To understand carbon nanotubes, you first have to understand carbon. It exists in two crystalline forms: graphite and diamond. Nanotubes are structurally similar to graphite, the chief ingredient in pencil lead.

The first person to see carbon nanotubes was Sumio Iijima of NEC Corp. in Tokyo, who discovered them in 1991 while studying electron microscope images of the soot produced by electrical discharges between carbon electrodes. He saw molecules made up of carbon atoms, cylindrical in shape, exquisitely thin and impressively long. These early structures had the form of cylinders within cylinders, like Russian matryoshka nesting dolls. Then, in 1993, Iijima and Donald Bethune of IBM independently found that adding small amounts of metal catalysts to the carbon electrodes could produce nanotubes that were not nested together; that is, each nanotube was one macromolecule made of a single wall of carbon atoms. This achievement was significant, because nanotube transistors and circuits use such single-walled nanotubes.

In graphite, the carbon atoms are arranged into hexagons that form a honeycomb pattern A nanotube can be viewed as a single layer of graphite rolled into a seamless cylinder. One of the most alluring features of nanotubes as electronic devices is that you can change a device's characteristics merely by altering the physical traits of the nanotube. Two key traits are the width of the graphite layer that is rolled to make the tube, which determines the nanotube diameter, and the orientation of the honeycomb pattern with respect to the nanotube axis. In some nanotubes, the honeycomb pattern lines up with the nanotube axis; in others it spirals around the axis like the stripes on a candy cane. The combination of diameter and twist determines whether the nanotube is metallic or semiconducting.

In semiconducting nanotubes, the diameter of the tube affects how much energy an electron needs to move from the valence band, where it is bound to an atom, into the conduction band, where it is free to move about the semiconductor and conduct electricity. This required energy is called the band gap of the material. The importance of the tube diameter in determining the band gap comes from a quantum-mechanical property of electrons: they are not simply small, charged particles but have wave properties as well. And just as with light waves, the electron's wavelength determines its energy: the shorter the wavelength, the higher the energy.

Because of its wave nature, an electron can experience interference, just as light waves or sound waves do. As a result, an electron wave moving around the circumference of a nanotube can be only in states in which an integral number of wavelengths can fit around the nanotube circumference. Otherwise, the electron will interfere destructively with itself. This requirement restricts the electron's energy to certain discrete values (energy states). The smaller the nanotube diameter, the larger the separation between these allowed energies. An electron jumping from the valence band into the conduction band must have enough energy to jump into at least the lowest of these conductive energy states. That, in turn, determines the band gap.

The upshot is that by changing the diameter of the nanotubes, researchers can produce devices with any band gap from 0 (a metallic nanotube) to more than 1 electronvolt—roughly the band gap of silicon—and all gap values in between. This feature allows us to make devices that turn on and off at different voltages, which we can tailor for different applications. That kind of versatility isn't possible with conventional devices, which are limited to the band gap of whatever semiconductor they are made of.