Abstract In this work a complete semi-classical model ofan organic solar cell is presented. The different aspects ofconversion of light to electricity are taken into account. Cor-rect models for density of state and organic-metal interfaceare considered in order to include the effect of energeticallydisorder material properties. Most of the parameters for themodel are taken from literature while some were fixed byfitting with several experimental current-voltage character-istics. The comparison between modeling results and exper-imental data shows consistency and are in good agreement.Finally the model is used to investigate the optimizationof hole transport (PEDOT) and active (P3HT:PCBM) layerthicknesses in order to maximize the cell efficiency. The sim-ulation of the efficiency of the cell with varying thicknessshows a fine tuning between the exciton generation and thecharge recombination, giving clear indications on the opti-mization of cell performance.
Organic photovoltaic (OPV) devices based on solutionprocess-able organic semiconductors have attracted remark-
A. H. Fallahpour (B) · D. Gentilini · A. Zampetti · F. Santoni ·M. Auf der Maur · A. Di CarloCHOSE (Center for Hybrid and Organic Solar Energy),Department of Electronic Engineering, University of Rome“Tor Vergata”, Via del Politecnico 1, 00133 Rome, Italye-mail: [email protected]
A. GagliardiElectrical Engineering and Information Technology, TechnischeUniversität München, München, Germany
able interest as a possible alternative to conventional inor-ganic photovoltaic technologies. OPV offers good efficien-cies [1,2] up to 11 % [3,4], low cost for materials and fabri-cation equipment and a wide range of applications.
At the beginning the modeling of photoconversion inorganic devices was focused on the analysis of particularaspects of the generation/transport process in order to under-stand the limiting factor of every step. Pettersson et al. [5]were the first to use transfer matrix formalism to describeoptical absorption properties of OPVs [6–8]. Such calcu-lations allowed to establish the maximum reachable pho-tocurrent, whereas other models were developed in order toestimate the efficiency by given a fixed generation in theOPV [9–12]. These models made several approximationsabout the real morphology of the blend, assuming the disor-dered blend approximated by a geometrical ordered bilayerstructure [13,14]. Other approximations that were made areassuming a parabolic density of states similar to inorganiccrystalline materials [9–16], neglecting losses due to excitonquenching [17,18] assuming ohmic contacts [19–21]. Obvi-ously such models can propose boundaries to the maximumachievable efficiency by the electrical part of the photocon-version, but cannot quantitatively address the efficiency of areal device.
A further improvement in simulation was coupling theoptical and electrical models [20,22–24], however it doesn’taccount for the morphology of the blend which remainsan issue. In fact simple bilayer structures presented in[13,14] cannot describe the complex interface of a realblend. Consequently most of the simulations using drift-diffusion models were performed assuming an effectivematerial [10,17,18,25] where the conduction band is dom-inated by the acceptor and the valence band by the donor.These models replace all interface processes at the boundary,for example recombination and generation kinetics, between
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acceptor and donor as equivalent bulk processes. Besidethe exciton quenching, one of the most important processlimiting the charge current is the recombination. Recom-bination is called geminate if it occurs between electron-hole pairs generated by the same photon and non-geminateif it is provided by free electron-hole pairs [15,26]. ALangevin rate is usually used as an approximate model link-ing the recombination rate constant to electron and holemobilities.
Charge transport in disordered materials is described bythe hopping mechanism. This affects both mobility models[27] as well as the density of states, which shows a Gaussiandistribution of energy states [28–31]. Nevertheless, manymodels still describe transport considering constant mobil-ity [16,32,33] and parabolic density of states [9–16]. Thisapproximation assumes the presence of a well-defined energyband edge and the definition of an effective mass for chargecarriers.
Concluding, despite a wide spectrum of models andnumerical simulations in the field of OPVs, there is still roomfor improvement in order to quantitatively describe the bulkand interface processes occurring in an organic cell and toproperly describe the morphology of the blend beyond aneffective material model.
In this work we present an improvement of the numer-ical simulation of light absorption and charge transport inan OPV. We have developed a numerical model which isa part of the multiscale simulation tool TiberCAD [34], tosimulate optical and electrical properties of organic devicesusing drift-diffusion approximation. This model overcomesmost of the common approximations made in the field, suchas assuming ohmic contacts, parabolic density of states andneglecting exciton generation.
In our model, the contacts are treated as Mott-Schottkybarriers adapted for organic metal-interface in order to takeinto account the realistic effect of different work-functionsof the electrode, the correct Gaussian density of states inorder to describe the disordered material and finally an exci-ton model is inserted in order to take into account lossesin the photogeneration due to quenching of excitons. Theset of differential equations used to describe the system aresolved using a finite element method which potentially canbe solved over generic 1, 2 and 3 dimensional domains.A delicate issue concerning semiclassical models is theparametrization of both materials and electrical properties.Our model has been parametrized using values taken fromexperiments and few parameters have been indirectly esti-mated by fitting experimental J-V curves. Although the dif-ferent parts of our model have been treated separately bydifferent groups through assuming several approximation,this work is an attempt of combining and improving allthese aspects together to describe the behavior of an OPVdevice.
2 Model
The schematic diagram and physical processes of the devel-oped model are shown in Fig. 1a Generation of exciton as aresult of photon absorption and dissociation of exciton to freecharge carrier is explained in Sects. 2.1 and 2.2, respectively.Free charge carrier transport which coupled to continuum ofexciton state illustrated in Sect. 2.3. Energetic disorder inorganic material using proper model for density of state aswell as metal organic interface illustrated in Sects. 2.4 and2.5, respectively.
2.1 Optical absorption and exciton generation
Due to the typical dimension of the OPVs active layers, in therange of 20–300 nm [35], the interference effects of wave-length of the incident light lead to the formation of standingwaves which cannot be estimated by a simple Beer–Lambertmodel. In order to capture this optical feature, which influ-ences the efficiency of the cell, the optical absorption is mod-eled by a Transfer Matrix Model (TMM), a standard formal-ism used in OPV and OLED simulations [36].
The TMM can be used to calculate the density of excitonsin the active layer which is the sum of absorbed photons fromall wavelengths of light as a function of position in the device.In this work integrating the spectrum in the main absorptionregion between 350 and 800 nm and light source standard,AM 1.5 spectrum was investigated.
As the thickness of each layer composing the cell can beengineered in order to maximize the generation of excitonsin the active layer. In our case, the device simulated is an con-ventional OPV with an ITO/PEDOT/P3HT:PCBM/Al struc-ture. The complex refractive index of the different layers isgiven in Ref. [37]. The PEDOT and active layer thicknesseshave been varied in the range of experimental values. Fig-ure 1b reports the variation of blend thickness for a fixedthickness of PEDOT of 50 nm. A complex interplay betweenthe position of the resonance peaks and the size of the blend,showing a strong non-linearity in the exciton generation pro-file. The changing of the PEDOT influences only the powerintensity that reaches the active region and not its distrib-ution, causing a homogeneous generation of excitons (notshown).
2.2 Exciton dissociation
The generated excitons obtained from optical simulationmust split into free electrons and holes. This can occurat the interface between donor and acceptor materials.In our model we approximate the blend into a singlehomogenous effective material and real interface is notexplicitly included into the model. Accordingly the exci-ton diffusion equation is not implemented. However, the
Fig. 1 a Schematic diagram ofOPV structure (up) and physicalprocesses for thephotoconversion (down).Exciton generation processthrough photon absorption (a1),exciton decaying to ground state(a2), exciton splitting to freecharge carriers (a3),recombination of free chargecarriers (a4) and free chargetransport toward electrodes (a5).b Exciton generation profile inthe active layer blend varyingthicknesses from 60 and 280 nm
dissociation efficiency is considered defining a rate equationproposed by Koster [25] for exciton splitting/recombination.In the limit of an extremely efficient splitting mechanismwe can directly connect the drift-diffusion equations for freecarriers to the exciton generation, assuming that every exci-ton produces an electron-hole pair. On the contrary, if partof the exciton quench before reaching an interface, thenthe energy of the exciton (and the corresponding photon)is lost. In steady state the rate of electron-hole pair gener-ation is the balance between the process of exciton split-ting and its recombination. To compute this rate we usethe Onsager–Braun model [38]. The model includes theeffect of electric field and temperature on exciton disso-
ciation starting from the probability P of an exciton split-ting.
There is still an open debate [39–41] about the correctnessof the Onsager–Braun model to describe exciton dissociationwithin the effective medium approximation. In this approxi-mation in fact the electric field is the long range electric fieldwithin the blend. The presence of this field is still controver-sial and several authors assume a completely diffusion drivenmechanism for charges in the cell and the absence of an elec-tric field. Anyway, the presence of an interface electric fieldis correct and hence we can assume that in the limit of aneffective material the interface electric field which splits theexcitons is substituted by a bulk electric field.
One dimensional free charge carrier transport is described bydrift diffusion equations coupled to continuity equation forcharge conservation and to the Poisson equation to includethe electrostatic potential.
The continuity equations at the steady state are given by:
d Jn,(p)(x)
dx= q(G − Rn,(p)) (1)
Here, Jn,(p)(x) is the electron (hole) current, G is the rateof generation of free electron-hole pairs from excitons, andRn,(p) is the total recombination rate of electrons (holes).The local exciton density nexc(x) is calculated by means ofa local rate equation (neglecting exciton transport), given by
G R(n,p)(x) + Goptical(x)=kdecnexc(x) + kdissnexc(x) (2)
Here, kdissnexc(x) is the rate of separated exciton to freecarrier based on theory for field-dependent dissociation rateof Onsager,Goptical(x) is the generation rate of excitonsdue to the light absorption calculated from optical simula-tion. kdecnexc(x) describes radiative and non-radiative exci-ton recombination processes, excluding exciton dissocia-tion, whereas G R(n,p)(x) is the generation of excitons fromfree electron-hole pairs corresponding to free charge carrierrecombination. This process is modeled by the bimolecu-lar recombination with a Langevin rate constant μn+μp
εq.
Experimentally it is known [42–45] that Langevin rate, as afunction of charge carrier mobility, only gives an overesti-mated recombination rate. For this reason the recombinationis modulated by a prefactor (ϒ). The exact value of this pref-actor is one of the parameter in the model which is not takenfrom the literature, but directly estimated by fitting experi-mental data.
Finally the exciton density (Eq.2) is coupled to drift dif-fusion equations for free charge carrier transport. The twocomponents of the current (drift and diffusion) can be inte-grated into a single flux which depends on the gradient of theelectrochemical potential:
Jp(x) = −qp(x)μpdφp
dx
Jn(x) = −qn(x)μndφn
dx(3)
where μn,p are the electron (n) and hole (p) mobilities, n(x)and p(x) the densities of electrons and holes and φn,p theelectron (hole) electrochemical potential.
2.4 Gaussian density of state
Charge transport is admitted to be a hopping mechanismbetween molecules or different part of the polymer chain andis described by the hopping mobility model [27,46,47]. How-
ever, constant carrier mobility is a reasonable approximation,as in such device and operation condition the mobility is notconsiderably varying with density and electric field variation[48–50]. However disordered behavior had to be taken intoaccount. Typically active layers in OPVs are solution-basedpreparation and characterized by energetic disorder. The con-duction and valence bands in organic material are describedby the LUMO (lowest unoccupied molecular orbital) andHOMO (highest occupied molecular orbital) of the poly-mer/molecular respectively. However, in organic material,the energy levels are broadened, as effect of the spatial andconformation disorder.
Consequently the HOMO and LUMO of the active layershows an energetic distribution which can be approxi-mated with a Gaussian density of states. Several simulationapproaches neglect the Gaussian DOS by considering a par-abolic band approximation for disorder system which doesn’tdescribed the quantities thoroughly. However the Gaussianform of the density of state in organic semiconductor, whichis a better approximation [29,51,52],is fully considered inpresented model to study and analyze the device character-istics.
The charge carrier density is calculated through the inte-gral over the Gaussian density of state multiplied with theFermi–Dirac distribution ( f );
n, (p) =∫
gn,(p)(E, σ ) f (E, EFn,(Fp))d E (4)
Where the Gaussian density of state given by;
g(E, σ ) = N0
σ√
2πexp
(− (E − Eh,l)
2
2σ 2
)(5)
Where N0 is the density of transport site,Eh,l is the meanenergy of the LUMO (HOMO) for electrons (holes) and σ isthe broadening (variance) of the Gaussian distribution.
2.5 Organic-metal interface and charge injection
The boundary condition at contacts is the last step of the sim-ulation. Several models use organic/metal or organic/organicinterface which takes into account corrections in chargeinjection due to the presence of trap state at the interface[53,54]. However, such corrections mainly affect the injec-tion of charges from the contact into the organic, more thanthe extraction of photo-generated carriers as in a photo-voltaic cell. Accordingly we approximate the contact inter-face as Schottky contacts and the dipole shift induced bycharge accumulation trapped at intermediate states neglectedthrough assuming constant vacuum level between the organicand metal interface. This means that the energy alignmentbetween energy gap and Fermi energy is related only to thework-function of the metal at the contacts. The Schottky
barrier is then corrected by including the effect of imagecharge [55].Finally thermionic injection model for chargecarrier transfer at the metal-organic interface is describedusing a kinetic rate model [56]:
Jint = ν(n − n0) (6)
where ν represents the interface recombination velocity andn0 the equilibrium charge carrier density. For metallic con-tacts, ν is estimated to be extremely high (νn,(p) ≥ 106
cm/s). In conventional Schottky model this velocity is relatedto the effective mass of the semiconductor, however, anorganic material with a Gaussian density of states doesnot have a well defined effective mass. In this work,theinjection rate model for disordered materials generalized byScott and Malliaras [57] is considered. In their model sur-face recombination is due to interaction of charge carrierswith their image charge where it gives a considerable lowerrecombination velocity compared with crystalline inorganicsemiconductors.
3 Parameter extraction and validation of the modelcomparing with experimental measurements
As a reference system we have simulated a ITO/PEDOT/P3HT:PCBM/Al device, which is a conventional and stan-dard architecture for OPVs [58]. The model was tested try-ing to reproduce the experimental properties of twelve OPVdevices with the same structure with ITO and FTO substrate.
Devices were realized on an ITO (FTO) glass substrate(Kintec, 8�/�). The area of the substrate was 2.5×2.5 cm2.To realize small area test cells (0.5 × 0.5 cm2), substrateswere patterned by wet etching in hydrobromic acid. Beforeintroducing substrates in an inert ambient (N2), they werecleaned with ultrasonic bath in acetone and isopropylalcohol.Transferred cleaned substrates in glove-box, layer materialswere deposited by solution processing and thermal evapora-tion. First, PEDOT:PSS layer (50 nm) was spin coated andthermal annealed at 150 ◦C on hot plate. The active blend(P3HT:PCBM (1:0.7), 2 wt% in o-dichlorobenzene) was spincoated to achieve 200 nm of layer thickness. After a slow dryof active layer, the metal cathode (Al, 100 nm) was ther-mally evaporated at 10–6 mbar with a rate of 1.1 Å. Finally,the realized device was thermally annealed at 150 ◦C 10 minon a hot plate and sealed with a thermo-plastic polymers andresin. The sealed device was measured outside glove-boxunder sun AM1.5 (100 mW/ cm2) with a parameter analyzer(Agilent E5291A).
The modeling of OPV depends on many parameters. Allthe parameters directly used in the model are estimated byexperimental measurements and referenced in Table 1. Find-ing a well-established value for few parameters such as the
Table 1 List of parameters
Description Parameter Value Ref.
Active layer Thickness L 200 nm
Al work function cathode −4.1 [61]
PEDOT workFunction
anode −5.2 [62]
HOMO level E0p −5.1 eV [63–65]
LUMO level E0n −3.9 eV [63–65]
Electron mobility μe 2 × 10−3 cm2/V.s [66]
Hole mobility μh 4 × 10−4 cm2/V.s [67,68]
Decay rate kdec 104 1/s Fitting
Pair separationDistance
xa 1.15 nm Fitting
Recombinationreduction factor
ϒ 0.1 Fitting
Gaussian Width ofLUMO (HOMO)
σe, σh 0.13 eV [29,52,69]
pair separation distance, radiative and nonradiative recombi-nation rate of excitons and Langevin recombination reductionfactor was not possible.
As mentioned there is still an open debate on the rate forLangevin recombination. The reduction factor is introducedto cover the mismatch between experimental measurementsand the Langevin model. This mismatch could be high if theexciton dissociation is not explicitly included into the model.The coefficient here reduces one order of magnitude in orderto fit experimental J-V characteristics.
For the separation distance, the nominal values are in therange of 1–1.3 nm and it was fixed in our model to 1.15 nmwhich is precise or very close to the value taken from otherworks [8,20,25].
The last fitting parameter is decay rate of excitons (kdec) asan extra decay process in continuity equation of exciton state.Decay rate varied and was chosen in order to obtain a goodfitting between J-V curve of simulation and experimentallymeasured J-V characteristics of fabricated device.
In Fig. 2a good agreement between theory and experi-ments is shown by comparing simulated and experimentalJ-Vs curves of twelve reference structure.
Inset of Fig. 2a shows the J-V characteristic of the cell as afunction of the light intensity. The linear dependence of shortcircuit current (Jsc) is observed for the different incident lightintensity. The variation of Jsc with light intensity indicatesthat most of the photo generated carriers are efficiently col-lected (due to the large applied bias) prior to recombination.The obtained J-V curve with presented model for differentintensity is comparable with previous studies [59,60] of theintensity dependence of OPVs, presenting that the bimolec-ular recombination is a dominant losses mechanism near theVoc in OPVs.
Fig. 2 a J-V curve, b IPCE and c contribution of current density versuswavelength comparison between simulation and experiments
Simulation results are within experimental errors eventhough a more pronounced difference exists for the short cir-cuit current (Jsc). This can be attributed to small differencesbetween real and simulated optical generation. In order to elu-cidate this point we compare in Fig. 2b, c the simulated andmeasured Incident photon-to-current efficiency (IPCE) andthe contribution to the short circuit current density for eachwavelength, respectively. The agreement between experi-mental data and simulation results is rather good. The simu-
lation overestimate experimental IPCE for large wavelengthand this results in a slightly increase of Jsc (see Fig. 2a).
4 Efficiency dependence on active layer thickness
Light absorption of an OPV cell is strictly dependent on thethicknesses of different layers forming the device. In thissection we will perform a series of simulation to find therelation between electrical parameters and layer thicknesses.
We have simulated the reference structure presented inFig. 1 by varying the thickness ranges of the anode (PEDOT)from 20 to 200 nm and of the active layer (P3HT/PCBM)from 60 to 280 nm. In the first set of simulations we keptfixed the active layer (200 nm) varying the PEDOT (20–200nm) thickness. The J-V curves presented in Fig. 3a showna linear decreasing dependence on the PEDOT thickness, interms of Jsc and efficiency (Fig. 3b), while the Voc is onlymarginally affected by varying the PEDOT thickness (notshown).
The reduction in efficiency is therefore due to absorptioninside the PEDOT acting as an obstacle for photons as dis-cussed in Sect. 1. The maximum decrease of efficiency canbe quantified to be of 13 % (from 3.9 to 3.5 %) for 200 nm.Therefore the total efficiency of the device is only marginallyaffected by varying the PEDOT thickness.
Instead a completely different trend is obtained by vary-ing the blend thickness (60–280 nm) leaving the PEDOTlayer fixed (50 nm) as shown in Fig. 3c. The simulation ofexciton generation distribution in the active layer (Fig. 1b)shows an oscillating behavior due to the formation of stand-ing waves within the blend. This oscillating behavior isreflected in J-V curves, mainly affecting Jsc and only mar-ginally Voc, as shown in the Voc trend (inset of Fig. 3c).In order to understand the nature of this oscillating trend,we have deconvolved the optical absorption from the chargetransport. In Fig. 4a the total exciton generation at the equi-librium is shown as a function of active layer thickness.As expected an oscillating behavior is found and the max-imum absorption is obtained for a blend of 220 nm. How-ever, current is not directly correlated to exciton generationrather to the free carrier net-generation (effective free car-rier generated considering also the recombination process).In Fig. 4b the net-generation rate of free carriers inside theactive layer is shown for two working conditions: short circuitand maximum power point (MPP). Beside the fact that theamount of free charges decreases when the cell is working,we observe that at MPP condition the maximum free carri-ers net-generation is achieved for a cell with a blend layerthickness of 90 nm. Even though optical generation is largerfor a blend thickness of 220 nm compared to the 90 nm, thereduction of electron-hole recombination obtained in smallerdevices favors the 90 nm device. In Fig. 4c the trends in Jsc,
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J Comput Electron (2014) 13:933–942 939
Fig. 3 a Simulated J-V curves result for various PEDOT thicknesses. bResulting Jsc and efficiency. c J-V simulation results varying the activelayer thickness
fill factor and cell efficiency as a function of active layerthickness are shown. The efficiency of the cell, for the differ-ent thicknesses, shows a variation of 30 %, from a minimumof 3.1 % at 150 nm to a maximum value of 4.4 % at 90 nm.The efficiency, similar to the net-generation of free carries atMPP, has is maximum for the 90 nm device, however quiteinteresting is that the short circuit current is similar for 90and 220 nm while the fill factor is strongly reduced at 220 nm.This reflect an increased resistance due to the larger recom-bination. This suggests that reducing recombination can shiftthe maximum efficiency from a blend thickness of 90–220nm. Figure 5 shows the effect of DOS on the efficiency of the
Fig. 4 a Total exciton generation density varying the active layer thick-ness. b Net-generation of free charge carriers for various active layerthicknesses at short circuit and maximum power working points. c Shortcircuit, efficiency and fill factor of OPV simulations for various activelayer thicknesses
Fig. 5 Efficiency of the cell for various active layer thicknesses andGausian DOS widths
cell for various thicknesses. Approximately an improvementof 50 % in the efficiency is estimated for the highly orderedmaterial (σ = 50 m eV) for the various active layer thick-nesses. However by increasing the degree of disorder the
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efficiency start to drop dramatically, where for highly disor-dered material, the thickness of active layer would not playingan important role. The drop in efficiency is attributable to thehuge reduction of the Voc. Inset of Fig. 5 shows the Voc as afunction of degree of disorder. Due to a number of parame-ters dependent (e.g. mobility and recombination), the precisedependency of Voc is a complex subject to distinguished.However the Voc is associated to the quasi fermi levels dif-ference of electron and holes. For a very narrow GaussianDOS, arising from highly ordered materials, the quasi Fermilevel is very close to the HOMO and LUMO energy levelsin order to provide enough states for the photo generatedcarriers. On the contrary for a high disordered material, thebroadening of the HOMO and the LUMO is considerablylarger and long tails of states are present deep into the energygap. This means that as compared to more ordered materials,smaller quasi Fermi level splitting (lower Voc) is needed forthe same amount of photo generated charge carrier density.
Efficiency of OPVs for various layer thicknesses havebeen performed experimentally in several studies [70–74].The efficiency peak positions in terms of thickness ofthe blend can vary for different Blends, composition, tem-perature and solution process [58,75–78] but the periodictrend still exists. Concluding that our prediction with devel-oped model follows correctly the estimated trends observedwith numerous real cells summarized in Ref. [79].
5 Conclusion
We have presented a semi-classical model of charge gen-eration and transport for OPVs. Our formalism simulatesthe photoconversion in the solar cell treating the optical andthe electrical part on equal footing. These have been imple-mented by means of Transfer Matrix Model for what con-cerns light absorption and drift diffusion model for carriertransport. In this work we introduce, in the same simulativecontext some relevant improvements with respect to formermodels. Metal/organic junctions are described as Schottkycontacts which allow to include the effect of the metal’swork functions and consequently the influence of the work-function on open circuit voltage. Moreover, even though thetransport in the blend is treated as an effective medium,the disordered nature of the material is taken into accountby assuming a Gaussian density of states. Besides, the useof finite element method opens interesting perspectives forfuture simulations including the real blend morphology anddiffusion of excitons. Such a complex model has been para-meterized using measured values from the literature and thecomparison with experimental J-V and IPCE shows a goodagreement.
The model has been used to discuss optimization of P3HT-PCBM blend and PEDOT layer thicknesses in terms of opti-
cal and electrical behavior. In particular it has been shownthat while changing the PEDOT does only influence the opti-cal losses, the active layer thickness has a far more compleximpact on the performance of the cell. Due to the formation oflight standing waves within the blend, the optical total gener-ation is characterized by a nonlinear semi periodic trend withtwo peaks in generation at 90 and 220 nm. This semi peri-odic behavior reflects in the cell performance, where alsorecombination and charge collection play an important role.In fact, by increasing the blend thickness we increase alsocharge recombination and for this reason, the optimal effi-ciency peak occurs at a blend thickness of 90 nm and notat 220 nm where the generation is higher. Finally the effectof Gaussian DOS studied for the same range of active lay-ers shows highly ordered material are more sensitive to theactive layer thickness and they show higher efficiency.
Acknowledgments We acknowledge the “Polo Solare Organico—Regione Lazio”, MIUR PRIN “DSSCX”, projects for financial support.
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