We present here an overview of the Fourier Transform Scanning Tunneling spectroscopy technique (FT-STS). This technique allows one to probe the electronic properties of a two-dimensional system by analyzing the standing waves formed in the vicinity of defects. We review both the experimental and theoretical aspects of this approach, basing our analysis on some of our previous results, as well as on other results described in the literature. We explain how the topology of the constant energy maps can be deduced from the FT of dI/dV map images which exhibit standing waves patterns. We show that not only the position of the features observed in the FT maps, but also their shape can be explained using different theoretical models of different levels of approximation. Thus, starting with the classical and well known expression of the Lindhard susceptibility which describes the screening of electron in a free electron gas, we show that from the momentum dependence of the susceptibility we can deduce the topology of the constant energy maps in a joint density of states approximation (JDOS). We describe how some of the specific features predicted by the JDOS are (or are not) observed experimentally in the FT maps. The role of the phase factors which are neglected in the rough JDOS approximation is described using the stationary phase conditions. We present also the technique of the T-matrix approximation, which takes into account accurately these phase factors. This technique has been successfully applied to normal metals, as well as to systems with more complicated constant energy contours. We present results recently obtained on graphene systems which demonstrate the power of this technique, and the usefulness of local measurements for determining the band structure, the map of the Fermi energy and the constantenergy maps.

The effects of gold deposition on monolayer graphene (MG) epitaxied on SiC (0001) substrate are examined via scanning tunneling microscopy and scanning tunneling spectroscopy (STS). Two types of surfaces with distinctive topography are demonstrated: (i) intercalated gold clusters having no interaction with graphene and (ii) 13×13-G reconstruction attributed to a Moiré pattern arising from the intercalation of 1 ML of gold between a MG and the underlying SiC substrate. This surface also displays a 23×23R30-Au (111) surface reconstruction interpreted as surface corrugation. The STS curve shows a possible hole-doping effect in the latter case.

Carbon nanotubes are often grown by chemical vapor deposition on silicon substrates covered with an iron catalyst. Photoemission and scanning electron microscopy studies presented here reveal how the iron silicide interface phase formed at elevated temperatures influences the catalytic efficiency of the iron. Moreover, we will show how the deposition of a thin layer of dense titanium nitride between the silicon substrate and the iron catalyst effectively prevents the formation of the silicide phase and consequently improves the carbon nanotubes growth.

Using scanning tunneling microscopy (STM) and Fourier Transform STM (FT-STM), we have studied a point defect in an epitaxial graphene sample grown on silicon carbide substrate. This analysis allows us to extract the quasiparticle energy dispersion, and to give a first experimental proof of the validity of Fermi liquid theory in graphene for a wide range of energies from -800 meV to +800 meV . We also find evidence of a strong threefold anisotropy in the standing waves generated by the defect. We discuss possible relations between this anisotropy, the chirality of the electrons, and the asymmetry between graphene's two sublattices. All experimental measurements are compared and related to theoretical T-matrix calculations.