Structural Quantum Size Effects in Pb/Si(111)

1
Structural Quantum Size Effects in Pb/Si(111) P.
Czoschke, Hawoong Hong, M. Holt, L. Basile and
T.-C. Chiang Department of Physics, University of
Illinois at Urbana-Champaign 1110 W. Green St.,
Urbana, IL 61801
Introduction Ultrathin films of Pb on Si(111)
have exhibited a peculiar growth behavior in
which highly-uniform flat-topped islands of
preferred heights form at low temperature
(120-200 K). This behavior has been attributed
to quantum size effects (QSE). If QSE do play a
significant role in this system, wed expect to
see thickness-dependent structural effects as
well. In this study we determine if these
effects are present and try to correlate them
with QSE using surface x-ray diffraction.

• Experiment
• Specular integrated intensity was collected ?
  only sensitive to structure in the z-direction.
• Pb films were grown with molecular beam epitaxy
  at temperatures between 120-200 K.
• Data was taken for samples with films deposited
  on different interfaces and different coverages.
  Different interfaces have different physical and
  electronic properties.
• All spectra exhibit half-order features which are
  indicative of a quasi-doubling in the periodicity
  of the structural order along the surface normal.
  These features are not reproduced without taking
  into account interlayer relaxations within the Pb
  film.

2. Experimental Data (Specular Integrated
Intensity)

• Quantum Size Effects (QSE)
• Confinement of conduction electrons in the film
  leads to Friedel-like oscillations in the charge
  density.
• If present, atomic displacements should be
  approximately proportional to the first
  derivative of the charge density variations.
• The charge density variations in the metal film
  have a wavelength approximately equal to half the
  Fermi wavelength, as with Friedel oscillations.
• In Pb/Si(111), this is about 1.8 atomic layer
  spacings, so layers should relax with a
  bilayer-like periodicity.

3. Layer Relaxations
FIG. 3 Results for the layer relaxations of the
Pb overlayers for the samples in Fig. 2. Solid
curves are continuous functions for a model in
which the layer relaxations follow the
Friedel-like oscillations of the charge density.
The model contains four free parameters which are
used to fit the experimental data. Points are
the actual layer relaxation values for the Pb
overlayers i.e., the leftmost point is the
relaxation value for d12, the spacing between the
first and second atomic layers next to the Si
substrate. The abscissa is the distance into the
quantum well, where z 0 is the substrate side
of the well.
1. Friedel Oscillations in a Quantum Well

• Summary
• It has been shown that quantum confinement can
  have significant structural consequences in thin
  metal films.
• A free-electron model in which Friedel-like
  oscillations are present in the charge density
  can be used to quantitatively study the
  structural relaxations in Pb/Si(111).
• Such effects will have to be taken into
  consideration in the development of
  nanostructures that approach the atomic scale.
• See P. Czoschke, et al., Physical Review Letters,
  91, 226801 (2003)

FIG. 2 Experimental data (points) and fits
(lines) for (a) 8.5 ML Pb deposited on
Si(111)-7x7 at 185 K and (b) 4.5 ML Pb deposited
on the Pb/Si(111)-?3 x ?3 interface at 115 K and
annealed to 180 K. The abscissa is in surface
reciprocal lattice units such that the sharp
peaks at l 3 and 9 correspond to the (111) and
(333) Si bulk-indexed Bragg peaks, respectively.
In these units, the (111) and (222) bulk Pb
Bragg peaks would be at l 3.3 and 6.6,
respectively. The solid curves are fits to a
model following the Friedel oscillations of the
charge density. The dashed lines are fits
assuming all the Pb overlayers have the same
thickness. Half-order features are clearly
present in both spectra (arrows), indicating a
bilayer-like superperiod in the Pb film.
FIG. 1 A metal film adsorbed to a substrate acts
like an infinite potential well confining the
electrons in the metal. As a result, Friedel
oscillations in the charge density are present in
the film. The metal atoms are schematically
represented at the bottom of the figure, showing
the geometry of the quantum well. The surface
normal (z-direction) is horizontal in the figure.
The first derivative is used to predict the
atomic displacements due to QSE.
Acknowledgements The UNICAT facility at the
Advanced Photon Source (APS) is supported by the
University of Illinois at Urbana-Champaign,
Materials Research Laboratory (U.S. DOE, the
State of Illinois-IBHE-HECA, and the NSF), the
Oak Ridge National Laboratory (U.S. DOE under
contract with UT-Battelle LLC), the National
Institute of Standards and Technology (U.S.
Department of Commerce) and UOP LLC. The APS is
supported by the U.S. DOE, Basic Energy Sciences,
Office of Science under contract No.
W-31-109-ENG-38.