Unified behavior of alkali core-level binding-energy shifts induced by $\mathrm{sp}$ metals

Thin overlayers of Na, K, Rb, and Cs on different $\mathrm{sp}$-metal substrates have been investigated using photoelectron spectroscopy. The alkali core levels show clearly resolved binding-energy shifts between the surface layer, the intermediate layer(s), and the interface layer. The magnitude of these shifts depends on $\mathrm{sp}$ metal and on alkali metal. The layer-resolved core-level binding-energy shifts are well reproduced by models based on a thermodynamical description. For three-layer alkali films the core-level binding energy of the intermediate layer is found to exhibit a small but significant shift between different $\mathrm{sp}$-metal substrates. A simple relationship between the core-level binding-energy shift for the interface layer and the difference in $r_s$ value between the $\mathrm{sp}$ substrate and the adsorbate is shown to exist.