Quantum mechanical understanding of field dependence of the apex barrier of a single-wall carbon nanotube

The potential barrier at the apex of a single-wall carbon nanotube emitter is found to be strongly and nonlinearly dependent on the external applied field, due to a quantum mechanical mechanism instead of the correction of image potential in Fowler-Nordheim theory. The field enhancement factor depends on the applied field and is much smaller than that predicted by the classical theory. The field induced apex-vacuum barrier lowering is confirmed to be the essential mechanism for efficient field electron emission from capped carbon nanotubes.