The electronic band structure variations of single-walled carbon nanotubes (SWCNTs) using Huckle/tight binding approximation theory are studied. According to the chirality indices, the related expressions for energy dispersion variations of these elements are derived and plotted for zigzag and chiral nanotubes.

Carbon nanotubes (CNTs) are graphene sheets rolled up into cylinders with diameter of the order of a nanometer varying from 0.6 to about 3 nm [

Because of their extremely desirable properties of high mechanical and thermal stability, high thermal conductivity, and unique electrical properties such as large current carrying capacity [

Semiconducting CNTs are being extensively studied as the future channel material for ultrahigh performance and scaled field-effect transistors (FETs) and are expected to be the successors of silicon transistors. Interconnect technology has to be commensurately scaled to reap the benefits of these novel transistors. Metallic CNTs have been identified as possible interconnect material of future technology generations and the heir to aluminum (Al) and Cu interconnects [

Graphite is a 3D (three-dimensional) layered hexagonal lattice of carbon atoms and a single layer of graphite forms a 2D (two-dimensional) material, called 2D graphite or a graphene layer [

The periodic lattice of graphene consisting of the unit cell of two carbon atoms.

Each point on the periodic lattice of Figure _{y} atomic orbitals of atoms 1 and 2 in Figure

The energy dispersion variations of graphene lattice.

In Figure

The primitive unit cell and the Brillouin zone in graphene.

We can express the reciprocal lattice vectors

In Figure

Vectors definition of graphene for converting to a carbon nanotube.

Vectors definition for the reciprocal lattice of graphene.

For obtaining

Since an SWCNT is a rolled-up sheet of graphene, the energy band structure can be obtained simply from that of two-dimensional graphene. This work can be done easily by imposing appropriate boundary conditions in the circumferential direction around the SWCNT [

The 1D band structure of an SWCNT is obtained by cross-sections of 2D energy dispersions for (b) a metallic SWCNT and (c) a semiconducting SWCNT [

For the continuous wave vector

For a zigzag carbon nanotube with

The energy dispersion variations of zigzag carbon nanotubes. One nanotube is metallic with

For a chiral carbon nanotube with

The energy dispersion variations of a chiral carbon nanotube, with

In this paper we have studied the basic structure of graphene and its resulted element carbon nanotube. Using the tight binding approximation theory, we have analyzed the variations of energy band gap for SWCNTs (single-walled carbon nanotubes). According to the chiral indices, the related expressions for energy dispersion variations of these elements have been analyzed and also plotted using MATLAB [