bottom-up' modelling of charge transport in organic … · · 2010-08-17crystalline p3ht...

’Bottom-up’ modelling of charge transport inorganic semiconductors

David L. Cheung

Department of Chemistry & Centre for Scientific ComputingUniversity of Warwick

LCOPV 2010 Boulder 7th-10th August 2010

AcknowledgementsPeople

Alessandro Troisi, David McMahon

Denis Andrienko (MPI Mainz)

Guido Raos (Milan)

Sara Fortuna, Dan Jones, Tao Lui, Natalie Martsinovich, EmanueleMaggio, Jack Sleigh (Troisi group)

Computers

Centre for Scientific Computing, University of Warwick

Money

EPSRC

ERC

(University of Warwick) Charge transport in organic semiconductors LCOPV 2010 2 / 46

Outline

1 Introduction

2 Charge transport in polymer semiconductors

3 Modelling PCBM

4 Conclusions and outlook


Organic semiconductors

Organic semiconductors◮ crystalline organics

(e.g. pentacene)◮ polymer semiconductors◮ liquid crystals

Large-area/flexible electronicdevices

◮ lighting◮ displays◮ photovoltaics



Compared to inorganic materials, organic electronics have the potentialto tailor-make compounds for diverse applications

◮ we can make any material we want BUT

Relationship between structure and property (charge mobility) not known◮ we don’t know what we want to make


DLC & A Troisi PCCP 2008


Compared to inorganic materials, organic electronics have the potentialto tailor-make compounds for diverse applications

◮ we can make any material we want BUT

Relationship between structure and property (charge mobility) not known◮ we don’t know what we want to make

Need to understand charge transport mechanism◮ interplay between electronic & nuclear degrees of freedom◮ disorder (static & dynamic)◮ morphology



Molecular modelling of organic electronics

Charge transport is intrinsicallyquantum

◮ solid-state physics/ quantumchemistry

Organic materials are soft◮ (classical) molecular simulations

Morphology is important◮ coarse-grained simulations

Linking across length/ timescales


Model systemsMost investigated organic photovoltaic mixture

◮ P3HT◮ PCBM

Use combined MD/QC modelling to study mechanism of charge transportin these model systems

◮ MD simulations to study microstructure/morphology◮ use representative MD configurations as input to QC calculations


Outline

1 Introduction

2 Charge transport in polymer semiconductorsMicrostructureTransport mechanismConnection to phenomenological models

3 Modelling PCBM



Why study P3HT?Crystalline P3HT forms well-defined lamellar structure

◮ high degree of structural order

Electronic properties described by models for disordered materials◮ charge transport described by hopping models◮ optical properties: polaron models

Where’s the disorder?


MD simulationsClassical MD simulations of crystalline P3HT

◮ 12 chains, 40 rings per chain (Mw ≈ 6700 Da)

Marcon-Raos/OPLS forcefield

Anisotropic-NPT MD simulationsSimulation lengths up to 5 ns

◮ multiple short simulations (0.3-1 ns)


Microstructure

System well ordered up to 500 K

◮ type-II (low-molar mass)polymorph

Unremarkable dihedral angledistributions

Long range order in thedihedrals

Dynamic disorder not important

Signs of static disorder

Dihedral angle distributions

0

0.01

0.02

0.03

P(φ

1)

T=100 KT=300 K

90 135 180 225 270φi / degrees

0

0.01

P(φ

2)

Ring-ring

Ring-tail

Dihedral angle time series

0 1 2 3 4t / ns

100

150

200

250

300

φ / d

egre

es


DLC, DP McMahon, & A Troisi JPCB 2009

Charge carrier wavefunctionQuantum chemical calculations reveal long lived traps

◮ HOMO density (from AM1 calculations) at different times

t1 t2


DLC, DP McMahon, & A Troisi JACS 2009

Classification of statesStates classified by...

localization time dependence

◮ persistent (29%), non-persistent, double(or more) persistent



Where does it trap?

Localized traps◮ HOMO localized on

planar segments

Trap depth > kBTEHOMO − EHOMO−1

◮ localized: 0.104 ± 0.046eV

◮ non-localized:0.046 ± 0.031 eV



What about polarons?Charge localized by static disorder further localized by electron-phononcoupling

In P3HT both deformations are co-operative - molecular planarized byexcess charge



Phenomenological models’Top-down’ modelling - device physics

1 Assume transport model (e.g. GDM)◮ number of free parameters, e.g. density of states, transfer integrals

2 Fit parameters to experimental measurements3 Calculate charge mobility using KMC/Master equation

Can estimate key parameters from MD/QC calculations


N Tessler et al, Adv Mater 2009

Density of statesDistribution of site energies

Edge fit by double Gaussian◮ width of dominant Gaussian ≈ 0.1 eV



Transfer integralsBetween chains

◮ t̄(r): average transfer integral between rings of separation r

4 5 6 7r / A

0

0.05

0.1

0.15

0.2

0.25

t (r)

/ eV

H/HH-1/HH/H-1H-1/H-1

4 5 6 7r / A

0

0.05

0.1

0.15

0.2

t generally decreases with distance◮ peak in HOMO-1/HOMO-1, HOMO/HOMO-1, HOMO-1/HOMO transfer

integrals at r ≈ 5 Å



Beyond GDMNon-monotonic behaviour of transfer integrals not seen in models suchas GDM

◮ Strong coupling between ring separation and orientationsp1(r) = 〈u1.u2〉r

0

0.05

0.1

P (

r)

4 5 6 7r / A

-0.5

0

0.5

1

p 1 (r)

◮ close approach between S and C-C bond on rings on adjacent chains(overlap of HOMO-1)


Outline

1 Introduction

2 Charge transport in polymer semiconductors

3 Modelling PCBMMicrostructureElectronic states and disorderLocalization



What is PCBM?[6, 6]-phenyl-C61-butyric acidmethyl ester

◮ fullerene derivative◮ organic electron acceptor◮ side chain: solubility, little (direct)

effect on charge transport

Little studied as a stand-alonematerial

◮ partially disordered,nanocrystalline

◮ unknown electronic structure incondensed phase


MD simulationsSimulate 108 PCBM moleculesInitial configuration from low temperature (T ≈ 90 K) crystal structure

◮ orthorhombic crystal◮ 3x3x3 supercell

OPLS force field

Simulation lengths up to 2.5 ns


Microstructure & morphology

System forms partially ordered,’zig-zag’ layer structure

◮ similar to experimental crystalstructure

Radial distribution functions

0

2

4

6

8

4 6 8 10 12 14 16 18

r / Ao

0

5

10

150

0.5

1

1.5

g(r)

Fullerene-fullerene

Benzene-benzene

Fullerene-benzene

◮ fullerene-fullerene separation≈ 10 Å

◮ benzene-benzene separation(≈ 6 Å) larger than in typicalorganic crystals (≈ 3.4 Å)


DLC & A Troisi JPCC ASAP

Distribution of overlaps

Spatial distribution of overlapbetween LUMOs

10 11 12 13 14

r / Ao

0.0001

0.001

0.01

<|S

t (r)|

>

◮ exponential decay withseparation

◮ independent of T

Histograms of LUMO overlapsbetween neighbouring molecules

0.0001 0.001 0.01

|St|

0

0.01

0.02

0.03

P(|

St |)

◮ log-normal distribution◮ Largest and 2nd largest overlaps

per molecule



Density of statesLUMO density of states

-0.05 -0.045 -0.04 -0.035E / Hartree

0

0.005

0.01

DO

S(E

)

◮ three peaks (at LUMO energies for isolated molecules)◮ first peak width approx 0.02 eV



What are the states?Localization characteristics

◮ Lα localization length◮ spread (# of molecules containing 90% of density)

-0.05 -0.045 -0.04 -0.035E / Hartree

0

10

20

30

40

50

L α / Ao

-0.05 -0.045 -0.04 -0.035E / Hartree

0

0.1

0.2

0.3

0.4

0.5

Spr

ead/

N

Rapid changes in localization behaviour of closely spaced states



What are the states?

E = −0.0505 Hartree








Why does it localize?Energy difference between molecules (diagonal disorder)

◮ distribution of site energies has standard deviation ≈ 0.5kBT

Electron-phonon coupling◮ ZPE larger than energy difference at transition state

Electronic disorder (off-diagonal)



ConclusionsCombination of classical and quantum modelling provides a powerfulmethod for the study of the charge transport in ’soft’ materials

◮ interplay of nuclear and electronic degrees of freedom◮ disorder - dynamic and static

Polymer semiconductors◮ combination of MD/QC calculations used to infer charge transport

mechanism◮ transfer integrals calculated from MD trajectories show more complex

distributions then assumed in charge transport models

Organic electron acceptors◮ large differences in localization between different electronic states◮ localization largely due to electronic disorder

Further reading◮ D. L. Cheung, D. P. McMahon, and A. Troisi, J Phys Chem, 113, 9393 (2009)◮ D. L. Cheung, D. P. McMahon, and A. Troisi, J Am Chem Soc, 131, 11179

(2009)◮ D. L. Cheung and A. Troisi, J Phys Chem C ASAP


OutlookBottom-up modelling, from molecular to device scale

Classical MD Quantum chemistry LocalizationDOSTransfer integrals

Quantum Dynamics Coarse-grainedsimulations

Device modelling(e.g. Kinetic MC,master equation)



Classical MD ✚ Quantum chemistry ➜ LocalizationDOSTransfer integrals




Interfaces in OPV MixturesInterface microstructure and morphology

◮ atomistic study of P3HT:PCBM interface



Classical MD ✚ Quantum chemistry LocalizationTransfer integralsDOS




Quantum dynamicsConformational disorder indiscotic liquid crystal (HBC)

◮ timescale of electronicmotion≈timescale of nuclearmotion

Develop simplified semi-classicalmodel using MD data

◮ Langevin dynamics - frictioncoefficient γ (captures neglecteddegrees of freedom)

◮ numerically integrate◮ propogate the wavefunction

Calculated charge mobilityµ = 2.4 cm2 V−1 s−1

(c.f. experimentalµ ≈ 0.5 cm2 V−1 s−1)


A Troisi, DLC, & D Andrienko PRL 2009

Coarse-grain simulationsDPD simulations of PATs

Phase behaviour determined by molecular architecture

AmBn

Am(Bn)2

Lamellar [A1B1] and inverted hexagonal phases [A2B1]

Lamellar [A1(B1)2] and hexagonal phases [A1(B2)2]

Relationship between side chain length/density and phase behaviouragrees with experiment



Possible transport mechanisms

1 Hopping between localizedstates(Variable Range Hopping)

2 Distortion drags charge carrier(Conformationally gatedtransport)

3 Excitation from localized todelocalized state(Mobility edge)


Top-down modellingDevice physics

1 Assume transport model (e.g. GDM)◮ number of free parameters

2 Fit parameters to experimental measurements3 Calculate charge mobility using KMC/Master equation

No clear relationship between molecular structure and model parameters◮ not predictive

Instead of imposing a transport model from above, use theory to studysystems in microscopic detail and infer charge transport behaviour

◮ bottom-up modelling


Phenomenological theories?Phenomenological theories assume forms for density of states,distribution of transfer integrals....

Density of states

DOS edge approximated bydouble Gaussian

◮ width of dominantGaussian≈ 0.1 eV

Transfer integrals

4 5 6 7r / A

0

0.05

0.1

0.15

0.2

t / e

V

HOMO/HOMOHOMO-1/HOMOHOMO/HOMO-1HOMO-1/HOMO-1

Non-monotonic behaviour of t◮ contrary to common assumptions


DLC, DP McMahon, & A Troisi JACS 2009; JPCB 2009

Transfer integralsDistribution of intrachain transfer integrals

HOMO/HOMO, HOMO/HOMO-1, HOMO-1/HOMO, HOMO-1/HOMO-1

100 K (left), 300 K (right)

HOMO/HOMO transfer integral very much larger than the others (≈ 1.10eV)



Overlap computationPCBM too large for traditional QC calculations

◮ even semi-empirical calculations too expensive◮ approx 75 seconds per pair, 1.4 million pairs

Implement reduced QC analysis1 get standard structure and MOs (ZINDO) for isolated molecule2 for each pair of molecules superimpose standard structure/MO3 find atoms in these standard structures within 7.2 Å4 compute overlap between these atoms


Dynamic and static disorder

Localization may occur due tostatic disorder

◮ grain boundaries◮ chamical defects

Organic materials bound by ’soft’van der Waals forces

◮ disorder induced by thermalmotion


From molecular crystals to polymersIncreasing γ leads to transitionfrom dynamic to static disorder

◮ DOS independent of γ

Time evolution of wavefunction

low γ

intermediate γ

large γ


A Troisi & DLC JCP 2009

Properties of the transitionScaling mobility by temperature

T


A Troisi & DLC JCP 2009

bottom-up' modelling of charge transport in organic … · · 2010-08-17crystalline p3ht...

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