Current-voltage characteristic of the contact of a plasma with an electrode with a thin dielectric film on the surface

A model of the current flowing in the contact of a plasma with an electrode with a thin dielectric film on the surface has been developed to describe the observed features of the current-voltage characteristics of such a contact: a segment with small current near the floating potential corresponding to the film recharging and a segment with large current, where the mechanism of field electron emission through the film into the plasma occurs, leading to an $N$-shaped current-voltage characteristic. Such current-voltage characteristics are observed for W, Al, and Ta electrodes with a self-oxide film and for a stainless steel electrode with a silicon oxide film in a beam-plasma discharge in hydrogen. The model is based on the calculation of the equilibrium potential of the film surface faced to the plasma for the region of the negative bias of the electrode with respect to the plasma potential. Balance involves currents of ions and electrons from the plasma, secondary emission currents, and field electron emission current from the electrode into the plasma through the insulator. The film recharging voltage calculated within the model is in exact agreement with experimental data. This allows the determination of the thickness of the dielectric layer on the electrode surface from its current-voltage characteristic.