A R T I C L E S
Perez et al.
1).7-14 However, under normal operating conditions (i.e., room
temperature and 1 sun intensity illumination) the experimental
values for Voc can differ from those inferred from ∆EDA for
some materials systems. This disparity is a result of the
electronic properties of the donor, acceptor and the D/A
interface. A more thorough understanding of molecular materials
properties that influence Voc is important to develop new OPV
materials that lead to a high Voc.
Here, we identify a correspondence between molecular
composition and crystal morphology and the open circuit voltage
in small-molecule-based OPVs. Data are presented for several
OPVs in which different donor materials are used along with a
common acceptor (i.e., C60) to highlight the most important
factors governing this relationship.
JSC
JS
nkT
q
Voc
≈
ln
(3)
(
)
Hence, at a given JSC a low dark current (JS) results in a
high Voc. Insight can be gained by examining the origin of JS,
which is the current resulting from carriers generated thermally
at the D/A interface, or originating within the film bulk. The
saturation current due to interface charge generation has been
shown to vary exponentially with ∆EDA, which is represented
by eq 4 for systems where JS is dominated by recombination
(n ≈ 2), as observed for most OPVs.7,15,16,19
-∆EDA
2nkT
JS ) JSO exp
(4)
(
)
Physical Origin of the Open Circuit Voltage
The factor of 2 accounts for the thermal generation of both an
electron and hole at the D/A heterointerface, giving an activation
energy of ∆EDA/2 for the process. The magnitude of JSO depends
on a number of materials properties that determine the carrier
generation/recombination rate, independent of the energy barrier,
∆EDA. Materials properties affecting the magnitude of JSO
include the reorganization energy for DfA electron transfer,
the intermolecular overlap at the D/A interface, the layer
electrical conductivities, the area of the D/A interface, and the
density of states at the HOMO and LUMO energies of the D
and A materials.
The generalized Shockley equation, eq 1,15,16 describes the
current density (J) vs voltage characteristics of organic solar
cells:
Rp
q(V - JRs)
V
Rp
J )
J exp
- 1 +
- Jph(V)
(
)
s
[
]
{
}
Rs + Rp
nkT
(1)
Here, Rp is the parallel resistance, JS is the saturation current
density, q is the fundamental charge, n is the diode ideality
factor, and Jph(V) is the voltage-dependent photocurrent density.
For solar cells with minimal leakage current (Rp . Rs), eq 1
can be simplified to
Substitution of eq 4 into eq 3 yields
JSC
JSO
∆EDA
2q
nkT
q
Voc
)
ln
+
(5)
(
)
q(V - JRs)
J ) J exp
- 1 - J (V)
(2)
(
)
Equation 5 suggests a linear dependence of Voc on the
interface energy gap and a logarithmic dependence on JSC and
light intensity (JSC ∝ P0), as experimentally observed for both
bulk heterojunctions3,20,21 and lamellar OPVs.7,22,23 A linear
correlation of Voc to ∆EDA has been reported previously for
several materials systems.7,13,14 Here, ∆EDA is the thermal
activation energy for charge separation at the D/A interface,
such that at low temperatures the measured Voc approaches
∆EDA/2, as recently reported by Rand, et al. for vapor deposited
OPVs.7 Note that eq 5 is similar to, but with important physical
implications different from that recently reported by Potscavage,
et al.24 The equation reported in their publication has two
different ideality factors (n and n′) and suggests a scaling of
Voc by ∆EDA/q, rather than ∆EDA/2q, in contrast to what has
been observed experimentally. In addition, Potscavage, et al.,
have assumed that JSO is constant for different D/A pairs, which
is inconsistent with the data presented below.
S
[
]
ph
nkT
The first term describes the thermally generated current that is
typically dominated by recombination at the D/A interface, and
the second term accounts for photogenerated carriers, Jph(V).
Under open circuit conditions (J ) 0, V ) Voc), the rate of carrier
recombination equals the rate of optical carrier generation.
Assuming open circuit conditions, a short circuit current of JSC
) Jph(0) . JS, and a low series resistance, eq 2 can be solved
to give eq 3, in which Voc is given by7,17,18
(8) Brabec, C. J.; Cravino, A.; Meissner, D.; Sariciftci, N. S.; Fromherz,
T.; Rispens, M. T.; Sanchez, L.; Hummelen, J. C. AdV. Funct. Mater.
2001, 11, 374–380.
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W. J. H.; Kroon, J. M.; Hummelen, J. C. Org. Lett. 2007, 9, 551–
554.
In this work, we study the relationship of various materials
combinations to Voc as expressed by eq 5. In particular, we
explore the role of JSO in controlling the Voc, and what molecular
properties affect the magnitude of JSO. The intermolecular
overlap in the donor and acceptor layers and at the D/A interface,
(11) Mutolo, K. L.; Mayo, E. I.; Rand, B. P.; Forrest, S. R.; Thompson,
M. E. J. Am. Chem. Soc. 2006, 128, 8108–8109.
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