Characterization of field emission from random nano-structured surface in using fractional field emission models

It is known that field emission from random nano-structured surfaces cannot be well characterized with the original field emission model known as the Fowler–Nordheim (FN) law or the Murphy–Good (MG) law. To account for the roughness effects, the traditional approach was to introduce the arbitrary field enhancement factor β in the FN and MG laws. In this paper, by treating the random roughness of field emitters as a fractional dimension object with 0<α<1, fractional models of the FN and MG law, which were formulated recently may serve as alternate characterization tools. At α=1, the models will recover the traditional FN and MG laws valid for a perfect flat planar surface. These generalized fractional FN law (FNα) and the fractional MG law (MGα) will be used to characterize various field emission experiments by finding the best 0<α<1 values to account for the degree of the random roughness. The findings will be compared among the traditional and fractional emission models, where the best-fitting results will be shown for each case. It is found that the fractional field emission models provide more physical and appropriate field emission parameters, i.e., field enhancement factor and field emission area, in comparison with traditional field emission models.