Probing the Nanoscale

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PC4259 Chapter 5 Surface Processes in Materials
Growth Processing
When a growing sample is nearly in equilibrium
with vapor, nucleation and growth is mainly
governed by thermodynamics
Homogeneous nucleation solid (or liquid)
clusters nucleated in a supersaturated vapor of
pressure P0
Thermodynamic driving force --- free energy
change per unit volume of condensed phase
?Gv -nkT ln (P0/ P8)
(P8 equilibrium vapor pressure over solid, n
solid atomic density)
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Formation of spherical cluster of radius r
energy increase due to surface energy 4pr2? , so
total energy change
?Ghomo(r) (4pr3/3)?Gv (4pr2)?
?G
r rcrit
Critical cluster radius
Energy barrier
When r gt rcrit, the cluster becomes
thermodynamically stable
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Heterogeneous nucleation clusters are formed on
a substrate (Cluster/substrate interface energy
?int, substrate surface energy ?s)
Truncated sphere of contact angle
? cos-1(?s - ?int)/?
When ?s ? ?int ?, ? 0, complete wetting
When ?int ? ?s ?, ? 180, spherical ball
without any wetting
Free energy barrier for stable nucleation
?Ghet ?Ghomo(2 cos?)(1 - cos?)2/4
Hetero-nucleation barrier is significantly lower
than that of homo-nucleation in general!
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Epitaxy Crystalline film growth on a crystalline
substrate in a unique lattice orientation
relationship
Growth proceeds as atomic layers stacking up
sequentially
Three growth modes
?int ?s ?f ?int ?s ?f with misfit
?int ?s ?f
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Stranski-Krastanov growth of Ge on Si(001)
4 lattice mismatch between Ge Si
pyramids
huts
Wetting layer 2.5 ML Ge, 475 C, (44nm)2
3D islands formation 3.5 ML Ge, 475C, (110nm)2
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Atomic Processes in Nucleation Growth
Adsorption, diffusion, incorporation,
nucleation, desorption, coarsening
Si islands on Si(001)
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Atomic Diffusion on Terrace
Thermal activated process, hopping frequency
Diffusivity
Anisotropic diffusion
Diffusion barriers of Rh on Rh surfaces
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Migration of cluster on surface
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Islands grow in relatively compact shape at a
raised T
Fractal islands obtained in hit-and-stick or
diffusion-limited-aggregation (DLA) growth
Equilibrium island shape determined by step free
energy anisotropy
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Atom detachment makes small islands unstable. At
given T F, there is a critical island size i to
which addition of just 1 atom makes it stable
Island density N deposition amount ? are
related as
where
Fe on Fe(100) growth at F 0.016 ML/s, ? 0.07
ML but different T. Ediff 0.45 eV i 1 from
lnN vs 1/T
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Ns density of islands of size s, so
Island size distributions
Average island size
Scaling function
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Coarsening of islands
Island coalescence merging of islands in contact
Ostwald ripening vapor of smaller islands
absorbed by larger ones
Kelvin effect
Gradient of vapor pressure generates atomic flux
towards larger island
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4 stages in sub-ML nucleation growth

• Low coverage (L), nucleation dominates
• Intermediate coverage (I), island density
  approaches saturation
• Aggregation (A), island density saturates
• Coalescence (C), island density decreases

Variation of density of islands (nx) adatoms
(n1)
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Inter-layer atomic transport in growth
Layer-by-layer growth requires sufficient
inter-layer atomic transport
Ehrlich-Schwoebel barrier EES additional barrier
for adatom jumps down a step edge due to less
neighbors than at a regular terrace site
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Insufficient inter-layer transport leads to
multilayer growth a rough surface
If inter-layer atomic motion is completely
forbidden, the coverage of first layer ? 1
satisfies
Coverages of upper layers ?n, n 2, 3, can be
found in similar way (see Homework 9.1)
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Step-flow growth atoms quickly migrate to step
edges instead of island nucleation, film growth
proceeds as the advancement of existing steps
Three kinetic growth modes Phase diagram
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Monitoring growth morphology
STM AFM high resolution for atomic details for
both homo- and hetero-epitaxy but interrupt
growth, time consuming and limited sample size (
1 cm2)
AES for heteroepitaxy, monitoring film
substrate peak intensities. Different intensity
variation characters in different growth modes
If layer-by-layer
If island growth, nearly linear variations
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Reflection high-energy electron diffraction
(RHEED)
For real-time surface monitoring in molecular
beam epitaxy

• Surface reconstruction
• Period in layer-by-layer growth
• 2D or 3D growth

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RHEED in MBE System
Streaky diffraction pattern from a flat surface
RHEED Pattern
Surface reconstruction
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Rough vs. Smooth Surface
Smooth 2D Streaky pattern
Rough 3D Spotty pattern
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RHEED Intensity Oscillation
When electron waves from neighboring atomic
layers interfere destructively
1 oscillation cycle 1 ML
For precise growth rate film thickness control
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Modification of Growth Morphology by Surfactant
General surfactant adsorbed layer modifies
surface thermodynamic properties, e.g. surface
tension, friction coefficient, sticking power
Surfactant in film growth adsorbed impurities
which facilitate, thermodynamically or
kinetically, the growth proceed in a desired
mode, normally layer-by-layer
Surfactant should keep floating on surface so it
is not consumed in growth, so surfactant should
have a low surface energy, e.g. Sb (? 0.6 J/m2)

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Surfactant based on thermodynamics

• Film is covered with 1 ML of surfactant with a
  lower ?
• Deposited atoms exchange position with surfactant
  atoms in order to reduce ?
• Floating surfactant layer keeps film surface
  smooth

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Surfactant based on kinetics
Some surfactant atoms tend to decorate step
edges deposited atoms can take the sites of
surfactant atoms and push them outward, an
effectively lower EES
surfactant
Some surfactant atoms act as nucleation centers
to form a large density of islands with small
size. Atoms deposited later easily attach to
island edges instead of nucleation of upper-layer
islands. Such film surface appears rough at
small scale but smooth at large scale.