning electron microscopy studies show formation of hexagonal graphene crystals across the grain, grain boundaries and twin boundaries of polycrystalline Cu foil. Electron backscattered diffraction analysis is carried out before and after the growth to identify Cu grain orientation correlating with the graphene formation. The influence of growth conditions and Cu grain structure is explored on individual hexagonal graphene formation in the camphor-based AP-CVD process.     

Directed assembly of controlled-misorientation bicrystals

Grain boundaries play a vital role in determining materials behaviour, and the nature of these intercrystalline interfaces is dictated by chemical composition, processing history, and geometry (misorientation and inclination). The interrelation among these variables and material properties may be systematically studied in bicrystals. Conventional bicrystal fabrication offers control over these variables, but its ability to mimic grain boundaries in polycrystalline materials is ambiguous. Here we describe a novel solid-state process for rapidly generating intercrystalline interfaces with controlled geometry and chemistry, applicable to a broad range of materials. A fine-grained polycrystalline layer, contacted by two appropriately misoriented single-crystal seeds, is consumed by an epitaxial solid-state transformation until the directed growth fronts impinge. The seed misorientations establish the geometry of the resulting intercrystalline boundaries, and the composition of the sacrificial polycrystalline layer establishes the chemistry of the boundaries and their adjacent grains. Results from a challenging model system, titanium-doped sapphire, illustrate the viability of the directed assembly technique for preparing high-quality bicrystals in both twist and tilt configurations.     

Effect of Grain Boundary on the Wettability and Interfacial Morphology in the Molten Bi／Cu System

The wetting behavior of molten Bi on polycrystalline Cu substrate and single crystal Cu substrate was studied by the sessile drop method in the temperature range from 673 to 873K. At low temperature the wetting behaviors of molten Bi on both types of Cu substrate were similar. However, at high temperature, the equilibrium contact angle of polycrystalline Cu substrate was lower than that of single crystal Cu substrate, because the preferred dissolution of grain boundaries leads to a smaller liquid/solid interracial energy for polycrystalline Cu substrate. The formation mechanism of arrow-shaped Cu grains at the Bi/single crystal Cu interface is also discussed.     

High‐Quality Monolayer Graphene Synthesis on Pd Foils via the Suppression of Multilayer Growth at Grain Boundaries

The segregation of carbon from metals in which carbon is highly soluble, such as Ni (≈1.1 atom% at 1000 °C), is a typical method for graphene growth; this method differs from the surface‐catalyzed growth of graphene that occurs on other metals such as Cu (<0.04 atom%). It has not been established whether strictly monolayer graphene could be synthesized through the traditional chemical vapor deposition route on metals where carbon is highly soluble, such as Pd (≈3.5 atom%). In this work, this issue is investigated by suppressing the grain boundary segregation using a pretreatment comprising the annealing of the Pd foils; this method was motivated by the fact that the typical thick growths at the grain boundaries revealed that the grain boundary functions as the main segregation channel in polycrystalline metals. To evaluate the high crystallinity of the as‐grown graphene, detailed atomic‐scale characterization with scanning tunneling microscopy is performed.     

Long-range ordered single-crystal graphene on high-quality heteroepitaxial Ni thin films grown on MgO(111)

Large-area single crystal monolayer graphene is synthesized on Ni(111) thin films, which have flat terraces and no grain boundaries. The flat single-crystal Ni films are heteroepitaxially grown on MgO(111) substrates using a buffer layer technique. Low-energy electron diffraction and various spectroscopic methods reveal the long-range single crystallinity and uniform monolayer thickness of the graphene. When transferred onto an insulating wafer, continuous millimeter-scale single domain graphene is obtained.     

Prospects for nanowire-doped polycrystalline graphene films for ultratransparent, highly conductive electrodes

Traditional transparent conducting materials such as ITO are expensive, brittle, and inflexible. Although alternatives like networks of carbon nanotubes, polycrystalline graphene, and metallic nanowires have been proposed, the transparency-conductivity trade-off of these materials makes them inappropriate for broad range of applications. In this paper, we show that the conductivity of polycrystalline graphene is limited by high resistance grain boundaries. We demonstrate that a composite based on polycrystalline graphene and a subpercolating network of metallic nanowires offers a simple and effective route to reduced resistance while maintaining high transmittance. This new approach of "percolation-doping by nanowires" has the potential to beat the transparency-conductivity constraints of existing materials and may be suitable for broad applications in photovoltaics, flexible electronics, and displays.     

Synthesis and properties of nanocrystalline metals and alloys prepared by mechanical attrition

The grain size in powder samples can be reduced to nanometer scales during heavy cyclic mechanical deformation as produced in a standard ball mill. For pure bcc and hcp metals, intermetallic compounds and solid solutions, nanocrystalline materials can be synthesized at temperatures close to room temperature with a grain size ranging from 5 to 15 nm. During this process three different stages have been observed with (i) the deformation being localized in shear bands, (ii) formation of small angle grain boundaries separating the individual grains and (iii) formation of large angle grain boundaries with a completely random orientation of the nanosized grains. Thermal analysis of these samples reveals excess energies of up 40% of the heat of fusion and excess heat capacities of up to 20% in comparison to the undeformed state thus exceeding by far any values determined for conventional deformation processes and the energy of grain boundaries in fully equilibrated polycrystalline samples. These thermophysical data are in agreement with a theoretical model adopting a free volume approach for the grain boundaries based on the universal equation of state at negative pressure.     

Strain-induced conductance modulation in graphene grain boundary

Grain boundaries (GBs) are ubiquitous in polycrystalline graphene materials obtained by various growth methods. It has been shown previously that considerable electrical transport gap can be opened by grain boundaries. On the other hand, polycrystalline graphene with GBs is an atomically thin membrane that can sustain extraordinary amount of strain. Here, by using atomistic quantum transport numerical simulations, we examine modulation of electrical transport properties of graphene GBs. The results indicate the modulation of transport gap and electrical conductance strongly depends on the topological structure of the GB. The transport gap of certain GBs can be significantly widened by strain, which is useful for improving the on-off ratio in potential transistor applications and for applications as monolayer strain sensors.     

Graphene Single Crystals: Size and Morphology Engineering

Recently developed chemical vapor deposition (CVD) is considered as an effective way to large‐area and high‐quality graphene preparation due to its ultra‐low cost, high controllability, and high scalability. However, CVD‐grown graphene film is polycrystalline, and composed of numerous grains separated by grain boundaries, which are detrimental to graphene‐based electronics. Intensive investigations have been inspired on the controlled growth of graphene single crystals with the absence of intrinsic defects. As the two most concerned parameters, the size and morphology serve critical roles in affecting properties and understanding the growth mechanism of graphene crystals. Therefore, a precise tuning of the size and morphology will be of great significance in scale‐up graphene production and wide applications. Here, recent advances in the synthesis of graphene single crystals on both metals and dielectric substrates by the CVD method are discussed. The review mainly covers the size and morphology engineering of graphene single crystals. Furthermore, recent progress in the growth mechanism and device applications of graphene single crystals are presented. Finally, the opportunities and challenges are discussed.     

多晶材质电子结构及热电性能的模拟

发展了一种研究多晶体系电子态以及热电性质的计算机模拟方法。首先采用相场动力学方法模拟多晶材质图案，再利用其模型序参量构造晶界的势函数，用近自由电子近似构造体系的哈密顿量。求解薛定谔方程得到体系的本征态。通过电荷密度的分布研究电子的限域特征,分析模拟结果发现对于晶界为势垒的情况，电子的基态出现在最大晶粒中；而对于晶界为势阱的情况，电子更容易限域在多个晶粒交叉的晶界附近，由得到的本征能级和波函数可以计算出温差导致的电位差，即得到赛贝克系数随温度的变化。结果表明具有导电晶界的多晶体的赛贝克系数要高于具有导电晶粒的多晶体。     

Graphene induced surface reconstruction of cu

An atomic-scale study utilizing scanning tunneling microscopy (STM) in ultrahigh vacuum (UHV) is performed on large single crystalline graphene grains synthesized on Cu foil by a chemical vapor deposition (CVD) method. After thermal annealing, we observe the presence of periodic surface depressions (stripe patterns) that exhibit long-range order formed in the area of Cu covered by graphene. We suggest that the observed stripe pattern is a Cu surface reconstruction formed by partial dislocations (which appeared to be stair-rod-like) resulting from the strain induced by the graphene overlayer. In addition, these graphene grains are shown to be more decoupled from the Cu substrate compared to previously studied grains that exhibited Moiré patterns.     

Multiscale modeling of polycrystalline silicon

Polycrystalline solid is composed of randomly distributed grains and grain boundaries. The size of grains is usually in the nano/micro-scale. In this paper, the general micromorphic theory, as well as a specialized micromorphic theory for covalent and ionic crystals, is introduced. A statistical model for polycrystalline material is adopted. Each grain is modeled as crystallized solid by micromorphic theory, while the grain boundaries are modeled as in its amorphous phase by classical continuum theory. Size-dependent material properties of silicon are investigated. Finite element analysis of thermomechanical coupling phenomenon in polycrystalline silicon is performed and numerical results are presented and discussed.     

A progressive route for tailoring electrical transport in MoS<Subscript>2</Subscript>

Typically, molybdenum disulfide (MoS₂) synthesized by chemical vapor deposition (CVD) is polycrystalline; as a result, the scattering of charge carriers at grain boundaries can lead to performances lower than those observed in exfoliated single-crystal MoS₂. Until now, the electrical properties of grain boundaries have been indirectly studied without accurate knowledge of their location. Here, we present a technique to measure the electrical behavior of individual grain boundaries in CVD-grown MoS₂, imaged with the help of aligned liquid crystals. Unexpectedly, the electrical conductance decreased by three orders of magnitude for the grain boundaries with the lowest on/off ratio. Our study provides a useful technique to fabricate devices on a single-crystal area, using optimized growth conditions and device geometry. The photoresponse, studied within a MoS₂ single grain, showed that the device responsivity was comparable with that of the exfoliated MoS₂-based photodetectors.

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Mechanisms of interdiffusion in Pd-Cu thin film diffusion couples

Interdiffusion in sputter-deposited polycrystalline Pd-Cu bilayers (thickness of each sublayer: 50 nm) was studied in the temperature range 175 °C-250 °C by sputter-depth profiling in combination with Auger electron spectroscopy. X-ray diffraction and transmission electron microscopy investigations revealed that the layers are polycrystalline, consisting of columnar grains separated by grain boundaries oriented more or less perpendicularly to the film surface. Considerable diffusional intermixing occurred in the studied temperature range, which was accompanied by the sequential formation of (ordered) phases Cu₃Pd and CuPd. Volume interdiffusion coefficients were determined using the so-called ‘centre-gradient’ and ‘plateau-rise’ methods. Grain-boundary diffusion coefficients of Pd through Cu grain boundaries were determined by the Whipple-Le Claire method and grain-boundary diffusion coefficients of Cu through Pd grain boundaries were determined by the Hwang-Balluffi method. It was found that both volume and grain-boundary diffusion coefficients decreased roughly exponentially with annealing time. Activation energies were determined which pertain to the same (defect) microstructure at each temperature. The differences with literature results for macroscopic diffusion couples were discussed.