The tunneling time of an electron and the image force

Abstract

The image force acting on an electron tunneling through a dielectric film enclosed by metal electrodes depends on the dielectric constant of the film and the charge build-up in the electrodes which in turn are both dependent on the duration of the tunneling process. Therefore the tunneling time should be known at least qualitatively to calculate the tunneling probability correctly. In literature, however, very different tunneling times varying from 10 -3 to 10 -16 sec are quoted. The different methods used to estimate these values and the consequences for the image force to be assumed are discussed. A numerical integration of Schrödinger's equation for a tunneling wave packet leads to a tunneling time between 10 -14 and 10 -15 sec for typical parameters of film and electrodes. This value favors a quasistatic calculation of the image force using the optical dielectric constant. However, a final decision on the right value to be assumed for the tunneling time will be up to future research.