Elucidating Transport-Recombination Mechanisms in Perovskite Solar

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Elucidating Transport-Recombination Mechanisms in Perovskite Solar Cells by Small-Perturbation Techniques Elena Guillén, Francisco Javier Ramos, Juan Antonio Anta, and Shahzada Ahmad J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 12 Sep 2014 Downloaded from http://pubs.acs.org on September 16, 2014

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The Journal of Physical Chemistry

Elucidating Transport-Recombination Mechanisms in Perovskite Solar Cells by Small-Perturbation Techniques Elena Guillén,a F. Javier Ramos,a Juan A. Anta,b Shahzada Ahmada* a

b

Abengoa Research, C/ Energía Solar nº 1, Campus Palmas Altas, 41014, Sevilla, Spain

Department of Physical, Chemical and Natural Systems, University Pablo de Olavide, 41013 Sevilla, Spain

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

ACS Paragon Plus Environment

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small-perturbation techniques: EIS, intensity-modulated photocurrent and photovoltage spectroscopy (IMPS/IMVS). The employment of IMPS allowed us to identify two transport times separated by two 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.

KEYWORDS Perovskite solar cells, small perturbation techniques, intensity-modulated photovoltage spectroscopy, intensity-modulated photocurrent spectroscopy, electrochemical impedance spectroscopy

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 cost effective price.1 PCE underwent to an incredible increase from the first report by Miyasaka et al.2 with PCE of 3.8 %, to currently c.a 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


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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 dyesensitized solar cells (DSSCs), thus their working principles were reported.7–10 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 lengths11,12 and has 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 optimize and select new materials. In this work we have combined different electrochemical techniques for characterization of stateof-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 showed for DSSCs,13 while majority of the reports in perovskite deals with a single technique.8,9,14 Here in, we have combined electrochemical impedance spectroscopy (EIS) and intensity-modulated 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 to each part of the spectra. By comparing electron lifetimes as a function of voltage obtained from IMVS with those obtained by impedance (intermediate frequencies arc) an agreement was found which lead 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


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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 one and close to 1/2. Three different device configurations, deposited by sequential deposition15 or single step processes16 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 smallperturbation 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 cells. 2. Experimental The chemicals were purchased either from Sigma Aldrich or Agros and were used as such. Spiro-OMeTAD was acquired from Merck KGaA and TiO2 mesoporous paste (18NR-T) was procured from Dyesol. CH3NH3I was synthetized following previous literature.17 For device fabrication, FTO-coated glass NSG10 (Nippon Sheet Glass) was firstly 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/O3 treatment for 30 minutes. The TiO2 dense layer was deposited by spin coating (5000rpm, 30s) TiCl4 2 M solution over the sample and heated at 70ºC for 30 minutes. After that, the mesoporous titanium dioxide film was prepared with the Dyesol paste 18NR-T. TiO2 nanoparticles paste was diluted 1:3.5 (w:w) in pure ethanol and then spun coated (5000rpm, 30s). Then the photoanodes were sequentially sintered 5 minutes at 125ºC, 5 minutes 325ºC, 5 minutes 375ºC, 15 minutes 450ºC and 15 minutes 500ºC. On these photoanodes perovskite was deposited using three different


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techniques: CH3NH3PbI3 by sequential deposition,15 CH3NH3PbI3 by one step deposition, and CH3NH3PbI3-x Clx by one step process. For CH3NH3PbI3 (seq. dep.), a PbI2 film was deposited by spin coating (6500 rpm for 30s with 5500 rpm·s-1 as acceleration) using 50µL per cell of 1M PbI2 in N,N-dimethylformamide (DMF); lead iodide solution is kept at 70ºC under vigorous stirring to avoid insolubility issues during the whole deposition process. After the spin coating, the cells were placed onto a hot plate at 70ºC for 15 minutes for annealing and were allowed to cool down. The cells were then submerged in the methyl ammonium iodide (MAI) solution in 2propanol (8mg/mL) for 20s 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 2propanol and dried using the spin coater at 4000rpm for 30s. The samples were subject to annealing again at 70ºC for 15 minutes. For the CH3NH3PbI3 (one step), a solution together with PbI2 and CH3NH3I (40% in weight, 1:1 molar ratio) in γ-butyrolactone was prepared; the solution was spun coated at 2000rpm for 60s (1000rpm·s-1 as acceleration) and annealed at 100ºC for 15 minutes. Finally, for the CH3NH3PbClxI3-x perovskite (one step) synthesis, a solution 40% in weight that contains a mixture of PbCl2:CH3NH3I (1:3 in molar ratio) using DMF as solvent was deposited by spin coating (2000rpm, 60s, 1000rpm·s-1 as acceleration) onto the mesoporous film; it was annealed at 100ºC for 45 minutes. Spiro-OMeTAD (2,2’,7,7’tetrakis(N,N-di-p-methoxyphenyamine)-9,9-spirobifluorene) was selected as hole transporting material (HTM). 35µL of Spiro-OMeTAD solution were deposited onto the perovskite using spin coating technique at 4000rpm for 30s using an acceleration of 1650 rpm·s-1. The solution was prepared dissolving 72.3mg of Spiro-OMeTAD in 1mL of chlorobenzene. As additives, 21.9µL

of

tris(2-(1H-pyrazol-1-yl)-4-tert-butylpyrydine)

cobalt(III)

bis

(trifluoromethylsulphonyl) imide (FK209) stock solution (400mg of FK209 in 1mL of


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acetonitrile), 17.5µL of lithium bis(trifluoromethylsulphonyl) imide (LiTFSI) stock solution (520mg of LiTFSI in 1mL of acetonitrile) and 28.8µL of 4-tert-butylpyridine (96% w:w) were also added to the solution. To finish the device 80nm of gold were vacuum sublimed (pressure between 1x10-6 and 1x10-5torr) for the cathode deposition. Lead iodide, methyl ammonium iodide and Spiro-OMeTAD solutions were prepared under controlled levels of water and O2 using a glove box. PbI2 spin coating, MAI dipping and Spiro-OMeTAD spin coating depositions were carried out inside a dry box. For J-V curves, a 450W 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 0.2025cm2 using a mask and was recorded in reverse bias (from Voc) after 10s delay under illumination at a scan speed of 100mV/s, we have found this as an optimal condition to avoid hysteresis. Impedance spectroscopy (EIS) measurements in the dark and under illumination and intensity-modulated 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 mV8 perturbation in the 10-1-106 Hz range. EIS spectra have been measured under illumination applying the same voltage that 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.


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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.

Figure 1. a) J-V curves under full sun illumination for different configurations. Table 1 Photovoltaic parameters of the device with different configuration.a

Cell Configuration

Jsc [mA cm-2]

Voc [V]

FF

PCE [%]

1

FTO/bl-TiO2/mp-TiO2/CH3NH3PbI3 (sequential deposition)/Spiro-MeOTAD/Au

20.55

0.91

0.65

12.65

2

FTO/bl-TiO2/mp-TiO2/CH3NH3PbI3 (1:1; one step) /Spiro-MeOTAD/Au

13.56

0.76

0.52

5.62

3

FTO/bl-TiO2/mp-TiO2/CH3NH3PbI3-xClx (3:1, one step) /Spiro-MeOTAD/Au

20.84

0.71

0.54

8.35


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a

Jsc, (photocurrent density), Voc, (open circuit potential), FF, (fill factor) and PCE (power conversion efficiency). 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. Frequencydomain 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-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, EIS21 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 frequency-dependent impedance (voltage/current) is analyzed for different dc voltages.

Scheme 1 Input and output signals for each of the small perturbation techniques used and schemeatic of the device architecture formed by: Glass/FTO/TiO2 compact layer/mesoporous TiO2 /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


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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 state23 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 Detailed description of the procedure followed to check these conditions, including Lissajous and signal response plots measurements can be found in the Supporting Info. IMPS response appears as a semicircle in the lower quadrant for DSSCs. The time constant τIMPS can be obtained from the inverse of the minimum angular frequency (ωmin) in an IMPS plot: () = 1

(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


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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).

a)

b)

Figure 2 IMPS measurements of a perovskite solar cell of configuration 1 at three different illumination intensities. The voltages refer to the open circuit potential value induced by illumination. IMVS was used to characterize recombination in DSSCs19 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 perovskite solar cell in the frequency domain is a semicircle in the lower complex plane (Figure 3).


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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 (τn) can be obtained by considering the minimum of the semicircle located at an angular frequency that is equal to: ()

= 1

(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 cross-checked using Lissajous and signal response plots. EIS is used 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 to the responses observed in the spectra. This was thoroughly studied for DSSCs while reports on perovskite solar cells are limited.7–10 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 (Cµ) and a charge recombination resistance (Rrec), a lifetime can be defined as:21 ()

=

(3)

The feature in the spectrum related to lifetime is clearly identified in DSSCs, but it is not clear yet in perovskite solar cell.


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Figure 4 (a-f) Nyquist plots for EIS measurements of configuration 1 cell at different open circuit potentials (0.4 - 0.87V) 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.

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 features 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 medium


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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 (~0.5V). 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 (Rlf), transport resistance obtained from the transmission line (Rt) and charge transfer resistance and capacitance obtained at intermediate frequencies (Rmf and Cmf). 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 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 to the recombination process (Rrec) that determines the J-V curve and hence the performance of the device.


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3.2. Transport-recombination mechanisms in perovskite solar cells IMPS measurements (Figure 2) revealed two distinct transport times, separated by 1-2 orders of magnitude (102-103 Hz and ~104 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 TiO2 or via the perovskite itself. In principle, the two time constants could be related to the following transport mechanisms: i) electron transport in TiO2, 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 TiO2. As mentioned earlier, time constants τIMPS were obtained from the inverse of the minimum angular frequency (ωmin) in the IMPS plot and they can be related to the effective diffusion coefficient, Dn by:20 =

(4)

where γ is a numerical factor which depends on layer thickness (d), absorption coefficient and illumination direction.29 On the other hand, Dn can also be obtained from the transport resistance (Rt) and the chemical capacitance in an EIS spectrum (Figure S5): =

(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


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calculation was 270 nm thickness of the mesoporous film as measured by scanning electron microscope. a)

b)

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. A similar trend with the voltage was observed, (slope of ~ 14 V-1), while the diffusion coefficient values were shifted by c.a 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 Dn with respect to the voltage is an indication that transport is a multiple trapping mechanism30 although with a distribution parameter α different from the one observed in standard TiO2 DSSCs: %

= D e(!"#)($ ()"$ )&' (

(6)

where kB is the Boltzmann constant and T the temperature, Ef(n) and E0f (n) are the Fermi level of electrons under illumination and in the dark, respectively, and D0 represents the diffusion


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coefficient in the dark, i.e. when Ef(n) = E0f (n). Krüger et al.31 reported similar TiO2 diffusion coefficient values (between 10-6-10-7) for solid-state DSSCs obtained by IMPS. This, together with its voltage dependence, suggests that the slow component in the IMPS spectrum corresponds to transport of electrons in the TiO2 mesoporous structure, 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.33–35 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 trapfree 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 anode20,36 or to inhomogeneous light absorption in the film.34 Li et al.37 carried out a comprehensive analysis of the conductivity of TiO2 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 TiO2. In the EIS response, they observed two time constants in the 0.1-106 Hz range. The high frequency one (~104 Hz) was attributed to the Spiro-OMeTAD, while the lower frequency one to transport,


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recombination and chemical capacitance in the mesoporous TiO2 and both varied with voltage. Comparatively in this work, the low frequency response is most likely related to the transport in the mesoporous TiO2 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 0.017 cm2s-1 and 0.036 cm2s-1 have been measured for electrons in the perovskite film, and 0.011 and 0.022 cm2s-1for holes.11,12 Furthermore, a simple diffusion mechanism, not limited by traps, have 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 four and two 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 TiO2/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 TiO2 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 6 a,b) appears at similar frequencies that the main (and only) IMVS peak (around 102-103 Hz). Hence, both measurements give the similar


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dynamic information at this frequency range. Electron lifetimes have been obtained from the inverse of the minimum angular frequency in the IMVS spectrum (Equation 2) and from the capacitance and the charge transfer resistance obtained for the mid frequency feature in the impedance spectrum (Equation 3). Both lifetimes are compared in Figure 6c. a)

c)

b)

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. 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 help facilitates to interpret and perform the impedance spectra fitting. In particularly low and mid frequency features tend to merge and they are not often distinguishable (Figure 4). Using IMVS we can check that we are properly identifying the


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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 Equation 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 (Rmf) corresponds to the resistance to recombination (Rrec). 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 configurations studied here. As indicated, the charge transfer resistance was derived from the intermediate frequencies arc and measurements were carried out in the dark.


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Figure 7 Comparison of the charge transfer resistance obtained in the dark for the three different perovskite solar cells as mention in Table 1. Interestingly, recombination is more affected by the deposition method of perovskites rather than monovalent or bivalent halide anion (presence of chloride). Recombination resistance is lower (so recombination is stronger) for one step deposited perovskite, and thus pointing towards that it is not the nature of the perovskite but the interface between perovskite and TiO2/or HTM, which dictates the recombination rate. Therefore, the different recombination could be related to a better crystal formation, or to the conformal or un-oriented growth of the perovskite layer on TiO2. 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 MAPbI3-xClx compared to MAPbI3. 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 Rrec-potential curve is characterized by a β-factor smaller than 0.5 (~0.4): ./0 () − /0 1 = exp +−- 5 23 4

(7)

Christians et al.6 also reported a beta 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 TiO2 with holes in the perovskite (similar to recombination with oxidized dye molecules in DSSCs), iii)


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recombination between electrons in the perovskite and holes in the HTM, iv) recombination from TiO2 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 halftime for radiative recombination in perovskite films with inert contacts is in the order of 10 ns 12 which means that a semicircle centered at around 1010 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 case of two step method), recombination iv) must be low because the TiO2 is not in direct contact with the hole transport material. The high non-linearity 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 (approx. 0.5 + 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 TiO2).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 TiO2/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 on the origin and impact of the recombination loss, identified by the comparison of EIS and IMVS, reconstruction of the J-V curve from the small-perturbation


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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 TiO2 mesoporous film (Figure 5b). As this is a voltage-dependent magnitude, in analogy to a DSSCs,41 we have solved the following continuity equation 6(7, 9) 6 6 = : () ; + =(7) − 2 > 69 6 67

(8)

where Dn is a density-dependent (thus voltage-dependent) diffusion coefficient given by Equation 6, G(x) is the generation profile of electron-hole pairs due to light absorption in the active layer, k0 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 densitydependent recombination constant,39 which is in turn obtained from the recombination term k0nδ in Equation 8 2 () =

6?@ = A2 >"! 6

(9)

where JR is the recombination current density. This makes the recombination constant (and hence the lifetime), voltage-dependent, as inferred from the experimental EIS and IMVS data.


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Following the analogy with the DSSC model,41 the reaction order is δ = (β-α)/α, where α and β are respectively defined by Equation (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 absorption is adjusted to reproduce the experimental short-circuit photocurrent, whereas k0 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).

Figure 8 Experimental J-V curve (symbols) for cell 1 and results (dashed line) from the model of Eq. (8) for β = 0.5. Rs stands for series resistance and A is the geometrical surface area. Parameters used for the model: d = 0.5µm, D0 = 10-10 cm2s-1, α = 0.2


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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 Voc and Equation 9, τ ~ 2 × 10-4 s is quite close to the values derived from the small-perturbation 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 Voc. 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 to model recombination). This is consistent with the long diffusion lengths reported for electrons and holes in perovskite films11 and a fast injection rate. 4. Conclusions A comprehensive study consisting of an array of three small perturbation techniques on perovskite based solar cells was carried out, and deep insight on the functioning of devices are 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 TiO2, while the high frequency (rapid) may be due to the transport in the hole conductor, although transport in the perovskite itself


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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 JV 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.


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Further research is required in this direction to unravel the limiting mechanisms and its dependence on the preparation procedure. AUTHOR INFORMATION Corresponding Author *Shahzada Ahmad, ABENGOA RESEARCH Campus Palmas Altas C/ Energía Solar nº 1, Sevilla, Spain Phone: +34955404890 Email:[email protected]

ACKNOWLEDGMENT We wish to thank Michael Graetzel, M. K. Nazeeruddin, for using their experimental facilities and support, Juan Bisquert, Iván Mora-Seró and Gerko Oskam for fruitful discussions. SA acknowledges grant from Torres Quevedo, Ministry of Spain. ASSOCIATED CONTENT 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 http://pubs.acs.org.


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Elucidating Transport-Recombination Mechanisms in Perovskite Solar

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