Generalized Formula for the Electric Tunnel Effect between Similar Electrodes Separated by a Thin Insulating Film

TLDR

A formula is derived for the electric tunnel effect through a potential barrier of arbitrary shape existing in a thin insulating film. The authors apply the derived formula to a rectangular barrier, both with and without image forces, comparing the true image potential to the approximate parabolic solution of Holm and Kirschstein. The study resolves anomalies in Holm's intermediate voltage characteristic and shows that the dielectric constant of the insulating film influences the temperature dependence of the tunnel junction's J‑V characteristic.

Abstract

A formula is derived for the electric tunnel effect through a potential barrier of arbitrary shape existing in a thin insulating film. The formula is applied to a rectangular barrier with and without image forces. In the image force problem, the true image potential is considered and compared to the approximate parabolic solution derived by Holm and Kirschstein. The anomalies associated with Holm's expression for the intermediate voltage characteristic are resolved. The effect of the dielectric constant of the insulating film is discussed in detail, and it is shown that this constant affects the temperature dependence of the J-V characteristic of a tunnel junction.