Showing papers on "Graphene published in 2007"
TL;DR: In this paper, a colloidal suspension of exfoliated graphene oxide sheets in water with hydrazine hydrate results in their aggregation and subsequent formation of a high surface area carbon material which consists of thin graphene-based sheets.
12,756 citations
TL;DR: In this paper, it was shown that micrometre-size sensors made from graphene are capable of detecting individual events when a gas molecule attaches to or detaches from graphene's surface.
Abstract: The ultimate aim of any detection method is to achieve such a level of sensitivity that individual quanta of a measured entity can be resolved. In the case of chemical sensors, the quantum is one atom or molecule. Such resolution has so far been beyond the reach of any detection technique, including solid-state gas sensors hailed for their exceptional sensitivity1, 2, 3, 4. The fundamental reason limiting the resolution of such sensors is fluctuations due to thermal motion of charges and defects5, which lead to intrinsic noise exceeding the sought-after signal from individual molecules, usually by many orders of magnitude. Here, we show that micrometre-size sensors made from graphene are capable of detecting individual events when a gas molecule attaches to or detaches from graphene's surface. The adsorbed molecules change the local carrier concentration in graphene one by one electron, which leads to step-like changes in resistance. The achieved sensitivity is due to the fact that graphene is an exceptionally low-noise material electronically, which makes it a promising candidate not only for chemical detectors but also for other applications where local probes sensitive to external charge, magnetic field or mechanical strain are required.
7,318 citations
TL;DR: In this article, the authors focus on the origin of the D and G peaks and the second order of D peak and show that the G and 2 D Raman peaks change in shape, position and relative intensity with number of graphene layers.
6,496 citations
TL;DR: Graphene oxide paper is reported, a free-standing carbon-based membrane material made by flow-directed assembly of individual graphene oxide sheets that outperforms many other paper-like materials in stiffness and strength.
Abstract: Free-standing paper-like or foil-like materials are an integral part of our technological society. Their uses include protective layers, chemical filters, components of electrical batteries or supercapacitors, adhesive layers, electronic or optoelectronic components, and molecular storage. Inorganic 'paper-like' materials based on nanoscale components such as exfoliated vermiculite or mica platelets have been intensively studied and commercialized as protective coatings, high-temperature binders, dielectric barriers and gas-impermeable membranes. Carbon-based flexible graphite foils composed of stacked platelets of expanded graphite have long been used in packing and gasketing applications because of their chemical resistivity against most media, superior sealability over a wide temperature range, and impermeability to fluids. The discovery of carbon nanotubes brought about bucky paper, which displays excellent mechanical and electrical properties that make it potentially suitable for fuel cell and structural composite applications. Here we report the preparation and characterization of graphene oxide paper, a free-standing carbon-based membrane material made by flow-directed assembly of individual graphene oxide sheets. This new material outperforms many other paper-like materials in stiffness and strength. Its combination of macroscopic flexibility and stiffness is a result of a unique interlocking-tile arrangement of the nanoscale graphene oxide sheets.
5,117 citations
TL;DR: It is found 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.
Abstract: 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.
4,969 citations
TL;DR: These studies by transmission electron microscopy reveal that individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or air are not perfectly flat: they exhibit intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations reach 1 nm.
Abstract: Graphene — a recently isolated one-atom-thick layered form of graphite — is a hot topic in the materials science and condensed matter physics communities, where it is proving to be a popular model system for investigation. An experiment involving individual graphene sheets suspended over a microscale scaffold has allowed structure determination using transmission electron microscopy and diffraction, perhaps paving the way towards an answer to the question of why graphene can exist at all. The 'two-dimensional' sheets, it seems, are not flat, but wavy. The undulations are less pronounced in a two-layer system, and disappear in multilayer samples. Learning more about this 'waviness' may reveal what makes these extremely thin carbon membranes so stable. Investigations of individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or in air reveal that the membranes are not perfectly flat, but exhibit an intrinsic waviness, such that the surface normal varies by several degrees, and out-of-plane deformations reach 1 nm. The recent discovery of graphene has sparked much interest, thus far focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particles1,2,3. However, the physical structure of graphene—a single layer of carbon atoms densely packed in a honeycomb crystal lattice—is also puzzling. On the one hand, graphene appears to be a strictly two-dimensional material, exhibiting such a high crystal quality that electrons can travel submicrometre distances without scattering. On the other hand, perfect two-dimensional crystals cannot exist in the free state, according to both theory and experiment4,5,6,7,8,9. This incompatibility can be avoided by arguing that all the graphene structures studied so far were an integral part of larger three-dimensional structures, either supported by a bulk substrate or embedded in a three-dimensional matrix1,2,3,9,10,11,12. Here we report on individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or air. These membranes are only one atom thick, yet they still display long-range crystalline order. However, our studies by transmission electron microscopy also reveal that these suspended graphene sheets are not perfectly flat: they exhibit intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations reach 1 nm. The atomically thin single-crystal membranes offer ample scope for fundamental research and new technologies, whereas the observed corrugations in the third dimension may provide subtle reasons for the stability of two-dimensional crystals13,14,15.
4,653 citations
TL;DR: In this article, a detailed analysis of the thermal expansion mechanism of graphite oxide to produce functionalized graphene sheets is provided, where it is shown that the decomposition rate of the epoxy and hydroxyl sites exceeds the diffusion rate of evolved gases, yielding pressures that exceed the van der Waals forces holding the graphene sheets together.
Abstract: A detailed analysis of the thermal expansion mechanism of graphite oxide to produce functionalized graphene sheets is provided. Exfoliation takes place when the decomposition rate of the epoxy and hydroxyl sites of graphite oxide exceeds the diffusion rate of the evolved gases, thus yielding pressures that exceed the van der Waals forces holding the graphene sheets together. A comparison of the Arrhenius dependence of the reaction rate against the calculated diffusion coefficient based on Knudsen diffusion suggests a critical temperature of 550 °C which must be exceeded for exfoliation to occur. As a result of their wrinkled nature, the functionalized and defective graphene sheets do not collapse back to graphite oxide but are highly agglomerated. After dispersion by ultrasonication in appropriate solvents, statistical analysis by atomic force microscopy shows that 80% of the observed flakes are single sheets.
3,340 citations
TL;DR: The thinnest resonator consists of a single suspended layer of atoms and represents the ultimate limit of two-dimensional nanoelectromechanical systems and is demonstrated down to 8 × 10–4 electrons per root hertz.
Abstract: Nanoelectromechanical systems were fabricated from single- and multilayer graphene sheets by mechanically exfoliating thin sheets from graphite over trenches in silicon oxide. Vibrations with fundamental resonant frequencies in the megahertz range are actuated either optically or electrically and detected optically by interferometry. We demonstrate room-temperature charge sensitivities down to 8 × 10 –4 electrons per root hertz. The thinnest resonator consists of a single suspended layer of atoms and represents the ultimate limit of two-dimensional nanoelectromechanical systems.
2,769 citations
Journal Article•
TL;DR: It is shown that in graphene, in a single atomic layer of carbon, the QHE can be measured reliably even at room temperature, which makes possible QHE resistance standards becoming available to a broader community, outside a few national institutions.
Abstract: The quantum Hall effect (QHE), one example of a quantum phenomenon that occurs on a truly macroscopic scale, has attracted intense interest since its discovery in 1980 and has helped elucidate many important aspects of quantum physics. It has also led to the establishment of a new metrological standard, the resistance quantum. Disappointingly, however, the QHE has been observed only at liquid-helium temperatures. We show that in graphene, in a single atomic layer of carbon, the QHE can be measured reliably even at room temperature, which makes possible QHE resistance standards becoming available to a broader community, outside a few national institutions.
2,404 citations
TL;DR: Comparison of multilayered sheets revealed that the conductivity of the undermost layer is reduced by a factor of more than 2 as a consequence of the interaction with the Si/SiO2 substrate.
Abstract: Individual graphene oxide sheets subjected to chemical reduction were electrically characterized as a function of temperature and external electric fields. The fully reduced monolayers exhibited conductivities ranging between 0.05 and 2 S/cm and field effect mobilities of 2−200 cm2/Vs at room temperature. Temperature-dependent electrical measurements and Raman spectroscopic investigations suggest that charge transport occurs via variable range hopping between intact graphene islands with sizes on the order of several nanometers. Furthermore, the comparative study of multilayered sheets revealed that the conductivity of the undermost layer is reduced by a factor of more than 2 as a consequence of the interaction with the Si/SiO2 substrate.
2,322 citations
TL;DR: In this article, the authors used a scanning confocal approach to collect spectral data with spatial resolution, which allows them to directly compare Raman images with scanning force micrographs.
Abstract: We present Raman spectroscopy measurements on single- and few-layer graphene flakes. By using a scanning confocal approach, we collect spectral data with spatial resolution, which allows us to directly compare Raman images with scanning force micrographs. Single-layer graphene can be distinguished from double- and few-layer by the width of the D' line: the single peak for single-layer graphene splits into different peaks for the double-layer. These findings are explained using the double-resonant Raman model based on ab initio calculations of the electronic structure and of the phonon dispersion. We investigate the D line intensity and find no defects within the flake. A finite D line response originating from the edges can be attributed either to defects or to the breakdown of translational symmetry.
IBM1
TL;DR: This work reviews the progress that has been made with carbon nanotubes and, more recently, graphene layers and nanoribbons and suggests that it could be possible to make both electronic and optoelectronic devices from the same material.
Abstract: The semiconductor industry has been able to improve the performance of electronic systems for more than four decades by making ever-smaller devices. However, this approach will soon encounter both scientific and technical limits, which is why the industry is exploring a number of alternative device technologies. Here we review the progress that has been made with carbon nanotubes and, more recently, graphene layers and nanoribbons. Field-effect transistors based on semiconductor nanotubes and graphene nanoribbons have already been demonstrated, and metallic nanotubes could be used as high-performance interconnects. Moreover, owing to the excellent optical properties of nanotubes it could be possible to make both electronic and optoelectronic devices from the same material.
TL;DR: It is shown that when graphene is epitaxially grown on SiC substrate, a gap of approximately 0.26 eV is produced and it is proposed that the origin of this gap is the breaking of sublattice symmetry owing to the graphene-substrate interaction.
Abstract: Graphene has shown great application potential as the hostmaterial for next-generation electronic devices. However, despite itsintriguing properties, one of the biggest hurdles for graphene to beuseful as an electronic material is the lack of an energy gap in itselectronic spectra. This, for example, prevents the use of graphene inmaking transistors. Although several proposals have been made to open agap in graphene's electronic spectra, they all require complexengineering of the graphene layer. Here, we show that when graphene isepitaxially grown on SiC substrate, a gap of ~;0.26 eV is produced. Thisgap decreases as the sample thickness increases and eventually approacheszero when the number of layers exceeds four. We propose that the originof this gap is the breaking of sublattice symmetry owing to thegraphene-substrate interaction. We believe that our results highlight apromising direction for band gap engineering of graphene.
TL;DR: The observation of spin transport, as well as Larmor spin precession, over micrometre-scale distances in single graphene layers is reported, indicating that spin coherence extends underneath all of the contacts.
Abstract: Electronic transport in single or a few layers of graphene is the subject of intense interest at present. The specific band structure of graphene, with its unique valley structure and Dirac neutrality point separating hole states from electron states, has led to the observation of new electronic transport phenomena such as anomalously quantized Hall effects, absence of weak localization and the existence of a minimum conductivity. In addition to dissipative transport, supercurrent transport has also been observed. Graphene might also be a promising material for spintronics and related applications, such as the realization of spin qubits, owing to the low intrinsic spin orbit interaction, as well as the low hyperfine interaction of the electron spins with the carbon nuclei. Here we report the observation of spin transport, as well as Larmor spin precession, over micrometre-scale distances in single graphene layers. The 'non-local' spin valve geometry was used in these experiments, employing four-terminal contact geometries with ferromagnetic cobalt electrodes making contact with the graphene sheet through a thin oxide layer. We observe clear bipolar (changing from positive to negative sign) spin signals that reflect the magnetization direction of all four electrodes, indicating that spin coherence extends underneath all of the contacts. No significant changes in the spin signals occur between 4.2 K, 77 K and room temperature. We extract a spin relaxation length between 1.5 and 2 mum at room temperature, only weakly dependent on charge density. The spin polarization of the ferromagnetic contacts is calculated from the measurements to be around ten per cent.
TL;DR: In this article, the authors study the visibility of graphene and show that it depends strongly on both thickness of SiO2 and light wavelength, and they find that ≈100nm is the most suitable wavelength for its visual detection.
Abstract: Microfabrication of graphene devices used in many experimental studies currently relies on the fact that graphene crystallites can be visualized using optical microscopy if prepared on top of Si wafers with a certain thickness of SiO2. The authors study graphene’s visibility and show that it depends strongly on both thickness of SiO2 and light wavelength. They have found that by using monochromatic illumination, graphene can be isolated for any SiO2 thickness, albeit 300nm (the current standard) and, especially, ≈100nm are most suitable for its visual detection. By using a Fresnel-law-based model, they quantitatively describe the experimental data.
TL;DR: Electric conductivity measurements indicate a 10000-fold increase in conductivity after chemical reduction to graphene, and temperature-dependent conductivity indicates that the graphene-like sheets exhibit semiconducting behavior.
Abstract: Oxidation of graphite produces graphite oxide, which is dispersible in water as individual platelets. After deposition onto Si/SiO2 substrates, chemical reduction produces graphene sheets. Electrical conductivity measurements indicate a 10000-fold increase in conductivity after chemical reduction to graphene. Tapping mode atomic force microscopy measurements show one to two layer graphene steps. Electrodes patterned onto a reduced graphite oxide film demonstrate a field effect response when the gate voltage is varied from +15 to −15 V. Temperature-dependent conductivity indicates that the graphene-like sheets exhibit semiconducting behavior.
TL;DR: In this paper, the stability of graphane was predicted based on first-principles total energy calculations, which is a fully saturated two-dimensional hydrocarbon derived from a single graphene sheet with formula CH.
Abstract: We predict the stability of an extended two-dimensional hydrocarbon on the basis of first-principles total-energy calculations. The compound that we call graphane is a fully saturated hydrocarbon derived from a single graphene sheet with formula CH. All of the carbon atoms are in $s{p}^{3}$ hybridization forming a hexagonal network and the hydrogen atoms are bonded to carbon on both sides of the plane in an alternating manner. Graphane is predicted to be stable with a binding energy comparable to other hydrocarbons such as benzene, cyclohexane, and polyethylene. We discuss possible routes for synthesizing graphane and potential applications as a hydrogen storage material and in two-dimensional electronics.
TL;DR: In this article, the authors show that when epitaxially grown on the SiC substrate, a gap of ~ 0.26 is produced and this gap decreases as the sample thickness increases and eventually approaches zero when the number of layers exceeds four.
Abstract: Graphene has shown great application potentials as the host material for next generation electronic devices. However, despite its intriguing properties, one of the biggest hurdles for graphene to be useful as an electronic material is its lacking of an energy gap in the electronic spectra. This, for example, prevents the use of graphene in making transistors. Although several proposals have been made to open a gap in graphene's electronic spectra, they all require complex engineering of the graphene layer. Here we show that when graphene is epitaxially grown on the SiC substrate, a gap of ~ 0.26 is produced. This gap decreases as the sample thickness increases and eventually approaches zero when the number of layers exceeds four. We propose that the origin of this gap is the breaking of sublattice symmetry owing to the graphene-substrate interaction. We believe our results highlight a promising direction for band gap engineering of graphene.
TL;DR: It is demonstrated that the electronic gap of a graphene bilayer can be controlled externally by applying a gate bias and can be changed from zero to midinfrared energies by using fields of less, approximately < 1 V/nm, below the electric breakdown of SiO2.
Abstract: We demonstrate that the electronic gap of a graphene bilayer can be controlled externally by applying a gate bias. From the magnetotransport data (Shubnikov-de Haas measurements of the cyclotron mass), and using a tight-binding model, we extract the value of the gap as a function of the electronic density. We show that the gap can be changed from zero to midinfrared energies by using fields of less, approximately < 1 V/nm, below the electric breakdown of SiO2. The opening of a gap is clearly seen in the quantum Hall regime.
IBM1
TL;DR: In this article, the electrical properties of nano-ribboned field effect transistor (FE transistor) devices were investigated as a function of ribbon width, and it was shown that the resistivity of a ribbon increases as its width decreases, indicating the impact of edge states.
Abstract: We have fabricated graphene nano-ribbon field-effect transistor devices and investigated their electrical properties as a function of ribbon width. Our experiments show that the resistivity of a ribbon increases as its width decreases, indicating the impact of edge states. Analysis of temperature-dependent measurements suggests a finite quantum confinement gap opening in narrow ribbons. The electrical current noise of the graphene ribbon devices at low frequency is found to be dominated by the 1/f noise.
TL;DR: Atomic structures and nanoscale morphology of graphene-based electronic devices are revealed for the first time and a strong spatially dependent perturbation is revealed which breaks the hexagonal lattice symmetry of the graphitic lattice.
Abstract: We employ scanning probe microscopy to reveal atomic structures and nanoscale morphology of graphene-based electronic devices (i.e., a graphene sheet supported by an insulating silicon dioxide substrate) for the first time. Atomic resolution scanning tunneling microscopy images reveal the presence of a strong spatially dependent perturbation, which breaks the hexagonal lattice symmetry of the graphitic lattice. Structural corrugations of the graphene sheet partially conform to the underlying silicon oxide substrate. These effects are obscured or modified on graphene devices processed with normal lithographic methods, as they are covered with a layer of photoresist residue. We enable our experiments by a novel cleaning process to produce atomically clean graphene sheets.
TL;DR: In this paper, the authors studied the visibility of graphene and showed that it depends strongly on both thickness of silicon dioxide and light wavelength, and they used a Fresnel-law-based model to quantitatively describe the experimental data without any fitting parameters.
Abstract: Microfabrication of graphene devices used in many experimental studies currently relies on the fact that graphene crystallites can be visualized using optical microscopy if prepared on top of silicon wafers with a certain thickness of silicon dioxide. We study graphene's visibility and show that it depends strongly on both thickness of silicon dioxide and light wavelength. We have found that by using monochromatic illumination, graphene can be isolated for any silicon dioxide thickness, albeit 300 nm (the current standard) and, especially, approx. 100 nm are most suitable for its visual detection. By using a Fresnel-law-based model, we quantitatively describe the experimental data without any fitting parameters.
TL;DR: In this article, the electronic structure of a graphene sheet on top of a hexagonal boron nitride (h-BN) substrate was determined using ab initio density functional calculations.
Abstract: We determine the electronic structure of a graphene sheet on top of a lattice-matched hexagonal boron nitride (h-BN) substrate using ab initio density functional calculations. The most stable configuration has one carbon atom on top of a boron atom, and the other centered above a BN ring. The resulting inequivalence of the two carbon sites leads to the opening of a gap of 53 meV at the Dirac points of graphene and to finite masses for the Dirac fermions. Alternative orientations of the graphene sheet on the BN substrate generate similar band gaps and masses. The band gap induced by the BN surface can greatly improve room temperature pinch-off characteristics of graphene-based field effect transistors.
TL;DR: In this article, the authors propose a voltage-sensitive voltage-controlled voltage gate to the point contact region of a ballistic point contact with zigzag edges, where the polarity can be inverted by local application of a gate voltage to the region.
Abstract: The potential of graphene for carbon electronics rests on the possibilities offered by its unusual band structure to create devices that have no analogue in silicon-based electronics1,2. Conduction and valence bands in graphene form conically shaped valleys, touching at a point called the Dirac point. There are two inequivalent Dirac points in the Brillouin zone, related by time-reversal symmetry. Intervalley scattering is suppressed in pure samples3,4,5. The independence and degeneracy of the valley degree of freedom suggests that it might be used to control an electronic device6, in much the same way as the electron spin is used in spintronics7 or quantum computing8. A key ingredient for ‘valleytronics’ would be a controllable way of occupying a single valley in graphene, thereby producing a valley polarization. Here we propose such a valley filter, based on a ballistic point contact with zigzag edges. The polarity can be inverted by local application of a gate voltage to the point contact region. Two valley filters in series may function as an electrostatically controlled valley valve, representing a zero-magnetic-field counterpart to the familiar spin valve.
TL;DR: In this paper, the authors address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon and find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of flexible membranes.
Abstract: The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.
TL;DR: A graphene bilayer with a relative small angle rotation between the layers is considered and it is found that the low energy dispersion is linear, as in a single layer, but the Fermi velocity can be significantly smaller than the single-layer value.
Abstract: We consider a graphene bilayer with a relative small angle rotation between the layers--a stacking defect often seen in the surface of graphite--and calculate the electronic structure near zero energy in a continuum approximation. Contrary to what happens in an AB stacked bilayer and in accord with observations in epitaxial graphene, we find: (a) the low energy dispersion is linear, as in a single layer, but the Fermi velocity can be significantly smaller than the single-layer value; (b) an external electric field, perpendicular to the layers, does not open an electronic gap.
TL;DR: In this article, the magnetism in graphene induced by single carbon atom defects has been studied from first principles and the itinerant magnetism due to the defect-induced extended states has been observed.
Abstract: We study from first principles the magnetism in graphene induced by single carbon atom defects For two types of defects considered in our study, the hydrogen chemisorption defect and the vacancy defect, the itinerant magnetism due to the defect-induced extended states has been observed Calculated magnetic moments are equal to 1µB per hydrogen chemisorption defect and 112–153µB per vacancy defect depending on the defect concentration The coupling between the magnetic moments is either ferromagnetic or antiferromagnetic, depending on whether the defects correspond to the same or to different hexagonal sublattices of the graphene lattice, respectively The relevance of itinerant magnetism in graphene to the high-TC magnetic ordering is discussed
TL;DR: It is argued that the experimentally observed saturation of conductivity at low density arises from the charged impurity induced inhomogeneity in the graphene carrier density which becomes severe for n less, similarn(i) approximately 10(12) cm(-2).
Abstract: Carrier transport in gated 2D graphene monolayers is considered in the presence of scattering by random charged impurity centers with density n(i). Excellent quantitative agreement is obtained (for carrier density n>10(12) cm(-2)) with existing experimental data. The conductivity scales linearly with n/n(i) in the theory. We explain the experimentally observed asymmetry between electron and hole conductivities, and the high-density saturation of conductivity for the highest mobility samples. We argue that the experimentally observed saturation of conductivity at low density arises from the charged impurity induced inhomogeneity in the graphene carrier density which becomes severe for n less, similarn(i) approximately 10(12) cm(-2).
TL;DR: Two easy-to-use methods to determine the number of graphene layers based on contrast spectra are provided: a graphic method and an analytical method, which show that the refractive index of graphene is different from that of graphite.
Abstract: We have clearly discriminated the single-, bilayer-, and multiple-layer graphene (<10 layers) on Si substrate with a 285 nm SiO2 capping layer by using contrast spectra, which were generated from the reflection light of a white light source. Calculations based on Fresnel's law are in excellent agreement with the experimental results (deviation 2%). The contrast image shows the reliability and efficiency of this new technique. The contrast spectrum is a fast, nondestructive, easy to be carried out, and unambiguous way to identify the numbers of layers of graphene sheet. We provide two easy-to-use methods to determine the number of graphene layers based on contrast spectra: a graphic method and an analytical method. We also show that the refractive index of graphene is different from that of graphite. The results are compared with those obtained using Raman spectroscopy.
TL;DR: In this article, the Young's modulus of stacks of graphene sheets suspended over photolithographically defined trenches in silicon dioxide was measured using an atomic force microscope, with measured spring constants scaling as expected with the dimensions of the suspended section, ranging from 1to5N∕m.
Abstract: Using an atomic force microscope, we measured effective spring constants of stacks of graphene sheets (less than 5) suspended over photolithographically defined trenches in silicon dioxide. Measurements were made on layered graphene sheets of thicknesses between 2 and 8nm, with measured spring constants scaling as expected with the dimensions of the suspended section, ranging from 1to5N∕m. When our data are fitted to a model for doubly clamped beams under tension, we extract a Young’s modulus of 0.5TPa, compared to 1TPa for bulk graphite along the basal plane, and tensions on the order of 10−7N.