Optoelectronics with Carbon Nanotubes

In fact, we typically have no knowledge of the actual n and m values of a CNT used in an
electronic device, since getting a PL signal from a single tube (the only way to identify them) on
a surface is very difficult and laborious.
expressed as
Figure I-1. The honeycomb structure of a graphene sheet in real space, showing
the example of a (4, 5) SWNT. One carbon atom exists at each hexagonal point.
a1 and a2 are unit vectors, and C indicates the chiral vector for the SWNT. The
blue dotted lines indicate the primitive unit cell containing two translationally
inequivalent atoms.
Once the chiral vector and therefore the type of a SWNT is defined, its diameter d can be
2 2
3acc n mnm d (Eq. I.2)
where ac cis
the distance between neighboring atoms, known to be 0.142 nm. A typical SWNT
has the diameter in the order of only nanometers, so this confinement quantizes the component of
the momentum k in the circumferential direction of the cylinder. In other words, the quasi – 1D
nature of the nanotube imposes a true periodic condition around the circumference and defines
the Brillouin zone of the nanotube in that direction. The quantization condition,
4