Incorporation of electric-field penetration of the electrodes in the theory of electron tunnelling through a dielectric layer

The theory of electron tunnelling through a thin dielectric film is modified by taking into account the penetration of the electrodes by the applied field. The numerical predictions differ only slightly from the existing calculations but some significant differences in the asymmetry of the current-voltage characteristics are produced. In particular, it is shown that the direction of easy current flow can reverse twice with increasing voltage. This depends on the barrier asymmetry and the relative amount of field penetration of the junction electrodes. Also the peak of the thermal (J, V) curve no longer occurs at a voltage equal to the metal-insulator barrier height, but at a slightly higher voltage. Some of the predictions of the modified theory are confirmed by experiment.