1. Film Formation
1. Introduction
Thin film growth modes

2. (1)  Island (Volmer-Weber) Growth Mode
- Atoms in the film are more strongly bound to each other than
to the substrate.
- metal/insulator, alkali halide, graphite, mica
(2) Layer (Frank – van der Merwe) Growth Mode
- Atoms are more strongly bound to the substrate than to each other.
layer by layer growth
(3)  Layer + Island ( Stranski - Krastanow) Growth Mode
- Intermediate (1) & (2)
- eq. strain energy due to lattice mismatch trigger island formation
metal / metal, metal / semiconductor
- Capillarity Theory
- Atomistic Nucleation Processes
- Cluster Coalescence and Depletion
- Experimental Studies of Nucleation & Growth
- Grain Structures
- Amorphous thin films

3. 2. Capillarity Theory
Simple qualitative thermodynamic theory  lack of atomistic process
However, connections of T, deposition rate, critical nucleus size
can be obtained.
2-1. Homogeneous nucleation of a spherical solid phase of radius
 from a prior supersaturated vapor
 Nucleation occurs during the very early stages of phase change
Gas-to-solid transformation results in decrease of G :
Where,
Gv : change in free energy per unit volume
W    : atomic volume
Ps : vapor pressure above solid
Pv : pressure of supersaturated vapor

4. Vapor
supersaturation
without vapor supersaturation (S = 0), Gv = 0  no nucleation
with Pv > Ps, Gv < 0  nucleation
New surfaces and interfaces form :
G: total free energy change in forming the nucleus
: surface free energy
per unit area

5. G* : energy barrier to the nucleus process
If r < r* : cluster is unstable and shrink
r > r* : cluster is stable and grow larger while lowering
the energy of system

6. Nucleation rate

7. Where,
Nucleation rate is also S dependent in the gas phase.
S=0 : no nucleation
S>0 : nucleation is possible  troublesome in CVD

8. a3 r3 =  ( 2 - 3cos + cos3 ) / 3 r3 : volume
2.2 Heterogeneous nucleation of solid film on a planar substrate
a3 r3 =  ( 2 - 3cos + cos3 ) / 3 r3 : volume
a2 r2 =  sin2 r2 : projected circular area
a1 r2 = 2  ( 1 - cos ) r2 : curved surface area

9. Young’s equation: mechanical equilibrium among the interfacial tensions
sv = fs + vf cos
 island growth :  > 0  sv < fs + vf
 layer growth :  = 0  sv = fs + vf
If fs = 0 (no interface )  homo- or autoepitaxy
 S.K growth : sv > fs + vf
The strain energy of film overgrowth is large with respect to vf ,
permitting nuclei to form above the layer.
The critical nucleus size r*,

10. see < Fig. 1-19>
homogeneous
nucleation
Wetting(layer) : wetting factor = 0 at  = 0
Dewetting(sphere) : w. f. =1, at  = 180

11. 2.3 Nucleation Rate
The rate at which critical nuclei grow depends on the rate at which
adsorbed adatoms attach to it in the earliest stage of film growth.
a0 : atomic dimension
The impingement rate onto area A*
= jump frequency  na
adatom surface density

12. adatom diffusive jumps :  e -Es/kT
Es is the activation energy for surface diffusion.
* Random walk for a time t over a mean square distance <X2> :
<X2> = 2DSt
DS = D0 exp (-Es/kT)
* Residence time S of adatoms

13. During the residence time, adatoms diffuse a mean distance X :
surface diffusion coefficient DS :

14. high nucleation rate fine grained, amorphous
low nucleation rate coarse-grained, single crystal
steep dependence of on the vapor supersaturation ratio.
2.4. Nucleation dependence on substrate temperature
and deposition rate ( : atoms /cm2•sec)

15. Assuming an insert substrate, fs = vf
Assuming typical values,

16. Large r* and G*  large crystallites, monocrystal
hi substrate temp.
low deposition rate
Small r* and G*  polycrystallites

18. Time to consider an atomistic model instead of thermodynamic
capillarity model.
Let’s estimate r* ;
 = 20  cm3
 = 1000 ergs / cm2
PV = Torr
PS = Torr
For example
Then r* = 6  10 –8 cm Size is too small for continuous concepts
like surface tension and nucleus radius.
An atomistic model for heterogeneous
nucleation will be more realistic.

19. 3. Atomistic Nucleation Processes
3.1 The Walton-Rhodin Theory
The critical concentration of clusters of size i,
Ei* : critical dissociation energy which is required to disintegrate
a critical cluster containing i atoms into i separate atoms
n0 : total density of adsorption sites
N1 : monomer density

20. Critical monomer supply rate = (vapor impingement rate)
 (area by surface diffusion before desorbing)
Then,
Therefore, the critical nucleation rate ( cm-2  sec-1 )
Measuring i* and Ei* is better than G*, ,  for small nuclei.

21. One of the applications of this theory is the subject of epitaxy
At hi supersaturations & low temp.;
 i* = 1 (single adatom is the critical nucleus)

22. At hi temperature, 2~3 atom nuclei are possible
Epitaxy : stable nuclei (clusters) + adatoms
 same as original surface structure.
There exist the critical temperatures where the nucleus size
and orientation change.
T12 : transition temperature from one to two atom nucleus.

23. From Fig 5-4
 Edes + Es = 1.48ev at 1Å/sec
 obtain epitaxial transition temperature for a given Ŕ
T=577K for Ŕ= 8.5x1014 atoms/cm2-sec
There is another way to estimate epitaxial growth temperature
based on surface-diffusion.
For layer-by-layer growth,
ledge
terrace
atoms

24. A typical terrace width of 100-1000 atoms
During the monolayer growth time of 0.1 ~ 1 sec
This means different critical epitaxial growth temperatures exist
For different materials. (TE)

25. At Ds = 10-8 cm2/sec :
TE ~ 0.5 TM for layer growth on group IV semiconductors
 TE ~ 0.3TM for metals
TE ~ 0.1 TM alkali hilides
These epitaxial growth temperature agree qualitatively with
Experimental values.
From RHEED intensity oscillations,
TEs of 0.2 TM, 0.12TM, TM are also observed.