Electrical Properties

One way to think about nanotubes is as rolled-up sheets of films of pure carbon (described in the scientific literature as graphene). These sheets can either roll up evenly, or twist as they roll up, so that the exact structure depends on both the diameter of the tubes and the degree of twist. These varying structures can be defined by two indices, typically labeled n and m. Electronically, carbon nanotubes can be either semiconducting or metallic, depending on the value of (n-m).

Tubes in which (n-m) is either zero or a multiple of 3, have electrons in their conduction bands at room temperature, conduct electricity very well, and are called metallic nanotubes. All other structures produce nanotubes that are true semiconductors, with a band gap typically between 0.5 and 3.5 electron-Volts. The band gap varies inversely with the diameter of the tube, and for a tube of 1 nm diameter, the band gap is about 1 eV.

In an individual carbon nanotube there are many, many electrons, and different electrons can fill different energy levels within the tube. The following figure illustrates the relative abundance of electrons as a function of the electron energy for a single carbon nanotube. The blue shading indicates states filled with electrons, while the open areas are energy levels that could be populated by carbon nanotubes.

A photon whose energy is equal to the difference between a filled and unfilled state can be easily absorbed, causing an electron to transition between indicated by the dark blue arrow. Such photo absorptions give nanotubes a characteristic absorption spectrum for light in the ultraviolet to near-infrared wavelength range. One can identify the range of (m,n) for the tubes present in a sample by analysis of their light absorption spectrum.
Electrons and holes move very easily through carbon nanotubes. The electrical resistance of individual carbon nanotubes is comparable to that predicted for copper wires of the same size. In bundles (ropes) of carbon nanotubes, electrons flow down individual tubes, but occasionally jump from one tube to another. Carbon nanotube ropes have been measured to have a resistivity of 10-4 ohm-cm at room temperature [A. Thess et al., Science 273, 483 (1996)], making them the most electrically-conductive fibers known.

The energy levels of carbon nanotubes depend on their environment, as the electrons within a nanotube are highly polarizable. Application of an external field can shift the relative energies of these states, either enhancing or diminishing conductivity. This property makes nanotubes interesting as a printable semiconductor in transistor applications.

Likewise, the presence of some types of molecules can also shift these energy levels and affect conductivity and optical behavior; these shifts can depend on the types of molecules attached to the surface of a nanotube. In this way, custom functionalization of nanotubes can lead to sensors for certain types of molecules, or as probes for cell abnormalities in biomedicine.

Individual carbon nanotubes have been observed to conduct electrons ballistically, that is, with no scattering, for distances of a few microns [Tans, et al., Nature 393, 49 (1998)]. Ballistic conduction permits substantial current flow with minimal heat generation, which allows nanotubes to carry enormous amounts of current. In fact, carbon nanotubes can carry the highest current density of any known material, with conductivities measured as high as 109 A/cm2 [B.Q. Wei, et al., Appl. Phys. Lett. 79, 1172 (2001)]. In comparison, copper fails at current densities of about 107 A/cm2, so nanotubes can carry current densities about 100 times that of traditional metal conductors.

One consequence of ballistic conduction is that the charge carriers (electrons and holes) move very rapidly through nanotubes under the influence of an electric field. The charge carrier mobility in carbon nanotubes can exceed that in traditional electronic materials like silicon by at least an order of magnitude [Durkop et al., Nano Lett. 4, 35 (2004)], and should allow the manufacture of ultra-high-frequency transistors and circuit elements with carbon nanotubes. Another consequence of ballistic conduction is that one can make very low-noise transistors with nanotubes [Javey et al., Nature 424, 654 (2003)]. As the emerging field of molecular electronics matures, we can expect carbon nanotubes to play a central role.