We have studied the nanoscale structural evolution of Pb films grown at 110 K on a Si(111) substrate as they are annealed to increasingly higher temperatures. Surface x-ray diffraction from a synchrotron source is used to observe the morphology evolve from an initial smooth film through various metastable states before reaching a state of local equilibrium, at which point the coverage of different height Pb structures is analyzed and related to the thickness-dependent surface energy. Rich patterns are seen in the resulting energy landscape similar to the beating patterns heard from the interference of two musical notes of similar pitch. The explanation is, however, very simple, as demonstrated by a model calculation based on the confinement of free electrons to a quantum well.
Understanding the underlying physical principles that determine the internal structure of objects at the atomic scale is critical for the advancement of nanoscale science. We have performed synchrotron x-ray diffraction studies to determine the structural properties of smooth Pb films with varying thicknesses of 6 to 18 monolayers deposited on a Si(111) substrate at 110 K. We observe quasibilayer variations in the atomic interlayer spacings of the films consistent with charge density oscillations due to quantum confinement of conduction electrons and surface-interface interference effects. Quantum oscillations in atomic step height are also deduced.
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.
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.
We have performed in situ reflectivity measurements using synchrotron radiation of Ag films deposited on Ge͑111͒ over the thickness range of 3-12 atomic layers. The films deposited at a substrate temperature of 110 K are not well ordered, but become well ordered upon annealing, as evidenced by substantial changes in the x-ray reflectivity data. The thickness distribution for each annealed film, deduced from a fit to the reflectivity data, is remarkably narrow, with just two or three adjacent discrete thicknesses present, despite the large lattice mismatch between Ag and Ge. In some cases, the film thickness is nearly atomically uniform. The results are discussed in connection with recent models and theories of electronic effects on the growth of ultrathin metal films.
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