Energy barriers for Pb adatom diffusion on stepped ultrathin Pb(111) quantum nanofilms: First-principles calculations

Abstract

Various properties of Pb(111) nanofilms, prototypical quantum films, have been studied extensively. However, key ab initio-level energy barriers for Pb adatom diffusion on stepped Pb(111) nanofilm surfaces are still not available. Using first-principles density functional theory, we calculate these barriers for films with thicknesses of few monolayers (ML). We find that two-atom exchange is always much more favorable than direct hopping to cross A- or B-type steps. Ehrlich-Schwoebel (ES) barriers for downward transport to a higher-coordination step-edge site depend strongly on the film thickness. For such transport from 2- to 1-ML terraces, or from 4- to 3-ML terraces, there is no an ES barrier, but large ES barriers of more than 100 meV are found from 3- to 2-ML terraces. We also obtain the barriers for diffusion along the step edges and find that these step-edge barriers are significantly larger than terrace diffusion barriers. In addition, we analyze energetics for diffusion on the top flat surface of a nanofilm supported on a vicinal surface, and thus having underlying buried or ghost steps. We quantify the tilted potential energy surface in both ghost A- and B-step regions separating 2- and 3-ML (as well as 3- and 4-ML) terraces. Consequences are discussed for the growth kinetics of supported Pb nanofilms, where the support does not strongly affect electronic states within the film.