Temperature dependent charge transfer state absorption and emission reveal dominant role of dynamic disorder in organic solar cells
Clemens Göhler, Maria Saladina, Yazhong Wang, Donato Spoltore, Johannes Benduhn, Karl Leo, Carsten Deibel
TTemperature dependent charge transfer state absorption and emission revealdominant role of dynamic disorder in organic solar cells
Clemens Göhler, Maria Saladina, Yazhong Wang, DonatoSpoltore, Johannes Benduhn, Karl Leo, and Carsten Deibel ∗ Institut für Physik, Technische Universität Chemnitz, 09126 Chemnitz, Germany Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP) and Institute for Applied Physics,Technische Universität Dresden, Nöthnitzer Str. 61, 01187 Dresden, Germany (Dated: February 12, 2021)The energetic landscape of charge transfer (CT) states at the interface of electron donating andelectron accepting domains in organic optoelectronic devices is crucial for their performance. Centralquestions—such as the role of static energetic disorder and vibrational effects—are under ongoingdispute. This study provides an in-depth analysis of temperature dependent broadening of the spec-troscopic absorption and emission features of CT states in devices with small molecule–fullereneblends. We confirm the validity of the electro-optical reciprocity relation between the photovoltaicexternal quantum efficiency (
EQE PV ) and electroluminescence ( EQE EL ), enabling us to validate thedevice temperature during the experiment. The validated temperature allows us to fit our experi-mental data with several models, and compare extracted CT state energies with the correspondingopen circuit voltage limit at . Our findings unveil that the absorption and emission characteris-tics are usually not symmetric, and dominated by temperature-activated broadening (vibrational)effects instead of static disorder. Keywords: organic photovoltaics, charge transfer states, static energetic disorder
I. INTRODUCTION
Organic solar cells (OSCs) gain renewed interest sincetheir power conversion efficiency increased rapidly overthe last few years and are nowadays approaching 20%.[1–3] Many successful steps have been achieved in design-ing new materials, especially non-fullerene acceptors;yet the underlying working principles remain relativelyunchanged.[4–7] All efficient approaches favor a combina-tion of at least two materials, namely an electron donorand acceptor, forming a heterogeneously blended layersandwiched between selective electrodes. To facilitatethe dissociation of strongly bound photogenerated exci-tons usually free energy is sacrificed. This is realized atthe donor–acceptor interface by the formation of ener-getically more favorable and less strongly bound chargetransfer (CT) states.On the one hand, CT states are responsible for moreefficient charge carrier generation. On the other hand,they are limiting the open circuit voltage V oc in or-ganic solar cells[8] and determining both radiative andnon-radiative loss mechanisms.[9, 10] Nevertheless, a de-tailed description of their energetic nature is still miss-ing. The majority of studies in the field over the lastfew years determined the energetic properties utilizing(electro-)optical spectroscopy and interpreted the resultsbased on a molecular model of CT states,[8–17] andrecently computational multi-scale simulations togetherwith quantum-mechanical calculations.[18] One of themost discussed questions is whether CT states are domi-nated by static energetic disorder at the donor–acceptor ∗ [email protected] interface, which we would expect in organic semicon-ductor blends based on conclusions from trap state[19]and charge transport measurements,[20, 21] or can bedescribed by dynamic vibrational broadening alone. Asthis matter impacts the interpretation of measured deviceproperties, including the excited CT state energy E ct , itis essential to precisely quantify energy losses in organicsolar cells.[8, 10, 11, 22] A related question is whether V oc losses measured in a specific device are inherent to a ma-terial system, or can be potentially reduced by optimizingthe morphology in order to decrease static disorder.In this work, we address the role of energetic disor-der by investigating the validity of different theoreticalapproaches. We compare the predicted absorption andemission spectra to our experimental photovoltaic exter-nal quantum efficiency ( EQE PV ) and electroluminescence( EQE EL ) spectra, measured on a set of thermally evap-orated OSCs over a broad temperature range. Our mea-surements provide evidence for the validity of the electro-optical reciprocity between EQE PV and EQE EL , beingessential to confirm (or correct) the device temperatureduring experiments. We find that the multiple vibrationsmodel , which does not include static disorder, explainsour experimental results the best. In order to optimize V oc in the absence of static disorder, the emphasis shouldshift to the reduction of vibration-induced losses.[18] II. BACKGROUND INFORMATIONA. Electro-optical reciprocity relation
As absorption of CT states is usually very weak inOSCs, it is often measured by sensitive detected
EQE PV a r X i v : . [ phy s i c s . a pp - ph ] F e b spectroscopy. Absorption and EQE PV are related bythe internal photovoltaic quantum efficiency ( IQE PV ) forconversion of absorbed photons to extracted charge car-riers. Emission from CT states is quantified by spectralelectroluminescence (EL) yield ( EQE EL ) under forwardbias. Its integral value EQE
LED , the total EL quantumefficiency, represents all non-radiative voltage losses ofthe photovoltaic device, which scale with ln(EQE
LED ) .[9]While CT state emission can also be observed in termsof photoluminescence,[11] it may be more difficult dueto much stronger emission from pure donor and accep-tor phases which have to be subtracted first.[17] Opticalinterference might also affect the light out-coupling ef-ficiency of thin film devices, which was recently pointedout by List et al. [23] The effect was shown to be negligiblefor absorbing layer thicknesses below
80 nm ,[13, 23, 24]and to be independent of the device temperature.[17]
EQE PV and EQE EL of semiconductor devices are con-nected by Rau’s electro-optical reciprocity relation.[25]Assuming an IQE PV independent of the energy of the ab-sorbed photon[26] and negligible space-charge effects,[27]the emission flux from a solar cell operated under for-ward bias is proportional to its thermal emission spec-trum: both spectral distributions ( EQE PV & EQE EL )are correlated by the blackbody emission flux φ BB ( E, T ) of photons with energy E at temperature T , and scalewith the dark saturation current J of the device. Thevalidity of the reciprocity relation was shown to hold formost types of photovoltaic devices, including OSCs atroom temperature.[9, 13, 28, 29] Therefore, a theoreticaldescription of CT state emission and absorption charac-teristics is required to satisfy Rau’s reciprocity relation: EQE
LED ( T ) = (cid:90) ∞ EQE EL ( E, T ) d E (1) = qJ ( T ) (cid:90) ∞ EQE PV ( E, T ) φ BB ( E, T ) d E where q is the elementary charge.In the experiment, the temperature of the device un-der test is usually set to the temperature of a reservoir T set , for example by using a PID controlled heater in aninsulated cryostat. Most studies reporting temperature-dependent investigations discuss their findings in termsof T set ,[10, 17, 30] without verifying if that temperatureis actually valid under the measurement conditions (e.g.current injected to drive the electroluminescence, whichcan heat up the sample). If the reciprocity relation holdsover a broad temperature range, it allows us to validatethe solar cell temperature T valid during spectroscopicmeasurements: by using the Boltzmann approximationof the blackbody spectrum, the dark saturation current J and T valid can be extracted from the reciprocity rela-tion and the quotient of EQE EL and EQE PV .[26] Withthe Boltzmann constant k B , the speed of light in vacuum c , and Planck’s constant h , we find: ln (cid:18) qJ (cid:19) − Ek B T valid = (2) − E ) + ln (cid:18) c h π (cid:19) + ln (cid:18) EQE EL ( E )EQE PV ( E ) (cid:19)(cid:12)(cid:12)(cid:12)(cid:12) T set Employing equation (2), it can be tested if the de-vice really is at T set during the absorption and duringthe emission measurement. We calculate T valid of thegray body that would fulfill the reciprocity relation ofmeasured EQE EL ( T set ) and EQE PV ( T set ) . If we find T valid (cid:54) = T set , either one or both spectra were recordedat a device temperature other than T set . The crucialparameter in these cases is most likely the device tem-perature during EQE EL measurements, as injection con-ditions exceeding typical working parameters may causeunintended heating of the device. Monochromatic lightintensities for EQE PV spectroscopy are typically far be-low solar illumination and should not cause unintendedheating; an approximation of the power dissipated bythe devices during EQE EL and EQE PV measurements isgiven in sec. 2 in the Supplemental material. Accord-ingly, high injection currents have been shown to affectshapes of EQE EL spectra,[30] and to cause deviationsfrom the electro-optical reciprocity relation even at roomtemperature.[9, 26] As a consequence of equation (2), weexpect that the device temperature for EQE PV measure-ments is usually very close to T set , and the temperatureduring EQE EL measurements is often T valid ≥ T set dueto Joule heating caused by the higher current densities.We therefore suggest to estimate the device temperaturewith T valid for the analysis of emission characteristics. B. CT state models
Currently discussed theoretical descriptions of CTstates are based on the theory of electron transfer byMarcus et al .[31] The interfacial CT state is treated inanalogy to a molecular state, with photon absorptionand emission from excited electronic states. An appli-cation of this theory with regard to the electro-opticalproperties of a solar cell device was given by Vandewal etal. ,[8, 9] who were able to explain both the sub-bandgapcharacteristics of
EQE PV and EQE EL of OSCs at roomtemperature with Gaussian line shapes, EQE PV = E − × f ∗ σ √ πλ R k B T exp (cid:18) − ( E ct + λ R − E ) λ R k B T (cid:19) (3) EQE EL = E × f ∗ emis /n inj √ πλ R k B T exp (cid:18) − ( E ct − λ R − E ) λ R k B T (cid:19) . (4)The absorption and emission lines of the CT statewith energy E ct are separated by its reorganization en-ergy λ R , which also describes the respective linewidths (2 λ R k B T ) / ; only these two parameters are necessaryto describe the shape of the contribution of CT states to EQE EL and EQE PV spectra at temperature T . Furtherassumptions and quantum mechanical photo-physics, in-cluding transition matrix elements, are summarized inthe amplitudes f ∗ σ and f ∗ emis . The emission flux underLED conditions has to be normalized by the injectedcharge carrier density n inj . Using this model, the au-thors were able to predict V oc of the solar cell under sim-ulated solar illumination at room temperature from theextracted E ct .[9, 10]In this simple Marcus model , λ R accounts for dy-namic broadening from intra- and intermolecular vi-brations with small characteristic frequencies f vibr (cid:28) k B T /h . Higher frequency vibrations inherent to or-ganic molecules such as carbon–carbon stretching modes,which have been proposed to play an important rolefor non-radiative recombination in organic semiconduc-tor devices,[15] lead to additional absorption and emis-sion lines.[11, 32] For a single dominant vibration mode,the corresponding spectra can be explained by a sumof shifted Gaussian lines, leading to an extended Marcusmodel : EQE PV ∝ E − √ πλ R k B T × ∞ (cid:88) j =0 e − S S j j ! exp (cid:18) − ( E ct + j Λ vibr + λ R − E ) λ R k B T (cid:19) (5)The moment of the Poisson distribution character-ized by the Huang–Rhys factor S determines the rela-tive intensity of vibrational levels j . For vibration en-ergies Λ vibr >
100 meV , these contributions may notbe visible in the
EQE PV spectrum due to the overly-ing stronger absorption from donor and/or acceptor sin-glet states.[11] Characteristic carbon–carbon stretchingmode energies of fullerenes were found in the region of Λ vibr ≈ . . .
180 meV .[11, 17, 33] Note that excitationof phonons leads to additional absorption at higher en-ergies, whereas the respective photoluminescence spec-trum features additional emission lines redshifted by − j Λ vibr .[11, 32]Without taking these high-energy modes into account,the simple Marcus model (equations (3) and (4)) complieswith the reciprocity relation, equation (1). As a conse-quence, the reduced spectra ( EQE PV · E and EQE EL /E )are symmetric and mirror each other. However, whenthe electro-optical reciprocity relation is applied to the extended Marcus model’s EQE PV (equation (5)), we canderive a different expression for the EQE EL emission: EQE EL ∝ E √ πλ R k B T exp (cid:18) − E ct k B T (cid:19) × (6) ∞ (cid:88) j =0 e − S S j j ! e (cid:16) − j Λvibr k B T (cid:17) exp (cid:18) − ( E ct + j Λ vibr − λ R − E ) λ R k B T (cid:19) . We find that the
EQE EL does not longer mirror EQE PV , as it inherits the positive vibrational progression + j Λ vibr . The emission quantum efficiency from thesestates is however exponentially damped by the term e − j ,yielding an asymmetrical shape of the reduced spectra,in contrast to the simple Marcus model . C. Models based on static and dynamic disorder
Both models discussed above do not include static en-ergetic disorder, which is expected to be present in non-crystalline organic semiconductors, and even more so inthose made from heterogeneously blended films. An ex-tension to the
EQE PV description from the simple Mar-cus model was given by Burke et al. by assuming a Gaus-sian distribution of disordered excited CT state energies E (cid:48) ct with variance σ to represent static disorder. Withthis assumption, the EQE PV shape can still be describedby a reduced Gaussian, albeit with a modified varianceand E ct now representing the first moment of the distri-bution of CT state energies:[10] EQE PV ∝ E − √ π − (cid:112) λ R k B T + 2 σ exp (cid:18) − ( E ct + λ R − E ) λ R k B T + 2 σ (cid:19) (7) EQE EL ∝ E √ π − (cid:112) λ R k B T + 2 σ exp (cid:18) − E ct k B T + σ k B T ) (cid:19) × exp (cid:18) − ( E ct − λ R − σ /k B T − E ) λ R k B T + 2 σ (cid:19) . (8)The EL expression in this disordered Marcus model given here complies with EQE PV (equation (7)) and theelectro-optical reciprocity relation (equation (1)). Inboth the EQE PV and EQE EL spectra, the modified vari-ance σ = σ + 2 λ R k B T leads to a non-zero linewidthat T = 0 K , a trend that was experimentally confirmedby several temperature-dependent measurements of CTstates in EQE PV or EQE EL spectra.[10, 17, 18, 30]The model predicts an additional temperature depen-dent peak redshift of the EQE EL spectrum by − σ /k B T ,while reduced spectra should nonetheless remain sym-metric with equal EQE PV and EQE EL linewidths. Thisparticular peak shift should only be affected by the de-vice temperature; it has been reported for inorganic solarcells with a Gaussian distribution of bandgaps,[34] but isabsent in many studies on OSCs.[17, 30] Nevertheless,prominent EL peak blueshifts caused by increased injec-tion currents have been documented for OSCs with anexponential[30] and, less pronounced, with a Gaussiandistribution of sub-bandgap states.[13, 30, 35]Kahle et al. suggested a combination of the disor-dered and extended Marcus model to explain EQE PV ,in which each E (cid:48) ct in the normal distribution of disor-dered CT states was extended by vibrational states ofequal frequency (equation (9)).[11] If the electro-optical Table I. Comparison of the models included in this study,separated for inclusion of static disorder and phonon excita-tion. The expected symmetry between reduced absorptionand emission lines is included as an additional criterion. Al-lowing excitation of molecular vibrations disrupts the sym-metry except for the 0–0 transition; incorporating static en-ergetic disorder introduces a temperature dependent shift ofthe
EQE EL peak. w/o molecular vibrations w/ molecular vibrations w /o s t a t i c d i s o r d e r simple Marcus extended Marcusmodel a [Vandewal et al. ] model bc E ct = E PV , max − λ R E ct = E − , max − λ R E ct = E EL , max + λ R E ct = E − , max + λ R σ PV , EL = √ λ R k B T σ − , EL = √ λ R k B T multiple vibrations d E PV , max = f ( E ct , λ R ) E EL , max = f ( E ct , λ R , T ) σ PV (cid:54) = σ EL w / s t a t i c d i s o r d e r disordered Marcus extended disorderedmodel ae [Burke et al. ] model be [Kahle et al. ] E ct = E PV , max − λ R E ct = E − , max − λ R E ct = E EL , max + λ R + σ k B T E ct = E − , max + λ R + σ k B T σ PV , EL = (cid:113) λ R k B T + σ σ − , EL = (cid:113) λ R k B T + σ a symmetrical reduced EQE PV & EQE EL spectra b symmetrical only on 0-0 transition line of reduced spectra c asymmetrical envelope function d asymmetrical reduced EQE PV & EQE EL spectra, depending onvibrations involved e symmetry axis redshifted with decreasing temperature reciprocity relation is applied, we again find a descrip-tion for EQE EL involving both the temperature depen-dent peak redshift inherited from the disordered Marcusmodel , and the asymmetry of reduced spectra from the extended Marcus model : EQE PV ∝ E − √ π − (cid:112) λ R k B T + 2 σ × ∞ (cid:88) j =0 e − S S j j ! exp (cid:18) − ( E ct + λ R + j Λ vibr − E ) λ R k B T + 2 σ (cid:19) (9) EQE EL ∝ E exp (cid:16) − E ct k B T + σ k B T ) (cid:17) √ π (cid:112) λ R k B T + 2 σ ∞ (cid:88) j =0 e − S S j j ! e (cid:16) − j Λ vibr k B T (cid:17) × exp (cid:18) − ( E ct + j Λ vibr − λ R − σ /k B T − E ) λ R k B T + 2 σ (cid:19) . (10)This extended disordered Marcus model was discussedto be a simplification of a system with two characteristicvibrations; the second vibration was assumed to be in therange of Λ ≈ . . .
20 meV .[11, 36] The hypothetical vi-bration would, in connection with a high Huang–Rhysfactor S , transpose the Poisson distribution at roomtemperature into a Gaussian shape that is indistinguish-able from a normally distributed, statically disordered E ct at room temperature.[17] At lower temperatures, thisapproximation becomes inaccurate. Respective expres-sions for EQE PV [11] and reciprocity compliant EQE EL are given by: EQE PV ∝ E − √ πλ R k B T ∞ (cid:88) i =0 ∞ (cid:88) j =0 e − S S i i ! e − S S j j ! exp (cid:18) − ( E ct + λ R + j Λ vibr + i Λ − E ) λ R k B T (cid:19) (11) EQE EL ∝ E e ( − E ct /k B T ) √ πλ R k B T ∞ (cid:88) i =0 ∞ (cid:88) j =0 e − S S i i ! e − S S j j ! e (cid:16) − i Λ + j Λ vibr k B T (cid:17) exp (cid:18) − ( E ct − λ R + j Λ vibr + i Λ − E ) λ R k B T (cid:19) . (12)The idea of allowing only dynamic disorder effects forCT lineshape broadening may offer a solution for the EQE EL peak shift expected for statically disordered sys-tems, but experimentally not observed in OSCs. Yet in-terestingly, all models that deal with a progression ofvibrations also predict an EQE EL peak redshift with de-creasing temperature (albeit not as pronounced as withstatic disorder). Injected charge carriers will occupystates near the CT state minimum, which is representedin equation (12) by an exponential decrease of EQE EL intensity with i and j . For a high frequency vibration Λ vibr (cid:29) kT , this results in a vanishing emission from j > ; for a low frequency vibration Λ ≈ k B T , it man-ifests in a perceived peak shift and a further linewidth reduction. As a result of both properties, emission andabsorption linewidths will be inherently asymmetrical inthis model. A comparison of predicted peak propertiesbetween the multiple vibrations and extended disorderedmodel is shown in Fig. S4 in the Supplemental material. D. Consequences
The main parameters E ct and λ R for every model aresummarized in table I, with regard to the linewidths σ and peak positions E max of reduced EL and PV spec-tra, wherever possible. While all models share more orless the same set of molecular parameters to describeemission and absorption of CT states, their quantifica-tion from experimental data may differ depending onthe model of choice. This holds especially true for thedynamically disordered multiple vibrations model , wherethe more complex description prevents a simple extrac-tion of E ct and λ R . Therefore, even a set of temperaturedependent EQE PV and EQE EL measurements requirescomprehensive model fits to the spectral data to deter-mine these parameters correctly. III. RESULTSA. Methods
We investigate a set of organic bulk heterojunction so-lar cells with the small molecule donors 1,1-bis[4-(N,N-di-ptolylamino) phenyl]cyclohexane (TAPC) and 4,4’,4"-Tris(carbazol-9-yl)triphenylamine (TCTA), diluted with5 or 10 weight percent (wt%) in a C matrix. From EQE PV measurements under different bias voltages, itcan be concluded that these devices have a constant IQE PV , which is a prerequisite for the electro-optical reci-procity relation.[14] Temperature dependent measure-ments are realized with the devices in a contact gas cryo-stat. EQE PV is measured by comparing currents un-der short-circuit conditions from monochromatic illumi-nated OSCs with a calibrated reference detector. Rela-tive EQE EL is detected from constant current injection,and illumination dependent V oc is recorded while varyingthe output power of a cw–laser. Details about the de-vice architecture and experimental conditions are givenin sec. VI. B. Reciprocity and temperature validation
The recorded, temperature dependent
EQE PV and EQE EL spectra are shown in Fig. 1. While the shapesof EQE PV spectra are not significantly different at firstglance, apart from the decreased signal-to-noise ratio atlow temperatures, the deviations are more pronouncedin the EQE EL spectra of each system, most notably bya significant reduction of the linewidth with decreasingtemperature.First, we checked the validity of the electro-optical reci-procity by extracting T valid from EQE PV and EQE EL spectra measured at the same T set . The results areshown in Fig. 2. We find a very good agreement between
125 K and
300 K for the TAPC:C solar cell with 10%donor content; however, an increasingly higher T valid isextracted for the other devices when cooled below
250 K .To further investigate this discrepancy, we compared
EQE EL spectra at presumably equal T set (Fig. S1) andthe effect of the injection current density on T valid (Fig. S2) for the TAPC:C devices. Both control analy-ses show an increased device temperature during EQE EL measurements, as the increased T valid correlates with broader EQE EL spectra, and the effect becoming morepronounced at higher injection currents. We point outthat we did not change the experimental routines or thesetup between individual devices. Thus, a control mech-anism for the device temperature as given by the reci-procity becomes even more important. C. Single spectrum analysis
When analyzing the linewidth σ of EQE EL and EQE PV CT contributions individually in terms of a Gaussiandistribution, currently the most common method,[17,30] we find major differences between extracted valuesfrom
EQE PV and EQE EL spectra (Fig. 3; values forTCTA :C in Fig. S5). Rather than fitting a non-linear function to the spectrum, we applied a linear re-gression to the numerical derivative d / d E of the reducedspectra to decrease fitting errors[17] (see sec. 5 in theSupplemental material). In general, our EQE PV spectratend to be significantly broader than their EQE EL coun-terparts, requiring an asymmetrical model to describeboth spectra simultaneously. These findings show thatCT state models requiring reduced emission and absorp-tion spectra to be symmetrical—the simple and disor-dered Marcus model —cannot be correct.[9, 10]The slope of σ ( T ) and its extrapolated intercept at T = 0 K is used to extract values for σ ct and λ R basedon the disordered and extended disordered Marcus model (equations (7)-(10)).[10, 17, 30] The extracted param-eters are listed in table II. Both parameters dependon whether they are based on the supposed ( T set ) orvalidated temperature ( T valid ) during the measurement.Negative values for σ ct indicate a negative interpolatedintersection which would be unphysical in terms of the disordered Marcus model . Similar results were also re-ported for low-temperature EL measurements, challeng-ing the relevance of static energetic disorder for the CTstate ensemble compared to dynamic broadening.[17] Inaddition, we find unexpected quantitative differences ofthe parameters between absorption and emission, andwithin similar donor dilutions. Instead of relying on indi-vidual EQE PV or EQE EL peak analysis with all its flaws,our temperature validated combined data records allowus to extract model parameters from a simultaneous re-view of absorption and emission spectra. D. Global data analysis
To test the multiple vibrations model , we implementeda Levenberg-Marquardt optimizing algorithm to fit both
EQE PV and EQE EL spectra simultaneously for multi-ple temperatures. As discussed before, we assumedthe temperature T valid validated by the reciprocity re-lation for EQE EL -measurements, while maintaining T set for EQE PV -spectra. Each spectrum was weighted equallyby dividing its residuals by the number of supporting ! " ! ! " ! "$ ! "% ! "& ! "’ ! "( ! ") ! "* ! " ! ! ! + , - . / , : , " *;**;! ;$ ;& ;( ;* 3<,+=>227,68?@5A ’B CA &! ! " ! ! " ! "$ ! "% ! "& ! "’ ! "( ! ") ! "* ! " ! ! ! + , - . / , : , " *;**;! ;$ ;& ;( ;* 3<,+=>227,68 )!!*’!*!! ’! ? D ?@5A !B CA &! ! " ! "$ ! "% ! "& ! "’ ! "( ! ") ! "* ! " ! ! ! ! * + , - . / , : , " *;**;! ;$ ;& ;( ;* 3<,+=>227,68?A?@ !B CA &! !" Figure 1. Measured relative
EQE PV and EQE EL spectra for (a) TAPC:C bulk heterojunction solar cells with 5 wt% and (b)10 wt% donor content, and (c) TCTA:C bulk heterojunction solar cell with 10 wt% donor content. All measured curves wereshifted by a constant offset respective to T set .Table II. Energetic width of static disorder distribution σ ct and reorganization energy λ R extracted from individual fitsto reduced EQE PV and EQE EL spectra in accordance withthe disordered Marcus model . Negative values for σ ct , notedin parenthesis, occur when the CT linewidth interpolates tonegative values at T = 0 K . Both obtained parameters changesignificantly when the correction of T set is applied for EQE EL by utilizing the reciprocity relation. EQE EL EQE PV σ ct /meV λ R /meV σ ct /meV λ R /meVTAPC :C T valid (-14.8) 104.8 49.7 117.7 T set :C T valid (-38.9) 151.4 36.7 122.2 T set (-33.3) 145.9TCTA :C T valid (-41.3) 179.3 44.9 126.7 T set data points, in order to avoid over-emphasizing of EQE EL (with higher energy resolution than EQE PV ), and ofspectra from higher temperatures, which tend to providemore supporting data points due to their better signal-to-noise ration and broader signal range. The fitting rangeof models that do not describe excitation of molecularvibrations was reduced to the tail of each spectrum; oth-erwise, it is limited by the onset of the C -singlet ex-citation at . for EQE PV and the detection limit at . for EQE EL , and respective background noise lev-els. We applied the algorithm for all models summarized in table I with similar starting values.Fig. 4 shows measured reduced EQE PV and EQE EL spectra of TAPC :C at T = 150 K and
300 K andrespective fitted curves for the multiple vibrations model,extended and extended disordered Marcus model . Thebest agreement between data and model is found for the multiple vibrations model , while the others may properlyfit the spectra at room temperature and their respectivetail regions, yet lead to characteristic differences espe-cially at lower temperatures.Some values of the fitted CT energy E ct , reorganizationenergy λ R and the low-energy vibration ( Λ and S ) arelisted in table III, with the complete sets of parametersin table S3. We focus here on the more elaborate mul-tiple vibration , extended and extended disordered Marcusmodel . The latter two models imply a more than
100 meV higher CT state energy E ct and a lower reorganizationenergy λ R of the CT state than the former. Betweenthe different donor concentrations in TAPC:C blends,we find a low energy vibration of around
13 meV and avariation in the related Poisson distribution moment S .To add further plausibility to the numerically obtainedmodel parameters, we turned to the total EL quantumyield EQE
LED , which can be estimated by integration ofmeasured and predicted
EQE EL spectra. We find goodagreement for the models without static energetic disor-der, while the calculated EQE
LED in the extended disor-dered model becomes significantly larger than measuredvalues at low temperatures (Fig. S8). !!" % & ’ () * ++, - . !!" /01 ++,-.+%234 +%234 $!5 +%4%2 $!5 +% /01 +8+% &’()* Figure 2. Device temperature T valid obtained from the electro-optical reciprocity relation between EQE PV and EQE EL (equation (2)) with respect to the experimentally expectedtemperature T set . For the cell with 10% donor content, bothtemperatures are almost identical, whereas we see significantdeviations from the ideal case for the other two cells at lower T set .Table III. Extrapolated open circuit voltage limit V andfitted parameters for the multiple vibration (mv), extended(eM) and extended disordered Marcus model (edM). We sys-tematically find E ct to be at least
100 meV higher in the ex-tended and extended disordered Marcus model, in correspon-dence with a significant lower reorganization energy. E ct / eV λ R / meV Λ / meV S eM edM mv eM edM mv mvTAPC :C qV = 1 .
38 eV
TAPC :C qV = 1 .
32 eV
TCTA :C qV = 1 .
47 eV
In addition, we measured V oc for a range of tempera-tures and increasing illumination intensity G ; values andanalysis are discussed in sec. 6 in the Supplemental ma-terial. Regardless of the intensity, V oc ( T ) converges toa fixed limit when extrapolated to T → . The limit qV , shown in table III, should equal E ct in the case ofOSCs,[9] thus providing us with a supplementary mea-surement to validate the model parameters. IV. DISCUSSION
The agreement between T set and T valid forTAPC :C over a temperature range of
175 K !" & ’ (() * + , % - .!!%!! !!! / (()8-9:9 ;, (/=;> !? @> (/=;> ((A? @> ( ((9:9 B/ C Figure 3. Temperature dependency of the squared CTlinewidth σ in EQE EL (against validated EL temperature T valid ) and EQE PV (against expected device temperature T set )spectra for TAPC:C solar cells. We find smaller emis-sion linewidths for all devices. In the case of TAPC :C ,where we found T valid significantly increased for lower T set ,the linewidth narrowing appears less steep if T set would beused as reference (black crosses). implies the validity of the electro-optical reciprocityrelation between EQE PV and EQE EL , as T valid wasobtained by strictly comparing measured spectra takenat T set . However, we find this correlation to be violatedfor the other solar cells investigated in this study. Ifthe reciprocity relation remained valid as expected, wewould conclude that T set , the temperature of the heatreservoir, differs from the actual device temperatureeither during the EQE PV or EQE EL measurement, orboth. On the one hand, a lower solar cell temperaturewhile recording EQE PV is unlikely as we always de-creased T set during the experiment and no additionalcooling mechanisms were present. On the other hand,we always find T valid > T set , which leads us to concludethat the solar cell temperature is increased during the EQE EL measurements: T valid increases with higherinjection currents during the EL experiment. In thiscase, perfect agreement between T valid and T set is foundonly for injection current densities J inj <
10 mA cm − (Fig. S2). Due to the design of the experiment, in whichwe recorded consecutive EQE EL spectra for increasing J inj at each temperature T set before cooling down tothe next temperature step, we can safely assume thesolar cells have reached thermal equilibrium with thereservoir before we injected charge carriers. The mostlikely explanation for this behavior is additional heatingof the whole devices induced by electric transport andshunt currents, as suspected previously.[9] ! " ! "$ ! "% ! " ! ! ! & ’ ( ) * + , ’ - . / . --2 . / . . --2 ’ " %6%%6! 67 68 6 $%& ’ (% )*+ ,-,.%%,/ -<=(*+>(’-,+?&)*+@9A-’B*’9C’C-D)&E=A-’B*’9C’C-C+A@&C’&’C-D6<’)A=&’<’9*F-./. - -./. .5 ! " ! "$ ! "% ! " ! ! ! & ’ ( ) * + , ’ - . / . --2 . / . . --2 ’ " %6%%6! 67 68 6 $%& ’ (% )*+ ,-,$0%,/ -<=(*+>(’-,+?&)*+@9A-’B*’9C’C-D)&E=A-’B*’9C’9C-C+A@&C’&’C-D6<’)A=&’<’9*F-./. - -./. .5
123 143
Figure 4. Exemplary model fits at (a) T = 150 K and (b)
300 K for the solar cell with 10 wt% TAPC content. We find thebest combined agreement for
EQE PV and EQE EL at all temperatures with the multiple vibrations model . The extended Marcusmodel would require a defined substructure of additional absorption lines, separated by the characteristic vibrations energy Λ vibr . Respective peaks are not found at low temperatures, which could be explained by the extended disordered Marcus model ;however, it would require the EQE EL peak shifting at low temperatures, which is not observed experimentally. We applied the common method of fitting re-duced Gaussian distributions to sub-bandgap
EQE PV or EQE EL tails to determine energetic CT state parame-ters E ct , σ ct and λ R according to the disordered Marcusmodel (Tab. II). Even though we used a linear regressionmethod instead of non-linear fitting to reduce the uncer-tainties related to manual adjustment of fit ranges andstarting values,[17] the extracted parameter values fromindividual EQE PV and EQE EL analyses were inconsis-tent, or outright unphysical within the model.The systematic discrepancy between apparent CTstate linewidths in emission and absorption leads us tothe conclusion that reduced EQE PV and EQE EL distribu-tions are in fact asymmetrical. This rules out the simple and disordered Marcus model , both predicting symme-try, to describe emission and absorption by CT states.Instead, the experimental observations are compatiblewith the multiple vibrations model. As was describedbefore,[17] the Poisson distributions attributed with lowenergy vibrations merge into reduced Gaussians at hightemperatures. Yet, if incorrectly interpreted as Gaus-sians, the extracted parameters could be misleading, andmay even implicate apparent negative widths σ ct of theassumed static disordered E ct distributions.To analyze our measured data with the multiple vi-brations model , we reconstructed the measured EQE PV and EQE EL spectra for all temperatures simultaneouslyby a Levenberg–Marquard fitting algorithm (Fig. 4). Asimilar fit featuring the extended and extended disorderedMarcus model resulted in further arguments that thesetwo models do describe the physics of the investigateddevices. The distinct substructure of higher energetic molecular vibration peaks at low temperatures couldnot be replicated in the measured, comparably smooth EQE PV spectra. To compensate the missing substruc-ture, static energetic disorder would be required; how-ever, the static disorder models postulate a significant EQE EL peak shift below the low-energy edge of the fit-ting range at lower temperatures. This leads to increas-ing peak amplitudes as well as fit residuals in this region,and the estimated EQE
LED -values correspondingly de-viate from the integrated measured
EQE EL spectra atlower temperatures. While we cannot provide measuredemission data in this region to back up the prediction,we suspect this fitting behavior to solely be a numericalcompensation for a temperature dependent peak shift re-quired by the model, which is not present in the experi-mental data. Either way, both models fail to reconstructmeasured spectral data as a whole, which raises furtherdoubt about their validity.The multiple vibrations model yields a much more rea-sonable reconstruction of the experimental spectra. Weeven find agreement between the values of measured andreconstructed integrated EQE
LED (Fig. S8), and withinthe extracted parameter quantities for the donor materialTAPC in different dilutions (table III).The choice of the model to analyze measured data ob-viously has an effect on the extracted parameters val-ues, and we do not have to look further than the ex-cited CT state energy E ct to see the importance of themodel choice. In most discussed models, E ct is deter-mined by the EQE PV ’s (0–0) peak position and the re-organization energy λ R (values in table S3). This cor-responds to the intersection between reduced normalized !" ! ( ) *+ , -./ / !$5 !%$ !%5 !&$ !&5 63 -) !"
11 1,31<=1 1/=11.=1 1/.=1%&’( )* +( ,- %&’( .-* +( ,- %(%& .-* +( ,- / ! % - Figure 5. Fitted energies E ct , model of the CT state accord-ing to the simple (sM), extended (eM), disordered (dM), andextended disordered Marcus model (edM), and the multiplevibrations model (mV), compared to the extrapolated opencircuit voltage limit V oc ( T → . The black line repre-sents identity, which is best approximated by the multiple vi-brations model for TAPC:C blends. Models which includestatic energetic disorder (dM, edM) overestimate E ct . emission and absorption peak[9] if static energetic dis-order is not present; else, we would see a temperaturedependent emission peak shift as discussed earlier.In the multiple vibrations model , the absorption peakcenter is determined by the moment of the Poisson dis-tribution of vibration states with frequency Λ , and thusexceeds E ct + λ R . Accordingly, the reconstructed val-ues for E ct are here lower than in the other investigatedmodels. When compared to V oc extrapolated to , wefind them best approximated with the multiple vibrationsmodel ’s lower E ct values in the case of TAPC:C blends(see Fig. 5). In contrast, the static disorder models ( dis-ordered and extended disordered Marcus model ) overesti-mate the limit by more than
100 meV (table III).Here, we want to highlight that the most trusted re-sults of our analysis are gathered from the TAPC :C device, as this is the one that has been measured at thecorrect emission temperature, i.e., at T valid = T set . In allother devices, we were able to at least estimate EQE EL temperatures from the reciprocity relation, which we areconvinced of is much closer to the real device tempera-ture than the reservoir temperature T set , for the reasonsdiscussed earlier. Differences in the extracted param-eters, especially between the diluted TAPC solar cells,which only vary in their donor concentration and there-fore should not differ a lot in their fundamental energeticproperties, may partly be attributed to this temperatureuncertainty. From the EQE PV and EQE EL spectra alone,we find that E ct , λ R and S are strongly correlated, ina way that the E ct difference between the cells with 5wt% and 10 wt% TAPC concentration is compensatedby the difference in λ R and S , while Λ remains almostconstant. To verify the parameters even further, addi-tional experimental methods to access Λ and E ct would be necessary. V. CONCLUSION
We measured the
EQE PV and EQE EL properties of di-luted donor–acceptor solar cell model systems and testedcurrently discussed theoretical models concerning thetemperature behavior of CT state emission and absorp-tion.We applied the electro-optical reciprocity relation be-tween EQE PV and EQE EL spectra as a method to vali-date and correct the emission temperature of the devices.By showing that validated temperatures generally com-ply with expected temperatures, we confirm the validityof the reciprocity relation for this set of devices. Thevalidated temperature can be several
10 K higher thanassumed from the set temperature under different exper-imental circumstances, such as higher injection currentdensities during EL measurements. We attributed thisdiscrepancy to additional current-induced heating of thedevices, and recommend to carefully verify the emissiontemperature during EL experiments.We are missing experimental evidence for a
EQE EL peak shift and find no symmetry between absorption andemission spectra—both predicted by static disorder mod-els . Together with their inability to reconstruct measureddata and estimated values for EQE
LED , we have reason-able doubt about the general applicability of these modelsto describe CT state absorption and emission.Our measured spectra are indeed better described bya multiple vibrations model with two characteristic fre-quencies of around
150 meV and
13 meV for TAPC:C ,and for TCTA:C . As a consequence, we find theexcited CT state energy to be significantly smaller thansuggested by previous analyses of TAPC and TCTA:C blends.[15] We validated the multiple vibrations model further by showing agreement between extrapolated opencircuit voltage limit at T = 0 K and extracted values for E ct for TAPC:C devices. VI. EXPERIMENTAL SECTION
Materials: from CreaPhysGmbH (Germany), and Luminescence Technology Corp.(Lumtec, Taiwan); 4,7-diphenyl-1,10-phenanthroline(BPhen) was purchased from Abcr GmbH (Germany)and Luminescence Technology Corp., Molybdenumtrioxide from Luminescence Technology Corp. Device fabrication:
The devices studied in thiswork are fabricated layer by layer through thermal co-evaporation in ultra-high vacuum chamber (K. J. Lesker,UK) which has typical operating pressure of − mbar .0All of the involved organic molecules are thermally sub-limated before evaporation. Substrates are glass sub-strates (size ×
25 mm ) with pre-patterned ITO (in-dium tin oxide, Thin film devices, US). The ITO is
90 nm thick with a sheet resistance of
25 Ωcm − , with 84%transparency. ITO is covered with -thick hole trans-port layer of Molybdenum trioxide. The co-evaporateddonor–acceptor blends of TAPC:C and TCTA:C withweight ratios of 5:95 and 10:90 is further covered with -thick layer of the electron transport material BPhenand a
100 nm aluminum top contact. The active area ofthe device is defined by the intersection of the structuredITO electrode and the structured opaque aluminum topcontact and amounts to .
44 mm . Before device fabri-cation, substrates are cleaned with following procedure:coarse cleaning by detergent; rinsing with de-ionized (DI)water; sequentially dipping into N-Methyl-2-pyrrolidone(NMP), acetone, ethanol for ultrasonic bath with .for each solvent; rinsing with de-ionized water; after dry-ing up, oxygen plasma (Priz Optics, Germany) treatmentfor 10 min. After fabrication in ultra-high vacuum, de-vices are transferred into a nitrogen filled glovebox. Asthe final step, all devices are encapsulated with a smallglass lid to prevent moisture and oxygen induced degra-dation during device characterization in air ambient. Thetransparent glass lid is glued by UV-(ultra violet)-light-curing epoxy resin (XNR 5592, Nagase ChemteX, Japan)which is exposed with UV light for
196 s . External quantum efficiency : EQE PV is measured in-side a closed-cycle cryostat (Cryovac) with helium as thecontact gas. The monochromatic light source consists ofa mechanically chopped
100 W quartz-tungsten-halogenlamp coupled to a double monochromator with addi-tional optical bandpass filters (Quantum Design EuropeMSHD-300) for further stray light reduction. The pho-tocurrent, measured under short circuit conditions and without bias illumination, is amplified and converted toa voltage signal by a trans-impedance amplifier (ZurichInstruments HF2TA) and measured with a lock-in ampli-fier (Zurich Instruments HF2LI). A small fraction of themonochromatic light is directed onto a calibrated two-color photo-diode (Hamamatsu K1718-B) to record refer-ence excitation fluxes with an additional lock-in amplifier(Stanford Research DSP830).
Electroluminescence:
EQE EL spectra are recordedwith a
500 mm spectrograph (Princeton Instruments Ac-ton 500i) and a liquid nitrogen-cooled silicon CCD-camera (Princeton Instruments Spec-10:100). The con-stant EL driving current of
155 mA cm − is provided bya source–measure unit (Keithley 2368B). Open circuit voltage:
A frequency doubled Nd:YAG-LASER (Spectra Physics Millenia Pro) with optical out-put power of is used to illuminate OSCs inside thecustom-build cryostat. The incident irradiance is grad-ually increased over 10 orders of magnitude by pass-ing two motorized neutral-density filter wheels (ThorlabsFW102C & FW212C); V oc of the illuminated device ismeasured with a source–measure-unit (Keithley 2368B).A mechanical shutter, triggered by the source–measureunit, limits the illumination time of the devices. ACKNOWLEDGMENTS
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