Journal of Vacuum Science & Technology B, Vol.27, No.2, 766-771, 2009
Field emission pattern of carbon nanotubes and phase distribution of wave function in the end cap structure
The characteristic pattern of rings seen in field electron emission from capped carbon nanotubes is discussed. The states expected for the p-electrons on a pentagonal ring of carbon atoms are related to their angular periodicity, hence emission from states with a phase change around the ring is less attenuated than that from states with zero phase change. Solution of Schrodinger's equation for an emitting ring in a system with planar cathode and anode electrodes shows that the wave function at the anode is zero on the axis for any nonzero variation of the phase of emission with azimuthal angle. These considerations suggest that the observed dark centers of rings are due to emission principally from states in the nanotube cap that have nonzero periodicity around the pentagons. (C) 2009 American vacuum Society. [DOI: 10.1116/1.3058723]