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.

A Self-Consistent Parallel Plane Model for Fitting Nonlinear FN Plots of Field-Emission Strips

“…A self-consistent parallel plane (SCPP) model has been developed for fitting the nonlinear FN plots of field-emission strips [5,6]. Within the framework of an effective work function approximation and energy conservation, the FN and Poisson' s equations are solved self-consistently in the SCPP model.…”

Fitting nonlinear FN plots of field emission strips with a self-consistent parallel plane model

“…We have confirmed that the nonlinear FN plots are caused by the space charge effects. It is also found that the saturation IV characteristics can be fitted with the self-consistent parallel plane model very well [5,6]. The details of the MAGIC simulation and the fitting procedures of the SCPP model will be presented and discussed.…”

Physical nature of 'anomalous' electrons in high-current vacuum diodes

“…The problem of oversimplification was connected to zero initial by accurately taking into the account thermal electron velocities (Langmuir, 1923), (Jaffé, 1944). The extension of a single-species consideration to Child's law showed that adding positive ions weakens the SCL effects (Lin, 2005). Various investigations have been also carried out in order to relax the assumption of one-dimensionality.…”