Polymer: fullerene bulk heterojunction solar cells (Review article)

10 October 2011 The last ten years have seen an explosion of interest, both academic and industrial, in the application of π-conjugated molecular electronic materials to photovoltaic energy conversion. This interest has been driven both by a sharpening urgency to find affordable and…

10 October 2011

The last ten years have seen an explosion of interest, both academic and industrial, in the application of π-conjugated
molecular electronic materials to photovoltaic energy conversion. This interest has been driven both by a sharpening urgency to find affordable and low carbon sources of electricity, and unexpectedly rapid progress in the field of organic, or “plastic”, electronics generally.

The primary motivation behind the use of molecular, or organic, semiconductors in photovoltaics is the prospect of high throughput module manufacture by printing or coating from solution in a continuous process. Such low cost manufacture techniques together with the low quantities of organic semiconductor required could reduce the cost of modules to less than 1 €/Wp (Watts peak)1 and thereby accelerate the take-up of photovoltaic electricity generation, displacing carbon intensive sources. The inherent light weight, flexibility, and potential to tune the color and transparency of organic photovoltaics (OPV) are attractive attributes for the integration of PV into building components or other appliances. Moreover, the low embedded energy The efficiency of solar cells made from a conjugated polymer blended with a fullerene derivative has risen from around 1 % to over 9 % in the last ten years, making organic photovoltaic technology a viable contender for commercialization. The efficiency increases have resulted from the development of new materials with lower optical gaps, new polymer:fullerene combinations with higher charge separated state energies, and new approaches to control the blend microstructure, all driven by a qualitative understanding of the principles governing organic solar cell operation. In parallel, a device physics framework has been developed that enables the rational design of device structures and materials for improved organic photovoltaic devices. We review developments in both materials science and device physics for organic photovoltaics.

Jenny Nelson
Department of Physics and Centre for Plastic Electronics, Imperial College London, London SW7 2AZ, UK, and
Freiburg Institute for Advanced Studies, University of Freiburg, D-79104 Freiburg, Germany
E-Mail: jenny.nelson@imperial.ac.uk

The last ten years have seen an explosion of interest, both academic and industrial, in the application of π-conjugated molecular electronic materials to photovoltaic energy conversion.  This interest has been driven both by a sharpening urgency to find  affordable and low carbon sources of electricity, and unexpectedly  rapid progress in the field of organic, or “plastic”, electronics generally.

Early attempts to use molecular electronic materials in photovoltaics used an organic semiconductor as a direct replacement for the inorganic semiconductor in a conventional solar cell, and led to poor performance. This first promising approach was a heterojunction that contained two different organic semiconductor layers, one of which had a stronger affinity for electrons and the other for holes3. As explained in the next section, a heterojunction is necessary to separate the light generated excitons. Further work on solution processable conjugated polymers showed that a distributed or “bulk” heterojunction could be made by casting a layer from a mixture of two different polymers, or a polymer and a soluble fullerene molecule, in solution, and that such a heterojunction was effective at generating a photocurrent4,5 . Effective bulk heterojunction devices were made from blends of polymers with other small molecule, inorganic semiconductor nanoparticle, or metal oxide acceptors, and from evaporated small molecule combinations6 , but most research has focused on polymer:fullerene combinations. Key advances continued through the last decade, with the discovery of performance improvements resulting from the choice of  solvent7, use of a self ordering polymer8, processing treatments such as thermal annealing9, better matching of electrodes to organic layers10 , lower band gap polymers11, alternative acceptors12 , and higher ionization potential polymers13 , resulting in present day efficiency records of 8.3 % (certified)14 and over 9 % (uncertified)15. A wide range of material systems have been explored for OPV including solution processed polymer:acceptor systems, where the acceptor component may be a polymer, fullerene, soluble small molecule, inorganic semiconductor nanoparticle, or metal oxide. During the last five years, an increasing number of companies have become engaged in the development of OPV technology and materials1 , while academic research has burgeoned, with increasing attention paid to both fundamental and industrial issues. This review will provide a brief summary of the OPV concept and then review recent developments in the science of organic photovoltaic materials and devices over the last five years, focusing on the widely studied polymer:fullerene material system. Due to space limitations we do not address other material combinations, issues related to processing and production or the development of experimental probes of OPV materials. Earlier reviews of OPV device concepts and materials issues can be found in16,17 and a review of processing issues can be found in18.

Organic photovoltaic materials and devices
Organic semiconductors are carbon based molecular materials,
including both polymers of molecular weight 10 – 100 kDa and
“small” molecules of molecular weight of 100 – 1000, based around
a backbone of sp2
hybridized carbon atoms. Electronic interactions
between pz
orbitals on neighboring C atoms constitute a π electronic
system, with orbitals delocalized over conjugated segments several
nanometers in size. The energy gap between the highest of the filled
π orbitals, known as the highest occupied molecular orbital or HOMO,
and the lowest unoccupied molecular orbital or LUMO is typically in
the range 1 – 3 eV, much smaller than the gap between filled and
unfilled levels in a saturated (not π conjugated) carbon based molecule,
and, importantly, accessible to visible light. The delocalization of the
π orbitals means that charges, which may be generated electrically
or optically, are weakly bound and free to travel along and between
molecules by a hopping process. The disorder in molecular packing also
means that the energies of electronic states on different molecules
may be different, leading to a distribution in the HOMO and LUMO
energies. The states with the lowest lying LUMO energies and highest
lying HOMO energies may act as charge traps. As a result of both
the weak electronic interaction between conjugated segments and
the charge traps, the resulting charge mobilities are in the range
10-6
to 1 cm2
/Vs and much lower than those found in crystalline
inorganic semiconductors.
For photovoltaic applications, the most important feature that
distinguishes organic from inorganic semiconductors is the fact that
excited states are localized. When a photon is absorbed by an organic
semiconductor it generates a neutral excited state or exciton that
is localized on a single molecule or a single conjugated segment, so
within a volume of a few nm3
. This spatial confinement, together with
the low dielectric permittivity (ε ≈ 3 – 4) of organic semiconductors
makes it difficult for the exciton to dissociate into a separated electron
and hole, since the Coulomb energy binding such localized charges is
high (~1 eV) compared to kB
T. In comparison, the exciton in a crystal
of silicon has a diameter of tens of nm and a binding energy of around
0.1 eV, allowing charge pairs to be generated spontaneously at room
temperature. As a result, the exciton in an organic semiconductor tends
not to dissociate into charges but rather to decay to the ground state
within a few ns, sometimes releasing light. In organic solar cells and
photodiodes, this problem is solved by introducing a second molecular
component (the electron acceptor) that has a higher affinity for
electrons, such as a fullerene. Then when an exciton is photogenerated
within the first, donor phase but close to this second type of molecule,
the electron is attracted to the higher affinity molecule by the free
energy difference, and the lost exciton binding energy is provided by
the difference in free energies ΔG between the exciton and the charge
separated state, Fig. 1.
Once the charges are located on different types of molecule, the
electron on an acceptor molecule and the hole remaining on a donor
molecule, the charges at first form a geminate pair in which they
are held by Coulombic forces. Once this pair is separated, the two
types of charge may travel through the respective phase, and may
be collected when they encounter a low resistance contact to the
external circuit. This requires that the two phases percolate through
the medium.
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The requirements for photocurrent and photovoltage generation in
an organic donor-acceptor device are thus as follows:
• Visible light must be absorbed in the donor or acceptor material or
both.
• The width of domains of pure donor or acceptor material should
be shorter than the distance an exciton diffuses before decaying
(< ~10 nm), in order for most photogenerated excitons to dissociate,
i.e., the two components should be sufficiently well mixed.
• Both phases should form continuous percolating networks that
connect the bulk of the film to the electrodes.
• The electrodes should be electronically different, such that electrons
are preferentially collected at one and holes at the other, in order
to provide a direction for the photocurrent. Such selectivity can be
achieved using one high and one low work function electrode.
A typical device has the layer structure (Fig. 2):
Glass / indium tin oxide (ITO) / polyethylenedioxythiophene:
polystyrene sulphonate (PEDOT:PSS) / photoactive blend layer /
cathode interlayer (such as Ca or LiF / Al)
where the PEDOT:PSS is a doped conducting polymer that is used to
raise the work function of the bottom electrode in order to accept
holes, and the cathode interlayer (usually a low work function metal)
is used to lower the work function of the top electrode to accept
electrons. The photoactive layer is typically 100 – 200 nm thick while
other layers are some 50 – 100 nm. The same layer structure may
be deposited on a transparent flexible substrate such as polyethylene
terephthalate (PET) instead of glass. A similar structure with inverted
polarity such as:
Glass / ITO / metal oxide / photoactive blend layer / PEDOT:PSS / Ag
is now being widely studied, mainly for the reason that no evaporated
metal layers are required. A low work function metal oxide such as
TiO2
or ZnO can be cast from solution and the top silver contact can
be applied as a paste, allowing for production in a roll to roll process18
.
A typical current voltage characteristic of the best studied variety
of organic solar cell, a blend of poly-3-hexylthiophene (p3HT) and the
fullerene derivative [6,6]phenyl C61 butyric acid methyl ester (PCBM)
is shown in Fig. 3 (b) (black line), together with data for higher
performing materials systems. In comparison with inorganic solar cells,
OPV devices show a lower circuit current density (J
sc
) and fill factor
(FF) than inorganic devices while open circuit voltage (Voc
) values are
comparable to those of inorganic solar cells. However, in comparison
to inorganic PV cells, the value of e·Voc
(where e is electronic charge)
is lower than the optical energy gap of the light absorbing materials by
a larger margin, indicating that more of the electrochemical potential
generated by the light is lost.
The differences in comparison with inorganic solar cells can be
rationalized in terms of the properties of organic semiconductor
materials. In the case of J
sc
, the lower value in OPV is mainly due to
the larger optical gap of the organic semiconductors used, typically
1.5 to 2 eV compared to 1.1 eV for silicon. Thus there is a need for
stable organic semiconductors with light absorption further into the
infrared, however, it should be stressed that the optimum energy gap in
the standard solar spectrum is larger for a heterojunction solar cell than
for a homojunction such as silicon, because some energy has to be paid
for charge separation. In addition, the value of J
sc
in OPV is strongly
influenced by optical interference effects in the thin multilayered
structure.
Fill factor is controlled largely by the changing competition
between photocurrent generation and charge recombination as
Fig. 1 (a) Schematic energy level diagram of the heterojunction between
the electron donor and electron acceptor in an organic solar cell. A photon
absorbed in the donor promotes an electron to the donor LUMO level.
That electron may then transfer to the acceptor LUMO, and then away
from the junction by hopping. The nominal driving force is the difference
in LUMO energies, ΔE
e
. (b) State diagram showing the total energy of the
states involved in charge pair generation. From left to right, donor (singlet
and triplet states), acceptor (singlet and triplet), geminate pair, charge
separated state. The lower panel depicts the spatial evolution of the states at
the heterojunction. Red arrows show the processes leading to photocurrent
generation. Blue arrows show the loss processes of excited state decay,
geminate recombination, and non-geminate recombination.
(a)
(b)
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Fig. 2 Layer structure of an organic solar cell in the traditional (a) and inverted (b) polarity. (c) Schematic of the layers in an OPV module on a flexible substrate. (d)
Image of the microstructure within the active layer, obtained with electron tomography. Reprinted with permission from19
. © 2009 American Chemical Society.
Fig. 3 (a) Evolution of the record efficiencies of polymer:fullerene solar cells23
. (b) Device current density – voltage characteristics for the well studied P3HT:PCBM
system (black line) and several superior material combinations: P3HT with the bis adduct of PCBM12
(red curve); 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):PC70BM24
(orange curve); poly[N-9-hepta-decanyl-2,7-carbazole-alt-5,5-(4,7-di-2-thienyl-
2,1,3-benzothiadiazole) (PCDTBT):PC70BM13
(blue curve); and Poly[[4,8-bis[(2-ethylhexyl)oxy]benzo[1,2-b:4,5-b’]dithiophene-2,6-diyl][3-fluoro-2-[(2-ethylhexyl)
carbonyl]thieno[3,4-b]thiophenediyl]] (PTB7):PC70BM25
. Also shown are the Voc
and J
sc
of the most efficient certified organic solar cell14
.
(a) (b)
(c) (d)
(a)
(b)
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the bias between the electrodes varies. Recombination processes
are commonly distinguished as geminate and non-geminate (also
referred to as “bimolecular”). Geminate recombination refers to the
recombination of nascent charge pairs soon after (within ~100 ns)
exciton dissociation. It is an issue unique to OPV devices that results
from the difficulty of separating dissociated charges and it may be
assisted by an electric field, leading to a dependence on applied bias.
Non-geminate recombination refers to the recombination of separated
charges and is important in OPV because the low charge mobilities
and interpenetrating phases mean that opposite charges are likely to
encounter each other before they escape through the electrodes. For
both geminate and bimolecular processes, the competition between
charge generation or collection and recombination is influenced by the
internal microstructure of the blend.
Although Voc
is limited by the energy levels of separated charges,
i.e., the HOMO of the donor and LUMO of the acceptor, Voc
and FF
can both also be limited by imperfect contacts with the electrodes,
for example, due to poor energetic matching or resistive interfacial
layers10,20
. This affects OPV in particular because conjugated polymers
cannot readily be doped, and so the electrochemical potential at the
electrode is influenced by the electrode work function and the degree
of charge transfer with the organic semiconductor, rather than only by
the semiconductor HOMO and LUMO energies.
These features have led to some common goals in the development
of new materials for OPV, namely:
• A lower polymer optical gap to raise J
sc
.
• Higher ionization potential donors and lower electron affinity
acceptors to raise Voc
and reduce the energy loss during charge
separation.
• Self organizing materials with the capability to control blend
microstructure.
• The development of electrode materials with work function
matched to the new semiconductors as well as transparency and
conductivity.
These themes have been the focus of intense research and have led to
a steady series of efficiency increases, Fig. 3. They will be discussed in
the next section.
A separate goal has been the development of efficient OPV tandem
devices where two or more bulk heterojunction cells with different
optical gaps are integrated into a vertical device structure. Tandems
offer to raise efficiency by converting more of the absorbed photon
energy into useful work and can, in principle, be made using the
same multiple layer solution processing techniques used for single
junction OPV devices21
. The relative ease of depositing multiple layers
successively in a continuous process makes tandem structures very
accessible for organic semiconductors22
. Although we have no space to
review developments in OPV tandems here, we stress that an efficient
tandem device is built on efficient component cells, and the principles
described here for development of OPV materials and devices are
equally relevant for tandems.
Progress in design, synthesis, and control of
materials
Low optical gap materials
A number of strategies have been pursued in order to extend the
absorption range of donor polymers for OPV. These include strategies
aimed at extending the conjugation length of the π-conjugated
segments, for example, by replacing phenyl rings with thiophene rings
that help to planarize the polymer backbone through a reduced steric
effect or by planarizing neighboring monomers by using a bridging
atom24
. Planarization may reduce optical gap further by enabling
π-stacked aggregates to form26
. An alternative approach is to vary the
heteroatoms in the conjugated backbone: replacing the sulphur atom
in polythiophene with selenium leads to a lowered LUMO energy but
unchanged HOMO, due to the influence of the heteroatom on the
LUMO in this molecule27
. A third route, which is now widely used,
is to combine electron rich (e.g., thiophene containing) and electron
poor (e.g., benzothiadiazole [BT]) units in the polymer backbone in a
so called ‘push-pull’ structure. Here, the HOMO of the copolymer is
dominated by the HOMO of the electron deficient unit and the LUMO
by that of the electron rich unit. The strategy is widely adopted, due
to the large range of ‘push’ and ‘pull’ units that can be used and the
ability to control copolymer HOMO and LUMO energies independently.
Notable advances in OPV efficiency were made using push-pull
copolymers based on dithiophene – BT structures24,28
, carbazole – BT
structures13
, and dithienobenzene – modified BT structures25
and
diketopyrrolopyrrole – thiophene structures29
, Fig. 4.
Fig. 4 (a) Chemical structures of the backbones of the polymers, P3HT,
PCPDTBT, PCDTBT, PTB7 and a DPP-co-thienothiophene polymer. Side chains
are omitted for clarity. (b) Chemical structures of the fullerenes, PCBM and its
bis adduct and tris adducts, and a bis adduct of the indene fullerene (ICBA).
(a) (b)
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In the case of fullerenes, optical absorption in the visible is weak on
account of the high symmetry of the C60 cage and resulting symmetry
forbidden optical transitions. Here, optical absorption can be enhanced
by replacing the symmetric C60 cage with one of lower symmetry such
as C70. This leads to strong blue-green absorption by C70 fullerenes
and for this reason they are routinely used with low gap polymers to
complement the polymer absorption and span the visible spectrum.
Higher IP polymers and lower EA acceptors
The push-pull copolymer approach is also used to design polymers
with lowered HOMO energy in order to increase device Voc
, since
it allows control of the polymer HOMO and LUMO separately. There
is also some evidence that push-pull polymers may allow charge pair
separation at a lower value of ΔG than other classes of polymers30
.
Other approaches to push down the polymer HOMO include
substitution of bridging carbon atoms by the more electronegative
silicon31
and building torsion into the polymer backbone, although the
latter has the negative effect of increasing the optical gap.
An elegant route to higher Voc
is offered by reducing the fullerene
electron affinity by adding more side chains to derivatives such as
PCBM32
, the indenefullerene33
and also to metal hydride occupied
endohedral fullerenes34
(Fig. 4). The approach works beautifully with
the crystalline polymer P3HT but has not as yet succeeded with any
amorphous polymer. The reasons are thought to include the inferior
microstructure, and consequently transport, formed by the amorphous
fullerene adduct as well as a possible effect on charge generation due
to the reduced ΔG35
.
Control of blend microstructure
For efficient photocurrent generation the ideal polymer:fullerene
blend film should offer a sufficiently fine mixing of the phases
so that exciton dissociation is achieved, and a high degree of
molecular ordering and connectivity within the donor and acceptor
phases, as this aids charge transport. In addition, a certain degree
of phase segregation assists both the competition between charge
collection and recombination36
and the competition between charge
separation and geminate recombination. Ideally, the size of domains
should be comparable to the length over which excitons diffuse,
which is typically between some few nm (P3HT) and 10 nm for
polymers37,38
, though several tens of nm have been reported for
crystalline molecular semiconductors39
. Regarding the competition
between generation and recombination, a number of studies40,41
have shown that charge separation yield increases when at least one
of the phases is crystalline/well ordered, possibly due to the greater
delocalization of electronic states and lower resulting Coulombic
binding energy.
In practice the structure of a blend film cast from a single solution
is sensitive to many factors (solvent, casting method, temperature,
self organizing properties of materials, interaction between donor
and acceptor, any additives) and therefore hard to control. Strategies
used to control microstructure include building in a structural motif
to encourage self organization of polymer chains, as with regioregular
P3HT42
, and the use of processing additives28
or thermal annealing
regimes28,42
that control the solidification dynamics. The degree of
segregation or intermixing is strongly dependent upon the polymer
structure, in particular, upon the possibility of fullerene intercalation
between polymer chains either because of their amorphous chain
packing43
or because sufficiently wide side chain spacing permits
fullerene intercalation44
. Study of the phase behavior of the binary can
help to define the conditions in which a preferred blend microstructure
will be realized45
. All blend approaches lead to thermodynamically
unstable structures with the risk of disintegration of phases over time
or exposure to heat46
. Structures with better defined phase behavior
can be realized using multiblock copolymers where the length of
the blocks in the polymer backbone determine the domain sizes in
the blend film, although efficiencies have not yet surpassed those of
polymer:fullerene blend devices47,48
. Although not the subject of this
review, organic/inorganic hybrid structures are a promising route to the
control of microstructure, since a rigid and stable inorganic framework
can be built49,50
.
As well as control of three-dimensional phase structure, it is
desirable to control the vertical segregation of phases within the blend
film, since this may assist in electrode selectivity and in directing the
photocurrent. Approaches include the choice of electrodes combined
with post deposition processing51,52
and methods to apply different
successive layers from solution53,54
.
The complexity of blend film microstructure and the difficulty of
determining structure at nm length scales has led to a huge amount
of research into microscopic and combined microscopic/spectroscopic
structural probes including AFM, TEM, XRD, SE, Raman, and PET. These
are reviewed in26,55
.
Electrode materials
The development of new photoactive materials has been accompanied
by growing research into new electrode and interlayer materials. This
has been motivated partly by the need to find electrodes of higher
or lower work function in order to achieve Ohmic contacts with new
photoactive materials of higher lying LUMO or lower lying HOMO
energy, but also by the search for transparent conductive layers of
lower cost and embedded energy than the widely used indium tin
oxide, and by the search for more stable substitutes for reactive
cathode metals. Alternative electrode interlayers studied in OPV
include high work function oxides such as NiO10
, WO3
, MoO3
56
, stable
low work function oxides such as TiO2
, ZnO57,58
, polymer interlayers59
and organic conducting layers such as high conductivity PEDOT60
vapor
phase polymerized PEDOT61
, carbon nanotube62
, and metal nanowire
based layers. Solution processable oxide layers and conducting polymer
layers are preferred for large scale processing.
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As well as the goal of higher efficiency, the development of
new photoactive and electrode materials has been driven by the
requirement for longer device lifetimes. Particular objectives are the
design and development of organic semiconductors with improved
photochemical stability63
, blend formulations with greater robustness
under heating46
, and electrode materials with higher electrochemical
stability64,65
. Issues related to the degradation and stability of polymer
based solar cells are reviewed in66
.
Progress in device physics
The strategies for materials development mentioned above are largely
empirical. One of the major obstacles in developing OPV technology
has been the absence of a modeling framework that can relate
device performance to physical and chemical structure in a predictive
way. The challenge is greater than in conventional PV first because
of the huge diversity of possible materials and modes of material
organization and secondly because of the particular properties of
organic semiconductors (localization, disorder, heterogeneity). We may
distinguish two main challenges. The first is to simulate device current
density – voltage (J-V) characteristics from relevant optoelectronic
properties of materials. This requires finding an appropriate formulation
of the current, generation, and recombination terms in the electron
continuity equation that governs steady state device behavior:
1

e
∇.
J = G – R (1)
where J is photocurrent density, G the volume rate of charge
generation and R the volume rate of recombination, and of correctly
relating charge density to potential on the electrodes. The second
challenge is to relate the material optoelectronic properties to the
chemical structure of the materials in a quantitative way.
Models of device current-voltage behavior
Early approaches to OPV device modeling built upon the device physics
of conventional solar cells. A useful approach from Schilinsky et al. was
based on a modified ideal diode equation, where photocurrent is limited
by lifetime, and used empirical values for material properties67
. Later
approaches used a continuum model to solve the drift diffusion and
continuity equations for an effective medium possessing the HOMO of the
donor material and LUMO of the acceptor68-70
. In these models, charge
generation G is typically calculated with an optical model incorporating
measured optical properties of the materials, the transport terms in
J are linear in charge density, often using measured mobilities, and
recombination is modeled by the second order Langevin process such that
R =
e(

μ
—e

+
ε

μp
)
— np (2)
where μ
e
, μh
represent the electron and hole mobilities, n and p the
electron and hole densities and ε the dielectric permittivity. Two of the
direct consequences of such a bimolecular recombination process are,
first, that low charge mobilities will increase losses to recombination
and, secondly, that that the electron and hole mobilities in the device
should be reasonably well balanced in order to minimize recombination
losses for a given photogenerated charge density. However, such an
approach is unable to reproduce dark and light JV curves at the same
time71
and consequently unable to explain the low fill factor of OPV
devices.
Two explanations have been advanced for the low fill factor of
OPV devices, (i) that the net charge generation rate is dependent upon
applied bias72,73
, and (ii) that the rate of charge recombination depends
more strongly on charge carrier density than implied by equation 274
.
The field dependent generation argument is based on the Onsager
theory of dissociation as used by Braun72
. Here, charge generation
is modeled in terms of competition between the decay and field
dependent dissociation of photogenerated geminate pairs75
. Evidence
for field dependent generation yield remains controversial with
some time resolved spectroscopic studies showing field dependent76
and some field independent77
kinetics. In numerical models, this
field dependent geminate recombination process is folded into G.
Experimental results suggest that geminate pair survival depends, in
principle, upon the energetic line-up and the local molecular ordering
as well as electric field40,41
. However those effects are not yet
understood quantitatively.
Regarding the second point, the order of charge recombination
is important because of the low mobilities of charge carriers in
organic semiconductors. Here, experimental measurements by
several groups78-80
have shown that for P3HT:PCBM based solar
cells R depends on charge density to a higher power than 2, R ∝ nα
with α typically around 3. This can be related to the charge density
dependence of charge mobility in energetically disordered organic
semiconductors that results from the filling of low lying (trap)
charge states. When the non linear effects of charge trapping and
recombination via traps states are included in numerical models71,81
the models could explain the fill factor of P3HT:PCBM photovoltaic
devices71,81
(Fig. 5a) and also the voltage dependence of the
photocurrent and dark current71
. For other material systems a bias
dependent generation rate may also be needed. The effect of the
distribution of HOMO and LUMO energies on the electrochemical
potentials of the charge carrier populations at the respective electrodes,
and hence the output voltage, has also been simulated82
. These recent
developments indicate that key OPV performance characteristics can
be related quantitatively to the materials’ electronic properties.
In general the magnitude as well as the order of recombination has
to be modified for a bulk heterojunction, because phase segregation
tends to slow down the rate at which charges meet each other. This
effect is observed most clearly in P3HT:PCBM blend systems where
after thermal annealing the recombination is two to three orders of
magnitude slower than Langevin83,84
. Whilst this factor is expected
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to be greater for crystalline polymers that force phase segregation, it
cannot yet be quantitatively related to the properties of the materials
used.
Microscopic structure – property
relationships
The material parameters that are relevant for calculation of the solar
cell current voltage response thus include: (i) the optical gap; (ii) the
factors (ΔG, domain size, ordering, and electric field) that influence
charge separation; (iii) the blend film microstructure, in terms of
phase segregation and local ordering, which influences mobility and
recombination; (iv) the density of states of the materials, which
again influences the mobility and recombination rate, as well as the
dependence of output voltage on charge density. Although there is
as yet no agreed route to predicting these properties from chemical
structure, much progress has been made in developing methods.
The HOMO and LUMO energies that control the optical gaps of
the donor and acceptor and the driving force for charge separation
can be calculated fairly well using quantum chemical calculations of
polymers11,85
and fullerenes86
(Fig. 5b). However, the driving force may
differ from the value expected from the HOMO and LUMO energies as
a result of interfacial dipoles87
.
In simulating transport phenomena (mobility and transport limited
recombination) a combination of methods must be used. Starting
with the chemical structures, molecular dynamics simulations using
appropriate force fields can be used to simulate the structures
formed by assemblies of molecules88-90
(Fig. 5c). Transport can then
be simulated as the hopping of charges between conjugated units
on representative molecular assemblies, where the intermolecular
charge transfer rates are calculated quantum chemically and the
overall mobility is estimated from Monte Carlo or Master Equation
simulations91,92
. These approaches have yielded good qualitative and
quantitative agreement with experiment for several systems. Similar
methods could be applied to model transport limited recombination
and so to extract recombination parameters83
and to simulate exciton
diffusion93
. Whilst combined molecular modeling and quantum
chemical calculations are effective at reproducing the effects of disorder
on charge dynamics, they seldom reproduce the correct magnitude
of energetic disorder94
. No consensus exists on how to calculate the
density of states in OPV films, although large scale computation95
and
tight binding models96
have been proposed for P3HT.
Most of the tools are in place to simulate the properties and
response of OPV devices from knowledge of the chemical structures of
the materials, and we expect to see significant advances in the next few
years in method development, explanation of new material systems
and the development of design rules for new materials. The biggest
remaining conceptual challenge is to find an appropriate physical
model for charge separation. It is still unclear why the photogenerated
charge pairs separate with high efficiency in spite of a large Coulmbic
interaction energy. Among the explanations proposed for this are the
role of electric field75
, the role of vibrationally hot excited states97,98
and the effect of charge delocalization over extended domains40,99
.
There may also be a positive effect of intrachain polarization in
the case of push-pull polymers30
. A better understanding of the
charge separation process will involve further study of the role of
charge transfer states, interfacial states that are involved in pair
formation100,101
and voltage generation102
.
Conclusions
The last ten years have seen OPV develop from a scientific curiosity
with device efficiencies of around 1 % to a thriving area of research
and development with device performance competing with established
thin film technologies and substantial industrial involvement.
The improvements in performance can be assigned, first, to the
development of new organic semiconductor materials specifically for
use in OPV, based on largely empirical design principles, and second,
to the development of an appropriate device physics framework
enabling the first rational approaches to the design of device structures
and the choice of suitable materials. Power conversion efficiencies
look set to exceed 10 % within the next year. For significant uptake
of OPV technology, future efforts must address the design of more
stable materials, design of materials compatible with large volume
processing, environmentally benign and low cost production processes,
and development of system components and integration schemes that
exploit the light weight and flexibility of OPV materials to reduce the
overall cost of, and so increase access to, solar electricity.
Fig. 5 (a) Current-voltage characteristics simulated with a numerical model
that includes exponential tails of traps states for electrons and holes. Reprinted
with permission from81
. © 2011 American Chemical Society. The diagram
illustrates the distribution of states. (b) HOMO and LUMO orbitals of PCPDTBT
calculated using density functional theory. For this, and other, push-pull
polymers the LUMO is localized on the electron rich unit in the polymer
backbone30
. (c) A realization of the structure formed by P3HT chains and PCBM
molecules, simulated using molecular dynamics.
(a)
(b) (c)
MT1410p462_471.indd 469 21/09/2011 12:55:43REVIEW Polymer:fullerene bulk heterojunction solar cells
4 7 0 OCTOBER 2011 | VOLUME 14 | NUMBER 10

 

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Acknowledgements
I am grateful to Jarvist Frost, Thomas Kirchartz, James Kirkpatrick, and Rod MacKenzie for useful discussions, and to Jarvist Frost for help with the figures. I would like to acknowledge the support of the Royal Society through an Industry Fellowship and the support of the Freiburg Institute for Advanced Studies through a visiting fellowship. MT1410p462_471.indd 470 21/09/2011 12:55:44