3
Photocurrent generation in bulk
heterojunction solar cells∗
Abstract
In this chapter, the photogeneration in organic donor/acceptor photovoltaic
cells is discussed, with emphasis on the mechanism of charge dissociation and
the consequences of an unbalanced charge transport on photocurrent generation. It is demonstrated that the photocurrent in conjugated polymer:fullerene
blends is dominated by the dissociation efficiency of bound electron-hole pairs
at the donor/acceptor interface. A model based on Onsager’s theory of geminate charge recombination is proposed, which explains the observed fieldand temperature dependence of the photocurrent in polymer:fullerene blends.
At room temperature only 60% of the generated bound electron-hole pairs in
MDMO-PPV:PCBM blends are dissociated and contribute to the short-circuit
current, which constitutes a major loss mechanism in photovoltaic devices based
on this material system. With respect to the charge transport, it is demonstrated
that the photocurrent reaches the fundamental space-charge limit when the difference in electron and hole mobility exceeds two orders of magnitude. The experimental photocurrents reveal all the characteristics of a space-charge limited
photocurrent; a one-half power dependence on voltage, a three-quarter power
dependence on light intensity, and a one-half power scaling of the voltage at
which the photocurrent switches into full saturation with light intensity.
∗ The main results of this chapter have been published as: (a) V. D. Mihailetchi, L. J. A. Koster,
J. C. Hummelen, P. W. M. Blom, Physical Review Letters 93 (2004), 216601; (b) V. D. Mihailetchi, J.
Wildeman, P. W. M. Blom, Physical Review Letters 94 (2005), 126602.
39
40
Chapter 3: Photocurrent generation in bulk heterojunction solar cells
3.1 Photocurrent in polymer:fullerene blends
3.1.1
Introduction
The primary process of photocurrent generation in organic donor/acceptor photovoltaic cells is the generation of excitons after absorption of light, either by the
donor or by the acceptor. The excitons diffuse in either of the domains towards
the polymer (donor)-fullerene (acceptor) interface where rapid charge transfer
will occur [1]. After dissociation, a geminate pair of a hole at the donor and
electron at the acceptor is formed. Due to the low dielectric constants (ǫr ) of
the molecular materials and polymers (ǫr ranges typically from 2 to 4), these
electron-hole (e-h) or polaron pairs are strongly bound by Coulomb interaction, with binding energies of typically several tenths of an electron volt. In
order to generate a photocurrent, the bound e-h pairs must dissociate into free
charge carriers and subsequently move to the electrodes before recombination
processes take place.
In the bulk heterojunction devices using MDMO-PPV and PCBM as donor
and acceptor, respectively, an external quantum efficiency of more than 50% has
been reported [2]. Many fundamental aspects regarding the operation of these
devices are presently under strong debate: It has been observed that the photocurrent under short circuit conditions (JSC ) is relatively weakly dependent
on temperature [3]. This has been attributed to either the temperature dependence of the charge transport in combination with recombination with shallow
traps [4] or space-charge effects [5]. The voltage dependence of the photocurrent in bulk heterojunction devices has to our knowledge not been addressed,
so far only recently a device model for photocurrent in bilayer devices has been
developed [6]. Another important issue is the origin of the relatively large external quantum efficiencies in spite of the strong Coulomb binding between the
e-h pairs in organic materials.
In this section, a model is presented that consistently explains the voltageand temperature dependence of the photocurrent in PPV:PCBM bulk heterojunction devices. It is demonstrated that at voltages V close to the compensation voltage V0 (V0 -V <0.1 V), implying a small electric field in the device, the
photocurrent linearly increases with voltage. For V0 -V >0.1 V the photocurrent
enters the saturation regime, as expected for weak recombination. In this regime
the photocurrent is governed by the field- and temperature dependent dissociation of e-h pairs according to Onsager’s theory of ion pair dissociation [7, 8]. For
large (reverse) voltages > 10 V the photocurrent becomes field- and temperature
independent, implying that every generated bound e-h pair is dissociated into
free carriers by the applied field. From the observation of the fully saturated
current we obtain that under short-circuit conditions only 60% of the bound e-h
pairs in an MDMO-PPV:PCBM based photovoltaic device is dissociated.
3.1.2
Photocurrent-voltage characteristics
The measurements were performed on 20:80 wt. % blends of MDMO-PPV:PCBM
sandwiched between two electrodes (see Section 3.3) with different work func-
41
20
JD
JL
10
Jph=JL-JD
2
J [A/m ]
3.1. Photocurrent in polymer:fullerene blends
0
VOC
-10
V0
-20
0.5
0.6
0.7
0.8
0.9
V [V]
Figure 3.1: Current density under illumination (JL ), in the dark (JD ), and calculated net
photocurrent (Jph ); Jph =JL -JD . The arrows indicate the open-circuit voltage (VOC ) and
the compensation voltage (V0 ) determined when the Jph =0.
tion to generate an internal electric field, necessary to separate the photogenerated charges. The devices were illuminated by a white light halogen lamp with
an intensity of 800 W/m2 , in inert (N2 ) atmosphere. A reverse voltage sweep
from 1 V down to -15 V has been applied and the current density under illumination (JL ) has been recorded for a temperature range of 210 K - 295 K. In order
to determine the net photocurrent, the current density in the dark (JD ) was also
recorded. The experimental photocurrent is given by Jph =JL -JD . From the resulting Jph -V characteristics the compensation voltage (V0 ) at which Jph =0 was
determined, as is shown in the Figure 3.1.
3.1.3
The origin of the field-dependent (reverse bias)
photocurrent
In Figure 3.2 Jph is plotted, at room temperature, on a double logarithmic scale
against the effective voltage across the device, given by V0 -V . For a small effective voltage (V0 -V <0.1 V) the photocurrent increases linearly with the effective
voltage, which has not been noticed before, and then tends to saturate. At higher
reverse voltage (V0 -V >1 V) the photocurrent further increases with increasing
voltage. In order to qualitatively understand this behavior, let us first consider
the situation in which recombination of free charge carriers as well as spacecharge effects can be neglected. In that case the internal field in the device is
given by E=(V0 -V )/L, where V is the applied voltage. Without recombination
the photocurrent through the external circuit is [9]:
Jph = qGL,
(3.1)
where q is the electric charge, G the generation rate of e-h pairs, and L the thickness of the active layer. Thus in case of no recombination and a constant generation rate G of e-h pairs Jph is independent of V , as shown in Figure 3.2 by the
dotted line. However, Sokel and Hughes (SH) [10] pointed out that this result
42
Chapter 3: Photocurrent generation in bulk heterojunction solar cells
2
Jph [A/m ]
diffusion drift
10
1
0.01
0.1
1
10
V0-V [V]
Figure 3.2: Room temperature Jph -V characteristics of an MDMO-PPV:PCBM 20:80 device as a function of effective applied voltage (V0 -V ) (open circles), for a device with
thickness of 120 nm. The solid line represent calculated photocurrent from Equation 3.2
using G=1.56×1027 m−3 s−1 , whereas, the dotted line represent drift current calculated
from the Equation 3.1 using the same G.
is incorrect at low bias voltages because diffusion currents have been neglected.
Using the same approximation as above, but including diffusion, SH found an
analytical solution for the photocurrent:
exp(qV /kB T ) + 1 2kB T
,
(3.2)
Jph = qGL
−
exp(qV /kB T ) − 1
qV
where qGL is the saturated photocurrent, kB is the Boltzmann constant and T
is the temperature, respectively. The solutions of the Equations 3.1 and 3.2 are
shown schematically in Figure 3.2 together with the experimental data. Using
a G of 1.56 × 1027 m−3 s−1 , Equation 3.2 fits the experimental data at low effective fields, indicating that diffusion plays an important role in the experimental
photocurrent. It should be noted that the photocurrent given by Equation 3.2 is
independent of the mobility of either electrons or holes, since for none or very
weak recombination the carrier lifetime will always exceed the transit time.
It appears from Figure 3.2 that for effective voltages exceeding 1 V the experimental photocurrent does not saturate at qGL but gradually increases for
larger effective voltages. An important process which has not been taken into
account into the Equations 3.1 and 3.2 is that not all the photogenerated bound eh pairs (represented by Gmax ) dissociate into free charge carriers. Only a certain
fraction of Gmax is dissociated into free charge carriers, depending on field and
temperature, and therefore contributes to the photocurrent Jph . Consequently,
the generation rate G of free charge carriers can be described by:
G(T, E) = Gmax P (T, E),
(3.3)
where P (T, E) is the probability for charge separation at the donor/acceptor
interface.
3.1. Photocurrent in polymer:fullerene blends
3.1.4
43
A model for charge carriers dissociation at
donor/acceptor interface
The photogeneration of free charge carriers in low-mobility materials has first
been explained by the geminate recombination theory of Onsager [7, 8]. Onsager calculated the probability that a pair of oppositely charged ions in a weak
electrolyte, that undergo a Brownian random walk under the combined influence of their mutual Coulomb attraction and external electric field, would escape recombination. An important addition to the theory has been made by
Braun [11], who stressed the importance of the fact that the bound e-h pair
(or charge transfer state) has a finite lifetime, as schematically depicted in Figure 3.3. The bound e-h pair, formed after the dissociation of an exciton at the
donor/acceptor interface, can either decay to the ground state with a rate constant kF or separates into free carriers with an electric-field dependent rate constant kD (E). The decay rate (kF ) is dominated by phonon-assisted non radiative
recombination [12]. Once separated, the charge carriers can again form a bound
pair with a rate constant kR , as shown schematically in Figure 3.3. Consequently,
free carriers which are captured into bound pairs may dissociate again during
the lifetime of the bound pair. Therefore, long lived charge transfer states act as
a precursor for free charge carriers.
It has been demonstrated that after generation, bound e-h pairs in PPV:PCBM
blends can still be detected after microseconds and even milliseconds, depending on temperature [13, 14]. Furthermore, Onsager’s theory as discussed here
was extensively applied in the past to describe photogeneration in pure and sensitized conjugated polymers [15, 16]. It should be noted that Onsager’s model
describes charge dissociation in three dimensions. This is also applicable to bulk
heterojunction cells since the length scale of morphology, typically two times the
exciton diffusion length (10-15 nm), is in the order of Onsager radius of 17 nm.
In Braun’s model the probability that a bound polaron pair dissociates into free
charge carries at a given electric field E and temperature T is given by:
P (T, E) =
kD (E)
.
kD (E) + kF
(3.4)
Based on Onsager theory for field-dependent dissociation rate constants for
weak electrolytes [7, 8], Braun derives kD (E) for dissociation of a bound pair
Figure 3.3: Schematic diagram of charge carrier separation at interface between polymer
(donor; D) and fullerene (acceptor; A).
44
Chapter 3: Photocurrent generation in bulk heterojunction solar cells
to be [11]:
3 − kEBT
b3
b4
b2
B
kD (E) = kR
e
+
+
+ ··· ,
1+b+
4πa3
3
18 180
(3.5)
2 2
with a the initial separation of bound e-h pair at the interface, b=q 3 E/8πǫ0 ǫr kB
T ,
and EB the e-h pair’s binding energy. For low mobility semiconductors electronhole recombination is given by Langevin: kR =qhµi/ǫ0 hǫr i, where hǫr i is spatially
averaged dielectric constant and hµi the spatially averaged sum of electron and
hole mobilities. Furthermore, in disordered materials as conjugated polymers
and fullerenes it is unlikely that all donor/acceptor separations (a) would be
the same [17]. As a consequence, Equation 3.4 should be integrated over a distribution of separation distances
Z ∞
P (T, E) = NF
P (x, T, E)F (x)dx,
(3.6)
0
where P (x, T, E) is the probability that an electron and hole generated at a distance x, temperature T , and field E, will escape recombination; F (x) is a distribution function of donor-acceptor separations, and NF is a normalization factor
2
2
for the function F (x). The F (x) was assumed to be F (x) = x2 e−x /a , with
1/2 3
NF = 4/π a [17]. The bulk dielectric constant is εr =3.4 (which was taken as
the spatial average dielectric constant of PPV and PCBM). The final parameters
required in the model are the mobilities of the charge carriers in the 20:80 blends
of MDMO-PPV:PCBM, which have been determined (in Chapter 2 of this thesis)
to be µe =2.0 × 10−7 m2 /Vs and µh =1.4 × 10−8 m2 /Vs, at room temperature.
Combining Equations 3.3 and 3.6 the generation rate of producing free electrons and holes in blends of MDMO-PPV:PCBM for any temperature and electric field can be calculated. It should be noted that Equation 3.3 involves only
two adjustable parameters: the initial separation of e-h pairs a, and the ground
state recombination rate kF , since all the other parameters were experimentally
determined.
3.1.5
Comparing the model with the experimental
photocurrent
Figure 3.4(a) (solid lines) shows the calculated photocurrent from Equation 3.1
as a function of temperature, including the calculated field-dependent generation rate G(T, E). Using a=1.3 nm, and a room temperature recombination
lifetime kF−1 =1 µs, the calculations consistently describe the field- and temperature dependence of the experimental data in the saturation regime (V0 -V >0.3
V). In the inset of Figure 3.4(a) the spatial distribution F (x) is shown for a=1.3
nm corresponding to a mean e-h separation distance of typically 1.5 nm. In
Figure 3.4(b) the (normalized) temperature dependence of the predicted- and
experimental photocurrent is plotted, for two different effective voltages of 0.01
V and at short-circuit. The excellent agreement at both voltages demonstrates
that the activation energy of the photocurrent is completely dominated by the
rate of producing free electrons and holes (G) from the internal donor/acceptor
45
(a)
270 K
2
[A/m ]
295 K
250 K
230 K
0.6
J
F(x)
ph
10
210 K
0.4
0.2
0.0
0.0
0.7
1.4
2.1
x [nm]
1
0.1
1
V -V [V]
0
10
2.8
Jph/Jph(295 K), G/G(295 K)
3.1. Photocurrent in polymer:fullerene blends
(b)
1
0.8
∆=35.4 meV
0.6
∆=94.1 meV
0.4
Jph/Jph(295 K)
G/G(295 K)
0.2
3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8
-1
1000/T [K ]
Figure 3.4: (a) Temperature dependence of the photocurrent (symbols) versus effective
applied voltage (V0 -V ) for a device of 100 nm thickness. The solid line represents the calculated photocurrent from Equation 3.1 using field dependent generation rate G(T, E).
The inset shows the spatial distribution F (x) for a=1.3 nm. (b) Normalized experimentally photocurrent (Jph ) and normalized calculated generation rate [G(T, E)] from Figure
3.4(a), as a function of 1/T, taken in linear regime at 0.01 V (full symbols) and at short
circuit (empty symbols). The activation energies are written on the figure.
interface. It should be noted that the activation energy of G [shown in Figure
3.4(b)] arises from the combined effect of the distribution of binding energies,
the temperature dependence of both charge carrier mobility and decay rate kF−1
as well as the effect of applied field, and therefore it does not reflect directly the
bound e-h pair activation energy. As shown in Figure 3.4(a) at high effective
voltages of typically 10 V the photocurrent saturates and becomes field- and
temperature independent. At these voltages all bound e-h pairs are separated
and the maximum photocurrent Jsat =qGmax L is reached. By comparing the
photocurrent with the experimentally observed Jsat the dissociation efficiency
can be read directly from Figure 3.4(a). Under short-circuit conditions (V=0 V)
only 60% of the bound e-h pairs dissociate, and at the maximum-power-point
(V=0.64 V) this efficiency even further decreases to 52%. This incomplete dissociation of generated bound e-h pairs under operating conditions is therefore a
main loss mechanism in solar cells based on PPV:PCBM blends.
As a next step, the generation rate G(T, E) is combined with Equation 3.2, as
shown in Figure 3.5 by the dotted line, for 295 K. It is observed that this approach
underestimates the photocurrent in the low voltage regime. This apparent discrepancy arises from the fact that the analytical model has been deduced for
blocking contacts [10]. However, in case of Ohmic contacts (as the devices presented here), the internal electric field in the device is slightly modified due to
the band bending created by the accumulation of the charge carries at the interface. This effect is negligible at high reverse bias (in the saturation regime), but
it has a significant effect at voltage close to V0 (in the linear regime). Therefore,
the use of Equation 3.2 together with G(T, E) will not entirely fit the experimental data of the devices with Ohmic contacts. Furthermore, the analytical model
does not include the effects of space charge and recombination. Therefore, we
Chapter 3: Photocurrent generation in bulk heterojunction solar cells
2
Jph [A/m ]
46
10
295 K
250 K
1
0.01
0.1
1
10
V0-V [V]
Figure 3.5: Experimental photocurrent (Jph ) as a function of effective applied voltage
(V0 -V ) of MDMO-PPV:PCBM 20:80 device (symbols), at 295 and 250 K. The solid line
represents the numerical calculation including diffusion, field dependent of generation
rate G(T, E) and recombination, for a device with thickness of 120 nm. The dotted line
represents calculated Jph from Equation 3.2 using G(T, E), at 295 K.
have developed an exact numerical model that calculates the steady-state charge
distributions within the active layer with Ohmic contacts by solving Poisson’s
equation and the continuity equations, including diffusion and recombination
of charge carriers at donor/acceptor interface. This numerical model describes
the full current-voltage characteristics in the dark and under illumination, including the field dependent generation rate G(T, E) [18]. Figure 3.5 shows the
experimental photocurrent (symbols) together with the numerical calculation
(solid lines) for two different temperatures. At both temperatures, using the
same parameters as presented above, the calculated photocurrent fits the experimentally data over the entire voltage range.
3.1.6
Conclusion
In this section, the photocurrent in 20:80 blends of MDMO-PPV:PCBM solar
cells has been interpreted using a model based on Onsager’s theory of geminate
charge recombination. The model explains the field- and temperature dependence of the photocurrent in a large voltage regime. The long lifetime of 1 µs
is a precursor for the high external quantum efficiencies observed in MDMOPPV:PCBM blends. Under short-circuit conditions, at room temperature, only
60% of the bound e-h pairs are separated and contribute to the photocurrent.
3.2 Space-charge limitation in organic solar cells
3.2.1
Introduction
When a semiconductor is exposed to photons with an energy larger than the
band gap, charge carriers are produced. With a built-in field or an externally
47
3.2. Space-charge limitation in organic solar cells
applied bias these charge carriers can be separated, thereby producing a photocurrent in an external circuit. The efficiency of photocurrent generation depends on the balance between charge carrier generation, recombination, and
transport. The extraction of photogenerated electrons and holes from a semiconductor has been treated by Goodman and Rose [9]. With non-injecting contacts the external photocurrent becomes saturated when all photogenerated free
electrons and holes are extracted from the semiconductor. This implies that the
mean electron and hole drift lengths we(h) =µe(h) τe(h) E are equal or longer than
the specimen thickness L; with µe(h) the charge carrier mobility of electrons
(holes), τe(h) the charge carrier lifetime and E the electric field, respectively.
In this case no recombination occurs and the saturated photocurrent density
sat
is given by Jph
=qGL [9]. However, as is shown in Section 2.1, if either we <L or
wh <L or both are smaller than L, space-charge will form and recombination of
free charge carriers becomes significant. In the following, this specific case will
been analyzed with more details.
3.2.2
Goodman and Rose approximation
Suppose that the e-h pairs are photogenerated uniformly throughout the specimen and that the charge transport is strongly unbalanced, meaning that we 6=
wh . As is demonstrated in Section 2.1, in a semiconductor with wh ≪we and
wh <L, the holes will accumulate to a greater extent in the device than the electrons, altering the electric field. As a consequence, the electric field increases in
the region (L1 ) near the anode, enhancing the extraction of holes, as is shown
schematically in Figure 2.1(b). In Section 2.1 it has been shown that if
√ wh ≪we ,
the length of the region L1 is given by the mean hole drift length (L1 = µh τh V1 ).
Since almost the entire voltage V drops on the region of hole accumulation
(V1 ≈V ) and the photocurrent generated in this region is substantially the total
current, it follows directly that [9]:
Jph = qGL1 = qG(µh τh )1/2 V 1/2 .
(3.7)
It is evident that in the region L1 the accumulated holes are not neutralized
by an equal density of electrons, which results in a build-up of positive spacecharge. Goodman and Rose pointed out that there is a fundamental limit to be
expected for the build-up of space-charge in a semiconductor at high intensities;
The electrostatic limit of hole accumulation is reached when the photocurrent
generated in this region, Jph =qGL1 , is equal to the space-charge limited current:
JSCL =
9
V2
ε0 εr µh 13 ,
8
L1
(3.8)
where ε0 εr is the dielectric permittivity. By equating qGL1 with Equation 3.8 it
follows that the length of the region L1 in this space-charge limited (SCL) regime
is given by:
1/2
L1 = (9ε0 εr µh /8qG)1/4 V1
.
(3.9)
48
Chapter 3: Photocurrent generation in bulk heterojunction solar cells
Since V1 ≈V , the maximum electrostatically allowed photocurrent that can be
extracted from the device is [9]:
Jph = q
9ε ε µ 1/4
0 r h
G3/4 V 1/2 .
8q
(3.10)
Comparison of Equations 3.7 and 3.10 show that both in the absence and presence of the space-charge limitation Jph scales with the square-root of the applied
voltage and is governed by the slowest charge carrier mobility, although the
physical reasons of this are distinctly different. Experimentally, both regimes
can be discriminated by investigating their dependence on G. To our knowledge, the existence of SCL photocurrents has not been demonstrated experimentally in semiconductors so far.
3.2.3
Experimental evidence
In order to observe SCL photocurrents a semiconductor should fulfil a number
of requirements: First, the amount of photogenerated charge carriers should be
large, meaning a large G and a long carrier lifetime τe(h) after dissociation of
the e-h pairs. Furthermore, the charge transport should be strongly unbalanced,
leading to the formation of space-charge regions. Finally, the slowest charge carrier should have a low mobility such that the photocurrent can reach the SCL
current inside the space-charge region. A material system that fulfills most of
these demands are blends of conjugated polymers (electron donor) and fullerene
molecules (electron acceptor) [19]. In these blends light absorption leads to the
production of excitons that subsequently dissociate at the internal interface by
an ultrafast electron transfer (≈45 fs) from excited polymer to fullerene [1]. Since
the created electrons and holes are spatially separated the back-transfer process
is very slow leading to long-lived charge carriers, in the microsecond to millisecond range [13, 14]. In combination with the large internal donor/acceptor
interface these bulk heterojunctions enable a large generation rate of long-lived
charge carriers.
As is explained in the previous section, the important quantity which determines the formation of space-charge in photoconductors, is the difference in
the µτ product of electrons and holes. The most investigated system of polymer/fullerene solar cells are blends of MDMO-PPV and PCBM. The main recombination process found in these devices is bimolecular recombination of
photogenerated free electrons and holes (as discussed in Section 3.1), resulting
in an equal electron and hole lifetime. Therefore, a large mobility difference between electrons and holes is required for the generation of a SCL photocurrent in
this system. However, it turns out that the hole mobility of MDMO-PPV inside
the blend is enhanced by a factor of 400 as compared with the pure material (see
Section 2.3). The resulting mobility difference of only one order of magnitude
is not sufficient to induce a SCL photocurrent. As demonstrated in Section 2.3,
when symmetrical substituted PPV is used (such as BEH1 BMB3 -PPV), the hole
mobility in polymer phase is hardly affected by the presence of PCBM, resulting
in an increased mobility difference between electrons and holes in the blend.
The measurements here were performed on 20:80 weight percentage blends of
49
3.2. Space-charge limitation in organic solar cells
-7
-8
10
2
µ [m /Vs]
10
-9
10
-10
10
-11
10
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
-1
1000/T [K ]
Figure 3.6: Experimental charge carrier mobility of the electrons (µe ;
) and holes
(µh ; △) as a function of temperature T . The µe and µh have been determined from
space-charge limited measurements on 20:80 blends of BEH1 BMB3 -PPV:PCBM.
BEH1 BMB3 -PPV:PCBM sandwiched between two electrodes with asymmetric
work function, which are non-injecting under reverse bias operation.
In order to investigate the photocurrent in blends of BEH1 BMB3 -PPV:PCBM,
knowledge about the hole and electron mobility in the polymer and fullerene
phases is indispensable. In Chapter 5 is shown that the electron and hole mobilities in a blend can be determined from dark current-voltage measurements
by using suitable electrodes which either suppress holes or electrons. In Figure
3.6 the experimental electron and hole mobilities in 20:80 blends of BEH1 BMB3 PPV:PCBM are shown as a function of temperature (1/T ). It is observed that at
room temperature the electron mobility in the PCBM phase (µe =4×10−7 m2 /Vs)
is a factor of 125 larger than the hole mobility in the BEH1 BMB3 -PPV phase
(µh =3.2×10−9 m2 /Vs). This low hole mobility originates from a hopping process between localized sites, which consist of conjugated polymer chain segments. Due to strong disorder there is a variation in the on-site energies, reducing the coupling between these localized states [20, 21]. Since PPV and PCBM
have different energetic disorder, the activation energy of charge carrier mobility
is different in the case of electrons (0.18 eV) and holes (0.35 eV). Consequently,
as the temperature decreases the difference between µe and µh becomes larger.
For example, at 210 K the difference between experimental µe and µh increases
to a factor of 2000, thereby strongly unbalancing the transport in these blends.
Figure 3.7(a) shows the experimental Jph as a function of V0 -V in a 20:80
blend of BEH1 BMB3 -PPV:PCBM, for a temperature range of 210 K- 295 K. It is
observed that for V0 -V < 0.06 V Jph shows a linear dependence on voltage, due
to the competition between drift and diffusion of photogenerated free charges to
the electrodes, as discussed in the Section 3.1. However, above 0.06 V the experimental Jph clearly shows a square-root dependence on voltage for all measured
temperatures, as is predicted by the Equations 3.7 and 3.10 for very different
µe and µh . Furthermore, as the temperature decreases, the square-root part of
the Jph extends to larger voltages, since the difference between µe and µh be-
50
Chapter 3: Photocurrent generation in bulk heterojunction solar cells
2
[A/ m ]
(b)
295 K
ph
270 K
J
250 K
10
ph
10
J
2
[A/ m ]
(a)
1
V
sat
230 K
1
0.01
L=275 nm
T=210 K
210 K
0.1
0.1
1
V -V [V]
0
10
0.01
0.1
1
10
V -V [V]
0
Figure 3.7: (a) Temperature dependence of the photocurrent (symbols) in a 20:80 blend
of BEH1 BMB3 -PPV:PCBM versus effective applied voltage (V0 -V ) for a device of 275
nm thickness illuminated at an intensity of 800 W/m2 . The solid lines represent the
square-root dependence of the photocurrent Jph on effective voltage, used here as a guide
for the eye. (b) Incident light power (ILP) dependence of the photocurrent (Jph ) versus
the effective voltage (V0 -V ) measured at T =210 K. The solid (thick) lines represent the
calculated Jph from Equation 3.10 using µh =1.2×10−11 m2 /Vs, εr =2.6 and G∝ILP, where
ILP was varied from 800 to 60 W/m2 . The arrow indicates the voltage (Vsat ) at which
Jph shows the transition to the saturation regime.
comes larger. At even larger voltages (≈0.8 V at 295 K) the Jph shows a clear
transition to the saturation regime, where it becomes limited by the field- and
temperature dependence of the generation rate G(E, T ) (Equation 3.3). These
results are distinctly different than in the case of MDMO-PPV:PCBM blends,
where no square-root dependence of Jph is observed, as a result of the more balanced transport (see Section 3.1). The important question is whether Jph from
Figure 3.7(a) is limited by the space-charge (Equation 3.10) or by the mobilitylifetime product given by Equation 3.7. The unique test to distinguish between
the two processes is to investigate the dependence of Jph on G, since a different
dependence is predicted by Equations 3.7 and 3.10. A direct way to change the
amount of photogenerated charge carriers is to vary the light intensity. We have
demonstrated in the Section 3.1 that in the absence of SCL the Jph in reverse
bias is described by Jph =qG(E, T )L. Furthermore, for these non-SCL devices
Jph closely follows a linear dependence with light intensity [22, 23]. Combining
these two observations it follows that G is proportional with light intensity in
these type of devices. Therefore, the SCL photocurrent is expected to scale with
a 3/4 power dependence on light intensity (Equation 3.10).
Figure 3.7(b) shows the Jph -(V0 -V ) characteristics, of the same device from
Figure 3.7(a), as a function of incident light power (ILP), measured at 210 K. This
temperature was chosen because the Jph shows the largest square-root regime,
but the same effect is present also at room temperature. The ILP was varied from
800 W/m2 (upper curve) down to 60 W/m2 using a set of neutral density filters.
It appears from Figure 3.7(b) that the Jph shows weaker light intensity dependence in the square-root regime as compared with the saturation regime. Figure
51
3.2. Space-charge limitation in organic solar cells
3.8(a) shows, in the double logarithmic plot, the experimental Jph taken from
Figure 3.7(b) as a function of ILP for two different voltages, at V0 -V =0.1 V in the
square-root regime and at V0 -V =10 V in the saturation regime. The slope S determined from the linear fit (lines) to the experimental data amount to S=0.76 in
the square-root part and S=0.95 in the saturation part at high voltages. Furthermore, the SCL photocurrent predicted by Equation 3.10 is compared with the
square-root part of the experimental current in Figure 3.7(b) (solid lines). Note
that Equation 3.10 contains parameters as charge carrier mobility of the slowest
species (µh in this case), the relative dielectric permittivity εr of BEH1 BMB3 -PPV,
and the generation rate G of e-h pairs. Since µh was experimentally measured
(Figure 3.6) and εr of 2.6 was found from impedance spectroscopy experiments,
we can fit G at the highest light intensity. Using Equation 3.10 we can predict
the photocurrent at all other light intensities. As shown in Figure 3.7(b), the
predicted photocurrents (solid lines) are in excellent agreement with the experimental data. The 1/2 power dependence of Jph on voltage and 3/4 dependence
on ILP is a strong indication for the occurrence of a SCL photocurrent in this
materials system.
Another way to confirm the presence of a SCL photocurrent is to consider
the voltage Vsat at which Jph switches from the square-root dependence to the
saturation regime. This transition occurs when the hole accumulation region L1
becomes equal to the device thickness L. A schematic band diagram of this case
is shown in Figure 2.1(b). Thus the Equation 3.9 gives the value for Vsat to be:
Vsat = L2
8qG
9ǫ0 ǫr µh
1/2
.
(3.11)
From Equation 3.11 it appears that in case of a SCL photocurrent Vsat scales
with the square-root of light intensity. In contrast, in the absence of a spacecharge limit (Equation 3.7) the transition voltage will be independent on light
intensity [9]. In Figure 3.7(b) the voltage Vsat at which the transition occurs is
J
@V -V=10 V
J
@V -V=0.1 V
4
0
3
0
10
S = 0.95
2
S=0.53
J
V
ph
sat
10
[V]
ph
2
[A/ m ]
ph
1
S = 0.76
(a)
1
100
1000
2
Incid ent Light Power [W/ m ]
1
(b)
100
1000
2
Incid ent Light Power [W/ m ]
Figure 3.8: (a) Incident light power (ILP) dependence of the photocurrent Jph taken from
Figure 3.7(b) at an effective voltage of V0 -V =0.1 V and V0 -V =10 V (symbols). (b) Saturation voltage (Vsat ) versus ILP as determined for Figure 3.7(b). The slope (S) determined
from the linear fit (solid lines) to the experimental data is written on the figure.
52
Chapter 3: Photocurrent generation in bulk heterojunction solar cells
determined from the crossover point of the square-root dependence and the extrapolated saturation part, as indicated by the arrow. From Figure 3.7(b) it is
already demonstrated that Vsat shows a clear variation with light intensity. In
Figure 3.8(b) Vsat is plotted in double logarithmic scale as a function of ILP. A
slope S=0.51 is found, being in agreement with the space-charge limited prediction (of 0.5) from Equation 3.11. This is a further conformation that the photocurrent in 20:80 blends of BEH1 BMB3 -PPV:PCBM devices is truly limited by
space-charge effects.
3.2.4
Analytical prediction for the conversion efficiency
The SCL photocurrent is the maximum electrostatically allowed current that can
be generated into the external circuit of any solar cell. A Jph limited by spacecharge effect also has a strong impact on the power conversion efficiency of
this type of solar cells. For a photovoltaic device (Figure 3.7) the output power
density is given by P (V )=Jph (VOC -V ) · V , where VOC is the open-circuit voltage
(VOC ≈V0 ). For a device under space-charge limitation the Jph (VOC -V ) is given
by Equation 3.10. Thus P (V ) ∝ (VOC -V )1/2 · V , which reaches its maximum
(Pmax ) at V =Vmax =( 32 )VOC . Hence, from Equation 3.10 we obtain:
Pmax = qG3/4
9ǫ0 ǫr µh
8q
1/4
2
3/2
V .
33/2 OC
(3.12)
The fill factor (FF) of the photovoltaic cells is calculated from the ratio:
FF =
Jmax Vmax
× 100%,
JSC VOC
(3.13)
where Jmax Vmax =Pmax and JSC is the short-circuit current (applied voltage V =
0 V). Combining Equations 3.10 and 3.12 gives the maximum possible value of
the FF for a solar cell limited by the space-charge to be:
FF =
2
× 100% = 38.49%.
33/2
(3.14)
From Figure 3.7 and Equation 3.11 it is observed that Jph is limited by the buildup of space-charge for effective voltages V0 -V <Vsat , and is space-charge-free
for V0 -V ≥Vsat . The JSC of the solar cells is given at the effective voltage of V0 V ≈VOC (which is ≈0.8 V for the experimental data presented here). Thus, for
the Vsat >VOC , the JSC will fall into the space-charge limitation (square-root dependence on V ) and it will approach a 3/4 light intensity dependence (Equation
3.10). Consequently, the solar cell performance is fully limited by space-charge
effect (Equations 3.12 and 3.14). In order to reduce the effect of the space-charge
on device performance, the Vsat should be strongly reduced (Vsat −→0 V). From
Equation 3.11 it is observed that Vsat is mostly influenced by the film thickness
L and the light intensity (or G). A device could be space-charge-free under normal operation condition (1 Sun illumination), but become space-charge limited
at higher light intensity or in thicker films, as long as there is a difference between electron and hole mobility to build-up the space-charge accumulation.
3.3. Experimental section
53
Equations 3.12 and 3.14 qualitatively predict the maximum electrostatic allowed FF and power conversion efficiency (η=100%×Pmax /ILP) of any solar
cell limited by space-charge. It is important to note that for a quantitative analysis the effect of diffusion, recombination, field-dependent generation rate G(E)
and the effect of a non uniform electric field should be taken into account. For
example, as has been shown in this chapter, a linear dependence of Jph -(V0 -V )
characteristics is observed at very low effective voltages (close to V0 or VOC ) due
to diffusion. Such a linear dependence increases the maximum attainable FF of
the solar cell under space-charge limitation (Figure 3.7) to a value of approximatively 42%. A recent numerical model developed by Koster et al. incorporates
these processes and a quantitative fit to the experimental data can be given [18].
3.2.5
Conclusion
In this Section, we demonstrated the existence of a fundamental limit of the photocurrent in semiconductors. The photocurrent in 20:80 blends of BEH1 BMB3 PPV:PCBM solar cell devices reaches this electrostatic limit already under normal operational conditions (0.8 sun). The experimental photocurrents obey all
features characteristic for the space-charge limited regime: The photocurrent is
proportional with a 1/2 power dependence on voltage and a 3/4 power of light
intensity. Furthermore, the saturation voltage varies as the one-half power of
the light intensity. These results give further insight in the mechanism of photoconduction in semiconductors and are valuable for the design of new materials
in organic photovoltaic devices.
3.3 Experimental section
Materials: The material used were MDMO-PPV synthesized via the Gilchroute, PCBM (received from University of Groningen), a 25:75 random copolymer of poly[2,5-bis(2‘-ethylhexyloxy)-co-2,5-bis(2‘-methylbutyloxy)-1,4-phenylene vinylene] (BEH1 BMB3 -PPV; for molecular structure see Figure 2.14), PEDOT:PSS from Bayer AG (Baytron P VP Al 4083), LiF and Al from Aldrich. Glass
plates (3 cm × 3 cm) covered with ≈160 nm patterned ITO resulting in 4 different device areas (0.1, 0.15, 0.33, 1 cm2 ) were used for device preparation.
Device Preparation: The ITO covered glass substrates were wet-cleaned by
rubbing with soap, rinsing with water, and ultrasonic cleaning in acetone and
propanol. The substrates were further UV-ozone treated and a layer of PEDOT:PSS was subsequently spin-coated on the pre-cleaned ITO, using a Convac spin-coater. The PEDOT:PSS layer was dried at an elevated temperature.
The samples were then inserted into a glove box filled with nitrogen. An active layer was then spin-coated using a Karl Suss spin-coater following by the
evaporation of the metal top electrode which consist of a thin LiF (1 nm) layer
toped with Al (100 nm) to complete the devices. The active layer consist either
of a 20:80 weight percentage blend of MDMO-PPV:PCBM spin-coated from a
chlorobenzene solution (with a concentration of ≈3.3 mg PPV/mL), or by a 20:80
weight percentage blend of BEH1 BMB3 -PPV:PCBM spin-coated from a ortho-
54
Chapter 3: Photocurrent generation in bulk heterojunction solar cells
dichlorobenzene solution (with a concentration of ≈8.0 mg PPV/mL). In order
to determine the electron and hole mobility in blends of BEH1 BMB3 -PPV:PCBM
(Figure 3.6), the devices were prepared and characterized similar to that described in Section 5.5.
Device Characterization: All measurements were performed under a nitrogen atmosphere. J-V measurements were performed with a Keithley 2400
Sourcemeter. In forward bias ITO electrode was positively biased. The devices were illuminated at the transparent ITO electrode using a halogen lamp
with a spectral range of 400-850 nm calibrated using a Si diode. Light intensity
dependence was measured by varying the light power using a set of neutral
density filters with a constant optical density over the spectral range of the light
source. Subsequently, the resulting spectrum of each filter-lamp combination
was recorded and integrated over the absorption spectrum of the active layer,
which gives the intensity. Therefore, the generation rate (G) of electron-hole
pairs is proportional to the light intensity (G∝ILP).
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