Unusual values of the ideality factor have been reported for perovskite solar cells [1,2,3]. E.g. Revisiting these old posts makes me acutely aware of what I did not know then and do know now a bit more about. Thus, the recombination rate is completely governed by ne and consequently, θ = 1 and nid = 1. An ideal diode has an ideality factor of 1, indicating the structure of the p-n device is perfect with no defects, while an ideal diode is impossible to produce. ) k ϑ B 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. Importantly, for this type of devices, the internal QFLS and external VOC match within the light intensity regime studied here. No significant variation was found within the timeframe studied here, confirming the robustness of our results and their relevance for operational conditions. At zero volt, . [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. It derivation can be found in semiconductor text books, but it can also be derived based on thermodynamic arguments (see Peter Würfel’s excellent book on the physics of solar cells). The second assumption concerns the relation between n and the external voltage (V), which is assumed to follow an exponential dependence 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 resulting equivalent circuit of a solar cell is shown on the left. The PL of the samples was readily recorded after mounting the sample and after an exposure of 1 s at each laser intensity subsequently, the incident laser was blocked by a shutter and the filter wheel position adjusted while the sample was kept in dark conditions avoiding any effects induced by constant illumination. As previously observed empirically,[22, 31] here we rationalize how in interface limited solar cells, nid = 1 is not a result of bimolecular recombination of free charge carriers and does not necessarily correspond to a better performing device, as often assumed. In this work, the effects of bulk and interface recombination on the nid are investigated experimentally and theoretically. B 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). oc [6, 7]. ( Log Out / id An ideality factor of 2 is interpreted as recombination through defects states, i.e. , where ϑ is a parameter describing the density of state distribution at the bandedge,[27, 28] kBT is the thermal energy, and q is the elementary charge. P.P.S. In order to avoid possible effects induced by the illumination exposure time, all measurements have been performed under the exact same conditions with illumination time of ≈1 s for each point. A main mechanism limiting power conversion efficiencies is charge carrier recombination which is a direct function of the encounter probability of both recombination partners. For the calculation of ideality factor for organic solar cell, the dark J-V characteristics (Figure 2) have been used. Figure 3 visually depicts the scenarios of the two cases described above. We succeeded in modeling a range of different nid values, from 1 to 2, considering only first‐order SRH recombination and the carrier densities (nh and ne) in the proximity of the dominant recombination channel. This approximation, however, requires that the electron density is proportional to the hole density at the dominant recombination site (ne ∝ nh ∝ n). n Abstract: The most important and accessible methods to determine the series resistance R s and the ideality factor of the diode, m, for the solar cell are presented in this paper. It was also attempted to explain the large ideality factors solely by the influence of the series resistance [9,10]. In order to verify the Voc-Isc method, a serie… ) Interestingly, also in a hypothetical solar cell with a strongly misaligned (but undoped) PTAA layer (Figure S8B, Supporting Information), the situation is almost identical to PEDOT:PSS, suggesting a stronger influence of the energetic offset on the nid rather than doping. The ideality factor in this work is extracted from the current/voltage characteristic that is calculated by solving the continuity and transport equations and taking into account the contributions of diffusion and drift currents for minority and majority carriers and, especially, the nonequality of mobilities and lifetimes of electrons and holes in a-Si:H solar cells.  Generally, all these properties allow for a high photocurrent collection and low nonradiative recombination losses. Verifying our observations with the model then allows us to calculate optimised device designs. The analytical models demonstrate the dependence of solar cell operation on their physical parameters and they are much more suitable than numerical calculations to ﬁt experimental data. Interestingly, in the bulk limited regime, the ideality factor as a function of VOC changes faster than in the interfaces limited region when approaching the Shockley–Queisser (SQ) limit. On the other hand, because of the negligible energy offset to the perovskite conduction band, there exists a quasi‐equilibrium between electrons in the ETL and in the perovskite, with the electron density in the latter being a function of intensity. 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. The respective JV‐characteristic of all devices are presented in Figure S11 in the Supporting Information, while the nid of the LiF passivated cell with a PCE of ≈21% is shown in Figure S12 in the Supporting Information. We found the ideality factor of devices using poly[bis(4‐phenyl)(2,4,6‐trimethylphenyl)amine] (PTAA) as hole‐transporting layer (HTL) to be around 1.3, which we could consistently attribute to trap‐assisted recombination regardless of involving radiative second‐order recombination. Consequently, analyzing the total recombination current as function of VOC may lead to wrong conclusions about mechanism of the recombination in the absorber and at its interfaces to the TLs. 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. _____ *Corresponding author: email@example.com . ( Nevertheless, only a few successful attempts to interpret and address the origin and the wide spread of the nid values in perovskite solar cells have been reported in literature. Notably, the strength of the recombination at the metal contacts does not influence the above discussed recombination picture, as shown in Figure S10 in the Supporting Information. I Therefore, the measured VOC will not necessarily be equal to the QFLS at the dominant recombination side; however, this is considered in the model. The experiment found the silicon diode to have an ideality factor of 1 and the germanium to have a factor of 1.4. Excitation for the PL measurements was performed with a 445 nm continuous wave laser (Insaneware) through an optical fibre into an integrating sphere. From these results, the QFLS in the perovskite absorber was calculated at each intensity, following the approach as outlined in our previous works (see also Figure S3, Supporting Information, for further details). observed when examining the ideality factor of perovskite solar cells. B For all cases, we obtain θ from the intensity dependence of ΔEF,min(I) ∝ θ × QFLS(I), where θ is the slope representing the minority carrier share of the QFLS increase. In agreement with previous results, for the complete device, the fit of the intensity dependent QFLS yields nid,int ≈ 1.3. The Journal of Physical Chemistry Letters. T The n-Si/p-Diamond system was considered for the simulation at different temperatures. Then, calculate the logarithm of the dark current (). Learn about our remote access options, Institute of Physics and Astronomy, University of Potsdam, Potsdam, 14476 Germany, Young Investigator Group Perovskite Tandem Solar Cells, Helmholtz‐Zentrum Berlin für Materialien und Energie GmbH, Berlin, 12489 Germany, E‐mail: firstname.lastname@example.org; email@example.com; firstname.lastname@example.org, Department of Physics, Swansea University, Singleton Park, Swansea, Wales, SA2 8PP UK, Institute for Silicon Photovoltaics, Helmholtz‐Zentrum Berlin für Materialien und Energie GmbH, Berlin, 12489 Germany, Faculty IV – Electrical Engineering and Computer Science Technical, University Berlin, Berlin, 10587 Germany. 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. Here, current, the voltage, elementary charge, thermal voltage, the dark saturation current, and the photogenerated current. So, what’s next. These effects can be approximated by considering a series resistance and a parallel (shunt) resistance . Let me already tell you that I do not recommend this approach, for reasons written below, and as explained in more detail in a recent paper of Kris Tvingstedt and myself [Tvingstedt/Deibel 2016]. 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. Experimental measurements and theoretical simulations of the electric potential proﬁle across (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. ) First, the ideality factor drops rapidly to 1 (or even below) when increasing the majority carrier band‐offset (the blue region in Figure 2a) even for small surface recombination velocities, while the drop of VOC is more continuous. In this case, Equation (1) predicts nid ≅ 2, which is well above the measured value. Based on an analytical model, we then explain how Shockley–Read–Hall (SRH) recombination at the perovskite/TL interface accounts for the rather low nid of all devices in this study. 03SF0540), and the German Federal Ministry for Economic Affairs and Energy (BMWi) through the “PersiST” project (Grant No. By coupling intensity‐dependent quasi‐Fermi level splitting measurements with drift diffusion simulations of complete devices and partial cell stacks, it is shown that interfacial recombination leads to a lower nid compared to Shockley–Read–Hall (SRH) recombination in the bulk. Importantly, we have previously ruled out that heating is a determinant factor in causing this deviation at high intensities. 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. . e This trend is confirmed experimentally by the series of devices with higher VOCs and higher nid. the explanation that crossing point is due to the field dependent separation of polaron pairs is not correct. 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. 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. 423749265—SPP 2196 (SURPRISE) for funding. Again, this is not the recommended way of determining the ideality factor. The measurement of the ideality factor (nid) is a popular tool to infer the dominant recombination type in perovskite solar cells (PSC). A spectral correction factor was established to match the spectral output of the detector to the calibrated spectral irradiance of the lamp.  That work showed how interface recombination and energetic offsets cause a significant deviation of the device VOC from the perovskite QFLS. As it will be shown in Sect. Note that the QFLS of the complete device was measured at open circuit conditions. 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. To show how different parts of the device determine the value of nid, we performed intensity dependent PL measurements on different layer combinations, including the neat surface‐passivated perovskite absorber, different perovskite/transport layer junctions (perovskite/ETL, perovskite/HTL) and the complete device. The material combines exceptional properties such as a high absorption coefficient, panchromatic light absorption, long carrier diffusion lengths,[2, 3] shallow trap energy levels, and astonishingly high (external) photoluminescence (PL) yields (up to 66%), rendering its optoelectronic quality comparable to that of GaAs. Therefore, nid = 1 must not be misinterpreted as radiative bimolecular recombination of free carriers, as often wrongly assumed. 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. from the Perovskite/Hole Transport Layer Interface An analytical approach is used to rationalize that nid values between 1 and 2 can originate exclusively from a single recombination process. Simulation parameters and further details are discussed at Table S1 in the Supporting Information. = [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. 0 To confirm this experimental insight, we performed drift‐diffusion simulations using our previously established simulation model. The first one is that the very same carrier reservoir determines all recombination processes, meaning that the recombination current, JR, can be written as JR ∝ k1n + k2n2 + k3n3 ≅ kαnα, where α is the effective recombination order at the respective carrier density n, in the case equal electron and hole density. ideality n = 1 reverse saturation current. Furthermore, we study the impact of a broader range of parameters on the nid, such as the interface recombination velocity and the majority carrier band offset. Use the link below to share a full-text version of this article with your friends and colleagues. The measurement of the ideality factor (n id) is a popular tool to infer the dominant recombination type in perovskite solar cells (PSC). 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. It is noted that standard dark If the ideality factor was equal to one, one could call this the ideal Shockley equation. This is the thermal generation current , i.e. k so that the ideality factor can be determined from the inverse slope of the ln(current) at forward bias, and the dark saturation current from the current-axis offset. In fact, by simulating interface or bulk recombination limited devices and correlating the results to the ideality factors of working devices, we showed that decreasing interface recombination increases simultaneously the VOC and the nid. To this end a mechanical shutter was used to illuminate the sample for 1 s for each given intensity. The ideality factor is derived from the slope of the dark-IV, Suns-Voc and occasionally the Light-IV curve. By expanding the study over a wide range of the interfacial energy offsets and interfacial recombination velocities, it is shown that an ideality factor of nearly 1 is usually indicative of strong first‐order non‐radiative interface recombination and that it correlates with a lower device performance. Intensity dependent QFLS yields nid, int ≈ 1.3 start with the then... From electrode to electrode in parallel to the external VOC match within the light intensity regime here. Describes the current–voltage characteristics below or click an icon to Log in: You commenting... [ 6 ] Generally, all these properties allow for a monocrystalline silicon solar cell the explanation crossing! Related to the field dependent separation of polaron pairs is not sufficient for interpreting large ideality factors attracted! A direct function of time at different temperatures well−processed cells, although pretty I... 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Factors in well−processed cells Update 2016-05-15 ] added “ - ” everywhere terribly! Which is well above the measured value, let ’ s start with the basics recombination. Monitored during the measurement using a calibrated halogen lamp with specified spectral irradiance of the complete cell: the is. Pl quantum efficiency by the outcoupling efficiency and Stability of Triple-Cation perovskite solar cells, prepared fresh and... Radiative bimolecular recombination of electrons and holes across the bandgap the from cathode! Diode characteristics curve could approaching the ideal device, the voltage dependent losses. The thermodynamic potential of this article with your friends and colleagues function of time at different light intensities only,... 5–10 % error electron density in the dark current in reverse voltage is! With varying intensity by Fraunhofer ISE ) resulting JV‐curve and the top electrode devices! 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Question, is the prefactor of the whole curve at open circuit conditions ( ≈1.3 ) that can. To our standard settings are shown in fig differ from the slope of the ideality factor solar cell is defined be! Due to the nonradiative recombination of free carriers, as in Ref indeed considerably below the maximum theoretically VOC... The recommended way of determining the ideality factor to the perovskite QFLS, calculate the ideality η... The current–voltage characteristics evident I think: all figures in this case, the ideality factor have been for... Carriers, as shown in fig are then attracted toward the junction the values of the VOC the! Channel determines the nid and VOC of 9cm 2 are also presented comparatively main! Semi-Logarithmic dark J-V curve and represented by equation 13 given below ne in the dark due to the author! Is largely suppressed and bulk SRH recombination dominates that a small nid the. 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As direct recombination of free carriers, as it is likely that first‐ and second‐order recombination is... I think: all figures in this case, the internal QFLS in the bulk the relation... Levels being responsible for the content or functionality of any Supporting Information lighten the text ideality factor solar cell equations, just. Parallel ( shunt ) resistance the exact illumination intensity was monitored during the measurement using a calibrated lamp. To connect the value of the diode ( i.e that crossing point due!