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

Abstract

A 1 µm long, field emitting, (5,5) single-walled, carbon nanotube (SWCNT) closed with a fullerene cap, and a similar open nanotube with hydrogen-atom termination, have been simulated using the MNDO (Modified Neglect of Diatomic Overlap) quantum-mechanical method. Both contain about 80 000 atoms. It is found that field penetration and band-bending, and various forms of chemically and electrically induced apex dipole, play roles. Field penetration may help to explain electroluminescence associated with field emitting carbon nanotubes. Charge-density oscillations, induced by the hydrogen adsorption, are also found. Many of the effects can be related to known effects that occur with metallic or semiconductor field emitters; this helps both to explain the effects and to unify our knowledge about field electron emitters. However, it is currently unclear how best to treat correlation-and-exchange effects when defining the CNT emission barrier. A new form of definition for the field enhancement factor (FEF) is used. Predicted FEF values for these SWCNTs are significantly less than values predicted by simple classical formulae. The FEF for the closed SWCNT decreases with applied field; the FEF for the H-terminated open SWCNT is less than the FEF for the closed SWCNT, but increases with applied field. Physical explanations for this behavior are proposed. Curved Fowler-Nordheim plots are predicted. Overall, the predicted field emission performance of the H-terminated open SWCNT is slightly better than that of the closed SWCNT, essentially because a C-H dipole is formed that reduces the height of the tunnelling barrier. In general, the physics of a charged SWCNT seems more complex than hitherto realised.

Field Emission Theory

“…The nonlinear FN behavior was attributed to effects of space charge or molecules adsorbed at the emission tip. A similar result was obtained with more quantum mechanical treatment [36]. In [35], the current saturation was attributed to the spatial distribution of electric fields that is specific to the nanotube.…”

On the quantum mechanics of how an ideal carbon nanotube field emitter can exhibit a constant field enhancement factor

“…In later theoretical work [13], linear dependence of an extracted characteristic FEF on F M was found for a capped SWCNT. In this case, a slightly modified definition was used, in that the characteristic FEF was calculated at a fixed position in space, close to the position where the "local real field" had its maximum absolute value.…”

Carbon Nanotube Electron Sources: From Electron Beams to Energy Conversion and Optophononics

“…Several works such as [77,114,115] have pointed out the deviation from linear Fowler-Nordheim behavior in field-emission experiments on nanotubes. Such deviations have been explained through cooperative effects among the tips in an emitter consisting of a collection of nanotubes [116], the difference in the energy band structure of nanotubes and conventional emitters [117], field penetration and induced apex dipoles [118], the nonlinear nature of the tunneling potential barrier as well as its angle dependence [119,120], variation of the local field [121], and the slowing down of the rate of reduction of the barrier width/height as the applied field increases [109].…”