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

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 J(c) = mu x J(1D) at large electric field higher than a critical value E-c, and J(1D) is the classical one-dimensional CL law. It is found that the enhancement mu over the 1D CL law depends only on the calculated field enhancement factor (beta) of the emitter and is independent of the work function and gap spacing. In particular, mu increases with beta and it converges to a constant at b beta >> 1 for a very sharp tip with small emission area. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3695090]