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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
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introductiondefinition of Voc
Outline
2
generation
photocurrentpolaron pair dissociation
recombination
bulk recombinationsurface recombination
conclusions
open-circuit voltage
temperature dependencecarrier concentration
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‣ current
‣ continuity equations (here for holes with density p)
Definition
3
Open-Circuit Voltage
derivatives usually non-zero
jn and jp usually non-zero!
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‣ current
‣ continuity equations (here for holes with density p)
Definition
3
Open-Circuit Voltage
derivatives usually non-zero
jn and jp usually non-zero!
for free charge carriers
‣ from electron and hole continuity with current derivatives:
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‣ current
‣ continuity equations (here for holes with density p)
Definition
3
Open-Circuit Voltage
derivatives usually non-zero
jn and jp usually non-zero!
geminate dissociation & recombination nongeminate recombination
for free charge carriers
‣ from electron and hole continuity with current derivatives:
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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
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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
High steady state carrier concentration means higher Voc
needed: high generation combined with low recombination
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introductiondefinition of Voc
Outline
5
generation
photocurrentpolaron pair dissociation
recombination
bulk recombinationsurface recombination and S shape
conclusions
open-circuit voltage
temperature dependencecarrier concentration
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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
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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
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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?
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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)
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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?
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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)
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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)
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Acceptor
Donor
+
E-Field
!
Generation: Polaron Pair Dissociation
10
‣ Hopping transport
Kinetic Monte Carlo
‣ Gaussian density of states‣ Coulomb interaction
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Acceptor
Donor
+
E-Field
!
Generation: Polaron Pair Dissociation
10
‣ Hopping transport
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
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Acceptor
Donor
+
E-Field
!
Generation: Polaron Pair Dissociation
10
‣ Hopping transport
Kinetic Monte Carlo
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Kinetic Monte Carlo
Acceptor
Donor
E-Field
!
+
Polaron Pair Dissociation: Extended Chains
11
‣ Hopping transport
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Kinetic Monte Carlo
Acceptor
Donor
E-Field
!
+
Polaron Pair Dissociation: Extended Chains
11
‣ Hopping transport
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
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PP diss
internal
bulk rec
P rec
Generation: Polaron Pair Dissociation
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
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introductiondefinition of Voc
Outline
13
generation
photocurrentpolaron pair dissociation
recombination
bulk recombinationsurface recombination
conclusions
open-circuit voltage
temperature dependencecarrier concentration
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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
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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)
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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)
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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
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Better: look at it as extraction rate!
Surface „Recombination“
18
Charge Extraction Pathways
Alexander Wagenpfahl
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Better: look at it as extraction rate!
Surface „Recombination“
18
Charge Extraction PathwaysSimulated IV Curve
Alexander Wagenpfahl
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Reduced surface recombination of holes at anode
Simulation
19Alexander Wagenpfahl
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Energetic Structure at Voc
Charge carrier densities
20
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Energetic Structure at Voc
21
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Energetic Structure at Voc
22
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Energetic Structure at Voc
At open circuit conditions:
Surface recombination:
22
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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
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introductiondefinition of Voc
Outline
24
generation
photocurrentpolaron pair dissociation
recombination
bulk recombinationsurface recombination
conclusions
open-circuit voltage
temperature dependencecarrier concentration
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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
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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
Voc100x10
15
80
60
40
20
n [cm
-3 ]
300250200150100
temperature [K]
increasing PL
P3HT:PCBM 1:0.8 annealed
charge extraction
ITO/PEDOT/blend/Ca/Al
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Koster et al., APL 86, 123509 (2005)Cheyns et al., PRB 77, 165332 (2008)
Voc Models
26
‣ Eg‣ Neff
effective bandgap, determined by CT complexeseffective density of states
measured
fit parameters:
electron and hole concentration‣ n, p
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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
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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
Alexander Wagenpfahl
Eg = 1.1 eV1.1
1.1-(0.1+0.2)
1.1-(0.1+0.7)
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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
P3HT:PCBM 1:0.8 annealed
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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
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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
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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
open-circuit voltage
low T: usually contact limitRT: bimolecular recombination
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Acknowledgments
32
Bavarian Academy of Sciences and Humanities
EP VI
www.disorderedmatter.eu
BMBF GREKOS
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Thanks to EP VIThank You
Acknowledgments
32
Bavarian Academy of Sciences and Humanities
EP VI
www.disorderedmatter.eu
BMBF GREKOS