1. Film Nucleation and Growth
Section IV
Film Nucleation and Growth
© 1998, Angus Rockett

2. Nucleation
© 1998, Angus Rockett
Nucleation is a process of reversibly adding atoms to a small cluster until the cluster becomes stable.
Cluster energy rises initially (as r2) and then decreases (as r3).
When the cluster is large enough that it is unlikely to disappear, nucleation is said to have occurred.
2.0
surface energy
The critical radius r*
1.5
1.0
The nucleation energy barrier, E*
0.5
Cluster Energy (Arbitrary Units)
0.0
a “nucleus”
-0.5
volume energy
Substrate
-1.0
-1.5
-2.0 1 3 5 7 9 11
Cluster Size (atoms)

3. Nucleation
© 1998, Angus Rockett
The nucleation rate, R, is the number of nucleation events per second which occur in a given population.
Typically: R = rNa e -E*/kT
Thus, higher energy barriers and
lower temperatures delay nucleation.
r: an attempt frequency (constant)
N: the number of atoms/unit area
E*: the nucleation barrier
k: Boltzmann’s constant
T: Temperature
a: the effective reaction order
Cluster Energy (Arb. Units)
Cluster size (nm)
-2.0
-1.5
-1.0
-0.5
0.5
1.0
1.5
2.0 1 2
2.5 3
3.5
The gray curve shows the effect of atomic diffusion barriers on the energy curve.

4. © 1998, Angus Rockett
Nucleation
As atoms stick to the surface a population grows which eventually leads to nucleation of a layer.
Film Thickness
Nucleation Delay
Higher concentrations of adatoms decrease the nucleation delay.
Time (sec) or Dose (Monolayers)
Epitaxial growth on the same substrate does not require nucleation.

5. Growth
Once nuclei have been formed these grow by collection of atoms and transfer of atoms between the nuclei, and coalesce by moving as a unit until two nuclei meet.
Arriving atoms
Transfer among nuclei & coalescence
The rate at which nuclei grow depends on both the local atom density and the rate of supply of atoms by diffusion or arrival.
Substrate
Surface diffusion
A step edge on a nearly flat surface acts as an infinite size nucleus.
© 1998, Angus Rockett

6. Atomic-scale phenomena affecting nucleation & growth
Fast Ions & Neutrals
(and sometimes electrons)
Thermal Species
Adsorb
Diffuse
Desorb
Coalesce into clusters
Cluster growth
Create preferential nucleation sites
Disrupt small clusters
Increase effective adatom mobilities
Heat the surface
Substrate
© 1998, Angus Rockett

7. Strong chemical bonding
© 1998, Angus Rockett
Adsorption
Incident atoms or molecules must lose energy to bond.
Energy barriers may block transfer to stronger bonding structures.
Strong chemical bonding
Weak chemical bonding
van der Waals bonding
Core repulsion
0.2
0.4
0.6
0.8 1
Zero interaction
Energy (Arb. Units)
Energy barrier to strong bonding
Not all states shown may be present for a given system 1
1.5 2
2.5
Distance above the surface (Arb. Units)

8. Adsorption: Sticking Coefficient
© 1998, Angus Rockett
Adsorption: Sticking Coefficient
Some species stick only where a reactive site is available. If the adsorbing species stays on this site a limited time a steady state partial coverage results.
Total arrival rate: r
Adsorption 
Probability:
Reflection or very weak adsorption occurs at previously covered sites (~ 0).
Desorption
after average
Reflection 
time
Even on an open site the probabilityis less than 1.0
Surface Coverage: 
At steady state:  =  r 

9. Adsorption with Reaction
Chemical bonding during adsorption may require clearing a surface site.
Example: SiH4 adsorption on a hydrogen covered surface.
Significant reaction where unsaturated dangling bonds are present.
Little reaction where the surface bonds are saturated with hydrogen.
© 1998, Angus Rockett

10. Desorption rdes = Cn r0 e-G/kT
© 1998, Angus Rockett
Desorption
Atoms may leave a surface alone or in groups.
Desorption from chemically different areas proceeds at different rates
Associative desorption involves multiple atoms and is concentration dependent
Simple desorption is thermally activated and concentration independent
200
400
600
800
1000
1200
rdes = Cn r0 e-G/kT
Desorption Rate
rdes: the desorption rate T: Temperature
G: the desorption energy C: adatom concentration
k: Boltzmann’s constant r0: the desorption attempt rate
n: the desorption reaction order. 50
100
150
200
250
300
Temperature

11. Surface Diffusion D = D0 e-E/kT
© 1998, Angus Rockett
Surface Diffusion
Atoms move on simple surfaces by a series of jumps over energy barriers. The flux is given by Fick’s Law, F = -D dC/dx.
Barrier height is modified around surface steps and impurities.
The diffusivity, D:
Diffusion over individual barriers is given by:
D = D0 e-E/kT
Atoms spend the most time in the deepest energy minima.
Energy, E
D0: an attempt frequency (constant)
E: the energy barrier for a given hop
k: Boltzmann’s constant
T: Temperature
Position, x
A typical surface diffusion energy profile.

12. Surface Diffusion
Diffusion can be anisotropic if the surface structure lacks symmetry.
For example, on a reconstructed surface:
Slow diffusion across surface channels
Fast diffusion along surface channels
Anisotropic diffusion produces asymmetric island growth on the surface.
© 1998, Angus Rockett

13. Surface and Interface Structure
Thin films grow on substrates in such a way that they minimize interface energy. Critical points are:
the structures of the substrate and film lattices,
surface and interfacial energies [s, f , i,],
bonding configurations of substrate and film,
the relative sizes of the substrate and film lattices.
diamond
fcc f s i
3-fold coordinated
6-fold coordinated
tension
compression
© 1998, Angus Rockett

14. Grain Orientation in Polycrystals
Deposition on patterned substrates yields different microstructures for different orientations with respect to the incident flux.
Grains grow at similar rates leading to columns
Incident atom flux distribution
Poor quality underdense columnar structure.
Acceptable quality dense columnar microstructure
© 1997, Angus Rockett

15. Grain Orientation in Polycrystals
Polycrystalline films grown on amorphous substrates tend to have close packed planes outward. This maximizes atomic density on the initial surface and minimizes surface energy.
Thus fcc metals tend to have a (111) preferred orientation and bcc metals tend to have a (110) preferred orientation.
Substrate
This result is modified in some cases by:
The structure of a crystalline substrate / local epitaxy
Adsorbates on the substrate
Energetic particle bombardment
© 1998, Angus Rockett

16. Grain Structure in Polycrystals
As growth of polycrystalline films proceeds, some grains grow at the expense of others. This may lead to a change in texture with thickness.
Grains with the fast growing orientation
Substrate
Slower-growing grains
Growth rate differences due to:
Lower surface energies
Slower resputtering under ion bombardment
Higher reaction rate on some surface planes (in CVD)
© 1998, Angus Rockett

17. Surface Reconstruction
Most clean surfaces change their structure to:
reduce the number of dangling bonds,
minimize unpaired electrons in dangling bonds.
The simplest reconstruction to understand is the Si (100) surface.
Dangling bonds occur in pairs. Each is half filled with electrons.
Dangling bonds are filled.
New bonds are made.
These bonds act as hinges.
© 1998, Angus Rockett

18. Epitaxy
Growth of a single crystal on another single crystal with a specific alignment relation.
1000
Amorphous: atoms can not move even a few atomic spacings.
Amorphous
100
Single crystals require longer range atomic motion.
Growth Rate (arbitrary units)
Islanded surface
Flat: only in a narrow process window.
Slower growth of single crystals also typically reduces stacking faults
Polycrystalline 10
Flat surface
Single crystal 1
"Hot"
"Cold"
Inverse temperature (1/T)
The boundaries on this diagram are typically vague and depend on the length scale considered.
© 1998, Angus Rockett

19. Heteroepitaxy: Layer Morphology
The morphology of a heteroepitaxial layer depends on the change in surface energy and lattice constant.
2-dimensional layers
0.2
0.1
0.0
-0.1
2-dimensional layer + islands
Surface energy increases
Fractional change in surface energy 1 2 3 4 5 6
% change in lattice constant
3-dimensional islands
Surface energy increases
© 1998, Angus Rockett

20. Heteroepitaxy
The growth of one material on a chemically different single crystal substrate.
Strained:
Epitaxial layer has the substrate lattice spacing in the plane, different out of the plane.
Unstrained:
Epitaxial layer has its own lattice spacing.
© 1998, Angus Rockett

21. Heteroepitaxy
Lattice strain is relieved at a critical thickness where the elastic strain energy equals the interface energy increase upon strain relief.
Lattice strain energy per unit area increases linearly with increasing thickness
energy
The energy per unit area of defects associated with lattice mismatch (misfit dislocations) increases as the logarithm of thickness.
thickness 2
b: Burger’s Vector
: Poisson’s Ratio
: Dislocation core radius
: Angles defining the
dislocation
f: The misfit strain. h b ( 1 -  c o s  ) 
Critical thickness: h = l n [ c ] c
8f ( 1 +  ) c o s  b
© 1998, Angus Rockett

22. © 1998, Angus Rockett
Impurity Segregation
Impurities tend to redistribute across surfaces and interfaces and near crystallinity defects.
Atoms whose concentrations increase at surfaces:
Large atoms (relative to the matrix)
Atoms that reduce the surface energy (surfactants)
Attracted to the surface
Concentration
Rejected from the surface
Atoms whose concentration decreases at surfaces:
Atoms that increase the surface energy. 2 4 6 8
Depth (atomic layers)

23. Residual Stress in Thin Films
Two effects on residual stress:
Growth stress is intrinsic to the process and varies with deposition conditions such as rate.
Thermal stress
Growth stress
Deposition Temperature (T/T ) m 1
Total Stress
Film Stress (Arbitrary Units)
Thermal stress is intrinsic to the two materials in contact and varies with the temperature.
Tm: melting temperature
© 1998, Angus Rockett