Modeling of the effect of field electron emission from the cathode with a thin insulating film on its emission efficiency in gas discharge plasma

A model of field electron emission from the metal cathode with a thin insulating film under the strong electric field, generated in the film by ions bombarding its surface in gas discharge, is developed. It takes into account tunneling of electrons from the electrode metal substrate into the insulating film, their motion in the film and going out of it into the discharge volume. An analytical solution of the one-dimensional kinetic equation for the energy distribution function of emitted electrons in the film conduction band is found and an expression for the film emission efficiency equal to the fraction of emitted electrons, which escapes from the film and increases the cathode effective secondary electron emission yield, is obtained. It is demonstrated that calculated dependence of the emission efficiency on the electric field strength in the aluminum oxide film is in an agreement with experimental data for metal-insulator-metal tunneling cathodes. The proposed model can be used for investigation of an influence of the field electron emission from the cathode with a thin insulating film on its emission characteristics in gas discharge devices.