The essence and efficiency limits of bulk-heterostructure organic solar cells: A polymer-to-panel perspective

INVITED FEATURE PAPERS

Articles

The essence and efficiency limits of bulk-heterostructure organicsolar cells: A polymer-to-panel perspective

Muhammad A. Alam,a) Biwajit Ray, Mohammad Ryyan Khan, and Sourabh DongaonkarSchool of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47906

(Received 7 May 2012; accepted 5 December 2012)

Bulk-heterojunction organic photovoltaic (BHJ-OPV) technology promises high efficiency atultralow cost and weight, with potential for nontraditional applications such as building-integratedphotovoltaic (PV). There is a widespread presumption that the complexity of morphology makescarrier transport in OPV irreducibly complicated and, possibly, beyond predictive modeling.However, understanding the complex morphology is important because it not only dictates cellefficiency but also the panel performance and the operating lifetime. In this paper, we derive thefundamental thermodynamic as well as morphology-specific practical limits of BHJ-OPVefficiency and lifetime. We find that performance improvement relies not only on morphologyengineering but also on increasing the effective mobility–lifetime (ls) product, the cross-gapbetween donor/acceptors, and reducing the series resistance. Even if the OPV fails to achieve thehighest efficiency anticipated by the thermodynamic limit, its novel form factor, lightweight, andtransparency can make it a commercially viable option for many applications.

I. INTRODUCTION AND BACKGROUND

A bulk-heterojunction organic photovoltaic (BHJ-OPV)solar cell1–5 consists of two demixed, phase-segregated,bicontinuous, donor–acceptor organic semiconductors cap-ped by a transparent anode and ametallic cathode, see Fig. 1.Although a wide variety of organic semiconductors5–7

have been analyzed, we will consider hole-conductingP3HT and electron-conducting PCBM [red and blueregions in Fig. 1(a)] as an illustrative example8–11 andexplore how the fundamental physical properties of poly-mers translate to ultimate panel efficiency reported in theliterature. The operation of BHJ-OPV is often explained asfollows12–15: excitons generated by sunlight in such organicsemiconductor composite are localized in single conjugatedunit of few nanometers and held together by undilutedCoulomb attraction between the charges, typical of lowdielectric constant materials. Therefore, if the excitonsare not dissociated into free electrons and holes by atom-ically sharp quasielectric field of donor/acceptor interface[see Figs. 1(b)–1(d)], they would be lost due to self-recombination. If the phase-segregated morphology isviewed as entangled (or intercalated16) regions of donor-rich and acceptor-rich organic semiconductors, as inFig. 1(a), one finds that the effective cross-sectional

“diameter” of each phase evolves continuously withanneal time, i.e., WD(ta). During the initial transient ofphase separation, the donor/acceptor (D/A) interface isdiffuse, and the quasifield may not be strong enoughfor exciton dissociation. However, the annealing con-ditions need to be precisely controlled for fabricating theefficient morphology,17 which should have the followingproperties: both the D–A phases form percolating path-ways to the electrodes, the average D/A domain size(WD) is comparable to the exciton diffusion length,Lex ¼ ffiffiffiffiffiffiffiffiffiffi

Dsexp

, and the D/A interface is sharply defined,so that the excitons can reach and be dissociated bythe heterojunction with high efficiency, see Fig. 1(c).Once dissociated, electrons and holes are spatially sepa-rated in their respective polymer channels and remainisolated from each other by the D–A heterojunction(which is typically a type II heterobarrier18) with staggeredband gaps, as shown in Fig. 1(d). The lack of minority car-riers in the electron-transporting and hole-transporting re-gions suppresses bulk recombination, and the high internalfield created by the electrode work–function difference[Fig. 1(b)] sweeps the free carriers out before they can recom-bine at the interface. This efficient exciton dissociation, spatialfree carrier isolation, and drift-dominated transport of photo-generated carriers explain the exceptionally high quantumefficiency of a BHJ-OPV.Does improvement in JSC guarantees high efficiency

of an organic solar cell?15,19–21 Not necessarily! Sinceg5 JSC� VOC� FF, overall efficiency can only improve

a)Address all correspondence to this author.e-mail: [email protected]

This paper has been selected as an Invited Feature Paper.DOI: 10.1557/jmr.2012.425

J. Mater. Res., Vol. 28, No. 4, Feb 28, 2013 �Materials Research Society 2012 541

if both the open-circuit voltage (VOC) and the fill factor(FF) improve with morphology and device parameters.A key concern is that a large D/A interfacial area (Aitf)not only increases JSC but also the recombination ofcounterpropagating fluxes of free electron and holes[see Fig. 1(d)]. Such generation-dependent recombination,Jrec, is known to reduce FF and VOC. Moreover, significantparasitic shunt conduction associated with thin filmstructure and high series resistance typical of transparentconductor further erode the overall efficiency of the cell atthe panel level, as discussed later in the paper.

In this review article, we emphasize the importance offour simple concepts to explain broad range of empiricalobservations regarding OPV operation and performancefrom cell to panel level. They are the three-dimensional(3D) percolation threshold,22 the power law growth ofaverage cluster size (WD),

23,24 simultaneous dependence ofJSC and Jrec through total interfacial area (Aitf) betweenthe donor–acceptor phases, and statistically distributedshunt/series resistances at the panel level. We find that(i) the requirement of abrupt band discontinuity at theinterface, (ii) the negative impact of larger interfacial areaon dark current (Idark) and FF, and (iii) the use of ther-modynamically unstable morphology constrain practical

achievable efficiency of OPV in fundamental ways. Futureimprovement in OPV performance must address thesefundamental limits of solar cell performance. Here, we onlysketch the outline of the arguments; details are described ina series of recent articles from our group.17,24–27

The paper is organized as follows. We first discuss thethermodynamic efficiency limits of organic solar cellsbased on a slightly modified Shockley–Queisser approach.Next, we illustrate the fundamental role of morphologyon the solar cell performance and outline an approach tountangle the complexity of the morphology. Then, wepropose few novel concepts for the further enhancementof OPV cell performance. And finally, we show how therequirements of series connection explain the gap betweencell and panel performance and identify the critical param-eters responsible for panel level efficiency loss.

II. THERMODYNAMIC LIMITS OF OPV: THESHOCKLEY–QUEISSER APPROACH

A photovoltaic (PV) device converts the energy ofphotons to useful electrical energy. As a photon engine,the theoretical limit of its efficiency can be calculated basedon general considerations of thermodynamics, as formulatedby Shockley–Queisser (SQ).28 For a material with band

FIG. 1. (a) The red and blue regions define the donor and the acceptor materials of a BHJ-OPV, respectively. EBL: electron-blocking layer; HBL:hole-blocking layer. (b–d) The band diagrams of BHJ-OPV from various perspectives. (b) The band diagrams along the lines (1) and (2) indicated in (a).The built-in field and the staggered type II discontinuity of the P3HT/PCBMband alignment are clearly shown. (c)When excitons are generated in one ofthe materials, they must find a donor/acceptor heterointerface for effective charge separation. (d) Once separated, the type II potential confines electronsand holes in their respective channels, so that recombination occurs only at the D/A interface.

M.A. Alam et al.: The essence and efficiency limits of bulk-heterostructure organic solar cells: A polymer-to-panel perspective

J. Mater. Res., Vol. 28, No. 4, Feb 28, 2013542

gap EG, the efficiency is calculated as the ratio of poweroutput, Pout, from the solar cells to the power input overthe entire solar spectrum Pin. The output power is thedifference of the total absorbed flux, equilibrated at thechemical potential (V � I0), and the power lost toblackbody spontaneous emission (V � Isp), i.e.:

gSQ ¼ Pout=Pin ¼ VðI0 � IspÞ=Pin ; ð1aÞ

I0 ¼ q

Z ‘

Eg

XS � DðEÞ � nBEðE;DlS ¼ 0;TSÞ

� cdE ; ð1bÞ

Isp ¼ q

Z ‘

Eg

XD � DðEÞ � nBE ðE;DlD ¼ qV ; TDÞ

� cdE ; ð1cÞ

Pin ¼ q

Z ‘

Eg

XS � DðEÞ � nBE ðE;DlS ¼ 0; TSÞ

� cEdE : ð1dÞ

Here, D(E) is the photon density of states, nBE is theBose–Einstein distribution, XS is the solid angle of theincident radiation from the sun, and XD is the solid angle ofreemission from solar cells.28,29 This angle mismatch isfundamental to loss of open-circuit voltage in solar cells,30 as:

VmaxOC ¼ 1 � TD

TS

� �Eg � kBTD ln

XD

XS

� �þ D

ffi 0:95Eg � 0:22 ; ð1eÞ

where the first, second, and third terms are related toCarnot loss, angle entropy loss, and photonic density ofstate,31 respectively. At room temperature, the right-handside of Eq. (1e) anticipates the maximum open-circuitvoltage within;2% of those obtained from the numericalsolution of SQ equations. The calculation also shows thatFFmax, 0.92 for solar materials withEg# 2 eV.30Wewishto emphasize that the constraints of, and hold true toall types of solar cell technology31,32 and not specific toexcitonic PV.31,32 Indeed, the angle entropy loss is implicitin all numerical calculations33 or explicit in analyticalformulation.28,29 In addition, VOC can be further degraded(i.e., VOC, Vmax

OC ) through nonradiative recombination andother loss mechanisms.

As already discussed, a BHJ-OPV differs from a classicalsolar cell because the discontinuity at the heterojunction,i.e., DE ([ LUMOD � LUMOA), is essential for cell op-eration, and therefore, the classical SQ formula must beadapted accordingly for BHJ-OPV. The photons are stillabsorbed at DEG ([ LUMOD � LUMOA), but theyrecombine at primarily at the D/A interface with cross-gapDEHL [ LUMOA � HOMOD [ EG � DE, see Fig. 1(c).This reduction in emission band gap increases the darkcurrent and reduces efficiency. In other words, Eq. (1c)should now be rewritten as30:

IBHJsp ¼ q

Z ‘

EHL

XD � DðEÞ � nBE ðE;DlD ¼ qV ; TDÞ

� cdE : ð2Þ

Figure 2(a) shows the OPV-specific “SQ limit” fordonor/acceptor OPV obtained by solving Eqs. (1) and (2).The blue solid line in Fig. 2(b) shows the correspondingthermodynamic limit of VOC [Eq. (1e)], with EG replaced

FIG. 2. The SQ efficiency limit for an OPV. (a) When the band discontinuity (DE) is small, classical SQ analysis suggests that peak efficiency isobtained close to the band gap of;1.45 eV. The band discontinuity between the organic semiconductors reduces efficiency (primarily through a lossin VOC) and shifts the peak efficiency curve to higher band gap. For DE5 0.5 eV (magenta line), maximum g occurs at;1.7 eV. (b) The relationshipbetween VOC and EG or EHL. Here, EHL is the cross-gap of the OPV and EG is the band gap of elemental semiconductor (e.g., Si, GaAs, CIGS). Theblue solid line represents the calculated (theoretical) approximation for VOC at different EHL or EG, see Eq. (1e). The symbols are experimental valuesobtained from literature34,35 (see Table II).


J. Mater. Res., Vol. 28, No. 4, Feb 28, 2013 543

by the cross-gap EHL of donor/acceptor organic semi-conductors. Remarkably, the measured VOC (filled squaresymbols) in OPV is close to its thermodynamic limit.The gap between red and the blue lines is attributedto fundamental angle entropy of the system [last term inEq. (1e)] that cannot be reduced by exciton engineering.In this regard, VOC of OPV, despite its morphologicalcomplexity, is no different from those of inorganic semi-conductors, such as Si, GaAs, CIGS, etc. [filled circles,Fig. 2(b)].32 As mentioned previously, actual VOC is lowerthan Vmax

OC due to nonradiative recombination losses.The key to improve VOC (as well as the efficiency) of

OPV is to increase the cross-gap EHL[ EG� DE. Note thatfor a discontinuity ofDE ([LUMOD� LUMOA);0.7 eV,the limiting efficiency at 2 eV (band gap of light-absorbingP3HT layers) is reduced from ;25% to ;13.5%, see

Fig. 2(a). This result should be viewed as an upper limitbecause we have assumed that the thermalization loss andthe free energy gain from the band discontinuity (DE)are sufficient to dissociate excitons into free electronhole pairs.19 We will now discuss the practical aspects ofOPV that reduce the efficiency from ;13.5% to ;5%(for P3HT/PCBMsystem) and evaluate themerits of variousstrategies for efficiency improvement.

III. MORPHOLOGY-AWARE MODELING OF OPV

The operation of BHJ-OPV depends on coupled trans-port of photons, excitons, electrons, and holes throughcomplex phase-segregated material under variable electricfield.12–15 Two types of modeling approaches have been usedto analyze these phenomena: some groups have focusedon calculating the output response of a cell by solving thecoupled transport problem in a homogenized effectivemedia approximation12,36,37 or in an idealized geome-try,38,39 while others have focused on the mesoscopicphysics of various subprocesses40 (e.g., exciton dissocia-tion at the D/A interface) that could potentially be the ratelimiting process for charge transport. The effective mediaapproach provides important insights about the impact ofvarious physical parameters (e.g., carrier mobility, activelayer thickness, polymer band gap, etc.) on the solar cellperformance and explains the experimentally measuredI-V characteristics. However, this approach fails to explainthe dependence of the I-V characteristics on the devicemorphologies fabricated under different processing condi-tions (e.g., annealing, mixing, etc.). Similarly, the modelingwork that exclusively focuses on the various subprocesses(e.g., exciton dissociation) can explain the role of hetero-junction morphology at the local scale but does not explainthe overall cell performance as a function of various mor-phologies and process conditions. Thus, the existing mod-eling approaches are not quite suitable for modeling themultiscale problem of OPV physics because both the localand the global morphology are essential to the performanceof OPV, and many characteristic features of the OPV wouldbe lost if these aspects are ignored. We believe that a third

TABLE I. Description of the terms in Eqs. (1) and (2).

Symbols Description

kB Boltzmann constantc Speed of lightq Charge of an electronD(E) Photon density of statesnBE(E, Dl, T) Bose–Einstein distributionDl Chemical potential or quasi

Fermi level splittingTS or TD Sun (S) or device (D) temperatureEg Electronic band gap of the materialD Photonic density of states contribution

in open-circuit voltageDE Band discontinuity at D-A heterojunction,

i.e., LUMOD � LUMOA

XS or XD Solid angle of the incident (S) light from thesun or emitted light from the device (D)

I0 The electric current corresponding to the inputphotons from the sun (short-circuit current)

ISP The electric current equivalent corresponding tothe photons lost through blackbodyradiation (at bias V)

Pout Output power of the solar cellPin Power input calculated by integrating

the AM 1.5 solar spectrum

TABLE II. Measured open-circuit voltage for organic and inorganic solar cell.

Inorganic cellEg (eV),VOC (V) Organic BHJ cell35 Eg (eV), VOC (V)

Organicbilayer cell34 Eg (eV), VOC (V)

S1 c-Si 1.12, 0.706 OP1 Poly-[(19dodecyl)-3,4-ethylenoxythiophene]

0.52646, 0.17015 OP11 Ru(acac)3/PTCDA 0.84951, 0.19424

S2 InP 1.344, 0.878 OP2 Poly(3-butylthiophene) 0.75293, 0.35192 OP12 Ru(acac)3/C60 0.71003, 0.33803S3 GaAs 1.44, 0.845 OP3 Poly(3-hexylthiophene) 0.80239, 0.58187 OP13 CuPc/C60 1.08, 0.7992S4 CdTe 1.424, 1.145 OP4 Poly[2,7-9,9-dioctylfluorene)-

alt-2,6-cyclopentadithiophene]0.94816, 0.67385 OP14 SubPc/C60 1.4108, 1.0195

... ... ... OP5 Poly(3-hexyl-4-nitroxythiophene) 1.1512, 0.75145 ... ... ...

... ... ... OP6 Poly[2,7-(9,9-dioctylfluorene)-alt-5,50-(49,79-di-2-thienyl-29,19,39-benzothiadiazole]

1.4505, 1.0303 ... ... ...



approach, based on a morphology-aware end-to-end devicemodeling17,24–27 of BHJ-OPV, can provide additionalinsights. We will discuss this approach below.

A. Processing of an OPV: Phase separation andOstwald ripening

The first step of end-to-end modeling of OPV in-volves a theoretical description of the morphologythat dictates cell performance.17,24 There have beenmany recent works on the physical characterizationof the BHJ morphology by electron tomography,41,42

x-ray diffraction,16 and other advanced scatteringtechniques.43 It is now believed that the exact nature ofthe nanomorphology critically depends on the specific D-Amaterial system. For example,McGehee et al.16 have shownformation of bimolecular crystals of fullerene, intercalatedbetween the side chains of the semiconducting donor poly-mers. Depending on the spacing between the side chains ofthe polymer molecules, the system may either intercalateor mix at the molecular scale (e.g., MDMO-PPV, pBTTT,pTT, etc.) or, alternatively, phase separate at large scale(e.g., P3HT, BEH-BMB-PPV). More recently, Darlinget al.43 have shown hierarchical nanomorphology in thePTB7: fullerene system, where nanocrystallite aggregates offullerene and polymer are observed in the polymer-rich andfullerene-rich domains, respectively. Thus, it is clear thatthere is no universal rule or form for the complex BHJmorphology, and hence, a complete generic modelingframework that provides precise and universal descriptionof this broad class of morphology is nearly impossible.

The common theme in the processing of BHJ morphol-ogy is the blending of the donor–acceptormolecules, whicheither leads to microscale phase separation (or molecularscale mixing, MDMO-PPV, pBTTT) or macroscale phaseseparation (or large-scale phase separation, e.g., P3HT).The kinetics of both these processes can be described bythe Cahn–Hilliard (C-H) approach, which requires conser-vation of D/A phases and an appropriate free energyfunction ( f ) describing the thermodynamics of the D-Ablend. The C-H formalism, however, is a mean field theory:it approximates the composition of D/A phases by an aver-age variable (f), and spatially resolved information regard-ingmicrophase is not available. The time evolution of phasevariable (f) is given by the following C-H equation44–46:

@u@t

¼ M0 =2 @f

@u� 2j=4u

� �; ð3Þ

where u(x, y, z, t) is the volume fraction of one of the D/Aphases,M0 is the Onsager mobility coefficient dictated bythe polymers and the solvent, and j is the gradient energycoefficient dictated by interfacial energy between twophases. The free energy function ( f ) of the homogenizedmixture depends on entropy, interaction energy (given bythe Flory parameter),44,46 and the relative sizes of the organic

molecules. The detailed description of the free energy andthe computationalmethodology is described in our previouspublications.17,26 In thismodeling framework,17,26we neglectthe effects of solvent evaporation and the substrate strain,although substantial work is being done in this regard by anumber of groups.47,48 The key limitation of this approachis that it cannot give the spatial distribution of the fullerenemolecules within the donor-rich or acceptor-rich domains(mean field approximation), i.e., the model cannot describethe formation of hierarchical morphology43 or formation ofBHJ structure starting from bilayer structure.49 However,so long the phase volumes are conserved and intercon-version is excluded, the general notion of phase separation(or intermixing) should apply to broad range of organicsemiconductors used for OPV, as a unifying feature of thisproblem. Modeling these microscopic effects may requiremulticomponent generalization of the C-H equation orCellular automata approach,50 generalization of free energiesrequiring characterization of broader range of parameters,etc. Indeed, developing such generalized formulation shouldbe an important goal of the field.

In Fig. 3, we show the simulation results for the mor-phology evolution during the fabrication process. The initialcondition for the simulation is a random mixture with com-position fluctuation around the mixing ratio between thetwo organic components. With anneal duration, as shownin Figs. 3(a)–3(d), the phase segregation of the D-Amolecules takes place with the formation of diffusedinterfaces between the donor-rich (red) and acceptor-rich (blue) domains. Even though the modeling approachis based on several assumptions, the simulated mor-phology closely resembles the fabricated morphologydepicted by tomography and various advanced scatteringtechniques.41–43,51–54

1. Power law growth of domains24

The phase-segregated morphology, as shown inFigs. 3(a)–3(d), is a random structure but can be charac-terized by average domain size,WD, as shown in Fig. 3(d).The average domain size is a statistical quantity, which isnumerically computed for a givenmorphology. In Fig. 3(e),we show the domain size growth with anneal duration.Except for the initial fast transient phase, during whichmorphology is presumed fractal, the size evolution isdetermined by the Lifshitz–Slyozov law,23,46 i.e.,WD ; M0 f 99

ffiffiffiffiffiffiffiffijDf

pta

� �n, where ta is the anneal time and

Df is the change in free energy. A single parameter (WD)description of the morphology evolution can only be takenas a first-order approximation; phase segregation in realpolymer blends is far more complex with crystallizationof one phase preceding that of the other,55 intercalationbetween the phases,16 etc. This Lifshitz–Slyozov approx-imation, however, allows one to calculate the interfacearea Aitf between donor and acceptors. Since the phase



volume is conserved, the effective surface area (S) scalesas WD(t)Aitf(ta) 5 C or Aitf(ta) ; (WD)

�1 ; t�na . The sur-

face area is the maximum in the well-mixed film, but itreduces as annealing coarsens the film. In our previouswork,24 we have shown that this annealing-dependentcoarsening of the morphology can accurately describethe thermal degradation of BHJ-based organic cells, onceother mechanisms such as contact degradation56–59 or interf-ace trap generation60 are minimized. Figure 3(f) shows theclose match between the thermal degradation results obtainedbymeasurements (symbols) and predicted bymodeling (solidline) based on domain coarsening. Once again, we emphasizethat since the approach to morphology evolution describedabove was primarily developed for polymer–polymer sys-tem, it may not accurately or specifically reflect the complexmicro- or macrophase segregation of organic polymers.Rather, the results should be viewed as an approximation ofthe phase segregation process, appropriate for multiscalepolymer-to-panel simulation of organic solar cells.

2. Percolation threshold

Mixing ratio between the D-A molecules is an importantparameter for the fabrication of high performance organicsolar cells.22 Experimentally, it has been shown that fora given D-A material pair, there exists an optimum

weight ratio for fabricating the most efficient cell.61

The origin of such optimum weight ratio has been recentlyexplained in terms of the degree of intercalation of thefullerene molecules in the side chain of donor polymer.

In this work, we show that the optimum weight ratio oforganic semiconductors is fundamentally constrained byconnectivity of phases to respective contacts, which could inturn be related to percolation theory in 3D random geometry.In Fig. 4, we plot the fractional volume of a given phase(donor: red, acceptor: blue) connected to the appropriatecontact, as a function of the volume fraction of the acceptorphase in the mixture. For example, for a donor/acceptorvolume mixing ratio of 1:2, the “donor blend phase” (redcurve) is fully connected (;1), but the acceptor phase (blueline) forms islands within the donor phase, and only 60–65%of the acceptor volume is actually connected to the contact.The connectivitymaximizes for donor:acceptor ratios of 0.8:1to 1.25:1 because both volumes are almost 100% connectedto the respective contacts. Further increase in donor/acceptorratio leads to island formation for the donors and rapid loss ofconnectivity to the contacts.

Figure 4 can be interpreted in a two-component percola-tion framework as follows. It is well known that percolationthreshold (p3Dc ) for an infinite random system is ;0.362;therefore, the donor phase volume ratio must be smaller than2:1 to form a bicontinuous film without large number of

FIG. 3. (a–d) Evolution of active layer morphology is plotted with increasing anneal time. We find that the effective width, of the phase-segregateddomains scales with anneal time (power-exponent) as shown in (e). The figure also shows that the domain growth is an activated process with strongtemperature dependence. Such domain growth is called Oswald ripening and it is a common feature of many polymer/organic blends. (f) Thedegradation in the short circuit current due to morphology coarsening is plotted. The symbols are experimental data and the solid lines are the model.Details of the model derivation are discussed in Ref. 24.



islands. Three additional considerations apply: (i) the realBHJ-OPV cells are neither infinite (thickness ;100 nm)nor random (phase segregation is correlated); therefore,pBHJc ; 0.2, p3Dc . (ii) On the other hand, conductivity at pcis exponentially suppressed,62 and quasiohmic transportis restored only at 2 � pBHJc ; 0.4. Finally, (iii) light isprimarily absorbed in the donor polymer; therefore, it isdesirable to have pD ! 0.55 and pA ! 0.45. Given thesethree constraints, it is easy to see why ;1:1 volume ratiobetween the donor and acceptor phase gives near optimumperformance and moving away from this ratio is so difficult(see Fig. 4).

Finally, one can related the weight ratio to volumeratio using the formula:

VD

VA

¼ aA � aoptaopt � aD

� �1qD

þ aDqA

� ��1qD

þ aAqA

� �; ð4Þ

where qD and qA are density of donor and acceptormolecules, aD, aA, and aopt are the weight ratios offullerene (or PCBM) molecules to donor molecules indonor-rich phase, acceptor-rich phase, and in the active

layer, respectively. As shown in Table III (symbols inFig. 4), despite significant variation in D/A weight ratio,the D/A phase volume ratios are indeed close to thoseanticipated by the phase connectivity argument.

B. The three metrics of practical OPV

For a given morphology, the output I-V character-istics can be calculated by solving the coupled transportequations for excitons, electrons, and holes. In Fig. 5, weshow such I-V characteristics of organic solar cells fordifferent anneal durations. We use drift–diffusion-basedtransport equations to describe the carrier dynamics in theOPV morphology. It is well known that drift–diffusion doesnot describe the complex charge transport in soft polymersfully38,68,69; however, the technique has been widely used asa first-order approximation that captures the essential aspectsof the transport problem.36,70–73 The detailed descriptionof the model equations and the boundary conditions aredescribed in our previous publications.17,26 Here, wereport the essence of the morphology-aware transportanalysis for BHJ-OPV. Our analysis shows that theempirical features of the key PV matrices61,74 (i.e., JSC,

FIG. 4. Optimum mixing ratio (by volume) of donor and acceptor materials. By simulation, we find that 1:1 phase volume ratio ensures that both thedonor and acceptor phases form continuous (percolating) pathways for charged carriers between the electrodes. In the figure, VA and VD denote thetotal volumes of acceptor and donor phases, respectively, and VC,A and VC,D are the volumes of the acceptor and donor phases connected to bothcontacts, respectively. The shaded area in the plot shows the desirable volume fraction of the acceptor/donor phases, which ensures almost 100%connectivity for both phases. The experimentally observed optimum mixing ratios (w/w) falls within the shaded window after converting the weightratios into the phase volume ratios using Eq. (4) for three different donor polymers.



VOC, and FF) can be intuitively interpreted in terms ofthe total interfacial area Aitf(ta) between the D-A phasesof the BHJ morphology. Similar characterization of thecomplex morphology with an effective average quantitysuch as interfacial area or domain width is also reportedby various groups.75–77 The analysis identifies the im-provements in materials and device configurations nec-essary to close the substantial gap between efficiencyreported in the literature and the corresponding SQ limitdiscussed earlier.

1. Morphology-dependent short-circuit current

It is easy to calculate the efficiency of the exciton dis-sociation at the donor/acceptor interface as17,24,25:

Iex }GexLexAitf tanhÆWDæ2Lex

� �; ð5Þ

where Gex is the effective exciton generation rate (fordetails, see Monestier et al.78), TD ([ gDTfilm) is thethickness of the donor layer [Fig. 1(a)], with gD beingthe donor volume fraction in the active layer of film thick-ness Tfilm. For sufficiently long anneal time that allowsthe emergence of abrupt D/A interface, WD $ 2Lex andIex ; GexAitf ; t�n

a . In other words, the efficiency of ex-citon dissociation reduceswith anneal time as themorphology

coarsens, and many excitons are lost to self-recombinationbefore reaching the interface [as shown in Fig. 4(a)], con-sistent with the classical view of BHJ operation. Bothexperimental results and numerical simulations verify thisprediction.17,24,79,80

Equation (4) may suggest that annealing is counterpro-ductive because annealing would coarsen the morphology(i.e., lower Aitf), which would lead to lower exciton col-lection. Morphology coarsening with annealing is not theentire story though; annealing has two other importantfunctions, which improve the device performance. First,one can show via a one-dimensional analysis of the C-Hequation that there is aminimum anneal time to sufficientlyphase separate the interface boundaries to produce sharpheterobarrier discontinuity.81 The diffused and disorderedinterface creates interfacial defect states,60,82–84 whichincrease the interfacial recombination.85 Second, al-though Jex}Aitf , but so is the interface recombinationcurrent,25 i.e., Jrec}Aitf (see Sec. III. B. 2). In otherwords, while finer morphology improves exciton collec-tion, the proximity of the counterpropagating electronand hole channels enhances recombination at the D/Ainterface and reduces JSC (5 Jex � Jrec). The annealingtime, therefore, must be optimized to maximize JSC.Experiments show that a properly optimized cell canachieve quantum efficiency approaching 100% at theshort-circuit condition.7

TABLE III. Relationship between weight ratio (donor molecule:acceptor molecule) and volume ratio (donor phase:acceptor phase). Density ofPCBM (qA) is assumed 1.5 g/cc and the acceptor phase consists of only PCBM.16

PolymerDensity of donor

molecules (qD) (g/cc)

Weight ratio of fullereneto donor molecules indonor phase (aD)

Optimum mixing ratio byweight of fullerene:donor

molecules (aopt)Phase–volume ratio ofD/A phase (VA/VD)

P3HT 1.163 ;016 1:1 (w/w)61,64 1:1.25 (v/v)MDMO-PPV 163 ;1:1 (w/w)65 4:1 (w/w)65 1:0.83 (v/v)pBTTT 1.163 ;1:1 (w/w)16 4:1 (w/w)16,66 1:0.79 (v/v)

FIG. 5. Annealing time-dependent I-V characteristics for BHJ cells. (a) Experimentally measured67 I-V and (b) the corresponding simulated17 I-Vare shown side by side to demonstrate that the simulation captures the trends in the I-V variation.



2. Morphology-independent open-circuit voltage

The introduction of BHJ improves JSCð}Aitf Þ dramat-ically, but remarkably, all empirical evidences suggest thatannealing has very little effect on VOC.

25,67,86–88 Again, anappreciation of the unique operation and geometry ofthe BHJ-OPV resolves the puzzle, as follows.25 At theopen-circuit condition, the total recombination current(Irec 1 Idark) cancels the photogeneration current (;Iex),making the net current zero, see Fig. 6. The recombinationcurrent at VOC is given by:

Irec ¼ZZ

cðnIðzÞpIðzÞ � n2intÞdSðzÞ} Aitf ; ð6Þ

where c is the bimolecular recombination constant, nint isthe intrinsic carrier concentration at the D-A interface,nðzþI Þpðz�I Þ ¼ n2int exp½qðVOCÞ=nkT � ¼ C2, and the in-tegral spans over the entire D/A interface. SincenðzþI Þpðz�I Þ ¼ C2, independent of the vertical loca-tion (z) within the cell, the constant can be takenout of the integral, i.e., Irec }

RRdSðzÞ ¼ Aitf . Since

VOC ;nkBTq lnð1þ ISC=IrecÞ and both Irec and ISC scale

linearly with Aitf, VOC does not change significantlywith interface area, see Fig. 4(b), and neither annealingnor engineering of the morphology by any othermeans would affect VOC. The only parameter directlydetermining the VOC is therefore the cross-gap EHL.This somewhat counterintuitive conclusion is consistentwith a broad range of experimental results from the OPVliterature.67,86–88

3. The ls product and FF

For a given polymer pair and specific set of electrodes,the cell can be designed so that JSC is close to the theo-retical maximum.7 And, as discussed in Sec. III. B. 2, VOC

is dictated by the cross-gap (EHL [ EG � DE).25,34

Therefore, the gap between theoretical SQ efficiencyand that of practical BHJ-OPV must be traced to the

difference in FF. The “intrinsic FF” reflects the ability ofcontacts to collect the photogenerated carriers,33,89–93 espe-cially at low-field, when the cell is forward biased to achievemaximum power output. Although FF can ideally reach 0.9,the experimentally reported FFBHJ values for P3HT:PCBMare in the range of;0.5–0.6.94 The origin of the low FF canbe understood as follows.

The voltage dependence of the photocurrent, whichdecides the FF in OPV, is generally explained by thefield-dependent charger transfer (CT) exciton dissocia-tion models.95,96 Recently, it has been shown by variousgroups33,89–93 that the CT excitons almost invariably leadto free charge carriers, and hence, voltage-dependent pho-tocurrent (and hence the FF) is dictated by the recom-bination of the free charges at the D-A interfaces. This canbe understood more clearly from the band diagramshown in Fig. 7(a), where we show the various currentfluxes originating at the D-A interfaces. Here, Jex is theexciton diffusion flux or the rate of charge generation,Jph is the photocurrent or the rate of charge extraction,and Jrec is the recombination rate at the interface, suchthat Jex [ Jph(V) 1 Jrec(V). See Fig. 7(a) for the def-inition of these current components and Fig. 7(b) plotsthe results from numerical simulation. Since excitonsare neutral, exciton flux (Jex) is voltage independent(red line) and it is determined by total absorption andexciton diffusion length. The photocurrent [blue linein Fig. 7(b)] is predominantly the drift current96–98

dictated by the electric field and the mobility, i.e.,Jph 5 qnIlE 5 qnImd. Here, md is the drift velocity andnI is the free carrier density at D-A interface. Similarly,the recombination current [black line in Fig. 7(b)] isproportional to the recombination speed at the interface,given by mrec 5 Wint/srec. Here, Wint is the effective width(;1 nm) of the interface and srec is the charge re-combination time. For bimolecular recombination mech-anism, srec is inversely proportional to the bimolecularrecombination coefficient (c). Thus, the voltage de-pendence of the photocurrent can be expressed as

FIG. 6. (a) Both the short-circuit current, JSC (right axis), and dark current (or diode reverse saturation current), J0 (left axis), depend on interfacial area,Aitf. Since ABHJ ; t�n

a , both short-circuit current and the dark current reduce with anneal duration. (b) Despite this dramatic change in ABHJ with annealtime, VOC does remain insensitive to anneal time. (c) The combination produces an optimized anneal time for maximum efficiency.



JphðVÞ ¼ vdvd þ vrec

� Jex ¼ lsE

lsEþWint

� Jex. Here, the electric

field � (Vbi � V)/Tfilm, where Vbi is the built-in voltagedefined by the work function of the electrodes andV is the operating voltage. At short-circuit condition,V 5 0 V, so that E is high and Jph(V 5 0) ; Jex—theefficiency of carrier collection is high. At maximumpower point (V 5 Vm), electric field is suppressed, sothat Jph(V); lsEJex/Wint, which suggests that even withperfect exciton dissociation at the D/A interface, thepoor ls product (typical of polymers and polymer interfaces)ensures dramatic reduction of the total photocurrent closeto maximum power point, leading to empirically observedlow FF. The expression for Jph(V) suggests that the FF

BHJ

can be improved with higher mobility polymers99,100 orimproved quality of interface that suppresses recombination(higher srec), strategies that we will discuss below.

IV. STRATEGIES FOR EFFICIENCYENHANCEMENT

The organic semiconductors used in OPV literature areoften characterized by unique morphology and nature ofcarrier transport could vary depending on specific tech-nologies. Nevertheless, the generic theory of BHJ-OPVdiscussed can help us assess the prospects of several strat-egies of performance improvement suggested by severalgroups101–103 in the recent past to improve OPV efficiency,as discussed next.

A. Improved efficiency from morphologyengineering

There is a perception that regularized fin-like mor-phology based on top-down templated heterostructure(Fig. 8)101,102 or self-assembled kinetically trapped mor-phologies like double gyroids could fundamentally im-prove PV efficiency by providing connected conduction

channels to the respective contacts for every electron/holegenerated by exciton dissociation. Indeed, two-dimensional(2D) cross-sectional images of a random phase-segregatedmorphology do show a large number of electrically isolatedislands that appears to contribute to extinction of exciton,without contributing to Jph.

Like a network in “plumber’s nightmare,” a 2D cutprovides an incomplete representation of the 3D system.Elementary results from percolation theory suggest thatthe notion of random1:1 structure containing a large numberof islands is flawed. Since the percolation threshold of a 3Dthin film is expected to be substantially below the bulk valueof ;0.3, a typical ;1:1 mixture cannot have a significantnumber of islands.16 Indeed, it would be difficult to explain;100% quantum efficiency7 in BHJ-OPV, if excitonquenching in isolated islands led to substantial loss inphotocurrent. We have recently shown that “randommorphology is close to optimum” and morphology engi-neering does not yield substantial benefits in terms ofperformance or variability (Fig. 8).26

The kinetically trapped morphology and/or tem-plated structures, however, may improve long-termthermal stability. A key stability concern for solution-processed BHJ-OPV fabricated at low temperature isits propensity for phase segregation even at operatingconditions.24 If optimized for peak efficiency before in-stallation, a dramatic degradation in efficiency is expected(and has been experimentally observed) during operation.In this regard, the top-down template structure may improvethermal stability of the film and increase the lifetime of thesolar cells.

B. Approaches for improved mobility orsuppressed recombination

Numerical simulations show that improving mobilityincreases FF substantially.26 Awide variety of ideas have

(a) (b)

FIG. 7. Various current fluxes at the heterointerface of OPV. (a) Typical OPV band diagram with the current fluxes indicated by arrows.(b) Components of the J-V characteristics of a BHJ-OPV. The maximum power point in the J-V curve is indicated as dark circle. The maximum powerpoint current and voltage are denoted by Jm and Vm, respectively. The low FF of the BHJ-OPV (blue line) is attributed to rapid increase in Jrec (blackline) at the maximum power point of the J-V curve.



been offered but none without important drawbacks.For example, improving crystallinity improves mobilityof a polymer,99 but the film may no longer be processablein solution. Percolation doping by carbon nanotubes103

or nanostructured electrodes104–107 are expected to reducethe path lengths of charge collection and improve FF[Fig. 9(a)]; however, the initial results are inconclusive.In fact, theoretical calculations show that if these electrodesbreach the junction, Jrec may be substantially enhanced,and the efficiency gain is completely lost. Finally, therehave been several recent efforts to reduce recombination atthe interface.108–110 This technique appears promising, butadaptability to BHJ-OPV remains an open question. As analternative to mobility enhancement, one can also try tosuppress interfacial recombination by introducing a thincharged layer [Fig. 9(b)] at the D-A interface, so that thefree carriers are pushed away from the interface and therecombination is suppressed. Initial theoretical calculationsuggests that this approachmay increase the FF dramaticallyto;80%.111While similar concepts have been demonstratedfor planar heterojunction cells,108 its feasibility for BHJ-OPVis yet to be demonstrated.

C. Low band gap and low cross-gap materials

The HOMO–LUMO gap of a typical polymer in usetoday ranges between 1.7 and 1.9 eV, andmany researchersfeel that lowering the band gap to 1.2–1.5 eV may improveJSC and efficiency. In a recent article, Nelson5 summarizesvarious techniques to develop low band gap polymerssuch as planarization of the polymer backbone, addition ofheteroatoms, alternating electron-rich units with electron-poor units in a push–pull configuration, etc. Figure 2,however, shows that for typical band discontinuity ofDE ([ LUMOD� LUMOA); 0.5 eV, the change in bulk

band gap EG ([ LUMOD � HOMOD) does not improveefficiency significantly. Instead, it is more important toreduce the band discontinuity between the HOMO levelof the donor polymer and LUMO level of the acceptorpolymer, i.e., increase the cross-gap between the polymerpairs. Efforts to lower band discontinuity by either increas-ing the LUMO level of PCBM by adding various sidechains or decreasing HOMO level of P3HT by replacingC with Si have already been demonstrated. Finally, anapproach based on including low band gap dye at the D/Ainterface seems promising,112 but the efficiency gain bythis approach needs to be quantified.

The efficiency enhancement strategies, as reviewed inthis section, focus on improving the intrinsic material ordevice properties and hence must be implemented at celllevel. To translate these improvements into higher panelefficiencies, we must also identify and minimize theparasitic losses responsible for reducing the panel effi-ciency. In Sec. V, we outline a combined device–circuitapproach for capturing theses aspects and discuss theinsights it offers.

V. ORIGIN OF POOR PANEL EFFICIENCY IN OPV

A common challenge for all PV technologies is the lossof efficiency when cells are connected in series to createthe solar panel. This gap between cell and panel efficiencyis universal for all technologies, including OPV, wherepanel aperture area efficiencies are as low as 2–3%.113–115

There are many factors responsible for this loss in efficiencyat the panel level, arising from challenges in large area de-position of thin absorber and contact layers, while using lowtemperature high throughput processes. The two major lossmechanisms responsible for this gap between cell and panelare resistive losses in the transparent conducting oxide(TCO) layer and losses due to parasitic local shunt currents,distributed across the cell surface. These loss mechanismsare common to all solar cell technologies27,116–118 and, aswe show in this section, account for a large percentage ofpanel efficiency loss. To analyze the panel efficiency, weuse an equivalent circuit approach, which allows us torepresent small individual cells using equivalent circuits,and connect them in series and parallel to forma panel.27,116–118

The intrinsic I-V characteristics obtained from themodeling approach discussed in the preceding sectionscan be used for analyzing small laboratory-scale cells(see Fig. 5). To simulate panel characteristics, however,we need to use an equivalent circuit framework, as shownin Fig. 10(a). This can incorporate the intrinsic physics ofgeneration and recombination inside the cell, as well as thephysics and statistics of parasitic shunts, and contact sheetresistance, as shown in Fig. 10(a). In thin film solar cells,the shunt current shows a power law voltage dependence,which can be understood as a localized space-charge-limited

FIG. 8. Design space for optimum templated morphology (FIN-OPV),showing optimal morphology (see gopt). For Hfin 5 0, the structure cor-responds to Planar Heterojunction (see gPHJ) cell; and for Hfin 5 Tfilm, itbecomes Ordered Heterojunction (see gOHJ), as shown. The plot showsthe efficiency variation of FIN-OPV as a function of Fin height, whilekeeping Fin width constant at Wfin 5 1.5Lex.



shunt path, in parallel to diode current.27 These shunt defectsare distributed spatially randomly on the cell surface, withtheir magnitudes showing a lognormal distribution.116

To quantify the impact of these parasitic effects at panellevel, we create an equivalent circuit of the panel, by usingthe cell equivalent circuit shown in Fig. 10(a). As shown inFig. 10(b), for a typical thin film PV panel with Nseries cellsin series, we divide individual cells into 1 � 1 cm subcells,which are connected in series and parallel using the TCOsheet resistance to form a panel equivalent circuit.117 Eachsubcell is represented by an equivalent circuit with differentshunt current values, obtained from the measured lognormaldistribution of shunt current values [Fig. 10(b)]. This ap-proach enables us to carry out and end-to-end (i.e., process–device–panel) simulation, by including the effect of parasiticloss mechanisms.

Figure 11(a) shows the schematic of a typical OPVpanel, with geometrical dimensions obtained from data

sheets of Konarka� Technologies (Lowell, MA). We usethe circuit approach discussed above and assign varyingshunt current values to each subcell, as shown in Fig. 11(bi).We assume that all other properties of the subcells areidentical, except for the variation in parasitic shunt current.The subcell efficiency without any shunt losses is assumedto be 5%, a typical value for a high quality P3HT:PCBMcell. We can now simulate the whole panel circuit usingSPICE and explore the effect of shunt variability on moduleperformance. The impact of such randomly distributedshunts can be understood from Fig. 11(bii), which showsthe power output of individual subcells when the panelis operating at its maximum power point. Note that thehighly shunted subcell (highlighted) actually consumesthe power produced in the neighboring regions and hasa disproportionately large impact on panel efficiency.This illustrates the importance of these correlated effectswhen cells are connected to form modules. The moduleefficiency is not a simple average of various cell efficienciesbut is determined by these effects related to interconnectionand biasing.

To get a more quantitative assessment of these losses, wealso perform Monte Carlo simulations of panel efficiencyin presence of random shunt defects and calculate the panelefficiency distribution for a given shunt distribution, asshown in Fig. 11(c). Note that for best subcell efficiency of5%,10,11,119 the panel efficiency reduces to 2.7–3% fortypical module dimensions.113–115 The simulation alsoservers to highlight the respective contribution to panelefficiency loss from contact sheet resistance (about 1.6%absolute) and the shunt current variability (about 0.5%absolute). This gap between cell and module efficiency inOPV is fairly consistent with other PV technologies.118

In this analysis, we have analyzed the losses due to shuntvariability, due to its universal nature and availability ofrobust statistical data.27,116,117 The SPICE framework used,

FIG. 9. New device concepts for the improvement of the FF in OPV.(a) Inserted electrode for better charge collection. (b) Implanted fixedcharge layers at the interface to reduce interfacial charge recombination.

FIG. 10. (a) Schematic of an organic BHJ solar cell, showing the intrinsic region, parasitic shunt, and contact series resistance regions. These componentsare captured in the compact model shown at the bottom, with the various generation and recombination fluxes, as well as the parasitic components.(b) (clockwise from top) Schematic representation of the SPICE simulation approach for a typical thin film PV panel withNseries cells in series, subdividedintoNparallel subcells, each of which is represented by the equivalent circuit in part (a). This circuit incorporates the relevant physics as well as the statisticaldistribution of shunt current magnitude (red box). Finally, we obtain the 2D network of equivalent circuit for simulating panel performance.



however, is very general and can be easily adapted to an-alyze other sources of variability and panel level losses.This analysis highlights the “practical” efficiency limit ofthe OPV panels because of the inevitable shunt and seriesresistance losses. And, in addition to the various strategiesfor efficiency improvement at the cell level, mitigation ofthese losses will require an enhanced emphasis on improve-ment in TCO properties and improved process control inmanufacturing.

VI. PROGNOSIS AND CONCLUSION

The analysis in this paper leads to a number of sur-prising conclusions regarding the efficiency of BHJ-OPVfrom cell to panel level.

(i) A simple derivation of the thermodynamic limit ofefficiency for BHJ-OPV shows that while the band gapdiscontinuity (DE) between donor/acceptor material isessential for exciton dissociation, it is also responsiblefor loss of intrinsic efficiency below the classical SQlimit, gSQ(EG) . gBHJ

SQ (EG, DE).(ii) The gBHJ

SQ (EG, DE) limit is yet to be achieved inpractice. A combination of processmodeling and a coupledsolution of exciton, electron, and hole transport tracesthis difference in efficiency to low FF arising frompoor mobility of polymers and high recombination atthe D/A interface; otherwise, JSC is already close tomaximum limit and VOC cannot be changed with mor-phology engineering.

(iii) Various approaches to improve mobility (e.g.,crystalline, projected electrode, doping by nanowiresor nanotubes) are being explored and could improveperformance—however, each approach also has importantdrawbacks whose implication should be understood in acomprehensive framework.

(iv) Our use of 3D percolation theory suggests that(a) random morphology is close to optimum, i.e., the

performance of OPV cannot increase significantly withregularizing the structure and that (b) the volume ratiocannot significantly deviate from 1:1 mixture.

(v) We find that efficiency improvement requires thatwe simultaneously reduce EG and band discontinuity DE.UnlessDE is reduced significantly, exclusive focus on bandgap reduction may not improve efficiency significantly.

(vi) Finally, we used combined device–circuit simulationsto study the practical constraints in translating OPV cell effi-ciency to panel efficiency. The analysis points to the domi-nant role of contact sheet resistance and random shunt defectsin reducing the panel level performance.

Despite the constraints of morphology and transportdiscussed in this article, the low cost of solution-processedpolymers and the impressive increase in efficiency over thelast decade suggests bright prospects of OPV in applicationslike building-integrated PV where its low-cost unique formfactor, reduced weight, semitransparency, “aesthetics appeal”may not be matched by more traditional PV technologies.

ACKNOWLEDGMENTS

The work was supported by the Center for Re-DefiningPhotovoltaic Efficiency through Molecule Scale Control,an Energy Frontier Research Center funded by the U.S.Department of Energy, Office of Science, and Office ofBasic Energy Sciences under Award No. DE-SC0001085.

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Supplementary Material

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The essence and efficiency limits of bulk-heterostructure organic solar cells: A polymer-to-panel perspective