Charge density and screened potential near a (5,5) capped carbon nanotube from density functional computation

Further results from an earlier computation by density functional theory for the ground state of a capped (5,5) carbon nanotube in the zero applied field show details of (a) self-consistent charge density in the cap and (b) potential in the transition from emitter to vacuum. In this structure, the exchange potential displaces outwards the transition from the Fermi level to the vacuum level and so creates the work function of the emitter, in agreement with Bardeen’s 1936 calculation for sodium. Our self-consistent, multistate calculation provides a physical basis for the initial rise in the widely used Schottky–Nordheim potential for field emission. The axial electric field near the start of the potential barrier shows small discontinuities, at potentials that align with those calculated previously for specific molecular orbitals in the emitter. The multistate calculation thus suggests that a small fraction of charge incident on the barrier has an energy between the Fermi level and the vacuum level. These hot electrons seem unlikely to explain the experimental observations agreeing with Fowler–Nordheim tunneling theory but may contribute to the current at the onset of field emission.