Surface x-ray diffraction study and quantum well analysis of the growth and atomic-layer structure of ultrathin Pb/Si(111) films

We present surface x-ray diffraction results from Pb films grown on pretreated Si(111) substrates at 110 K. Time-resolved data show that the films follow a metastable layer-by-layer growth mode. The resulting film roughness is small, allowing for a thickness-dependent study of the film layer structure and its distortion (strain) relative to the bulk. The strain arises as a result of quantum confinement of the electrons in the film, which leads to charge distortions similar to Friedel oscillations. The charge distortions in turn lead to lattice distortions, for which two models are derived based on a free-electron gas confined to a quantum well. Extended x-ray reflectivity data show evidence of quasibilayer distortions in the film that are well-described by the free-electron models. Oscillations in the relaxations of the Pb layers closest to the film boundaries as a function of thickness are also observed. Calculations of the net expansion or contraction of the films as a function of thickness are made which also exhibit quasibilayer variations and are consistent with the results of previous studies.