When the thickness of a metallic film is in the nanometre range, electrons in the film as well as those transmitting through the film can both manifest the quantum size effect (QSE). For the former, electrons are confined in the quantum well of a metal film to form quantum-well states. For the latter, electrons scattered by the quantum well in the film can bring about the phenomenon of transmission resonance. Scanning tunnelling microscopy (STM) combined with spectroscopy is a powerful tool to explore these two kinds of QSE. In this paper, we review our recent studies on the QSE of thin Pb and Ag films by using STM. We demonstrate that the formation of the quantum-well states in the Pb film can significantly affect the morphology, thickness, growth process and electronic structures of Pb films. On the other hand, the transmission resonance can be observed on the Ag film with Z-V spectroscopy in STM. The energy level of the transmission resonance varies with the film thickness and can be shifted by the electric field. Moreover, in the studies of transmission resonance, it is unavoidable to observe the standing-wave states, i.e. Gundlach oscillations, which are the QSE in the tunnelling gap. We have also discovered that the Gundlach oscillation can be exploited to measure the work function of thin metal films with very high precision.
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