Space-charge effects of electrons and ions on the steady states of field-emission-limited diodes

Abstract

Space-charge effects of electrons and ions on the steady state of a field-emission-limited diode (FELD) are investigated via a self-consistent approach. The field-emission process is described quantum mechanically by the Fowler–Nordheim equation. The cathode plasma and surface properties are considered within the framework of the effective work function approximation. Ionization effects at the anode as well as electron space-charge effects are described by Poisson’s equation. The numerical calculations are carried out self-consistently to yield the steady states of the bipolar field-emission-limited flow of the FELD. We found that the stationary state of the diode exhibits a cut-off voltage. The electric field on the cathode surface is found to be saturated in the high voltage regime and is determined by the effective work function approximately. In addition, the ion current included in the Poisson’s equation has been treated as a tuning parameter. The analytical formula of the electron current density has been derived. The field-emission currents in the presence of saturated ion currents can be enhanced to be nearly 1.8 times of the case with no ion current.