Raman imaging of graphene

in Solid State Communications (2007), 143(1-2), 44-46

A Raman spectrum of a solid contains information about its vibrational and electronic properties. Collecting spectral data with spatial resolution and encoding it in a 2D plot generates images with ... [more ▼]

A Raman spectrum of a solid contains information about its vibrational and electronic properties. Collecting spectral data with spatial resolution and encoding it in a 2D plot generates images with information complementary to optical and scanning force imaging. In the case of few-layer graphene the frequency of the G line and especially the width of the D ' line turn out to be sensitive to single layers. The thickness of the few-layer graphene flake is reflected in the intensity of the G line and in the reduced intensity of the dominant peak of the underlying silicon oxide. (c) 2007 Elsevier Ltd. All rights reserved. [less ▲]

The phonon dispersion of graphite revisited

in Solid State Communications (2004), 131(3-4), 141-152

We review calculations and measurements of the phonon dispersion relation of graphite. First-principles calculations using density-functional theory are generally in good agreement with the experimental ... [more ▼]

We review calculations and measurements of the phonon dispersion relation of graphite. First-principles calculations using density-functional theory are generally in good agreement with the experimental data since the long-range character of the dynamical matrix is properly taken into account. Calculations with a plane-wave basis demonstrate that for the in-plane optical modes, the generalized-gradient approximation (GGA) yields frequencies lower by 2% than the local-density approximation (LDA) and is thus in better agreement with experiment. The long-range character of the dynamical matrix limits the validity of force-constant approaches that take only interaction with few neighboring atoms into account. However, by fitting the force-constants to the ab initio dispersion relation, we show that the popular 4th-nearest-neighbor force-constant approach yields an excellent fit for the low frequency modes and a moderately good fit (with a maximum deviation of 6%) for the high-frequency modes. If, in addition, the non-diagonal force-constant for the second-nearest neighbor interaction is taken into account, all the qualitative features of the high-frequency dispersion can be reproduced and the maximum deviation reduces to 4%. We present the new parameters as a reliable basis for empirical model calculations of phonons in graphitic nanostructures, in particular carbon nanotubes. (C) 2004 Elsevier Ltd. All rights reserved. [less ▲]