the open-circuit voltage in organic solar cells

The Open-Circuit Voltage in Organic Solar Cells

Carsten Deibel, Andreas Baumann, Alexander Förtig, Markus Mingebach, Daniel Rauh, Thomas Strobel,

Alexander Wagenpfahl, Vladimir Dyakonov

Julius-Maximilians-University of Würzburg, Germany

8th April 2010, MRS Spring Meeting in San Francisco

introductiondefinition of Voc

Outline

2

generation

photocurrentpolaron pair dissociation

recombination

bulk recombinationsurface recombination

conclusions

open-circuit voltage

temperature dependencecarrier concentration

‣ current

‣ continuity equations (here for holes with density p)

Definition

3

Open-Circuit Voltage

derivatives usually non-zero

jn and jp usually non-zero!

‣ current


Definition

3




for free charge carriers

‣ from electron and hole continuity with current derivatives:

‣ current


Definition

3




geminate dissociation & recombination nongeminate recombination

for free charge carriers

‣ from electron and hole continuity with current derivatives:

Koster et al., APL 86, 123509 (2005)Cheyns et al., PRB 77, 165332 (2008)

Models

4

‣ Eg‣ Neff

‣ n, p

effective bandgap, determined by CT complexeseffective density of stateselectron and hole concentration


Models

4

‣ Eg‣ Neff

‣ n, p

effective bandgap, determined by CT complexeseffective density of stateselectron and hole concentration

High steady state carrier concentration means higher Voc

needed: high generation combined with low recombination


Outline

5

generation


recombination

bulk recombinationsurface recombination and S shape

conclusions



Photocurrent

Generation: Photocurrent= Current(illumination) - Current(dark)

POS =point of optimal symmetryOoi et al, J. Mater. Chem., 18, 1644 (2008)

photocurrent symmetric with respect to POSvoltage independentoffset

6

-8

-6

-4

-2

0

ph

oto

cu

rre

nt

de

nsity J

Ph [

mA

/cm!]

-1.0 0.0 1.0

applied voltage [V]

POS

voltage-independent

offset

Photocurrent

Generation: Photocurrent= Current(illumination) - Current(dark)

POS =point of optimal symmetryOoi et al, J. Mater. Chem., 18, 1644 (2008)

photocurrent symmetric with respect to POSvoltage independentoffset

6

-8

-6

-4

-2

0

ph

oto

cu

rre

nt

de

nsity J

Ph [

mA

/cm!]

-1.0 0.0 1.0

applied voltage [V]

POS

voltage-independent

offset

open circuit voltageslightly above POS

What is the origin of POS?

Point of Optimal Symmetry

-8

-6

-4

-2

0

photo

curr

ent density J

Ph [m

A/c

m!]

-1.0 0.0 1.0

applied voltage [V]

POS

voltage-independent

offset

7

built-in potential?

flat band in bulk?

What is the origin of POS?

Point of Optimal Symmetry

-8

-6

-4

-2

0

photo

curr

ent density J

Ph [m

A/c

m!]

-1.0 0.0 1.0

applied voltage [V]

POS

voltage-independent

offset

7

POS isQuasi Flat Band in the bulk,

not built-in potentialVoltage-independent offset (in part) due to finite field at

electrodes PRB 81, 085203 (2010)

Generation: Photocurrent

8

Voc is close to quasi flatband case

finite field at electrodes promotes polaron pair dissociationfree charge generation at Voc!

field in bulk almost zero at Vocis there still free charge generation?

Photocurrent

2

3

45678

1

2

3

456

|JPh

- J P

h(V P

OS)

| [m

A/cm

2 ]

0.01 0.1 1 10

|V - VPOS| [V]

3

4

5

6

7

8

9

1

experiment

Onsager-Braun Sokel-Hughes combination

Photocurrent Fit => Polaron Pair Dissociation= Current(illumination) - Current(dark)

has two contributionsrelative to POS! Mihailetchi et al, PRL 93, 216601 (2004)

• charge extractionSokel-Hughes, JAP 53, 7414 (1982)

• polaron pair dissociationBraun-Onsager, JCP 80, 4157 (1984)

9PRB 81, 085203 (2010)

Acceptor

Donor

+

E-Field

!

Generation: Polaron Pair Dissociation

10

‣ Hopping transport

Kinetic Monte Carlo

‣ Gaussian density of states‣ Coulomb interaction

Acceptor

Donor

+

E-Field

!


10


Kinetic Monte Carlo

‣ simulation does not reach experimental yield at short circuit exp: PRB 81, 085203 (2010)

0.01

2

3456

0.1

2

3456

1

Pola

ron

Pair

Dis

soci

atio

n Yi

eld

106 107 108 109

Electric Field [V/m]

CL····· 1

!f 100ns 10µs

fit to experiment

SimulationExperiment

Acceptor

Donor

+

E-Field

!


10


Kinetic Monte Carlo

Kinetic Monte Carlo

Acceptor

Donor

E-Field

!

+

Polaron Pair Dissociation: Extended Chains

11


Kinetic Monte Carlo

Acceptor

Donor

E-Field

!

+

Polaron Pair Dissociation: Extended Chains

11


finite polaron pair dissociation at low fields

‣ considerable generation‣ intermolecular: hopping

0.01

2

3456

0.1

2

3456

1

Pola

ron

Pair

Dis

soci

atio

n Yi

eld

106 107 108 109

Electric Field [V/m]

CL····· 1–·– 4– – 10

!f 100ns

fit to experiment

Experiment Simulation

PP diss

internal

bulk rec

P rec


12

simulated polaron pairdissociation‣ high yield similar to

experiment due to delocalisation along polymer chains

‣ significant bulk generation even at zero field‣ thus, also at Voc

‣ generation@oc ~4/5th of sc‣ almost no loss in Voc


Outline

13

generation


recombination


conclusions



P3HT:PCBM (annealed) measured by photo-CELIV

Bulk Recombination

14

‣ Langevin recombination prefactor

1020

1021

1022

n [m

-3]

10-7 10-6 10-5 10-4 10-3 10-2

tdelay [s]

125 K

300 K

P3HT:PCBM 1:0.8annealed

Andreas Baumann APL 93, 163303 (2008)

‣ temperature dependencetypical for Langevin recombination

P3HT:PCBM (annealed) measured by TPV@Voc

Bulk Recombination

15

‣ temperature dependencetypical for Langevin recombination

Alexander Förtig

1024

1025

1026

1027

reco

mbi

natio

n ra

te [m

-3s-1

]

10212 4 6 8

10222 4 6 8

1023

charge carrier density [m-3]

P3HT:PCBM (annealed) T [K] 200 225 250 275 300

‣ recombination rate higher at higher temperature(proportional to the charge carrier mobility)

APL 95, 052104 (2009)

Bulk Recombination

16

3.4

3.2

3.0

2.8

2.6

2.4

2.2

2.0

reco

mbi

natio

n or

der

300250200150

T [K]

P3HT:PCBM 1:0.8

pristine annealed

BR

P3HT:PCBM (annealed) measured by photo-CELIV

Reduced Recombination RateOrder of Decay

Andreas Baumann

10-20

10-19

10-18

10-17

k BR [m

3 /s]

1020 1021 1022

n [m-3]

P3HT:PCBM 1:0.8annealed fit Langevin125 K 175 K 300 K

PRB 80, 075203 (2009); Hilczer&Tachiya, JPCC (2010)

Bulk Recombination: SummaryRecombination of Free Charges

‣ bimolecular recombination

‣ Langevin type: depending on mobility

‣ reduced recombination rate

‣ order larger than two: due to trapping

Open Circuit Voltage

‣ at room temperature, bimolecular recombination is significant

‣ limits Voc

17

Better: look at it as extraction rate!

Surface „Recombination“

18

Charge Extraction Pathways

Alexander Wagenpfahl

Better: look at it as extraction rate!

Surface „Recombination“

18

Charge Extraction PathwaysSimulated IV Curve


Reduced surface recombination of holes at anode

Simulation

19Alexander Wagenpfahl

Energetic Structure at Voc

Charge carrier densities

20


21


22


At open circuit conditions:

Surface recombination:

22

Surface Recombination: SummaryS-shaped IV-characteristicscalculated by reduced surface recombination

Interpretationsurface „recombination“ is actually extraction rateaccumulation of surface space charge

‣ reduces Voc (and fill factor)

‣ transition from ohmic to space charge limited current

23


Outline

24

generation


recombination


conclusions



Voc(T) and n(T): annealed

0.7

0.6

0.5

0.4

Vo

c [

V]

300250200150100

temperature [K]

increasing PL

P3HT:PCBM 1:0.8 annealed

Voc

ITO/PEDOT/blend/Ca/Al

Voc(T) and n(T): annealed

0.7

0.6

0.5

0.4

Vo

c [

V]

300250200150100

temperature [K]

increasing PL


Voc100x10

15

80

60

40

20

n [cm

-3 ]

300250200150100

temperature [K]

increasing PL


charge extraction

ITO/PEDOT/blend/Ca/Al


Voc Models

26

‣ Eg‣ Neff

effective bandgap, determined by CT complexeseffective density of states

measured

fit parameters:

electron and hole concentration‣ n, p

Voc: Modelling the experiment

annealed pristine

0.70

0.65

0.60

0.55

0.50

0.45

0.40

Vo

c [V

]

300250200150100

temperature [K]

measurement fit in linear Voc(T) range

P3HT:PCBM 1:0.8annealed

0.75

0.70

0.65

0.60

0.55

Vo

c [V

]

300250200150100

temperature [K]

measurend fit in linear Voc(T) range

P3HT:PCBM 1:0.8as cast

• model fits well in linear Voc(T) range at T > 150 K• from carrier concentration at T < 150 K, higher Voc is expected

Daniel Rauh

Voc: Injection Barriers by Simulation

• ohmic contacts: Voc extrapolates to effective bandgap• Voc is usually contact limited at low T• model predictions due to carrier concentration yield ohmic case

Voc charge extraction

1021

1022

1023

1024

Cha

rge

carri

er d

ensi

ties

[m-3

]400350300250200150100

Temperature [K]

electron !n / !p hole 0.0 / 0.0 eV 0.1 / 0.2 eV 0.1 / 0.7 eV

1.0

0.8

0.6

0.4

0.2

Ope

n ci

rcui

t vol

tage

[V]

400350300250200150100

Temperature [K]

Sim !n / !p Model 0.0 / 0.0 eV 0.1 / 0.2 eV 0.1 / 0.7 eV


Eg = 1.1 eV1.1

1.1-(0.1+0.2)

1.1-(0.1+0.7)

Voc: Light Intensity

Daniel Rauh

‣ low light intensity: monomol. recombination

‣ 1 sun: bimolecular

‣ 100K: contact limited(as seen in Voc(T) plot)

Experiment Again!

0.7

0.6

0.5

0.4

0.3

Ope

n C

ircui

t Vol

tage

[V]

0.001 0.01 0.1 1Illumination Density [suns]

100K 200K 300K

MR BR


Voc: Light Intensity

Daniel Rauh

‣ low light intensity: monomol. recombination

‣ 1 sun: bimolecular

‣ 100K: contact limited(as seen in Voc(T) plot)

Experiment Again!

‣ 130mV

0.7

0.6

0.5

0.4

0.3

Ope

n C

ircui

t Vol

tage

[V]

0.001 0.01 0.1 1Illumination Density [suns]

300K P3HT:PCBM 1:0.8

annealed

Voc: Conclusionshigh TVoc determined by blend properties (CT complex energy)bimolecular recombination is limiting Voc @ 1 sunif only monomolecular: 130mV higher Voc @ RT

low Tgeneration rate lower

‣ recombination rate lower

‣ steady state carrier concentration higher

‣ Voc higherfor non-ohmic contacts usually contact limited

Conclusions

31

significant generation even at low fields

dissociation due to band bending at electrodesdelocalisation along effective conjugation length

recombination

bulk recombination limits at room TS shape due to low extraction rates


low T: usually contact limitRT: bimolecular recombination

Acknowledgments

32

Bavarian Academy of Sciences and Humanities

EP VI

[email protected]

www.disorderedmatter.eu

BMBF GREKOS

mailto:[email protected]


http://www.disorderedmatter.eu


Thanks to EP VIThank You

Acknowledgments

32

Bavarian Academy of Sciences and Humanities

EP VI

[email protected]

www.disorderedmatter.eu

BMBF GREKOS





the open-circuit voltage in organic solar cells

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