Abstract
In this paper, we formulate a self-consistent model to study the space charge limited current emission from a sharp tip in a dc gap. The tip is assumed to have a radius in the order of 10s nanometer. The electrons are emitted from the tip due to field emission process. It is found that the localized current density J at the apex of the tip can be much higher than the classical Child Langmuir law (flat surface). A scaling of J proportional to V-g(3/2)/D-m, where V-g is the gap bias, D is the gap size, and m = 1.1-1.2 (depending on the emission area or radius) is proposed. The effects of non-uniform emission and the spatial dependence of work function are presented. (C) 2015 AIP Publishing LLC.