Onset of space charge limited current for field emission from a single sharp tip

Abstract

A protrusive model of the Child-Langmuir (CL) law is proposed for non-uniform electron field emission from a sharp tip of either Lorentzian or hyperboloid shape. The model is expressed as Jc = μ×J1D at large electric field higher than a critical value Ec, and J1D is the classical one-dimensional CL law. It is found that the enhancement μ over the 1D CL law depends only on the calculated field enhancement factor (β) of the emitter and is independent of the work function and gap spacing. In particular, μ increases with β and it converges to a constant at β≫ 1 for a very sharp tip with small emission area.