Surface relaxations in quantum-confined Pb

Abstract

The relationship between electronic and atomic structure of quantum confined objects is a key issue in nanoscience. We performed low-energy electron diffraction to determine the surface relaxations of ultrathin Pb films on Si͑111͒7 ϫ 7 with thicknesses ranging from four to nine atomic layers. The results indicate a contraction of the first interlayer spacing d 12 for all films. The d 12 contraction exhibits a small bilayer modulation as a function of thickness, indicative of a quantum size effect. The oscillatory relaxations furthermore suggest an interesting correlation with the work function oscillations predicted from density functional theory ͓Wei and Chou, Phys. Rev. B 66, 233408 ͑2002͔͒ and can be understood qualitatively on the basis of the jellium model.

Mass enhancement parameter in free-standing ultrathin Pb(111) films: The effect of spin-orbit coupling

“…42 Available experimental information relates to thin Pb(111) films grown on a substrate. 8,43,44 The LEED results 8 reported for ultrathin Pb films on Si(111) are shown in Fig. 1 for comparison.…”

“…[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] The experimental findings inspired a great amount of theoretical work focused on the thin film properties such as the critical temperature of superconductivity, 5,12,13 the electron-phonon coupling, 5,19,20 film surface vibrations, [17][18][19][20] electronic characteristics 14,15,[22][23][24] as well as on the impact of quantum size effect on the physical properties.…”

Self-consistent study of electron confinement to metallic thin films on solid surfaces

“…This may explain the large values 11,[21][22][23] obtained by this scheme in comparison to other experiments. [7][8][9] The reason for this disagreement is the basic fact that Eqs. ͑5͒ and ͑6͒ correspond to the infinite-potential well, whereas a finite potential well is closer to reality.…”

“…experiments, but with the corrected scheme we propose, it would be of one ML, as reported in other experiments. [7][8][9] In a recent paper 54 concerning Pb/ Cu͑111͒, the energy differences are used to estimate the thickness of the slab to be 22 ML, while the comparison to our calculation suggests that it is only 20 ML.…”

“…The oscillations in energy are the origin of the "magic" islands heights. [3][4][5][6][7][8][9][10][11][12][13][14][15][16] In a previous publication 13 we successfully applied a one-dimensional ͑1D͒ pseudopotential model to gain physical insight into the magic heights of Pb islands on Cu͑111͒, by studying the energetics of that system. In fact, the beating pattern obtained has been measured in the Pb/ Si͑111͒ system.…”