Elucidating Transport-Recombination Mechanisms in Perovskite Solar Cells by Small-Perturbation Techniques

Transcription

1 Article pubs.acs.org/jpcc Elucidating Transport-Recombination Mechanisms in Perovskite Solar Cells by Small-Perturbation Techniques Elena Guilleń, F. Javier Ramos, Juan A. Anta, and Shahzada Ahmad*, Abengoa Research, C/Energía Solar n 1, Campus Palmas Altas, Sevilla, Spain Department of Physical, Chemical and Natural Systems, University Pablo de Olavide, Sevilla, Spain *S Supporting Information ABSTRACT: Solar cells using perovskite as semiconducting pigment have recently attracted a surge of interest owing to their remarkable solar-to-electric conversion efficiencies and ease of processing. In this direction various device architectures and materials have been employed, and attempts were made to elucidate the underlying working principles. However, factors governing the performance of perovskite devices are still obscure. For instance, the interpretation of electrochemical impedance spectroscopy (EIS) is not straightforward, and the complexity of the equivalent circuits hinders the identification of transport and recombination mechanisms in devices, especially those that determine the performance of the device. Here in we carried out a comprehensive and complementary characterization of perovskite solar cells by using an array of small-perturbation techniques: EIS and intensity-modulated photocurrent and photovoltage spectroscopy (IMPS/IMVS). The employment of IMPS allowed us to identify two transport times separated by 2 orders of magnitude and with opposite voltage dependences. For recombination, well agreement was found between lifetimes obtained by IMVS and EIS. The feature associated with recombination and charge accumulation in an impedance spectrum through correlation to the IMVS response was experimentally identified. This correlation paves the way to reconstruct the current voltage curve using a continuity equation model for transport and recombination in the working device. The adopted methodology demonstrates that complementary techniques facilitate the interpretation of EIS results in perovskite solar cells, allowing us for the identification of the transport-recombination mechanisms and providing new insights into the efficiency-determining steps. 1. INTRODUCTION The use of organohalide perovskite as semiconducting pigment in solar cells is attractive due to their unparalleled power conversion efficiencies (PCE), ease of processing, and possibility to collect the charges at a cost-effective price. 1 PCE underwent an incredible increase from the first report by Miyasaka et al. 2 with PCE of 3.8% to currently ca. 18% reported by Seok et al. 3 This quantum jump was possible due to the substitution of the liquid electrolyte by a solid hole transport material (HTM). Several factors were found to affect the performance of the cell: thickness and nature of the HTM, perovskite deposition process, mesoporous/planar photoanode, etc. Consequently, PCE in excess of 10% can be achieved in varying configurations: planar/mesoporous configurations, choice of electron selective layers, conductive or insulating materials, 4 and range of HTM. 5,6 The technology arises from the knowledge gained from dye-sensitized solar cells (DSSCs); thus, their working principles were reported However, factors governing the device performance and operation are still obscure. Perovskite acts as an absorber and shows ambipolar behavior (electron and hole conduction), with having long diffusion lengths 11,12 and having the capability of storing charge. 8 Though there is a lack of understanding about what leads to such a facile transport within the perovskite layers, the role of the selective contacts on transport and/or charge extraction, the properties of the recombination losses, and the nature of capacitance observed in perovskite layers. Understanding the processes governing the cell is key to optimizing and selecting new materials. In this work we have combined different electrochemical techniques for characterization of state-of-the art devices. The coincident responses can provide an understanding of the mechanisms of electron transport and recombination that control the performance in devices. An extensive study comprising small perturbation techniques can be vital to unravel this, as it was shown for DSSCs, 13 while the majority of the reports in perovskite deal with a single technique. 8,9,14 Herein, we have combined electrochemical impedance spectroscopy (EIS) and intensitymodulated photocurrent/photovoltage spectroscopy (IMPS/ IMVS). EIS is a very powerful technique, but to take advantage of EIS fully it is important to clearly identify the physical processes associated with each part of the spectra. By Received: July 10, 2014 Revised: September 10, 2014 Published: September 12, American Chemical Society dx.doi.org/ /jp J. Phys. Chem. C 2014, 118,

2 The Journal of Physical Chemistry C comparing electron lifetimes as a function of voltage obtained from IMVS with those obtained by impedance (intermediate frequencies arc), an agreement was found which leads us to conclude that the appearing arc in the spectra is the main cause for recombination losses in the solar cell and the charge accumulation. EIS and IMPS were employed to study electron and hole transport. IMPS measurements reveal two transport constants which show opposite dependences with respect to voltage. The recombination resistance obtained from EIS shows an exponential behavior, with a β-factor smaller than 1 and close to 1/2. Three different device configurations, deposited by sequential deposition 15 or single step processes 16 were fabricated. In-depth analysis of the recombination and electron transport processes in perovskite solar cells and reconstruction of the J V curve from the small-perturbation data together with a cross-correlation and comparison between different cell configurations will allow us to elucidate the processes governing the performance in this type of cell. 2. EXPERIMENTAL SECTION The chemicals were purchased from either Sigma-Aldrich or Agros and were used as such. Spiro-OMeTAD was acquired from Merck KGaA, and TiO 2 mesoporous paste (18NR-T) was procured from Dyesol. CH 3 NH 3 I was synthesized following previous literature. 17 For device fabrication, FTO-coated glass NSG10 (Nippon Sheet Glass) was first laser etched. Then, the substrates were cleaned and brushed using Hellmanex solution and rinsed with deionized water and ethanol; subsequently, they were ultrasonicated in 2-propanol and dried using compressed air. Before the blocking layer deposition, samples were subjected to ultraviolet/o 3 treatment for 30 min. The TiO 2 dense layer was deposited by spin-coating (5000 rpm, 30 s) TiCl 4 2 M solution over the sample and heated at 70 C for 30 min. After that, the mesoporous titanium dioxide film was prepared with the Dyesol paste 18NR-T. TiO 2 nanoparticles paste was diluted 1:3.5 (w:w) in pure ethanol and then spincoated (5000 rpm, 30 s). Then the photoanodes were sequentially sintered 5 min at 125 C, 5 min at 325 C, 5 min at 375 C, 15 min at 450 C, and 15 min at 500 C. On these photoanodes perovskite was deposited using three different techniques: CH 3 NH 3 PbI 3 by sequential deposition, 15 CH 3 NH 3 PbI 3 by one-step deposition, and CH 3 NH 3 PbI 3 x Cl x by one-step process. For CH 3 NH 3 PbI 3 (sequential deposition), a PbI 2 film was deposited by spin-coating (6500 rpm for 30 s with 5500 rpm s 1 as acceleration) using 50 μl per cell of 1 M PbI 2 in N,N-dimethylformamide (DMF); lead iodide solution was kept at 70 C under vigorous stirring to avoid insolubility issues during the whole deposition process. After the spincoating, the cells were placed onto a hot plate at 70 C for 15 min for annealing and were allowed to cool down. The cells were then submerged in the methylammonium iodide (MAI) solution in 2-propanol (8 mg/ml) for 20 s to form the perovskite. The perovskite formation was observed due to the change of color from yellow to dark brown-black; subsequently, they were rinsed in pure 2-propanol and dried using the spincoater at 4000 rpm for 30 s. The samples were subject to annealing again at 70 C for 15 min. For the CH 3 NH 3 PbI 3 (one step), a solution together with PbI 2 and CH 3 NH 3 I (40 wt %, 1:1 molar ratio) in γ-butyrolactone was prepared; the solution was spin-coated at 2000 rpm for 60 s (1000 rpm s 1 as acceleration) and annealed at 100 C for 15 min. Finally, for the CH 3 NH 3 PbCl x I 3 x perovskite (one step) synthesis, a 40 wt % solution that contains a mixture of PbCl 2 :CH 3 NH 3 I (1:3 in Article molar ratio) using DMF as solvent was deposited by spincoating (2000 rpm, 60 s, 1000 rpm s 1 as acceleration) onto the mesoporous film; it was annealed at 100 C for 45 min. Spiro- OMeTAD (2,2,7,7 -tetrakis(n,n-di-p-methoxyphenyamine)- 9,9-spirobifluorene) was selected as hole transporting material (HTM). 35 μl of Spiro-OMeTAD solution was deposited onto the perovskite using the spin-coating technique at 4000 rpm for 30 s using an acceleration of 1650 rpm s 1. The solution was prepared dissolving 72.3 mg of Spiro-OMeTAD in 1 ml of chlorobenzene. As additives, 21.9 μl of tris(2-(1h-pyrazol-1- yl)-4-tert-butylpyridine)cobalt(iii) bis(trifluoromethylsulfonyl)imide (FK209) stock solution (400 mg of FK209 in 1 ml of acetonitrile), 17.5 μl of lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) stock solution (520 mg of LiTFSI in 1 ml of acetonitrile), and 28.8 μl of4-tert-butylpyridine (96% w:w) were also added to the solution. To finish the device 80 nm of gold was vacuum-sublimed (pressure between and Torr) for the cathode deposition. Lead iodide, methylammonium iodide, and Spiro-OMeTAD solutions were prepared under controlled levels of water and O 2 using a glovebox. PbI 2 spin-coating, MAI dipping, and Spiro-OMeTAD spin-coating depositions were carried out inside a drybox. For J V curves, a 450 W Xe lamp (Oriel) with a Schott K113 Tempax sunlight filter (Praezisions Glas & Optik GmbH) was employed as a light source. A digital source meter (Keithly Model 2400) was used to apply the voltage to the cell while the current was recorded. For J V measurements the active area was fixed to cm 2 using a mask and was recorded in reverse bias (from V oc ) after 10 s delay under illumination at a scan speed of 100 mv/s; we have found this as an optimal condition to avoid hysteresis. Impedance spectroscopy (EIS) measurements in the dark and under illumination and intensitymodulated spectroscopies (IMPS and IMVS) were carried out using an Autolab PGSTAT30 including a FRA module. The illumination for the frequency response techniques was provided by a 530 nm LED over a wide range of dc light intensities. EIS measurements were performed using a 20 mv 8 perturbation in the Hz range. EIS spectra have been measured under illumination applying the same voltage as the one induced by the light. The amplitude of the sinusoidal modulation for IMVS and IMPS measurements was checked to obtain a linear response. Zview equivalent circuit modeling software (Scribner) was used for fitting impedance spectra. 3. RESULTS AND DISCUSSION 3.1. Characterization of Perovskite Solar Cells by Small Perturbation Techniques. The photovoltaic parameters of the devices approach routine state-of-the art values reported for mesoporous perovskite solar cells. Table 1 summarizes the photovoltaic characteristics of the devices, and Figure 1 shows a J V curve for each configuration. We have found that the devices fabricated by one-step method were less stable; thus, comprehensive analysis by small perturbation techniques (IMPS/IMVS/EIS) was carried out for sequentially deposited cells only. In order to study the transport recombination mechanism in the mesoporous and perovskite layers, the cells were analyzed close to operation (maximum power point), and for this the response at low forward bias was discarded in this analysis. Frequency-domain techniques that involve a small-amplitude modulation of the photon flux incident on the cell superimposed on a steady-state illumination level (Scheme 1) comprise IMPS and IMVS. 18 Both techniques lead to the determination of a time constant for the frequency dx.doi.org/ /jp J. Phys. Chem. C 2014, 118,

3 The Journal of Physical Chemistry C Table 1. Photovoltaic Parameters of the Device with Different Configurations a cell configuration 1 FTO/bl-TiO 2 /mp-tio 2 / CH 3 NH 3 PbI 3 (sequential deposition)/spiro- MeOTAD/Au 2 FTO/bl-TiO 2 /mp-tio 2 / CH 3 NH 3 PbI 3 (1:1; one step) /Spiro-MeOTAD/Au 3 FTO/bl-TiO 2 /mp-tio 2 / CH 3 NH 3 PbI 3 x Cl x (3:1, one step) /Spiro-MeOTAD/Au J sc [ma cm 2 ] V oc [V] dependent photocurrent or photovoltage response which is a signature of a certain transport or recombination process occurring in the device. 19,20 Contrary to IMPS/IMVS, EIS 21 monitors the current response of the device produced by frequency-dependent modulation of an applied voltage superimposed to a dc voltage (Scheme 1). The resulting frequencydependent impedance (voltage/current) is analyzed for different dc voltages. FF PCE [%] a J sc = photocurrent density, V oc = open circuit potential, FF = fill factor, and PCE = power conversion efficiency. Figure 1. J V curves under full sun illumination for different configurations. Scheme 1. Input and Output Signals for Each of the Small Perturbation Techniques Used and Schematic of the Device Architecture Formed by Glass/FTO/TiO 2 Compact Layer/ Mesoporous TiO 2 /Perovksite/Spiro-OMeTAD/Au The advantage of EIS over IMPS/IMVS is that, apart from transport and recombination time constants, it provides information about internal resistances in the devices, which can be used to reconstruct the J V curve under operating conditions. However, an adequate extraction of parameters from an EIS spectrum relies on the availability of a physically meaningful equivalent circuit, which can be very complex in certain cases. In perovskite solar cells up to three different equivalent circuits depending on dc voltage bias have been proposed, and the origin of certain features, as those appearing between high and intermediate frequencies, remains obscure. 9 In the past IMPS has been used to characterize DSSCs in both the liquid, 19,22 and the solid state 23 and provides information about the electron transport processes in the cells. For DSSCs community, IMPS has emerged as a complementary technique to EIS, when the value of transport resistance for the transmission line becomes lower than the resistance of the cathode. 13 In the case of perovskite solar cells, where the transport-recombination mechanism is not well understood, it is paramount to use complementary techniques to probe transport. However, before using IMPS, it is necessary to check and adapt the IMPS procedure used in DSSC to perovskite solar cell. To ascertain the validity of our measurements, the following conditions were tested: linearity, causality, and stability. 24 A detailed description of the procedure followed to check these conditions, including Lissajous and signal response plots measurements, can be found in the Supporting Information. IMPS response appears as a semicircle in the lower quadrant for DSSCs. The time constant τ IMPS can be obtained from the inverse of the minimum angular frequency (ω min ) in an IMPS plot: τ = 1/ ω Article IMPS min (1) The time constant for the photocurrent response depends on both electron transport and electron recombination. 25 Under short-circuit conditions in DSSCs, electron lifetime is assumed to be much larger than the electron transport time; thus, the measured photocurrent response is nearly equal to the transport time. In Figure 2a,b we can see IMPS spectra of perovskite solar cell (configuration 1) under three different illumination intensities. The most significant finding is the presence of two well-defined semicircles (Figure 2a), corresponding to two different transport processes in the cell emerging at different frequencies (Figure 2b). IMVS was used to characterize recombination in DSSCs, 19 and a similar procedure to IMPS one has been carried out to check linearity, causality, and stability during IMVS measurements of perovskite solar cells. The IMVS response of a Figure 2. IMPS measurements of a perovskite solar cell of configuration 1 at three different illumination intensities. The voltages refer to the opencircuit potential value induced by illumination dx.doi.org/ /jp J. Phys. Chem. C 2014, 118,

4 The Journal of Physical Chemistry C perovskite solar cell in the frequency domain is a semicircle in the lower complex plane (Figure 3). Figure 3. IMVS response of a perovskite solar cell at three different illumination intensities. The voltage refers to the open-circuit potential value induced by illumination. The effective electron lifetime (τ n ) can be obtained by considering the minimum of the semicircle located at an angular frequency that is equal to: (IMVS) n τ = 1/ ω min (2) IMVS provides a ready estimation of the recombination lifetime without the need of fitting to a complex equivalent circuit. The accuracy of the EIS measurements was also crosschecked using Lissajous and signal response plots. EIS is used Article to probe different electronic processes occurring in the devices. 21 The use of this technique implies that it is necessary to clearly identify the physical processes associated with the responses observed in the spectra. This was thoroughly studied for DSSCs while reports on perovskite solar cells are limited One of the most valuable information which can be obtained from EIS is the electron lifetime in the characterized cell. Provided a certain interface can be identified in the EIS spectrum in the form of a semicircle, characterized by a chemical capacitance (C μ ) and a charge recombination resistance (R rec ), a lifetime can be defined as: 21 τ n (EIS) = CR μ rec (3) The feature in the spectrum related to lifetime is clearly identified in DSSCs, but it is not clear yet in perovskite solar cell. Figure 4a f shows the evolution of the impedance spectrum from low to high forward bias. Depending on the voltage, two or three regions [high frequency (hf), medium frequency (mf), and low frequency (lf)] can be observed in the EIS spectrum of a perovskite solar cell. For voltages over 0.8 V (Figure 4f), the lf feature was too small and was not clearly observed in the spectrum. The spectrum exhibits only two semicircles, and the transmission line can be detected. The lf feature appears below 0.8 V (Figure 4c e) and increases with voltage. Low and Figure 4. (a f) Nyquist plots for EIS measurements of configuration 1 cell at different open circuit potentials ( V) in increasing order, induced by illumination. Experimental data (dots) and fitting (lines) are included. High, mid, and low frequencies (hf, mf, lf) are indicated in one of the plots dx.doi.org/ /jp J. Phys. Chem. C 2014, 118,

5 The Journal of Physical Chemistry C Article Figure 5. (a) Transport times obtained from the low frequency and high frequency features in an IMPS spectrum, as a function of open circuit voltage induced at different illumination intensities. (b) Diffusion coefficient obtained from IMPS response at low frequencies and obtained from the transport resistance in an EIS spectrum, as a function of the open circuit voltage induced at different illumination intensities. medium frequency features start to merge below 0.7 V (Figure 4a d) and are no longer identifiable as separate features in the spectrum. This fact can make the fitting inaccurate. At voltages lower than 0.5 V (Figure 4a,b) only two semicircles are observed. In accordance with other groups, the transmission line is only detected in a potential range. In less efficient cells, sometimes an extra semicircle at high frequencies is observed (Figure S6) at intermediate forward bias ( 0.5 V). Dualeh et al. 9 also reported on an additional RC element at those frequencies in the impedance spectrum. Different equivalent circuits have been used for the fitting depending on the voltage (Figure S4), and the most relevant parameters obtained are plotted versus potential (Figure S5): charge transfer resistance at low frequencies (R lf ), transport resistance obtained from the transmission line (R t ), and charge transfer resistance and capacitance obtained at intermediate frequencies (R mf and C mf ). In the past also the feature at low frequencies was observed but remains unassigned to any process in the device. Snaith et al. 26 pointed out that hysteresis became more extreme as the scan rate was slow, and this feature in the impedance spectrum appears at low frequencies. During the submission process of this article, reports appeared discussing the origin of this feature, which was ascribed to slow dynamics and hysteresis processes in perovskite. 27,28 The feature at mid frequencies has been attributed to recombination process in the perovskite solar cell in analogy to DSSCs, but to the best of our knowledge, there is still no experimental evidence for the validation of this analogy. Since the perovskite solar cells are in the preliminary stage of understanding, it is paramount to have complementary techniques to facilitate the analysis of the impedance spectrum. Here in we demonstrate how IMVS can help in the fitting procedure to identify the medium and low frequency parts in order to clearly identify the feature associated with the recombination process (R rec ) that determines the J V curve and hence the performance of the device Transport-Recombination Mechanisms in Perovskite Solar Cells. IMPS measurements (Figure 2) revealed two distinct transport times, separated by 1 2 orders of magnitude ( and 10 4 Hz). Figure 5a shows those transport times measured at different illumination intensities plotted versus the bias potential induced at the same illumination. The behavior of the two transport times as a function of the bias voltage induced by the illumination is the opposite (Figure 5a), although the voltage dependence of the high frequency transport time is weak. The recent reports suggests that the current flow can happen in the mesoporous TiO 2 or via the perovskite itself. In principle, the two time constants could be related to the following transport mechanisms: (i) electron transport in TiO 2, (ii) electron and hole transport in the perovskite, or (iii) hole transport in the Spiro-OMeTAD. In analogy to DSSCs the slower transport time could be related to electron transport in TiO 2. As mentioned earlier, time constants τ IMPS were obtained from the inverse of the minimum angular frequency (ω min ) in the IMPS plot, and they can be related to the effective diffusion coefficient, D n,by 20 τ IMPS 2 = d γdn (4) where γ is a numerical factor which depends on layer thickness (d), absorption coefficient, and illumination direction. 29 On the other hand, D n can also be obtained from the transport resistance (R t ) and the chemical capacitance in an EIS spectrum (Figure S5): D n = 2 d RC t μ (5) The diffusion coefficient obtained from the IMPS transport time at lower frequencies using a γ value of 2.5 and that from the transport resistance extracted from the transmission line in the EIS measurements is compared in Figure 5b. For this analysis the thickness employed for the calculation was 270 nm thickness of the mesoporous film as measured by a scanning electron microscope. A similar trend with the voltage was observed (slope of 14 V 1 ), while the diffusion coefficient values were shifted by ca. 100 mv. This shift can be due to the different position of the Fermi level in the IMPS (short circuit) and in the EIS measurement (open circuit). 13 The exponential behavior of the D n with respect to the voltage is an indication that transport is a multiple trapping mechanism 30 although with a distribution parameter α different from the one observed in standard TiO 2 DSSCs: D (1 α)( Ef( n) Ef )/ k T n = D0e 0 B where k B is the Boltzmann constant and T the temperature, E f (n) and E f 0 (n) are the Fermi level of electrons under illumination and in the dark, respectively, and D 0 represents the diffusion coefficient in the dark, i.e., when E f (n)=e f 0 (n). Kru ger et al. 31 reported similar TiO 2 diffusion coefficient values (between 10 6 and 10 7 ) for solid-state DSSCs obtained by IMPS. This, together with its voltage dependence, suggests that (6) dx.doi.org/ /jp J. Phys. Chem. C 2014, 118,

6 The Journal of Physical Chemistry C Article Figure 6. (a) Imaginary part spectra of EIS and (b) IMVS for cell configuration 1 as a function of frequency, at an open circuit voltage of 0.78 V induced by illumination. (c) Comparison of lifetimes obtained from IMVS and EIS as a function of potential. the slow component in the IMPS spectrum corresponds to transport of electrons in the TiO 2 mesoporous structure, which is in well accordance with DSSCs. 14 The origin of the second time constant appearing at high frequencies remains unanswered. In the case of solid-state DSSCs using spiro-ometad only one semicircle in the IMPS spectra was observed, 31 while for liquid-state device sensitized with perovskite no hints on the observation of two semicircles were reported. 32 Similarly Zu et al. 14 measured IMPS for solid-state perovskite solar cells, and no information was given about a second time constant in the spectra. In the past, two separate components in the IMPS spectrum have rarely been reported Halme et al. 34 attributed it to two distinct transport lengths: the faster component related to electrons that diffuse directly to the contact and the slower component to those that find their way to the opposite direction and are reflected back at edge of the film. Two semicircles in the IMPS spectrum depending on the film thickness were observed and assigned as two different diffusion modes for electron transport: the high-frequency semicircle to a trap-free mode while the low-frequency semicircle to a trap-limited mode. 35 In DSSCs a feature appearing at high frequencies in the spectrum was also attributed to the attenuation of the IMPS response by the series resistance and capacitance of the anode 20,36 or to inhomogeneous light absorption in the film. 34 Li et al. 37 carried out a comprehensive analysis of the conductivity of TiO 2 and Spiro-OMeTAD in solid-state DSSCs by EIS and found that hole conductivity of the Spiro-OMeTAD phase is larger than the electron conductivity of the mesoporous TiO 2. In the EIS response, they observed two time constants in the Hz range. The high frequency one ( 10 4 Hz) was attributed to the Spiro-OMeTAD, while the lower frequency one to transport, recombination, and chemical capacitance in the mesoporous TiO 2, and both varied with voltage. Comparatively in this work, the low frequency response is most likely related to the transport in the mesoporous TiO 2 electrode, while the high frequency response could be attributed to transport in the Spiro-OMeTAD, although the voltage dependence of this time constant is very weak. We speculate that the rapid constant could be the signature of transport in the perovskite itself. Diffusion coefficients of and cm 2 s 1 have been measured for electrons in the perovskite film and and cm 2 s 1 for holes. 11,12 Furthermore, a simple diffusion mechanism, not limited by traps, has been proposed for perovskite, 11,12 as there is evidence that the material is highly crystalline and defect-free. 38 Simple diffusion will not have a bias dependence of the diffusion coefficient a fact that can be connected with the behavior of the rapid time constant in our results. However, the reported values of the diffusion coefficient of electrons and holes in perovskite films are 4 and 2 orders of magnitude higher than those obtained from the two time constants observed by us, respectively. Hence, the response of the perovskite should appear at very high frequencies, which is not the case in the present work. It is to be mentioned that the experiments of Xing et al. 12 and Strank et al. 11 were performed on a flat configuration, with thin films of perovskite in contact with either an electron or a hole quencher. On the contrary, our devices are fabricated using a mesoporous TiO 2 /perovskite. This may result in slower transport and/or a different effective thickness for transport. To mention here there are two layers in the cell: a capping layer of perovskite and the mesoporous TiO 2 films filled by the perovskite. This question remains open, and further studies are required to elucidate this point. IMVS gives us information about the total recombination loss in the solar cell. The mid frequencies feature in the EIS spectrum (Figure 6a,b) appears at similar frequencies that the main (and only) IMVS peak (around Hz). Hence, both measurements give similar dynamic information at this frequency range. Electron lifetimes have been obtained from the inverse of the minimum angular frequency in the IMVS spectrum (eq 2) and from the capacitance and the charge transfer resistance obtained for the mid frequency feature in the impedance spectrum (eq 3). Both lifetimes are compared in Figure 6c. Strikingly, we observed a well agreement between the electron lifetime obtained from IMVS and EIS (mid frequency arc). This states that IMVS is not only useful as a means to quantify the total recombination loss in the cell but also helps facilitate to interpret and perform the impedance spectra fitting. In particular, low and mid frequency features tend to merge, dx.doi.org/ /jp J. Phys. Chem. C 2014, 118,

7 The Journal of Physical Chemistry C and they are not often distinguishable (Figure 4). Using IMVS, we can check that we are properly identifying the two features during the fitting procedure so the validity of the equivalent circuit used for fitting can be confirmed. We have thus experimentally established that the arc which appears at intermediate frequencies is the one related to recombination and charge accumulation. It is pertinent to mention here that only when the capacitance has a chemical origin, the electron lifetime can be obtained from eq 3. The fact that there is agreement between IMVS and EIS lifetime suggests that the capacitance extracted from the EIS experiment has a chemical nature. Through IMVS measurements we have identified that charge transfer resistance at mid frequencies (R mf ) corresponds to the resistance to recombination (R rec ). Once we have clearly identified the limiting recombination parameter in the EIS spectrum, we can compare the recombination resistances for different configurations. The device PV efficiency depends on the deposition method adopted for perovskite (Table 1). Figure 7 compares the charge transfer resistance for the three different Figure 7. Comparison of the charge transfer resistance obtained in the dark for the three different perovskite solar cells as mention in Table 1. configurations studied here. As indicated, the charge transfer resistance was derived from the intermediate frequencies arc and measurements were carried out in the dark. Interestingly, recombination is more affected by the deposition method of perovskites rather than single or binary halide anion (presence of chloride). Recombination resistance is lower (so recombination is stronger) for one step deposited perovskite, and thus pointing toward that it is not the nature of the perovskite but the interface between perovskite and TiO 2 /or HTM, which dictates the recombination rate. Therefore, the different recombination could be related to a better crystal formation or to the conformal or unoriented growth of the perovskite layer on TiO 2. The role of chloride in the performance or the amount of chloride left in the final perovskite solar cells is still not clear. In planar configuration better performance and longer charge carrier diffusion lengths have been reported for MAPbI 3 x Cl x compared to MAPbI 3. This led to conclude that small amount of chloride improve the charge transport. 11,12 Similar to DSSC, recombination resistance exhibits an exponential behavior with respect to voltage (Figure 7). It seems that there is one main recombination path, as the same trend is maintained along all the studied voltage range. However, in contrast to standard DSSC, the slope of the R rec potential curve is characterized by a β-factor smaller than 0.5 ( 0.4): R 0 ( E f( n) Ef) = R exp β kt B (7) ct 0 Article Christians et al. 6 also reported a β factor lower than 0.5 for perovskite solar cells based on two different hole transport materials (Spiro-OMeTAD and CuI). We have to consider, as initial hypothesis, that there are several possible recombination mechanisms in a perovskite solar cell: (i) electron and hole recombination within the perovskite film, (ii) electrons in the TiO 2 with holes in the perovskite (similar to recombination with oxidized dye molecules in DSSCs), (iii) recombination between electrons in the perovskite and holes in the HTM, and (iv) recombination from TiO 2 to HTM (analogous to electron/ electrolyte recombination in DSSC). We can discard mechanism i as the diffusion lengths for electrons and holes within the perovskite are very long. 11,12 In fact, it has been inferred from fluorescence measurements that the half-time for radiative recombination in perovskite films with inert contacts is on the order of 10 ns, 12 which means that a semicircle centered at around Hz should in theory be observed in the EIS spectrum. However, this is far beyond the detection limit of EIS. On the other hand, we can assume that if perovskite deposition is impeccable (in the case of the two-step method), recombination iv must be low because the TiO 2 is not in direct contact with the hole transport material. The high nonlinearity of the recombination process limiting the solar cell performance, evidenced by such β < 1, suggests that recombination is mediated by surface states. The fact that β < 0.5 indicates that the mechanism is quite different than typical DSSC where β > 0.5 (approximately α). 39 In this context, recently it was reported that two semiconductors in contact in which recombination takes place via charge transfer between two exponential distributions of surface trap states, a β < 0.5 is predicted (in fact, β = α is predicted, but α < 0.5 in many cases, like TiO 2 ). 40 Hence, we consider this finding, together with the discard of processes i and iv, as a strong indication that the main recombination loss in the perovskite cell is via the selective contacts: either the TiO 2 /perovskite or the perovskite/htm interface or a combination of both. This mainly arises from the somehow uncontrolled growth of perovskites. It is in accordance with our findings that recombination is much affected by deposition method as the main recombination loss is occurring at the interface. To provide further insight into the origin and impact of the recombination loss, identified by the comparison of EIS and IMVS, reconstruction of the J V curve from the smallperturbation measurements was attempted. For this we have considered the magnitude n(x,t) as the total density of photogenerated electron hole pairs or excitations (following the interpretation by Stranks et al. 11 ) which are effectively contributing to a measurable photocurrent. In principle, this is a time-dependent quantity and can also vary with the perpendicular distance to the external contacts x. Next, we assumed (Xing et al., 12 Stranks et al. 11 ) that transport of both electrons and holes occur by diffusion only. Furthermore, and according to the findings of the IMPS measurements, we have assumed that the transport of charges is limited by the slowest transport contribution, that is, the diffusion coefficient of electrons in the TiO 2 mesoporous film (Figure 5b). As this is a voltage-dependent magnitude, in analogy to a DSSCs, 41 we have solved the following continuity equation dx.doi.org/ /jp J. Phys. Chem. C 2014, 118,

8 The Journal of Physical Chemistry C nx (, t) = + t n D n n n() Gx () kn x 0 where D n is a density-dependent (thus voltage-dependent) diffusion coefficient given by eq 6, G(x) is the generation profile of electron hole pairs due to light absorption in the active layer, k 0 is a recombination constant, and δ is the reaction order for recombination of electrons and holes. The detailed resolution of this equation can be found in the Supporting Information. A voltage-dependent lifetime can be inferred from the inverse of the density-dependent recombination constant, 39 which is in turn obtained from the recombination term k 0 n δ in eq 8 = JR kn( n) n = δkn δ 1 0 where J R is the recombination current density. This makes the recombination constant (and hence the lifetime) voltagedependent, as inferred from the experimental EIS and IMVS data. Following the analogy with the DSSC model, 41 the reaction order is δ =(β α)/α, where α and β are respectively defined by eqs 6 and 7. Hence, α accounts for the density dependence of the diffusion coefficient and β for the voltage dependence of the recombination resistance. As shown in ref 41, the shape of the J V curve only depends on the value of β and the series resistance acting in the cell. The simulated J V curve for β = 0.5 and cell configuration 1 is presented in Figure 8. To simulate the curve, the total Figure 8. Experimental J V curve (symbols) for cell 1 and results (dashed line) from the model of eq 8 for β = 0.5. R s stands for series resistance, and A is the geometrical surface area. Parameters used for the model: d = 0.5 μm, D 0 =10 10 cm 2 s 1, and α = 0.2. δ (8) (9) absorption is adjusted to reproduce the experimental shortcircuit photocurrent, whereas k 0 is adjusted to get the experimental open-circuit voltage. In turn, the series resistance is fixed by imposing that the current gives the correct current at the maximum power point. Further predictions of the model with and without series resistance and for β = 0.6 are reported in the Supporting Information (Figure S8). We observe that there is a good agreement between the simulated curve and the experimental data, which suggests that an analogous model to that of a DSSC, based on diffusion of charges and a density-dependent, i.e., voltage-dependent, recombination constant is capable of reproducing the electrical output of the perovskite solar cell. Furthermore, the lifetime that is obtained from fitting to the experimental V oc and eq 9, τ s is quite close to the values derived from the smallperturbation measurements (Figure 6c) close to open circuit. This can be interpreted as a confirmation that the lifetime obtained from the EIS response at mid frequencies represents the main recombination loss in the solar cell and the one that determines the shape of the J V curve as the voltage approaches V oc. Furthermore, a recombination parameter of β close to 0.5 (as shown in the Supporting Information, β = 0.6 gives very similar results) confirms the interpretation advanced above that interfacial recombination, via surface states, is the most likely mechanism of recombination, rather than recombination between electrons and holes within the perovskite (in DSSC, β values well above 0.5 are more typical of model recombination). This is consistent with the long diffusion lengths reported for electrons and holes in perovskite films 11 and a fast injection rate. 4. CONCLUSIONS Article A comprehensive study consisting of an array of three small perturbation techniques on perovskite-based solar cells was carried out, and deep insight into the functioning of devices is provided. Intensity-modulated photocurrent spectroscopy measurements reveal the presence of two clearly separated time constants in the frequency range. We speculate that the low frequency one (slow) corresponds to transport in the mesoporous TiO 2, while the high frequency (rapid) may be due to the transport in the hole conductor, although transport in the perovskite itself cannot be discarded. Recombination process in perovksite solar cells was studied by combining intensity-modulated photovoltage spectroscopy and electrochemical impedance spectroscopy. Both these techniques elucidated similar time response at similar frequencies; thus, well agreement between lifetimes was found. With the help of complementary techniques we have experimentally identified the semicircle in the impedance spectra related to recombination processes and charge accumulation in a perovskite solar cell. Recombination behavior in three different types of perovskite solar cells, different deposition processes, and different perovskite precursors were analyzed. Devices prepared using the sequential deposition method exhibit higher resistance to charge recombination than those prepared by the one-step method and irrespective of the precursor used. This result is in accordance with the importance of perovskite interfaces on recombination which we have revealed. Furthermore, it allowed us to reconstruct the J V curve using a continuity equation for the total density of electron hole pairs in the active layer, where transport and recombination are assumed density dependent in accordance to the small-perturbation measurements and in analogy to DSSC. The agreement between the experimental J V curve and this simplified model was found, indicating the main recombination loss identified by the comparison of EIS and IMVS is the one that determines the shape of the J V curve. Although these results suggest that the perovskite solar cell works analogy to DSSC, the recombination parameter β of around 0.5 found in the EIS and used in the model suggests that the mechanism of recombination is different, possibly determined by electron transfer across the solid interfaces present in the cell. In spite of an agreement between the model and the experimental curve, it is to be noted that this is a simplified model, and other contributions to transport (for instance by drift) and recombination may also play a role in perovskite solar cells. Further research is required in this dx.doi.org/ /jp J. Phys. Chem. C 2014, 118,

9 The Journal of Physical Chemistry C Article direction to unravel the limiting mechanisms and its dependence on the preparation procedure. ASSOCIATED CONTENT *S Supporting Information Checking procedure used for testing accuracy of small perturbation measurements, equivalent circuits used, fitting parameters as a function of voltage, impedance spectrum, and details of the continuity equation model. This material is available free of charge via the Internet at AUTHOR INFORMATION Corresponding Author *Phone ; shahzada.ahmad@research. abengoa.com (S.A.). Notes The authors declare the following competing financial interest(s): Authors (from Abengoa Research) may have competing interests as Abengoa is an international company and has significant interest in the renewable energy sector. ACKNOWLEDGMENTS We thank Michael Graetzel and M. K. Nazeeruddin for using their experimental facilities and support and Juan Bisquert, Ivań Mora-Sero, and Gerko Oskam for fruitful discussions. S.A. acknowledges a grant from Torres Quevedo, Ministry of Economy and Innovation of Spain. REFERENCES (1) Kazim, S.; Nazeeruddin, M. K.; Graẗzel, M.; Ahmad, S. Perovskite as Light Harvester: A Game Changer in Photovoltaics. Angew. Chem., Int. Ed. 2014, 53, (2) Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131, (3) Jeon, N. J.; Lee, H. G.; Kim, Y. C.; Seo, J.; Noh, J. H.; Lee, J.; Seok, S. I. O-Methoxy Substituents in Spiro-OMeTAD for Efficient Inorganic-Organic Hybrid Perovskite Solar Cells. J. Am. Chem. Soc. 2014, 136, (4) Lee, M. M.; Teuscher, J.; Miyasaka, T.; Murakami, T. N.; Snaith, H. J. Efficient Hybrid Solar Cells Based on Meso-Superstructured Organometal Halide Perovskites. Science 2012, 338, (5) Qin, P.; Tanaka, S.; Ito, S.; Tetreault, N.; Manabe, K.; Nishino, H.; Nazeeruddin, M. K.; Graẗzel, M. Inorganic Hole Conductor-Based Lead Halide Perovskite Solar Cells with 12.4% Conversion Efficiency. Nat. Commun. 2014, 5, (6) Christians, J. A.; Fung, R. C. M.; Kamat, P. V. An Inorganic Hole Conductor for Organo-Lead Halide Perovskite Solar Cells. Improved Hole Conductivity with Copper Iodide. J. Am. Chem. Soc. 2014, 136, (7) Juaŕez-Peŕez, E. J.; Wu, M.; Fabregat-santiago, F.; Lakus-wollny, K.; Mankel, E.; Mayer, T.; Jaegermann, W.; Mora-Sero, I. Role of the Selective Contacts in the Performance of Lead Halide Perovskite Solar Cells. J. Phys. Chem. Lett. 2014, 5, (8) Kim, H. S.; Mora-Sero, I.; Gonzaĺez-Pedro, V.; Fabregat-Santiago, F.; Juaŕez-Peŕez, E. J.; Park, N. G.; Bisquert, J. Mechanism of Carrier Accumulation in Perovskite Thin-Absorber Solar Cells. Nat. Commun. 2013, 4, (9) Dualeh, A.; Moehl, T.; Te treault, N.; Teuscher, J.; Gao, P.; Nazeeruddin, M. K.; Graẗzel, M. Impedance Spectroscopic Analysis of Lead Iodide Perovskite-Sensitized Solid-State Solar Cells. ACS Nano 2014, 8, (10) Gonzaĺez-Pedro, V.; Juaŕez-Peŕez, E. J.; Arsyad, W. S.; Barea, E. M.; Fabregat-Santiago, F.; Mora-Sero, I.; Bisquert, J. General Working Principles of CH 3 NH 3 PbX 3 Perovskite Solar Cells. Nano Lett. 2014, 14, (11) Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J. P.; Leijtens, T.; Herz, L. M.; Petrozza, A.; Snaith, H. J. Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in an Organometal Trihalide Perovskite Absorber. Science 2013, 342, (12) Xing, G.; Mathews, N.; Sun, S.; Lim, S. S.; Lam, Y. M.; Graẗzel, M.; Mhaisalkar, S.; Sum, T. C. Long-Range Balanced Electron- and Hole-Transport Lengths in Organic-Inorganic CH 3 NH 3 PbI 3. Science 2013, 342, (13) Guilleń, E.; Peter, L. M.; Anta, J. A. Electron Transport and Recombination in ZnO-Based Dye-Sensitized Solar Cells. J. Phys. Chem. C 2011, 115, (14) Zhao, Y.; Nardes, A. M.; Zhu, K. Solid-State Mesostructured Perovskite CH 3 NH 3 PbI 3 Solar Cells: Charge Transport, Recombination, and Diffusion Length. J. Phys. Chem. Lett. 2014, 5, (15) Burschka, J.; Pellet, N.; Moon, S.-J.; Humphry-Baker, R.; Gao, P.; Nazeeruddin, M. K.; Graẗzel, M. Sequential Deposition as a Route to High-Performance Perovskite-Sensitized Solar Cells. Nature 2013, 499, (16) Park, N. Organometal Perovskite Light Absorbers Toward a 20% Efficiency Low-Cost Solid-State Mesoscopic Solar Cell. J. Phys. Chem. Lett. 2013, 4, (17) Im, J. H.; Lee, C. R.; Lee, J. W.; Park, S. W.; Park, N. G. 6.5% Efficient Perovskite Quantum-Dot-Sensitized Solar Cell. Nanoscale 2011, 3, (18) Peter, L. Dynamic Aspects of Semiconductor Photoelectrochemistry. Chem. Rev. 1990, 90, (19) Halme, J. Linking Optical and Electrical Small Amplitude Perturbation Techniques for Dynamic Performance Characterization of Dye Solar Cells. Phys. Chem. Chem. Phys. 2011, 13, (20) Dloczik, L.; Ileperuma, O.; Lauermann, I.; Peter, L. M.; Ponomarev, E. A.; Redmond, G.; Shaw, N. J.; Uhlendorf, I. Dynamic Response of Dye-Sensitized Nanocrystalline Solar Cells: Characterization by Intensity-Modulated Photocurrent Spectroscopy. J. Phys. Chem. B 1997, 101, (21) Fabregat-Santiago, F.; Garcia-Belmonte, G.; Mora-Sero, I.; Bisquert, J. Characterization of Nanostructured Hybrid and Organic Solar Cells by Impedance Spectroscopy. Phys. Chem. Chem. Phys. 2011, 13, (22) Wang, H.; Nicholson, P. G.; Peter, L.; Zakeeruddin, S. M.; Graẗzel, M. Transport and Interfacial Transfer of Electrons in Dye- Sensitized Solar Cells Utilizing a Co(dbbip) 2 Redox Shuttle. J. Phys. Chem. C 2010, 114, (23) Jang, S.; Zhu, K.; Ko, M. J.; Kim, K.; Kim, C.; Park, N.; Frank, A. J. Voltage-Enhancement Mechanisms of an Organic Dye in High Open-Circuit Solar Cells. ACS Nano 2011, 5, (24) Lvovich, V. F. Impedance Spectroscopy: Applications to Electrochemical and Dielectric Phenomena; Wiley: Somerset, NJ, (25) Schlichtho rl, G.; Park, N. G.; Frank, A. J. Evaluation of the Charge-Collection Efficiency of Dye-Sensitized Nanocrystalline TiO 2 Solar Cells. J. Phys. Chem. B 1999, 103, (26) Snaith, H. J.; Abate, A.; Ball, J. M.; Eperon, G. E.; Leijtens, T.; Noel, N. K.; Stranks, S. D.; Wang, J. T.; Wojciechowski, K.; Zhang, W. Anomalous Hysteresis in Perovskite Solar Cells. J. Phys. Chem. Lett. 2014, 5, (27) Sanchez, R. S.; Gonzalez-pedro, V.; Lee, J.; Park, N.; Kang, Y. S.; Mora-sero, I.; Bisquert, J. Slow Dynamic Processes in Lead Halide Perovskite Solar Cells. Characteristic Times and Hysteresis. J. Phys. Chem. Lett. 2014, 5, (28) Juarez-perez, E. J.; Sanchez, R. S.; Badia, L.; Garcia-belmonte, G.; Kang, Y. S.; Mora-sero, I.; Bisquert, J. Photoinduced Giant Dielectric Constant in Lead Halide Perovskite Solar Cells. J. Phys. Chem. Lett. 2014, 5, (29) Jennings, J. R.; Ghicov, A.; Peter, L. M.; Schmuki, P.; Walker, A. B. Dye-Sensitized Solar Cells Based on Oriented TiO 2 Nanotube Arrays: Transport, Trapping, and Transfer of Electrons. J. Am. Chem. Soc. 2008, 130, (30) Bisquert, J.; Vikhrenko, V. S. Interpretation of the Time Constants Measured by Kinetic Techniques in Nanostructured dx.doi.org/ /jp J. Phys. Chem. C 2014, 118,

10 The Journal of Physical Chemistry C Article Semiconductor Electrodes and Dye-Sensitized Solar Cells. J. Phys. Chem. B 2004, 108, (31) Kru ger, J.; Plass, R.; Graẗzel, M.; Cameron, P. J.; Peter, L. M. Charge Transport and Back Reaction in Solid-State Dye-Sensitized Solar Cells: A Study Using Intensity-Modulated Photovoltage and Photocurrent Spectroscopy. J. Phys. Chem. B 2003, 107, (32) Zhao, Y.; Zhu, K. Charge Transport and Recombination in Perovskite (CH 3 NH 3 )PbI 3 Sensitized TiO 2 Solar Cells. J. Phys. Chem. Lett. 2013, 4, (33) Liou, Y.; Hsiao, P.; Chen, L.; Chu, Y.; Teng, H. Structure and Electron-Conducting Ability of TiO 2 Films from Electrophoretic Deposition and Paste-Coating for Dye-Sensitized Solar Cells. J. Phys. Chem. C 2011, 115, (34) Halme, J.; Miettunen, K.; Lund, P. Effect of Nonuniform Generation and Inefficient Collection of Electrons on the Dynamic Photocurrent and Photovoltage Response of Nanostructured Photoelectrodes. J. Phys. Chem. C 2008, 112, (35) Hsiao, P.; Tung, Y.; Teng, H. Electron Transport Patterns in TiO 2 Nanocrystalline Films of Dye-Sensitized Solar Cells. J. Phys. Chem. C 2010, 114, (36) Oekermann, T.; Zhang, D.; Yoshida, T.; Minoura, H. Electron Transport and Back Reaction in Nanocrystalline TiO 2 Films Prepared by Hydrothermal Crystallization. J. Phys. Chem. B 2004, 108, (37) Li, F.; Jennings, J. R.; Wang, Q.; Chua, J.; Mathews, N.; Mhaisalkar, S. G.; Moon, S.-J.; Zakeeruddin, S. M.; Graẗzel, M. Determining the Conductivities of the Two Charge Transport Phases in Solid-State Dye-Sensitized Solar Cells by Impedance Spectroscopy. J. Phys. Chem. C 2013, 117, (38) Deschler, F.; Price, M.; Pathak, S.; Klintberg, L. E.; Jarausch, D.; Higler, R.; Huẗtner, S.; Leijtens, T.; Stranks, S. D.; Snaith, H. J.; et al. High Photoluminescence Efficiency and Optically Pumped Lasing in Solution-Processed Mixed Halide Perovskite Semiconductors. J. Phys. Chem. Lett. 2014, 5, (39) Bisquert, J.; Fabregat-santiago, F. Electron Lifetime in Dye- Sensitized Solar Cells: Theory and Interpretation of Measurements. J. Phys. Chem. C 2009, 113, (40) Mandujano-Ramírez, H. J.; Gonzaĺez-Vaźquez, J. P.; Oskam, G.; Dittrich, T.; Garcia-Belmonte, G.; Mora-Sero, I.; Bisquert, J.; Anta, J. A. Charge Separation at Disordered Semiconductor Heterojunctions from Random Walk Numerical Simulations. Phys. Chem. Chem. Phys. 2014, 16, (41) Anta, J. A.; Idígoras, J.; Guilleń, E.; Villanueva-Cab, J.; Mandujano-Ramírez, H. J.; Oskam, G.; Pelleja, L.; Palomares, E. A Continuity Equation for the Simulation of the Current-Voltage Curve and the Time-Dependent Properties of Dye-Sensitized Solar Cells. Phys. Chem. Chem. Phys. 2012, 14, dx.doi.org/ /jp J. Phys. Chem. C 2014, 118,