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 = at large electric field higher than a critical value , and is the classical one-dimensional CL law. It is found that the enhancement over the 1D CL law depends only on the calculated field enhancement factor () of the emitter and is independent of the work function and gap spacing. In particular, increases with and it converges to a constant at 1 for a very sharp tip with small emission area.
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