Quantum Electronic Effects on Growth and Structure of Thin Films
P. Czoschke, Hawoong Hong, L. Basile, C.-M. Wei,
M. Y. Chou, M. Holt, Z. Wu, H. Chen and T.-C. Chiang
Introduction
When the dimensions of a nano-device approach the de Broglie wavelength of the device’s conduction electrons, quantum
effects become increasingly important to the physical properties of the system. We have performed surface x-ray diffraction
studies with high-intensity synchrotron radiation to probe the growth behavior and structure of ultrathin films of lead on
silicon. We observe an unusual “magic height” effect that results in alternating island and layer-by-layer growth as well as
significant quasi-bilayer layer relaxations in the structure of the films. Both effects have been linked to the electronic
properties of the system.
Growth Behavior and Morphology
• 1st stage - a wetting monolayer (ML) forms
• 2nd stage - uniform-height (5 ML) magic islands form on the
wetting layer and grow laterally to fill the surface
• 3rd stage - layer-by-layer growth beyond 6 ML
CCD Image taken during growth
Quantum Oscillations in Film Structure
• Using the layer-by-layer growth mode, flat films with near
atomic uniformity are grown and studied.
• 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 quasi-bilayer periodicity.
A schematic of the quantum well formed by
a thin metal film and the Friedel oscillations
in the charge density that result.
Pb(10L)
Extracted Profiles of the Pb(10L) Rod
Si(10L)
1300 s
379 s
(a) Beyond ~6 ML, smooth
evolution
of
multilayer
satellite peaks implies layerby-layer growth
Reflectivity
1300 s
941 s
788 s
635 s
379 s
(b)
(c)
379 s
327 s
276 s
Extended x-ray reflectivity data show multiple interference fringes
due to the Pb overlayers for (a) a 10 layer thick film and (b) an 8
layer thick film. The features pointed out with arrows are halfway
between the Pb Bragg peaks (at l = 3.3 and 6.6) and are thus an
indication of a quasi-bilayer periodicity in the interlayer spacings
of the film. The solid curves are fits to a model following the
Friedel oscillations of the charge density and the dashed lines are
fits assuming all the Pb overlayers have the same thickness. The
model accurately reproduces the features of the data.
(a)
225 s
174 s
123 s
21 s
(b) 1.5 – 6 ML, constant
profile; islands of height 51
ML growing laterally to fill
surface
X-rays illuminate the substrate at
a grazing angle. The surface
normal is parallel to the
horizontal direction. Direct beam
is at bottom left-hand side of the
picture (not pictured).
10
(b)
5
0
Relaxation (% dbulk)
Intensities (arb. units)
(a)
Pb(102)
Intensity (arb. units)
Pb(101)
(c) Sharp onset of Pb Bragg
peaks at ~350s (1.5 ML) –
formation of Pb islands
-5
-10
0
5
10
15
20
25
10
5
0
-5
0
1
2
Perpendicular Crystal Momentum L
(a)
• Both freestanding and supported films show oscillations with period  = 1.8 ML
(1/2 of the Fermi wave length), which is very close to 2 ML.
• Beating period /(2-)= 9 ML for the envelope function (dotted curves)
• Phase of beating pattern depends on boundary conditions
• A phase change for Pb on Si leads to two deep minima at N = 1 and 6.
• Energy minimization results in spontaneous phase separation into a wetting layer
and magic islands.
• At higher coverages, smooth layer growth takes place to minimize step and kink
energies
3
4
5
6
l = qzd/2
7
8
9
10
-10
0
Experimental Data Points
Fits to Model with Interlayer Relaxations
Fits without Relaxations
5
10
z (Å)
15
20
Physical Review Letters, 91, 226801
Summary
0.2
-0.6
oscillations and beating
(b)
Pb Films on Si(111)
-0.7
magic islands
kBT
wetting layer
-0.8
0
Physical Review Letters, 90, 76104 (2003)
2
0.3
Relative Surface Energy ES (eV)
First-principles electronic structure calculations
Freestanding Pb Films
1
Layer relaxations resulting
from the model fits to the
experimental data (points).
The origin corresponds to
the substrate side of the
quantum well. The solid
lines are derived from the
first derivative of the
charge density.
2
4
6
8
10 12 14 16
Film Thickness N (ML)
• The global energy landscape, rather then the local stability as emphasized in previous studies, is key to
understanding this type of film growth involving alternating layer and magic-island formation.
• It has been shown that quantum confinement can have significant consequences on the structure and growth
behavior of thin metal films.
• A free-electron model in which Friedel-like oscillations are present in the charge density can be used to
quantitatively understand the structural relaxations in Pb/Si.
• These effects have significant implications and must be taken into consideration in the development of
nanostructures that approach the atomic scale.
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.