5

Charge Transport in Organic Materials

Table of Contents

188

1 h 4 h 1 h 3 h 3 h 1 h 1 h 1 h 6 h 1 h 2 h 2 h 1 h 6 h 1 h 2 h 2 h 1 h 6 h 2 h 2 h 2 h

1. Introduction and Overview 2. Electron Delocalization in Organic Molecules and Polymers

2.1. Chemical Bonding in Organic Molecules 2.2. Intramolecular Electron Delocalization in -Conjugated Systems

3. Supramolecular Organization in the Solid State and Intermolecular Electron Delocalization 3.1. The Origin of - Interactions 3.2. Supramolecular Organization of -Conjugated Molecules in the Solid State 3.3. Intermolecular Electron Delocalization

4. Chemical Synthesis of Small Molecules and Polymers for Organic Electronic Materials 4.1. General Strategies for the Synthesis of Conjugated Oligomers and Polymers 4.2. Poly(phenylene)s, Poly(phenylene vinylene)s, and Poly(thiophene)s (and Their Oligomers) 4.3. Acenes, Coronenes, Perylenes, Porphyrins, and Other Selected Examples 4.4. Fullerenes, Carbon Nanotubes, and Graphene

5. Charge Transport in Organic Materials 5.1. Interaction of -Conjugated Systems with Light 5.2. Charge Carriers in -Conjugated Molecules 5.3. Charge Carriers in Organic Materials 5.4. Macroscopic Charge Transport in Organic Materials

6. Fabrication and Characterization of Organic Electronic Devices 6.1. Organic Field-Effect Transistors 6.2. Organic Photovoltaic Devices 6.3. Organic Light-Emitting Diodes

5.1

Interaction of -Conjugated Molecules with Light

electron excited to higher MO by light absorption if photon energy matches MO energy differenceFrom Molecular Orbitals to Optoelectronic Properties

190

HOMOLUMO gap (free electronhole pair) optical transition energy (bound electronhole pair) exciton binding energy due to coulomb interaction between an electron and a hole (0.1 to 1 eV )

h

h

intersystem crossing (ISC)

excitation to vibrationally excited (hot) state of S1 with inappropriate bond lengths like those in S0 subsequent vibrational relaxation results in energy loss as heat when electron relaxes to ground state (same rules apply), photon with lower energy is emitted

Franck-Condon principle: fast vertical excitation (1015 s), initially without geometry changes (1012 s) Franck-Condon Principle

191

0 1

2 3

4

E

geometry coordinate r

electronic ground state S0

1st excited electronic state S1

0 1

2 3

4

vibrational levels

vibrational levels

+

ground state S0 1st excited state S1

absorption and emission (fluorescence) spectra of a perylene bisimide in solutionFluorescence and Stokes Shift

192

emission is usually at higher wavelengths compared to absorption Stokes shift is the difference in the wavelengths of maximum absorption and emission

0 1

2 3

4

E

geometry coordinate r

electronic ground state S0

1st excited electronic state S1

0 1

2 3

4

vibrational levels

vibrational levels

300 400 500 600 700 / nm

norm

alize

d abs

orpt

ion / e

missi

on

531 540

461

493

576

Jablonski diagram illustrates the electronic states of a molecule and the transitions between themJablonski Diagram

193

intersystem crossing (ISC) is a non-radiative transition to a state with a different spin multiplicity the much larger time scale of phosphorescence is caused by spin-forbidden" transition

1st singletexcited state S1

1st tripletexcited state S1

electronicground state S0

absorption fluorescence phosphorescence

intersystemcrossing (ISC)

2nd singletexcited state S2

E

Optical Gap and Degree of Delocalization

194

with increasing conjugation length the main absorption shifts towards longer wavelength

SS

SS

SS

SS

S SS

SS

SS

SS

SS

SS

S SS

SS

SS

SS

S SS

SS

402

324353

372

386

396

400

250 450350 550Wavelength / nm

650

2.5

2

1.5

1

0.5

0

Abso

rptio

n (a.u

.)

SS

SS

SS

SS

S SS

SS

SS

SS

SS

SS

S SS

SS

SS

SS

S SS

SS

402

324353

372

386

396

400

250 450350 550Wavelength / nm

650

2.5

2

1.5

1

0.5

0

Abso

rptio

n (a.u

.)

linear extrapolation would yield band gap of 2.7 eV for high molecular weight poly(thiophene) but data deviate starting from 810 units and eventually saturate (effective conjugation length)

Kuhn plot of transition energy E = h c / (in eV) versus inverse length of the -conjugated systemEffective Conjugation Length

195

4.0

3.5

3.0

2.50 0.1 0.2 0.3 0.4 0.5

E / eV

1/(n+0.5)

n

S

blue/red shifted H-type/J-type spectroscopic aggregates from head-head/head-tail transition dipoles not related to solid state red shift due to (limited) intermolecular delocalization by -stacking

dipolar coupling of transition dipoles of chromophores with defined orientation in the crystalline state splitting of the transition state, but only one transition allowed (predominant), depending on geometry

Spectroscopic Aggregates

196

/ 10

4 L m

ol-1 cm

-1

wavelength / nm250 650450

12

8

4

0

422385H aggregates single

molecules

SRS

SS

SS R

H aggregate J aggregate

S1

S0

E

S1

S0

S2

S1

S2

S0monomer head-to-tail

dimerface-to-facedimer

5.2

Charge Carriers in -Conjugated Molecules

Selected Examples of Polymer Semiconductors

198

x x

R

poly(acetylene)s

x R

R

x xS

xNH

xS

OO

xS

Rpoly(phenylene)s

poly(phenylene vinylene)s

poly(thiophene)s

poly(pyrrole)

RR

x

poly(fluorene)s

x

RR

R R

ladder-type poly(phenylene)s

x x

R

R

Z

Z

PEDOT

e.g., P3HTPTPPP

PPV e.g., MEH-PPV PPy

poly(acetylene) is the only -conjugated polymer with two equivalent resonance structuresDegenerate Ground States In Poly(acetylene)

199

poly(acetylene) has two degenerate ground states (energetically and geometrically equivalent) all other -conjugated polymers have benzenoid ground state and quinoid excited state

benzenoid (aromatic)

quinoid (antiaromatic)

E E

ground state A ground state B ground state

excited state

polyene polyene

Peierls distorion

at finite temperature, lattice defects associated with domain boundaries result in neutral solitonsSpontaneous Formation of Neutral Solitons in Poly(acetylene)

200

lattice distortion results in additional, localized energy level in band gap, with limited delocalization in organic chemistry view: solitons are (delocalized) radicals (spin s= and charge q=0) neutral solitons do not carry charge, can not contribute to conduction, but are easily oxidized/reduced

7

ground state A ground state Bdomainboundaryq = 0, s =

electronic structure lattice defect

chemically doped poly(acetylene) in the crystalline state becomes semiconducting or even metallicChemical Doping ofPoly(acetylene)

201

different from inorganic semiconductor impurity doping (at ppm concentrations) dopant is strong single electron transfer oxidant/reducant, but must not induce follow-up reaction dopant is applied at high concentrations (0.110 mol%), strongly disturbs structure/geometry conductivity & mobility increased by several orders of magnitude by chemical doping

I2, AsF5, SbF5

poly(acetylene) poor semiconductor

p-type doping good semiconductor

oxidant single electron acceptor

xx x

Na, K, Li

n-type doping good semiconductor

reductant single electron donor

chemical doping converts neutral solitons into positive or negative soliton charge carriersFormation of Positive or Negative Soliton Charge Carriers

202

positive/negative solitons have no spin (s = 0) but carry a charge (q = e) in organic chemistry view: carbocations or carbanions (delocalized over 723 carbon atoms) isolated charge carriers with limited delocalization; doped poly(acetylene) becomes a semiconductor

Naq = 0 s =

q = e s = 0

I2q = +e s = 0

positive soliton negative solitonneutral soliton

+

formation of soliton defects would be energetically costly, soliton pairs spontaneously recombine charge separation/transport additionally impeded by energy for geometry rearrangement typical pristine -conjugated polymers are insulators, become semiconductors only upon doping (etc.)

energy difference aromatic and quinoid state for typical -conjugated polymersDegenerate Ground States In Poly(acetylene) Different from Other -Conjugated Polymers

203

benzenoid

quinoid

E

ground state

excited state

n

n

E

exciton formation by excitation of electron from ground state S0 to first singlet excited state S1 Exciton Formation Upon Irradiation

204

singlet excitons are neutral (q = 0) and spin-less (s = 0) species associated with a lattice defect in organic chemistry view: tightly bound radical cation/anion pairs with limited delocalization excitons diffuse slowly under geometry rearrangement, transport excitation energy

q = 0 s = 0

ground state excitonn

h

hfundamental

band gapoptical

band gap +

chemically doped poly(acetylene) in the crystalline state becomes semiconducting or even metallicChemical Doping ofPoly(acetylene)

205

different from inorganic semiconductor impurity doping (at ppm concentrations) dopant is strong single electron transfer oxidant/reducant, but must not induce follow-up reaction dopant is applied at high concentrations (0.110 mol%), strongly disturbs structure/geometry conductivity & mobility increased by several orders of magnitude by chemical doping

I2, AsF5, SbF5oxidant

single electron acceptor

Na, K, Lireductant

single electron donor

typical -conjugated polymer poor semiconductor

p-type doping good semiconductor

n-type doping good semiconductor

x x x

chemical oxidation results in formation of positive polaron and/or bipolaron charge carriersFormation of Positive Polarons or Bipolarons

206

positive polarons have charge (q = +e), spin (s = ); delocalized radical cations plus lattice defect positive bipolarons have charge (q = +2e), no spin (s = 0); delocalized dications plus lattice defect polarons/bipolarons are one single species, correlation length = effective conjugation length

ox.q = +e s =

q = +2e s = 0

+

+

+

n npositive polaron positive bipolaron

ox.

chemical reduction results in formation of negative polaron and/or bipolaron charge carriersFormation of Positive Polarons or Bipolarons

207

negative polarons have charge (q = e), spin (s = ); delocalized radical anions plus lattice defect negative bipolarons have charge (q = 2e), no spin (s = 0); delocalized dianions plus lattice defect polarons/bipolarons are one single species, correlation length = effective conjugation length

red.q = e s =

q = 2e s = 0

negative polaron negative bipolaron

red.

n n

2

polarons typically have two optical absorption bands P1 and P2 in the red or near infrared rangeCharacterization of Positive Polarons by Near Infrared Spectroscopy

208

wavelengths (P1) > (P2); other bands forbidden due to orbital symmetry considerations

P1

++P2

geradeungerade

geradeungerade

/ 10

3 L m

ol-1 cm

-1

wavelength / nm200015001000500

1

2

0

0

1766

20

400

1

2

3

20

853

705 1171

369

T6

T44S RR 6S RR

T4 T6

Energy Gap and Poltroons of Oligothiophenes

209

the optical gap decreased (slightly) by increasing the oligomer length, and further to polaron gap P2 polaron transition P1 becomes smaller, lower polaron level closer to valence band but due to effective conjugation length, Eg, P1 , and P2 reach saturation values

+

++ + + +

T3 T4 T5 T6 T7 T8

R. Rathore, J. Am. Chem. Soc. 2009, 1780-1786

chemical oxidation can be used for quantitative polaron formationCrystal Structure of the Quaterphenyl and its Radical Cation

210

quinoidal structure of polaron requires planarization of molecular structure polaron structure is better delocalized than ground state, bond lengths become similar

NO SbF6

NOSbF6

Rder et al., Macromolecules 1999, 32, 1073.

effective conjugation length is the correlation length of the exciton/polaron/bipolaron wave packageEffective Conjugation Length (2)

211

correlation length decreased by chain twisting due to steric repulsion and/or structural dynamics correlation length increased by packing in the solid state, reinforced by favorable crystallinity correlation length drastically increased by enforced molecular rigidity and planarity

delocalized polaron

H H

H H

1015 in solution

25 in crystal

SS

H

H

SS

R

R

poly(thiophene) (amorphous)

P3HT (highly crystalline)

RR

poly(phenylene)

poly(fluorene)s

poly(phenylene) (solution)

poly(phenylene) (solid state)

H H

n

correlation length decreased by chain twisting due to steric repulsion and/or structural dynamics Delocalization and Dynamic Disorder on the Molecular Level

212

dynamic disorder increases, charge carriers become more localized with increasing temperature band gap and also distance between valence/conduction band and polaron levels increase

+

temperature

++

SS

SS

SS

SS

SS

SS

SS

SS

correlation length decrease by chain twisting disfavored by increasing molecular rigidityDelocalization and Molecular Rigidity

213

dynamic disorder decreases, charge carriers become more delocalized with increasing molecular rigidity band gap and also distance between valence/conduction band and polaron levels decrease

+

molecular rigidity

++

R R

R R

R R

R R

correlation length decrease by chain twisting disfavored by favorable crystalline packingDelocalization and Packing Effects on Dynamic Disorder on the Molecular Level

214

dynamic disorder decreases, charge carriers become more delocalized with improved crystalline packing band gap and also distance between valence/conduction band and polaron levels decrease

+

supramolecular rigidification

++

SS

SS

SS

SS

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13PT (amorphous)P3HT (crystalline)

SS

SS

SS

SS

5.3

Charge Carriers in Organic Materials and Devices

- stacking between polarons and neutral molecules has charge-transfer characterIntermolecular Delocalization of a Polaron Defect

216

- stacking interaction energetically more favorable and stronger, higher correlation - stacking results in intermolecular delocalization of the charge (typically over several molecules)

two neutral benzene molecules

++

benzene radical cation and a neutral benzene molecule

benzene radical anion and a neutral benzene molecule

E

intermolecular delocalization decreased by molecular motions in the solid stateDelocalization and Dynamic Disorder on the Molecular Level

217

dynamic disorder increases, charge carriers become more localized with increasing temperature band gap and also distance between valence/conduction band and polaron levels increase

+

temperature (dynamic disorder)

++

intermolecular delocalization increases with crystallinity and crystalline order in the solid stateDelocalization and Static Disorder oin the Solid State

218

static disorder decreases, charge carriers become more delocalized with improved crystalline packing static disorder are packing defects, lattice disorder, domain boundaries, impurities,

+

static disorder

++

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13S

SS

SS

SS

S

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13

C6H 13

at high doping levels (0.1 mol%) the polaron defect states start to interact with one anotherBand Formation in Highly Delocalized Systems at High Charge Carrier Densities

219

at doping level >1/1000 molecules, polaron defect every 1/10 molecules along any lattice direction interaction of defect states results in MO splitting and formation of a narrow polaron band

++ +n

number of charge carriers

+

for more disordered systems, the threshold concentration of polaron defects increasesBand Formation in Less Delocalized Systems at High Charge Carrier Densities

220

increase above threshold will initially locally create more extended states the bandwidth of the final polaron band is lower than for highly ordered systems

number of charge carriers

+ + + +n+++ +++

for highly disordered (amorphous) systems, no polaron bands are formed even at high doping levelsFormation of Extended States in Highly Disordered Systems at High Charge Carrier Densities

221

even in amorphous solids, however, polaron defects can locally start to interact with one another formation of more extended polaron defect states with limited delocalization

++ ++ +++ ++ +n

number of charge carriers

SS

SS

SS

SS

S

S S

SS

SS

S

SS

SSSS

SS

S

SS

SS

S

from single-crystalline to polycrystalline to amorphous materials, static and dynamic disorder increaseEffect of Combined Static and Dynamic Disorder

222

not only the correlation length and the extended nature of the polaron levels change also the local structure of both neutral states and polaron defects and, hence, their energy levels change

static & dynamic disorder

++++ ++++++ ++++n ++++ ++++++ +++

SS

SS

SS

S

S

S S

SS

SS

S

SS

SSSS

SS

S

SS

SS

S

Active Regions in p-Type and n-Type Organic Semiconductors

223

+n ++++ ++++++ +++p-type transport

active region

n-type transport active region

n

Fermi-Dirac distribution for thermal distribution of electron energiesFermi Distribution and Fermi Level

224

for EEF kBT, the Fermi-Dirac distribution becomes the Boltzmann distribution Fermi energy EF is defined (!) as the energy level where probability to find an electron is f(EF)= 0.5

Fermi energy EFenergy

occu

patio

n prob

abilit

y f(E,

T)T = 0 K

T

T

f (E) = 1e(EEF )/kB T +1

electronic structure of a material is described by the density of occupied states (DOS)Density of Occupied States (DOS)

225

density of states g(E) represents all available allowed states of a material (e.g., the 3s band in Na) these available states filled according to Fermi-Dirac distribution f(E,T) density of occupied states is g(E) f(E,T), represents the states of all electrons at given temperature

Fermi energy EF

dens

ity of

occu

pied s

tates

g(E) f(E

,T)

Fermi-Dirac distribution f(E,T)density of states

g(E)

4 kBT0.1 eV (300 K)3.2 eV for Na

density of occupied states

for metallic conductors, Fermi level is, by definition, equal to the work function (ionization energy) for semiconductors and insulators, the Fermi level is, by definition, in the middle of the band gap however, density of states within the band gap g(E) = 0; Fermi level not equal to work function

Density of States in Metals, Semiconductors, Insulators

226

only a tiny fraction of intrinsic charge carriers even in semiconductors, increasing with temperature for silicon with a band gap of 1.1 eV, 1010 cm3 (1012 at%) at 300 K,1014 cm3 (109 at%) at 500 K

E

EF

metal

0 1

semiconductor insulator

f(E,T)

0 1

f(E,T)

0 1

f(E,T)

E

EF

0 1

semiconductor

f(E,T)

0 1

f(E,T)

0 1

f(E,T)

upon bringing different materials into contact, Fermi level is defined for the whole materials systemp-Type Organic Semiconductors in Contact with a Metal Electrode

227

due to large excess of free charge carriers in the metal, this adjusts Fermi level to the one of the metal ideal combination is noble metal (large work function) near the (high) HOMO of the semiconductor

not in contact in contactE/eV

0

5.1

Au

0 1

f(E,T)EF

EF

Au

++++ ++++++ +++

E/eV0

5.1

Au

0 1

f(E,T)EF

upon bringing different materials into contact, Fermi level is defined for the whole materials systemn-Type Organic Semiconductors in Contact with a Metal Electrode

228

due to large excess of free charge carriers in the metal, this adjusts Fermi level to the one of the metal ideal combination is non-noble metal (small work function) near the (low) LUMO of the semiconductor

not in contact in contactE/eV

0

4.2

Al

0 1

f(E,T)

EFEF

E/eV0

4.2

Al

0 1

f(E,T)EF

Al

Typical p-Type and n-Type Organic Semiconductors

229

typical are Au electrodes for p-type, Al or Ca electrodes for n-type semicoductors Au electrodes are also often used for n-type semicoductors, due to reactivity/passivation of Al and Ca

Ph

Ph

Ph

Ph

SS

S

E/eV

Au

Al

Cugraphene

2

3

4

5

6

7

ORN O

ONR

O

ORN O

ONR

O

CNNC

ONR

O

ORN O

p-type n-type

230

5.4

Charge Transport in Organic Materials

models have initially been developed for disordered inorganic semiconductors these do not really apply to molecular organic materials, mostly because of strong coupling different experimental techniques emphasize different aspects of transport mechanisms

Transport Mechanism Models in Organic Semiconductors

232

for different incoherent transport models, start / end point look the same in structure / energy models aim to describe thermal distribution of involved levels, traps, transport probability different mechanisms in parallel, which one dominant depends on temperature, material, disorder (...)

band conductivity

band-like conductivity

tunneling & self-exchange

multiple trap-and-release

variable range hopping

nearest neighborhopping

incoherent transport via increasingly localised states

increasing static & dynamic disorder

coherent transport

Band Transport

Kittel, Introduction to Solid State Physics, John Wiley & Sons, Inc., New York, 1996.

band transport occurs via coherent Bloch waves, extended states in a periodic lattice intramolecular transport through lattice of repeating units intermolecular transport via lattice of molecules with intermolecular -interaction

Band Conductivity

234

injected charge drifts at constant velocity v, acceleration in electric field F versus scattering in the crystal mobility = v / F is materials property (but may be non-linear and field-dependent at high fields) limited to intramolecular transport or intermolecular transport in single crystals, at low temperatures

+nn

material material

Bredas et al., Proc. Natl. Acad. Sci. USA 2002, 99, 5804.

negative temperature factor, i.e., mobility decreases with temperature T (not a sufficient criterion)Criteria for Band Conductivity

235

only in this way mean free path of electron much larger than intermolecular distance function of temperature because W = f(S), typically only at very low temperatures crystal defects result in traps, detrimental for band transport

W = ~vib

0.10.2eV

ddT

< 0

/ T 3/2

for semiconductor in which band transport is limited by scattering from acoustical phonons:

band width W must be sufficient to enable transport before geometric relaxation (vibration time vib)

Karl, Charge-Carrier Mobility in Organic Crystals, Springer, Germany, 2001.

aromatic molecules exhibit metallic conductivity in single crystals at low temperaturesExample of Band Transport at Low Temperature

236

band transport at T < 100 K, in all three lattice directions, with different mobilities at room temperature, incoherent transport in two lattice directions becomes equal

3.2 Well-Ordered Systems: Organic Single Crystals 71

30

0.3

1

3

10

b = 1.48

b = 1.48

1

3

2

b = 1.47

100 300

[c

m2

V1

s1

]

T [K]

Figure 3.2 Three principal components of the mobility tensor in a naphthalene crys-tal measured by ToF, and fitted to a Tb dependence. A clear T3/2 dependence is ob-served only below 100 K. (Reprinted with permission from Ref. [9]. Copyright (2001) bySpringer-Verlag.)

In ToF measurements, charge is generated by using radiation that is wellabove the bandgap and as a consequence is in an excited state. This situation is notnecessarily representative of what happens in an electronic device in which electrons(holes) are injected at the bottom (top) of the conduction (valence) band. Recentexperiments pioneered by Podzorov et al. using vacuum-gap field-effect transistor(FET) structures fabricated with elastomers showed that a negative temperaturedependence of the mobility can be observed in single-crystal electronic devices[1518]. Rubrene FETs displayed an increasing mobility from room temperature(10 cm2 V1 s1) down to 150 K (>20 cm2 V1 s1). The mobility was also foundto depend on the crystallographic direction [1719]. At T < 150 K, the mobilitywas thermally activated with an activation energy of 70 meV. A gated Hall-effectmeasurement showed that the activated behavior was because of shallow traps nearthe valence-band edge (the FETs were hole-only devices): the mobility of the freecarriers keeps increasing as the temperature is decreased, even at temperatures atwhich the apparent mobility shows the opposite trend (Figure 3.3).

Owing to constraints in the experimental set-up, the measurements could notbe carried out at temperatures low enough to observe the T3/2 dependence of, and therefore, a weaker temperature dependence was observed. The use ofFET structures also somewhat relaxes the purity and quality requirements of thecrystal. Indeed, in FETs, the areal charge density is much higher than in ToFmeasurements and the gate voltage can be used to populate traps and push theFermi level close to the valence-band edge. It should be noted, however, that

Phys. Rev. Lett. 1988, 60, 1418.

Charge Transfer Salt of TTF and TCNQ

237

Tetrathiafulvalene (TTF) Tetracyanoquinodimethane (TCNQ)NC

NC

CN

CNS

S

S

S

105 S cm1 = 2 cm2/Vs

105 S cm1

TTF TCNQ Single Crystal

= 500 S cm1, metallic at T < 54 K

Charge Transfer Complexes between Electron Donor and Acceptor Materials (1)

238

if electron donors and acceptors crystallized in pairs, electron transfer would just yield localized charges charge transfer complex with poor conductivity

NCNC CN

CN

SS

SS

NCNC CN

CN

NCNC CN

CN

SS

SS NC

NC CNCN

SS

SS

NCNC CN

CN

SS

SS

SS

SS

e

NCNC CN

CN

SS

SS

NCNC CN

CN

NCNC CN

CN

SS

SS NC

NC CNCN

SS

SS

NCNC CN

CN

SS

SS

SS

SS

Charge Transfer Complexes between Electron Donor and Acceptor Materials (2)

239

electron donors and acceptors crystallize in segregated stacks, charge transfer between stacks electron transfer yields strongly delocalized charge carriers charge transfer complex with high (even metallic) conductivity

NCNC CN

CN

NCNC CN

CN

NCNC CN

CN

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

NCNC CN

CN

NCNHC CN

CNe

NCNC CN

CN

NCNC CN

CN

SS

SS

SS

SS

SS

SS

SS

SS

NCNC CN

CN

NCHNHC CN

CNSS

SS

NCNC CN

CN

240

Band-Like Transport

often negative temperature factor observed, but mean free path smaller than intermolecular distance localization due to dynamic disorder, but transport associated with coupled molecular motions

Band-Like Transport in Highly Ordered Crystalline Solids

242

transport looks like coherent transport, although mediated by incoherent (localized) charge carriers expected ~ T2.1 but typically weaker temperature dependence due to disorder and trap states typically, inversion to positive temperature factor at about T = 150 K

+ + + e+ + e + + +

material material material

Incoherent Charge Transport Mechanisms

fluctuations of transfer integral S on the order of S itself due to dynamic disorder at room temperature static disorder is slow on the time scale of charge transport, results in energetic heterogeneity

Incoherent Transport in Disordered Organic Solids

244

premises for band or band-like transport usually not fulfilled in partially ordered organic solids even in (partially) crystalline solids, molecular motions at r.t. destroy translational symmetry

++++ ++++++ +++++++ ++++++ +++

polycrystalline solid amorphous solid

charge carriers with limited delocalization move in electric field independently and statistically random walk with a directional bias by electric field

Incoherent Charge Transport Mechanisms

245

+ + + + + + + + + + + +

e e

material material

charged state (positive polaron) interacts with nearby neutral state (HOMO) if lower polaron level and neutral HOMO level are close in energy, increases probability of exchange hence, large -conjugated systems with good intramolecular delocalization and good overlap preferred

charge carriers with limited delocalization move in electric field independently and statistically random walk with a directional bias by electric field

Incoherent Charge Transport Mechanisms

246

charged state (negative polaron) interacts with nearby neutral state (LUMO) if upper polaron level and neutral LUMO level are close in energy, increases probability of exchange hence, large -conjugated systems with good intramolecular delocalization and good overlap preferred

e e

material material

electronic frequency unchanged, but probability decreases exponentially with distance process itself has no temperature dependence, but since disorder does, one observes ~ Tn

finite potential well results in certain probability to find electron outside the well tunneling to nearby molecules if energy levels identical (required for resonant exchange)

Charge Transport by Tunneling

247

ktun / eB d

M1 M2 M1+ + M2

E

G = 0

M1 + M2

initial state final stateM1 M2+

transfer integral J large (large systems), (energetic/geometric difference) small weak temperature dependence, typical activation energies 50200 meV (520 kJ/mol)

hopping is a thermally promoted process at higher temperatures (thermally assisted tunneling)Charge Transport by Hopping

248

M1 M2 M1+ + M2

kCT =|J |2~

r

kB Te

4kB T

G = 0

EA

geometry

EM1 + M2

initial state final stateM1 M2+

with increasing disorder, increases, J decreases, activation energy EA increases for certain steps with increasing disorder lower energy states increasingly become traps for charge carriers

hopping also allows for transport between different states in disordered systemsCharge Transport by Hopping in Disordered Systems

249

M1 M2 M1+ + M2

EA

geometry

EM1 + M2

initial state final stateM1 M2+

band edge disorder model assumes disorder, distribution of states near the band edge states more located within the bands more extended, states more at the band edge more localized traps

Multiple Trap and Release (MTR) Model

250

charge carriers temporarily trapped in localized trap states, but no deep traps if disorder not too large promotion of charge above mobility edge into more extended state allows for drift in electric field subsequent retrapping into more localized resting state

material material material

trapped above mobility edge trapped

band edge disorder model assumes disorder, distribution of states near the band edge states more located within the bands more extended, states more at the band edge more localized traps

Multiple Trap and Release (MTR) Model

251

charge carriers temporarily trapped in localized trap states, but no deep traps if disorder not too large promotion of charge above mobility edge into more extended state allows for drift in electric field subsequent retrapping into more localized resting state

+ + +

material material material

trapped above mobility edge trapped

in highly disordered (amorphous) systems, only hopping through states with limited delocalization nearest neighbor hopping (NNH) for highly disordered systems and /or at low temperatures (E kB T)

Nearest Neighbor Hopping and Variable Range Hopping

252

variable range hopping (VRH) for less disordered systems and /or at higher temperatures (E kB T) VRH and Motts law abundant in the literature, but lack physical basis, superseded by other models

variable range hopping (VRH)

kVRH =C VRH e(T0/T )1/4Motts law

nearest neighbor hopping (NNH)

Charge Transport in Amorphous Polymers

253

amorphous conjugated polymers inherently low mobility; but mechanical toughness, strength

S

S

S

SS

S S

S

S

S S SS S S

S

S

S

SS

S SS S

S SS S

SS

S

S

S

S

S

SS

S S

S

S

S S SS S S

S

S

S

SS

S

S SS S

SS

S

S

S

S

S

S

S

S

S SS

SS

S S

S

S

S S SS S S

S

S

S

SS

S SS S

S SS S

SS

S

S

S

S

S

S

S

S

A B

C D

S

S

S

SS

S S

S

S

S S SS S S

S

S

S

SS

S SS S

S SS S

SS

S

S

S

S

S

positive polaron crystalline domain

E E

E E

Charge Transport in Single-Crystalline Solids

254

single-crystalline organic solids comparably high mobility; but mechanically brittle

A B

C D

positive polaron grain boundary

E E

E E

Summary

255

-conjugated molecules: polarizable electrons, low HOMO-LUMO gap extended -conjugated systems: electron delocalization for low band gap doping for charge carrier generation (polarons, bipolarons) high doping levels for band conductivity

amorphous -conjugated polymers: band conductivity within molecules, as long as coplanarity not interrupted by conformation intramolecular hopping as molecular level static and dynamic disorder increase intermolecular hopping/tunneling, depending on intermolecular order

single crystalline solids of -conjugated molecules: band(-like) conductivity within domains (grains), depending on packing and constructive -overlap intermolecular hopping within domains as static and dynamic disorder increase hopping at grain boundaries and defects, depending on size, orientation

256

5.5

The Interplay of Short-Range Order and Microstructure for Macroscopic Charge Transport

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Length Scales in Organic Electronic Materials and Devices

258

carrier dynamics, and advanced computational and simulationtechniques, organic electronics has progressed toward completeand general quantitative descriptions of relevant systems, whichwill continue to facilitate rational synthetic molecular engineer-ing and processing parameter selection.To this end, we describe the contributions made by X-ray

science to elucidate the film morphology and microstructureover 5 orders of magnitude in length scales. Access to such abroad range of length-scales is possible through theextraordinary versatility of X-ray techniques. Recent reviewshave focused on a select range of structural features anddescribed a broad range of techniques that can be used to probethem.4,5 In this review, we discuss the broad range of physicalphenomena and their importance and focus solely on the use ofX-ray based techniques, and specifically quantitative X-raytechniques, for the accurate determination of structuralproperties ranging from molecular packing and defects todevice-scale phase segregation.First, it is important to understand the complexity of

molecular arrangement and film composition in the solid state,as well as what optoelectronic properties are at play in differentstructural regimes. We start at the smallest length scales withstudies of atomic bonding and molecular orbital interactionsand zoom out to describe device-scale phase arrangements anddomain alignment. We choose to highlight organic TFTmaterials and those for organic photovoltaics (OPVs) asexamples of pristine and blend films with a number of distinctmaterials requirements. We also focus on OTFT and OPVmaterials because they are the most frequent subjects of organicelectronic structural characterization by X-ray techniques.

2. RELEVANT LENGTH SCALES IN ORGANICSEMICONDUCTORS

An outstanding challenge for the development of high-performing organic semiconductor devices is to arrange theindividual phases (and molecules within those phases) in amanner that optimizes all relevant optoelectronic processesrequired for efficient operation. For OTFTs, these processesinclude charge injection and charge transport on both themolecular and device-size scales. In organic photovoltaics,efficient solar radiation absorption and exciton diffusion anddissociation rely on features found at the molecular andnanoscopic-size scale. Charge transport for carrier collectionrelies on details of molecular and mesoscale microstructure andmorphology. Unfortunately, however, it is challenging tocontrol how molecules arrange at different length scales.Organic solids are held together by weak intermolecularattractive forces that make it difficult to engineer stable anddefect-free microstructures and morphologies. One can finelycontrol the absorption and local intermolecular charge transferamong neighboring molecules by finely tuning the molecularstructure and chemistry,4,6,7 but these chemical changes oftenaffect the film-forming properties and, therefore, the larger-scalemorphology in a way that may be detrimental to otherelectronic processes. Often it is convenient to focus on onespecific length scale due to access to a particular set ofexperimental techniques or tools, but it has become clear thatthe most enlightening work comes from combining techniquesthat deliver insight into the microstructure and morphologyover a wide range of size scales. These size scales, and thestructural order or physical arrangements that are commonlyaddressed, are outlined in Figure 2; additionally, Table 1

Figure 2. Size scales and relevant morphological features in organic electronic devices. Within each schematic, the square denotes the enlargedregion preceding it. Each type of physical feature shown is assigned a range of length scales on the scale at center, described in the text. Althoughmany materials systems and device types/architectures are often investigated, two examples are chosen to display the various morphologies andmicrostructures possible. Top row: a two-component blend film typical of a bulk heterojunction used in organic photovoltaic devices. Themorphology of phase separation is invariably more complex than the schematic shown here, with impure/mixed phases coexisting with purecrystalline phases. Bottom row: single-component small-molecule semiconductor film used in OTFTs. Domains refer to regions composed ofsimilarly oriented grains.

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Structural and Energetic Disorder

259

summarizes examples of the optoelectronic processes that arerelevant for the physical structures at play at these size scales, aswell as the X-ray techniques suited to study them.For the purposes of this discussion of X-ray-based analyses

for the quantitative determination of microstructure in organicsemiconductors, these rough groupings of length scale areuseful because they are closely linked to specific experimentaltechniques, which are described later. The following sectionswill focus on each of the microstructural size categories, startingwith the smallest length scales.2.1. 1 10 nm: Chemistry, Local Molecular Packing, andDefects

The chemistry of a molecule influences the energetics of asystem at the most basic level. The -orbital delocalization orconjugation length8,9 and induction or hybridization effects10

are common methods used to control the bandgap and theenergy of the highest occupied and lowest unoccupiedmolecular orbitals (HOMOs and LUMOs) (Figure 3). Thelocation of energy levels with respect to each other and/orvacuum determines the onset of absorption, charge carrierinjection, band alignment, and environmental stability. Tounderstand these properties, it is therefore important to focuson the molecular scale, where the chemical structure bothdirectly and indirectly influences other microstructural features.Molecule size, rigidity, or the presence of solubilizing sidegroups (as is necessary for solution-processable materials)dictate the local molecular packing,4,6 the interaction with thesubstrate surface,1113 and the solubility, which in turninfluence domain size and phase segregation. The structuralfeatures in question are those related to the moleculararchitecture and its associated interactions with neighboringmolecules, which spans the ngstrom to nanometer scale.Ultimately, packing order at the molecular scale affects chargeand exciton localization. Localized cahrges are incapable ofdiffusing in a concentration gradient or drifting in a weakelectric field.Although the molecular structure is a starting point, the

specific solid-state arrangement of (macro)molecules ultimatelyinfluences the local optoelectronic properties of the sys-tem.1517 Molecular packing profoundly affects the interactionwith neighboring molecular orbitals, which dictates intermo-lecular charge transfer, charge delocalization, and opticalabsorption. In the solid state, high-performing materials oftenhave a tendency to partially arrange in a periodic lattice or inaggregates. The specific symmetry and packing structure has

been found to sensitively depend on the aspect ratio, planarity,size, and density of side-chains or solubilizing groups.4,18 Forexample, the packing motif of pentacene is edge-to-face (Figure4). When a solubilizing side-group is added at the 6 and 13positions, packing adopts a face-to-face brickwork-like motif. Ifthis side-group is shifted over by one position (5, 14) on theacene core, a mixed-motif is observed, called a sandwichherringbone, where cofacial dimers of the molecules form edge-to-face arrangements with each other.6 Ultimately thecrystalline lattice arrangement will control the ease (efficiency)of transport (drift and diffusion) for both free charges andbound electronhole pairs (excitons). These structural featuresare characteristically 110 nm in size and are important for thecharge generation, exciton diffusion, exciton recombination,and free charge carrier collection steps often considered inOPVs, as well as charge injection and local charge transport inOTFTs.

Table 1. Important Basic Morphological Features Commonly Discussed in Organic Semiconductors, Their Relevant Size Scale,X-Ray-Based Technique Used to Probe That Feature, And the Most Important Optoelectronic Properties That Are at Play forEach Feature

morphological or physical feature size scaleappropriate experimental X-ray

technique relevant optoelectronic processes

molecular packing/chemistry

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Structure Determination

260

Unfortunately, the data-collection process is serial, where eachscattering direction/angle is measured separately, making dataacquisition times long; because small diffracting volumes areprobed, damage to the film is a constant consideration.Conversely, an area detector setup (Figure 5C) allows for

rapid data collection over a large range of scattering angles butsuffers from lower accuracy and resolution. The detector in thiscase essentially takes a snapshot of the scattered X-rays, withthe exposure time depending on the detector, source intensity,diffracting volume, and crystalline qualityvarying from a fewseconds to tens of minutes.82 Shorter acquisition timesminimize beam damage and allow in situ and time-resolvedmeasurements. The scattering angle resolution of the recordedprofile depends on the pixel size of the detector, the beam size,the incidence angle, and the sample-to-detector distance. Alarge illumination area can produce broadening artifacts in thescattering peaks, limiting the measurement resolution.88

Another constraint of area detectors in 2D GIXD is the fixedincidence angle and sample orientation. Because of thescattering geometry, nominal cuts along qz (qxy = 0) on thearea detector are not true specular scans but instead providescattering data from planes that are misoriented from thesubstrate normal by a few degrees with larger distortions athigher scattering angles. This effect also occurs for the in-planescattering for single crystals and films that are highly orientedin-plane. These distortions have been mentioned before8991

and addressed by completely removing the near-specular regionfrom the 2D pattern88 or by labeling the scattering vectors asapproximate (i.e., qz) and using slices or cuts to make

qualitative or relative comparisons. This distortion however, isoften ignored in the literature.

4.1.2. Molecular Crystal Packing. To determine themolecular packing of the ordered regions of poly- andsemicrystalline films, the size and symmetry of the unit cellmust be determined first, and then the basis or atomicarrangement within that repeating unit cell. This information iscontained in the peak positions and intensities of diffractionpeaks. The general analysis is analogous to structuraldetermination used for biological systems, for example, todetermine protein structures. Similarly to biological entities,one must obtain rather large single crystals to adequatelyperform single-crystal diffraction measurements, such thatthousands of peaks can be observed. Unfortunately, it can bedifficult or impossible to grow large single crystals of organicsemiconductors, and often, the phase of a single crystal isdifferent from what is encountered in a thin film that would beused in a device.92 Therefore, we discuss the quantitativemolecular packing determination as it applies to thin films ofpolycrystalline small molecules and semicrystalline polymers.Diffraction peaks from a polycrystalline thin film or single

crystal only occur at discrete scattering vectors q, specificallythose for which the scattered waves from adjacent lattice planesinterfere constructively. This is Braggs law and is expressed bythe Bragg condition (eq 2) that links the allowed q values (qB)to the interplanar lattice spacings in the crystalline sample.87,93

Although the real lattice vectors (a, b, c) describe the distanceand orientation of unit cells in the crystal, the magnitudes andorientations of the corresponding interplanar spacings dhkl for afamily of lattice planes with Miller indices hkl form a lattice oftheir own, called the reciprocal lattice (a*, b*, c*):

* = * =

* =

a b ca b c

b c aa b c

c a ba b c

2( )

, 2( )

,

2( ) (3)

It is convenient to discuss diffraction within the context of thereciprocal lattice, because q values that satisfy the Braggcondition (qB) can be constructed from the reciprocal latticevectors:

= * + * + *h k lq a b c( ).hkl (4)Because of the relationship between real and reciprocal spacelattices, the real space unit cell can be reconstructed fromdiffraction data in a two-step process. First, the q values fromthe crystalline sample are determined from the positions of theexperimentally observed diffraction peaks (typically qxy, qz forsamples that are isotropic in plane). In the second step, thepeaks are indexed by assigning a set of integers h, k, l to eachpeak. The reciprocal lattice can then be reconstructed byapplying eq 4, and the corresponding real space unit cell followsdirectly by application of the inverse relationships from eq 3.94

This analysis has been demonstrated for both vapor-depositedand solution-deposited small-molecule films95 where thenumber of measurable diffraction peaks is typically in therange of 1040. This analysis of diffraction images only yieldspurely geometrical information (the unit cell size and shape)and does not reveal the arrangement of the molecules withinthat cell.With extended organic semiconductor systems, it is crucial to

know the exact molecular packing in order to evaluatefundamental material parameters such as electrical conductivity

Figure 5. Wide-angle X-ray scattering geometries on thin films. (A)Specular diffraction (also used in X-ray reflectivity (XRR) and powderdiffraction). (B) Grazing incidence wide-angle X-ray diffraction(GIXD) with a point detector. is the incidence angle, and is anin-plane, azimuthal, rotation. (C) Grazing incidence X-ray scattering(GIXS) with a 2D image plate (a similar setup is used for grazingincidence small-angle scattering, with the detector at a larger distance,L; see Figure 16).

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yields more efficient charge transport. The information aboutthe size of crystalline grains is contained in the width of thediffraction peaks, and at the simplest level the Scherrer equationcan be employed to extract a grain size.87,93 The Scherrerequation relates the peak width to the coherence length Lc,

= LK2

qc

(6)

where K is a shape factor (typically 0.81) and q is the fullwidth at half-maximum of a diffraction peak. It should be wellunderstood that calling this a grain or crystallite size isrigorously correct when the only factor affecting the measuredpeak breadth is the finite size of the crystalline assemblies. Inorganic semiconductors, especially those that include solubiliz-ing alkyl chains or polymeric species, this is rarely the case, andthe width of a f irst order peak cannot provide a grain size.Many of the recent advances in the analysis of diffraction line

shape for organic semiconductors have focused on decouplingthe effects of finite size from those of cumulative disorder,which is well-established and has been used for inorganicmaterials and bulk polymers over 60 years.118,119 Cumulativedisorder describes variations in lattice parameter within the filmor the loss of predictive ability regarding the position of a unitcell as the displacement along a certain direction of a latticeincreases, and is due to the accumulation of distortions anddefects.86,118 In other words, when cumulative disorder ispresent, the lattice forgets its origin (initial location) aftersome distance. This is distinct from noncumulative disorder(e.g., thermal motion) where the average lattice is retainedindependent of distance between lattice sites; cumulativedisorder is often called paracrystalline disorder or latticedisorder (Figure 9D and E).120,121 When analyzing a diffractionpattern, one often observes (or expects to observe) aprogression of higher-order diffraction peaks corresponding toa specific set of crystal planes, i.e., (100), (200), (300). While adiffraction profile from a finite-size-dominated sample has peaksof equal breadth for this progression, one with cumulativedisorder shows successive broadening of the higher-order peaks(Figure 10). This distinction along with the specific peakshapes and functional dependence of the peak broadening ondiffraction order allow for the quantitative decoupling of thecrystallite size and lattice disorder. Such decoupling isimportant from the standpoint of the electronic properties.Indeed, an overall low diffracted intensity can be interpreted asthe presence of a large volume fraction of disorderedcrystallites, through which charges and excitons can percolate.On the other hand, the same signal could be due to a smallvolume fraction of relatively perfect crystallites, in which casecharges and excitons will have to migrate through anamorphous matrix. Hence, quantitative analysis methods areinstrumental in distinguishing these two very differentsituations.Implementation of well-known models that decouple the

effects of size and disorder are limited in organic semi-conductors. Weakly scattering materials, such as polymers,rarely exhibit enough peaks to enable such analysis.Furthermore, the directions that usually limit charge orexcitonic transport are those where intermolecular couplingoccurs. In these directions molecules typically only exhibit vander Waals bonds. As a result, the directions that are mostimportant for transport are also the most disordered ones. Thispoint is interesting considering that the weak scattering (for

higher order peaks) may be due to a low crystalline fraction, butmore likely, it is due to a high degree of paracrystalline disorder,making these analyses (Figure 10) important for both accuratedetermination of crystallite size and quantification of latticedisorder.When both finite size and disorder are present, the functional

form with which higher diffraction order peaks broaden can beattributed to different types of disorder or defects.122 Therefore,by plotting the peak breadth versus diffraction order m (or m2)(Figure 10A, inset), one can extract the coherence length fromthe intercept (m = 0), while the functional form of thebroadening, q(m), can reveal the mechanism and magnitudeof the lattice nonidealities.122,123 This integral breadth method(related to the analyses of Hall of Williamson),124,125 is usefulin strongly diffracting materials, but it is not a reliable tool fordiffraction patterns where only two or three diffraction ordersare present. Nevertheless, this approach has been applied with

Figure 10. Peak breadth, shape, and diffraction-order dependentbroadening to decouple size and disorder related terms. (A) Schematicof hypothetical diffraction profile from crystalline lattices affected byfinite size, with (red) and without (blue) the contribution ofcumulative disorder. Inset: Integral peak breadth (q) approach fordecoupling coherence length, Lc, from disorder-related terms usingmultiple diffraction order peak widths. Fourier transform-basedtechniques, such as the WarrenAverbach analysis, rely on peakisolation (B and C), followed by Fourier transform (D and E) analysisto decouple the average column length, M, its size distribution, wM,and cumulative disorder terms (g, erms).

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Crstallite Orientation

261lamellar stacking thiophene-based liquid crystalline polymerswhere a number of well-resolved out-of-plane peaks areobserved.91,126 Similar analyses (based on ref 126) have beenperformed by Lilliu et al.127,128 where size and paracrystallinityare decoupled to show the crystal growth and orderingdynamics upon annealing of P3HT/PCBM solar cell blends.They find a growth of crystallites in the alkyl stacking directionof the P3HT and an increase in order on annealing that isdependent on PCBM concentrationindicative of PCBMacting as a plasticizer.127

More accurate techniques involve utilizing the entire peakshape, in the form of a Fourier-transform (FT) analysis ofindividual peaks (Figure 10D and E). The power of suchtechniques, first introduced by Warren and Averbach,119,129 isthat contributions from cumulative disorder and a finitecrystallite size can be decoupled because of their specificfunctional dependences on both the diffraction peak order andthe Fourier frequency. The Fourier components of the peakscan be represented as the product of contributions from a finitecrystallite size, which is independent of peak order, and peak-order-dependent terms related to paracrystalline disorder. Inone variant of this WarrenAverbach (WA) model, eachdiffraction peak is constructed from the superposition of wavesscattered by units whose distortions from the ideal lattice aredescribed by Gaussian statistics and belong to columns of unitcells along the [hkl] direction. The normalized nth coefficientof the Fourier transform of the mth-order diffraction peak isthen given by

= +A n A n m ng n e( ) ( ) exp[ 2 ( )]m mS 2 2 2 2 rms2 (7)where Am

S (n) is the size-related broadening contribution thatdepends on the column length distribution in the sample, g isthe paracrystalline disorder parameter, and erms is the latticeparameter fluctuation reduced variance.130,131 The general WAmethodology has been applied to the alkyl-stacking (nontran-sport) direction in polyalkylthiophenes, monitoring the changein disorder parameters when heating through a glass

transition.130 Although this routine is normally applied in amultistep manner, which is hampered by iterative fits andaccumulating errors, a full fit to eq 7 can be employed, withthorough error propagation analysis to gain confidence in fitresults.131 The -stacking analysis of conjugated polymersystems is usually particularly inaccessible, because only thefirst-order peak is measurable. Rivnay, Noriega, and co-workersused alignment methods (see section 4.1.5) to measure asecond-order peak of PBTTT -stacking, which allowed for fullanalysis; it was found that the -stacking disorder in PBTTT isg = 7.3%, a value that is close to a 1D amorphous assembly(10%).131 This finding also showed that, in -stackedpolymers, paracrystalline disorder completely dominates thepeak breadth (coherence), opening up the possibility of aScherrer-based single-peak estimation of paracrystallinity fordisordered polymers when specific assumptions are satisfied.Furthermore, using a tight binding model, it was found thatincreasing the paracrystalline disorder in the -stacking ofPBTTT oligomers introduces a tail of localized states extendinginto the optical band gap that can act as shallow traps, whichlimit charge transport.29 Such a finding provides physicaljustification for transport models that involve interplay oflocalized and delocalized states, such as the mobility edgemodel. Furthermore, it highlights the importance of disen-tangling the effect of paracrystallinity (g) and crystallite sizebecause of the effects of these microstructural parameters onthe physics of charge transport.Although the physical source of paracrystalline disorder is

unknown, it is thought to be an accumulation of intrinsic andextrinsic defects that yield a statistical, static disorder. Intrinsiccontributions may be due to polydispersity, molecular weightand related chain-end effects,132 regioregularity couplingdefects,133 or side-chain disorder. The role and concentrationof typical crystallographic defects (e.g., dislocations) has notbeen studied in depth. There have been numerous accounts ofobservations of screw dislocations (mostly by AFM and TEM)and other local defects (by scanning tunneling microscopy) in

Figure 11. Texture in thin films. (A) Randomly oriented (similar to powder) arrangements of crystallites, with no preference for a specificcrystallographic orientation (100) with respect to the substrate normal produce rings in the diffraction patterns. (B) Textured or oriented films witha distribution of crystallite orientations produce arcs of diffracted intensity. (C) Highly oriented films produce spots or ellipses. The corresponding2D GIXD patterns for PBTTT that are solid state pressed (A), as spun from solution (B) and annealed (C), are used as examples at bottom. Thepressed sample, A, is mostlynot completelyrandomly oriented.

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Crystal Structure of P3HT

262

fiber axis stacking

[010]

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

SS

alkyl packing [100]

chain repeat [001]

Melting of poly(alkylthiophene)s

263

melting of side chains hard to observe for longer P3HT, kinetically trapped separation of backbone and side chains persists after melting

T. Thurn-Albrecht et al., Macromolecules 2010, 43, 4646.

DSC heating/cooling trace

Tg

Tm,side

Tm,back

Phase I Phase II III

Morphology of poly(alkylthiophene)s

264

AFM phase images reveal hard-soft contrast, not topology (height)T. Thurn-Albrecht et al., Macromolecules, 2010, 43, 4646

P3HT (Mn 3000) P3HT (Mn 6000) P3HT (Mn 12000)

Kline et al., Polym. Rev. 2006, 46, 27

Crystallinity of P3HT Thin Films

265

XRD, out-of-plane GIXS, in-plane

Kline et al., Polym. Rev. 2006, 46, 27

Crystallinity of P3HT Thin Films

266

high molecular weightlow molecular weight

High resolution GIXS on P3HT

267

F.P.V. Koch et al. / Progress in Polymer Science 38 (2013) 1978 1989 1985

Fig. 5. (A) Grazing-incidence X-ray diffraction patterns obtained with a 2D-image plate for solution-processed thin films of selected P3HT of Mn given inthe figure. (B) Evolution of the interplanar spacings d1 0 0 and d0 2 0 as well as the !-stacking disorder parameter g (see Refs. [3538]) with Mn. At Mn Mc,d1 0 0, d0 2 0 and g become essentially independent from the materials molecular weight.

being interconnected by individual macromolecules. Thissuggests that charge-transport in FETs seems to bestrongly limited in thin-film architectures comprised ofnon-interconnected chain-extended crystals such as thoseobtained with low-molecular weight materials, possiblybecause grain boundaries between the crystalline regions(alluded to above) can act as deep traps or transport bar-riers [43,44]. Hence, in order to obtain efficient deviceperformance in semicrystalline polymer semiconductors itseems to be critical to work with material of sufficientlyhigh Mn that provides for a high crystalline interconnec-tivity through tie molecules, as already postulated, e.g., byKline et al. [12,13]. It is intriguing, however, to also note thatthe dependency of !FET with Mn closely follows the devel-opment of Tm and "Hf (measured in solution-cast films)

with Mn (Fig. 6B and C), while it is inversely correlated withthe !-stacking disorder deduced from g (Fig. 5B/bottompanel). Indeed, materials featuring low g-values (i.e., betterorder along the !-stack) display the worst device perfor-mance. Molecular order in the !-stacking direction may bedecoupled from the order along the chain backbone; how-ever molecular order seems relevant since !FET directlycorrelates with "Hf, which is used in classical polymer sci-ence to compare the molecular order between systems [1].Moreover, higher !FET are measured for architectures com-prising crystalline moieties of an increased lamellar crystalthickness (as deduced from the higher melting tempera-tures), suggesting that processing methods that allow l tobe manipulated might assist in reaching optimum deviceperformance.

Thermomechanical Properties of P3HT

268

F.P.V. Koch et al. / Progress in Polymer Science 38 (2013) 1978 1989 1981

Fig. 2. Differential scanning calorimetry, DSC, heating (A) and cooling (B) thermograms obtained for melt-solidified P3HT samples of a range of molec-ular weights (heating/cooling rate = 10 C/min). Melting- and crystallization temperatures Tm and Tc varied with Mn. In addition, it is indicated how thesupercooling, !T, for P3HT of Mn = 130 kg/mol was deduced from the difference between its Tm and Tc.

charge transport as measured in transistors, among otherthings. For instance, on the basis of a range of P3HTs ofrelatively low Mw (2.4 kg/mol < Mw < 18 kg/mol), Zhanget al. [11] established a correlation between weight-average contour length, LW (with LW being a measurefor the lamellar crystal thickness, l, for these short-chainmolecules [7]) and field-effect transistor charge-carriermobilities "FET, such that "FET increases with increasingLW, in accord with findings presented in Refs. [1214].

A more detailed discussion of the interrelationship ofcharge transport and polymer solid-state microstructurewill be given after highlighting how processing can affectthe molecular assembly process.

2.1. Melt processing

2.1.1. Thermal phase behaviourThermal analysis, viscosity measurements and mechan-

ical testing are useful tools to identify the molecular weightabove which the two-phase morphology of interconnectedlamellar crystals and amorphous regions can be observed.We applied these methodologies to P3HT. For this pur-pose, we selected materials of a wide range of molecularweights; number-average molecular weights, Mn rangedfrom 4 to 128 kg/mol, and Mw from 5.5 to 260 kg/mol(see gel permeation chromatography data displayed inFig. 1B).

1982 F.P.V. Koch et al. / Progress in Polymer Science 38 (2013) 1978 1989

Table 1P3HT of the given number-average molecular weights, Mn, and polydispersity indices (PDI) were investigated in this study. Melting temperatures, Tm andcrystallization temperatures, Tc, for melt-processed materials of these P3HT samples are listed. Larger supercoolings !T = Tm Tc were required to solidifythe P3HT of higher Mn from the melt due to the entangled nature of these systems.

Mn (kg/mol) 4.0 4.8 5.2 7 8 25 35 80 90 95 110 130Tm (C) 189 204 211 221 227 236 237 230 235 225 229 223Tc (C) 172 181 186 190 196 203 203 183 193 176 184 180!T (C) 17 23 25 31 31 33 34 47 42 49 45 43PDI () 1.3 1.4 1.4 1.7 1.6 1.8 1.5 2.5 2.2 3.7 2.9 2.0

Mn and PDI were measured via GPC; Tm and Tc were determined via DSC, as per the procedures described in the Experimental section.

Thermal analysis data is presented in Fig. 2. For melt-processed samples of Mn 25 kg/mol, we observe anessentially linear increase in melting temperature, Tm(deduced from the end of melting endotherm in differen-tial scanning calorimetry (DSC) thermograms), with Mn.For P3HT of higher molecular weight, the melting pointat first slightly decreased with Mn, levelling off around230 C for materials of Mn 60 kg/mol (Fig. 2A). Consid-ering that Tm depends on chain length (with Tm beinghigher for longer-chain material) [13,26,28] and lamellarcrystal thickness l (with Tm increasing with l) [13,26,28],we assign this dependency of Tm with Mn to the factthat the microstructure is evolving from fully extended-chain structures into entangled, interconnected two-phasefringed-micelle architectures [1,2] at Mn 25 kg/mol, invery close agreement with the classification for the struc-tural evolution of P3HT with chain length forwarded inRefs. [914]. Clearly, higher molecular-weight materials(Mn 25 kg/mol) entangle in the melt, which is reflectedby the large supercooling !T = Tm Tc, (with Tc being thecrystallization temperature; see Fig. 2B) that is requiredto crystallize these polymers from the melt. Table 1 sum-marizes the !T values obtained for the systems discussedhere; in addition !T for P3HT of Mn = 130 kg/mol is indi-cated in Fig. 2 with red arrows and lines (for interpretationof the references to colour in text, the reader is referred tothe web version of this article). Note also that the entanglednature of the P3HT samples of higher molecular weight,which can lead to chain folding, results in thinner crys-talline, lamellar moieties [1,2] and, hence, lowers their Tm.

In contrast, P3HT of lower molecular weight(Mn 25 kg/mol) can readily crystallize because themacromolecular chains are not entangled (hence, theobserved, relatively small !T; cf. Table 1) and can there-fore form chain-extended crystals of a thickness l thatessentially corresponds to the length of the individualmolecules [18]. For these structures l is linearly correlatedwith Mn. Since thicker crystal lamellae are more stable[3,26,28], this increase in l results in an increase in Tm.

2.1.2. Mechanical propertiesThe structural classification for P3HT, with materi-

als of Mn 25 kg/mol forming chain-extended structuresand samples of higher Mn fringed-micelle microstruc-ture, is supported by mechanical analysis of a selectedseries of melt-processed P3HT tapes (Mn = 20, 25, 90 and110 kg/mol; Fig. 3A). The low molecular-weight material(Mn = 20 kg/mol) displayed brittle tensile behaviour imply-ing that this sample is indeed comprised of unconnected,chain-extended crystals that cannot withstand large strain.

For P3HT of Mn = 25 kg/mol, we start to observe, at higherelongations at break, a deviation from the linear relation ofstress, ", and elongation, , which signifies the onset of plas-tic (i.e., irreversible) deformation. This is a clear indicationthat elastic percolation is reached, which results from thecrystalline entities being connected through tie molecules.P3HT samples of higher molecular weight (here, 90 and

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Fig. 3. (A) Mechanical properties of four selected P3HT tapes of differentMn that had been solidified from the melt. (B) Top panels: Transmissionwide-angle X-ray diffraction patterns on as-prepared (left) and mechani-cally elongated (right) P3HT samples of Mn = 110 kg/mol. After uniaxiallystretching well-defined diffractions are observed that are characteristicfor anisotropic structures (right panel). Bottom panels: Reflection opticalmicrographs taken with crossed polarizers. The oriented tape (P3HT ofMn = 110 kg/mol) was thereby positioned parallel (left) and at 45 (right)with respect to the polarizer/analyser system.

The Role of Entanglement in Crystallization

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Fig. 1. (A) Schematic illustration of the evolution of the molecular arrangement of a (semi-)flexible polymer such as the macromolecular semiconductorpoly(3-hexylthiophene), P3HT (see inset in (B) for the chemical structure of P3HT), in the melt (T > Tm; top panel) and in the solid state (T < Tm; bottompanel). The molecular weight between entanglements Me and the long period L, i.e., the total thickness of the crystalline and amorphous region, are definedas indicated in red. In addition, the crystallographic directions [1 0 0] alkyl stacking, [0 1 0] (!-stacking) and [0 0 1] (direction along polymer backbone)are specified in the schematic. (B) Gel permeation chromatography data obtained for the various P3HT systems, measured at 80 C in chlorobenzeneagainst polystyrene standards. From these plots, their number-average molecular weight, Mn, weight-average molecular weight, Mw, and polydispersity,PDI (PDI = Mw/Mn), were determined.

employed in FETs and PVs. For this material, studies basedon transmission electron microscopy (TEM) have indicatedthat the structural evolution from chain-extended crys-tals to an architecture comprised of interlinked crystallinelamellae and amorphous regions occurs at a weight-average molecular weight, Mw, of around 2535 kg/mol[9,10]. Tellingly, chain folding, which leads to lamellar crys-talline units found in classical systems such as polyolefinsand poly(ethylene oxides) of sufficiently high molecu-lar weight [15,26], was visualized in longer-chain P3HTmolecules by scanning tunnelling microscopy (STM) as

early as 2000 by Mena-Osteriz et al. [27] Note, here, thatthe (1 0 0) distance in such mono-layer architectures devi-ated from the lamellar stacking distance measured forP3HT crystals. This observation by Mena-Osteriz et al. [27],nonetheless, indicates that higher-molecular weight P3HTchains can fold and, hence, similar crystalline moieties asfound in classical polymers may form in P3HT of high Mw.

On the other hand, short-chain P3HT seem to adoptchain-extended microstructures (observed in TEM andatomic-force microscopy (AFM) [913]), typical for com-mon oligomers, e.g., paraffins [2,6,7]. This directly affects

Charge Carrier Mobilities in P3HT

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Fig. 6. Comparison of the development with number-average molecularweight, Mn of (A) field-effect transistor mobility, !FET, collected from lit-erature [1114,41,42], (B) melting temperature, Tm, and (C) enthalpy offusion, "Hf (both obtained for solution-solidified material) of the variousP3HT samples investigated here.

3.2. Bulk charge transport

Bulk hole mobilities seem to be less dependent onan interconnected microstructure than the FET mobility,as already shown by Ballantyne et al. [16]. This can bededuced from time-of-flight photoconduction measure-ments on as-cast P3HT films of selected Mn that werea few micrometres thick and sandwiched between twonon-injecting electrodes. As a consequence, charge trans-port parallel to the film normal are assessed in TOF, while

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in transistors charge transport parallel to the substratesurface is analyzed. Photo-transients recorded at roomtemperature are displayed in Fig. 7A. Despite the relativelydispersive transport evident in the transients, which is afeature often observed in TOF data of conjugated polymerswith a significant degree of disorder, the indicative transittimes tt (obtained from the intersection of the asymptotesto the long-time and short-time transients when plottedon double-logarithmic axes, and indicated in Fig. 7A forthe data obtained for P3HT of Mn = 4.8 kg/mol, could stillbe distinguished for all materials tested. This allowed usto calculate the time-of-flight hole mobilities !TOF usingthe expression: !TOF = d2/Vtt where d is the sample thick-ness, tt is transit time and V is the applied voltage. Thededuced mobility values are plotted as function of molec-ular weight in Fig. 7B (squares). Highest time-of-flight hole

1986 F.P.V. Koch et al. / Progress in Polymer Science 38 (2013) 1978 1989

Fig. 6. Comparison of the development with number-average molecularweight, Mn of (A) field-effect transistor mobility, !FET, collected from lit-erature [1114,41,42], (B) melting temperature, Tm, and (C) enthalpy offusion, "Hf (both obtained for solution-solidified material) of the variousP3HT samples investigated here.

3.2. Bulk charge transport

Bulk hole mobilities seem to be less dependent onan interconnected microstructure than the FET mobility,as already shown by Ballantyne et al. [16]. This can bededuced from time-of-flight photoconduction measure-ments on as-cast P3HT films of selected Mn that werea few micrometres thick and sandwiched between twonon-injecting electrodes. As a consequence, charge trans-port parallel to the film normal are assessed in TOF, while

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Fig. 7. (A) Typical time-of-flight (TOF) photoconductivity hole transientsmeasured at the same electric field for solution-cast films of P3HT ofdifferent molecular weights (casting temperature 25 C). (B) Molecular-weight-dependence of the bulk hole mobility !TOF for P3HT films castfrom solution at room temperature (squares) or at 115 C (circles). NB.The reported trend is in agreement with the one observed in Ref. [16].

in transistors charge transport parallel to the substratesurface is analyzed. Photo-transients recorded at roomtemperature are displayed in Fig. 7A. Despite the relativelydispersive transport evident in the transients, which is afeature often observed in TOF data of conjugated polymerswith a significant degree of disorder, the indicative transittimes tt (obtained from the intersection of the asymptotesto the long-time and short-time transients when plottedon double-logarithmic axes, and indicated in Fig. 7A forthe data obtained for P3HT of Mn = 4.8 kg/mol, could stillbe distinguished for all materials tested. This allowed usto calculate the time-of-flight hole mobilities !TOF usingthe expression: !TOF = d2/Vtt where d is the sample thick-ness, tt is transit time and V is the applied voltage. Thededuced mobility values are plotted as function of molec-ular weight in Fig. 7B (squares). Highest time-of-flight hole

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Long-Range versus Short-Range Order

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a

b

c

Figure 1 |Microstructure of conjugated polymer films. ac, Schematics of the microstructure of a semicrystalline polymer film, for example P3HT (a),disordered aggregates (b) and a completely amorphous film (c). Note the coexistence of ordered (darker shadowed areas) and spaghetti-like amorphousregions. This microstructure is similar to the concept of fringed micelles. If the molecular weight is high enough and there is a large enough density ofordered material, long polymer chains (highlighted in red) can connect ordered regions without a significant loss of conjugation, greatly improving chargetransport.

relationship relating order at the segmental level to transport at thedevice scale. A survey of over ten years of literature data confirmsthe generality of these concepts.

Charge transport and the importance of aggregatesThe microstructure of high-molecular-weight poly(3-hexyl-thiophene), P3HTamodel semicrystalline conjugated polymerexhibits a continuous variation in order parameters17,18 wheresemi-ordered and amorphous spaghetti-like regions coexist;long polymer chains are responsible for the connectivity betweenadjacent crystallites (Fig. 1a)19. Semi-ordered regions may becomprised of large domains with three-dimensional long-rangeperiodicity (crystallites) or smaller domains with short-rangeordering of a few molecular units (aggregates, which may also beidentified as fringed micelles; Fig. 1b).

In such a heterogeneous microstructure, the ordered regionsare largely responsible for charge transport because chargesmust overcome an energy barrier to move from ordered toamorphous regions. Indeed, owing to its reduced conjugationlength, the amorphous fraction of regio-regular P3HT (RR-P3HT) has a larger bandgap compared to the aggregates andwe find no evidence of energetic overlap of electronic statesin amorphous and ordered P3HT regions (Supplementary Fig.S2). This energetic offset hinders carrier migration into theamorphous regions, and makes it energetically and statisticallyfavourable for charges at the order/disorder interface to migrateback into the ordered regions. Because, in principle, this offsetcould be reduced by polaronic effects, we test our hypothesisby studying blends of regio-random P3HT (RRa-P3HT) withcontrolled amounts of RR-P3HT nanofibrils (see Methods)20. Evenfor a low concentration of aggregates (10% by volume), atcurrent densities comparable to those encountered in electronicdevices, the electroluminescence spectra resemble that of RR-P3HT (Fig. 2, and Supplementary Figs S3 and S4). Consequently,transported charges recombine within fibrils. Thus, at realisticcurrent densities, charge carriers remain confined in the orderedregions of a heterogeneous microstructure when such orderedregions are spatially close enough to form an interconnectednetwork through tie-molecules.

This conclusion may be challenged by the oft-encounteredassumption, based on calorimetric measurements, that semicrys-talline polymer films have a low degree of crystallinity. However,these measurements systematically underestimate the amount ofordered material (Supplementary Fig. S5). In P3HT, we assessthat such an underestimation is approximately a factor of two,with the aggregate volume fraction in P3HT films near 4050%(refs 21,22). Hence, in high-mobility polymers the fraction of

the film comprised of ordered material is sufficiently large to beinterconnected by bridging polymer chains, creating a network thatsustains efficient charge transport. Such networks of crystalliteshave been previously observed in conjugated polymers21,23.

The nature of the connections between aggregates is poorlyunderstood and should be the subject of further study.Nevertheless,we are able tomake a few qualitative considerations. Polymer chainsare semiflexible24,25that is, rigid at length scales comparableto their persistence length and flexible at larger length scales.If the spacing between neighbouring crystallites is only a fewpersistence lengths, a chain that exits one ordered region and enters

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Figure 2 | Photo-physical characterization of pre-aggregated P3HTfibril:amorphous-blend films. a, Reference electroluminescence spectrafrom pure RR and RRa P3HT. Vertical dashed lines are theelectroluminescence peak positions for the amorphous, and 0-0, 0-1aggregate transitions of the pristine films, respectively.b, Photoluminescence spectrum (dotted) showing the signature ofaggregated and amorphous material, along with electroluminescencespectra for increasing values of current in the devices made with films of10% pre-aggregated RR-P3HT. Unlike the photoluminescence spectrum,the low-current (typical of normal device application) electroluminescencespectra show only emission from aggregates, indicating that it is dueexclusively to recombination within the aggregates and not to excitonenergy transfer to the aggregates before recombination. Only at largecurrent densities does the blue-shifted spectral feature from RRa-P3HTappear, indicating emission from the disordered matrix.

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Disorder and Electronic Performance

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dependence, static cumulative disorder is significant in thesematerials. Dynamic disorder will induce further fluctuationsaround the static positions, but these refinements do not qualita-tively alter our conclusions.

The spatial extent of the calculated wavefunctions for thedisordered stack (Fig. 3eh) shows that disorder-induced states thatlie deeper into the DOS tail are increasingly localized. Even stateswithin the originally delocalized band becomemore localized withincreasing paracrystallinity. In the limit of large positional disorder(g 10%), the distinction between band and tail disappears: asingle broad distribution of localized states with a monotonicallydecreasingDOS extends into the bandgap, reproducingwell-knownresults of electronic structure theory of amorphous materials34,35.In the intermediate paracrystallinity regime (g 37%) we observea coexistence of localized and delocalized states, indicating that inparacrystalline aggregates charge is transported by a mechanismwhere mobile charge is temporarily trapped in localized states, akinto multiple trapping and release1,36.

Measuring paracrystallinity in conjugated polymersUsing X-ray diffraction peak-shape analysis (details in Supplemen-tary Text) we quantify paracrystallinity in polymer crystallites todetermine whether this disorder dominates their DOS. In PBTTT,a polymer considered to exhibit an exceptional degree of order37,we find a highly anisotropic lattice disorder. In the lamellar stack-ing direction, glam = 2.6% owing to side chain interdigitation38,39.Long-range lamellar order however does not translate to order inthe-stacks, where g=7.3%, a value close to that of an amorphousstack. Thus, we conclude that the DOS of a PBTTT -stack isdictated by paracrystalline disorder.

The low amount of paracrystalline disorder measured in a smallmolecule film and its small anisotropy (Fig. 4 and SupplementaryTable S1) shows that organic solids are not inherently disorderedin spite of their weak intermolecular forces. Conversely, thedistinguishing feature of polymers is the pron