warren averbach analysis of xrd peak shapes: … · warren averbach analysis of xrd peak ... 1 Å 1...

SSRL X-ray scattering school | Spring 2012

Warren Averbach analysis of XRD peak shapes:

Measuring disorder in soft organic materials

Rodrigo NoriegaApplied Physics, Stanford University

Jonathan Rivnay, Alberto SalleoMaterials Science, Stanford University

Michael ToneyStanford Synchrotron Radiation Lightsource


How will organic semiconductors continue improving?

PolyIC

Applications:

Complementary Logic

Display Backplanes

RFID Tags

Sensors

Organic Thin Film Transistors (OTFTs)

Can we develop design rules to continue to improve performance/understanding?

c-Si

a-Si

poly SiPentacenes

Oligothiophenes

Polythiophenes

single crystal

1985 1990 1995 2000 2005 201010

-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

Mo

bil

ity (

cm2/V

s)

Year


Must understand and control morphology over vast range of length scales

Molecular-scale packing

Local defects, lattice disorder

Crystalline grains and domains

Domain orientation Device-scale morphology

Molecular-scale packing

Nano-scale order

Grain size distribution

Short-range phase segregation

Long-range phase segregation

molecule

defect

domain boundary

grain boundary

grain

domain

defect crystallite

1 Å 1 nm 10 nm 100 nm 1 µm 10 µm

Rivnay (Chem. Rev., submitted)


Disorder is important for organic materials

6.0 6.5 7.0 7.5 8.0 8.5

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Relative energy (eV/monomer)

π−π distance (bohr)

g=8%

Top performers are disordered

Noriega (in preparation)

HOMO=-4.99 eV

HOMO=-5.25 eV

Crystalline-amorphous interfaceCrystalline Amorphous

It’s easier to melt disordered crystals


Paracrystalline parameter characterizes disorder

∆2 is the variance of interplanar spacing d:

Can now define the “paracrystallinity parameter”, g:

∆2 = d 2 − d2

g2 = ∆2 / d2

P(d)

d<d>

d

P(d)

d<d>


Using g to rank materials from crystalline to amorphous

Cry

sta

lline

Para

crys

talli

ne

Am

orp

hou

s/M

elt

Bo

ltzm

an

n g

as

0% 1% 10% 100%

Most of peak-broadening due to

paracrystalline disorder (g)

Statistical deviation from mean lattice spacing

Hindeleh (J. of. Physics C, 1988)


Paracrystalline disorder: a picture

g=1% g=5% g=10% g=15%


Paracrystallinity in Silicon

Crystalline silicon Amorphous silicon

Is this the whole story?

Treacy (Science, 2012)

Paracrystalline silicon


Bragg’s law recap

Constructive interference happens if2dsinθ=nλ

λ

d

θ

In terms of the scattering vector:q=4πsinθ/λ=Qrec


X-ray scattering is sensitive to imperfections

Finite-size crystals have nonzero breadth diffraction peaks.

Warren and Averbach (JAP, 1950 and 1952)

Observed intensity

Observed intensity


X-ray scattering is sensitive to imperfections

The width of a diffraction peak is increased when we add disorder to the lattice.More importantly, the peak width increases with diffraction order.

Observed intensity

Different position means waves pick up

extra phase

Observed intensity


Prosa et al. (Macromolecules, 1999)


Measuring disorder quantitatively using X-ray diffraction

Effect of

Cumulative Disorder

Increasingdisorder200nm

20nm

5nm

(no disorder)

Effect of Grain Size

paracrystalline disorderLattice parameter fluctuation

erms

Grain sizeM

g


Prosa et al. (Macromolecules, 1999)

An = 1−dhkln

M

e

−2π 2m2ng2e−2π 2m2n2 e2

dhkl


Warren-Averbach Graphical approach

)()()()( nAnAnAnA g

m

e

m

S

m =

22

22

3

)(

)(2/)(ln)(ln

engnf

nnfmNnNnAm

+=

−= π

Diffraction peaks can be represented by Fourier series

Warren (1951)

T.J. Prosa, Macromolecules (1999)

+ Extracting more information from peaks

- Prone to inaccuracies

Multiple steps

Fitting lines to as few as 2-3 points

Basing fits on previous fit results


Line-shape analysis applied to Polyera N2200

-0.1 0 0.1q-q

peak (Å-1)

Norm. Intensity

-0.1 0 0.1q-q

peak (Å-1)

-0.1 0 0.1q-q

peak (Å-1)

-0.1 0 0.1q-q

peak (Å-1)

-0.1 0 0.1q-q

peak (Å-1)

0 2 4 6 8 10 12 14 16 180

0.2

0.4

0.6

0.8

1

n

Normalized Am(n)

0 5 10 15

10-1

100

0 20 40 60 80 1000.0

0.5

1.0

0 5 10 150.0

0.5

1.0

No

rma

lize

d P

rob

ab

ilit

y

Crystallite Size, M (nm)

An(m

)

n

MδMγ

wγ

δ-function

γ-distribution

An = 1−dhkln

M

e

−2π 2m2ng2e−2π 2m2n2 e2

Rivnay (PRB, 2011)


Fits converge quickly with more data


Data is not always that nice

0.00001

0.0001

0.001

0.01

0.1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

q (A-1)

Normalized intensity (arb. u.)


Beam damage is something to be aware of

1.50E-03

1.70E-03

1.90E-03

2.10E-03

2.30E-03

2.50E-03

2.70E-03

2.90E-03

3.10E-03

3 3.2 3.4 3.6 3.8

q (A-1)


Fresh

after 35 mins


A model system for anisotropic disorder: PBTTT

Chabinyc (JACS, 2007), Wang (Adv. Mat., 2010)

Delongchamp (Adv. Mat., 2011)


PBTTT appears very ordered in the direction perpendicular to the substrate

glamellar~2.5%

Delongchamp (Adv. Mat., 2011)

gπ-π~7.3%


M:g:

erms:

47 ± 7 nm0.9 ± 0.6 %≈ 0 %

High performing materials vary in paracrystallinity

0% 1% 10%g:

In plane[100] direction

In plane[010], π-stacking

SSS

S

H29C14

H29C14 n

Si

Si

TIPS-Pentacene PBTTT

M:g:

erms:

34 ± 7 nm2.6 ± 1.4 %1.3 ± 0.6 %

Small Molecule Polymer

µFET≈0.5-5 cm2/VsµFET≈0.1-1 cm2/Vs

M:g:

erms:

55 ± 8 nm≈ 0%≈ 0 %

Out of plane[001] direction

Out of plane[100], lamellar-stacking

M:g:

erms:

n/a7.3 ± 0.7 %0.9 ± 0.6 %



Shortcuts are sometimes OK, sometimes not

1.5 2.0 2.5 3.0 3.5

0.01

0.1


Q (A-1)

3.10 3.15 3.20 3.25 3.30 3.35

700

800

900

1000

1100

1200

1300

1400

1500

1600

Scan 1 (after a long scan) Scan 2 (fresh spot) Scan 3 (fresh spot)

Det

Q

gestimate~4.7% gfull~2.7±0.6%

Mfull~18 nmg =

∆q2πqo

1st and 2nd order π-πdiffraction on a P3HT oligomer (13 monomers)


Molecular-weight dependence of disorder is related to transport in P3HT

Mobility µFET(cm2/V.s)

Mw (kg/mol)

limited by connectivity limited by paracrystallinity

~g (%)



Potential Sources of Disorder

Extrinsic

Impuritiescatalysts, degradation impurities, additives

Polydispersitybroad distribution of

chain lengths

Regioregularitydefects

IntrinsicSide chain-

induced

Alkyl chain (or side chain)

disorderEven for perfectly RR

chains, side chains may cause perturbation in local

packing

Chain entanglement dependent

Poor lateral stackingCan cause repulsion and vary π-stacking

StackingFaults

Torsion from entanglement

McMahon (J. Phys. Chem., 2011), Xie (PRB, 2011)


Paracrystalline disorder creates electronic traps

Modeling inter-chain disorder in PBTTT pi-stacks:

g=1%

g=5%

g=10%

Localization length vs. energy

Tail states are highly localized, but for higher disorder, even states within the band become more localized

Large disorder causes localization (traps) and creates deep tail states.



0% 1% 10%g:

Small Molecules Polymers

Grain boundaries dominate performance

Disorder within crystallites prevalent;complicates analysis

Macromolecules can span transport regimes

Low MW High MW

Kline (Macromolecules, 2005)


Conclusions – round 1

• Synchrotron-based XRD allows to quantify lattice disorder.

• Tradeoff between good statistics and beam damage.

• Every little thing counts toward making your life easier when it comes to data

analysis: align the film, use the right scattering geometry, etc.


Conclusions – round 2

• Disorder at all length-scales affect transport in organic semiconductors.

• Lattice disorder can be described as a continuous scale, it can be quantified.

• Most (all until now) high Mw, high mobility polymers are disordered in the π-πstacking direction.

0% 1% 10%g:


Acknowledgements

Funding:

Center for AdvancedMolecular Photovoltaics(CAMP), funded by KAUST

Collaborators:

Stanford Synchrotron Radiation Lightsource

Mike ToneyStefan Mannsfeld (WxDiff)

Palo Alto Research CenterJohn Northrup

Imperial CollegeMartin HeeneyIain McCullochNatalie Stingelin

Polyera Corp.Antonio Facchetti

Nat. Inst. of Standardsand Technology

Joe Kline

Northwestern Univ.Tobin Marks

28

Stanford Global Climateand Energy Program

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