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

Abstract

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.

The roles of apex dipoles and field penetration in the physics of charged, field emitting, single-walled carbon nanotubes

“…5 of Ref. 9. Local-field induced dipoles (with their negative ends outwards) are clearly visible on the carbon atoms in the top pentagonal ring.…”

“…The charges in other parts of the nanotube contribute interactions to the subsystem as if they were point charges. The principles of our general approach have been described elsewhere 8,9 . In the present paper, a total of 1600 to 2000 sub-regions is used in the quantum-mechanical part of the calculation.…”

“…A key decision is to divide the long CNT into sub-regions 8,9 . Each sub-region consists of 40 atoms, except the apex which consists of 80 atoms.…”

“…7 shows the predicted emission currents I calculated as described in Ref. 9, using the approximate formula…”

“…A few years ago, it became possible to simulate long CNTs (up to several µm in length) by a hybrid approach involving both quantum mechanics and classical analysis 8,9 . A (5,5) single-walled carbon nanotube (SWCNT) closed with a fullerene hemisphere was simulated in this way (we refer to this as the "closed CNT").…”