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TECHNION - Department of Materials Engineering

The role of grain boundary and interface diffusion in solid state dewetting of thin metal films deposited on ceramic substrates

E. RabkinDepartment of Materials Science and Engineering, TECHNION – Israel

Institute of Technology1. Introduction: short-circuit diffusion in solids;

2. Solid state dewetting of thin films;

3. Diffusion along the film-substrate interface;

4. Grain boundary self-diffusion and sliding;

5. Diffusion-controlled growth of nanowires.

ER’s group: D. Amram, L. Klinger, O. Kovalenko, A. KosinovaIn the US: Prof. D.J. Srolovitz, Prof. J.R. Greer Financial support: US-Israel Bi-national Science Foundation; Israel Science Foundation; Russell Berry Nanotechnology Institute, Technion;

Workshop on Modeling and Simulation of Interface Dynamics, Singapore, May 2018


Minimization of surface/interface energyFor T<Tm ,the process is surface diffusion controlled - solid state dewetting

Solid state dewetting of thin films, final stage

SubstrateFilm

T

T

Particles equilibration – surface self-diffusion


Dewetting of isotropic single crystalline film, initial stage

Au

Sapphire

H. Wong et al., Acta mater., 2000 Depression Depression

Particle Particle

“Shedding mass” mechanism


Classical hierarchy of diffusion paths in solids

bulk

grain boundary

surface

Mishin, Kaur, Gust: Fundamentals of grain- and interphase boundary diffusion; Wiley, 1995


Final stages of Au film dewetting (particles)

We followed the size and shape changes of individual particles


Single crystalline particles are extraordinarily stable950 °C, in air

0 h

11 h

1 h

65 h0 100 200 300 400

0

50

100

150

Heig

ht, n

m

Length, nm

0h 1h 11h 65h

(e)

0 100 200 300 4000

50

100

150

Heig

ht, n

m

Width, nm

0h 1h 11h 65h

(f)O. Malyi, E. RabkinThe effect of evaporation on size and shape evolution of faceted gold nanoparticles on sapphireActa mater. 60 (2012) 261-268


Bi-crystalline particles readily change their size and shape

0 h 1 h

1 h0 h

“Rotation”


Bi-crystal single crystal transformation


Why faceted single crystal particles are so stable?

Coupled diffusion/surface islands nucleation may be difficult (Mullins & Rohrer, J. Amer. Ceram. Soc., 2000).

Movement of large faceted bump is slow

Chatain & Wynblatt, Interf. Sci., 2004: equilibration of Cu particles on sapphire is slow


As-deposited Ni film

SEM

35°AsB

Films are textured out-of-plane ([111]) and in-plane:

-Two orientation variants – 60° rotation around [111];

-Orientation relations:

-(common for fcc metals on c-plane sapphire).

Mazed bicrystal microstructure:

-columnar grains of 0.2-1 µm in size;

-Rrms=0.5 nm, FWHM(ω111)=0.2°

<111> tilt GBs

α−

α−

2 3

2 3

Ni Al O

Ni Al O

(111) || (0001)

[211] ||[1120]

Details in: D. Amram, L. Klinger, N. Gazit, H. Gluska, E. Rabkin, Acta mater. 69 (2014) 386


GB grooving + solid state dewetting

STEM HAADF


What is wrong with these GB grooves?

Apparent mass imbalance is caused by Ni self-diffusion along N/sapphire interface


A consequence: film thickening


Extension of Mullin’s model: interphase diffusion

Assumptions:

-no Ni accumulation at the GB;

-homogeneous film thickening;

-slow surface diffusion;

-small slope approximation

= →∞

= ==

= =′ ′′′= = =′′

=− ′′′′&0

0 00

0 0

( : 0)0t x

x xx

z z

z m Mullins zz

z Bz


Model predictions

MODE L

E X P.

The solution:

Groove dimensions:

Depth-

Width-

Film thickening-

Estimate for interphase diffusivity:

( )( )

14

14

( ) ,= ≡ xBt

z m Bt F u u

( )1

41.708=d m Bt

( )1

46.53=w Bt( )

12

1.13∆ =Bt

H mL

Di>Ds=(4.3±1.6)x10-13 m2/s

Interphase boundary diffusion is faster than surface diffusion!


Dewetting of thin Au films

15 min

60 min

25 nm thickness;Annealed at 400°C in air

Terraced morphology of the rim


SEM of terraced rim

Annealed for 180 min at 400°C in air

111

100

110

110

Pole figure (111)


Interface diffusion & GB sliding

1,1,1,111,1 )()( +−+++−− ++−+−=>< nnnnnnnnnnnnnnnn ffhVVhVVl ηησ

<−>

=knygb

knykn hh

hhf

,,

, γγγ

Details in: Kosinova, Kovalenko, Klinger & Rabkin, Scripta mater 82 (2014) 33

Grains grow upwards due to Au accretion at the Au-sapphire interface.

Generalization of “weighted mean curvature” approach of Taylor, Cahn and Carter:

W.C. Carter et al., ActaMater 43 (1995) 4309.


Thermodynamics of strongly anisotropic surfaces

L

δn

WMC=4γ L δn / L2δn = 4γ/L

The chemical potential averaged along the facet is equal to WMC

Weighted mean curvature (WMC):W.C. Carter, et al. Acta metall mater 1995; 43:4309.

( , )G x y ndAδ µ δΩ = ∫1 ( , )x y dAA

µ µ= ∫GV

δµδ

= Ω


Results, 1D model

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0

20

40

60

80

100

120

∆h0x10

∆h3x10

∆h2x10

∆h1x10

l0

nm

time, ks0.0 0.5 1.0 1.5 2.0 2.5

0

20

40

60

80

100

120

∆h0x10

∆h3x10

∆h2x10

∆h1x10

l0

nm

time, ks

ηn = 1×1019 Js/m4 ηn = 0


The effect of annealing atmosphere

Air Ar+10%H2

Annealed for 180 min at 400°C

Surface anisotropy of Au is higher during annealing in forming gas


Holes morphologies


2D model of dewetting (square-shaped grains)

A. Kosinova, O. Kovalenko, L. Klinger & E. Rabkin, Acta mater. 83 (2015) 91.

∑= iyx I

dtlhld )(

),min()()(

211

1

2

xxiiyy

iiiy ll

kTllDI µµν

−+

Ω=

Facet and interface chemical potentials:

1sx

y x

Ghl l

δµδ

=1

ix y

Gl l h

δµδ

=


Annealing in air (low surface anisotropy)

Dsmax/Dsmin=50


Annealing in forming gas (high surface anisotropy)

Dsmax/Dsmin=5


Dewetting of thin Fe films: what is wrong here?

Hole without rim of material

Hillock

25 nm thickness;Annealed at 750°Cfor 30 min


15 min 30

45 60 6045

3015 min

Kinetics of individual holes growth

Details in: Kovalenko, Greer & Rabkin, Acta mater 61 (2013) 3148


Where is the material from holes gone?

5h nm∆ ≈

The film gets thicker, the mass of Fe is conserved


Dewetting without surface diffusion: 1-D model

• One perfect sink grain in the vicinity of hole.• No surface diffusion. The interface is the only possible route for material

transfer.• The wall of the hole is flat and moves uniformly as a facet.

2i iDv

kT h Lδ γ∆ Ω

≈ −Di – interface self-diffusion coefficient;∆γ – driving force for dewetting


Dewetting without surface diffusion: 2-D model

2

b i i bh hD D u

dS w wdt kTh L

+ ∆ + Ω =

δ γ γ

2.42×10-21 m3/s <Dbδb <5.08×10-21 m3/s

Literature values for Dbδb at 750 °C:

2.6-2.8×10-21 m3/s [1]3.3×10-21 m3/s [2]

Dbδb

[1] Divinski et al., Z Metallkd; 2004,95:945

[2] Hänsel at al., Acta Metall; 1985, 33:659


Further example: mass-conserving growth of Fe nanowires

4 nm Fe on sapphire, 1100 °C

D. Amram, O. Kovalenko, L. Klinger, E. RabkinCapillary-driven growth of metallic nanowiresScripta mater. 109 (2015) 44-47


Au nanowires growth in passivated Au films

10 nm thick discontinuous Au film on glass, covered with 5 nm thick Al2O3layer produced by atomic layer deposition (ALD) method

A. Kosinova, D. Wang, P. Schaaf, A. Sharma, L. Klinger, E. RabkinWhiskers growth in thin passivated Au filmsActa mater. 149 (2018) 154-163


Au nanowires growth during annealing

800 °C, 1 h

900 °C, 1 h

Perfect single crystals with occasional stacking faults


Diffusion-controlled nanowires growth

)2()/ln(21

80

20

2

RhhHkTRD

dtdH γγν

−∆

+Ω

=

SubOAlOAlAuSubAu /// 3232γγγγ −+=∆ - driving force for nanowires growth


Interface diffusion is a primary suspect


Conclusions1. Single crystalline faceted particles are extraordinary stable;

remnant grain boundaries play an important role in shape evolution;

2. The surface-moving self-diffusion along singular facets is many orders of magnitude slower than along the non-singular surfaces;

3. In highly textured thin films, diffusion along the film-substrate interface, film-passivation layer interface, and along the grain boundaries is as important as the self-diffusion along the upper surface;

4. Interphase diffusion is a fundamental factor which should be accounted for in the models of microstructure evolution.


Thank you!

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