Statistical analysis of atomic force microscopy and Raman spectroscopy data for estimation of graphene layer numbers

In this work we present the results on preparation and analysis of structural and electronic properties of graphene flakes with different number of layers. Since the material electronic properties depend strongly on the layer number, a simple and reliable way to estimate this parameter should be found. In this work we propose to perform a quantitative analysis based on the atomic force microscopy (AFM) which was exploited by another authors rather as an illustrative technique. The graphene flakes were prepared by a micromechanical cleavage of highly oriented pyrolytic graphite (HOPG). Numerous flakes have been studied with AFM in order to estimate the number of graphene layers in each of them. The thickness distribution over the individual graphene flake, averaged over the all flakes investigated, has exhibited a row of maxima: 0.7 nm, 1.1 nm, 1.4 nm, 1.7 nm, 2.1 nm, etc. These values correspond perfectly to the one-, two, three-, and etc layers of graphene. The flakes characterized by AIM were studied afterwards with a two-phonon Raman spectroscopy. This method is known to be sensitive to the number of layers due to a double resonance mechanism. To interpret the Raman spectra the electronic structure of the graphene flakes of different thickness has been calculated using the density functional method. A perfect correspondence between the number of graphene layers in different flakes measured by AFM and by Raman techniques has been obtained. This demonstrates a possibility to estimate correctly the graphene layer number using the atomic force microscopy supplied with the statistical analysis. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim