Quantifying defects in graphene via Raman spectroscopy at different excitation energies.

We present a Raman study of Ar(+)-bombarded graphene samples with increasing ion doses. This allows us to have a controlled, increasing, amount of defects. We find that the ratio between the D and G peak intensities, for a given defect density, strongly depends on the laser excitation energy. We quantify this effect and present a simple equation for the determination of the point defect density in graphene via Raman spectroscopy for any visible excitation energy. We note that, for all excitations, the D to G intensity ratio reaches a maximum for an interdefect distance ∼3 nm. Thus, a given ratio could correspond to two different defect densities, above or below the maximum. The analysis of the G peak width and its dispersion with excitation energy solves this ambiguity.

Related papers:

title: Raman Spectrum of Graphite
abstract: Raman spectra are reported from single crystals of graphite and other graphite materials. Single crystals of graphite show one single line at 1575 cm−1. For the other materials like stress‐annealed pyrolitic graphite, commercial graphites, activated charcoal, lampblack, and vitreous carbon another line is detected at 1355 cm−1. The Raman intensity of this band is inversely proportional to the crystallite size and is caused by a breakdown of the k‐selection rule. The intensity of this band allows an estimate of the crystallite size in the surface layer of any carbon sample. Two in‐plane force constants are calculated from the frequencies.

title: Characterization of diamond films by Raman spectroscopy
abstract: As the technology for diamond film preparation by plasma-assisted CVD and related procedures has advanced, Raman spectroscopy has emerged as one of the principal characterization tools for diamond materials. Cubic diamond has a single Raman-active first order phonon mode at the center of the Brillouin zone. The presence of sharp Raman lines allows cubic diamond to be recognized against a background of graphitic carbon and also to characterize the graphitic carbon. Small shifts in the band wavenumber have been related to the stress state of deposited films. The effect is most noticeable in diamond films deposited on hard substrates such as alumina or carbides. The Raman line width varies with mode of preparation of the diamond and has been related to degree of structural order. The Raman spectrum of hexagonal diamond (lonsdaleite) is distinct from that of the cubic diamond and allows it to be recognized.

title: First- and second-order resonant Raman scattering in graphite.
abstract: We report a determination of the Raman-scattering efficiency for first- and second-order phonon lines in graphite. These measurements are of interest for the analysis of the Raman spectra of amorphous carbon films, materials of increasing technological interest.

title: General equation for the determination of the crystallite size La of nanographite by Raman spectroscopy
abstract: This work presents a systematic study of the ratio between the integrated intensities of the disorder-induced D and G Raman bands (ID∕IG) in nanographite samples with different crystallite sizes (La) and using different excitation laser energies. The crystallite size La of the nanographite samples was obtained both by x-ray diffraction using synchrotron radiation and directly from scanning tunneling microscopy images. A general equation for the determination of La using any laser energy in the visible range is obtained. Moreover, it is shown that ID∕IG is inversely proportional to the fourth power of the laser energy used in the experiment.

title: Measuring the absolute Raman cross section of nanographites as a function of laser energy and crystallite size
abstract: In this paper, the dependence of the differential Raman cross section of the D, G, D, and G bands of nanographites on the excitation laser energy and also on the crystallite size is reported. We show that G is proportional to the fourth power of the excitation laser energy El, as predicted by the Raman scattering theory. For the bands which arise from the double-resonance mechanism D, D, and G, the differential cross section does not depend on El, explaining the strong dependence of the ratio ID /IG on the excitation laser energy El used in the Raman experiment. The La dependence of D and D band differential cross sections is measured, confirming that the proportionality ID /IGLa originates from the strong dependence of D on the inverse of the crystallite size. In the G band case, the data show that its differential cross section increases with the increasing crystallite size La, following an opposite behavior when compared with the disorder induced D and D bands. An analysis on the dependence of the full width at half maximum of the D, G, D, and G bands on the crystallite size La of nanographites is performed, showing that the phonon lifetime is proportional to the crystallite size. The interest in the Raman spectrum of nanographite struc- tures increased recently with the report on the massless and relativistic properties of the conduction electrons in a single graphene layer responsible for the unusual properties of the quantum Hall effect in this system, 1-3 and the focus is justi- fied by the richness of Raman spectroscopy of graphitic sys- tems. The Raman spectrum of nanographites can be used to determine the in-plane size L a of the crystallites, 4-11 and the disorder-induced bands in the Raman spectrum of a graphite edge can be analyzed in order to identify the local atomic arrangement, defining if the edge has an armchair or zigzag shape. 12 Raman scattering can be used in order to determine if a nanographite sample presents stacking order or turbostratic structure. 13-16 In the case of graphene samples with a few layers, Raman spectroscopy gives a fingerprint for the determination of the number of stacked planes which compose the graphene piece. 17-19 Besides its many practical applications, Raman scattering in nanographitic systems is also a rich scientific subject, involving resonance conditions and defect-induced pro- cesses. 20-24 The intensities of the features present in the Raman spectrum of nanographites are known to be strongly dependent on their structural defect-related properties. The ratio between the intensities integrated areas of the disorder-induced D band 1350 cm �1 and the first-order allowed G band 1580 cm �1 is inversely proportional to the crystallite size La of nanographites, that is, ID /IG 1/ La. 4-8 Another remarkable characteristic in the Ra- man spectrum of nanographites is the strong dependence of the ratio ID /IG on the excitation laser energy El used in the Raman experiment, i.e., ID /IGE l . 7,8 These properties have attracted the attention of many theoretical and experimental groups to the theme. 9,10,20-28 Despite the large amount of experimental data available in the literature concerning the values of the ratio ID /IG, 6-11 the experimental study of the absolute intensities of the D and G Raman bands of nanographite systems is still missing. In this case, the origin of the dependence of the ratio ID /IG on the excitation laser energy could not be surely explained until now, since the dependence of the G and D band absolute intensities on El are both unknown. In this paper, an experi- mental study of the absolute Raman cross section of the main features in the Raman spectrum of nanographite samples with different crystallite sizes L a and using different values of excitation laser energies in the visible range is presented. The analysis includes the disorder-induced D band 29 1620 cm �1 and the two-phonon band associated with the D band, the so-called G band, occurring at 2700 cm �1 . 30,31 The samples have no stacking order and present well defined crystallite borders, being considered as prototypes of two-dimensional nanographite systems. 7,16 The Raman data obtained reveal the dependence of the absolute intensities D and G on the crystallite size and excitation laser energy El for nanographites, showing that the depen- dence of the ratio ID /IG on El is caused by a deviation of the D band intensity from the 4 dependence predicted by the Raman scattering theory. 32-40 The absolute differential cross section for the G band is also obtained, giving support to the analysis of the D band intensity dependence on the excitation laser energy and indicating that such a deviation from the 4 dependence occurs for those bands which originate from the double-resonance process. Moreover, this result indicates that the deviation of the D and D intensities from the 4 dependence cannot be associated with the electron-defect in- teraction matrix elements. The La dependence of D and D band differential cross sections is measured, confirming that the proportionality ID /IGL a originated from the strong de- pendence of D on the inverse of the crystallite size. The data allow us to establish a general equation giving the de- pendence of the ratio ID /IG on the excitation laser energy and crystallite size La. In contrast with the disorder-induced D and D bands, the results show that the differential cross

title: First- and second-order Raman scattering from finite-size crystals of graphite
abstract: First- and second-order Raman scattering from graphite has been studied. The second-order spectra of single crystals and of highly oriented pyrolytic graphite are continuous and exhibit several well-defined bands which can be attributed to features in the density of vibrational states as determined from current lattice-dynamics models. The density of states deduced from the lattice-dynamics model of Nicklow, Wakabayashi, and Smith provides the best replication of the second-order Raman spectrum, but is nevertheless somewhat deficient in this regard, and in need of improvement. The dependence of the first- and second-order graphite Raman spectra on crystallite size has also been studied for a series of samples with typical dimensions L/sub c/ and L/sub a/ as small as 30 A. With decreasing crystal size the features in the second-order spectrum broaden noticeably and additional broad features appear in both the first- and second-order spectra. The additional first- and second-order features are also attributed to structure in the vibrational density of states and arise from the wave-vector selection-rule relaxation that results from finite-crystal-size effects. Evidence is presented to demonstrate that the above described spectral features are intrinsic and not associated with impurity excitations.

title: Caracterisation de materiaux carbones par microspectrometrie Raman
abstract: A fast and non destructing characterization of the local state of a material may be achieved with the Raman microprobe, since spectra from areas as small as 1 square micrometer can be obtained and recorded. An obvious application of this new technique is in the field of composite materials. 
 
Characterization of the degree of gaphitization is one of the most important problems in the case of carbons: we have undertaken to investigate quantitatively the effects of gaphitization on the Raman spectrum. Various materials (both graphitizing and non graphitizing) were selected: pitch cokes, anthracene cokes, and saccharose cokes, fibers from PAN, and pyrocarbons deposited from methane at 2100°C. These carbons were subsequently heat-treated at temperatures up to 3000°C. Their degree of graphitization was first characterized by measurements of the mean diamagnetic susceptibility \gc and by X-ray determination of the average interlayer spacing d002. Raman spectra from all the samples were then recorded with the microprobe and four “graphitization indices” were selected: the frequency νE2g and the line-width Δν(E2g) of the E2g line  the ratio R of the intensities of the 1350 cm−1 and E2g lines , and the line-width Δν (2700) of the main line in the second order spectrum . A good correlation was found for all types of carbons between these indices and both \gc and d002 (Figs. 3–6). The values of νE2g and Δν(E2g) are easily determined with a good precision and their range of variation is sufficient: they may be used to characterize the extent of two-dimensional graphitic domains. The line width Δν(2700) is also easily measured and its wide range of variation, with a minimum value, is convenient for an estimation of both the two-dimensional growth of graphitic layers and the three dimensional ordering of the graphite lattice. The final stage of the graphitization process may be monitored by the splitting of 2700 cm−1 line . The complete “graphitization path” of a carbon is shown with the Δν(2700) and Δν(E2g) indices as an example in Fig. 8. 
 
An application of these findings is presented in the field of carbon-carbon composite materials, where the Raman spectra of the substrate and matrix can be obtained separately and compared . Several carbon fiber substrates were selected: FV (carbon felt from a viscose precursor), TC (carbon cloth from PAN heat-treated at 2000°C), FC (cloth from T 300 high strength PAN fibers), G (polycrystalline graphite). They were densified by vapor phase deposition (CVD) from methane at 1000–1100°C of two different matrices: LR (rough laminar) is a graphitizing pyrocarbon, while LL (smooth laminar) is non-graphitizing. The Raman spectra of the substrates and matrices were separately recorded with the Microprobe, in the as-deposited state (TD) and after heat-treatments (HIT) at 1900, 2100 and 2700°C. A comparison was made of the spectra of the matrix at increasing distances (0–8μm) from the fiber edge. The characteristic differences in the evolutions of each type of substrate  and pyrocarbon  are clearly shown. No evidence is found of any influence of either the matrix on the evolution of the substrate  or the substrate on the evolution of a non-graphitizing matrix. But there are indications that a non-graphizing substrate does inhibit slightly the evolution of a graphitizing pyrocarbon matrix at 2100 and 2700°C .

title: Comparative performance of X-ray diffraction and Raman microprobe techniques for the study of carbon materials
abstract: This paper compares the information provided by X-ray diffraction and Raman spectrometry in terms of the structural order in a wide set of carbon solids. A special emphasis is placed in checking the validity of the commonly used formula of Tuinstra and Koenig and establishing the magnitude of errors potentially derived from its application. For this, a total number of 45 carbon materials aiming to cover the whole spectrum of properties and applications of these solids were jointly characterised by X-ray diffraction and Raman microprobe spectrometry. The comparison of d 
 002 
 interlayer spacing and the ratio of D to G Raman band intensities allows one to conclude that both techniques are complementary rather than equivalent. The different types of factors affecting the D and G band intensities and widths are discussed, it being concluded that their contributions are difficult to separate. The overall conclusion is that Tuinstra and Koenig's formula is valid only as a first approximation to L 
 a 
 values, and that errors as high as 100% are possible, so that, whenever feasible, direct measurements by XRD are recommended.

title: Raman spectroscopic studies on well-defined carbonaceous materials of strong two-dimensional character
abstract: Using 514 nm radiation and a careful experimental protocol allowing us to make quantitative intensity analyses, we have examined the first- and second-order Raman spectra of five varieties of graphite. These include single-crystal graphite and highly oriented pyrolytic graphite as references, then two with a significant content of c-axis translation faults introduced through grinding and exfoliation, and a last sample which is purely turbostratic. We show that full c-axis stacking disorder results in a strong increase of the scattered E2g-mode intensity. We have further shown that even in those strongly disordered stacking sequences, but in which the AB sequence persists over only a few layers, the doublet around 2700 cm−1 is resolved. We argue against assigning the peak around 1355 cm−1 to “disorder,” as is so often done, but to the finite in-plane domain size as proposed a number of years ago; moreover, we suggest that this peak is a more sensitive probe of such small domains than is x-ray diffraction.

title: Interpretation of Raman spectra of disordered and amorphous carbon
abstract: The model and theoretical understanding of the Raman spectra in disordered and amorphous carbon are given. The nature of the G and D vibration modes in graphite is analyzed in terms of the resonant excitation of \ensuremath{\pi} states and the long-range polarizability of \ensuremath{\pi} bonding. Visible Raman data on disordered, amorphous, and diamondlike carbon are classified in a three-stage model to show the factors that control the position, intensity, and widths of the G and D peaks. It is shown that the visible Raman spectra depend formally on the configuration of the ${\mathrm{sp}}^{2}$ sites in ${\mathrm{sp}}^{2}$-bonded clusters. In cases where the ${\mathrm{sp}}^{2}$ clustering is controlled by the ${\mathrm{sp}}^{3}$ fraction, such as in as-deposited tetrahedral amorphous carbon (ta-C) or hydrogenated amorphous carbon (a-C:H) films, the visible Raman parameters can be used to derive the ${\mathrm{sp}}^{3}$ fraction.

title: Resonant Raman spectroscopy of disordered, amorphous, and diamondlike carbon
abstract: The Raman spectra of a wide range of disordered and amorphous carbons have been measured under excitation from 785 to 229 nm. The dispersion of peak positions and intensities with excitation wavelength is used to understand the nature of resonant Raman scattering in carbon and how to derive the local bonding and disorder from the Raman spectra. The spectra show three basic features, the D and G around 1600 and 1350 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for visible excitation and an extra T peak, for UV excitation, at \ensuremath{\sim}1060 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The G peak, due to the stretching motion of ${\mathrm{sp}}^{2}$ pairs, is a good indicator of disorder. It shows dispersion only in amorphous networks, with a dispersion rate proportional to the degree of disorder. Its shift well above 1600 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ under UV excitation indicates the presence of ${\mathrm{sp}}^{2}$ chains. The dispersion of the D peak is strongest in ordered carbons. It shows little dispersion in amorphous carbon, so that in UV excitation it becomes like a density-of-states feature of vibrations of ${\mathrm{sp}}^{2}$ ringlike structures. The intensity ratio $I(D)/I(G)$ falls with increasing UV excitation in all forms of carbon, with a faster decrease in more ordered carbons, so that it is generally small for UV excitation. The T peak, due to ${\mathrm{sp}}^{3}$ vibrations, only appears in UV Raman, lying around 1060 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for H-free carbons and around 980 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in hydrogenated carbons. In hydrogenated carbons, the ${\mathrm{sp}}^{3}{\mathrm{C}\ensuremath{-}\mathrm{H}}_{x}$ stretching modes around 2920 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ can be clearly detected for UV excitation. This assignment is confirmed by deuterium substitution.

title: Raman spectroscopy of hydrogenated amorphous carbons
abstract: We present a comprehensive multiwavelength Raman investigation of a variety of hydrogenated amorphous carbons $(a\text{\ensuremath{-}}\mathrm{C}:\mathrm{H})$, ranging from polymeric $a\text{\ensuremath{-}}\mathrm{C}:\mathrm{H}$ to diamond-like $a\text{\ensuremath{-}}\mathrm{C}:\mathrm{H}$ and ta-C:H, which allows us to derive values for their bonding, density, band gap, hydrogen content, and mechanical properties. The Raman spectra of $a\text{\ensuremath{-}}\mathrm{C}:\mathrm{Hs}$ show two different trends. In one case, the $G$ peak width increases with $G$ peak dispersion. In the second case, the opposite trend is found. In the first case, the Raman parameters vary with optical, structural, and mechanical properties in the same way as in hydrogen-free carbon films. In the second case, typical of polymeric $a\text{\ensuremath{-}}\mathrm{C}:\mathrm{H}$, the $G$ peak width correlates with the density, while the $G$ peak dispersion varies with the optical gap and hydrogen content. This allows a unified picture of bonding and disorder of all carbon films. UV Raman is particularly useful for $a\text{\ensuremath{-}}\mathrm{C}:\mathrm{Hs}$, as it gives clear measurements in the $D$ and $G$ peaks spectral region even for highly hydrogenated samples, for which the visible Raman spectra are overshadowed by photoluminescence. On the other hand, the slope of the photoluminescence background in visible Raman spectra can be used to estimate the H content. UV Raman measurements also allow the detection of $\mathrm{C}\mathrm{H}$ stretching vibrations.

title: Properties of amorphous carbon-silicon alloys deposited by a high plasma density source
abstract: The addition of silicon to hydrogenated amorphous carbon can have the advantageous effect of lowering the compressive stress, improving the thermal stability of its hydrogen, and maintaining a low friction coefficient up to high humidity. Most experiments to date have been on hydrogenated amorphous carbon–silicon alloys (a-C1−xSix:H) deposited by rf plasma enhanced chemical vapor deposition. This method gives alloys with sizeable hydrogen content and only moderate hardness. Here we use a high plasma density source known as the electron cyclotron wave resonance source to prepare films with higher sp3 content and lower hydrogen content. The composition and bonding in the alloys is determined by x-ray photoelectron spectroscopy, Rutherford backscattering, elastic recoil detection analysis, visible and ultraviolet (UV) Raman spectroscopy, infrared spectroscopy, and x-ray reflectivity. We find that it is possible to produce relatively hard, low stress, low friction, almost humidity insensitive a-C1−xSix:H allo...

title: Interpretation of infrared and Raman spectra of amorphous carbon nitrides
abstract: A general framework for the interpretation of infrared and Raman spectra of amorphous carbon nitrides is presented. In the first part of this paper we examine the infrared spectra. The peaks around 1350 and 1550 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ found in the infrared spectrum of amorphous carbon nitride or hydrogenated and hydrogen-free amorphous carbon are shown to originate from the large dynamic charge of the more delocalized \ensuremath{\pi} bonding which occurs in more ${\mathrm{sp}}^{2}$ bonded networks. The IR absorption decreases strongly when the \ensuremath{\pi} bonding becomes localized, as in tetrahedral amorphous carbon. Isotopic substitution is used to assign the modes to $\mathrm{C}=\mathrm{C}$ skeleton modes, even those modes around 1600 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ which become strongly enhanced by the presence of hydrogen. The infrared spectrum of carbon nitride may resemble the Raman spectrum at some excitation energy, but the infrared activity does not primarily result from nitrogen breaking the symmetry. In the second part we examine the Raman spectra. A general model is presented for the interpretation of the Raman spectra of amorphous carbon nitrides measured at any excitation energy. The Raman spectra can be explained in terms of an amorphous carbon based model, without need of extra peaks due to CN, NN, or NH modes. We classify amorphous carbon nitride films in four classes, according to the corresponding N-free film: $a\ensuremath{-}\mathrm{C}:\mathrm{N},$ $a\ensuremath{-}\mathrm{C}:\mathrm{H}:\mathrm{N},$ $ta\ensuremath{-}\mathrm{C}:\mathrm{H}:\mathrm{N},$ and $ta\ensuremath{-}\mathrm{C}:\mathrm{N}.$ We analyze a wide variety of samples for the four classes and present the Raman spectra as a function of N content, ${\mathrm{sp}}^{3}$ content, and band gap. In all cases, a multiwavelength Raman study allows a direct correlation of the Raman parameters with the N content, which is not generally possible for single wavelength excitation. The G peak dispersion emerges as a most informative parameter for Raman analysis. UV Raman enhances the ${\mathrm{sp}}^{1}$ CN peak, which is usually too faint to be seen in visible excitation. As for N-free samples, UV Raman also enhances the C-C ${\mathrm{sp}}^{3}$ bonds vibrations, allowing the ${\mathrm{sp}}^{3}$ content to be quantified.

title: Raman spectroscopy of single-wall carbon nanotubes and graphite irradiated by γ rays
abstract: Graphite and single-wall carbon nanotubes irradiated by γ rays of energy of 1.3 MeV were investigated by Raman spectroscopy. Irradiation generates defects in the lattice as confirmed by the increase of the intensity of the defect-induced D line in both materials. On the other hand, the intensity of the radial breathing mode of nanotubes is lowered. The intensity of the G line does not change for graphite but increases for carbon nanotubes. For the latter, this behavior cannot be explained by the defect-mediated double-resonance mechanism. Softening of the q=0 selection rule is suggested as a way to explain the results.

title: Length characterization of DNA-wrapped carbon nanotubes using Raman spectroscopy
abstract: A systematic resonance Raman study has been carried out on DNA-wrapped single walled carbon nanotubes (SWCNTs) of three different average lengths ⟨Ltube⟩ using seven different values of laser excitation energy Elaser. The dependence of the intensity ratio of the D-band and G-band Raman features (ID∕IG) on ⟨Ltube⟩ indicates that nanotube length can be used as an important structural parameter for Raman characterization. By systematically varying Elaser, the ratio ID∕IG is found to be much stronger for metallic than for semiconducting SWCNTs but appears to have the same functional dependence on Elaser and ⟨Ltube⟩ or crystallite size as does nanographite.

title: Modification of graphene properties due to electron-beam irradiation
abstract: The authors report micro-Raman investigation of changes in the single and bilayer graphene crystal lattice induced by the low and medium energy electron-beam irradiation (5–20 keV). It was found that the radiation exposures result in the appearance of the strong disorder D band around 1345 cm−1, indicating damage to the lattice. The D and G peak evolution with increasing radiation dose follows the amorphization trajectory, which suggests graphene’s transformation to the nanocrystalline and then to amorphous form. The results have important implications for graphene characterization and device fabrication, which rely on the electron microscopy and focused ion beam processing.

title: Quantifying ion-induced defects and Raman relaxation length in graphene
abstract: Raman scattering is used to study disorder in graphene subjected to low energy (90 eV) Ar+ ion bombardment. The evolution of the intensity ratio between the G band (1585 cm−1) and the disorder-induced D band (1345 cm−1) with ion dose is determined, providing a spectroscopy-based method to quantify the density of defects in graphene. This evolution can be fitted by a phenomenological model, which is in conceptual agreement with a well-established amorphization trajectory for graphitic materials. Our results show that the broadly used Tuinstra-Koenig relation should be limited to the measure of crystallite sizes, and allows extraction of the Raman relaxation length for the disorder-induced Raman scattering process.

title: Evolution of the Raman spectra from single-, few-, and many-layer graphene with increasing disorder
abstract: We report on the micro-Raman spectroscopy of monolayer, bilayer, trilayer, and many layers of graphene (graphite) bombarded by low-energy argon ions with different doses. The evolution of peak frequencies, intensities, linewidths, and areas of the main Raman bands of graphene is analyzed as function of the distance between defects and number of layers. We describe the disorder-induced frequency shifts and the increase in the linewidth of the Raman bands by means of a spatial-correlation model. Also, the evolution of the relative areas A{sub D}/A{sub G}, A{sub D}{sup '}/A{sub G}, and A{sub G}{sup '}/A{sub G} is described by a phenomenological model. The present results can be used to fully characterize disorder in graphene systems.

title: Raman spectrum of graphene and graphene layers.
abstract: Graphene is the two-dimensional building block for carbon allotropes of every other dimensionality. We show that its electronic structure is captured in its Raman spectrum that clearly evolves with the number of layers. The D peak second order changes in shape, width, and position for an increasing number of layers, reflecting the change in the electron bands via a double resonant Raman process. The G peak slightly down-shifts. This allows unambiguous, high-throughput, nondestructive identification of graphene layers, which is critically lacking in this emerging research area.

title: Raman spectroscopy of graphene edges.
abstract: Graphene edges are of particular interest since their orientation determines the electronic properties. Here we present a detailed Raman investigation of graphene flakes with edges oriented at different crystallographic directions. We also develop a real space theory for Raman scattering to analyze the general case of disordered edges. The position, width, and intensity of G and D peaks are studied as a function of the incident light polarization. The D-band is strongest for polarization parallel to the edge and minimum for perpendicular. Raman mapping shows that the D peak is localized in proximity of the edge. For ideal edges, the D peak is zero for zigzag orientation and large for armchair, allowing in principle the use of Raman spectroscopy as a sensitive tool for edge orientation. However, for real samples, the D to G ratio does not always show a significant dependence on edge orientation. Thus, even though edges can appear macroscopically smooth and oriented at well-defined angles, they are not necessarily microscopically ordered.

title: Raman scattering at pure graphene zigzag edges.
abstract: Theory has predicted rich and very distinct physics for graphene devices with boundaries that follow either the armchair or the zigzag crystallographic directions. A prerequisite to disclose this physics in experiment is to be able to produce devices with boundaries of pure chirality. Exfoliated flakes frequently exhibit corners with an odd multiple of 30°, which raised expectations that their boundaries follow pure zigzag and armchair directions. The predicted Raman behavior at such crystallographic edges however failed to confirm pure edge chirality. Here, we perform confocal Raman spectroscopy on hexagonal holes obtained after the anisotropic etching of prepatterned pits using carbothermal decomposition of SiO(2). The boundaries of the hexagonal holes are aligned along the zigzag crystallographic direction and leave hardly any signature in the Raman map indicating unprecedented purity of the edge chirality. This work offers the first opportunity to experimentally confirm the validity of the Raman theory for graphene edges.

title: Influence of the atomic structure on the Raman spectra of graphite edges.
abstract: A study of step edges in graphite with different atomic structures combining Raman spectroscopy and scanning probe microscopy is presented. The orientation of the carbon hexagons with respect to the edge axis, in the so-called armchair or zigzag arrangements, is distinguished spectroscopically by the intensity of a disorder-induced Raman peak. This effect is explained by applying the double resonance theory to a semi-infinite graphite crystal and by considering the one-dimensional character of the defect.

title: Double resonant raman scattering in graphite
abstract: We find that the electronic dispersion in graphite gives rise to double resonant Raman scattering for excitation energies up to 5 eV. As we show, the curious excitation-energy dependence of the graphite D mode is due to this double resonant process resolving a long-standing problem in the literature and invalidating recent attempts to explain this phenomenon. Our calculation for the D-mode frequency shift ( 60 cm(-1)/eV) agrees well with the experimental value.

title: Probing phonon dispersion relations of graphite by double resonance Raman scattering.
abstract: The phonon dispersion relations of graphite can be probed over a wide range of the Brillouin zone by double resonance Raman spectroscopy. The double resonance Raman process provides us with new assignments for the dispersive and nondispersive features observed in the Raman spectra of disordered graphite and carbon nanotubes, some features having been incorrectly assigned previously, or not assigned at all.

title: Geometrical approach for the study of G band in the Raman spectrum of monolayer graphene, bilayer graphene, and bulk graphite
abstract: In this paper, a geometrical approach is presented for the study of the double-resonance process, giving rise to the ${G}^{\ensuremath{'}}$ band in monolayer graphene, bilayer graphene, and bulk graphite. It is shown that there are four discrete peaks present in the ${G}^{\ensuremath{'}}$ band spectrum obtained from the stacking of two graphene layers, and these discrete peaks arise from the quantization of the first Brillouin zone caused by its finite size along the $c$ axis. Our analysis includes the study of the selection rules imposed on the electron-radiation and electron-phonon Hamiltonian interactions involving $\ensuremath{\pi}$ electrons near the $K$ point. We show that the anisotropy in the optical absorption (emission) near the $K$ point in the first Brillouin zone of graphite should be taken into account in order to gain an understanding of the selection rules for optical transitions in bilayer graphene. The validity of considering a linear dispersion for $\ensuremath{\pi}$ electrons along the $K\text{\ensuremath{-}}\ensuremath{\Gamma}$ direction is taken into consideration. We present four numerical equations, giving the dependencies of the frequencies of the four peaks composing the ${G}^{\ensuremath{'}}$ feature in the Raman spectrum of bilayer graphene on the laser excitation energy in the visible range. We also show that the two-peak shape of the ${G}^{\ensuremath{'}}$ band in the Raman spectrum of bulk graphite is in fact caused by the convolution of an infinite number of peaks.

title: Double-resonant Raman scattering in graphite: Interference effects, selection rules, and phonon dispersion
abstract: We present a comprehensive analysis of double-resonant Raman scattering in graphite and derive an analytical expression for the Raman cross section of the D mode in one dimension. The extension to two dimensions does not change the double-resonant phonon wave vectors. In the full integration of the Raman cross section, the contributions by phonons from exactly the K point cancel due to destructive interference. We calculate the D mode explicitly based on recent experimental data of the graphite phonon dispersion. Applying the selection rules, a mapping of additional disorder-induced and second-order Raman modes onto the Brillouin zone of graphite is obtained.

title: Calculation of the Raman G peak intensity in monolayer graphene: role of Ward identities
abstract: The absolute integrated intensity of the single-phonon Raman peak at 1580?cm?1 is calculated for a clean graphene monolayer. The resulting intensity is determined by the trigonal warping of the electronic bands and the anisotropy of the electron?phonon coupling, and is proportional to the second power of the excitation frequency. The main contribution to the process comes from the intermediate electron-hole states with typical energies of the order of the excitation frequency, contrary to what has been reported earlier. This occurs because of strong cancellations between different terms of the perturbation theory, analogous to Ward identities in quantum electrodynamics.

title: The influence of strong electron and hole doping on the Raman intensity of chemical vapor-deposition graphene.
abstract: Electrochemical charging has been applied to study the influence of doping on the intensity of the various Raman features observed in chemical vapor-deposition-grown graphene. Three different laser excitation energies have been used to probe the influence of the excitation energy on the behavior of both the G and G' modes regarding their dependence on doping. The intensities of both the G and G' modes exhibit a significant but different dependence on doping. While the intensity of the G' band monotonically decreases with increasing magnitude of the electrode potential (positive or negative), for the G band a more complex behavior has been found. The striking feature is an increase of the Raman intensity of the G mode at a high value of the positive electrode potential. Furthermore, the observed increase of the Raman intensity of the G mode is found to be a function of laser excitation energy.

title: Controlling inelastic light scattering quantum pathways in graphene
abstract: Inelastic light scattering spectroscopy has, since its first discovery, been an indispensable tool in physical science for probing elementary excitations, such as phonons, magnons and plasmons in both bulk and nanoscale materials. In the quantum mechanical picture of inelastic light scattering, incident photons first excite a set of intermediate electronic states, which then generate crystal elementary excitations and radiate energy-shifted photons. The intermediate electronic excitations therefore have a crucial role as quantum pathways in inelastic light scattering, and this is exemplified by resonant Raman scattering and Raman interference. The ability to control these excitation pathways can open up new opportunities to probe, manipulate and utilize inelastic light scattering. Here we achieve excitation pathway control in graphene with electrostatic doping. Our study reveals quantum interference between different Raman pathways in graphene: when some of the pathways are blocked, the one-phonon Raman intensity does not diminish, as commonly expected, but increases dramatically. This discovery sheds new light on the understanding of resonance Raman scattering in graphene. In addition, we demonstrate hot-electron luminescence in graphene as the Fermi energy approaches half the laser excitation energy. This hot luminescence, which is another form of inelastic light scattering, results from excited-state relaxation channels that become available only in heavily doped graphene.

title: Theory of double-resonant Raman spectra in graphene: Intensity and line shape of defect-induced and two-phonon bands
abstract: We calculate the double resonant (DR) Raman spectrum of graphene, and determine the lines associated to both phonon-defect processes, and two-phonons ones. Phonon and electronic dispersions reproduce calculations based on density functional theory corrected with GW. Electron-light, -phonon, and -defect scattering matrix elements and the electronic linewidth are explicitly calculated. Defect-induced processes are simulated by considering different kind of idealized defects. For an excitation energy of $\epsilon_L=2.4$ eV, the agreement with measurements is very good and calculations reproduce: the relative intensities among phonon-defect or among two-phonon lines; the measured small widths of the D, $D'$, 2D and $2D'$ lines; the line shapes; the presence of small intensity lines in the 1800, 2000 cm$^{-1}$ range. We determine how the spectra depend on the excitation energy, on the light polarization, on the electronic linewidth, on the kind of defects and on their concentration. According to the present findings, the intensity ratio between the $2D'$ and 2D lines can be used to determine experimentally the electronic linewidth. The intensity ratio between the $D$ and $D'$ lines depends on the kind of model defect, suggesting that this ratio could possibly be used to identify the kind of defects present in actual samples. Charged impurities outside the graphene plane provide an almost undetectable contribution to the Raman signal.

title: Defect scattering in graphene.
abstract: Irradiation of graphene on SiO2 by 500 eV Ne and He ions creates defects that cause intervalley scattering as is evident from a significant Raman D band intensity. The defect scattering gives a conductivity proportional to charge carrier density, with mobility decreasing as the inverse of the ion dose. The mobility decrease is 4 times larger than for a similar concentration of singly charged impurities. The minimum conductivity decreases proportional to the mobility to values lower than 4e(2)/pih, the minimum theoretical value for graphene free of intervalley scattering. Defected graphene shows a diverging resistivity at low temperature, indicating insulating behavior. The results are best explained by ion-induced formation of lattice defects that result in midgap states.

title: Boron nitride substrates for high-quality graphene electronics.
abstract: Graphene devices on standard SiO(2) substrates are highly disordered, exhibiting characteristics that are far inferior to the expected intrinsic properties of graphene. Although suspending the graphene above the substrate leads to a substantial improvement in device quality, this geometry imposes severe limitations on device architecture and functionality. There is a growing need, therefore, to identify dielectrics that allow a substrate-supported geometry while retaining the quality achieved with a suspended sample. Hexagonal boron nitride (h-BN) is an appealing substrate, because it has an atomically smooth surface that is relatively free of dangling bonds and charge traps. It also has a lattice constant similar to that of graphite, and has large optical phonon modes and a large electrical bandgap. Here we report the fabrication and characterization of high-quality exfoliated mono- and bilayer graphene devices on single-crystal h-BN substrates, by using a mechanical transfer process. Graphene devices on h-BN substrates have mobilities and carrier inhomogeneities that are almost an order of magnitude better than devices on SiO(2). These devices also show reduced roughness, intrinsic doping and chemical reactivity. The ability to assemble crystalline layered materials in a controlled way permits the fabrication of graphene devices on other promising dielectrics and allows for the realization of more complex graphene heterostructures.

title: Breakdown of the adiabatic Born-Oppenheimer approximation in graphene.
abstract: The adiabatic Born-Oppenheimer approximation (ABO) has been the standard ansatz to describe the interaction between electrons and nuclei since the early days of quantum mechanics. ABO assumes that the lighter electrons adjust adiabatically to the motion of the heavier nuclei, remaining at any time in their instantaneous ground state. ABO is well justified when the energy gap between ground and excited electronic states is larger than the energy scale of the nuclear motion. In metals, the gap is zero and phenomena beyond ABO (such as phonon-mediated superconductivity or phonon-induced renormalization of the electronic properties) occur. The use of ABO to describe lattice motion in metals is, therefore, questionable. In spite of this, ABO has proved effective for the accurate determination of chemical reactions, molecular dynamics and phonon frequencies in a wide range of metallic systems. Here, we show that ABO fails in graphene. Graphene, recently discovered in the free state, is a zero-bandgap semiconductor that becomes a metal if the Fermi energy is tuned applying a gate voltage, Vg. This induces a stiffening of the Raman G peak that cannot be described within ABO.

title: Phonon linewidths and electron-phonon coupling in graphite and nanotubes
abstract: We show that electron-phonon coupling EPC is the major source of broadening for the Raman G and G � peaks in graphite and metallic nanotubes. This allows us to directly measure the optical-phonon EPCs from the G and Glinewidths. The experimental EPCs compare extremely well with those from the density functional theory. We show that the EPC explains the difference in the Raman spectra of metallic and semiconducting nanotubes and their dependence on tube diameter. We dismiss the common assignment of the Gpeak in metallic nanotubes to a resonance between phonons and plasmons and we attribute it to a resonance between phonons and electron-hole pairs. For metallic tubes, we assign the G + and Gpeaks to TO circumferential