Field emission calculations revisited with Murphy and Good theory: a new interpretation of the Fowler–Nordheim plot

Abstract

The Murphy and Good (M–G) theory for thermo-field emission [1] was used to calculate the emission current densities over the 300–5000 K temperature range in order to bridge the gap with the simpler zero temperature version of the Fowler–Nordheim (F–N) equation. A comparison between the two sets of data reveals that the F–N equation as it is used in the analysis of F–N plots underestimates the true current density by a factor of 102 for all fields known to produce significant current in the case of carbon nanotubes arrays. We propose a new equation for field emission that is consistent with experimental current densities and that can still provide the field enhancement factor β of field emitter arrays. This equation is obtained over the 300–3000 K temperature range by fitting the temperature and field dependences of JM–G using a f(Ts, Es, ϕ0) function using work function values ϕ0 of 4.5 and 2.6 eV. Our complete parametric equation for the fitted M–G current density is found to apply within a 1% error margin for f(Ts, Es, ϕ0) functions computed for each value of ϕ0 and for Es > 1.2 × 109 V m−1.