Quantum Beating Patterns in the Surface Energy of Pb Film Nanostructures

1
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.
Structure Stability
Extended X-Ray Reflectivity
Surface Morphology
Surface Energy
Results The relative stability of different
thicknesses (the discrete second derivative of
pN) shows bilayer variations with the preference
for even/odd thicknesses alternating
approximately every 9 AL. Assuming that the pN
values follow a Boltzmann distribution, this
beating effect is accurately reproduced by a
two-parameter (A and DN) 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.
Film Evolution (Annealing)

• 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)

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.
The fractional surface area covered by exactly N
Pb layers, pN, 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.