TABLE OF CONTENTS Carbon nanotubes are high aspect ratio hollow cylinders with diameters ranging from one to tens of nanometers, and with lengths up to centimeters. As the name implies, carbon nanotubes are composed entirely of carbon, and represent one of many structures that carbon adopts in the solid state. Other forms of solid carbon include for example diamond, graphite, and buckyballs. These many different forms arise because of the ability of carbon to form hybridized orbitals and achieve relatively stable structures with different bonding configurations. Carbon nanotubes exist because of sp 2 hybridization, the same orbital structure that leads to graphite. In this chapter, we discuss the atomic and electronic structure of carbon nanotubes, and establish the basic nanotube properties that will be utilized in the following chapters on nanotube devices.
To understand the atomic structure of carbon nanotubes, one can imagine taking graphite, as shown in Fig. 1.1, and removing one of the two-dimensional planes, which is called a graphene sheet; a single graphene sheet is shown in Fig. 1.2 (a). A carbon nanotube can be viewed as a strip of graphene (strip in Fig. 1.2) that is rolled-up to form a closed cylinder. The basis vectors 
and 
generate the graphene lattice, where a = 0.142 nm is the carbon-carbon bond length. The two atoms marked A and B in the figure are the two atoms in the unit cell of graphene. In cutting the rectangular strip, one defines a "circumferential" vector
