Field emission properties and electronic structures of ultra small diameter carbon nanotubes

The field emission mechanisms of the ultra small armchair and zigzag single-walled carbon nanotubes with finite and infinite length are studied individually by using the first principle theory. For carbon nanotubes with finite length, the field emission is affected not only by the electronic behaviors related to the magnitude of diameter, but also by the geometrical conditions at the edge of finite nanotubes. On the other hand, for the ultra small carbon nanotube with infinite length, the work functions are enhanced significantly due to their remarkable curvature effects compared to the large one. For the open-ended carbon nanotubes, the no-bonding valence electrons induced at the mouth layer after geometrical relaxations are corresponding to the variation of work functions. The localized states at the mouth layer of the open-ended (3,0) and (5,0) exhibit the stable sp³-like and sp² structures, which will influence the occupied and the unoccupied states near the Fermi level and improve the field emission properties of carbon nanotubes.