Charge Transport and Recombination in Organic Solar...

Max Planck Institute for Polymer Research 11

Charge Transport and Recombination in

Organic Solar Cells

Paul Blom

Max Planck Institute for Polymer Research, Mainz, Germany

[email protected]


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


Vbias (V)

0.1 1 1010

-4

10-3

10-2

10-1

100

0.13m 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 !!

Vs

cm 27105


SCLC: PLED acts as a Capacitor

ITOAuPPV

V=0

ITOAu PPV

V>

+ + ++++

++

ITO

AuPPV

+ + ++

+ +

++

V>>

++

+

+

++

+

+

J=charge velocity

CV V/L

Charge density and Electric field ~ V


x=0 x=L

Ohmic contact

JxxE

2)(

E(x)

Voltage=area under E(x) curve

p(x)

Field- and density distribution


Background Charge p0

X=0 X=L

p

p0

V<

pi

X=0 X=L

p

p0

V>

pi

JV

L

9

8

2

3

L

VepJ 0

Log J

Log V

1

2


+

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)


At High Voltages deviations from SCLC model

PRB 55, R656 (1997)

0.1 1 1010

-6

10-5

10-4

10-3

10-2

10-1

100

101

102

T=296 k

T=267 K

T=256 K

T=235 K

T=223 K

T=209 K

L=125 nm

J (

A/m

2)

Vbias (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)


0

Transport level

Equilibrium level

0

Ef

Low carrier density Higher carrier density

Ef

2

1ln

T T

1ln

Effect of Carrier Density?


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)


Electron Transport in PPV

Low Electron Current, Steep J-V: Traps ?

Ca CaHoles

Electrons

0.34 um

0.22 um 0.37 um

0.3 um

APL 68, 3308 (1996)


Shallow Trap (single level)

3

2

8

9

L

VJ

trapfree

free

nn

n

Log J

Log V

2

2Trap-filled limit


Traps exponentially distributed in energy

Ec

tt

t

kT

E

kT

NEDOS exp)(

Nt=amount of traps

Tt=characteristic constant for trap distribution

E=0

rCL

V

qNtqNJ

r

rr

rnc 12

1

0

TTr t /


Exponential Trap Distribution

Exp. Trap model:

r=Tt/T)(12

1

)(

0 rCL

V

eNeNJ

r

rr

efft

rnc

E

)exp(~)(t

tt

kT

EEEN

Nt(eff)=5*1017 cm-3

Tt=1500 K

MDMO-PPV:

tTT

c

ttN

nNn

/


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)


n-type doping:

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


• 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:


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)


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

Cu

rre

nt

De

nsity (

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

Cu

rre

nt

De

nsity (

A/m

²)

OC1C

10-PPV

L = 300 nm

(b)

290 K

275 K

255 K

235 K

215 K

Cu

rre

nt

De

nsity (

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)


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


Trap-free SCL current in PCBM

0.1 110

0

101

102

103

104

T = 294 K

170 nm90 nm

J [

A/m

2]

V-VRs

-Vbi [V]

3

2

08

9

L

VJ er

e2.0x10-7 m2/Vs

PEDOT:PSS

LiF

6.1 eVPEDOT:PSS

LiF/AlVbi

3.7 eV

5.2 eV

Adv. Funct. Mater. 2003, 13, No. 1


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!!!


-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

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


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!!


Exciton Diffusion Coefficient

Bulk Quencher

PCBM

C-PCPDTBT


PL decay PCPDTBT

All Single exponential!!


PL decay Analysis (exp. decay)

1 14

f

rDc

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


0q c c

0

1 14 4

f

rDc rDq

0

0

1 14

f

rDc

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


Graphical Representation c0

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


PL from integrating sphere

τ0knr=0.72


PLED Operation:

› Trap-Free SCL Hole Transport

› Trap-limited Electron Transport

› Langevin Recombination, Shockley-Read-Hall Recombination

Ca

ITO


Outline










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

En

erg

y

x

L

EC

EV

Before light excitation

•field: E=V/L

• mean carrier drift lengths:

wn = nnE

wp = ppE

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:


Built-in Voltage:

V=0

V=Vbi

LiF PEDOT

Vbi

LiFVbi

PEDOT

V=0

Goodman and Rose:

BHJ Solar Cell:

Veff=V-Vbi


• main carrier drift length wn=nnE and wp=ppE <<L ,

E=V/L=constant.

+

_hn

V=VOC-Vbias

L

• J-V characteristic (Ohmic regime):

After light excitation

L

VeGJ ppnn

J

V

V

Small applied voltage:


• nn > pp , wn>> L, wp< L

Recombination ( Limited regime:

2/12/12/1 ; GVJVeGJ nn

J

V

V

V1/2+_

hn

L1

V=VOC-bias

Intermediate voltage:


• 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:


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:

• nn > pp , p<<, p>>


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


Recap:

eV

kT

kTeV

kTeVeGLJ

2

1)/exp(

1)/exp( L

VeGJ ppnn

8

92/14/3

4/1

VGq

qJp

Low voltage: Ohmic behaviour:

2/12/1VeGJ nn

eGLJ

Intermediate voltage: Square root behaviour:

Saturation regime: Voltage independent

or ??

Drift vs diffusion

or ??


LUMO PPV

LUMO PCBM

HOMO PPV

HOMO PCBM

Excitondiffusion

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


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:


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


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


D D*hnD+… A-exciton

diffusion

kD(E)

kR

Free carriers

CT1 state

D… A

CT0 state

kF

Schematic diagram for charge-carrier formation in

polymer(donor)/fullerene(acceptor) films

kD - rate constant for produces free carriers (Onsager)

kF - rate constant for decay to the ground state of CT0

kR - rate constant for recombination of free carriers back to CT1

Braun: J. Chem. Phys. 80, 1984, 4157 !! eV 0.5 isenergy bindingthen

,3 and nm 1 If 0 rr


• no direct methods to determine kD(E).

• analytical approach (Onsager 3D model):

180183

14

3)(

432

3

bbbbe

akEk kT

E

RD

B

22

0

3 8/ TkEeb r

r

R

ek

0

Langevin rate for recombination of free carriers:

Charge separation: Model

The model predict the probability that free charge carriers will be produced

at particular field (E), temperature (T), and donor-acceptor separation

radius (a):

FD

D

kEk

EkETaP

)(

)(),,(


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


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

Jlig

ht-J

dark [

A/m

2]

Voc-V [V]

Phys. Rev. B 72, 085205 (2005)

MDMO-PPV:PCBM


-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

-30

-20

-10

0

10

LiF/Al

Ag

Au

Pd

J L [

A/m

2]

V [V]

The effect of metal electrodes on performance

Experimental details:

• active layer: 20:80 wt.% MDMO-PPV:PCBM (95 nm thickness).

• top electrodes: LiF/Al (Ohmic contact), Ag, Au, Pd

•constant illumination condition (halogen lamp: 80 mW/m2).

different !!!

VOC; JSC; FF; h


Effect of top electrode material on photocurrent

• the extraction current is independent of the workfunction of

the metal electrode.

JEXT = constant

LUMO PCBM

HOMO PPV

LiF/Al

AgAu

Pd

VOC

EXTRACTION metal

workfunction

• VOC(LiF/Al;Ag;Au;Pd) ≈ 0.90; 0.67; 0.59; 0.39 V

J. Appl. Phys., 2003, 94, 6849

• mobility = constant

• illumination = constant

• experimental = constant

Why different JSC , FF, and h?


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

5

10

15

20

25

30

35

J ph=

J L-J

D [

A/m

2]

V0-V [V]

PdAu

Ag

LiF/Al

Ag

Au

Pd

Calculation

LiF/Al

The dependency of the photocurrent on effective voltage (V0-V) is

responsible for the observed change in: JSC, FF, h.

Photocurrent vs. effective applied voltage

photocurrent vs. effective voltage for all electrodes coincides with universal curve


Model results

once the open-circuit voltage (VOC) is known → all other device

parameters can be elucidated.

Appl. Phys. Lett., 2004, 85, 970

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0

5

10

15

20

25

30

35LiF/Al

Ag

Au

Pd

PMAX

[W/m2]

JSC

[A/m2]

VOC

[V]


Solar cell performance versus PCBM fraction ?

20 30 40 50 60 70 80 90 100

0.0

0.2

0.4

0.6

0.8

1.0

weight percentage PCBM [wt.-%]

pow

er

con

vers

ion e

ffic

iency

Why do the devices perform better when the absorption is less?


20 30 40 50 60 70 80 90 10010

-11

10-10

10-9

10-8

10-7

10-6

e

h


[m

2/V

s]

Electron and hole mobility in MDMO-PPV:PCBM blends

h – pure MDMO-PPV

T=295K

• electron mobility increases due to the increase number of percolated pathways.

• more balanced transport: e ≈ 10 × h.


0.01 0.1 1 10

1

10

100

80 wt.% (L=106nm) 67 wt.% (L=75 nm) 50 wt.% (L=85 nm)

J ph=

J L-J

D [

A/m

2]

V0-V [V]

PPV:PCBM solar cells with different composition

saturation JSAT=qGMAXL

L = active layer thickness.

GMAX = maximum generated

free electrons and holes.


20 30 40 50 60 70 80 90 100

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5


GM

AX [

102

7m

-3s-1

]

Maximum generation rate in PPV:PCBM solar cells

More recombination !? Less absorption

• more recombination: due to an increase number of isolated PCBM clusters.

• less absorption: due to decreasing fraction of the absorbing material (MDMO-PPV).


Photocurrent versus effective voltage

20 40 60 80 10010

-11

10-9

10-7

electrons

holes

wt.% PCBM

mob

ilit

y [

m2/V

s]

0.01 0.1 1 10

0.1

1

Jp

h/q

GM

AXL

V0(J

ph=0) - V [V]

80 wt.%

50 wt.%

Calculation:

80 wt.% (reference)

50 wt.% ( varied)

50 wt.% (+<r> varied)

JSC


Numerical Simulation

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

95 wt.%80 wt.%67 wt.%40 wt.%

J L [

A/m

2]

V [V]

Adv. Funct. Mat., May 2005

By only modifying μh , μe (exp.) and <ε> the photocurrent at any

PCBM fraction can be predicted !


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. %


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)


P3HT:PCBM Cells: Charge Transport

20 40 60 80 100 120 140 160

10-12

10-11

10-10

10-9

10-8

10-7

10-6

pristine P3HT

holes

P3HT:PCBM

electrons

holes

as cast

[

m2/V

s]

Annealing Temperature [oC]

Upon annealing P3HT hole mobility increases to its pristine value

Adv. Funct. Mat. 2006, 16, p. 699 (2006)

S n


P3HT:PCBM Cells: Modeling

0.01 0.1 1 10

1

10

100

as-cast

Annealed:

70 oC

120 oC

Jp

h [A

/m2]

V0-V [V]

JSC

eGMAXL

eGMAXL

1) Increase of GMAX upon annealing

2) Presence of V1/2 regime in non-optimal devices



Presence of V1/2 regime indication of SCL photocurrent:

Dependence on light-intensity?

0.01 0.1 1 10

1

10

100

76 W/m2

Jp

h [A

/m2]

V0-V [V]

JSC

T=295 K

L=96 nm

1000 W/m2

100 1000

10

100

S = 0.950.005

Jph

@ V0-V=0.1 V

Jph

@ V0-V=3.0 V

Jp

h [A

/m2]

Light Intensity [W/m2]

S = 0.7680.019

70 °C

Occurrence of SCL Photocurrent due to μe=103μh @70 °C anneal



Procedure: a and kf-1 determined from device annealed @ 120 °C,

GMAX (absorption) and μe , μh (dark current) known vs Tanneal

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8

-80

-60

-40

-20

0

20

40

60

80

30 60 90 120 150 180

0.3

0.4

0.5

0.6

0.7

0.8

0.9

PS

C [

-]

Annealing Temperature [oC]

as cast

as-cast

70 oC

120 oC

170 oC

JL [A

/m2]

V [V]

No adjustable parameters!!


|

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)

??


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]

Max Planck Institute for Polymer Research 7070| 70

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

/m2]

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


Intensity dependence of Photocurrent:

0.1 1 10

10

100

Jp

h [A

/m2]

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


|

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= E L ; ppnn

VqGJ hhph

0.1 1 10

10

100

Jp

h [A

/m2]

V0-V [V]

Jph α V 1/2

Jph α G

Vsat= constant

Vsat

L1L

V1

G


Outline










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?


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!!!!!


All-polymer solar cells: Electron traps

• Recombination

1. Langevin

2. Shockley-Read-Hall

-

+

-

+

- - -

+ + +

-

--

-12

Parameters:

Nt, Tt, Cn, Cp

1111 / ppCnnCnppnNCCR pntpnSRH

)(2

iLangevin nnpR )(0

pn

r

q


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


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


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

diffusionN

N

N

N

H H

H H

4.5 eV

TCNQ


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


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?


Measure PLED as a solar cell:

MEH-PPVCn=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)


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

Ca

ptu

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)


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!


V=0

Ca ITO

Vbi

V=Vbi

CaVbi

ITO

V>Vbi

Ca

V

ITO

Diffusion Current V<Vbi

Drift Diffusion

DriftDiffusion 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

h

3

2

8

9

L

VJ

leakageR

VI

“Ideality Factor”


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)


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

kTh


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


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

Inte

nsity [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.


Outline






-Bimolecular Recombination, Trap-assisted Recombination




Charge transport in BJH Solar Cell

0.1 110

0

101

102

103

104

T = 294 K

170 nm90 nm

J [

A/m

2]

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


• Slope=kT/q: Only Bimolecular Recombination

Other Polymer:fullerene solar cells:


CT state electroluminescence in OPV

• Weak electroluminescence from the charge-transfer state is

observed in organic solar cells

Cathode

Anode

Acceptor

Donor


EL Ideality factor?

• Ideality factor of 1 is

measured for the CT

electroluminescence

• Emission originates from a

free-carrier bimolecular

recombination process!


Voc vs Light intensity

• A contribution of trap-assisted recombination is observed for

P3HT:PCBM

• Recombination is bimolecular for other solar cells


Nonradiative SRH recombination?

• Can be exposed by looking at the voltage dependence of the

EL quantum efficiency

P3HT:PCBM

Competition

SRH and

Bimolecular!


P3HT:PCBM solar cells

Pt< 2×1015 cm-3 ? SRH small

Hole traps in P3HT?



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)



102

103

0.50

0.52

0.54

0.56

0.58

0.60

Reduced Langevin + SRH

V

oc [

V]

Light Intensity [W/m2]

Langevin + SRH

kT/q

Adv. Energy Mater. 2012, 2, 1232–1237


Bipolar current:

OLED and Dark Current in BHJ Solar Cell

Weak Recombination:

Strong Recombination:

3

22/1

pre

2/1

IP /28

9

L

VJ np

3

2

BB )(8

9

L

VJ np

L. M. Rosenberg, M. A. Lampert, J. Appl. Phys. 1970, 41, 508.

)(prepre npLR

qkk

(Reduced) Langevin


Bipolar current:



Bipolar current:


Exact Solution: R. H. Parmenter, W. Ruppel, J. Appl. Phys. 1959, 30, 1548.

)/()8/9( 32

effD LVJ

32

23

23

232

eff)!1(

)!1()!1(

)!1()!1(

)!1][(

3

2

np

np

np

np

npRnn

nn

nn

nnnn

q

kRR

2

R

p

p

n

R

nn

n

.


2

IP

2

BBD JJJ

Bipolar current:


Approximation:

Then:

22

D

pre)(9

16

np

np

JJJ

JJ


Validity of Approximation


Experiment

Electron-only PCBM

Hole-only polymer

Dark Current SC


Result for P3HT:PCBM

Adv. Energy Mater. 2013, DOI: 10.1002/aenm.201300251


Result for MEH-PPV:PCBM


-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.010

-4

10-2

100

102

104

106

Au bottom electrode

ITO bottom electrode

Simulation pre

= 0.003

Curr

ent

Density [

A/m

2]

Voltage [V]

Note! Reduced Series Resistance


Ultimate Efficiency:??

P3HT

PCBM

ephoton

3.8

4.8

2.7

6.1

-

Band diagram of P3HT/PCBM devices

1 S. Barth and H. Bässler, Phys. Rev. Lett. 79, 4445 (1997).2 J. J. M. Halls et al., Phys. Rev. B 60, 5721 (1999).3 C. J. Brabec et al., Adv. Funct. Mater. 12, 709 (2002).

1. LUMO(D)-LUMO(A) offset ≥ exciton binding energy

(0.4 eV)1 to ensure charge transfer2

2. To be on the safe side: at least 0.5 eV

3. Efficient device reported with 0.3 eV offset3


400 600 800 10000

1

2

3

4

P3HT/PCBM film

P3HT part red shifted

Ab

so

rba

nce

[a

.u.]

Wavelength [nm]

Optimization: lowering Egap

1. In order to mimic absorption spectrum of low band gap

polymer, shift P3HT part of spectrum down in energy

2. Recalculate generation rate of charge carriers


1.5 1.6 1.7 1.8 1.9 2.0 2.13

4

5

6

7

Donor

Acceptor

4.8

6.1

3.8

Eff

icie

ncy [

%]

Polymer bandgap [eV]

Optimization: lowering Egap

1. Shift LUMO of polymer only:

• most favorable, no loss in Voc

2. Stop when LUMO(D)-LUMO(A) offset = 0.5 eV (charge transfer)

3. Egap = 1.5 eV => efficiency 6.6%


0.5 0.6 0.7 0.8 0.9 1.0 1.13

4

5

6

7

8

9

Donor

Acceptor

4.8

2.7

6.1

Effic

iency [%

]

LUMO(A) - LUMO(D) [eV]

Optimization: LUMO offsets

1. Only change LUMO of acceptor => no extra absorption

2. Efficiency >8% with high (2.1 eV) band gap polymer

3. All due to increase in Voc


1.5 1.6 1.7 1.8 1.9 2.0 2.16

7

8

9

Donor

Acceptor

4.8

6.1

Effic

iency [%

]

Polymer bandgap [eV]

Optimization: combined effect

1. Keep LUMO(D)-LUMO(A) at 0.5 eV, while decreasing

band gap of polymer

2. Optimal band gap 1.8-2.1 eV, broad maximum

3. Low band gap less efficient due to low Voc


100 150 200 250 300

6

8

10

12

h=e

h as is

Effic

iency [%

]

Active layer thickness [nm]

Optimization: high p

1. Higher hole mob. allows for thicker films => more absorption

2. Recalculate generation rate from absorption coefficients, taking

reflection at cathode into account

3. Ultimate efficiency 11%


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



Valentin Mihaeletchi

Magda Mandoc

Jan Anton Koster

Gert-Jan Wetzelaer

Martijn Kuik

Herman Nicolai

Bert de Boer†

Dago de Leeuw

Kees HUmmelen

Rene Janssen

Acknowledgement:

MEPOS Group RuG


Thank you for your attention!!!

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