Scanning Tunneling Microscopy and Spectroscopy

Scanning tunneling microscopy (STM) and spectroscopy (STS) can both be considered as the ultimate technique to assess the electronic properties as well as the structure of individual SWNTs. Although Raman and optical absorption can provide some of the information generated by a STS experiment, the unique advantage of STM and STS is the possibility to probe both the morphology and the electronic structures of SWNT at the atomic level. In this section, some of the most impressive results and applications of this powerful technique are presented. For more details, the reader is referred to any of the extensive reviews published on this subject [46, 47].

STM and STS are both based on the tunneling effect. In short, a very sharp metal tip is scanned across the surface to be analyzed, which must be conducting, at a distance of the order of typically 1 nm. A bias voltage is applied between the tip and the sample (typically a few millivolts), which leads to a tunneling current of the order of pico- to nano-amperes. This tunneling current is extremely sensitive to the distance between the tip and the sample. Therefore, by measuring the tunneling current while keeping the distance or the bias voltage constant, information on the topography of the surface can be obtained. Moreover, since the tunneling current is also dependent on the electronic structure of the surface (i.e., density of states of the surface being probed) very reliable information about the electronic structure of the sample can be obtained [48].

Figure 5 shows how STM can provide information on a SWNT at the atomic level. In this case, individual SWNTs with different chiral angles were probed [49]. Together with the information on the chiral angle, a direct measurement of the diameter can also be performed. The combination of these two pieces of information provides the (n, m) indexes, which fully characterize the molecular structure of the nano-tube. It is necessary to mention that STM images should be carefully analyzed before a direct assignment of the chiral angle and diameter of SWNT can be made. For instance, the geometrical orientation of the STM tip respect to the nano-tube greatly influences the image recorded. For a cylindrical structure such as a SWNT, the shortest distance between the tip and the nanotube is perpendicular to the nanotube wall only when the tip is on top of the nanotube. Only in this case the image observed represents the true structure of the probed SWNT. In any other case, the information obtained is that of a stretched lattice [49-51].

While STM can yield insight into the SWNT lattice arrangement, STS provides information on its electronic structure. Tunneling spectroscopy can be performed by recording the current as function of the bias voltage at fixed positions of the STM tip over the sample. That is, in STS the

Figure 5. STM images of atomically resolved carbon nanotubes. For each nanotube the apparent angle between hexagon rows and the tube axis is indicated. The 1-nm bar indicates the scale for all four images. (a), (b) Two chiral nanotubes with small chiral angles. (c), (d) Two chiral nanotubes with large chiral angles near 30°. Reprinted with permission from [49], L. C. Venema et al., Phys. Rev. B 61, 2991 (2000). © 2000, American Physical Society.

tip is not scanned across the sample. In this way information of the electronic structure of the sample can be obtained with a resolution that is essentially of a single atom. The normalized conductance (V/I) dl/dV is a good measure of the local density of states [48].

These measurements have been used to confirm the predictions made by theory about the diameter and helicity dependence of the electronic properties of SWNTs [52-54]. With the adequate energy range, the experimental density of states (DOS) can be obtained on atomically resolved SWNTs and compared quantitatively with the calculated DOS for specific (n, m) indices. Kim et al. [55] performed the first comparison of this sort, for a nanotube with (13, 7) indices. In Figure 6 the STS data are compared with the theoretical band structure calculations based on a n-n tight binding model [56, 57]. Due to the one-dimensional nature of their band structure, SWNTs exhibit high peaks (or spikes) in the density of states. The experimental data show good agreement between the positions of the spikes and the van Hove singularities determined from these calculations. The agreement between theoretical calculations and STS data was particularly good below the Fermi level, where the first seven singularities corresponded very well. Above the Fermi level some deviations between the experimental data and the calculations were observed. The differences were attributed to band repulsion, which arises from curvature induced hybridization [58, 59].

Figure 6 also shows a similar result obtained by Odom et al. who worked on a small diameter (10, 0) semiconducting nanotube and compared the experimental data with a tight binding theoretical prediction [55-57]. Similar to the results obtained by Kim et al., the normalized conductance

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