warren averbach analysis of xrd peak shapes: … · warren averbach analysis of xrd peak ... 1 Å 1...
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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
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Slide 2SSRL X-ray scattering school | Spring 2012
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
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Slide 3SSRL X-ray scattering school | Spring 2012
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)
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Slide 4SSRL X-ray scattering school | Spring 2012
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
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Slide 5SSRL X-ray scattering school | Spring 2012
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>
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Slide 6SSRL X-ray scattering school | Spring 2012
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)
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Slide 7SSRL X-ray scattering school | Spring 2012
Paracrystalline disorder: a picture
g=1% g=5% g=10% g=15%
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Slide 8SSRL X-ray scattering school | Spring 2012
Paracrystallinity in Silicon
Crystalline silicon Amorphous silicon
Is this the whole story?
Treacy (Science, 2012)
Paracrystalline silicon
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Slide 9SSRL X-ray scattering school | Spring 2012
Bragg’s law recap
Constructive interference happens if2dsinθ=nλ
λ
d
θ
In terms of the scattering vector:q=4πsinθ/λ=Qrec
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Slide 10SSRL X-ray scattering school | Spring 2012
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
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Slide 11SSRL X-ray scattering school | Spring 2012
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
Warren and Averbach (JAP, 1950 and 1952)
Prosa et al. (Macromolecules, 1999)
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Slide 12SSRL X-ray scattering school | Spring 2012
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
Warren and Averbach (JAP, 1950 and 1952)
Prosa et al. (Macromolecules, 1999)
An = 1−dhkln
M
e
−2π 2m2ng2e−2π 2m2n2 e2
dhkl
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Slide 13SSRL X-ray scattering school | Spring 2012
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
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Slide 14SSRL X-ray scattering school | Spring 2012
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)
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Slide 15SSRL X-ray scattering school | Spring 2012
Fits converge quickly with more data
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Slide 16SSRL X-ray scattering school | Spring 2012
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.)
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Slide 17SSRL X-ray scattering school | Spring 2012
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)
Normalized intensity (arb. u.)
Fresh
after 35 mins
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Slide 18SSRL X-ray scattering school | Spring 2012
A model system for anisotropic disorder: PBTTT
Chabinyc (JACS, 2007), Wang (Adv. Mat., 2010)
Delongchamp (Adv. Mat., 2011)
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Slide 19SSRL X-ray scattering school | Spring 2012
PBTTT appears very ordered in the direction perpendicular to the substrate
glamellar~2.5%
Delongchamp (Adv. Mat., 2011)
gπ-π~7.3%
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Slide 20SSRL X-ray scattering school | Spring 2012
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 %
Noriega (in preparation)
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Slide 21SSRL X-ray scattering school | Spring 2012
Shortcuts are sometimes OK, sometimes not
1.5 2.0 2.5 3.0 3.5
0.01
0.1
Normalized intensity (arb. u.)
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)
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Slide 22SSRL X-ray scattering school | Spring 2012
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 (%)
Noriega (in preparation)
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Slide 23SSRL X-ray scattering school | Spring 2012
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)
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Slide 24SSRL X-ray scattering school | Spring 2012
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.
Noriega (in preparation)
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Slide 25SSRL X-ray scattering school | Spring 2012
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)
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Slide 26SSRL X-ray scattering school | Spring 2012
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.
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Slide 27SSRL X-ray scattering school | Spring 2012
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:
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Slide 28SSRL X-ray scattering school | Spring 2012
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