Tunnel current across super-thin film electrets

When a super-thin film electret is evaporated with metal electrodes on two sides, the electrons in electrodes have the possibility of crossing potential area in film. Suppose the electrons obey Fermi-distribution, it is found that the tunnel current across the film depends on both exerted voltage between the film and the thickness of the film. The temperature and work function of electrode-metal also have significant effects on the current. If exerted electrical field is very large, the result of calculation shows that the current can be proportional to exerted voltage in certain conditions.