Tunnel current in the presence of nanosized film at the cathode

We use the classic approach to get the quantum mechanical potential, and consider the field emission in a flat vacuum diode with size d and thin dielectric film with sufficient permittivity. Using the potential in the form of series of images we have calculated the forms of potential barriers at different film thicknesses and voltages at the anode. It can be explained by the fact that the film reduces the intensity of a field.