Interpretation and evolution of open-circuit voltage, recombination, ideality factor and subgap defect states during reversible light-soaking and irreversible degradation of perovskite solar cells

Abstract

Metal halide perovskite absorber materials are about to emerge as a high-efficiency photovoltaic technology. At the same time, they are suitable for high-throughput manufacturing characterized by a low energy input and abundant low-cost materials. However, a further optimization of their efficiency, stability and reliability demands a more detailed optoelectronic characterization and understanding of losses including their evolution with time. In this work, we analyze perovskite solar cells with different architectures (planar, mesoporous, HTL-free), employing temperature dependent measurements (current–voltage, light intensity, electroluminescence) of the ideality factor to identify dominating recombination processes that limit the open-circuit voltage (V_oc). We find that in thoroughly-optimized, high-V_oc (≈1.2 V) devices recombination prevails through defects in the perovskite. On the other hand, irreversible degradation at elevated temperature is caused by the introduction of broad tail states originating from an external source (e.g. metal electrode). Light-soaking is another effect decreasing performance, though reversibly. Based on FTPS measurements, this degradation is attributed to the generation of surface defects becoming a new source of non-radiative recombination. We conclude that improving long-term stability needs to focus on adjacent layers, whereas a further optimization of efficiency of top-performing devices requires understanding of the defect physics of the nanocrystalline perovskite absorber. Finally, our work provides guidelines for the design of further dedicated studies to correctly interpret the diode ideality factor and decrease recombination losses.

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Broader context

Perovskite solar cells have recently emerged as a technology with high potential to provide low-cost electricity. Considering the progress of conventional solar cell technologies and the evolution of the cost structure of photovoltaic systems, the balance of system (i.e. non-solar cell) costs become increasingly dominating. Hence, novel solar cells have to be, above all, highly efficient to lower the cost of solar electricity. Perovskite solar cells already show efficiencies above 20% with the major loss mechanism limiting further progress being the recombination of photogenerated charge carriers. This article presents approaches to characterizing recombination and identifying its major sources. These can be, for example, defects in the perovskite absorber layer or at its interfaces with charge transport layers. The study also addresses the issue that, as solar cells degrade, changes to recombination processes can occur. We discuss this in light of certain peculiarities of perovskite solar cells, such as vulnerability to reversible performance losses upon light-soaking. Finally, we demonstrate, how better understanding of recombination processes in PSCs can contribute to further improvements in device efficiency and stability.

Introduction

It was not foreseeable ten years ago that a known material would be able to revolutionize research in photovoltaics. But it happened. Metal halide perovskites, processable from solution, are about to outcompete not only emerging but also established material systems. With efficiencies above 22%¹ and the possibility to realize multijunction devices,^2,3 perovskite solar cells have the potential to become a leading photovoltaic technology, combining high efficiency and low production cost. On the one hand, the reasons for this success are found in obvious properties required for a good solar cell material, such as a high absorption coefficient,^4,5 a suitable bandgap,⁶ and sufficiently high charge carrier mobilities⁷ and diffusion lengths.^8,9 These properties allow for a high photocurrent at maximum power point. On the other hand, perovskites show additional features that are less obvious but still essential for high performing solar cells. These include a steep absorption onset,⁵ extraordinarily low non-radiative recombination rates, and high luminescence yields, which are the reason behind the high photovoltages, facilitating the high efficiencies reported.^10,11 These properties are due to high crystallinity, low density of deep traps, and high defect tolerance.^12–14 Nevertheless, comparing the values for photocurrent and voltage achieved experimentally with the theoretical predictions, it becomes evident that further optimization of perovskite solar cells with the target of 30% efficiency needs to focus on increasing the open-circuit voltage (V_oc) through reduction of recombination losses.^14–16 This requires a better understanding of (still) prevailing recombination mechanisms and their origins in absorber materials and at interfaces including the identification of, albeit low, defect densities. As discussed in recent dedicated studies,^17–19 the whereabouts of recombination are under lively debate.

In this study, recombination is investigated by means of the so-called diode ideality factor extracted from current–voltage curves measured in the dark, electroluminescence data, and analysis of V_oc as a function of illumination intensity. To disentangle bulk from surface processes and reach relevant conclusions, we use high performing solar cells with different contact layers (comprising mesoporous, planar, and hole-transport layer free implementations). As V_oc and therefore recombination has been reported to be affected by light-soaking^20,21 or aging,²² solar cells that have been exposed to heat or light are also investigated in this study. Intragap defect states introduced upon light soaking and degradation are identified using Fourier-transform photocurrent spectroscopy.

Theory

Ideality Factor from V_oc

In the following paragraphs we want to briefly review the concept of the diode ideality factor and its relation to charge carrier recombination. From semiconductor theory using the Born–Oppenheimer approximation and Boltzmann statistics, and assuming a perfectly contacted homogeneous absorber with bandgap E_g, V_oc can be expressed as:^23,24

The second term results from the chemical potential of electrons with concentration n and holes (p) partially occupying their effective density of states in the conduction and valance band (N_C, N_V, respectively). The prefactor of this second term (“thermal voltage” k_BT with Boltzmann constant k_B) is mainly responsible for the temperature (T) dependence of V_oc, whereas n and p result from the equilibrium between optical charge carrier generation G and recombination R, yielding the following equation valid at open circuit:

G = R(n,p). (2)

Here, G is proportional to the light intensity. For the recombination rate as a function of the charge carrier densities we can write dependent on the recombination mechanism:

with β as radiative recombination rate constant, and τ_n and τ_p describing the non-radiative lifetimes of electrons and holes, respectively. These lifetimes are inversely proportional to the trap densities.^24,25 Replacing np in eqn (1), we find for direct recombination ((3a) in (2) in (1)):

Assuming an intrinsic semiconductor or that n and p are predominantly photogenerated, i.e. n = p, we get for SRH recombination ((3b) in (2) in (1)):

In both cases, V_oc depends logarithmically on the light intensity (via G), and we can introduce a prefactor, the so-called diode ideality factor n_ID, which can be determined from a measurement of V_oc as a function of light intensity I:

Here, I₀ is a constant with the same unit as I. In a MIM (metal–intrinsic semiconductor–metal) or p–i–n solar cell with a homogeneous recombination profile in the intrinsic (low-mobility) absorber, the experimentally determined n_ID can be directly used to identify the dominating recombination mechanism according to eqn (4)–(6).

However, assuming that a high equilibrium of electron (or hole) density exists in the absorber, e.g. introduced by doping, n = p does not hold any more. For a considerably n-doped material, n would equal the concentration of ionized dopants (n ≈ N⁺_D) independent of light intensity. Thus, in this case, photogenerated holes are minorities p ≪ n. Instead of reaching eqn (5), we get:

The ideality factor is 1 and V_oc increases with the doping concentration, because the electron quasi Fermi level is fixed by the large N_D. Thus, for a Schottky or pn junction, n_ID = 1 for recombination in the so-called quasi-neutral region (i.e. N⁺_D = n ≫ p), whereas n_ID = 2 for recombination in the depletion region. To establish distinct space-charge and quasi-neutral regions in a 500 nm thin perovskite film, (unintentional) high doping densities in the order of 10¹⁷ cm⁻³ would be required. In a MIM device, recombination close to the contacts, where high dark carrier densities prevail, yields n_ID = 1 as well.

Furthermore, in a real perovskite solar cell, redistribution of photogenerated charges, defect distributions, and recombination at the contacts (which we so far ignored) complicate the situation. R becomes a function of the spatial coordinate x and eqn (2) is not valid any more at each x, but just holds integrated over the absorber thickness.

Fig. 1 gives an overview of how n_ID depends on recombination processes. Besides the discussed cases, surface recombination due to non-selective contacts is considered as well. It leads to an n_ID<2 despite SRH recombination and even <1 if V_oc is limited by a built-in potential (V_bi, e.g. originating from the difference of work function of the electrodes) and saturates with light intensity once it approaches V_bi because the “driving force” for charge separation vanishes.²⁶ This case of surface recombination is an example for a correlation of V_oc and n_ID that is contrary to common belief. A lower ideality factor is not necessarily beneficial for solar cell performance and can come along with a lower V_oc compared to a case where SRH recombination in the bulk limits V_oc and n_ID > 1. This is e.g. observed at perovskite solar cells with an unmodified PEDOT:PSS electrode, where n_ID = 1, but V_oc is low (<1 V).^14,27,28

Fig. 1 Ideality factor for different recombination mechanisms and corresponding trends in V_oc with illumination intensity (gradient). The shaded areas show possible combinations of n_ID and V_oc, where V_oc is not to scale. The ideality factor can change with illumination intensity and increase for lower V_oc (tilted areas), in particular if radiative or surface recombination appear paired with SRH recombination, with the latter dominating at lower light intensities. However, high V_oc is possible for high n_ID and n_ID is not a simple quality factor correlated with V_oc. SRH recombination can lead to ideality factors between 1 and 2. The left diagram shows three examples, how a measurement of V_ocvs. illumination intensity would look like in cases A–C.

Cases with spatially varying R can be treated with numerical drift-diffusion simulations of e.g. a simple MIM architecture. Assuming parameters considered realistic for perovskite solar cells (β = 3 × 10⁻¹¹ cm³ s⁻¹, SRH lifetime 1 μs, mobilities 10 cm² V⁻¹ s⁻¹),^10,14 we get an n_ID of 1.6. This is because the recombination zone is not limited to a narrow space charge region but extends over the absorber layer. Similar results including those discussed above have been obtained by simulation studies on p–i–n and pn structures.^29,30

In a real solar cell, G is not constant either, but a function of x and the wavelength of the light due to thin film optics and a wavelength-dependent absorption coefficient. It seems to have less influence on n_ID (assuming mobilities of 10 cm² V⁻¹ s⁻¹) but can be exploited to some extent when explaining changes of V_oc and for identifying localized recombination processes in case of imbalanced and/or low mobilities, where recombination happens faster than a redistribution of charges, as reported for meso-TiO₂ based^10,20 or aged¹⁹ devices.

Ideality factor from electroluminescence

Alternatively to using charge carrier densities (eqn (1)), V_oc can be derived from a detailed-balance analysis of absorbed and emitted photon flux:^31,32

Being consistent with eqn (1), eqn (8) describes the complete device using currents (J_ph: photocurrent, J_em,0: dark emission current) instead of local charge carrier densities. The first term V_oc,rad describes the radiative limit of V_oc, which is 1.33 V for CH₃NH₃PbI₃ with a band gap of around 1.56 eV.^33,34 For the mixed cation mixed halide perovskites employed in this work, V_oc,rad is 1.36 V, calculated based on the IPCE and the PL spectrum with a maximum at 760 nm (1.62 eV) (Fig. S1, ESI†). The second term of eqn (8) contains a V_oc-loss due to non-radiative recombination described by the EQE_EL, which is the external quantum efficiency of electroluminescence (EL). Comparing eqn (8) with eqn (6), we see that n_ID is contained in the EQE_EL as a function of illumination intensity: V_oc scales with . Thus, for n_ID = 1, the EQE_EL should be constant, whereas it should increase linearly with light intensity for n_ID = 2.^35,36 Therefore, determining n_ID from the EQE_EL as a function of the injection current, is a complementary way to analyzing V_ocvs. light intensity.

Ideality factor from dark JV curve

The EL, which is measured in the dark, links us to a further method employed in this work to determine n_ID: directly using the JV curve of the diode measured in the dark:

This is the ideal diode equation, which does not take into account parasitic resistances. Here, n_ID can be determined from the “slope” in the exponential region of a measured JV curve. Determining V_oc with the superposition principle (J_dark(V_oc) = J_ph in eqn (9)), shows that also this equation is consistent with the previous ones.

In summary, the three methods presented should yield the same value for n_ID if n_ID can be well-determined and is independent of illumination intensity and applied voltage. In the following, we analyze whether this is the case for experimental data from perovskite solar cells and draw conclusions on dominant recombination mechanisms.

Experimental

The ideality factor is analyzed at state-of-the-art devices (FTO/electron selective contact/perovskite/spiro-MeOTAD/Au) containing ≈500 nm thin mixed ion (“Cs_0.05(MA_0.17FA_0.83)_0.95Pb(I_0.83Br_0.17)₃”) perovskite³⁷ absorber layers (optical characterization in Fig. S1, ESI†). Such devices are well-suited for a study of relevant recombination limits, as they can deliver an efficiency >20% and a V_oc > 1.2 V.³⁸ The data presented in the following is selected based on results from various measurements on devices containing the following architectures: devices with (i) planar SnO₂ ^38,39 and (ii) mesoporous (plus compact) TiO₂ electron selective layer, both with doped Spiro-MeOTAD as the hole-transport layer (HTL), (iii) aged (8 days under 1 Sun white-light LED illumination at 65 °C in N₂) device of the second architecture and (iv) device without the HTL (Fig. 2). Where relevant, data upon light soaking is added to the analysis. Representative JV curves measured under simulated sunlight are shown in Fig. S2 (ESI†) and the characteristic parameters in Table S1 (ESI†).

Fig. 2 Schematics of investigated devices. Cmp + meso TiO₂ stands for a compact and mesoporous TiO₂ layer deposited onto fluorine-doped tin oxide (FTO).

Perovskite solar cells are not entirely stable and suffer from reversible and irreversible degradation that can occur during measurements,^20,40 in particular when varying temperature.²² Therefore, it is challenging to perform measurements in the time window between ionic response (reversible) and degradation (irreversible).⁴¹ In this study reproducibility is guaranteed by repeating measurement series and designing sequences in temperature and intensity containing forward and reverse sweeps. Measurement time is optimized to minimize the effect of slow changes due to light soaking or the application of voltage bias. Therefore, the intensity sweeps are performed rather quickly (3 s settling time, see Fig. S3, ESI†) instead of waiting for minutes for a stabilized V_oc, which would result in a reduced V_oc in particular at high illumination intensity and temperature, where reversible losses would superimpose the results and reduce reproducibility. Illumination is provided by white LEDs (emission between 400 and 700 nm) and temperature is controlled with a Peltier element. Devices are kept in an airtight chamber under nitrogen flow to avoid irreversible degradation during the measurements. Selected and processed data is used in this work to analyze trends rather than single specific values.

Results

Dark JV curves

To study recombination in the dark, we measured JV curves and extracted n_ID with the aid of eqn (9) (JV curves under LED illumination in Fig. S4 and S5, ESI†). Fig. 3 shows the JV curves obtained from a voltage loop with a sweep rate of 20 mV s⁻¹ starting at 0 V. All devices show a hysteresis, which mainly affects the shunt regime at low currents. Eqn (9) is valid only in the exponential region (around 1 V), whereas most of the JV curve is dominated by parasitic effects due to shunt and series resistances. Therefore, in line with previous studies^42,43 we analyze the phenomenological differential ideality factorobtained at each voltage and plotted in Fig. 3b. The traces show a minimum in the exponential region of the diode curve while increasing towards higher and lower voltages due to a reduced slope of the JV curve caused by a series and shunt resistance, respectively. A minimum of ñ_ID that is very sharp in voltage indicates that the parasitic resistances hardly allow to correctly determine the intrinsic n_ID as the recombination limited slope is not reached. Therefore, the obtained values have to be seen as an upper limit for n_ID (n_ID ≤ ñ_ID). From the minima we determine a value of approx. 1.7 for the fresh planar and mesoporous devices with HTL, 2.2 for the aged one and <1.6 for the one without HTL. Note that the ideality factor does not correlate with the onset of forward current and thus the V_oc expected for the different devices. Generally, the dark JV curves can be corrected for a simple parasitic parallel (shunt) and series resistance to extract the n_ID more reliably. However, non-constant (i.e. voltage dependent) resistances and hysteresis effects make this correction still problematic as shown in Fig. S6 (ESI†). The origin of these phenomenological resistances, which can limit the fill factor under illumination, are classical series resistance from the FTO and limited charge transport capabilities of selective layers such as TiO₂, SnO₂, or spiro-MeOTAD.^35,38 Even grain boundaries in the perovskite film can be responsible for a series resistance effect.¹⁵ The shunt resistance is mainly due to parasitic leakage currents.

Fig. 3 Dark analysis of the diode ideality factor (a) JV curves measured in the dark at 20 °C. (b) Phenomenological differential ideality factor ñ_ID extracted from the differential slope of the JV curves according to eqn (10). Limitations by resistances render this approach unreliable for the investigated perovskite solar cells.

Light intensity dependent V_oc

The limitations by the series resistance can be completely overcome when analyzing V_ocvs. illumination intensity, as the net current is 0 at V_oc, and thus voltage is not lost due to the series resistance. Fig. 4 shows V_oc as a function of illumination intensity in an intensity range covering four orders of magnitude and during a sweep from dark conditions to 1.5 Suns equivalents (“upward”, open symbols in Fig. 4) and back (“downward”, closed symbols). The data is extracted as shown in Fig. S3 (ESI†). The V_oc at 1 Sun is ≈1.2 V for the fresh devices, whereas the aged device shows a V_oc of 1 V and the one without HTL of 0.8 V. All traces look approximately linear in this plot and limitations by a too low shunt resistance (as often observable) are visible only in the aged device at low light intensity (which is not necessarily due to the fact that it was aged but due to device-to-device variations). Despite the linear appearance, it is advisable to perform a differential analysis^36,44 of the slope here as well and deduce a phenomenological ideality factor analogously to eqn (10):

Fig. 4 The diode ideality factor from light-intensity dependent open-circuit voltage analysis at 20 °C. Data obtained in “upward” (open) and subsequent “downward” (closed symbols) intensity sweep with 3 s settling time at each light intensity. (a) V_ocvs. light intensity, where dashed lines show a logarithmic fit and the numbers indicate n_ID deduced from the slope. (b) Phenomenological ideality factor extracted from the slope of the data in (a) according to eqn (11). The numbers give an estimate of an intrinsic n_ID obtained from the intermediate intensity regime. At higher intensities, surface recombination leads to a reduction of n_ID.

This data is plotted in Fig. 4b and reveals that the slope is not perfectly constant but shows several trends. It increases for the upward trace for all devices toward low light intensity due to the measurement procedure and an observed slow response of a device after it has been kept in the dark, which is consistent with observations of hysteresis in perovskite solar cells.^41,45,46 For the aged device it increases also for the downward trace (closed symbols) because of the already mentioned shunt. Therefore, this low-intensity part of the data is not to be further analyzed. Most of the traces show a constant phenomenological n_ID* at intermediate light intensity (10⁻³–10⁻¹ Suns), which justifies attribution to an intrinsic n_ID in eqn (6). It is between 1.6 and 1.7 for the planar device (the 2 directions deliver slightly different values), around 1.8 for the meso device, 2 for the aged device, and 1.3 for the device without HTL. In the cases here, these values roughly coincide with an ideality factor extracted from a logarithmic fit of the overall data (dashed lines and numbers in Fig. 4a). They also follow the trends deduced from the dark JV curves, but are slightly lower and more reliable because the series resistance effects are avoided, as also found for organic solar cells.³⁶

The ideality factor hardly depends on the electron selective layer (SnO₂vs. TiO₂) or the planar or mesoscopic nature of the electron contact indicating that charge recombination is not dominated by these interfaces. Interestingly, n_ID tends to decrease for higher illumination intensities, in particular for the aged and the HTL-free device where it approaches 1 indicative of surface recombination setting in for higher V_oc (cf.Fig. 1).²⁶ The dependence of n_ID* on light intensity (and therefore on voltage) also explains potentially observed discrepancies between n_ID obtained from JV curves and from V_ocvs. light intensity around 1 Sun, because the latter is measured at higher voltages. Real differences between both methods, which would indicate different recombination mechanisms, might be possible if poor conductivities cause large gradients in quasi-Fermi levels at V_oc. Further interpretations of the data will be given in the discussion section.

Temperature dependent n_ID

To reliably identify n_ID, it is important to perform measurements at different temperatures because n_ID appears paired with the thermal energy k_BT in the presented equations. Therefore, the above analyses on the dark JV curves and the V_ocvs. light intensity plots were repeated at different temperatures, starting at 20 °C, followed by a decrease to −10 °C, a rise to 50 °C (in steps of 10 K) and completed at 20 °C. The obtained values for the phenomenological n_ID are summarized in Fig. 5. If the measured slopes were independent of temperature, the deduced n_ID would follow the black dotted line. In that case, an interpretation of the measurement results at room temperature using n_ID and above equations would not be meaningful. However, for most of the measurements the deduced n_ID seems rather independent of temperature in the measured range and fluctuations are within the experimental error, which is already significant considering the dependence of n_ID* on light intensity (cf.Fig. 4b). Nevertheless, the major conclusions are solid: consistent with the room temperature analysis, the planar device exhibits an average ideality factor derived from the different techniques between 1.6 and 1.8 (Fig. 5a) (JV backward scan is an exception), similar to the mesoporous TiO₂ device (Fig. 5b). Interestingly the backward JV scan of the planar device and the forward JV scan for the meso device result in values larger than 2 indicative of a hysteresis-induced change of recombination mechanism towards a regime observed at the aged device, which shows an ideality factor close to 2 also when deduced from the V_oc (Fig. 5c). On the other hand, resistive effects caused by ion-induced changes in charge injection rate, might be responsible for this observation, which is not seen for every device (cf.Fig. 6c). For the device without HTL, the previously observed low n_ID between 1.1 and 1.3 is confirmed by the temperature dependent V_oc (Fig. 5d). The strong temperature dependence of n_ID obtained from the JV curve of this device without HTL is due to a strong increase of series resistance when decreasing T, as already indicative by the JV curves measured at 20 °C (cf.Fig. 3) and does therefore not describe the real n_ID. In general, n_ID obtained from the JV curves is less reproducible compared to the V_ocvs. light intensity method.

Fig. 5 The ideality factor from forward (fw) and backward (bw) scan JV curves and from V_ocvs. light intensity data in upward (uw) and downward (dw) trace. The dashed lines paired with the displayed number denote the mean value. If data traces are missing, it would have been too arbitrary to extract an ideality factor from the experimental data. The black dotted line represents the trend expected in case of slopes in eqn (9) and (10) independent of temperature resulting into an apparent dependence of the ideality factor on temperature. Values extracted from JV curves are affected by hysteresis and less reliable compared to those from V_ocvs. light intensity.

Fig. 6 Temperature dependent electroluminescence of meso-TiO₂ (a and b) and planar SnO₂ (c–f) device. (a) EQE_EL as a function of the injection current obtained during a forward voltage sweep followed by a backward sweep. EQE_EL of an HTM-free device recorded at 25 °C is added (magenta, right axis), yielding an ideality factor of ≈1.3. (b) Emitted photon flux for a constant current of 0.1 mA applied for 1 minute starting at 10 s. (c) Dark JV curves at different temperatures, (d) extracted differential ideality factor from dark JV curves, (e) extracted differential ideality factor from EQE_EL, (f) comparison of ideality factors as a function of temperature.

Ideality factor from electroluminescence

For the meso-TiO₂ device, n_ID obtained from temperature dependent EL measurements (eqn (8)) is added to Fig. 5b as well, resulting in values between 1.7 and 2. They have been extracted from the data in Fig. 6, showing the EQE_EL as a function of the injection current in a double logarithmic scale. The EQE_EL and its “slope” are rather independent of temperature as expected for an unmodified n_ID. However, a strong hysteresis occurs at elevated temperatures, where the EQE_EL undergoes a considerable reduction while applying currents larger than 0.1 mA, resulting in an order of magnitude lower values in the backward scan. This instability is seen in Fig. 6b as well, where the photon flux is monitored at a constant injection current of 0.1 mA, leading to a rapid decay of the EL signal for T > 40 °C. The final measurement at 20 °C (dash-dotted) shows that this decrease is reversible. The rise time of the EL after applying the constant current decreases with T, indicating that a certain ion displacement is required to reach the highest share of radiative recombination.⁴¹ This could have several reasons, e.g. related to a more balanced injection of electrons and holes upon ion accumulation or the removal of non-radiative recombination centers in the perovskite film. Whereas this transient behavior remains subject for further studies, the stabilized EL is of importance in the context of this study. We observe that the stabilized EL value does not depend on the temperature in the investigated T range, which is a requirement to apply aforementioned equations to describe V_oc and proceed with the following analysis. The main advantage of this method against the dark JV analysis is its independence of series resistance as the EQE_EL is analyzed as a function of the current (instead of voltage). A device without HTL (magenta in Fig. 6a) shows low EQE_EL as expected from eqn (8) and the deduced ideality factor is ≈1.3 consistent with the other data. Fig. 6c–f show a detailed example on a planar device, where ideality factors between 1.5 and 1.7 are deduced from JV curves and EL.

Activation energy of recombination from temperature dependent V_oc

We plot V_oc as a function of temperature for different illumination intensities and compare the traces with the prediction from eqn (1). This equation predicts that V_oc should be linear in T and reach E_g/e independent of illumination intensity when extrapolated for T → 0 K. The planar device in Fig. 7a seems to follow this linear trend, with extrapolated values between 1.5 and 1.6 V. It has to be noted that the extrapolation from values close to room temperature introduces a considerable uncertainty and accuracy is not expected to reach values smaller than ±0.1 V in our experiment. The meso-TiO₂ device (Fig. 7b) shows less clear linear dependence in particular at higher light intensities, which can be partially explained by a fast reversible decrease of V_oc at elevated T, already during the measurement (cf. Fig. S7, ESI†). Nevertheless, the linear extrapolation yields values close to E_g/e, but a bit lower in particular for lower light intensities. This could indicate partially filled trap states at the TiO₂, an effect that is more pronounced for low-V_oc devices.⁴⁷ In contrast, the degraded device (Fig. 7c), which has 0.2 V lower V_oc at 20 °C and 1 Sun, exhibits decreasing values for T → 0 K with increased light intensity. As the linear trend seems still observable, we can fit the data with a linear function but introducing a general activation energy of recombination, E_a, (as e.g. done in ref. 48) that replaces E_g and will be discussed later:

Fig. 7 Temperature dependence of V_oc and light soaking. (a–d) V_ocvs. T for different light intensities and linear fits yielding an activation energy E_a for T → 0 K. (In case of b, for 1 and 0.1 Sun, T > 30 °C have been ignored for the fit, see Fig. S7 (ESI†); in c, values below 0 °C have been ignored due to too slow response; in d different regimes are observed for 1 and 0.1 Sun indicated by fitting two lines.) (e) V_ocvs. T at 1 Sun for all devices investigated (f) transient V_oc during light soaking (g) V_ocvs. light intensity before and after light soaking. During the recovery period, the devices were kept in the dark for 2 hours.

E _a is around 1.4 eV for the aged device and decreases for higher light intensity where V_oc seems to saturate. The device without HTL (Fig. 7d) shows an E_a of around 1 eV, which is significantly lower than the actual E_g. The two lines for the higher intensity visualize that fitting a single linear function becomes more difficult in this regime. For a better comparability, the data for 1 Sun illumination of all devices is summarized in Fig. 7e, showing that the planar and meso devices are limited by bulk recombination.

Light-soaking

We now investigate the devices after they have been exposed to 1 Sun (LED equivalent) illumination for 80 minutes at open circuit (“light soaking”). The transients of V_oc are monitored and plotted in Fig. 7f showing a strong decrease of V_oc for the meso-TiO₂ and planar device, whereas V_oc of the aged devices changes less and even improves for early times. Directly after 80 minutes of light soaking the temperature dependence of V_oc at 1 Sun was recorded which is added to the graphs in Fig. 7a–c (circles). Fitting with eqn (9) yields an E_a of around 1.3 to 1.4 eV, much lower than E_a for meso-TiO₂ and planar devices, but slightly larger than for the aged device. These data is added as dash-dotted lines to Fig. 7e as well. The light soaking effect is reversible as shown by V_ocvs. light intensity data collected at 20 °C before light soaking and after recovery, which are almost identical (Fig. 5g).

Discussion

We now want to interpret the obtained results for n_ID and E_a to better understand recombination for the different devices. We start with E_a. An E_a < E_g is commonly attributed to recombination of charge carriers that do not reside at the band edges of the absorber, but e.g. at interfaces of heterojunctions or surfaces (Fig. 8). This is because the potential energy of electron–hole pairs recombining through a heterojunction interface can be lower than E_g of the absorber due to a lower (higher) conduction (valence) band edge of the adjacent material. Furthermore, tail states and non-selective contacts can lead to a reduced E_a as illustrated in Fig. 8.

Fig. 8 Illustration of the value of E_a (in eqn (12)) dependent on the recombination process. Blue are conduction and valence band edge of the absorber (perovskite). An E_a < E_g is due to recombination at heterojunctions, surfaces or via tail states.

To determine whether such states with energies below E_g exist, sensitive measurements of the incident-photon-to-current-efficiency (IPCE) onset were carried out using Fourier Transform Photocurrent Spectroscopy (FTPS). Fig. 9a shows data for the light-soaking experiment performed at a meso TiO₂ device. The band gap at around 1.6 eV and the Urbach energy of around 15 meV remain unchanged upon light soaking. However, a new feature appears (or becomes more pronounced) with a peak at 1.35 eV extending towards 1.1 eV. It is strongest directly after the light soaking and tends to disappear after a recovery period in the dark. Interestingly, the energy of this feature coincides with E_a obtained from the temperature dependent measurements after light soaking (Fig. 7d). Therefore, we conclude that the reduced V_oc after light soaking is due to a reversible photoinduced formation of defect states, which open up new recombination channels. Observing that this happens in all investigated architectures independent of the contacts, corroborated also by the V_ocvs. time in Fig. 7f, we attribute it to photogenerated defects in the perovskite. It seems as these defects form during the reversible degradation upon light exposure as hypothesized in ref. 49, where surprisingly V_oc showed the opposite trend. However, in a control experiment, light-soaked films do not show increased PL quenching compared to films kept in the dark under N₂ atmosphere (Fig. S8 and S9, ESI†), confirming that the perovskite composition is photostable. In some samples the PL rather slightly increases consistent with what is commonly seen in PL studies,⁵⁰ but in contrast to a recent study, where a reduced PL yield and emission from subgap states have been reported after illumination.⁵¹ The photobrightening has been attributed to a photoinduced halide redistribution, decreasing the density of bulk defects.⁵² Therefore, to explain our V_oc decrease, we rule out a solely photoinduced defect formation in the bulk of the perovskite. Instead the defects might become active at an interface and could be indeed mobile ions, e.g.,⁵² I⁻ that lead to the reversible photo degradation.⁴⁰ Repeating the lightsoaking PL study on films deposited on FTO/TiO₂, we see a similar trend as on glass (Fig. S10, ESI†). In contrast, on complete devices the PL yield is indeed decreased after lightsoaking (Fig. S11, ESI†) providing strong evidence that interfaces to charge transport layers (such as HTL) play a crucial role. A similar effect on V_oc has been reported very recently and attributed to enhanced interfacial recombination at the TiO₂ interface due to an accumulation of cations and holes leading to increased surface recombination.²¹ The importance of changes in surface recombination during light-soaking are also evident at (inverted) devices with initially very low V_oc, where suppressed surface recombination upon ion migration leads to the opposite effect, i.e. an increase of V_oc.⁵³ In our study, we do not have the means to identify the interface (ETL or HTL) but note that we observe the same behavior at planar SnO₂ based devices yielding the same E_a despite the different energetics expected at the SnO₂ interface.³⁹ Even the IPCE of the non-light soaked device seems to show a weak response around 1.35 eV, indicating that the high V_oc in pristine devices might still be limited by this feature. It could also be a reason why the V_oc of pristine devices shows variations from batch to batch. This hypothesis is consistent with results from admittance spectroscopy on CH₃NH₃PbI₃ perovskite solar cells, where a trap state was found 0.28 eV below the band-gap energy dependent on processing conditions and correlated with hysteresis.⁵⁴

Fig. 9 Subgap states from IPCE onset collected by FTPS measurements. (a) Light-soaking of a meso TiO₂ device leading to a subgap state at 1.35 eV. (b) Comparison of different devices.

The FTPS spectra in Fig. 9a show an additional feature located at 0.9 eV, whose values are close to the resolution limit of our measurement, but observed in all kinds of devices. This feature needs further investigation but could be a deep trap state which is responsible for the SRH recombination leading to n_ID > 1. Comparing to calculations of intrinsic point defects, the light-induced defect could result from iodine interstitials as already mentioned, whereas the deep trap could be due to antisites^55,56 such as Pb_I, I_Pb, which show high formation energies and are therefore expected to be permanent and mainly generated during film formation. On the other hand, impurities could cause such deep trap states as well.⁵⁷ Signatures of both features⁵⁸ and deep traps^59,60 in CH₃NH₃PbI₃ perovskite solar cells have been identified with other techniques as well, showing that they are not specific to the mixed perovskite composition used in our work.

The E_a of the device without HTL is lowest and seems to increase with light intensity (Fig. 7d). We analyze FTPS data of this device (Fig. 6b) and observe a very broad distribution of subgap states which can explain the low and non-constant E_a. A similar distribution has been reported at low-performance devices, where a correlation between V_oc and hysteresis was found.⁶¹ Here, we have evidence that these defects are introduced by the direct contact of Au and the perovskite, which is consistent with the extremely pronounced tail reported for planar devices where Au is used for both electrodes.⁶² The low values of n_ID indicate that these defects are mainly localized close to the interface to the Au, where we expect a high hole density (cf.Fig. 1). Interestingly the aged device shows the same tail feature as well confirming that Au migrates during degradation, as has already been shown by ToF-SIMS measurements.²² However, for the aged device, n_ID is around 2 and E_a higher for low light intensities, indicating that SRH recombination through deep defects is responsible for the lower V_oc compared to a pristine device. To exclude that recombination centers are generated in the perovskite film itself by the elevated temperatures, we kept films at 65 °C for the same time in an N₂ glove box and could not observe a decrease of the PL yield, but rather a small increase, possibly due to an annealing effect (Fig. S12, ESI†). Therefore, it is most likely that the Au, which is more distributed in the perovskite layer, is responsible for recombination in a depletion region. For higher illumination intensities, the limit by surface recombination becomes visible for the aged device as n_ID decreases towards 1 (Fig. 4) and E_a towards values similar to those of the device without HTL (Fig. 7c). Consistent with the tail states in Fig. 9b, we find an increased doping density in a Mott–Schottky analysis when going from a pristine device to a degraded one to a device without HTL (Fig. S13, ESI†).

Now we shift focus to the pristine devices with high V_oc to understand which recombination mechanism has to be addressed to further improve these devices. First, the similar behavior between planar SnO₂ and meso-TiO₂ based devices lets us conclude that V_oc around 1 Sun is not limited by the electron selective layer despite the fact that most of the light is absorbed in its vicinity. This finding confirms the results from our¹⁶ and others'^19,47 previous studies, but is in contradiction to a recent impedance study, which is interpreted by recombination at the electron selective contact with time constants in the order of 1 s.¹⁸ According to Fig. 1 and 8, an n_ID between 1.5 and 2 and an E_a = E_g is attributed to SRH recombination in the bulk of a mostly intrinsic or depleted perovskite film. This interpretation is consistent with reported PL analyses⁵⁰ and enforced by the fact that n_ID does not change over orders of magnitude of illumination intensity, which excludes that the dominant recombination mechanism changes or that the influence of radiative recombination is already visible in n_ID. As the characteristics of this recombination mechanism are different from the case of light-soaking, we speculate that it is less likely related to intrinsic point defects which are mobile and might be formed by a light-assisted process. One candidate for these permanent recombination centers might be grain boundaries that give rise to defect states. However, experimental data on the perovskite material employed in this study, does not give clear indications that grain boundaries affect V_oc at 1 Sun.¹⁶ Furthermore, a recent PL mapping study collected evidence for benign grain boundaries⁶³ in contrast to a former PL study,⁶⁴ which might be explained by different processing conditions and material compositions leading to modified surface termination.⁶⁵

Another explanation might be related to the FTPS signal at 0.9 eV, which could result from a well-defined recombination center introduced by an antisite defect or an impurity as discussed above. Potential fluctuations due to surface or grain boundary states might be expected to follow a much broader distribution and rather causing an exponential tail in the FTPS instead of a distinct state, as observed for polycrystalline silicon.⁶⁶ We measured devices with smaller grain size¹⁶ as well, which did not show a more pronounced feature in the FTPS spectrum. Therefore, we conclude that whereas low-performance devices with unoptimized perovskite films are most likely limited by recombination at surfaces (interfaces and grain boundaries), the search for recombination centers in the best perovskite solar cells should not be performed ignoring the bulk. More detailed and sophisticated studies will be required to identify the nature of the recombination centers, not only focusing on intrinsic point defects but other intrinsic and extrinsic defects as well, such as impurities.

Conclusions

We have studied recombination in perovskite solar cells employing temperature dependent measurements to determine ideality factor and activation energy, which characterize the predominant recombination process. In doing so, we compared the ideality factor from light-intensity dependent V_oc, dark JV, and electroluminescence measurements, which yielded similar values. However, parasitic resistances hamper an unambiguous determination of the ideality factor from JV curves. Therefore, light-intensity dependent V_oc is a more reliable method, which is additionally able to resolve changes of recombination regime dependent on charge carrier densities and voltage.

We have investigated different devices (Fig. 10) including planar and mesoporous architectures and found that recombination is not severely affected by the n-type contact. On the other hand, devices without hole-transport layer clearly showed the signature of surface recombination. Degraded devices suffered from high defect-recombination, most likely induced by gold migrating into the perovskite. FTPS measurements indicated that Au in contact with perovskite causes a broad distribution of intragap states. In contrast, devices exposed to light-soaking showed a reversible formation of a narrow defect state situated 0.25 eV below the band gap which acts as dominant recombination center.

Fig. 10 Summary of the conclusions.

For pristine optimized devices with V_oc of around 1.2 V, an ideality factor of ≈1.6 and the band gap energy as activation energy for recombination indicate that recombination happens in a rather intrinsic/depleted bulk of the absorber layer. Therefore, a further optimization of perovskite solar cells needs to focus on identifying and eliminating defect states in the perovskite film including those of intrinsic and extrinsic nature. This requires a shift of focus in the perovskite solar cell research from compositional and morphology engineering towards identification and characterization of defects and impurities in the ppm regime.

Author contributions

WT designed the study, performed the experiments, analyzed the data and wrote the paper. KD did additional temperature dependent JV measurements. MY and J-P C-B prepared solar cells. BN performed FTPS measurements with WT. PY performed impedance measurements and together with J-P C-B contributed to detailed discussions. AH and MG supervised the students. All authors contributed to the final version of the manuscript.

Conflicts of interest

The authors declare no competing financial interests.

Acknowledgements

WT acknowledges funding by the Swiss National Science Foundation under an Ambizione Energy grant and MG the King Abdulaziz City for Science and Technology (KACST) for financial support under a joint research project. This work was partially funded by the Nano-Tera.ch “Synergy” project, the Swiss Federal Office of Energy under Grant SI/501072-01, and the Swiss National Science Foundation via the NRP70 “Energy Turnaround” project “PV2050”. We thank our technical staff in particular Benjamin Le Geyt for the excellent collaborative support.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7ee02415k

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