Charge Injection and Transport

in Conjugated Polymers

George Malliaras

Department of Materials Science and Engineering, Cornell University

&

Cornell NanoScale Facility

Email: ggm1@cornell.edu

Outline

• Brief introduction to PLEDs

• Charge transport: theory and experiments

• Charge injection: theory and experiments

• Outlook

Chemical structure of conjugated polymers

C8H17 C8H17

n

n

n

S

O O

n

S n

PPP

PFO

PPV

PEDOT

P3HT

Carbon as a semiconductor

CH2=CH2

En = n2

n=1,2,3,...

ħ2π2

2mL2

LUMO

HOMOEG ≈ ħ2π2

2maN

• Hybridization: sp2 and pZ

• Particle in a box:

EG

Tuning of optical propertiesBlue

Red

R.E. Gill et. al., Adv. Mater. 6, 132 (1994).Covion

PLED structure and operation

ITO

Ca

h+

Anode

LUMOCathode

HOMO

e-

Electroluminescence: charge injection, charge transport, recombination

Outline

• Brief introduction to PLEDs

• Charge transport: theory and experiments

• Charge injection: theory and experiments

• Outlook

Hierarchy of transport models

First order correction:Space charge effects J = (9/8)·ε·ε0·µ·V2/L3

Disorder:Energetics Localized statesInfluence on mobility µ=µ(E,T)

Manifold filling:Charge density dependence of mobility µ=µ(n)

Charge generation:Electric field dependence of charge density n=n(E)

J = e · n · µ · E + e · D · dn/dx

Space charge effects

Low voltages: Ohm’s lawJOHM = e⋅Ν0⋅µ⋅V/L

High voltages: Space charge limited currentJSCL = (9/8)⋅ε⋅ε0⋅µ⋅V2/L3

Log(J)

Log(V)

JOHM

JSCL

V0

Lampert and Mark, Current Injection in Solids (Academic Press,1970).

V0 = (8/9)⋅e⋅N0⋅L2/ε⋅ε0

Energetics of semiconductors

Figure of merit: mobility, µ (cm2/V·sec)

Conductionband

Valenceband

Shallowtrap

Deeptrap

v=µ·E

ε

x

+-

Energetics of amorphous semiconductors

N. Mott, Nobel Lecture (1977)

Localizedstates

Extendedstates

Time-of-flight (TOF)

Light pulse

OSC

RV

µ = _______tTR · V

L2

P. M. Borsenberger, D. S. Weiss, Organic photoreceptors for Xerography (Marcel Decker, Inc., New York, 1998).

Non-dispersive hole transport in TFB

0.0 0.5 1.0 1.5 2.0 2.5

0.0

0.5

1.0

Pho

tocu

rren

t (m

A)

Time (µs)

0.078 MV/cm295K

n

H17C8 C8H17

N

ITO/PEDOT:PSS(CH8000)/TFB(6.4µm)/Al

H.H. Fong, A. Papadimitratos, and G.G. Malliaras, Appl. Phys. Lett. 89, 172116 (2006).

0 1 2 3 4 5 6 710-3

10-2

ITO PEDOT:PSS(60nm) Au(20nm)

Hol

e m

obili

ty (c

m2 V-1

s-1)

Thickness (µm)

295K0.1 MV/cm

Electric field dependence of mobility

200 300 40010-3

10-2

220K

240K

260K280K

320K295K

H

ole

mob

ility

(cm

2 V-1s-1

)

[Electric field (V/cm)]1/2

350K

Molecularly dispersed polymers

+

Solid solutions of conjugated molecules in inert host

Hopping sites are well-defined

Control over the average distance between hopping sites

Gaussian disorder model

LUMO

HOMO

ε

x

ε

σ = 0.1 eV

DOS

• Energetic disorder • Positional disorder

Gaussian disorder model (II)

H. Bässler, Phys. Stat. Sol. (b) 175, 15 (1993).

Density of states:

DOS(ε) = (2·π·σ2)-0.5·exp[-(ε2/2σ2)]

Hopping rate:

νij = ν0·exp-(2·γ·a·∆Rij/Rij)·

Mobility:

µ=µ0·exp[-(2σ/3kT)2]·exp{C·[(σ/kT)2-Σ2] ·E0.5}

{ exp[-(εj-εi)/kT] ; εj>εi

1 ; εj>εi

εiεj

Rij

Gaussian disorder model (III)

H. Bässler, Phys. Stat. Sol. (b) 175, 15 (1993).

Carriers relax at:

σ2/kT

µ ~ exp[-(σ/kT)2]

Electric field dependence of mobility (II)

5 10 15 20 2510-3

10-2

10-1

µ 0 (cm

2 V-1s-1

)

(1000/T)2 (1/K2)

σ = 65.9 ± 0.5 meVµ

∞ = 0.19 cm2V-1s-1

2 4 6 8 10 12 140.00.51.01.52.02.53.0

β (x

10-3) (

cm/V

)1/2

(σ/kT)2

Σ = 2.2C0 = 2.8 x 10-4

µ=µ0·exp[-(2σ/3kT)2]·exp{C·[(σ/kT)2-Σ2] ·E0.5}

High mobility in conjugated polymers

10-2 10-3100 10-1 10-4 10-5 10-710-6

n

H17C8 C8H17

N

TFBTFB

MEHMEH--PPVPPV

O

O

n

N N

CH3CH3

TPDTPD

PFOPFO

C8H17

n

C8H17

Organic Organic CrystalsCrystals

RubreneRubrenePentacenePentacene

aa--SiSi

cm2/V·sec

Correlated disorder model

LUMO

HOMO

ε

x

Deeper valleys are also wider.

D.H. Dunlap, P.E. Parris and V.E. Kenkre, Phys. Rev. Lett. 77, 542 (1996).

µ=µ0·exp[-(σ/kT)2 + 2·(σ/kT)·(e·a·E/kT)0.5]

Correlated disorder model (II)

S.V. Novikov, J. Polym. Sci. Part B: Polym. Phys. 41, 2584 (2003).

Black/white: sites with energy above/below the

mean.

Correlated disorder in polymers

S.V. Rakhamanova and E.M. Conwell, Appl.Phys. Lett. 76, 3822 (2000).

Correlations in site energy arise from fluctuations in:

-Conjugation length

-Density

Mobility vs. change density

W.F. Pasveer, J. Cottaar, C. Tanase, R. Coehoorn, P.A. Bobbert, P.W.M. Blom, D.M. de Leeuw, and M.A.J. Michels, Phys. Rev. Lett. 94, 206601 (2005).

σ=0.1eV

Manifold filling

A. Troup et al., J. Non-Crystalline Solids 35, 151 (1980).

1 0 -9

1 0 -8

1 0 -7

Mob

ility

(cm2 /V

sec)

1 0 -6 1 0 -4 10 -2 10 0

D oping R atio

DOS

σ2/kTx<<1

Ex=0.5

x=1

Y. Shen, K. Diest, M.H. Wong, B.R. Hsieh, D.H. Dunlap, and G.G. Malliaras, Phys. Rev. B. 68, 81204(R) (2003).

Mobility vs. charge density (II)

C. Tanase, E.J. Meijer, P.W.M. Blom, and D.M. de Leeuw, Phys. Rev. Lett. 91, 216601 (2003).

Charge density vs. electric field

B.A. Gregg, J. Phys. Chem. B 108, 45 (2004).

Field ionization of impurities leads to n=n(E)

Charge density vs. electric field (II)

0 200 400 600 80010-16

10-15

10-14

Ca Al Au (98 nm) Au (168 nm)

JL3 /(V

appl-V

bi)2 (m

Acm

/V2 )

((Vappl-Vbi)/L)0.5 ((V/cm)0.5)

G.G. Malliaras, J.R. Salem, P.J. Brock, and J.C. Scott, Phys. Rev. B. 58, R13411 (1998).

JSCL≈(9/8)εε0µ0V2exp[0.89(V/E0L)0.5]/L3

Charge transport

First order correction:Space charge effects J = (9/8)·ε·ε0·µ·V2/L3 √

Disorder:Energetics Localized states √

Influence on mobility µ=µ(E,T) √

Manifold filling:Charge density dependence of mobility µ=µ(n) √

Charge generation:Electric field dependence of charge density n=n(E) ?

Outline

• Brief introduction to PLEDs

• Charge transport: theory and experiments

• Charge injection: theory and experiments

• Outlook

Injection vs. transport

Is the flow limited by the valve or the hose?

Water hose and valve

Semiconductorcontacts

-

--

--

--

- -

--

- -

-

-

--

-

Is the current limited by injection or transport?

Hole injection in TFB

0.0 0.2 0.4 0.6 0.8 1.010-910-810-710-610-510-410-310-210-1100101

C

urre

nt (A

/cm

2 )

Electric field (V/cm)

SCLC

AuITO

PEDOT:PSS(CH8000)

Hierarchy of injection models

Mechanism:Thermionic emission J = A·exp(-φ/kT)Tunneling J = A·E2·exp(-B·φ3/2/E)

First order corrections:Barrier lowering J ~ exp(E0.5)Recombination with image force J ~ µ

Disorder:Gaussian disorder J ~ exp(E0.5)

Thermionic emission and tunneling

Ec

Lampert and Mark, Current Injection in Solids (Academic Press,1970).

Energetics of conjugated polymers

-15 -10 -5 0 5

experiment (UPS/IPES) calculation

Energy w.r.t EF

DO

S

-15 -10 -5 0 5

DO

S

experiment (UPS/IPES) calculation

Energy w.r.t EF

J. Hwang et al., J. Phys. Chem. C, in press. V

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Energetics at the contact

-18 -16 -4 -2 0 2 4 6

F8IP : 5.7 eV

Eg : 3.35 eV

-16.17

Inte

nsity

EF

2.7.65

Energy w.r.t EF

*5.1

0.65

IE=5.75

PEDOT:PSS F8HOMO edge

EF

2.65

* Work function of PEDOT:PSS substrate measured on separate sample produced in same batch.

(energies in eV)

LUMO edgeEA=2.50

UPS IPES

Evac

EF

Evac Evac

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Ionization energy (IE) and electron affinity (EA) measured from HOMO and LUMO edges w.r.t vacuum level

Hole injection barriers for TFB contacts

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TFB

5.5eV

Evac

Au

4.75eV TFB

5.5eV

Evac

ITO

4.85eV

TFB

5.5eV

Evac

PED

OT:

PSS

5.15eV

0.25eV

0.6eV

0.75eV 0.65eV 0.6eV

Hole injection in TFB

0.0 0.2 0.4 0.6 0.8 1.010-910-810-710-610-510-410-310-210-1100101

C

urre

nt (A

/cm

2 )

Electric field (V/cm)

SCLC

AuITO

PEDOT:PSS(CH8000)

Barrier lowering

Lampert and Mark, Current Injection in Solids (Academic Press,1970).

Field dependence of injection

10-7

10-6

10-5

10-4

10-3

Cur

rent

Den

sity

(A/c

m2 )

500400300200E0.5 (V/cm)0.5

52C 7C -38C

PEDOT:PSS/PFO

Low mobility

P.R. Emtage and J.J. O’Dwyer, Phys. Rev. Lett. 16, 356 (1966)

J = N·e·µ·E·exp(-ϕB/kT)

Recombination with image charge

J = Cexp(-ϕB/kT) -en0S(E)

• Surface recombination as a hopping process in the

image charge potential.

• No current flow at zero field.

C = 16πεε0N0(kT)2µ/e2

S(0) = 16πεε0 (kT)2µ/e3

J.C. Scott and G.G. Malliaras, Chem. Phys. Lett. 299, 115 (1999)

_+

Dependence of injection on mobility

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

J (A

/cm

2 )

1 0-6

10-5

10-4

10-3

10-2

M obility (cm2/Vsec)

JS C L

JINJ

0 .4 M V /cm

Y. Shen, M.W. Klein, D.B. Jacobs, J.C. Scott, and G.G. Malliaras, Phys. Rev. Lett. 86, 3867 (2001).

Gaussian disorder

LUMOEF σ2/kT

First hop is the rate limiting step

V.I. Arkhipov, E.V. Emelianova, Y.H. Tak, and H. Bässler, J. Appl. Phys. 84, 848 (1998).

( ) ( )[ ] ( ) ( )( )[ ]ExUgEBoldExwxdxeJa

espInj −⋅⋅⋅⋅⋅−⋅⋅= ∫ ∫∞ ∞

∞−0000 2exp γν

Gaussian disorder (II)

V.I. Arkhipov, E.V. Emelianova, Y.H. Tak, and H. Bässler, J. Appl. Phys. 84, 848 (1998).

Field dependence resembles thermionicemission

Gaussian disorder (III)

S.V. Novikov, and G.G. Malliaras, Phys. Rev. B 73, 033308 (2006).

Energetic disorder due to charge-dipole interactions

different at the interface

Gaussian disorder (III)

0.0 0.2 0.4 0.6 0.8 1.010-8

10-7

10-6

10-5

10-4

10-3

Hol

e in

ject

ion

effic

ienc

y

Electric field (MV/cm)

Au

ITO

0.65eV 0.75eV

Charge injection

Mechanism:Thermionic emission J = A·exp(-φ/kT)Tunneling J = A·E2·exp(-B·φ3/2/E)

First order corrections:Barrier lowering J ~ exp(E0.5) √

Recombination with image force J ~ µ √

Disorder:Gaussian disorder J ~ exp(E0.5) ?

Opportunities

• There is rich physics to be explored in organic light emitting diodes

• Conjugated polymers that show ideal transport characteristics and high mobilities have become available

• Charge injection in TFB is poor (and poorly understood) – opportunity for major improvements in OLED performance

Challenges

• Picture of metal/organic interfaces from spectroscopy is only now getting incorporated in injection models

• Injection expected to be spatially inhomogeneous due to correlated disorder

• J ~ exp(E0.5) ubiquitous, temperature range rather small – need other tests for theories

Acknowledgments

PostdocsHon Hang FongMaria NikolouAram AmassianNa Young Shim

Graduate studentsJason SlinkerMatthew LloydDan BernardsJohn DeFrancoAlexis PapadimitratosYee-Fun LimVladimir PozdinChung-Han Wu

Visiting ScientistsKiyoshi Morimoto (Panasonic)Satoyuki Nomura (Hitachi)

DOE funded collaboration:PrincetonJaehyung HwangAntoine Kahn

Georgia TechEung-Gun KimJean-Luc Brédas

General ElectricAnil Duggal

Also:University of New MexicoDave Dunlap

Frumkin InstituteSergey Novikov

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