Manifestation of work function difference in high order Gundlach oscillation

Gundlach oscillation (or the standing-wave state) is a general phenomenon manifesting in the tunneling spectrum acquired from a metal surface using scanning tunneling spectroscopy. Previous studies relate the energy shift between peaks of the lowest-order Gundlach oscillation observed on the thin film and the metal substrate to the difference in their work functions. By observing Gundlach oscillations on Ag/Au(111), Ag/Cu(111), and Co/Cu(111) systems, we demonstrate that the work function difference is not the energy shift of the lowest order but the ones of higher order where a constant energy shift exhibits. Higher order Gundlach oscillations can thus be applied to determine the work function of thin metal films precisely.