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 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‐Vcharacteristic of a tunnel junction

By the substitution V(x) = η+φ(x), we have inherently assumed that the width Δs of the barrier in the range Ex>V(x)>η is constant and equal to the barrier width at the Fermi level. This assumption is justified for practical barriers, because Δs varies slowly below the Fermi level, and the integral has effective values only when Ex≃η.Google Scholar

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