In this work, we demonstrated the application of intensity dependent QFLS measurements on perovskite/transport layer junctions to gain a comprehensive understanding of the processes determining the ideality factor in perovskite solar cells. This is the thermal generation current , i.e. Thus, generation = recombination — or more specifically, thermal generation current = recombination current — which essentially implies that 0V correspond to the open circuit voltage in the dark. Intensity dependent VOC measurements were performed illuminating the respective solar cell at exactly the same illumination condition and exposure time (1 s) as during the PL measurements in order to have the same experimental condition for the two measurements. In contrast, if we consider only bulk recombination (device with ideal interfaces), then the ideality factor is considerably higher (≈1.8). The experiment found the silicon diode to have an ideality factor of 1 and the germanium to have a factor of 1.4. The corresponding data and simulation results are shown in Figure S5 in the Supporting Information. Importantly, for this type of devices, the internal QFLS and external VOC match within the light intensity regime studied here. Second, a strong interface recombination would drive a current of electrons and holes toward the respective TL even at VOC, potentially causing the VOC to be smaller than the quasi‐Fermi level splitting (QFLS) in the perovskite bulk. In the extreme case, where the majority carrier density is fixed and the increase of the QFLS is only due to the increase of the minority carriers, the ideality factor is 1 despite the fact that all recombination is due to first order non‐radiative processes (see Section S7, Supporting Information, for derivation). Overall, this can explain the rather small increase of ne(I) in the ETL and as a consequence, the ratio θ at which EF,min increases with respect to the increase of the total QFLS with the light intensity, is 0.77 and equivalent to nid = 1.3. charge carriers excited across the bandgap just by thermal energy — and therefore very little. The fill factor of a solar cell is given as: A semiconductor p–n junction can be made to operate as a solar cell. q As it will be shown in Sect. Verifying our observations with the model then allows us to calculate optimised device designs. An elegant and already well‐established approach to determine the nid is to measure the VOC as a function of the light intensity (I). Moreover, the ideality factor of the device is identical (≈1.3) regardless whether recombination in perovskite bulk (both radiative and SRH) is implemented or not. [17, 18, 21-23] This figure of merit describes the deviation from the ideal diode behavior where only bimolecular recombination is considered as recombination process. Modern solar cell technologies are driven by the effort to enhance power conversion efficiencies. Essentially, these ideality factor values could be explained by an asymmetric shift of the electron/hole quasi‐Fermi levels with increasing light intensity. § 1. More on that in a later post, let’s start with the basics. Through the years, several studies spotlighted the perovskite surface[7-9] and the grain boundaries[9, 10] as main recombination centers in the perovskite absorber. Under illumination and at open circuit conditions, , we can rewrite the Shockley equation as. The Shockley diode equation describes the current–voltage characteristics of a diode. In this work, the effects of bulk and interface recombination on the nid are investigated experimentally and theoretically. Note that from here on we will discuss the impact of these parameters on the external nid. n The PLQY was measured by exciting the sample inside an integrating sphere with a 455 nm laser diode with varying intensity. id The results showed that the real reason for high ideality factor in organic solar cells is energy disorder. Through experiments and numerical simulations, we found that the ideality factor of ≈1.3 in our efficient perovskite cells (≈20% PCE) is a direct consequence of interfacial recombination at the C60 interface and is not a result of the interplay between SRH and bimolecular recombination in the absorber layer. The situation becomes less complicated if this band bending exists only at one of the interfaces and if this is the interface of predominant recombination. Yet, the ideality factor is close or equal to 1. M.S. The neat perovskite is surface‐passivated with trioctylphosphine oxide (TOPO)[6, 35] in order to probe mainly the recombination in the perovskite bulk (PLQY ≈5% under 1 sun conditions). ϑ I Unusual values of the ideality factor have been reported for perovskite solar cells [1,2,3]. This study presents experimental results of accurate ideality factor determination for representative organic photovoltaic cells (OPV) evaluated at different temperatures over a large current density regime. Overall, this work summarizes important aspects regarding the true meaning of the nid values typically observed in perovskite solar cells and provides detailed insight into the underlying recombination processes in working devices. Here, the electron (, a) Numerically simulated intensity‐dependent, orcid.org/https://orcid.org/0000-0002-3465-2475, I have read and accept the Wiley Online Library Terms and Conditions of Use. ∝ It is now commonly applied to silicon cells by assuming a unity ideality factor - even when the cells are not in low injection - as well as to non-silicon cells. However, the true meaning of its values is often misinterpreted in complex multilayered devices such as PSC. solar cells the defect levels being responsible for this effect never could be identified. It is only in the case of optimized interfaces and highly suppressed interface recombination that an nid of 1 would be again desirable, being representative of predominant free carrier recombination and reduced SRH in the bulk. If we again look at what happens for , we get. Revealing Energy Loss and Nonradiative Recombination Pathway in Mixed-Ion Perovskite Solar Cells. Thus, the recombination rate is completely governed by ne and consequently, θ = 1 and nid = 1. On the other hand, when ne and nh at the dominant recombination site are nearly equal (for example, when the recombination happens in the bulk or in case of a near‐ideal interface),the quasi‐Fermi levels for electron and holes (EF,e and EF,h) would share the total QFLS symmetrically, resulting in an nid of 2. Defect/interface recombination limited quasi-Fermi level splitting and open-circuit voltage in mono- and triple cation perovskite solar cells. [33, 34] For the considered cells, the PLQY is ≈0.1%. (Please note that under realistic conditions, is not only pretty small and difficult to measure in principle, it is also hidden behind shunt currents in the device. ) Importantly, both ne and nh depend on the illumination intensity, yet the dependence of ne is weaker. ( Log Out /  Saturation current (I0) and ideality factor (n) of a p-n junction solar cell are an indication of the quality of the cell. q The ideality factor could only be determined from the dark characteristics using the “remaining” part of the exponential current–voltage regime. Therefore, it is likely that first‐ and second‐order recombination processes are controlled by different carrier reservoirs. It is evident that a larger nid corresponds to larger VOC in the interface limited region, while the trend is opposite in the bulk limited regime. Figure 3 visually depicts the scenarios of the two cases described above. [13, 15] Therefore, we conclude that 1) interfacial recombination leads to lower nid compared to the recombination in the bulk and 2) the recombination at the least optimum interface (here the perovskite/C60 interface) determines the ideality factor of the complete cell. the term becomes zero as the open circuit voltage is “measured” without current flow, so the series resistance does not apply. 0 This is shown in Figure S9 in the Supporting Information for the PTAA device, where the same analysis is done using the carrier densities in the bulk, which results in nid = 1.8 as expected for SRH in the bulk of our cells. the fill factor of a solar cell depends critically on the diode ideality factor[18] (besides, of course, the resistances and the saturation current). [39, 40]. In the case of polymer:fullerene solar cells, the ideality factors derived by the two methods usually differ substantially. [12, 20] Importantly, given the large energetic offset and the strong interface recombination, these two systems exhibit a significant mismatch between the QFLS in the bulk and the VOC. Measuring Ideality Factor. J The ideality factor of a diode is a measure of how closely the diode follows the ideal diode equation. Any queries (other than missing content) should be directed to the corresponding author for the article. The single diode model, as shown in fig. . In other words, the value of nid is given by the share of the QFLS that EF,min gets when the QFLS increases as function of light intensity. In this case, the internal QFLS in the bulk is equal to the external VOC, resulting in nid of nearly two. I plan to write two more posts on the ideality factor, one on its relation to the recombination rate, and one the transport resistance (see recent papers by [Würfel/Neher et al 2015] and [Neher/Koster et al 2016]. e Thanks, good point. Here we show that perovskite-based solar cells have two universal features: an ideality factor close to two and a space-charge-limited current regime. Similarly, ideality factor should be determined with the () pairs (yielding in the figure, which corresponds to the “reference” for the internal voltage ) and not from the dark characteristics (yielding . A spectral correction factor was established to match the spectral output of the detector to the calibrated spectral irradiance of the lamp. B I Radiative second‐order recombination, on the other hand, is believed to originate strictly from the perovskite absorber, as there is no evidence for additional interfacial radiative recombination in the electroluminescence and PL emission spectra of the complete devices. One reason is that the large energy offset in combination with interface recombination prevents that holes in the HTL exhibit a quasi‐equilibrium with holes in the perovskite, meaning that nh in the HTL becomes nearly independent of illumination intensity. In Figure 2, we plot the ideality factor (Figure 2a) and the device VOC (Figure 2b) versus S and Emaj. The ideality factor affects the fill factor of the solar cell and it is so the as n increases the fill factor decreases. Working off-campus? These effects can be approximated by considering a series resistance and a parallel (shunt) resistance . No significant variation was found within the timeframe studied here, confirming the robustness of our results and their relevance for operational conditions. A second optical fiber was used from the output of the integrating sphere to an Andor SR393i‐B spectrometer equipped with a silicon charge‐coupled device camera (DU420A‐BR‐DD, iDus). [15, 16] All simulation parameters are listed in Table S1 in the Supporting Information. Only then, the ideality factor is related to the recombination order via the well‐known relation nid = ϑ/α. ( from the Perovskite/Hole Transport Layer Interface Unusual noninteger and voltage-dependent ideality factors, which are difficult to explain using the classical diode theory, have been reported for perovskite solar cells and remain unex-plained. [16], Considering the relevance of the perovskite/TL interface in determining nid, we performed simulations for a wide range of interfacial recombination velocities (S) and majority carrier band offsets (Emaj) at the HTL/perovskite interface. In particular, we find that the perovskite/C60 junction and the complete device exhibit an almost identical ideality factor, which suggests that this interface governs the ideality factor of the cell. Therefore, the measured VOC will not necessarily be equal to the QFLS at the dominant recombination side; however, this is considered in the model. Change ), You are commenting using your Twitter account. Again, this is not the recommended way of determining the ideality factor. Through detailed numerical modeling, we identify the mechanisms that lead to these universal features. The n-Si/p-Diamond system was considered for the simulation at different temperatures. Figure 2 illustrates the operation of the solar cell. Simulation parameters and further details are discussed at Table S1 in the Supporting Information. This can also be seen when comparing the dark current-voltage characteristics for an internal voltage with the same current plotted at the external voltage , which is reduced compared to the internal one by the (series) resistance. _____ *Corresponding author: kalgarmawy@ksu.edu.sa . However, when the C60 layer is attached to the perovskite (on glass), the nid value drops to roughly 1.3; the same value as of the complete cell. n [Update 2016-05-15] added “-” everywhere, terribly sorry! The spectral photon density was obtained from the corrected detector signal (spectral irradiance) by division through the photon energy (hf) and the photon numbers of the excitation and emission obtained from numerical integration using Matlab. The value and temperature dependence of the ideality factor provides essential information about the dominant recombination route in solar cells. , In the case of PEDOT:PSS as HTL, PEDOT:PSS (Heraeus Celivious 4083) was spin coated at 2000 rpm for 40 s (acceleration 2000 rpm s−1) and subsequently annealed at 150 °C for 15 min. That means, the internal voltage at the solar cell is reduced by a voltage drop across the series resistance, and the diode current is essentially superpositioned on a shunt current. Importantly, as expected from Equation (1), k2 has a certain impact on the ideality factor at high intensities, above 1 sun, when the PLQY becomes significantly large (Figure S7, Supporting Information). In this work, the … Importantly, none of the input parameters yields nid = 2, as it would have been predicted for predominant trap‐assisted recombination by the simple model introduced above. A simplified expression for the current density, as a function of the applied voltage, has been systematically derived from a charge transport model, based on drift-diffusion theory, that includes ion migration in the perovskite layer [4,5]. ), but reduced by the recombination current. This indicates that nid values between 1 and 2 do not originate from a competition of different recombination mechanisms, which would rather result in a change of slope when a different recombination mechanism takes over. To confirm this experimental insight, we performed drift‐diffusion simulations using our previously established simulation model. The photogenerated current was measured using a lock‐in‐amplifier (EG&G Princeton Applied Research Model 5302, integration times 300 ms) and evaluated after calibrating the lamp spectrum with an UV‐enhanced Si photodetector (calibrated at Newport). This allowed us to explain the mixed ideality factor values typically observed in perovskite solar cells. int The active area was 6 mm2 defined as the overlap of ITO and the top electrode. As pointed out above, the recombination under a 1 sun equivalent illumination intensity in p‐i‐n‐type perovskite solar cells is mainly a first‐order non‐radiative trap‐assisted process at the perovskite/TL interfaces. The ideality factor η is a number between 1 and 2. Use the link below to share a full-text version of this article with your friends and colleagues. T Surprisingly, this value is nearly identical to the value of nid,ext ≈ 1.3 as deduced from the intensity dependence of the VOC, provided that leakage through the thin PTAA layer can be avoided. ) Then, calculate the logarithm of the dark current (). [15, 16] We kept an S of 2000 cm s−1 with no energy offset at the n‐interface, while the injection barrier at the metal at both sides was kept constant. The exponential regime of the current–voltage characteristics, from which we determined both the ideality factor and the dark saturation current above, is now partly hidden: at low voltages the shunt resistance dominates the current, and at high voltages the series resistance drags the exponential current into a linear one. However, the true meaning of its values is often misinterpreted in complex multilayered devices such as PSC. In case of only one dominant interface this QFLS is then equal to the VOC (see Figure 3 and Figure S8A, Supporting Information). In order to delineate a more general picture, we studied the effects of energy misalignment and interface recombination on the nid and VOC. Note that interface recombination may cause a significant bending of the majority quasi‐Fermi levels in the perovskite bulk (EF,e at the ETL and EF,h at the HTL), which has its origin in the depletion of the majority carrier density in the perovskite near the TL due to a large energy offset in combination with fast surface recombination. From these results, the QFLS in the perovskite absorber was calculated at each intensity, following the approach as outlined in our previous works[16] (see also Figure S3, Supporting Information, for further details). [16, 17] This allows us to study the impact of a particular interface on the nid with the aim to ultimately understand which recombination mechanism controls its value in the full cell. 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