Improving the extraction of characteristic field enhancement factors from non-linear Fowler-Nordheim plots: role of the irregular morphology of large area conducting field emitters

We show that the dependence between the effective emission area and the macroscopic electric field, $F_{M}$, allow for the introduction of a new correction, $\omega$, in the elementary slope characterization parameter (SCP) for extracting the characteristic field enhancement factor, $\gamma_{C}$, from (precise) orthodox cold-field electron emission measurements [1,2]. First, we discuss the effects of the Hurst exponent (H) on the local electric field distribution and the slope of the Fowler-Nordheim (FN) plot when considering the cold field electron emission
properties of rough Large-Area Conducting Field Emitter Surfaces (LACFESs) [3]. We discuss also the case where the local macroscopic enhancement factors, $\gamma$, are Gaussian-distributed [4], as has been experimentally determined for the potential candidates of cold-field electron emission applications [5]. In this case, using the recent developments in cold-field electron emission theory, we found that for the typical experimental range of 1 V/$\mu$m $\leq F_M \leq$ 10 V/$\mu$m, the nonlinearities that are often observed in cold-field electron emission experiments may appear in $J_{M}$-$F_{M}$-type Fowler-Nordheim (FN) plots. Finally, our results show that depending on the distribution of $\gamma$ over the LACFES, the error in estimating the $\gamma_{C}$ using the elementary SCP (a common practice for experimentalists) may be relevant.

[1] R. G. Forbes, J. H. B. Deane, \textit{Proc. R. Soc. Lond. A}, \textbf{463} 2907 (2007).

[2] R. G. Forbes, \textit{Proc. R. Soc. A } {\bf 469}, 20130271 (2013).

[3] T. A. de Assis, \textit{Sci. Rep.} \textbf{5}, 10175 (2015).

[4] T. A. de Assis, \textit{J. Vac. Sci. Tech. B} \textbf{33}, 052201 (2015).

[5] M. T. Cole \textit{et al.}, \textit{Sci. Rep.}, \textbf{4} 4840 (2014).