Effect of aspect ratio and anode location on the field emission properties of a single tip based emitter

The effect on the field emission characteristics of the aspect ratio of an isolated emitter, together with the position of the anode electrode are reported. We show by computational simulation that the field enhancement factor $β$ is only dependant on the emitter height $h$⁠, radius $r$⁠, when the anode to cathode separation $D$ is greater than three times the height of the emitter away from the tip. In this regime the enhancement factor is independent of the anode location and approaches a value depicted by $h$ and $r$ alone and is described by the expression $β0=(1+h∕αr)m$ where $α=2$ and $m=1$⁠. As the anode is brought close to the tip of the emitter, the emitter tip and anode approximate a parallel plate configuration and the enhancement factor tends to unity. Extracted enhancement factor and threshold fields are described by a modified applied electric field taking $D−h$ as the separation. Comparison with previously reported experimental results is also given.