Abstract
This work considers 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). A LACFES is represented by a self-affine Weierstrass-Mandelbrot function in a given spatial direction. For 0.1 ≤ H < 0.5, the local electric field distribution exhibits two clear exponential regimes. Moreover, a scaling between the macroscopic current density () and the characteristic kernel current density (), , with an H-dependent exponent , has been found. This feature, which is less pronounced (but not absent) in the range where more smooth surfaces have been found (), is a consequence of the dependency between the area efficiency of emission of a LACFES and the macroscopic electric field, which is often neglected in the interpretation of cold field electron emission experiments. Considering the recent developments in orthodox field emission theory, we show that the exponent must be considered when calculating the slope characterization parameter (SCP) and thus provides a relevant method of more precisely extracting the characteristic field enhancement factor from the slope of the FN plot.
Highlights
It is becoming increasingly clear that modified Fowler-Nordheim-type (FN-type) equations must be developed to address CFE from rough thin-film emitters[12]
Motived by the aforementioned studies, in this work, we present the first consideration of the role of the Hurst exponent H of an irregular Large-Area Conducting Field Emitter Surfaces (LACFESs) in determining the related local electric field distribution and field electron emission properties using orthodox field emission theory
A LACFES is represented by a self-affine Weierstrass-Mandelbrot (WM) function in a given spatial direction such that all surfaces are assumed (i) to exhibit no roughness along any other spatial direction and (ii) to have the same global roughness
Summary
The results indicate that for any H, the local electric field distribution over a LACFES exhibits two exponential regimes, implying a non-linear (power-law) relation between the macroscopic current density and the characteristic current density, if orthodox field electron emission is assumed. This finding indicates that our LACFES model captures the main features of the experimental results, namely, the local electric field distribution and the field emission properties (in the orthodox theory) of irregular conducting surfaces.
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