Application of fractional Fowler-Nordheim law on field electron emission from tungsten and lanthanum hexaboride nano-scale emitters

The Murphy-Good Fowler-Nordheim equation was derived for planar and smooth conducting surfaces based on the Sommerfeld free-electron theory. It is applicable to a wide range of micro-emitters. The analyses of experimental field emission data from nano-scaled emitters showed deviation from the theoretical predictions. This has either been noticed in the mismatch of the current–voltage characteristics and/or in the FN-plot behaviour. Such deviation is attributed to the non-planar character of the emitting surface and the shape of the surface potential barrier through which the emitting electrons are tunnelling. Recently, Zubair et al. derived a FN-type equation that takes into account the reduced dimensionality of the emission surface and the non-parabolic energy dispersion [Zubair et al., IEEE Transactions on Electron Devices 65(6) 2018]. In this model, the constants of the conventional FN equation become two variables that depend on the fractional parameter expressing the surface complexity. In the present work, the fractional law is applied to field electron emission from clean tungsten (W) nano-emitter and lanthanum hexaboride (LaB6) nano-protrusions. This has been accomplished in the whole range of the fractional parameter in order to find the value that reproduces a better fit with the experimental data. The application requires determining the geometrical parameter of the emitter and the field emission setup. Results show that the experimental data can easily be reproduced at certain values of the fractional parameter. These 'certain' values depend on the geometrical parameters and thus the method used to calculate the electric field value at the emitter surface.