A 3-dimensional calculation of the field emission current and emission angle of a vacuum transistor as a function of gate voltage and radius of curvature of the emitter

We have calculated the electrical characteristics of a vacuum transistor withsharp, pointed emitter and collector with a radius of curvature R<20nm with the aim of revealing the advantages of such emitters. For such surfaces the traditional Fowler-Nordheim theory which pertains to a parallel plate configuration is not valid. We have used a 3-dimensional WKB theory capable of calculating the distribution of the current in space. We have shown that for values of emitter radius in the range of a few nanometers the current density is enclosed within a cone of angle of approximately 6°–16° thus minimizing current losses. The Id–Vd characteristics were calculated and found to exhibit a exponential behavior and a saturation region spanning currents from 10−14A to 10−6A by only 2 Voltsvolts change in gate voltage Vg, i.e. exhibiting an extraordinary transconductance.