Derivation of a generalized Fowler–Nordheim equation for nanoscopic field-emitters

Abstract

In this paper, we derive analytically from first principles a generalized Fowler–Nordheim (FN) type equation that takes into account the curvature of a nanoscopic emitter and is generally applicable to any emitter shape provided that the emitter is a good conductor and no field-dependent changes in emitter geometry occur. The traditional FN equation is shown to be a limiting case of our equation in the limit of emitters of large radii of curvature R. Experimental confirmation of the validity of our equation is given by the data of three different groups. Upon applying our equation to experimental FN plots complying with the above limitations, one may deduce (i) R and (ii) standard field emission parameters—e.g. enhancement factor—with better accuracy than by using the FN equation.