Dynamical image interaction in scanning tunneling microscopy

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Abstract
We consider the effect of the motion of the electron on the image interaction, a problem investigated earlier by Persson and Baratoff [Phys. Rev. B 38, 9616 (1988)]. If one is interested in the semiclassical description of the image interaction for the tunneling process, arising from the interaction of the charge of the electron with the surface plasmons, then one should make use of a trajectory for the electron such that the plasmon system is not excited as a result of tunneling. We show how such a trajectory may be obtained. Our analysis leads to the conclusion that the trajectory obeys boundary conditions different from the ones used by Persson and Baratoff. Calculations of the tunneling exponent using this trajectory indicate that dynamical effects can modify the image interaction to a much larger extent than found by them.