Space charge effects on the current-voltage characteristics of gated field emitter arrays

Abstract

Microfabricated field emitter arrays (FEAs) can provide the very high electron current densities required for rf amplifier applications, typically on the order of 100 A/cm2. Determining the dependence of emission current on gate voltage is important for the prediction of emitter performance for device applications. Field emitters use high applied fields to extract current, and therefore, unlike thermionic emitters, the current densities can exceed 103 A/cm2 when averaged over an array. At such high current densities, space charge effects (i.e., the influence of charge between cathode and collector on emission) affect the emission process or initiate conditions which can lead to failure mechanisms for field emitters. A simple model of a field emitter will be used to calculate the one-dimensional space charge effects on the emission characteristics by examining two components: charge between the gate and anode, which leads to Child’s law, and charge within the FEA unit cell, which gives rise to a field suppression effect which can exist for a single field emitter. The predictions of the analytical model are compared with recent experimental measurements designed to assess space charge effects and predict the onset of gate current. It is shown that negative convexity on a Fowler–Nordheim plot of Ianode(Vgate) data can be explained in terms of field depression at the emitter tip in addition to reflection of electrons by a virtual cathode created when the anode field is insufficient to extract all of the current; in particular, the effects present within the unit cell constitute a newly described effect.