Space charge limited current emission for a sharp tip

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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 ∝ Vg3/2/Dm, where Vg 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.