How to determine optical gaps and voltage losses in organic photovoltaic materials

K. Vandewal *, J. Benduhn and V. C. Nikolis
Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP), Institute for Applied Physics, Technische Universität Dresden, Nöthnitzer Straße 61, 01187 Dresden, Germany. E-mail: koen.vandewal@iapp.de

Received 15th December 2017 , Accepted 2nd February 2018

First published on 2nd February 2018


The best performing organic solar cells (OSC) efficiently absorb photons and convert them to free charge carriers, which are subsequently collected at the electrodes. However, the energy lost in this process is much larger than for inorganic and perovskite solar cells, currently limiting the power conversion efficiency of OSCs to values slightly below 14%. To quantify energy losses, the open-circuit voltage of the solar cell is often compared to its optical gap. The latter is, however, not obvious to determine for organic materials which have broad absorption and emission bands, and is often done erroneously. Nevertheless, a deeper understanding of the energy loss mechanisms depends crucially on an accurate determination of the energies of the excited states involved in the photo-conversion process. This perspective therefore aims to summarize how the optical gap can be precisely determined, and how it relates to energy losses in organic photovoltaic materials.


Introduction

In the past 15 years, the power conversion efficiency (PCE) of organic solar cells (OSCs) has increased from about 1% to now almost 14%.1 This development has been accomplished by the synthesis of new electron donating and electron accepting materials of which high performing combinations have been discovered. The highest external quantum efficiencies (EQEPV) exceed 80%,2 and fill-factors (FF) approach 80%,3 being on-par with those of higher efficiency technologies, such as gallium arsenide (GaAs) and crystalline silicon (c-Si). Up to now, it is the open-circuit voltage of OSCs (VOC) which is lagging behind, making OSCs currently still less efficient than established inorganic photovoltaic technology or the emerging perovskite solar cells. Therefore, research is nowadays focusing on the identification of the elementary processes responsible for the large difference between eVOC and the optical gap of the main absorber (Eopt), where e is the elementary charge. At the same time, new materials are being synthesized,4 as well as new device architectures have been developed,5 with the aim to minimize these voltage losses.

Under solar illumination, the total energy loss per absorbed photon is equal to the difference between the photon energy and the product of e with the voltage at the point of maximum electrical power output. A lower limit for these energy losses is given by the difference between the device's optical gap (Eopt) and eVOC. Indeed, the potential energy of the extracted charge carriers is limited to eVOC, while Eopt is given by the lowest energy singlet exciton, either of the donor (ED*) or the acceptor (EA*). For the remainder of this perspective, we refer to Eopt/eVOC as “voltage loss”.

To precisely characterize and study energy and voltage loss mechanisms for OSCs, an accurate determination of the energies of the relevant electronic states in organic semiconductors is crucial. Following photon absorption, several electron-transfer steps introduce energy losses. Fig. 1 depicts the energy levels of singlet and triplet states on the neat donor (D) and acceptor (A) in a Jablonski diagram. Following electron transfer, an intermolecular charge-transfer (CT) state, comprising an electron on the acceptor and a hole on the donor, is formed. This state can decay to the ground state or dissociate into a state comprising fully free charge carriers (FC).


image file: c7se00601b-f1.tif
Fig. 1 Jablonski diagram, showing the energy levels which are important for OSCs. The lowest optical excitations in the absorber molecules, i.e. A and D, are singlet excitons (EA*(S1) and ED*(S1)). The optical transition from the ground state to the triplet excited state (EA*(T1) and ED*(T1)) are forbidden. The intermolecular CT state between D and A has the energy ECT. In OSCs, charge generation and recombination takes place via this state, therefore, we can define voltage losses with respect to this state, or with respect to the strongly absorbing singlet states on the neat materials. The energy difference between the lowest energy singlet exciton and eVOC forms a lower limit for the energy lost in the conversion of strongly absorbed photons to charges collected at the electrodes.

The energy and voltage losses in OSCs relate to the chemical potential of the free charge carriers under solar illumination, which is determined by the energies of the relevant excited states, as well as the transition rates between these states and the ground state. However, the excited state energies are often empirically determined. For example, CT state energies are sometimes estimated by taking the difference between the energy of the highest occupied molecular orbital of the donor, HOMO(D), and lowest unoccupied molecular orbital of the acceptor, LUMO(A). This approach however, neglects polarization and binding energies,6 and values for the driving force for electron transfer can be over- or underestimated by several tenths of electron volts (eV). The singlet energies EA*(S1) or ED*(S1) of acceptor and donor, of which the lowest one can be considered as the optical gap (Eopt) of the blend, are often taken as the onset of the absorption spectrum, which is rather ill-defined. It is clear that further progress in the fundamental understanding of OSC operation needs an unambiguous method to determine voltages losses, so that they can be compared between research groups. This perspective aims therefore to summarize how optical gaps and CT state energies can be consistently determined and how they relate to voltage losses in OSCs.

Absorption, emission and the optical gap

Spectral broadening in organic materials

For a hypothetical solar cell with an ideal step-wise absorption spectrum, determination of Eopt is trivial, as it corresponds to the lowest energy for which photons are strongly absorbed. In reality, OSCs exhibit rather shallow absorption tails, due to the presence of static and dynamic disorder, as well as the presence of weakly absorbing CT states. In order to unambiguously determine Eopt, it is instructive to consider the origins of the spectral broadening.

The absorption and emission spectra of organic materials are strongly affected by electron–phonon coupling and molecular vibrations. Fig. 2a shows how the high frequency vibrations, for example ring breathing modes, are responsible for discrete peaks in the spectra.7 For these high frequency modes the spacing between the vibrational energy levels is much larger than the thermal energy and electrons populate solely the lowest energy vibrational level ν = 0. Photon absorption and emission solely occurs for discrete photon energies related to transitions between a vibrational level of the ground state ν, and a vibrational level of the excited state ν′. The 0–0 transition occurs at the energy E0–0, which is the difference between vibrationally relaxed ground- and excited state.


image file: c7se00601b-f2.tif
Fig. 2 Optical transitions depicted in an energy diagram with displaced potential wells for the ground state (GS) and excited state (ES), taking into account that the reaction coordinate remains invariant during the transition (Franck–Condon principle). Vertical blue arrows represent absorption and vertical red arrows emission. (a) Absorption and emission spectra are dominated by high frequency vibrations, with a relaxation energy λH. In this case, the spacing between vibrational levels is larger than the thermal energy. Photon absorption occurs by promoting an electron from the vibrational ground state level ν = 0 to an excited state vibrational level ν′, indicated by the black lines in the corresponding absorption spectrum. In the emission spectrum, transitions from the lowest excited state vibrational level ν′ = 0 to ground state levels ν dominate, as indicated by the black lines in the emission spectra. Absorption and emission spectra overlap around the 0–0 transition energy (E0–0). (b) Peak broadening by low frequency vibrations with reorganization energy λL. The spacing between vibrational levels is less than the thermal energy. Optical transitions from higher energy thermally populated levels results in absorption at photon energies below E0–0 and emission at energies above E0–0. The resulting peak width depends on temperature and λL.

However, the absorption and emission spectra of organic thin films seldom consist of well resolved, discrete peaks: a main source of peak broadening are low frequency vibrations with an energy spacing less than the thermal energy (Fig. 2b).7 Optical transitions from thermally (Boltzmann) populated low frequency vibrational modes result in absorption at photon energies below E0–0 and emission at photon energies above E0–0. Treating the low frequency vibrations as harmonic oscillators results in Gaussian absorption (A(E)) and emission (N(E)) line-shapes

 
image file: c7se00601b-t1.tif(1)
 
image file: c7se00601b-t2.tif(2)
hereby, E corresponds to the photon energy and kB is the Boltzmann constant. The line-width is proportional to the temperature T and the low frequency relaxation energy λL. The energy difference between vibrational relaxed ground- and excited state, E0–0, is the crossing point of the appropriately normalized absorption and emission spectra, as shown in Fig. 2b.

Extracting singlet and charge-transfer state energies

In what follows, we outline how eqn (1) and (2) can be used to accurately extract the energy levels ED*(S1) or EA*(S1) and ECT for OSC blends. Hereby, we consider that the absorption spectrum of a donor–acceptor blend for OSCs will be mainly determined by high oscillator strength optical transitions on the neat materials. However, within their gap, much weaker absorption related to direct excitation of CT states is present. The optical gap (Eopt) is identified as the E0–0 transition energy of the singlet localized on either donor or acceptor. The E0–0 of the CT state (ECT) is often lower than Eopt. Both Eopt and ECT can be determined from the optical spectra by a fit of the low energy absorption tail or high energy emission tail with eqn (1) or (2), respectively. Alternatively, one can make use of the fact that E0–0 coincides with the energy at which the appropriately normalized absorption and emission spectrum cross. Dividing A(E) by E and N(E) by E3, yields the so-called reduced absorption and emission spectra. When normalizing the reduced spectra to the maximum of the corresponding peak, eqn (1) and (2) intersect exactly at E = E0–0. In the case of mirror-image spectra, E0–0 is the midpoint between the absorption and emission maxima (Stokes shift), separated by 2λL.8

As a concrete example, Fig. 3a shows the determination of Eopt (ED*(S1)) and ECT for vacuum-processed OSCs based on ZnPc:C60 and F4ZnPc:C60 active layers. Photovoltaic diodes comprising both neat donors and their blends with C60 were fabricated. The electroluminescence (EL) and photovoltaic external quantum efficiency (EQEPV) spectra of these diodes were measured and provide a reliable measurement of the emission and absorption tails. It should be noted that EQEPV and absorption spectra are interchangeable here, since the internal quantum efficiency (IQE) of D:A photovoltaic blends is rather constant at their low energy tail.9 Furthermore, EL spectra were measured at low injection currents, keeping the system in quasi-equilibrium.9 For the neat phthalocyanines, the crossing point between the normalized reduced absorption (EQEPV) and reduced emission (EL) spectra yields a similar value for Eopt (ED*(S1)) around 1.52–1.53 eV. For the blends with C60, reduced EQEPV and EL curves are plotted on a logarithmic scale, on which for ZnPc:C60, an additional CT absorption band becomes visible. The EL spectrum of the blend is dominated by CT emission. Fits of EQEPV and EL with respectively eqn (1) and (2) yield similar values for ECT, which coincide rather well with the crossing point of the spectra at 1.17 eV. Fluorination of the phthalocyanine donor leads to a decrease of both its HOMO and LUMO. Therefore, we observe a blue-shift of the CT absorption band for F4ZnPc:C60 blend as compared to ZnPc:C60. In fact, the CT absorption becomes indistinguishable from the neat F4ZnPc absorption tail. A fit of the EL spectrum with eqn (2) and the crossing point between reduced EL and EQEPV yield an E0–0 energy of 1.46 eV, i.e. 60 meV lower than the Eopt of F4ZnPc. In this case optical transitions related to CT state excitation and low energy F4ZnPc excitation are indistinguishable.


image file: c7se00601b-f3.tif
Fig. 3 Examples of determining the Eopt and ECT for 2 different OSCs: (a) neat ZnPc, (b) ZnPc:C60 and (d) neat F4ZnPc, (e) F4ZnPc:C60. In every sub-figure, the black arrow shows the position of the crossing point between reduced and normalized EQEPV and EL spectra. (c) and (f) summarize the voltage losses in the two exemplary devices. The Eopt of the donor and ECT of the blend are obtained as described in the main text, Vr is calculated from the EQEPV spectra, and VOC is measured at 1 sun illumination for the corresponding device. Further details on the voltage losses are given in the main text.

With the knowledge of Eopt and ECT for both material systems, we can now perform a detailed analysis of the voltage losses, summarized in Fig. 3c and f. The VOC was measured under simulated solar illumination for both ZnPc:C60 (VOC = 0.56 V) and F4ZnPc:C60 (VOC = 0.73 V) with the latter being 0.17 V higher.

The conversion of the lowest energy singlet excited state on the donor to a free electron–hole pair with a chemical potential eVOC occurs at the cost of ΔEloss, given by

 
ΔEloss = EopteVOC (3)

The associated voltages losses ΔVloss = ΔEloss/e are 0.97 V for ZnPc:C60 and 0.79 V for F4ZnPc:C60. The lower loss for F4ZnPc:C60 is largely due to a reduced energy loss in the charge-transfer process, converting a relaxed phthalocyanine singlet exciton to a relaxed CT state.

 
ΔECT = EoptECT (4)

While the electron transfer process in ZnPc:C60 is accompanied by a ΔECT of 0.36 eV, this loss is only 0.06 eV in F4ZnPc:C60, and the absorption and emission tails for blend and neat F4ZnPc almost coincide. Here, we want to emphasize that the optical determination of ΔECT, as described above, is a much more accurate way of determining the “driving force” for charge transfer as simply taking the LUMO(D)–LUMO(A) or HOMO(A)–HOMO(D) difference, which ignores exciton binding and polarization energies. Indeed, in the initial photo-induced electron transfer event, donor (or acceptor) excitons, with minimum energy (Eopt) are converted to CT states, with energy ECT. Seeing this process as free electrons (holes) in the LUMO(D) (HOMO(A)), converted to free electrons (holes) in the LUMO(A) (LUMO(D)) would certainly be wrong.

The chemical potential at open-circuit conditions, eVOC is lower as compared to ECT due to recombination of free charge carriers.

 
image file: c7se00601b-t3.tif(5)

For ZnPc:C60, the recombination loss ΔVrec is 0.61 V while for F4ZnPc:C60 the total voltage loss is almost fully due to recombination. In general, recombination losses often comprise a substantial fraction of the total voltage losses in OSCs and are often found to be around 0.6 V, when VOC is measured at room temperature and under 1 sun illumination.10,11

To understand the origin of the recombination caused voltage losses in more detail, it is useful to consider the influence of radiative and non-radiative recombination on VOC separately. When only radiative recombination would occur, VOC would reach its upper limit, the so-called Vr, which can be calculated as:12,13

 
image file: c7se00601b-t4.tif(6)
where JSC is the short-circuit current density obtained by integrating the product of the EQEPV spectrum and the solar AM1.5G spectrum, and Jr0 is the radiative limit of the dark current, obtained by integrating the product of the EQEPV spectrum and black body spectrum at room temperature. More details on this procedure, which assumes thermal equilibrium between CT states and free charge carriers, can be found in ref. 13.

Voltage losses due to radiative recombination, ΔVr are given by

 
image file: c7se00601b-t5.tif(7)

They are in a sense fundamental, because they are a direct consequence of the fact that OSCs absorb light.14 From the available sensitively measured EQEPV spectra we calculate a Vr of 0.93 V for ZnPc:C60 and a Vr of 1.12 V for F4ZnPc:C60, corresponding to ΔVr = 0.24 V and ΔVr = 0.34 V, respectively. The latter radiative losses are higher due to stronger absorption of the radiatively recombining species in F4ZnPc:C60.

The difference between the radiative limit of the VOC, the Vr, and the in reality measured VOC corresponds to non-radiative voltage losses, ΔVnr

 
ΔVnr = VrVOC (8)

They are caused by due to non-radiative decay processes. It has been shown theoretically and experimentally that:

 
image file: c7se00601b-t6.tif(9)

With EQEEL being the quantum yield of radiative decay, which is the ratio of the radiative recombination rate to the total sum of radiative and non-radiative recombination rate. To determine ΔVnr via a measurement of EQEEL one should take care that the applied injection current is low, so that quasi-equilibrium conditions are ensured and the charge density in the device corresponds to that under solar conditions. For ZnPc:C60 and F4ZnPc:C60 these ΔVnr are 0.38 V and 0.39 V, respectively. In both cases, this is a substantial part of the total recombination losses, corresponding to an EQEEL of about 3 × 10−7, which is a low value as compared to other photovoltaic technologies. The resulting large non-radiative voltage losses have been proposed to be intrinsic for fullerene OSCs, limiting their maximum achievable power conversion efficiency.11

Temperature and illumination intensity dependence of the voltage losses

For an analysis of the voltage losses, one should keep in mind that VOC is temperature and illumination intensity dependent. Most expressions for VOC are of the general form:15
 
VOC = V0βT[thin space (1/6-em)]ln(Jph) (10)
hereby is Jph the photocurrent density and β a temperature and light intensity independent parameter. The extrapolation of temperature dependent VOC measurements to 0 K leads to V0 and delivers β, which depends on the details of the free carrier recombination processes.

For OSCs, V0 has been found to correspond to ECT, rather than HOMO(D)–LUMO(A).13,16 It has been shown that this is due to the fact that the CT states are in thermal equilibrium with the free charge carriers.17,18 As a result, the total recombination losses ΔVrec, radiative and non-radiative, are temperature dependent. Besides the optical method described above, temperature dependent measurements of VOC therefore provide and an alternative method to determine ECT and the recombination losses.

Even when static disorder is present, the absorption and emission tails which are already broadened by electron–phonon coupling are additionally broadened by the site energy spread. When fitting EQEPV and EL with eqn (1) and (2), this will result in a temperature dependent ECT. However, the extrapolation of VOC to 0 K will still correspond to the extrapolation of ECT to 0 K.17 Therefore, the optical method of determining ECT and the temperature dependent VOC method are consistent with each other.13

Minimizing energy losses for strongly absorbed photons

To finalize this perspective, we summarize some of the characteristics which benefit low-voltage-loss OSCs. As exemplified by the ZnPc:C60 and F4ZnPc:C60 systems, increasing ECT to minimize ΔECT can be done by chemical design, controlling the frontier energy levels of donor and acceptor. For several new donor–acceptor combinations for OSCs, ΔECT is vanishingly small, while still high EQEPV values can be achieved.5,19,20 In those cases, the recombination losses ΔVrec are the dominant ones. Up to now, only few strategies to suppress these losses have been proposed, including the suppression of the donor–acceptor interfacial area to reduce ΔVr,21–23 and the use of a cascaded device architecture, suppressing partly ΔVnr.5

It is however important to note that even if the voltage losses EopteVOC are minimized, this does not necessarily mean that the solar cell will be highly efficient. Complementary to a high VOC, a high PCE requires also high photocurrent and FF. For this to be the case, charge generation and extraction has to be efficient at low ΔECT and the EQEPV needs to be high (near unity) for all photons with an energy higher than Eopt. However, the shallow absorption edge of organic materials results in low EQEPV for photon energies close to Eopt (see Fig. 4a).


image file: c7se00601b-f4.tif
Fig. 4 (a) An ideal step-wise EQEPV spectrum and an exemplary real EQEPV spectrum, exhibiting a shallow absorption edge, for a hypothetical OSC. Optical and transport losses reduce the maximum obtainable EQEPV of solar cells (grey area). The shallow absorption edge induces low EQEPV for photons with energy just above Eopt. For a steep absorption edge, this photocurrent loss is minimized. (b) Graphical determination of λedge as the intersection of the extrapolated linear part of the absorption edge, and the isoline passing through the peak at the low-energy edge (EQEedge) of the EQEPV spectrum. Eedge corresponds to the energy of the absorbed low-energy photons which highly contribute to the device's photocurrent, and is obtained as 1240/λedge (nm). Considering energy losses from eVOC to Eedge takes into account the steepness of the absorption edge, and promotes solar cells exhibiting Eedge close to Eopt. Here, λopt is the wavelength associated with Eopt as λopt = 1240/Eopt (eV). With known Eopt, the offset EedgeEopt is a measure of the absorption edge steepness. Efficient solar cell performance requires the lowest EedgeeVOC difference at the highest possible EQEedge.

We have recently introduced a metric which takes this into account and considers voltage losses for strongly absorbed photons, at the low-energy tail of the EQEPV spectrum, as the difference EedgeeVOC.5 Hereby, Eedge is defined as illustrated in Fig. 4b. For efficient solar cells, a low difference EedgeeVOC at very high EQEedge is required. Energy losses related to the steepness of the main absorber's absorption edge are quantified by EedgeEopt, implying that for OSCs exhibiting the desired steep absorption edge, the EedgeEopt offset will be minimal. To keep these losses low, Fig. 2 shows that small low-frequency relaxation energies of the neat material excitons are required.

The determination of the voltage losses for strongly absorbed photons with this metric requires only standard EQEPV and JV measurements. This has the advantage that basically every photovoltaic device whose EQEPV spectrum and JV curve are known can be compared in terms of voltage losses. However, for a deeper physical insight and identification of the voltage limiting factors, exact determinations of Eopt and ECT are essential.

Concluding statement

More systematic analysis of voltage losses of future donor–acceptor combinations for organic photovoltaics is required for a rigorous comparison between results and materials from different research groups. With this perspective, we encourage the reader not to use ill-defined absorption onsets, at which virtually no photons are absorbed, as reference point for voltage losses. Nor do we promote the use of HOMO and LUMO energy levels to determine the relevant energies of excited states in OSCs. The optical measurements described above, or temperature dependent measurements of VOC contain much more useful and precise information. Finally, we would also like to encourage researchers working on the minimization of voltage losses in OSCs, to accompany claims of low voltage losses with a measurement of the EQEEL (measured at an applied voltage similar to VOC), since solar cells with truly low voltage losses will also be efficient LEDs.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work received funding from the German Federal Ministry for Education and Research (BMBF) through the InnoProfile Projekt “Organische p–i–n Bauelemente 2.2” (03IPT602X).

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Footnote

Current address: Instituut voor Materiaalonderzoek (IMO), Hasselt University, Wetenschapspark 1, BE-3590, Diepenbeek, Belgium, E-mail: E-mail: koen.vandewal@uhasselt.be.

This journal is © The Royal Society of Chemistry 2018