Transport and Recombination in Polymer:Fullerene Solar Cells Paul Blom Max Planck Institut für Polymer Forschung, Mainz
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
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, 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
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
< 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
Light intensity (W/m2)
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
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
< 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
P3HT:PCBM solar cells
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
P3HT:PCBM solar cells
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
P3HT:PCBM solar cells
• 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
Exciton Diffusion Coefficient
Bulk Quencher
PCBM
C-PCPDTBT
< 91
Exciton Diffusion Coefficient
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
Light intensity (W/m2)
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