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Dynamical resonance tunnelling—a theory of giant emission from carbon field emitters

We describe in this paper the likely physical mechanisms that underlie the enormously enhanced electron emission observed from certain carbon field emitters. Our key ideas link the enhancement to dynamic resonant tunnelling and to the image interaction in a more general form than is usual. We have recently proposed a giant enhancement of the dynamic surface potential that could explain the anomalously large field emission currents observed in carbon-based emitters with predominantly non-Fowler–Nordheim I–V characteristics. Here we report further results on this effect which can best be described as an image-induced dynamical resonant tunnelling phenomenon, and in particular the applied field dependence of the inverse potential enhancement factor κ(ω), which seems to be a hallmark of such systems. The latter is studied by a consideration of the non-linear second-order susceptibility γ(ω) which couples the static applied field to the dynamic field. We derive the criterion for this mechanism to operate and demonstrate that it does indeed provide the linear field dependence of κ(ω) found in our earlier work. We further provide a link between γ(ω) and other microscopic parameters of the surface plasmon model, notably the anharmonicity coefficient, via a Duffing oscillator model. Through the use of a one-dimensional fluctuating barrier model with a self-consistent approach, we further assess the significance of other non-linear damping effects.