Quantum size effects in the reflection of slow electrons from thin films

The transmission coefficient of very low energy electrons (⩽10 eV) incident on epitaxial films on single crystal substrates is modulated by interference between reflection at the vacuum/film and film/substrate interfaces. We have observed these quantum size effect (QSE) oscillations for various systems: Cu and Ag/W(110), Cu/Ni(001), Ag/Cu(111) and Ag and Cu/Si(111)-7 × 7 for thickness from a few monolayers to ∼ 100 Å. The sensitivity of the quantum size oscillations to the abruptness of the interfaces is illustrated by a reduction in their amplitude with increasing disorder on an atomic scale at either the vacuum/film or the film/substrate interface. Using the W(110) LEED (00) beam width as an index of substrate surface roughness produced by mild ion bombardment prior to film deposition, we find that the QSE amplitude decreases linearly by 70% for an increase in monoatomic step densities from 1 to only 3% at the Cu/W interface. Quantum size oscillations for epitaxial Cu/Ni(001) were found to be characteristic of the thickness of the film with 1 ML resolution from 1 to several tens of monolayers. The experimental features are well explained by a one-dimensional theory of electron transmission for overlayer crystal based on LEED theory and including a reasonable description of the band structures of the film and the substrate.