Transport and Recombination in Polymer:Fullerene Solar Cells · Transport and Recombination in...

Transport and Recombination in

Polymer:Fullerene Solar Cells

Paul Blom

Max Planck Institut für Polymer Forschung, Mainz

Outline

1. Charge transport in Organic Semiconductors

-Hole Transport, Electron Transport

2. Photocurrent Generation in Organic Solar Cells

-Space Charge, Recombination

3. Recombination in organic solar cells

-Bimolecular Recombination, Trap-assisted`Recombination

4. Origin of the Recombination in Organic Solar Cells

-CT electroluminescence, ideality factor, Exciton Diffusion

< 2

Vbias (V)

0.1 1 10 10

-4

10 -3

10 -2

10 -1

10 0

0.13 m 0.3 m 0.7 m J (

A/m

2 )

JV

L

9

8

2

3

APL 68, 3308 (1996)

Current-Voltage characteristic of a PPV Hole-Only Device

PPV

Au ITO

Hole Current is Space Charge (Bulk) Limited !!

V s

cm 27105

< 3

< 4

SCLC: PLED acts as a Capacitor

ITO Au PPV

V=0

ITO Au PPV

V>

+ + + + + +

+ +

ITO

Au PPV

+ + + +

+ +

+ +

V>>

+ +

+

+

+ +

+

+

J=charge velocity

CV V/L

Charge density and Electric field ~ V

1019

1020

1021

1022

1023

1024

1025

1026

10-10

10-9

10-8

10-7

FET

h,

FE

T (

m2/V

s)

p (m-3)

LED

OC1C

10-PPV

T=295 K

Mobility is Density Dependent !

Phys. Rev. Lett. 91, 216601 (2003)

< 5

0

Transport level

Equilibrium level

0

Ef

Low carrier density Higher carrier density

Ef

2

1ln

T T

1ln

Effect of Carrier Density? < 6

1 10 10010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

T=298 K

T=272 K

T=252 K

T=233 K

V (V)

J (

A/m

2)

Theoretical model for µ(p,T,E) developed

Phys. Rev. Lett. 94, 206601 (2005)

< 7

Electron Transport in PPV

Low Electron Current, Steep J-V: Traps ?

Ca Ca Holes

Electrons

0.34 um

0.22 um 0.37 um

0.3 um

APL 68, 3308 (1996)

< 8

10-5

10-4

10-3

10-2

10-5

10-4

10-3

10-2

10-1

100

101

2 3 4 5 6 7 8 910 20 3010

-5

10-4

10-3

295 K

275 K

255 K

235 K

215 K

195 K

Curr

ent D

en

sity (

A/m

²)

(a)

(c)

NRS-PPV

L = 320 nm

MEH-PPV

L = 270 nm

295 K

273 K

251 K

230 K

211 K

Curr

ent D

en

sity (

A/m

²)OC

1C

10-PPV

L = 300 nm

(b)

290 K

275 K

255 K

235 K

215 K

Curr

ent D

en

sity (

A/m

²)

V-Vbi (V)

Gaussian LUMO and Gaussian Traps?

Trap-limited Electron currents in

PPV derivatives also described

by Gaussian trap distribution

Nt ~ 2×1017 cm-3

σt = 0.10 eV

Et ~ 0.6-0.7 eV

Phys. Rev. B 83, 183301 (2011)

< 9

Slope vs LUMO position

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.20

1

2

3

4

5

6

7

8

Slo

pe

LUMO (eV)

NRS-PPV

OC1C

10-PPV

P3HT

F8BTPF10TBT

PCPDTBT

PCBM

P(NDI2OD-T2)

PF1CVTP

PCNEPV

Trap-free

Explained by change of Gaussian Trap Depth!!!

< 10

-3.8

-3.6

-3.4

-3.2

-3.0

-2.8

-2.6

-2.4

-2.2

Trap

NRS-PPVOC

1C

10-PPV

F8BTPF10TBT

PCPDTBT

P3HT

LUMO

Electron Trapping in OLEDs:

One kind of trap responsible for trapping in all OLEDs!!!

Nt ~ 2-3×1017 cm-3

σt = 0.10 eV

Electron current can be predicted when LUMO is known

< 11

Nature Materials 11 , p.882 (2012)

Origin of Trap?

Photo-oxidation?

Water-polymer complexes?

Hydrated-oxygen complexes O2(H2O)2

Trap-depth 0.1-0.2 eV

Potential Deep Trap

Peter Ho et al., Adv. Mat. 21, 4747 (2009)

C. Campbell, C. Risko, J. L. Brédas, Georgia Tech

< 12

Outline








-CT electroluminescence, ideality factor, Eciton Diffusion

< 13

Goodman and Rose: J. Appl. Phys. 42, 1971, 2823

Energ

y

x

L

EC

EV

Before light excitation

•field: E=V/L

• mean carrier drift lengths:

wn = ntnE

wp = ptpE

Assumptions:

• uniform generation of e-h pairs throughout the volume of the active layer

• non injection contacts for both electrons and holes

• one dimensional case

• diffusion ignored

Photocurrent in a semiconductor: < 14

Built-in Voltage:

V=0

V=Vbi

LiF PEDOT

Vbi

LiF Vbi

PEDOT

V=0

Goodman and Rose: BHJ Solar Cell:

Veff=V-Vbi

< 15

• main carrier drift length wn=ntnE and wp=ptpE <<L ,

E=V/L=constant.

+

_ hn

V=VOC-Vbias

L

• J-V characteristic (Ohmic regime):

After light excitation

L

VeGJ ppnn tt

J

V

V

Small applied voltage: < 16

• ntn > ptp , wn>> L, wp< L

Recombination (t Limited regime:

2/12/12/1 ; GVJVeGJ nn t

J

V

V

V1/2 + _

hn

L1

V=VOC-bias

Intermediate voltage: < 17

• saturation regime:

• wn> L, wp> L, E=V/L=constant

• equal electron and hole current.

• J-V characteristic is:

eGLJ

+ _

hn

V=VOC-bias

L

J

V

V

V1/2

Constant

High Voltage Regime: < 18

SCL Photocurrent:

J

V

V1/2 + _

hn

L1

V=VOC-bias

Space-Charge Limited Photocurrent:

2/14/32/14/3

4/1

; 8

9VGJVG

qqJ

p

3

1

2

11

118

9

d

Vjj hSCLCph

Maximum electrostatically allowed current:

• ntn > ptp , p<<, tp>>

< 19

LUMO PPV

LUMO PCBM

HOMO PPV

HOMO PCBM

Exciton diffusion

Donor

Acceptor

Anode

ITO/PEDOT

5.2 ev

Cathode

LiF/Al

3.8 ev

Light

Electron transport

Hole transport

Charge transfer

CT-state

CT-state:

If r0=1 nm and r=3, then

binding energy is 0.5 eV !!

Photocurrent in a Polymer:Fullerene Solar Cell < 20

G. Yu, J. Gao, J. C. Hummelen, F.

Wudl, A. J. Heeger, Science 1995,

270, 1789.

Apply GR Model to BHJ Solar Cell:

HOMOPPV

HOMO C60

LUMO C60

2.9 eV

3.7 eV

5.1 eV

6.1 eV

PEDOT:PSS

jM5.2 eV

LUMOPPV

LiF/Al

jM3.0 eV

LUMO=LUMOPCBM

HOMO=HOMOPPV

Effective Medium:

< 21

0.01 0.1 1 101

10

J ph=

J L-J

D [

A/m

2]

V0-V [V]

driftdiffusion

Photocurrent in PPV:PCBM (1:4 wt.%) solar cells

• deviation at high (reverse) voltages due to field-dependence of G?

0.0 0.2 0.4 0.6 0.8 1.0

-30

-20

-10

0

10

20

VOC

V0

JD

JL

Jph

=JL-J

D

J [A

/m2]

V [V]J V

J=qGL

L=120 nm

T=295 K

< 22

Saturation Regime:

MDMO-PPV:PCBM

Saturated regime: photocurrent J=e G(E,T) L due to dissociation of

bound electron-hole pairs

Braun: J. Chem. Phys. 80, 1984, 4157

0.1 1 101

10

295 K270 K250 K230 K210 K

J ph [

A/m

2]

VOC

-V [V]

Phys. Rev. Lett., 93, 216601 (2004)

60% Jsc

At Jsc only 60% of bound

e-h pairs is dissociated !!

eGMAXL

< 23

Solar Cell Device Model

Inclusion of (Langevin) recombination and G(E,T) requires numerical

modeling

10-2

10-1

100

101

100

101

data 295 K

data 250 K

q G(V) L 295 K

q G(V) L 250 K

simulation 295 K

simulation 250 K

J

light-J

dark [A

/m2]

Voc-V [V]

Phys. Rev. B 72, 085205 (2005)

MDMO-PPV:PCBM

< 24

3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8

10-11

10-10

10-9

10-8

10-7

O

O*

O

O

*1

3 ran

O

O*

O

O

*1

3 ran

L1L

V1

G

L1L

V1

G

[

m2/V

s]

1000/T [K-1]

Electrons

Holes

At T=210 K factor 103 difference in e/h mobilities

Transport in a BEH-BMB PPV/ PCBM blend

1:4 wt. %

< 25

0.01 0.1 1 10

100

101

295 K

270 K

250 K

230 K

210 K

J ph=

J L-J

D [

A/m

2]

V0-V [V]

Jph V

1/2

Light-intensity (G) dependence ?

Photocurrent in the BEH-BMB PPV/ PCBM blend

Observation of SCL photocurrent

0.01 0.1 1 100.1

1

10

J ph [

A/m

2]

V0-V [V]

L=275 nm

T=210 K

Vsat

10

1

10

10 100

1

2

3

4

Jph

@ V0-V=10 V

S = 0.76

J ph [

A/m

2]

S = 0.95

Jph

@ V0-V=0.1 V

S = 0.51

Vsa

t [V

]

Incident Light Power [mW/cm2]

Light-intensity dependence:

80 mW/cm2

6 mW/cm2

At Jsc losses due to bimolecular recombination weak (4%)

Phys. Rev. Lett. 94, 126602 (2005)

< 27

| 28

Low Bandgap Polymer PCPDTBT (Konarka)

Voc = 0.65 V

Jsc = 90 A/m2 (PC61BM)

= 110 A/m2 (PC71BM)

FF ≤ 47%

PCE = 2.67 % (PC61BM)

= 3.16 % (PC71BM)

Mühlbacher et al, Adv. Mater., 18, 2884–2889 (2006)

Poly [2,6-(4,4-bis-(2-ethylhexyl)-4H-

cyclopenta[2,1-b;3,4-b′]dithiophene)-alt-4,7-

(2,1,3-benzothiadiazole)]

(PCPDTBT)

??

< 28

PCPDTBT:PCBM Solar Cells

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-60

-50

-40

-30

-20

-10

0

10

295

270

250

230

210

JL[A

/m2]

V [V]

Low Fill Factor (~40-45%) combined with square root regime in photocurrent:

Space-Charge Limited???

0.1 1

10

100

T [K]

295

270

250

230

210

Jp

h[A

/m2]

V0-V [V]

< 29

| 30

Single Carrier Devices

0.0 0.4 0.8 1.2 1.6 2.0

10

100

1000

10000

J [

A/m

2]

V-Vres

-Vbi [V]

e=7x10

-8 m

2/Vs

0.0 0.7 1.4

1

10

100

1000

J [

A/m

2]

V-Vbi-V

rs

h=3x10

-8 m

2/Vs

LUMO

HOMO

LUMO

HOMO

Hole/Electron mobility almost balanced: SC Limit Unlikely!!!

Polymer:Fullerene Blend

< 30

Intensity dependence of Photocurrent:

0.1 1 10

10

100

Jp

h [

A/m

2]

V0-V [V]

Jph α V 1/2

Jph α G

Vsat= constant

Vsat

Fingerprint of recombination limited current!!!

Adv. Funct. Mater. 2009, 19, 1106–1111

< 31

| 32

Square Root Dependence; μτ vs sc limited

Two different origins for a square root dependence of Jph

Space Charge Limited: e >> h

VqGJ hrph

25.0

0

75.0

8

9)(

Jph α V 1/2

Jph α G 3/4

Vsat α G 1/2

V. D. Mihailetchi et al., Phys. Rev. Lett. 94, 126602 (2005)

A. M. Goodman and A. Rose, J. Appl. Phys. 42, 2823 (1971)

μτ-limited: wn,p= tE<L ; ptp<ntn

VqGJ hhph t

0.1 1 10

10

100

Jp

h [

A/m

2]

V0-V [V]

Jph α V 1/2

Jph α G

Vsat= constant

Vsat

L1 L

V1

G

< 32

Outline








-CT electroluminescence, ideality factor

< 33

< 34

Limited by Diffusion of Electrons and Holes towards each other

Critical Coulomb Radius: binding energy hole-electron = kT

q2/4kT (20 nm) >> mean free path in PPV (1-3 nm)

20nm

1-3 nm

Bimolecular Langevin recombination

U. Albrecht and H. Bässler, Phys. Status Solidi B 191, 455 (1995)

P. Langevin, Ann. Chem. Phys. 28, 289 (1903)

Study Recombination at Voc !!

Measure Voc ~ Light Intensity!!

Solar cell with bimolecular recombination:

PG

NP

q

kT

q

EV cgap

oc

21

ln

APL 86, 123509 (2005)

E. A. Schiff, Sol. Eng. Mater. Sol. Cells 2003, 78, 567.

How to characterize recombination? < 35

Light intensity dependence of Voc

Linear dependence of Voc on ln(I) with slope kT/q, n=1 !

1 2 3 4 5

0.65

0.70

0.75

0.80

0.85

0.90

Vo

c [V

]

Ln (intensity) [a.u.]

295 K

250 K

210 K

APL 86, 123509 (2005)

MDMO-PPV:PCBM

Only bimolecular Recombination!!!!!

< 36

All-polymer solar cells: Electron traps

• Recombination

1. Langevin

2. Shockley-Read-Hall

-

+

-

+

- - -

+ + +

-

- -

- 1 2

Parameters:

Nt, Tt, Cn, Cp

1111 / ppCnnCnppnNCCR pntpnSRH

)(2

iLangevin nnpR )(0

pn

r

q

< 37

Voc light intensity dependence

10 100 1000

1.25

1.30

1.35

1.40

1.45

1.50

Light intensity (W/m2)

Vo

c (V

)

Only Langevin recombination included

S[kT/q]=1

At Voc only losses via Recombination!!!!!

MDMO-PPV:PCNEPV

< 38

All-polymer: SRH recombination effects on Voc

10 100 1000

1.25

1.30

1.35

1.40

1.45

1.50


Vo

c (V

) Cn,p = 1.4×10-18 m3s-1

5.0×10-17 m3s-1

5.0×10-20 m3s-1

< 39

Photocurrent of MDMO-PPV:PCNEPV

-10 -8 -6 -4 -2 0 2-50

-40

-30

-20

-10

0

10

20

Voltage (V)

J (

A/m

2)

JD

JL

Gmax = 9.4×1027 m-3s-1

Kf = 6.7×102 s-1

a = 0.62 nm

<εr> = 2.6

Nt = 9.6 ×1022 m-3

Tt = 2500 K

Cn,p = 1.8×10-18 m3s-1

Both Langevin and SRH recombination included

Adv. Funct. Mat. 17, 2167 (2007)

What does it mean?

< 40

Measure PLED as a solar cell:

MEH-PPV Cn=Cp=1×10-18 m3/s

kT/q

M.M. Mandoc et al. App. Phys. Lett. 91, 263505 (2007)

M.M. Mandoc et al. Adv. Funct. Mater. 17, 2167-2173 (2007)

< 41

Origin of SRH Capture Coefficient:

3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.810

-21

10-20

10-19

10-18

p

q

C = solar cell

C = - hole-only device

Captu

re C

oeff

icie

nts

(m

3/s

)

T-1 (10

-3 K)

pNq

pNCk tptpSRH

Nt=electron trap

Phys. Rev. Lett. 107, 256805 (2011)

< 42

Origin of SRH Capture Coefficient:

20nm

1-3 nm

pNkr tS R H

)0( pS R H

qk

Trapping

Idem as Langevin with immobile electron!

< 43

< 44

V=0

Ca ITO

Vbi

V=Vbi

Ca Vbi

ITO

V>Vbi

Ca

V

ITO

Diffusion Current V<Vbi

Drift Diffusion

Drift Diffusion Diffusion

dx

dpeDEepJ

)/exp(~ nkTqVJ

v=μE

OLED Current-voltage characteristics:

• Three regimes:

1. Leakage current

2. Diffusion regime

3. Drift regime

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.510

-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

J [

A/m

2]

V [V]

1.

2.

3.

Vbi

1exp0

kT

qVJJ

3

2

8

9

L

VJ

leakageR

VI

“Ideality Factor”

< 45

Origin of Ideality Factor?

• Ideality factor equals 2 in the case of trap-assisted

recombination in a classical p-n junction

1

2exp0

kT

qVJJ

C. T. Sah et al., Proc. IRE 45, 1228 (1957)

< 46

Super Yellow PPV LED

• The ideality factor for a Super

Yellow LED was determined

to have a value of 2 at room

temperature.

• This corresponds to SRH

recombination from trapping

sites:

1

2exp0

kT

qVJJ

1

ln

V

J

q

kT

< 47

White OLEDs: Emissive SRH recombination?

• Trap-assisted recombination in conventional polymers

appears to be non-radiative.

• In a white emitting polymer, red dyes in the blue backbone

function as emissive traps.

HOMO

LUMO

< 48

Langevin & SRH recombination!

-0.2 -0.1 0.0 0.1

1

2

3

4 Current

Light – 550 nm Longpass Filter

Light – Blue Dichroic Filter

(kT

/q

lnJ/

V)-1

V-Vbi [V]

2.0 2.5 3.0 3.510

-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

400 500 600 7000

20

40

60

80

100

EL

In

ten

sity [

a.u

.]

Wavelength [nm]

550 nm Longpass Filter

Blue Dichroic Filter

Lu

min

an

ce

[a

.u.]

V [V]

› Luminance of red dyes follows SRH recombination,

whereas the blue light follows Langevin recombination.

< 49

Outline






-Bimolecular Recombination, Trap-assisted Recombination


-CT electroluminescence, ideality factor

< 50

Charge transport in BJH Solar Cell

0.1 110

0

101

102

103

104

T = 294 K

170 nm90 nm

J [A

/m2]

V-VRs

-Vbi [V]

3

2

08

9

L

VJ er

e2.0x10-7 m2/Vs

Adv. Funct. Mater. 2003, 13,

Electron transport in PCBM and Hole transport in Donor Polymers are trap-free: No SRH recombination expected

< 51

• Slope=kT/q: Only Bimolecular Recombination

Other Polymer:fullerene solar cells: < 52

CT state electroluminescence in OPV

• Weak electroluminescence from the charge-transfer state

is observed in organic solar cells

Cathode

Anode

Acceptor

Donor

< 53

EL Ideality factor?

• Ideality factor of 1 is

measured for the CT

electroluminescence

• Emission originates from a

free-carrier bimolecular

recombination process!

< 54

Voc vs Light intensity

• A contribution of trap-assisted recombination is observed for

P3HT:PCBM

• Recombination is bimolecular for other solar cells

< 55

Nonradiative SRH recombination?

• Can be exposed by looking at the voltage dependence of

the EL quantum efficiency

P3HT:PCBM

Competition

SRH and

Bimolecular!

< 56

P3HT:PCBM solar cells

Pt< 2×1015 cm-3 ? SRH small

Hole traps in P3HT?

< 57


In P3HT:PCBM solar cells the Langevin recombination

is strongly reduced ~103 (CELIV)

Pivrikas, Osterbacka, Juska et al., Phys. Rev. Lett. 94, 176806 (2005)

Two dimensional Langevin recombination in the

lamellar structure of RR-P3HT

Juska, Osterbacka et al., Appl. Phys. Lett. 95, 013303 (2009)

< 58


102

103

0.50

0.52

0.54

0.56

0.58

0.60

Reduced Langevin + SRH

Voc [

V]

Light Intensity [W/m2]

Langevin + SRH

kT/q

Advanced Energy Materials, accepted

< 59

Exciton Transport?

› Photo-excitation

› Langevin Recombination, Trap-assisted Recombination

Ca

ITO

< 61

Neat Polymer PL decay:

0 200 400 600 800

10-1

100

exp.

calc.

MEH-PPV t=300ps

Lum

inescence (

a.u

.)

Time (ps)

Intrinsic Exciton Lifetime ~ 300 ps?

Exciton diffusion

Change Energetic disorder in PPV derivatives

• Reduced energetic disorder enhances exciton diffusion!!

7

Polymer σ, meV D, cm2/s μ(300K), m2/Vs

NRS-

PPV 125 3 × 10-4 1.5 10-12

MEH-

PPV 105 1.1 × 10-3 5 10-11

BEH-

PPV 92 2 × 10-3 2 10-9

O

On

O

O

O

0.5

0.5

O

On

NRS-PPV

MEH-PPV

BEH-PPV

E

D

E

D

PHYSICAL REVIEW B 72, 045217 � 2005

< 63

Neat Polymer PL decay:

0 200 400 600 80010

-1

100

exp.

calc.

NRS-PPV t=800ps

Lum

inescence (

a.u

.)

Time (ps)

0 200 400 600 800

10-1

100

exp.

calc.

MEH-PPV t=300ps

Lu

min

esce

nce

(a

.u.)

Time (ps)

0 200 400 600 80010

-2

10-1

100

exp.

calc.

Lu

min

esce

nce

(a

.u.)

Time (ps)

BEH-PPV t=200ps

-Less disorder, shorter

PL decay

-Less disorder, mono-

exponential decay

D=3×10-4cm2/s

D=1×10-3cm2/s

D=2×10-3cm2/s

Exciton diffusion

Energetic disorder in PPV derivatives

• Exciton diffusion length 5-7 nm is independent on the

amount of energetic disorder!!!!

8

0 20 40 600.0

0.2

0.4

0.6

0.8

1.0

NRS-PPV; LD=5 nm

Quenchin

g e

ffic

iency

Polymer film thickness [nm]

MEH-PPV; LD=6.3 nm

BEH-PPV; LD=6 nm

constL

DL

D

D

D

t

t and

- quenching

centers?

< 65

Are electron traps also exciton quenchers?

Universal electron trap density ~ 5×1017 cm-3

Distance between traps 1/(5×1017)1/3 = 12.6 nm

Exciton has to travel 6 nm to reach a trap……

Measure electron transport and exciton diffusion

independently in a model system with single

exponential PL decay!!

< 66

Model System PCPDTBT poly[2,6-(4,4-bis-(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b']dithiophene)-alt-

4,7-(2,1,3-benzothiadiazole)] (PCPDTBT)

Hole Transport:

Electron Transport:

μh= 6×10-8 m2/Vs

σ = 0.075 eV

Nt=5×1017 cm-3

Et=0.3 eV

< 67

PL decay PCPDTBT

All Single exponential!!

< 68

PL decay Analysis (exp. decay)

1 14

f

rDct t

Stern-Volmer formula: τ= PL decay time of blend with PCBM concentration c

τf = PL decay time of pristine PCPDTBT

r = Sum of the exciton radii

D = Exciton diffusion coefficient.

r~ 1 nm

D=3×10-3cm2/s

< 69

0q c c

0

1 14 4

f

rDc rDq t t

0

0

1 14

f

rDct t

q=0: Intrinsic Exciton Lifetime τ0

Background Quenchers

PCBM

Background Quenchers

+Stern Volmer:

τf = PL decay time of pristine PCPDTBT

τ0 = PL decay time of solution

< 70

Graphical Representation c0

c0=6×1017 cm-3 , equal to Ntrap electrons !!!!!

< 71

What about PL efficiency?

t f =1

G + knr + kdiff

t 0 =1

G + knr

kdiff =1

t f

-1

t 0

= 4p rDc0

g =G

G + knr + kdiff

=G

1

t 0

+ 4p rDc0

=1-t 0knr

1+ 4p rDc0t 0

Measured lifetime in film

Measured lifetime in solution

Stern-Volmer

PL Yield

< 72

PL from integrating sphere

τ0knr=0.72

Conclusions

• Imbalanced transport and strong recombination lead to a

square-root dependence of the photocurrent, FF~0.4

• Nature of recombination can be identified from charge-

transfer state electroluminescence

CT-state emission is of bimolecular origin

Weak trap-assisted recombination is present in


• The amount of exciton quenchers is equal to the amount of

electron traps. The exciton diffusion length and liftetime

are not intrinsic but are determined by extrinsic defects

< 73

RuG

Cristina Tanase

Denis Markov

Jan Anton Koster

Magda Mandoc

Irina Craciun

Yuan Zhang

Herman Nicolai

Gert-Jan Wetzelaer

Paul de Bruyn

Niels van der Kaap

Bert de Boer †

Dago de Leeuw

Acknowledgement:

UCSB

Alex Miknenko

Martijn Kuik

Jason Lin

Quyen Nguyen

GeorgiaTech

Jean-Luc Bredas

Chad Risko

Casey Campbell

Thank you for your attention!!!

< 75

< 76

• Injection: Barrier Height

• Transport: Mobility, Traps, Space Charge

• Recombination

2.1 eV Ca

ITO

O

H 3 C O n

Burroughes et al., Nature 347, p. 539 (1990)

Transport and Recombination in a PLED

Exponential Trap Distribution: Modified Model

Exp. Trap model:

r=Tt/T )(12

1

)(

0 rCL

V

eNeNJ

r

rr

efft

rnc

E

)exp(~)(t

tt

kT

EEEN

Ntrap=5*1017 cm-3 Tt=1500 K

MDMO-PPV:

t

tctefft

T

kTENN

)2/(exp

2

)(

tTT

c

ttN

nNn

/

< 77

LUMO PPV

How can we determine μe, Nt, and Etc ??

Trap-limited Electron Transport?

Deep Traps

Shallow Traps

Hopping in

modified DOS

Etc

v. Mensfoort et al., PRB

80, 033202 (2009)

< 78

n-type doping:

A. Kahn et al., Org. Electr. 9, 575 (2008)

< 79

• After n-doping:

Electron current equal to hole current

Temperature dependence equal to temperature dependence of hole current

μe = μh

Traps located > 0.4 eV below the LUMO

Phys. Rev. B. 81, 085201 (2010)

n-type doping: < 80

Gaussian LUMO and Exponential Traps?

Use Approximation in Intermediate Voltage Regime:

G. Paasch and S. Scheinert, J. Appl. Phys. 107, 104501 (2010).

1014

1016

1018

1020

1022

1024

1026

1018

1019

1020

1021

1022

1023

1024

1025

LUMO

E

Single level

Exponential

Gaussian

nt (

m-3)

n (m-3)

< 81

• Polymer:PCBM bulk heterojunction solar cells have an

ideality factor of ~1.3

Ideality factor solar cells: Dark Current

1exp

kT

qVJJ sD

n>1: Evidence for trap-assisted recombination?

< 82

Single Carrier Dark-Current (no rec!!)

• Ideality factor single-carrier

devices of separate materials

match ideality factors of the

blend

=> Ideality factor is determined by transport-dominating

constituent of the solar cell blend.

Appl. Phys. Lett. 99, 153506 (2011)

Other conjugated polymers?

0.1 1 1010

-3

10-2

10-1

100

101

102

103

104

148 nm PCPDTBT

85 nm PF10TBT

173 nm F8BT

300 nm OC1C

10-PPV

Cu

rre

nt

De

nsity (

A/m

²)

V (V)

Slope of Trap-limited Electron Current varies for different polymers

< 84

PLED Operation:

› Trap-Free SCL Hole Transport

› Trap-limited Electron Transport

› Langevin Recombination, Shockley-Read-Hall Recombination

Ca

ITO

< 85

L

• J-V characteristic is:

No recombination losses:

+

_ hn

V=VOC-bias

eV

kT

kTeV

kTeVeGLJJJ pn

2

1)/exp(

1)/exp(

Hughes and Sokel: J. Appl. Phys. 52, 1981, 6743

J

V

V

diffusion drift

Assumption: Diffusion neglected < 86

Recap:

eV

kT

kTeV

kTeVeGLJ

2

1)/exp(

1)/exp( L

VeGJ ppnn tt

8

92/14/3

4/1

VGq

qJp

Low voltage: Ohmic behaviour:

2/12/1VeGJ nnt

eGLJ

Intermediate voltage: Square root behaviour:

Saturation regime: Voltage independent

or ??

Drift vs diffusion

or ??

< 87

• Poly(F2D) allows formation of a completely

immobilized well-defined heterostructure

• LD=5-7 nm

N

O

O

C4H

9

C4H

9

F2D

0 400.0

0.2

0.4

0.6

0.8

1.0

PL q

uenchin

g [a.u

.]NRS-PPV film thickness [nm]

NRS-PPV/poly(F2D)

LD= 5 nm

Time-independent!!

Photovoltaic response: 7 nm

J.J.M.Halls et.al., Appl. Phys. Lett., 1996, 68, 3120

Exciton Diffusion Length

J. Phys. Chem. A 2005, 109, 5266-5274

),(),()(),(

)(

),(),(2

2

txgtxnxSx

txnD

t

txn

t

txn

t

0 200 400 600 8000.0

0.2

0.4

0.6

0.8

1.0

PL inte

nsity [a.u

.]

Time [ps]

Neat NRS-PPV

Film thickness

15.5 nm

8 nm

4 nm

s

cmD

NRS

2

4103 Photo-induced defect quenching:

D=2·10-4cm2/s M. Yan et. al.,

Phys. Rev. Let., 1994, 73, 744

Exciton Diffusion Coefficient

Neat Polymer used as reference PHYSICAL REVIEW B 72, 045216 2005

< 90


Bulk Quencher

PCBM

C-PCPDTBT

< 91


Relative quenching efficiency

dtPL

dtPLQ

pristine

blend1

Intimate

mixture:

no clusters!

MC simulation:

D=3×10-3cm2/s

LD=10 nm

Energy Environ. Sci., 2012, 5, 6960

< 92 Neat Polymer PL decay

PL decay is not single exponential.

-relaxation of excitons in Gaussian DOS

J. Phys. Chem. B 2008, 112, 11601–11604 11601

Movaghar, B.; Grünewald, M.; Ries, B.; Bässler, H.; Würtz, D.

Phys. Rev. B 1986, 33, 5545–5554.

< 93

Recap:

Reduction of disorder leads to increase of

exciton diffusion coefficient

For exciton diffusion coefficient >10-3 cm2/Vs

the PL decay is single exponential

The exciton diffusion length ~5-7 nm is

independent on disorder.

0.01 0.1 1 10

0.1

1

constant G

JV MDMO-PPV:PCBM Si p/n cell

J/J

ma

x

Voc-V [V]

field dependent G

• The generation rate in blends of MDMO-PPV:PCBM is field dependent!

Organic BHJ vs. Si-based Solar cell < 94

Introduction of TCNQ electron traps:

Can we prove that recombination with trapped electrons is

responsible for the enhanced dependence of Voc on light

intensity?

LUMO MDMO-PPV

LUMO PCBM

HOMO MDMO-PPV

HOMO PCBM

Exciton

diffusion N

N

N

N

H H

H H

4.5 eV

TCNQ

< 95

10 100 1000

0.2

0.4

0.6

0.8

1.0

S[kT/q]=3


Vo

c (

V)

No Traps

S[kT/q]=1

TCNQ Traps

Voc light intensity dependence

Appl. Phys. Lett. 91, 263505 2007

< 96

< 97

PL decay PCPDTBT

τ0 =212 ps

τf = 146 ps

+

3-D Transport by hopping

between conjugated parts

of the chain

Disorder dominated charge transport

Low mobility:~ Vs

cm 27105

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

< 98

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