Transient Currents in a Field Emitter

We seek to understand the transient behavior that is occasionally observed in field emitter experiments, as well as the relationship between the Fowler-Nordheim parameters deduced from pulsed and steady-state experiments. To this end, a model is constructed to study the effects of the gap capacitance and the base resistance on the evolution of the emitted current from a field emitter that is subjected to a voltage pulse of various rise times. The field emitter is assumed to obey the Fowler-Nordheim law. The effect of space charge on the surface electric field is included. Numerical examples will be presented to illustrate the time scale required to reach the steady state, together with the scaling law to be constructed from the data.