We report phonon renormalization in bilayer graphene as a function of doping. The Raman G peak stiffens and sharpens for both electron and hole doping as a result of the nonadiabatic Kohn anomaly at the Gamma point. The bilayer has two conduction and valence subbands, with splitting dependent on the interlayer coupling. This gives a change of slope in the variation of G peak position with doping which allows a direct measurement of the interlayer coupling strength.

The introduction of computer simulations has promoted significant design optimisation and cost reduction in many fields of engineering. Nowadays, atomistic modelling of materials is becoming time and cost effective not only for pure research, but also for cutting-edge engineering applications. In this paper we present an overview of atomistic materials modelling, with particular emphasis on Quantum Mechanical (QM) simulations based on the Density Functional Theory (DFT). As examples of applications to ceramics, we report about computational investigations of the oxidation of metal surfaces, of the chemical reactivity of biomaterials, of the reinforcement mechanisms in nano-composites, and of graphitisation of SiC.

We present a kinetic transport model describing the transport of charge carriers and optical phonons in graphene. The Boltzmann transport equations are solved numerically by a set of deterministic methods. Our simulations provide a deep insight into the coupled dynamics of electrons and phonons including features unique to graphene. We demonstrate the importance of such effects when turning to the high field transport regime.

Raman spectroscopy is a fast and nondestructive means to characterize graphene samples. In particular, the Raman spectra are strongly affected by doping. While the resulting change in position and width of the G peak can be explained by the nonadiabatic Kohn anomaly at Gamma, the significant doping dependence of the 2D peak intensity has not been understood yet. Here we show that this is due to a combination of electron-phonon and electron-electron scattering. Under full resonance, the photogenerated electron-hole pairs can scatter not just with phonons but also with doping-induced electrons or holes, and this changes the intensity. We explain the doping dependence and show how it can be used to determine the corresponding electron-phonon coupling. This is higher than predicted by density-functional theory, as a consequence of renormalization by Coulomb interactions.

Graphene nanoribbons are the counterpart of carbon nanotubes in graphene-based nanoelectronics. We investigate the electronic properties of chemically modified ribbons by means of density functional theory. We observe that chemical modifications of zigzag ribbons can break the spin degeneracy. This promotes the onset of a semiconducting-metal transition, or of a half-semiconducting state, with the two spin channels having a different band gap, or of a spin-polarized half-semiconducting state, where the spins in the valence and conduction bands are oppositely polarized. Edge functionalization of armchair ribbons gives electronic states a few eV away from the Fermi level and does not significantly affect their band gap. N and B produce different effects, depending on the position of the substitutional site. In particular, edge substitutions at low density do not significantly alter the band gap, while bulk substitution promotes the onset of semiconducting-metal transitions. Pyridinelike defects induce a semiconducting-metal transition.

We demonstrate n- and p-type field-effect transistors based on Si nanowires (SiNWs) implanted with P and B at fluences as high as 10(15) cm(-2). Contrary to what would happen in bulk Si for similar fluences, in SiNWs this only induces a limited amount of amorphization and structural disorder, as shown by electrical transport and Raman measurements. We demonstrate that a fully crystalline structure can be recovered by thermal annealing at 800 degrees C. For not-annealed, as-implanted NWs, we correlate the onset of amorphization with an increase of phonon confinement in the NW core. This is ion-dependent and detectable for P-implantation only. Hysteresis is observed following both P and B implantation.

We compare the electronic properties of graphene nanoribbons, with either bulk or edge substitutions, edge functionalization, or chemisorption. Chemical modifications can cause semiconductor-metal transitions, lifting of spin degeneracy, widening of bandgap, or appearance of non-dispersive impurity bands and doping. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

The recent discovery of graphene1,2,3 has led to many advances in two-dimensional physics and devices4,5. The graphene devices fabricated so far have relied on SiO2 back gating1,2,3. Electrochemical top gating is widely used for polymer transistors6,7, and has also been successfully applied to carbon nanotubes8,9. Here we demonstrate a top-gated graphene transistor that is able to reach doping levels of up to 5×1013 cm−2, which is much higher than those previously reported. Such high doping levels are possible because the nanometre-thick Debye layer8,10 in the solid polymer electrolyte gate provides a much higher gate capacitance than the commonly used SiO2 back gate, which is usually about 300 nm thick11. In situ Raman measurements monitor the doping. The G peak stiffens and sharpens for both electron and hole doping, but the 2D peak shows a different response to holes and electrons. The ratio of the intensities of the G and 2D peaks shows a strong dependence on doping, making it a sensitive parameter to monitor the doping.

We present a detailed study of the vibrational properties of Single Wall Carbon Nanotubes (SWNTs). The phonon dispersions of SWNTs are strongly shaped by the effects of electron-phonon coupling. We analyze the separate contributions of curvature and confinement. Confinement plays a major role in modifying SWNT phonons and is often more relevant than curvature. Due to their one-dimensional character, metallic tubes are expected to undergo Peierls distortions (PD) at T=0K. At finite temperature, PD are no longer present, but phonons with atomic displacements similar to those of the PD are affected by strong Kohn anomalies (KA). We investigate by Density Functional Theory (DFT) KA and PD in metallic SWNTs with diameters up to 3 nm, in the electronic temperature range from 4K to 3000 K. We then derive a set of simple formulas accounting for all the DFT results. Finally, we prove that the static approach, commonly used for the evaluation of phonon frequencies in solids, fails because of the SWNTs reduced dimensionality. The correct description of KA in metallic SWNTs can be obtained only by using a dynamical approach, beyond the adiabatic Born-Oppenheimer approximation, by taking into account non-adiabatic contributions. Dynamic effects induce significant changes in the occurrence and shape of Kohn anomalies. We show that the SWNT Raman G peak can only be interpreted considering the combined dynamic, curvature and confinement effects. We assign the G+ and G- peaks of metallic SWNTs to TO (circumferential) and LO (axial) modes, respectively, the opposite of semiconducting SWNTs.

We measure the temperature dependence of the Raman spectra of metallic and semiconducting nanotubes. We show that the different trend in metallic tubes is due to phonon re-normalization induced by the variation in electronic temperature, which is modeled including non-adiabatic contributions to account for the dynamic, time dependent nature

. We review the optical phonon dispersions of graphene. In particular, we focus on the presence of two Kohn anomalies in the highest optical phonon branch at the Γ and K points of the Brillouin zone. We then show how graphene can be used as a model for the calculation of phonons in carbon nanotubes. Finally, we present the beyond Born-Oppenheimer corrections to their phonon dispersions. These are experimentally revealed in the Raman spectra of doped samples.

Raman spectroscopy is a powerful non destructive technique for the characterization of carbon materials, and is a fundamental tool in the recent advances in the understanding of single wall carbon nanotubes (SWNTs). Raman experiments probe the optical phonons, allowing to assess the vibrational properties of the analyzed materials. A strong interplay exists between temperature (T ) and phonon frequencies. Indeed, because of anharmonic effects in the atomic oscillations, an increase in T usually results in a downshift of the phonon energy and a lifetime reduction [1]. For Raman active modes, this corresponds to a downshift and a broadening of the Raman peaks [1]. The temperature dependence of the Raman spectra is extremely effective for the evaluation of the local heating in a variety of electronic devices [2, 3], and provides valuable information for the characterization of nanomaterials [4]. Since SWNTs are at the center of nanotechnology research, a thorough investigation and understanding of the temperature effects on their Raman spectra is needed, especially in view of their foreseen application in high current nanodevices. Several groups reported changes of the Raman spectra of single-, doubleand multi-wall tubes as a function of T. Some focussed on the G band [5, 6, 7, 8, 9, 10, 11, 12, 13]. Others considered the position [5, 6, 7, 8, 11, 12, 14] and the intensity [14] of the Radial Breathing Modes (RBM). A few reported the temperature evolution of the 2D [5, 13] and 2D’ modes [5]. However, the different components of the G band, which crucially distinguish metallic from semiconducting nanotubes, were not independently studied, in order to ascertain if those would have a different temperature evolution in semiconducting and metallic SWNTs, thus fingerprinting each material. Here we present an extensive set of temperaturedependent measurements of the G and G peaks in metallic and semiconducting SWNTs. We show that there is a significant difference in the measured trends. We detect a re-normalization of the G peak, ruled by the variation in the electronic temperature, in metallic SWNTs. Furthermore, we prove that this can only be explained by considering the dynamic nature of the phonons and the resulting breakdown of the Born150

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.

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 G(-) linewidths. 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 G(-) peak 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 G(-) peaks to TO (circumferential) and LO (axial) modes, the opposite of what is commonly done in literature.

Raman spectroscopy is a standard tool for the characterisation of carbon materials, from graphite to diamond-like carbon and carbon nanotubes. An important factor is the dependence of the Raman spectra on excitation energy, which is due to resonant processes. Here, we calculate the resonant Raman spectra of tetrahedral amorphous carbon. This is done by a tight-binding method, using an approach different from Placzek's approximation, which allows calculation of Raman intensities also in resonant conditions. The calculated spectra confirm that the G peak arises from chains of sp2 bonded atoms and that it correlates with the atomic and electronic structure of the samples. The calculated dispersion of the G peak position with excitation energy follows the experimental observations. Our ab initio calculations also show that the sp3 phase can only be seen by using UV excitation above 4 eV, confirming the assignment of the T peak at ∼1060 cm−1, seen only in UV Raman measurements, to C–C sp3 vibrations.

Received 2 December 2005DOI:https://doi.org/10.1103/PhysRevLett.95.249901©2005 American Physical Society

We demonstrate the key role of phonon occupation in limiting the high-field ballistic transport in metallic carbon nanotubes. In particular, we provide a simple analytic formula for the electron transport scattering length, which we validate by accurate first principles calculations on (6, 6) and (11, 11) nanotubes. The comparison of our results with the scattering lengths fitted from experimental I-V curves indicates the presence of a nonequilibrium optical phonon heating induced by electron transport. We predict an effective temperature for optical phonons of thousands Kelvin.