Cao Z. (Ed.) Thin Film Growth: Physics, materials science and applications

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398 Thin ﬁlm growth

As can be seen in Fig. 16.8(a) and (b), the re-emission process which is

the dominant process in normal angle growth promotes an exponential degree

distribution; while shadowing which is the governing effect during oblique

angle deposition leads to a power-law distribution. On the other hand, CVD

shows an exponential degree distribution at initial times of growth, while it

becomes closer to power-law type for higher sticking coefcients, s > 0.5.

This is believed to be competing forces of re-emission and shadowing effects,

where the re-emission is more dominant for smaller sticking coefcients

and at initial times of the growth when the lm is smoother, leading to an

exponential degree distribution. However, the shadowing effect originating

from the obliquely incident particles within the angular distribution of CVD

ux can lead to a power-law behavior at higher sticking coefcients especially

when the lm gets rougher at later stages of growth. A power-law degree

distribution corresponds to a more correlated network that is consistent with

the long-range, column-to-column trafc observed in surface-degree plots

of high sticking coefcient CVD above (Fig. 16.6(b)). It is also realized

that especially for high sticking coefcients, there exist high degree nodes

represented with data points at the tails of the degree distributions. These

relatively small percentage but highly connected nodes are mainly located at

the column edges as seen in the surface degree plot of Fig. 16.6(b) and are

likely to be the ‘hubs’ of the network. Therefore, briey, degree distribution

during cVD growth can be similar to the universal line of normal incidence

growth for smaller sticking coefcients (s < 0.5) showing an exponential

behavior with a short range network trafc; or it can converge to the universal

power-law degree distribution of oblique angle deposition for higher sticking

coefcients (s > 0.5) leading to a highly correlated network driven mostly

at column edges.

In addition, it is revealed from average distance versus degree plots of

Fig. 16.8(c) and (d) that nodes with high degree are mainly linked with long-

distance surface points. Independent of the deposition method, the average

distance changes with degree k according to a power-law behavior, where

the value of the exponent increases as the ux becomes more oblique (i.e.,

A0 Æ A85 Æ CVD in Fig. 16.8(c) and (d)), sticking coefcient increases,

and the lm gets thicker (i.e., Fig. 16.8(c) Æ (d)). In other words, when

the shadowing effect becomes more dominant and lm morphology gets

more columnar, high degree nodes can exchange atoms with longer distance

surface points. This also implies that high degree nodes placed on column

edges (Fig. 16.6(b)) of high sticking coefcient growth are more likely to

transfer particles with other more distant column edges as well. This process

is further supported by the distance distribution plots of Fig. 16.8(e) and

(f) where as the sticking coefcient is increased (i.e. less re-emission) and

more obliquely deposited particles are introduced (more shadowing effect),

a higher percentage of particles start to travel longer distances. On the other

ThinFilm-Zexian-16.indd 398 7/1/11 9:46:41 AM

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399Network behavior in thin ﬁlms & nanostructure growth dynamics

hand, for smaller sticking coefcients and normal angle deposition, where

the re-emission effect is more dominant, average distances particles travel

from high degree nodes become signicantly less compared to high sticking

coefcient and oblique angle depositions. This suggests networking during

re-emission dominated growth occurs mainly among smaller size hills and

valleys, consistent with the surface-degree plot of Fig. 16.6(a).

A more interesting universal behavior is observed in a ‘weighted and

scaled average distance’ versus degree plots of Fig. 16.9(a) and (b). Here

we re-scale average distance for nodes with degree k, <l

>, rst with degree

k, then with the average distance value of all nodes <l> (average distance

of all links), and plot <l

>/(k<l>) versus k. After re-scaling, independent of

the deposition technique used, sticking coefcients, and the growth time,

all curves fall on a similar line obeying a power-law behavior with <l

(k<l>) ~ k

–1.2

. The origin of the –1.2 value of the exponent is not clear and

is under investigation.

Another universal behavior is observed in distance distribution plots.

Independent of sticking coefcients, normal incidence growth shows a

power-law behavior with P(l) ~ l

–3

. A similar power-law behavior with an

exponent of –2.75 has been observed in the distance distribution plots during

a normal incidence growth simulation with re-emission (p. 83 of Ref. [14]).

The authors of that work did not use a snapshot state approach, surface

morphology changed continuously, and therefore they measured a kind of

average distance distribution of the whole growth simulation. However, their

exponent value is still close to our results and agrees with our ndings that

dynamic network behavior during normal incidence deposition does not

change signicantly due to the relatively smooth morphology throughout

the growth. On the other hand, the behavior in distance distribution plots is

exponential for oblique angle deposition (conrmed in the semi-log plots,

not shown here). CVD has a power-law behavior similar to that of normal

incidence growth with P(l) ~ l

–3

at smaller coefcients and at initial times

of growth, and becomes exponential similar to oblique angle deposition at

higher sticking coefcients apparent especially in later stages of growth.

16.5 Conclusions

In conclusion, we presented a new network modeling approach for various

thin lm growth techniques that incorporates re-emitted particles due to the

non-unity sticking coefcients. We dene a network link when a particle is

re-emitted from one surface site to another. Monte Carlo simulations are used

to grow lms and dynamically track the trajectories of re-emitted particles.

We performed simulations for normal incidence, oblique angle, and CVD

techniques. Each deposition method leads to a different dynamic evolution

of surface morphology due to different sticking coefcients involved and

ThinFilm-Zexian-16.indd 399 7/1/11 9:46:41 AM

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400 Thin ﬁlm growth

different strength of shadowing effect originating from the obliquely incident

particles. Traditional dynamic scaling analysis on surface morphology cannot

point to any universal behavior. On the other hand, our detailed network

analysis reveals that there exist universal behaviors in degree distributions,

weighted average degree versus degree, and distance distributions independent

of the sticking coefcient used and sometimes even independent of the

growth technique. We also observe that network trafc during high sticking

coefcient CVD and oblique angle deposition occurs mainly among edges

of the columnar structures formed, while it is more uniform and short-range

among hills and valleys of small sticking coefcient CVD and normal angle

depositions that produce smoother surfaces.

A0, s = 0.1

A0, s = 0.5

A0, s = 0.9

A85, s = 0.1

A85, s = 0.5

A85, s = 0.9

CVD, s = 0.1

CVD, s = 0.5

CVD, s = 0.9

A0, s = 0.1

A0, s = 0.5

A0, s = 0.9

A85, s = 0.1

A85, s = 0.5

A85, s = 0.9

CVD, s = 0.1

CVD, s = 0.5

CVD, s = 0.9

–2

>/(k <l >)<l

>/(k <l >)

(a)

(b)

–1.2

16.9 Weighted average distance <l

>/(k<l>) versus degree k for

network models of a Monte Carlo simulated normal incidence

evaporation (A0), oblique angle deposition (A85), and CVD thin

ﬁlm growth for various sticking coefﬁcients s and for two different

deposition times t (a: t = 1.25 ¥ 10

particles, and b: t = 23.75 ¥ 10

particles).

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401Network behavior in thin ﬁlms & nanostructure growth dynamics

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404

Index

adatoms, 11–15, 391

schematic illustration, 11

Ag lm, 26–7

all-order re-emission, 391

AlN, 297–300

angle-resolved photoemission

spectroscopy, 25–8

Ag on Fe(100) normal emission

photoemission spectra, 27

silver energy band structure, 26

anisotropic diffusion, 64

anisotropy, 55

anti-Bragg oscillations, 102–6

antiferroelectric thin lms, 370–1

Apollonius packing, 156

ARPES see angle-resolved photoemission

spectroscopy

atomic force microscope, 212

atomic force microscopy, 90, 233

atomic layer deposition, 70

atomic steps

morphological instability, 15–16

evolution of atomic step instability,

motion on growing and evaporating Si

(111) surface, 11–15

adatoms schematic illustration, 11

atomic steps temperature

dependence, 13

circular terraces radii, 15

SEM images circular atomic steps,

step-ow evaporation, 12

step-ow growth and evaporation

illustration, 14

observation method, 6–8

SEM image in quenching method, 8

SEM image on phase transition

temperature, 7

atomically uniform lms, 28–9

Ag lms normal emission

photoemission spectra, 29, 30

principles and nanostructure

development, 35–46

normal emission photoemision

intensity, 36

relative surface energy, 43

schematic growth of Pb on Si (111),

stability temperature and density-

functional calculation, 38

temperature stability, 45

thickness of Pb on Si (111), 44

quantum electronic stability, 22–48

angle-resolved photoemission

spectroscopy, 25–8

electronic growth, 23–5

future trends, 47–8

particle-in-a-box, 46–7

thermal stability, 29–35

auger electron spectroscopy (AES), 101

BCF model, 53

bending energy, 343, 345, 349, 355

Bohr-Sommerfeld, 27–8

Boltzmann distribution, 275

Brillouin zone, 25, 37

Brownian forces, 157

buckling, 317–37

diamond-like thin carbon lm

deposited on a glass substrate,

318

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405Index

experimental observations, 320–2, 323

buckling induced by substrate

plasticity, 321–2

buckling structures, 320–1

nickel thin lm 150 nm thick

deposited on LiF single crystal,

323

nickel thin lms deposited on LiF

single crystals, 322

primary slip systems orientation,

321

localisation of buckling structures,

329–30

above the steps formed during

dislocations in the substrate,

329

effects of uniaxial strain on a thin

lm, 330

mechanical properties measurement,

333–6

effect of adhesion on evolution of

buckle height vs applied stress

on its edges, 335

modelling, 322–9

buckling on crystalline substrates,

325–9

comparison between two

benchmarks, 328

evolution of delaminated strip of the

lm, 326

Föppl–von Kármán theory of

buckling, 322–5

theoretical prole associated with

fundamental solution of a lm

undergoing displacements, 327

theoretical prole of a straight-sided

buckle, 325, 328

slip systems, 330–1

straight-sided buckle formed during

the activation of two symmetric

slip systems, 331

straight-sided buckles on 100 nm thick

lm, 319

telephone cord buckling patterns on a

thin lm, 319

tensile tests, 331–3, 334

evolution of thin lm deposited on

crystalline substrate, 332

thin lm strain in tension on step

formed during emergence of

dislocations, 334

unstressed thin lm on a step

formed during emergence of

dislocations, 332

vertical displacement of thin lm in

equilibrium state on crystalline

substrate, 337

buckling amplitude, 345, 346, 350

buckling prole, 355

buckling wavelength, 345

buffered oxide etchant (BOE), 212

CAICISS see coaxial impact collision in

ion scattering spectroscopy

carbon-nanotube lms, 225

carbon supersaturation, 245

catalyst-enhanced chemical vapour

deposition, 75

CBED see convergent beam electron

diffraction

chemical etching, 289–90

chemical vapour deposition, 60–1, 127,

211

circular photogalvanic effect (CPGE),

291–2

coalescence, 67–8