Thickness dependent of phase shift between surface energy and work function in Pb ultrathin films

Abstract

Through first-principles calculations within density functional theory, the phase shift between surface energy and work function in FCC (111) and HCP (0001) Pb and Pb1–xBix alloy films has been investigated. Deviating from the previously described phase mismatch between the surface energy and work functions, an additional phase shift of about one monolayer is identified at small thickness of the Pb and Pb alloy films. The additional phase shift depends on the film thickness and will disappear as thickness increases. Moreover, we give an interpretation of the one-monolayer deviation in the framework of the free electron model, attributing it to the unique structure of the Fermi surface in Pb ultrathin films.