Quantum size effects in the surface energy of Pb∕Si(111) film nanostructures studied by surface x-ray diffraction and model calculations

We have used surface x-ray diffraction from a synchrotron source, along with models based upon a free-electron gas confined to a quantum well, to study quantum size effects in the surface energy of ultrathin Pb films grown on pretreated Si(111) substrates. Films grown at 110  K are smooth, but as they are annealed to near room temperature, their morphology is observed evolving through various metastable states and eventually to a roughened state in local equilibrium. Strong variations in the stability of different island heights are observed, consistent with quasibilayer oscillations in the surface energy found from the theoretical free-electron calculations. By analyzing the quasiequilibrium distribution of thicknesses, empirical information on the film surface energy is obtained for a wide range of thicknesses. The morphological annealing behavior of the films is also found to be explained by the deduced surface energy.