VVéékonyrkonyréétegektegek elelőőáállllííttáása sa éés alkalmazs alkalmazáásaisai

Dr. Geretovszky Zsolt

2010. szeptember 13.

Basic modes of thinBasic modes of thin--film growthfilm growth

deposit is more strongly bound to each other than to substrate (e.g. metals and semiconductors on oxide substrates)is

land

the formation of one or a few ML is followed by island growth; (fairly common in metal-metal or metal-semiconductorsystems)

S-K

atoms are more strongly bound to the substrate than to each other (e.g. semiconductors)la

yer

The growth of the film usually takes place in one of the three most common growth modes (categories proposed in 1958 by Ernst G. Bauer):

• island growth (Volmer-Weber)• layer+island growth (Stranski-Krastanov)• layer growth (Frank - van der Merwe)

StranskiStranski--KrastanovKrastanov growth growth of of GeGe on Si(001)on Si(001)

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

huts

pyramids

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

4% lattice mismatch between Ge and Si

!

Thermodynamics of nucleation:Thermodynamics of nucleation:

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 formation:

where PS: equilibrium vapor pressure above solid, PV: pressure of supersaturated vapor, Ω: atomic volume, and

When a growing sample is nearly in equilibrium with vapor, nucleation and

growth is mainly governed by thermodynamics.

)1ln(ln SkT

P

PkTG

S

Vv +

Ω−=

Ω−=∆

S

SV

P

PPS

−= supersaturation

Capillary theory: conceptually simple, but quantitatively inaccurate model

gas-to-solid transformation

( )( ) ( )b

eqBB

a

eqAA

c

eqCC

aaaa

aaRTG

)()(

)(

//

/ln=∆

solidvapor CA →

Formation of spherical cluster of radius r: energy increase due to surface

energy 4πr2γ , so total energy change:

Critical cluster radius:

Energy barrier:

When r > rcrit, the cluster becomes thermodynamically stable

v

HOMOcritG

r∆

−=γ2

,

2

3

,3

16

v

HOMOcritG

G∆

=∆πγ

γππ 23

43

4)( rG

rrG vHOMO +∆=∆

appearance of new surface

∆GHOMO

rcrit,HOMO

∆Gcrit,HOMO

r

Heterogeneous nucleation:

clusters of mean dimension, r are formed on a substrate

1

2

Let’s describe the surface energy using the surface tensions: (cluster/substrate interface energy γfs, substrate surface energy γsv)

Constants a1 and a2 come from the top area of the spherical cup and the circle underneath it, while a3 comes from the volume of the cup:

svfsfvvHETERO rararaGrarG γγγ 2

2

2

2

2

1

3

3)( −++∆=∆

surface area of the nucleus towards the gas phasevolume of the nucleus area of the interface between

nucleus and substrate

( )

( )θθπ

πθ

θπ

333

3

22

2

22

1

coscos323

,sin

),cos1(2

+−=

=

−=

rra

rra

rra

ππ 22 aRh

AAA basetopcup

+=

=+=

( )hRhVcup −= 33

2π

θcos⋅=− RhR

θ

VVéékonyrkonyréétegektegek elelőőáállllííttáása sa éés alkalmazs alkalmazáásaisai

Dr. Geretovszky Zsolt

2010. szeptember 14.

Tangential component:

θγγγ cosfvfssv +=

if γsv ≥ γfs + γfv, θ = 0, complete wetting

if γfs ≥ γsv + γfv, θ = 180˚, spherical ball without any wetting

Young’s equation

Mechanical equilibrium defines the contact angle, θ (i.e. as the force exerted on line of unit length)

Critical cluster radius:

Energy barrier:

( )

v

svfsfv

HETEROcritGa

aaar

∆

−+−=

3

221

,3

2 γγγ

( )( )

22

3

3

221

,,27

4

v

svfsfv

HETEROcritHETEROHETEROcritGa

aaarGG

∆

−+=∆=∆

γγγ

In equilibrium: 0)(=

∆

dr

rGd HETERO

A

The normal component of the force at point A is

compensated by the substrate.

the relationship between the surface tensionsfv

fssv

γ

γγθ

−=cos

Critical cluster radius:

Energy barrier:

( ) ( )=

∆

−−=

∆

−+−=

v

fvfv

v

svfsfv

HETEROcritGa

aa

Ga

aaar

3

21

3

221

,3

cos2

3

2 θγγγγγ

( )( )

=∆

−+=∆=∆

22

3

3

221

,,27

4

v

svfsfv

HETEROcritHETEROHETEROcritGa

aaarGG

γγγ

HOMOcritHETEROcrit GG ,, ∆<∆

2

3

,3

16

v

fv

HOMOcritG

G∆

=∆πγ

fv

fssv

γ

γγθ

−=cos

v

fv

HOMOcritG

r∆

−=γ2

,

( ) ( ) ( )HOMOcritHOMOcrit

v

fv

v

fvr

a

aar

a

aa

GGa

aa,

3

21,

3

21

3

21

3

cos

3

cos2

3

cos2=

−=

−

∆−=

∆

−−=

θθγθγ

=1

HOMOcritHETEROcrit rr ,, =

fv

fssv

γ

γγθ

−=cos

( ) ( ) ( )=

−∆=

⋅

−

∆

⋅=

∆

−=

∆

−=

π

θ

π

θγπθγθγγ

4

cos

94

cos

3

44

27

cos4

27

cos421

,2

3

3

21

2

3

22

3

3

21

3

22

3

3

21 aaG

a

aa

GGa

aa

Ga

aaHOMOcrit

v

fv

v

fv

v

fvfv

( ) ( )4

coscos32

4

coscos3233

4

3 3

,

3

,3

,

θθ

π

θθπ

π

+−∆=

+−

∆=∆= HOMOcritHOMOcritHOMOcrit GGa

G

<1since Vcap<Vsphere

The substrate catalyses condensation by lowering ∆G* through the reduction of contact angle.

wetting factor, fw

In general, hetero-nucleation barrier is significantly lower than that of

homo-nucleation!

When the film wets the surface 000 , =∆⇒=⇒°= HETEROcritw Gfθ

When the film de-wets the surface HOMOcritHETEROcritw GGf ,,1180 ∆=∆⇒=⇒°=θ

The density of stable nuclei:kTG

sitenucleationcritcritenN/∆−

=

Further processes can also be incorporated, e.g. strain due to lattice misfit

∆G

rcrit,HETERO

∆Gcrit,HETERO

r

∆Gcrit,HOMO

Three growth modes Three growth modes

θγγγ cosfvfssv +=γsv

γfv

γfs

θ

autoepitaxy0if

0hence

=

+≥⇒≈

fs

fvfssv

γ

γγγθ

+ lattice mismatch

initially +>fvfssv

γγγ fvfssvγγγ +<

fvsvfsγγγ <⇒≈ 0if

θ > 0since

Metals tends to ball-up (cluster) on semiconductors and ceramic substrates.

Ease of growing compound semi-conductor superlattices, as opposedto metal/semiconductor structures.

Making a surface and its Making a surface and its consequenceconsequence

The surface will attempt to minimize the surface energy.

Geometric strategies to reduce Geometric strategies to reduce surface energysurface energy

An exampleAn exampleExposing an interior plane of a lattice produces energetic broken bonds, the so called dangling bonds.

Consequence for a III-V semiconductor (e.g. (111) GaAs): can only be cleaved between AA and BB; + As (BB) surface is electronically more active than Ga (AA) one. The AA and BB surfaces behave differently (etch rate, polishing, roughness, epitaxy).

e.g. As

e.g. Ga

Surface reconstructionSurface reconstruction

The absence of some bonding forces results in new equilibrium positions which deviate from those in the bulk lattice. A disturbed surface layer, known as the “selvedge”, will be formed. Within this layer the atoms relax in such a way as to preserve the symmetry of the bulk lattice parallel to the surface, but not normal to it. Surface atoms rearrange into a structure with a symmetry that differs from that of the bulk solid. This phenomenon is known as surface reconstruction and can alter surface structure-sensitive properties, like chemical, electrical, optical or sorption behaviour.

An exposed bulk plane

Surface reconstructionSurface reconstructiona simple case: Si (100)a simple case: Si (100)

bulk exposed planeSi(100)-(1×1)

Si(100)-(2×1)reconstructed surface

Surface reconstruction is a process by which atoms at the surface of a crystal rearrange themselves to form a structure with a different periodicity and/or symmetry than that of the bulk crystal. The driving force of the process is the reduced atomic coordination.

dimer formation

further images @ http://www.fhi-berlin.mpg.de/~hermann/Balsac/pictures.html

AdsorptionAdsorption

When an atom or molecule is trapped on a

solid surface by an attractive interaction, it

becomes an adsorbate with adsorption

energy Eads

To minimize the surface energy the system may also “react”. → Yet another “strategy”is adsorption (i.e. interaction of the coordinatively unsaturated surface atoms with species (molecules) from the gas or liquid phase).

Physisorption/ChemisorptionPhysisorption/Chemisorption

Depending on the nature of interactions between the adsorbent and the adsorbate adsorption is classified as:

physisorption:

• the adsorbate is stretched or bent but retains its chemical identity

• weak, undirected interactions due to van der Waalsforces;

• little change in electronic configuration;

• Eads ~ meV (0.25eV is typical)

chemisorption:

• the adsorbate and adsortive are chemically different

• formation of a true chemical bond (ionic and/or covalent).

• This strong, directed interaction involves a substantial rearrangement of electron density.

• Eads ~ 1eV (1-10eV is typical)

Associative Associative vs.vs. dissociativedissociative

Chemisorption can be dissociative (i.e. a molecule may dissociate during chemisorption).

Physisorption is always associative (molecular or non-dissociative).

The The energeticsenergetics of of physisorptionphysisorption

see also http://www.chem.qmul.ac.uk/surfaces/scc/

EnergeticsEnergetics of dissociative of dissociative chemisorptionchemisorption

PE

Transition between Transition between

physisorptionphysisorption and and

cchemisorptionhemisorption

Activation energy for

chemisorption, Eact

Molecular physisorption & dissociative

chemisorption potential curves

intersect at transition point z’

Z’

Precursor statefor chemisorption

Barrier from precursor (physisorbed)

to chemisorbed state:

εa = Eact + εd

Physisorbed and non-dissociative

chemisorbed species:

Edes = Eads

Desorption of recombined

dissociative chemisorbed species:

Edes = Eads + Eact

Activation Energy for DesorptionActivation Energy for Desorption

ComparisonComparison

low high

Adsorption kineticsAdsorption kinetics

Let’s assume that we deposit material from the vapor phase containing potential adatoms at a partial pressure of P. The rate of surface coverage will be:

At very long times the surface coverage is:

which is the Langmuir isotherm for associative adsorption.

If KP >> 1 the surface coverage is unity.

θθθ

desads kPkdt

d−−= )1(

( )tKPkdeseKP

KP )1(1

1

+−−

+=θ

des

ads

k

kK = Tk

E

adsB

ads

ek−

∝Tk

E

desB

des

ek−

∝

KP

KP

+=1

θ

Coalescence mechanismsCoalescence mechanisms

Ostwald ripeningLarger islands grow/ripen at the expense of the smaller ones. Sintering

Sintering is a coalescence mechanism

involving islands in contact.

Cluster migrationCoalescence occurs via collision of islands as

they execute random motion.

Potential mass transport mechanisms:

Ostwald ripening 1.Ostwald ripening 1.

Driving force: minimize surface free energy of the island structure

ii

i

iii

rdn

dG

rnrG

i

γµ

πγπ

Ω∝=

Ω∝=∆

i hence and

3

4,4

32

This is a mechanism in which there is no need for the islands to be in direct contact to change their size.

Ostwald ripening 2.Ostwald ripening 2.

Cu islands on stepped Cu(111)

Ostwald ripening occurs by evaporation of atoms from one cluster, which then transfer to another. This is a dynamic process: both clusters exchange atoms, but the rate of loss from the smaller cluster is higher, because of the lower average coordination of atoms at the surface and their relative ease of removal. Thus big clusters get bigger at the expense of smaller clusters, which shrink and eventually disappear. This process is more common for metal clusters on a supported surface that are well spaced apart.The presence of a surface results in surface-mediated Ostwald ripening in which material is transferred from one cluster to another by diffusion across the surface, and not through the gas phase.

SinteringSinteringSintering is a coalescence mechanism involving islands in contact.

The driving force for neck growth is to reduce total surface energy of the island.

The magnitude of µ is larger for atoms on aconvex surface than on a concave one (neck).-> A concentration gradient develops which increases the neck.

X: neck radius; r: sphere radius; A(T): temperature dependent constant; t: time

For bulk diffusion: n=5, m=2, whereas for surface diffusion n=7, m=3.

tTAr

Xm

n

)(=

SinteringSinteringt=0 t=0.06s t=0.18s

t=0.50s t=1.06s t=6.18s

Au islands on M

oS2

Cluster migrationCluster migration

D: effective diffusion coefficient, [D]=cm2/sr: projected radius of cap-shaped clusterEC: activation energy (related to surface self-diffusion)

EC is smaller for smaller clustersB(T): temperature-dependent constant1<s<3

Thermally activated process that involves collision of clusters that move due to random motion.

kT

E

s

C

er

TBrD

−

=)(

)(

Migration of cluster on surface Migration of cluster on surface

Crystallites of 5-10nm in diameter may migrate as distinct entities provided that the Tsubstrate is high enough.