Quantum stability and reentrant bilayer-by-bilayer growth of atomically smooth Pb films on semiconductor substrates

Abstract

Quantum growth of ultrathin Pb films on Ge(111) and Si(111) substrates is studied using scanning tunneling microscopy, total-energy calculations within density functional theory (DFT), and phenomenological modeling. Atomically smooth Pb films can be grown over mesoscopic length scales, but only above a critical film thickness of five or more monolayers. In the smooth growth regime, there exists an intriguing re-entrant bilayer-by-bilayer (RBBB) mode, characterized by strong preference for bilayer growth with periodic interruption of monolayer or trilayer growth. The salient features of the RBBB mode are attributed to the quantum nature of the film stability, as confirmed quantitatively in DFT calculations for $\mathrm{Pb}∕\mathrm{Ge}(111)$. The robustness of the quantum stability is further shown to originate from strong Friedel oscillations in the electron density within the Pb films.