SWNT Ends Structure and Electronic Properties

Another example of localized geometric structures in nanotubes is the ends. Analogous to the surface states of a 3D crystal and the edge state of a 2D electron gas, end states are expected at the end of the 1D electron system. The ends of a 1D electronic system can be considered as the "surface" of the 1D bulk. Both resonant and localized states are possible at the ends of nanotubes. Resonant end states are expected for metallic nanotubes because there are no gaps in the 1D band structure of metallic SWNTs to localize the end states. In the same way, localized end states are possible for semiconducting nanotubes since they exhibit energy gaps in their DOS.

The end states associated with carbon nanotubes may arise from pentagons in a capped end or an open nanotube [42,43]. In accordance with Euler's rule, a capped end should contain six pentagons. The presence of these topological defects can cause dramatic changes in the LDOS near the end of the nanotube. Kim et al. [25] reported the first detailed investigation of the electronic character of a capped SWNT end (Fig. 8a), with bulk indices (13, —2). The expected metallic behavior of the (13, —2) tube was confirmed in (V/I)dI/dV data recorded away from the end (Fig. 8c). Significantly, spectroscopic data recorded at and close to the SWNT end show two distinct peaks at 250 and 500 mV that decay and eventually disappear in the bulk DOS recorded far from the tube end.

To investigate the origin of these new spectroscopic features, tight-binding calculations were carried out for a (13, —2) model tube terminated with different end caps (Fig. 8b). Both models exhibit a bulk DOS far from the end (lower curve in Fig. 8d); however, near the nanotube ends the LDOS show pronounced differences from the bulk DOS: Two or more peaks appear above Ef, and these peaks decay upon moving away from the end to the bulk. These models were chosen to illustrate the relatively large peak differences for caps closed with isolated versus adjacent pentagons. The LDOS obtained for cap I shows excellent agreement with the measured LDOS at the tube end, while cap II does not (Fig. 8d). The positions of the two end LDOS peaks as well as the first band edge of cap I match well with those from the experimental spectra. These results suggest that the arrangement of pentagons is responsible for the observed DOS peaks at the SWNT ends, and are thus similar to conclusions drawn from measurements on MWNTs that were not atomically resolved [43].

Besides characterization of capped ends in metallic tubes, Avouris and coworkers [40] reported spectroscopic data on an atomically resolved semiconducting SWNT and its end. Interestingly, as tunneling spectra were recorded along the tube axis to the end, the Fermi level position shifted to the center of the energy gap. This is the first reported evidence of band-bending behavior observed by STM spectroscopy in individual nanotubes. Future studies could provide important and much needed information addressing the nature of nanotube-metal contacts.

Energy (eV)

Fig. 8. STM image and spectroscopy of a SWNT end. (a) Image of a nano-tube end. The symbols correspond to the locations where the tunneling spectra in (c) were recorded. The scale bar is 1nm. (b) A model (13, —2) SWNT recorded two different cap configurations; the pentagons are shaded gray. (c) Experimental tunneling spectra from the end •, near the end ▼, and far from the end A. (d) LDOS obtained from tight-binding calculations on capped (13, —2) tubes for caps I and II. Similar features in • and cap I are highlighted by gray arrows. The bulk DOS for both cap models are identical and is shown in the lowest curve [25]

2.4 Finite-Size SWNTs

The studies reviewed above have focused on SWNTs that have always retained characteristic features of a periodic 1D system. What happens when this 1D system is made increasingly smaller? Conceptually, as the length of a SWNT is reduced, one ultimately will reach the limit of a fullerene molecular cluster-a 0D object. In this regard, studies of finite-size SWNTs offer a unique opportunity to probe the connection between and evolution of electronic structure in periodic molecular systems. Investigations of finite-sized effects in SWNTs are also important to the future utilization of nanotubes in device applications. Low-temperature transport experiments on metallic SWNTs have shown that |im long tubes behave as islands in single electron transistors, with an island energy level spacing characteristic of the 1D particle-in-a-box states [44,45]. Since the coulomb charging energy Ec <x. 1/L (L is the nanotube length), shorter nanotubes allow the working temperature of such devices to increase. In addition, finite-size effects should be visible at room temperature if A E > kB T; thus a resonant tunneling device may be conceived with nanotubes whose lengths are less than 50 nm.

To first order, the 1D energy levels and spacing may be described by either quantization of the metallic band structure or by recollection of the textbook particle in a 1D well. To first order, the bulk metallic nanotube band structure is characterized by two linear bands (n and n*) that cross the Fermi energy, and these bands contribute a finite, constant DOS at low energies. Confinement of the electrons due to reduced axial lengths produces a discretization A k = n/L on the crossing bands. The intersection of A k and the linear bands in the zone-folding scheme results in an energy level spectrum. An alternative, simpler analysis of this problem is to consider the finite-length nanotube as a 1D particle-in-a-box, whose well-known eigenvalues (E) are E = h2k2/2m. The energy level spacing is easily derived:

where h is Planck's constant and vF = 8.1 x 105 m/ s is the Fermi velocity for graphene.

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