Quantum Beating Patterns in the Surface Energy of Pb Film Nanostructures Peter Czoschke, Hawoong Hong, Leonardo Basile and Tai-Chang Chiang Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign Introduction Ultrathin metal films grown on semiconductor substrates exhibit a rich variety of growth behavior and morphology at different temperatures due to quantum size effects. We have used the surface x-ray diffraction station at Sector 33ID (UNICAT) to study the nanoscale structural evolution of Pb films grown on Si(111) at 110 K as they are annealed to 280 K. The film morphology passed through various different metastable phases before reaching a state of local equilibrium, at which point the coverage of different height Pb structures was analyzed and related to the thickness-dependent surface energy. Rich patterns are seen in the resulting energy landscape, consistent with a model calculation based on a free-electron gas confined to a one-dimensional quantum well. Summary  Quantum confinement of electrons in a metal film leads to oscillations in the surface energy. We have observed this effect experimentally with surface x-ray diffraction, effectively measuring the surface energy through the film structure.  We observed the surface morphology evolve from a smooth film, through the “magic thickness” phase, to a highly roughened state near room temperature and have correlated such behavior with details of the global energy landscape.  In Pb(111) films, such quantum effects produce bilayer oscillations with a “beating” pattern that results in a strong preference for even/odd thicknesses. P. Czoschke, et al., Physical Review Letters (submitted) Film Evolution (Annealing) Extended X-Ray Reflectivity Surface Morphology Extended x-ray reflectivity of a sample with an initial thickness of 11 AL of Pb after annealing to the temperatures indicated. Curves are fits to a kinematic model which reveal the relative coverage of different film thicknesses present on the sample surface. The small fringes near the half-order point between the Pb Bragg peaks in the data at higher temperatures are due to quasibilayer variations in the stability of different thicknesses. Surface Energy The fractional surface area covered by exactly N Pb layers, p N, obtained from fits to the x-ray data. After deposition, the film is relatively smooth due to the layer-by-layer growth mode. As the sample is annealed, the film bifurcates into the preferred thicknesses of 10 and 12 AL. Near room temperature, the film has become very rough with variations that reveal details of the surface energy. E S (N) Results The relative stability of different thicknesses (the discrete second derivative of p N ) shows bilayer variations with the preference for even/odd thicknesses alternating approximately every 9 AL. Assuming that the p N values follow a Boltzmann distribution, this “beating” effect is accurately reproduced by a two-parameter (A and  N) † fit to the free-electron form of the surface energy. †  N is a phase factor to account for the presence of the Si substrate. From the fit to the experimental data, the details of the thickness-dependent surface energy are obtained. Their functional form and overall energy scale are consistent with independent first-principles calculations done for related systems. Structure Stability