Abstract:We show that optical reflection microscopy is a reliable method to simultaneously locate and count graphene layers deposited on bulk, transparent substrates such as soda-lime glass. The visible contrast in optical reflection versus graphene layer number is resolvable on bulk substrates. A simple Fresnel theory based on the universal optical conductance of graphene layers accurately models optical reflection images taken at a wavelength of 550±5 nm. We directly count one to nine layers of graphene using reflect… Show more
Monolayer graphene exhibits extraordinary properties owing to the unique, regular arrangement of atoms in it. However, graphene is usually modified for specific applications, which introduces disorder. This article presents details of graphene structure, including sp2 hybridization, critical parameters of the unit cell, formation of σ and π bonds, electronic band structure, edge orientations, and the number and stacking order of graphene layers. We also discuss topics related to the creation and configuration of disorders in graphene, such as corrugations, topological defects, vacancies, adatoms and sp3-defects. The effects of these disorders on the electrical, thermal, chemical and mechanical properties of graphene are analyzed subsequently. Finally, we review previous work on the modulation of structural defects in graphene for specific applications.
Monolayer graphene exhibits extraordinary properties owing to the unique, regular arrangement of atoms in it. However, graphene is usually modified for specific applications, which introduces disorder. This article presents details of graphene structure, including sp2 hybridization, critical parameters of the unit cell, formation of σ and π bonds, electronic band structure, edge orientations, and the number and stacking order of graphene layers. We also discuss topics related to the creation and configuration of disorders in graphene, such as corrugations, topological defects, vacancies, adatoms and sp3-defects. The effects of these disorders on the electrical, thermal, chemical and mechanical properties of graphene are analyzed subsequently. Finally, we review previous work on the modulation of structural defects in graphene for specific applications.
“…As the dielectric substrate does not show any measurable nonlinear signal, the nonlinear contrast is very large and limited only by the noise from the detector: for a mono- layer C ¼ 1:7 Â 10 6 compared to C ¼ 0:08 for standard optical reflection microscopy [9]. (Enhanced imaging of carbon nanotubes using nonlinear optics has been recently observed in Ref.…”
Section: Prl 105 097401 (2010) P H Y S I C a L R E V I E W L E T T Ementioning
confidence: 99%
“…In Fig. 4 we compare the images measured by four-wave mixing to those obtained on the same flakes by the standard optical reflection microscopy [9,15]. The striking difference in the visibility of the flakes can be quantified in terms of the image contrast, defined as…”
Section: Prl 105 097401 (2010) P H Y S I C a L R E V I E W L E T T Ementioning
confidence: 99%
“…Optical microscopy is currently an important tool to find, align, and characterize graphene flakes [9,[14][15][16]. Although it is possible to see even one atom thick graphene with optical microscopy, in practice this technique is difficult to implement due to very low imaging contrasts.…”
Section: Prl 105 097401 (2010) P H Y S I C a L R E V I E W L E T T Ementioning
confidence: 99%
“…Prior to investigation in the nonlinear microscope, the layer thickness is estimated via contrast measurements under an optical microscope, using a method similar to Ref. [9]. To investigate the nonlinear response of graphene flakes, we employ the four-wave mixing technique [10].…”
We investigate the nonlinear optical properties of graphene flakes using four-wave mixing. The corresponding third-order optical susceptibility is found to be remarkably large and only weakly dependent on the wavelength in the near-infrared frequency range. The magnitude of the response is in good agreement with our calculations based on the nonlinear quantum response theory. DOI: 10.1103/PhysRevLett.105.097401 PACS numbers: 78.67.Wj, 42.65.Ky, 78.47.nj Graphene, a single sheet of carbon atoms in a hexagonal lattice, is the basic building block for all graphitic materials. Although it has been known as a theoretical concept for some time [1], a layer of graphene has only recently been isolated from bulk graphite and deposited on a dielectric substrate [2]. The great interest in studying graphene is driven by its linear, massless band structureand many unusual electrical, thermal, mechanical, and optical properties [3,4] [here the upper (lower) sign corresponds to the electron (hole) band, p is the quasimomentum, and V % 10 6 m=s is the Fermi velocity]. For example, the optical absorption of graphene has been shown to be wavelength independent ('2:3% per layer) in a broad range of optical frequencies [5][6][7]. Recently, it has been predicted that the linear dispersion described by Eq. (1) should lead to strongly nonlinear optical behavior at microwave and terahertz frequencies [8]. At higher, optical frequencies one can also expect an enhanced optical nonlinearity as, due to graphene's band structure, interband optical transitions occur at all photon energies. Here we report on the first observation of the coherent nonlinear optical response of graphene at visible and nearinfrared frequencies. We show that graphene has an exceptionally high nonlinear response, described by the effective nonlinear susceptibility j ð3Þ j $ 10 À7 esu (electrostatic units). This nonlinearity is shown to be essentially dispersionless over the wavelength range in our experiments (emission at e ' 760-840 nm). These results are in good agreement with predictions derived from nonlinear quantum response theory. The large optical nonlinearity of graphene can be used for exceptionally high-contrast imaging of single and multilayered graphene flakes.Single-and few-layer graphene samples are fabricated using the method of mechanical exfoliation [2] and deposited onto a 100 m thick glass cover slip. Prior to investigation in the nonlinear microscope, the layer thickness is estimated via contrast measurements under an optical microscope, using a method similar to Ref. [9]. To investigate the nonlinear response of graphene flakes, we employ the four-wave mixing technique [10]. This involves the generation of mixed optical frequency harmonics 2! 1 À ! 2 under irradiation by two monochromatic waves with the frequencies ! 1 and ! 2 .Figure 1(a) illustrates the principle of the method: two incident pump laser beams with wavelengths 1 (tunable from 670 nm to 980 nm) and 2 (1130 nm to 1450 nm) are focused collinearly onto a sample and mix together...
In the way of making graphene an industry‐friendly material, it must be mass‐produced with high‐quality and reduced cost over large areas. Assisted by machine‐learning techniques, rapid, nondestructive and accurate determination of large graphene sheets on SiO2/Si substrates has been made possible in recent years by the optical microscopy method. Optimization of the substrate to achieve the maximum contrast can further extend the application of the optical microscopy method for quality control of the mass‐produced graphene. Graphene/n2/n3three‐layer structures, where n2 and n3 are refractive indices, are routinely used for identifying the number of graphene layers by optical reflection microscopy. In this paper, two analytical equations are derived that can be easily used for high‐contrast optical imaging of graphene sheets without any need to resort to the cumbersome numerical methods. One of the equations is derived for choosing the best material with refractive index n2 that when coated on a substrate with refractive index n3, maximizes the optical contrast. The other equation is derived for finding the best thickness of the SiO2 layer in graphene/SiO2/Si structures, which are in common use for fabrication of graphene‐based devices. The results are implemented in a MATLAB GUI, see Supporting Information, to assist the users in using the equations.
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