TSF I - Ch. 5 - p. 1

5. Thin Film GrowthBasic steps of thin film growth:

1. adsorption (physisorption) of atoms/molecules2. surface diffusion3. formation of molecule-molecule and substrate-molecule bondings (chemisorption)4. nucleation: aggregation of single atoms/molecules5. structure and microstructure formation (amorphous- polycrystalline - single-crystalline, defects, roughness, etc.)6. changes within the bulk of the film, e.g. diffusion, grain growth etc.

Ji: incoming flux: physisorption coefficient: chemisorption coefficient

Sc: sticking coefficient

jump length

re-adsorption

Smith 5.1

TSF I - Ch. 5 - p. 2

5.1 Adsorptionmolecule arrives from the vapor phase:

attractive force at distance of a few atomic diameters from the substratenon-polar molecules: van-der-Waals forcespolar molecules: stronger forcestransfer of kinetic energy to the substrate, adsorption

: fraction of molecules that dissociate and form chemical bondingsSc: fraction of molecules that stay adsorbed on the experimental time-scalein case of solid-vapor equilibrium: Sc 0 and > 0

TSF I - Ch. 5 - p. 3

precursor adsorption: weak bonding as a precursor to strong bondingSiH4 (g) ... SiH4 (p) Si (c) + 2H2 (g)

alloy films: 2 components in the vapor phaseZn (g) + Zn (c) Zn2 (p)Zn (g) + Se (c) ZnSe (c)

H- passivated surface:Si (g) + H (c) Si (p)

chemisorption only on non-passivated sites Si (g) + Si (c) Si (c)

physisorption chemisorption

(p) (c) stronger bonding at surface steps

metal atoms on non-metallic substrates: metal-metal bondings stronger than metal-substrate bondings

TSF I - Ch. 5 - p. 4

advantageous: condensation directly into chemisorbed statehigh kinetic energy and molecule dissociation in the vapor phase required (sputtering, PLD)

Ep=0: enthalpy in the vapor phase,no kinetic energyfH: enthalpy of formation of Y2Ed: desorption barrier (physisorbed)Er: reaction barrier (p) (c)Ea: reaction barrier vapor (c)Ec: enthalpy in chemisorbed state

1kJ/mol 1eV/atom

Smith 5.2

TSF I - Ch. 5 - p. 5

rate of chemisorption Rr = rate constant kr ML concentration nS0 coverage rate of desorption Rd = rate constant kd ML concentration nS0 coverage

nS0: number density of surface atoms in a ML

rates are thermally activated (Arrhenius laws) ii i0S

Ek exp RT

i r dJ 1 R R # of physisorbed species

that can chemisorb or desorb

(conservation of mass)

i S0r r S0 i i

i S0 r d 0d r d

0r S

J n R k n J JJ n k k E E1 exp RT

chemisorptioncoefficient

TSF I - Ch. 5 - p. 6

assumption: ki independent of surface site (no surface steps etc.)TS low enough to avoid thermal decomposition

(Er-Ed) > 0: activation energy for chemisorption, Rr if TS (e.g. CVD, decomposition of SiH4 - can also be induced by nucleation at nucleation sites like steps or non-passivated surface atoms)

(Er-Ed) < 0: Rr

if TS , desorption rate increases stronger than reaction rate(e. g. CVD at too high TS)

nucleation is problematic if precursor-precursor bonding is stronger than precursor-substrate bonding island growth, inhomogeneous coverage, e.g. Zn/Cd on glass or NaCl high Ea : metal atoms stay physisorbed, desorb or nucleate to islands

TSF I - Ch. 5 - p. 7

5.2 Surface Diffusionextremely important for thin film formation

allows adsorbed species to form clusters (homogeneous nucleation) allows adsorbed species to find heterogeneous nucleation sites (steps etc.) adsorbed atoms move in potential energy "landscape" generated by substrate or thin film surface atoms: diffusion, hopping

Ed 40meVEs 20meVEc 100meV

(100kJ/mol 100meV)Ed

Ec

Smith 5.4

TSF I - Ch. 5 - p. 8

Es < Ed, Ec: only partial breaking of bonds

molecular hopping rate: (influence of substrate temperature, TS)

(0s 1013...1016Hz: attempt frequency)s s

S

s0

Ek exp R T

diffusion: random walk, not directed, equal hopping probabilities for forward and backward motiondiffusion length,

: (r: rms change in distance per hopping event, N0: number of hopsa: lattice constant, t: diffusion time)

0 0 sr N a N a k t

30s

s

s

1 110 s

T 1000Kt 1s

a

E 20meV300 m (physisorbE 200meV5nm (chemisorbed)

0.3n

)

m

ed

strong influence of bonding conditions!

TSF I - Ch. 5 - p. 9

i

S

0s 0 sbi S

n Et a expJ 2 R T

1 cd 0c

c S

1 Et expk R T

c s0sd0c S

E Et a exp 2 R T

diffusing molecules may desorb or be buried

average time between adsorption and burial by incident molecules: tb=n0/Ji n0: adsorption site density (#cm-2), Ji: incident flux (#cm-2s-1)

desorption from chemisorbed state after

maximum in

close to re-evaporation temperaturebest film quality (smoother, less defects, more homogeneous)

Smith 5.5

TSF I - Ch. 5 - p. 10

ss

dnJ Ddx

s0

S

E2 Dt D D exp R T

macroscopic quantities:

JS: flux (#m-1s-1), nS: adatom density (#m-2), D: surface diffusion coefficient (m2s-1)

5.3 Nucleation

surface energy per unit area, : energy per unit area needed to create or increase a surface(non- constant number of surface atoms) unit: Jm-2surface stress: force per unit length needed to increase a surface (constant number of surface atoms, solids only) unit: Nm-1, includes strain contributionconfusion in German: spezifische Oberflchenenergie & Oberflchenspannung are used synonymouslyJm-2 = Nm-1

TSF I - Ch. 5 - p. 11

x

b

F

W 2 A 2 x bF W 2b x b

soap filmforce acts tangentiallytends to decrease surface area

surface energy exists because bonds are broken to create/increase the surface(surface stress: bonds are elastically strained)

strong driving force: minimization of surface energy (spherical soap bubble)

fundamental to thin film growth:surface energy can be minimized by surface diffusion

chemical compositioncrystallographic orientationatomic reconstruction

A min

surface topography

TSF I - Ch. 5 - p. 12

usually is anisotropic, i.e. differently oriented surfaces have different (differences in metals are of the order of % - larger in covalent or ionic systems)

fcc- crystal (Au, Al): {111} surfaces have lowest surface energyatoms in closed- packed (111) lattice planes have most in-plane bonding partnersand smallest interplanar bonding

bcc (Cr, Fe): {110}hcp (Zn, Mg): {0001}diamond (Si, Ge): {111}

Zinc blende (GaAs, ZnSe): {110}CaF2: {111}NaCl: {100}

surface reconstruction: atomic positions and surface bonds are differentfrom those in the bulk in order to decrease ( 50%!) - can increase Er (PSCS)surface passivation: addition of a ML of an element, dangling bonds react to terminatedbonds - prevents reconstruction, often more effective than reconstruction

polar/ionic bonding,planes with lowest havesame number of cationsand anions

TSF I - Ch. 5 - p. 13

thin film nucleation: interplay of 3 surface energies per unit areaS: substrate free surfacef: film free surfacei: substrate/film interface

relative magnitudes of these quantities strongly influence nucleation (provided that nucleation is not kinetically limited and can approach equilibrium)

i f S layer-by-layer growth (Frank-van der Merwe)

i S f

i S f

island growth (Volmer- Weber)minimization of total surface energy: low- facets of islands

j jA min

few ML layer-by-layer, then crossover to island growth(not only a - effect, see Ch. 7 - Epitaxy) (Stranski-Krastanov)

Smith 5.8 or Ohring 5.2//7.2

TSF I - Ch. 5 - p. 14

island growth: Au/graphite (STM image, U. Geyer)

scansize: 500nm

TSF I - Ch. 5 - p. 15

3D- nucleation (islands) is usually undesirablemitigation strategy: change one or more of the j such that

- i is lower for materials with same type of bonding (metallic/covalent/ionic)- i is lower in case of chemical reactivity

Au on glass 3D- nucleationCr on glass 2D- nucleation O-Si Si-Cr/O-Cr bondingsAu on Cr 2D- nucleation, strong metallic bonding--------------------------------------------------------------------------------------------------Au / Cr / glass layer-by-layer, wetting

Cr is an intermediate 'glue' layer; 3-10nm sufficient (continuous layer)

Ti: similar good bonding material

i f S

TSF I - Ch. 5 - p. 16

alternative methods to prevent island growth:ion beam irradiation of the substrate surface (breaks bonds, enhances reactivity, destroys islandsi.e. disturbs equilibrium - ion beam irradiation is often very effective)

apply a surfactantreduces f more than S (water on glass: drops - soapy water on glass: layers)

i f S

' 'i f S

TSF I - Ch. 5 - p. 17

5.3.1 Classical Nucleation

heterogeneous nucleation takes place at "active" surface sites (steps, defects, contamination); low local i atoms reach these sites by diffusion or directly from the vapor phase

homogeneous nucleation at random positions if sufficient high number of atoms meet through diffusion to form a stable nucleus surface energy critical radius for nucleation

JiJi Ji

Jv

radius of curvature, r (isotropic f)

Similar to Smith 5.3

TSF I - Ch. 5 - p. 18

formation of a nucleus:1.) Gibb's free enthalpy of the nucleus, GV, decreases if Jc/Jv>1 (Jc: condensing molecular flux, Jv: evaporating molecular flux)

2.) surface energy balance:

33V v cmol v mol

V p a rG RT lnV p V v

p :p

supersaturation

2S 1 f

22 i

22 S

G a ra ra r

curved surface of the nucleusinterfacesubstrate surface

V SG G G

TSF I - Ch. 5 - p. 19

growth of nuclei with r > r* lowers total enthalpy - stable nucleinuclei with r < r* spontaneously disintegrate (surface energy contribution too high)critical radius r* and nucleation barrier decrease with increasing supersaturation

V 1

pp

V 2

pp

(p/pV)1 > (p/pV)2

2

1 f 2 i 2 S 1 f 2 i 2 S2

23 3mol V mol V

2 a a a 4 a a ar* G r *RT p RT p3a ln 27a lnV p V p

Smith 5.10

TSF I - Ch. 5 - p. 20

1

22

33

a 2 1 cosa sina 2 3cos cos 3

for a spherical nucleus

balance ofsurface forces (acting tangentially)

S i f cos

3 3f 2mol V

16 2 3cos cosG r* 4RT p3 lnV p

= 0: G(r*) = 0 ideal wetting, layer-by-layer growth, no nucleation barriernucleation even if p < pV (oxidation of metals at very low oxygen partial pressure) = 180o: G(r*) = max - corresponds to bulk homogeneous nucleation

Smith 5.12

TSF I - Ch. 5 - p. 21

5.3.2 2D- Nucleation

= 0: no nucleation barrier? sufficient surface diffusion: adsorbed atoms form "2D- gas" at the surfaceReplace surface energy by step energy (bonding partners are missing)

(energy / unit length)p nS (surface density of adsorbedatoms)pV nV (equilibrium surface density of

adsorbed atoms in 2D- gas)

2 2S 2 S

mol V mol V

r* G r*RT n RT na ln a lnV n V n

homogeneous nucleation on terrace

Smith 5.13

TSF I - Ch. 5 - p. 22

spiral growth of thin films (only if surface diffusion is strong):no homogeneous nucleation necessary, always steps present

screw dislocation

t1

TSF I - Ch. 5 - p. 23

spiral growth of thin films

YBa2Cu3O7-film on MgO (U. Geyer)(scansize 500nm)

TSF I - Ch. 5 - p. 24

5.3.3 Nucleation Rate

Definition: nucleation rate = d/dt (surface density of stable! nuclei)is zero at start of depositionincreases thenbecomes lower again, when there are sufficient number of stable nuclei,

the latter will grow by absorbing arriving atoms instead of arriving atoms forming further nuclei

early stages: nuclei don't grow through direct by impingement of gas phase atomsmore important: rate at which adsorbed atoms attach a (critical!) nucleus

adsorbed atoms remain until desorption for (adatom lifetime)

if atoms aggregate during c they stay on the substrateEc is highest at steps, contaminations, etc. - higher density of nuclei

1 cc 0c

Eexp RT

TSF I - Ch. 5 - p. 25

Nucleation Rate/parametersnucleation rate:

: equilibrium concentration of critical nuclei, nS: total nucleation site density: attachment area of the critical nucleus

: rate at which adatoms impinge onto A*

* *N N A

**S

G rN n exp RT

* *A C r

= jump rate surface density of adatoms = jump rate vapor impingement rate c 1S A c

0s 0cE pN Eexp expRT RT2 MRT

assume 0s 0c: *c S* A

S

E E G rpNN C r n exp RT2 MRT

complex expression, but exponential dominates: nucleation strongly depends on G(r*), thus can be influenced by T, p, ns

TSF I - Ch. 5 - p. 26

*

p

r 0T

r* increases with TS because supersaturation decreaseslate film coalescence (@ high average thickness)

*p

G r0

T

density of stable nuclei increases slower with increasing Tlate film coalescence (@ high average thickness)

**T T

G rr 0, 0p p

higher deposition rate smaller r*, faster increase of density of nuclei

TRRkTG

eqV

ln

V

sifGa

aaar

3

321

32

*

(See chpt. 5 p. 19)= evaporation rate from surface TReq

Interpretation:

TSF I - Ch. 5 - p. 27

summary:high deposition rate & low substrate temperature:

fine- grained polycrystalline or amorphous film, coalescenceat small average thickness, relatively smooth

low deposition rate & high substrate temperature: coarse- grained polycrystalline (or single- crystalline film),

coalescence at high average thickness, relatively rough

Cr2N films (U. Geyer),tf=500nm

STM - scansize: 500nm

T=300K, z=10nmT=550K, z=30nm

TSF I - Ch. 5 - p. 28

models used here ("capillarity theory") give a simple picture and correct tendenciesbut: results are not exact

calculations often result in too small r*, even if correct parameters (j,...) are usedvalidity of macroscopic concepts (like j) is questionable

everything is based on the assumption of a system in thermodynamical equilibriumbut: most preparation processes are subject to kinetic constraintsKinetic nucleation theories can be found in the books by Smith and Ohring

starting point:

rate equations for clusters andthe respective adsorption and desorption

Ohring 5.7//7.16

TSF I - Ch. 5 - p. 29

5.4 Cluster Coalescence

kinetic theories of nucleation: number density of stable nuclei decreases after a certain time

coalescence of nucleidriving force: minimization of surface energy

a. cluster migration & rotation, coalescence results from random collisions of clusters

cs1 ED r expr RT Ec related to ES, s=1...3

TSF I - Ch. 5 - p. 30

chemical potential, i, of a spherical nucleus consisting of i atoms (: atomic volume):

ii 0

i

pr RT ln p2p r p exp rRT

Ostwald ripening sintering

b.mass transport by "evaporation"growth of large nucleusat the expense of the small one

vapor pressure pi

c.convex surface (r>0):atoms evaporate

concave surface (r

TSF I - Ch. 5 - p. 31

time sequence of Au on MoS2 @ 400oC, TEM investigation:

0s

6.18s

Ohring 5.10//7.18