PC4259 Chapter 5

Surface Processes in Materials Growth & Processing

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:

ΔGv = -nkT ln (P0/ P∞)

(P∞: equilibrium vapor pressure over solid, n: solid atomic density)

When a growing sample is nearly in equilibrium with vapor, nucleation and growth is mainly governed by

thermodynamics

Formation of spherical cluster of radius r: energy increase

due to surface energy 4πr2γ , so total energy change:

G

r rcrit

Critical cluster radius: 2

critv

rG

Energy barrier:

3

2163crit

v

GG

ΔGhomo(r) = (4πr3/3)ΔGv + (4πr2)γ

When r > rcrit, the cluster becomes thermodynamically stable

Heterogeneous nucleation: clusters are formed on a

substrate (Cluster/substrate interface energy int, substrate surface

energy s) Truncated sphere of contact angle:

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!

θ = cos-1[(γs - γint)/γ]

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

γint ≤ γs – γf γint ≤ γs – γf with misfit γint ≥ γs – γf

Stranski-Krastanov growth of Ge on Si(001)

3D islands formation~ 3.5 ML Ge, 475°C, (110nm)2

huts

pyramids

Wetting layer~ 2.5 ML Ge, 475 °C, (44nm)2

4% lattice mismatch between Ge & Si

Atomic Processes in Nucleation & Growth

Adsorption, diffusion, incorporation, nucleation, desorption, coarsening

Si islands on Si(001)

Thermal activated process,

hopping frequency:

Atomic Diffusion on Terrace

)/exp(0 kTEdiff

Diffusivity: )/exp(4

20 kTEa

D diff

Diffusion barriers of

Rh on Rh surfaces

Anisotropic diffusion

Migration of cluster on surface

Fractal islands obtained in hit-and-stick or diffusion-

limited-aggregation (DLA) growth

Equilibrium island shape determined by step free

energy anisotropy

Islands grow in relatively compact shape at a raised T

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

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

Island density N & deposition amount are related as:

2~ ii

FN

where:

kT

Ediffexp0

Island size distributions:

Ns density of islands of size s, so:

is

sNN

1s

ssN

Average island size:

)/(2

ssfsN is

NsNsis

s /

Scaling function: )/( ssf i

Coarsening of islands

Island coalescence: merging of islands in contact

Ostwald ripening: vapor of smaller islands absorbed by larger ones

Gradient of vapor pressure generates atomic flux towards larger island

rkT

mrprp

pvv

2exp)()(Kelvin effect:

4 stages in sub-ML nucleation & growth:

1. Low coverage (L), nucleation dominates

2. Intermediate coverage (I), island density approaches saturation

3. Aggregation (A), island density saturates

4. Coalescence (C), island density decreases

Variation of density of islands (nx) & adatoms (n1)

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

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:

)1( 11

Fdt

d

Coverages of upper layers n, n = 2,

3…, can be found in similar way (see Homework 9.1)

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

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:

d

II SS exp0

dII FF exp1

If island growth, nearly linear variations

Reflection high-energy electron diffraction (RHEED)

For real-time surface monitoring in molecular beam epitaxy

1. Surface reconstruction

2. Period in layer-by-layer growth

3. 2D or 3D growth

RHEED Pattern

RHEED in MBE System

Surface reconstruction

Streaky diffraction pattern from a flat surface

Rough vs. Smooth Surface

Rough & 3D: Spotty pattern

Smooth & 2D Streaky pattern

RHEED Intensity Oscillation

When electron waves from neighboring atomic layers interfere destructively

1 oscillation cycle = 1 MLFor precise

growth rate &

film

thickness

control

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)

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

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

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.

surfactant