Effect of Light and Voltage on Electrochemical Impedance

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The Effect of Light and Voltage on Electrochemical Impedance Spectroscopy of Perovskite Solar Cells: an Empirical Approach Based on Modified Randles Circuit Xiaoqing Chen, Yasuhiro Shirai, Masatoshi Yanagida, and Kenjiro Miyano J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10712 • Publication Date (Web): 23 Jan 2019 Downloaded from http://pubs.acs.org on January 25, 2019

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The Journal of Physical Chemistry

The Effect of Light and Voltage on Electrochemical Impedance Spectroscopy of Perovskite Solar Cells: an Empirical Approach based on Modified Randles Circuit Xiaoqing Chen*, Yasuhiro Shirai, Masatoshi Yanagida and Kenjiro Miyano*

Global Research Center for Environment and Energy based on Nanomaterial Science (GREEN), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan

AUTHOR INFORMATION

Corresponding Author E-mail: [email protected] (X.C.) Present address: Key Laboratory of Advanced Functional Materials, Ministry of Education, College of Materials Science and Engineering, Beijing University of

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Technology, 100 Ping Le Yuan, Chaoyang District, Beijing 100124, China E-mail: [email protected] (K.M.)


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ABSTRACT The voltage (V)- and light power (P)-dependencies of electrochemical impedance spectroscopy (EIS) curves of perovskite solar cells (PSCs) are investigated over the entire (V, P) space rather than limited to short circuit or open circuit conditions. For the first time, we report under fixed V and increasing P, the EIS curves show complicated behaviors. Employing a modified Randles circuit, we successfully fitted the data using three newly proposed empirical equations. From the behaviors of the fitting parameters in the (V, P) space, we conclude that the dynamics inside PSCs consist of two parts, 1) the migration of mobile ions/vacancies and their capturing the free carriers at the perovskite layer boundary and 2) a classical diode involving the migration and recombination of free carriers. Our calculated diffusivity and mobility agree with previous reports. We further found that the mobile ion density inside the perovskite layer is proportional to light power, which could explain the inverse linear power-dependence of the amplitude of the slower EIS feature and the resonance time and amplitude of the faster one.



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1. Introduction

The perovskite solar cells based on organic-inorganic halide perovskites are promising next generation photovoltaics due to its good stability, power conversion efficiency, low cost and compatibility to flexible substrates.1–9 In spite of their excellent performance, many questions regarding the device physics still remain unanswered.9– 12

In the study of a real device of multiple layers, the frequency-domain experiments,

e.g. electrochemical impedance spectroscopy (EIS) and intensity-modulated photovoltage spectroscopy (IMVS), are frequently employed. Compared to analysis based on DC and transient experiments, in which multiple dynamic processes cannot be easily distinguished,13–21 various dynamic processes could be easily separated on the frequency-domain spectroscopy so that each process could be analyzed independently. However, up to now, the analysis and interpretation based on EIS are not satisfactory in at least the following three points.

1) Previous works based on impedance technique are usually only under two conditions, namely, short circuit, and open circuit conditions.

22–30

Lacking in a more

systematic research under various biases (V) and light powers (P), it is difficult to arrive


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at a convincing conclusion. When discussing the EIS under open circuit condition, researchers sometimes only discuss the dependence of EIS results on open circuit voltage (VOC).22,23,25,28 Namely, although the device is under illumination when carrying out the open circuit measurement, the effect of light on the EIS signal is analyzed as a voltage source providing VOC across the device. When such simplification is accepted, we should expect under a given bias value, the EIS result should be independent of light power which however contradicts other reported EIS results. For example, 1) earlier publications showed that under short circuit condition (V = 0), the capacitance changed a lot, suggesting in addition to bias, the EIS could be influenced by light as well.22,24 2) It is reported that the VOC relaxation of a pristine PSC and a light-soaked PSC are not the same.18 Beside the reported EIS results, there are other theory and experiment works suggesting that the light irradiation is essential to the kinetics of ions: the generation and dissipation of mobile ions31,32; the increment in ion conductivity33, the promotion of V- and H-centers34 and the annihilation of V/I Frenkel pairs35, to name a few. Therefore, the state in a device under illumination and open circuit conditions (VOC) is not the same as that in the same device in the dark under the applied bias voltage that equals to VOC. The bias voltage and the light illumination



should thus be treated as independent parameters. Since the short-circuit (V = 0, P = arbitrary) and open-circuit (V = VOC(P)) conditions are only particular cross-sections in the (V, P) parameter space, a more systematic analysis of the entire parameter space is required to study the influence of voltage and light on EIS (especially the photoeffect on ionic motion) separately.

2) According to most published EIS results, there are at least two features in the 1 Hz – 1 MHz frequency window.18,22–30,36–47 The faster feature (>300 Hz) is usually ascribed to the recombination of free carriers and symbolized as an RC circuit.18,22,23,30,36 The slower feature (1 – 100 Hz) is usually ascribed to the migration of ions (or ion vacancies)23,29,30,45,46 or the accumulated carriers22,26. When analyzing the EIS results with an equivalent circuit, choosing the proper equivalent circuit element could be helpful in assigning the slower feature to the correct dynamic process because each element has its own physical meaning.48 However, the treatment of the low frequency feature is debatable. In many previous publications, the slower feature is symbolized as a capacitor or RC circuit18,22–28,36,42,44 while other papers treated it as a constant phase element (CPE)37,38, Warburg element with absorbing boundary condition (ZW)29,30,39,46 or Gerischer element (ZG)40,41,43. The


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reason for lacking of agreement on symbolizing the low frequency feature could be that, the EIS results corresponding to RC circuit, ZW and ZG element are not distinguishable enough on the Cole-Cole plot.

3) Conventionally the EIS data measured in one experiment group but under different conditions (bias voltage and illumination), are fitted individually, yielding fully variable fitted parameter values (e.g. resistance, capacitance etc.). Obviously, these parameter values should be determined by other constant device ‘intrinsic’ parameters and the experiment conditions through a physical model to be unveiled. However, since all the circuit elements should represent the property of the same device under test, we should be able to obtain satisfactorily fitted curves over the entire V-P space while those parameters relating to the device intrinsic properties unchanged. Hereafter, we call this procedure as ‘global fitting’.

In this work, we carried out a systematic analysis of the EIS results under a series of voltage and light powers. For the first time, we report that under fixed bias and increasing light power, the amplitude of the slower EIS feature shows first-risethen-decrease behavior while the amplitude and resonance frequency of the faster



EIS feature shows first-unchange-then-increase behavior. The critical light power for both slower and faster EIS features is near to that corresponding to the zero injection current condition (open circuit). After analysis, a few empirical equations are proposed. Through our proposed picture, equivalent circuit and empirical equations, the EIS results are analyzed through global fitting.

2. Methods

The device structure under study is ITO/NiOx/MAPbI3/PC61BM/AZO/Ag. The details of device fabrication process, which is similar to our previous publications,38,49 is described in the supporting information. The device area is c.a. 0.26 cm2. The device

JV curves before and after measurement are shown in Figure S1 in the supporting information. After the EIS experiments presented in this work, the device power conversion efficiency reduced from 13.5% to 12.0%.

The light source used in this work is a laser diode operated at 638 nm. From our observation, a picture based on ion migration and recombination of free carriers is suggested. We propose an equivalent circuit composed of circuit elements with clear physical meanings. After analyzing the voltage- and power-dependence of the related


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circuit elements, we propose three empirical equations. The validity of our proposed empirical equations is finally supported by the satisfactory global fitting.

3. Results and discussion

3.1 The effect of voltage

As shown by the solid lines in Figure 1a, when the voltage increased, the resonance frequency of the faster EIS feature significantly increased. The resonance time of the faster dark EIS feature is defined as 𝜏𝑑𝑎𝑟𝑘 = 1/𝜔min where 𝜔min is the angular frequency corresponding to the minimum of Im(Z), the imaginary component of EIS. Note that -Im(Z) rather than Im(Z) is shown in Figure 1a. The dependence of 𝜏𝑑𝑎𝑟𝑘 on the applied bias is plotted in Figure 1b. We find that

𝜏𝑑𝑎𝑟𝑘 ∝ exp (𝑒𝑉/𝑛𝑘𝑇) (1)

where e, n, k and T are the elementary charge, fitting constant*, Boltzmann constant and temperature, respectively. Apparently Eq. 1 is similar to the well-established diode equation.

*

We notice that n is different from the ideality factor calculated via VOC-P

dependence as shown by Figure 1c. According to previous literatures, the behavior



of ideality factor was complicated,28,61 which could be influenced by the device structure or fabrication procedures.


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Figure 1. (a) The EIS results in dark (solid lines) and under open circuit condition (dash-dot lines) under various biases, along with (b) the exponential voltagedependence of the faster resonance time in dark (𝜏𝑑𝑎𝑟𝑘). (c) The VOC-P relationship and the fitted ideality factor.

3.2 The effect of light under fixed bias

The open-circuit EIS results are compared with the dark results in Figure 1a. There is an inductive signal in the slowest frequency range (shown by the dotted line in Figure 1a below 10 Hz). The physics of inductive impedance is discussed by other works27,36,50 but not in the scope of this paper because it lacks reproducibility in our lab. Except for this inductive signal, there are two other capacitive features dominant in the faster and slower frequency range (hereafter, named as faster and slower features, respectively). When light is illuminated onto the device, the faster feature is reduced in amplitude and shifts to the high frequency side (purple arrow) while the slower feature rises (red arrow). Clearly both light power and bias strongly influences the EIS result, suggesting that illumination should not be simplified as applying a voltage. In order to quantitatively analyze the light effect, the device is measured under



fixed bias and varied light intensity. As shown in Figure 2a, we take V = 1 V as an example (which equals to the VOC under illumination of 1660 μW/cm2 according to the fit shown in Figure 1c). Results under other bias voltages are shown in Figure S3 in the supporting information. When P increased, both the slower feature and the faster feature changed.

Figure 2. (a) The power dependence of EIS under fixed bias V = 1 V and (b) the power dependence of 𝜏fast at several bias voltages. The dotted lines in (a) are positive Im(Z) points. The gray cyan and yellow lines are guidelines of slope = -1/2, -1 and 1, respectively.


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2.2.1 The faster feature.

Under the bias voltage of 1 V, the amplitude and resonance frequency of the faster EIS feature shows first-unchange-then-increase behaviour with increasing P. When P < 1540 μW/cm2, the faster feature remains roughly unchanged. When P > 1540 μW/ cm2, the faster feature decreased rapidly in amplitude with increasing light power as indicated by the spheres in Figure 2a. In addition, the resonance frequency of the faster feature increased remarkably. The dependence of the faster resonance time (𝜏fast) on P under various bias voltage values (V = 0.5 – 1.05 V) is plotted in Figure 2b. In the high power region, all curves converge on a line of slope = 1 as indicated by the yellow line, i.e., 𝜏fast ∝ 1/𝑃, irrespective of V.

A similar inverse-proportion power dependence was once explained by Pocket et.al. via classical diode equation.28 However, their explanation to this relationship relies on that the EIS results are obtained under open circuit condition. Since our results are not limited to open circuit condition, we cannot directly borrow their scenario. Because the faster EIS shoulder is widely ascribed to the recombination lifetime of free carriers,

18,22,23,30,36,49

a natural idea is that there are two coexisting



recombination routes that dominate the low and high power ranges, respectively. When light is weak, the result is dominated by the dark recombination route described by Eq. 1. Because of the similarity of Eq. 1 and the conventional diode equation, this dark route is most-likely the conventional loss route in regular pn junctions, e.g. the electron-hole recombination or trap assisted recombination (SRH recombination). Under illumination, an additional light-induced recombination channel is enabled. This recombination channel could be reasonably ascribed to the recombination between the free carriers and some photogenerated species (other than free carriers). Depending on the relative contribution of the two recombination channels, the relaxation is dominant either by the dark process or the light-induced process. When the light power P > 4615 μW/ cm2, the number of this species is large enough so that the recombination between them and the free carriers is faster than the dark recombination channel. In this regard, the overall faster resonance time 𝜏fast of free carriers is described as

1 𝜏fast

1

1

= 𝜏dark + 𝜏light (2)


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As is found in Figure 2b in the high power region, the light-induced recombination rate is proportional to P in agreement with our earlier paper based on IMVS49. Therefore,

1

𝜏light = const ∗ 𝑃 (3).

As shown by the solid lines in Figure 2b the measured τ–P relationship could be well fitted according to Eq. 2 and Eq. 3.

In our previous paper49, we argued that this light-induced channel is dominated by the recombination between free bulk carriers and photo-generated carriers accumulated near the electrode/perovskite interface or the mobile ions (or ion vacancies). The mobile ions/vacancies are usually argued to be MA+, I- or iodine vacancies.23,29,30,46,51 Zarazua et.al. argued that the mechanisms behind the slower feature and the faster feature are related to the same charge carrier species (surface accumulated carriers) because their behaviors under short circuit and open circuit conditions are the same.22 In addition, according to our results shown in Figure 2a and Figure S3 and our analysis of the slower feature in the following section, the dependencies of both features on the voltage and power are tightly related under general (V, P) parameter space, which again confirms that the mechanisms behind



the two EIS features are related to the same charge carrier species. Therefore, the physics of the faster feature could be explained if that of the slower feature is unveiled. In this work, we argue that this carrier species are mobile I- or iodine vacancies because of the following three reasons.

a) The resonance time of the slower feature is related to the migration time across the perovskite bulk of ions. The time-resolved ion migration inside the perovskite layer is experimentally proved recently showing transit time across the 400 nm-perovskite layer is ~10 ms52 which is similar to the resonance time of the slower EIS feature. Peng et.al. showed that in devices based on single crystal perovskite, the slower resonance time is closely related to the crystal thickness, which thereby confirms the slower feature is related to ion migration across the bulk.53

b) The photo mobilization of ions is experimentally proved. Recent publications suggest that I- could be mobilized by light with the assistance of surface interstitial sites31–33. The photo mobilization of ions is necessary to explain the


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linear power dependence of the faster feature49 as well as other results to be introduced in this paper.

c) The capture of holes by mobile I- is supported by previous experiment and theory works.34,35,54

Other mobile charge carrier species that could satisfy the above two criteria (1.Transit time across the perovskite bulk agrees with the resonance time of the slower feature. 2. Particle number is proportional to light power) are also possible candidates to be responsible for the slower EIS feature. For simplicity, we only discuss the scenario based on I- migration and ignore the iodine vacancies. To sum up, the recombination routes of the free holes is illustrated by the blue and red arrows in Figure 3a.

2.2.2 The slower feature.

When the device is in dark, the slower feature is not pronounced.† When P increases, the amplitude of the slower feature gradually grows up (red arrow in Figure

†

Precisely speaking, the EIS in this frequency range is sometimes inductive

(Im(Z)>0) rather than capacitive (Im(Z) 1540 μW/cm2, the slower feature amplitude turns to reduce with light power (blue arrow). Note that the critical light power intensity for the slower feature and the faster feature are the same (1540 μW/cm2), which is the reason that we claim the physics behind the faster and lower features are the same. A more interesting feature is that this critical light power is near to 1660 μW/cm2 which corresponds to

VOC = 1 V according to the fitting of Figure 1c. This observation is valid for all bias voltages (V) as shown in Figure S3 in the supporting information.

Figure 3. (a) Scheme of the recombination routes of free holes. (b) Cole-Cole plot under V = 0.85 V and P = 15.4 mW/cm2. The 45-degree slower feature in (b) which


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could be modeled as either (c) the Warburg element under absorption boundary condition (ZW) or (d) Gerischer element (ZG).

3.3 Physical picture and equivalent circuit

As mentioned in the introduction, it is controversial whether the slower feature should be regarded as a regular RC circuit, ZW or ZG. Usually, the three features are distinguished by their patterns on the Cole-Cole plot: an RC circuit corresponds to a semi-arc while ZW or ZG element start with a 45-degrees straight line. However, in the analysis of a perovskite solar cell, sometimes this method is difficult because the amplitude of the slower feature is very small compared to the faster feature. In the result shown in Figure 3b, the slower feature (right-hand side) is more like ZW or ZG rather than RC circuit. Another method to identify the impedance pattern is by examining the frequency-dependence of Im(Z). It can be easily found that on the righthand side (higher frequency) of –Im(Z) peaks of the log-log Bode plot, the slopes of RC circuit and ZW are -1 and -0.5 (see Eq. 4 below), respectively. As shown in Figure 2a, the slopes of the faster and slower features are -1 and -0.5, respectively. Consequently, we can very safely exclude using RC circuit as the equivalent circuit



element for the slower feature. Actually, if we are forced to fit the measured data with a simple RC circuit, the calculated ‘capacitance’ values will be too large. After excluding RC circuit, it is still difficult to confirm whether the impedance pattern is ZW or ZG. According to theoretical analysis, ZW and ZG are related to two different pictures.48 ZW corresponds to charge migration within finite distance before finally reacting at the boundary as shown in Figure 3c. ZG corresponds to reacting with constant lifetime during its migration inside the bulk as shown in Figure 3d.

According to the observation of Weber et.al., the transit time of I- across the 400 nm-thick perovskite layer is ~10 ms52, which is about the same as the slower feature (usually 1– 100 Hz, depending on bias and illumination as shown by Figure 2a, temperature23, fabrication batch and device structure22). Peng et.al. showed that the slower resonance time depends on the film thickness, suggesting the slower feature is related to ion migration across the bulk.53 Therefore we hereafter assume the slower feature corresponds to the migration of I- across the perovskite layer. Driven by the applied perturbation voltage, I- migrate inside the perovskite bulk until they are oxidized. Supposing the I- are oxidized to immobile I atoms after they capture the free holes, we can pick the correct circuit element to represent their dynamics if we know


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the hole distribution. If the holes are accumulated near the anode as indicated by the pink solid spheres in Figure 3a, ZW should be picked; otherwise if the holes are distributed uniformly inside the perovskite bulk, ZG should be chosen. Here we choose

ZW assuming the oxidation of I- dominantly occurs near the anode because of two reasons. 1) The free holes which can oxidize the I- is calculated to accumulate near the anode21,55. 2) As reported, the trapping and detrapping of free holes by I- are both efficient inside the perovskite.54 In this regard, the number of bulk I- is conserved due to local thermal equilibrium.

This picture is widely modeled with an equivalent Randles circuit as shown by the shaded circuit in Figure 4a.56–58 The Randles circuit is a widely-employed equivalent circuit to calculate the migration and reduction (or oxidation) of ions. Relevant theory and calculation can be found in previous papers. 59,60

In this circuit, the migration of I- is modeled with a Warburg element (ZW) with absorbing boundary condition because I- are supposed to capture the free holes near the anode side. Suppose only I- are involved (bulk density = C0 (in mol cm-3) or ρ0 (in cm-3)), ZW could be described as



𝑍𝑤 =

𝐴𝑤 (𝑖𝜔)

1

𝑅𝑇

2 and 𝜏 = 1 tanh ((𝑖𝜔𝜏) ) in which 𝐴𝑤 = 𝐴𝑣2𝐹2(2𝐷)1/2𝐶 0

2

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𝑑2 𝐷

(4)

where ω, d, D, R, A, v, F are angular frequency, layer thickness, diffusion coefficient, ideal gas constant, area, charge transfer valency (v=1 for I-), Faraday constant, respectively. Note the 𝜏 =

𝑑2 𝐷

relationship agrees with the work by Peng et.al. 53

AW could also be rewritten to the following form 𝑘𝑇

𝐴𝑊 = 𝐴𝑣2𝑒2(2𝐷)1/2𝜌 (5). 0

The loss of mobile I- (oxidized by the free holes) is modeled as a resistor (Rl). In ideal condition, Rl is inversely proportional to ρ0,

𝑅𝑙 ∝ 1/ 𝜌0 (6).

A simple derivation for Eq. 6 could be found in the supporting information.


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Figure 4. Comparison between the equivalent circuits employed (a) in this work and (b) by the Venkataraman group29,30,46.

In the conventional Randles circuit, the capacitance should be a double layer capacitance related to the Debye length. However in PSCs, In many published papers, the capacitance is regarded as geometric capacitance or bulk capacitance because it is almost a constant value22,23,27,28,36 For strictness, we still allow this capacitance to be voltage dependent. In order to represent the dark recombination between free electrons and holes inside the perovskite layer (including direct and SRH recombination), an additional resistor (Re(V)) is introduced. A series resistor (Rs) and



inductance (L) are added to describe the imperfection of the electrode contact and measuring circuit, which are supposed to be independent constants.

The Venkataraman group introduced a similar but more complex equivalent circuit as shown in Figure 4b.29,30,46 The main difference between Figure 4a and 4b is the double layer capacitor (Cdl). According to their results, the fitted Cdl is ~10 nF. In the frequency range of the slower feature (1– 100 Hz), the impedance of the capacitor is ~10 MOhm which is too high compared to other parallel circuit branches. Therefore removing this element will not cause major difference in the final result. After removing this capacitance, the two resistances Rtr + Rct will be merged into one resistance. Consequently, the equivalent circuit in Figure 4b will be the same as that in Figure 4a.

3.4. Calculation and analysis

In the following, we try to identify the physical meaning of the circuit elements in the equivalent circuit shown in Figure 4a. We obtained EIS results under 10 various DC biases (0, 0.6, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1, 1.05 V) and 11 light powers (0, 4.62, 15.4, 46.2, 154, 462 µW/cm2, 1.54, 4.62, 15.4, 46.2, 123 mW/cm2). The 110 EIS curves are shown in Figure 5. According to Figure 4a, 7 parameters (Aw, τ, Rl, Re, Cb,


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Rs, L) are required to fit one EIS curve. Therefore, if we fit the 110 obtained EIS curves individually in the conventional way, 770 values are needed. Apparently, the 770 parameter values should not be independent because

a) Re and Cb should be dependent only on voltage according to our discussion above (Eq. 1).

b) τ, which describes the resonance frequency of the slower feature (~ 20 Hz as shown by Figure 5), is nearly constant.

c) Rs and L should be independent on light power and bias because they are ascribed to the electrode and the test circuit.

In order to evaluate whether Rs and L could be regarded as constant, we still allow the two parameters to be voltage-dependent. Through the above restrictions, instead of the totally individual 770 values, only 261 values (Aw(V,P), Rl(V,P), Re(V), Cb(V), τ,

Rs(V) and L(V)) are employed in this ‘semi-global’ fitting of the EIS curves. The fitted EIS curves are compared with the measured results in Figure 5. Some technical issues in the fitting are described in the supporting information.



Figure 5. Comparison between the imaginary component of the first semi-global fitting results and the experiment data. The experiment data is the same as those shown in Figure S3.

The values for the fitting are plotted in Figure 6. From Figure 6a, L and Rs indeed vary little as expected. The Rs is dominated by the test resistor for current measurement (50 Ohm*0.26 cm2 = 13 Ohm cm2) of the employed frequency analyzer. Therefore, later these two parameters are treated as constants independent of P and

V. The fitted τ is 67 ms. The dependences of Cb and Re on V are plotted in Figure 6b.


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As expected, the dependence of Cb (which is usually regarded as geometric capacitance22,23,27,28,36) on V is not very large (from 83 nF to 103 nF). We would like to note that, if Cb(V) was treated as constant, the vertical position of the -Im(Z)-P fit in the high frequency range will be scaled accordingly making it slightly further from the data points One possible reason is that, the recombination of free carriers primarily take place near the boundary of the perovskite intrinsic layer while the intrinsic layer thickness could be slightly influence by the ion migration under electric field. The Re~V could be fitted to the following exponential equation like Eq. 1

𝑅𝑒 ∝ 𝑅𝑒0exp ( ― 𝑒𝑉/𝑛𝑘𝑇) (7)

where n=2.27 at T= 293 K. The Eq. 7 relationship is a support to our argument that Re describes the dark recombination between free electrons and holes. The dependences of AW and Rl on P and V are plotted in Figure 6c and 6d, respectively. We notice that, the power dependences of AW and Rl are inversely proportional to P (slope = -1 on the log-log plot) especially in the high light power range. Therefore, we can write

𝐴𝑊(𝑉,𝑃) = 𝐴𝑊0(𝑉)/𝑃 (8)

and



𝑅𝑙(𝑉,𝑃) = 𝑅𝑙0(𝑉)/𝑃 (9).

Figure 6 Parameters employed in the first semi-global fitting. (a) L and Rs. (b) Re and

Cb, in which the solid line indicates exponential fit according to Eq. 7 excluding two points (0 V and 0.6 V). (c) AW and (d) Rl. The gray lines are guide lines to slope = -1 indicating inverse linearity.


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The similarity of the power dependence of AW and Rl is a support to our argument that both AW and Rl are related to the same charge carrier species, –the mobile ions. AW corresponds to the migration of ions while Rl corresponds to the capture of free holes by I-. In addition, according to Eq. 5 and 9, we arrive at 𝜌0 ∝ 𝑃, namely, the density of mobile I- is proportional to light power. Although our results are similar to those reported by a previous study,22 our discussion is different in that: 1) an RC circuit of their equivalent circuit is replaced by ZW in this work and 2) by implementing the Re element, our equivalent circuit works well for general (V,P) conditions not restricting to the short circuit and open circuit condition. The three key behaviors of the experiment data (indicated by the three arrows and two guidelines in Figure 2a) are reproduced in the fitted results including

a) The slopes of the faster (-1) and slower feature (-1/2);

b) The first-unchanged-then-drop behavior of the faster feature amplitude;

c) The complicated first-rise-then-drop behavior of the slower feature indicated by the red and cyan arrows in Figure 2 and Figure 5.



The complicated first-rise-then-drop behavior is related to Eq. 7–9. As shown in Figure 4a, in the very low power range, the slower feature is not pronounced because

Rl is too large and the impedance of the whole equivalent circuit is dominant by the Re branch. When P grows up, although the amplitude of ZW (AW) keeps reducing, the slower feature amplitude becomes more pronounced because the Rl-ZW branch grows more conductive. After a critical light power, Rl is smaller than Re so that the impedance is dominant by the Rl-ZW branch. As P further increases, the amplitude of the slower feature starts to decrease because AW reduces with P. Meanwhile, the resonance time (𝜏fast= CbRl) and amplitude (= Rl/2) of the faster feature starts to decrease because they are both proportional to Rl.

In order to prove the validity of the three empirical equations (Eq. 7–9), we tried a further fitting in which the number of fitting parameters is reduced according to Eq. 7–9. Namely the 110 curves are fitted with only 35 parameter values (AW0(V), Rl0(V),

Cb(V), Re0, n, Rs, L, τ). This fitting is almost a completely global fitting because all the power-dependent parameters are eliminated. Similar to the abovementioned semiglobal fitting with 270 values, we reproduced the key EIS behaviors which thereby confirms the validity of Eq. 7–9. The fitted curves are shown in Figure S4. According


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to Eq. 5, the reciprocal dependence described by Eq. 8 indicates that 𝜌0 ∝ 𝑃. Consequently, according to Eq. 6, the reciprocity of Eq. 9 is understandable.

The fitting parameters obtained from the global fitting are shown in Figure 7 (voltage-dependent parameters) and Table 1 (voltage-independent parameters). The

AW0–V, Rl0(V)–V relationships should come from the voltage-dependencies of the fine distributions of ρ0 and free carrier distribution. This point is supported by earlier report61 that when the carrier distribution was changed by using different excitation wavelength, the amplitude of the slower EIS feature could be changed. We notice that the voltage-dependent variation of Rl0 is similar to, but smaller than that of AW0. Explicit explanation to the Figure 7 results requires a theoretical drift-diffusion calculation in future. A recent work by García-Rosell et.al. could be an example, although lightinduced mobile ions are not considered in their work.62

The fitted increase of Cb with increasing V is reasonable because the depletion region thickness is squeezed as the density of free carriers and ρ0 in the bulk is expected to increase with increasing V. In addition the fitted exponential AW0–V,



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Rl0(V)–V behaviors in the high voltage range agrees with the usual expectation that 𝜌0 𝑉

∝ exp (𝑥𝑘𝑇) where x is a coefficient.

Other device intrinsic parameters could be derived from the fitted result. According to the perovskite layer thickness (300 nm), the diffusion coefficient of Icould be calculated to be 1.6×10-8 cm2/s via Eq. 4. Consequently according to the Einstein relationship, the I- mobility is calculated to be 4×10-10 cm2/Vs which is near to the experiment result (~1.5×10-9 cm2/Vs)63,64. According to Eq. 5 and Eq. 8, the Iconcentration should be proportional to light power. For example, under V = 1.05 V the I- concentration is 1.0×1019 /cm3 when P = 10 mW/cm2 which is similar to the calculated value21

Table 1 Voltage-independent parameters (τ, Re0, n, L, Rs) employed in the second global fitting.

τ

R e0

n

L

Rs

56.1 ms

3.64 GOhm cm2

2.26

685 nH cm2

22.4 Ohm cm2


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Figure 7. Voltage-dependence of Cb, Rl0 and AW0 employed in the second global fitting.

4. Conclusion

To sum up, according to our analysis of the –Im(Z) Bode plot and other reports31–35,52–54, we propose that the slower EIS feature is out of the migration of mobile ions (most likely I- or I vacancy) while the faster EIS feature is from the relaxation of free holes. The relaxation of free holes is a combination of two parallel ways, i.e., 1) the recombination between free electrons and holes and 2) the capture by the mobile I-. We highlight that sometimes the log-log Bode plot of –Im(Z) could be more useful than the widely used Cole-Cole plot. Through our analysis, we confirm



that, when employing the equivalent circuit method, the slower EIS feature of PSCs (ion migration)should be symbolled as Warburg element with absorbing boundary condition (ZW) or Gerischer element (ZG) rather than a regular RC circuit. In this work, we chose ZW instead of ZG. Our final equivalent circuit is a Randles circuit modified with a parallel resistance (Re). This equivalent circuit suggests that the dynamics inside PSCs consist of two parts, 1) the migration of mobile ions/vacancies (slower EIS feature, described by ZW) and their interaction with the free carriers (one contributor to the faster EIS feature, described by Rl) and 2) a classical diode involving the migration and recombination of free carriers (the other contributor to the faster EIS feature, described by Re).

Based on the proposed equivalent circuit, the voltage- and powerdependencies of the involved circuit elements are calculated through global fitting 110 EIS curves under various biases and light powers. The key behaviors of the EIS under fixed bias and various illumination powers could be reproduced with simple empirical equations (Eq. 7–9). The calculated ion mobility (4×10-10 cm2/Vs) from our calculation agrees with previously reported value,63,64 which supports the validity of the proposed equivalent circuit. Through the analysis of the fitting parameters, we arrive at the


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following conclusions. 1) Re describes the diode-like dark recombination of free carriers. 2) ZW describes the migration of mobile ions which assumed to be mobile Ihere. 3) The inverse-linearity of the ZW amplitude (AW) suggests the mobile I- density is proportional to light power. 4) Rl describes the capture of free carriers by the mobile ions. 5) The reported reciprocal power dependence of the amplitude of the faster EIS feature22 is due to 𝑅𝑙 ∝ 1/ 𝜌0 (Eq. 6) and the linear power dependence of I- density mentioned above. Although the mobile ions is assumed to be mobile I- in this work, other mobile species could also be candidates as long as they satisfy that a) the migration time across the perovskite layer is ~1–100 ms to meet the timescale of the slower EIS feature and b) their number is proportional to light power.

As a phenomenological study, we offer a simplified description of the voltageand power-dependence of the EIS of PSCs through our proposed equivalent circuit and the empirical equations. Some other questions remain open. 1) Why the critical light power under a specific voltage (Rl0P = Re, so that the amplitude of the faster and slower EIS features start to decrease) equals to that corresponding to the open circuit condition. 2) A theoretical drift-diffusion calculation is required to calculate the voltagedependence of AW0, Rl0.



ASSOCIATED CONTENT

Supporting Information.

Experiment details of device preparation and characterization. Power-dependences of EIS results under various fixed biases. Derivation for Eq. 6 Technical issues about global fitting AUTHOR INFORMATION

Corresponding Author E-mail: [email protected]. (X.C.) Present address: Key Laboratory of Advanced Functional Materials, Ministry of Education, College of Materials Science and Engineering, Beijing University of Technology, 100 Ping Le Yuan, Chaoyang District, Beijing 100124, China E-mail: [email protected] (K.M.)

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT


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This work was supported by MEXT under the Program for Development of Environmental Technology using Nano-technology (GREEN).

REFERENCES (1)

Nrel solar cell efficiency chart https://www.nrel.gov/pv/assets/images/efficiencychart.png.

(2)

Khadka, D. B.; Shirai, Y.; Yanagida, M.; Miyano, K. Degradation of Encapsulated Perovskite Solar Cells Driven by Deep Trap States and Interfacial Deterioration. J. Mater. Chem. C 2017, 6, 162–170.

(3)

Islam, M. B.; Yanagida, M.; Shirai, Y.; Nabetani, Y.; Miyano, K. NiOx Hole Transport Layer for Perovskite Solar Cells with Improved Stability and Reproducibility. ACS Omega 2017, 2, 2291–2299.

(4)

Snaith, H. J. Perovskites : The Emergence of a New Era for Low-Cost , HighEfficiency Solar Cells. J. Phys. Chem. Lett 2013, 4, 3623−3630.

(5)

Domanski, K.; Alharbi, E. A.; Hagfeldt, A.; Grätzel, M.; Tress, W. Systematic Investigation of the Impact of Operation Conditions on the Degradation Behaviour of Perovskite Solar Cells. Nat. Energy 2018, 3, 61–67.

(6)

Christians, J. A.; Schulz, P.; Tinkham, J. S.; Schloemer, T. H.; Harvey, S. P.; Tremolet De Villers, B. J.; Sellinger, A.; Berry, J. J.; Luther, J. M. Tailored Interfaces of Unencapsulated Perovskite Solar Cells for >1,000 Hour Operational Stability. Nat. Energy 2018, 3, 68–74.

(7)

Zuo, C.; Vak, D.; Angmo, D.; Ding, L.; Gao, M. One-Step Roll-to-Roll Air Processed High Efficiency Perovskite Solar Cells. Nano Energy 2018, 46, 185–192.



(8)

Luo, Q.; Ma, H.; Hou, Q.; Li, Y.; Ren, J.; Dai, X.; Yao, Z.; Zhou, Y.; Xiang, L.; Du, H.; et al. All-Carbon-Electrode-Based Endurable Flexible Perovskite Solar Cells. Adv. Funct. Mater. 2018, 28, 1–8.

(9)

Correa-Baena, J.-P.; Abate, A.; Saliba, M.; Tress, W.; Jesper Jacobsson, T.; Grätzel, M.; Hagfeldt, A. The Rapid Evolution of Highly Efficient Perovskite Solar Cells. Energy Environ. Sci. 2017, 10, 710–727.

(10)

Fakharuddin, A.; De Rossi, F.; Watson, T. M.; Schmidt-Mende, L.; Jose, R. Research Update: Behind the High Efficiency of Hybrid Perovskite Solar Cells. APL Mater. 2016, 4, 091505.

(11)

Egger, D. A.; Bera, A.; Cahen, D.; Hodes, G.; Kirchartz, T.; Kronik, L.; Lovrincic, R.; Rappe, A. M.; Reichman, D. R.; Yaffe, O. What Remains Unexplained about the Properties of Halide Perovskites? Adv. Mater. 2018, 30, 1–11.

(12)

Almora, O.; Aranda, C.; Garcia-Belmonte, G. Do Capacitance Measurements Reveal Light-Induced Bulk Dielectric Changes in Photovoltaic Perovskites? J. Phys. Chem. C 2018, 122, 13450–13454.

(13)

Chen, Y.; Peng, J.; Su, D.; Chen, X.; Liang, Z. Efficient and Balanced Charge Transport Revealed in Planar Perovskite Solar Cells. ACS Appl. Mater. Interfaces 2015, 7, 4471–4475.

(14)

Chen, X.; Wu, B.; He, Z.; Xuxie, H.; Liang, Z.; Hou, X. Transient Photovoltage Study on the Dynamics of Excitons and Carriers in Tris-(8-Hydroxyquinolinato)Aluminum. J. Appl. Phys. 2014, 116, 153704.


Page 38 of 53

Page 39 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(15)

Peng, J.; Chen, X.; Chen, Y.; Sandberg, O. J.; Österbacka, R.; Liang, Z. Transient Extraction of Holes and Electrons Separately Unveils the Transport Dynamics in Organic Photovoltaics. Adv. Electron. Mater. 2016, 2, 1500333.

(16)

Peng, J.; Chen, Y.; Wu, X.; Zhang, Q.; Kan, B.; Chen, X.; Chen, Y.; Huang, J.; Liang, Z. Correlating Molecular Structures with Transport Dynamics in High-Efficiency Small-Molecule Organic Photovoltaics. ACS Appl. Mater. Interfaces 2015, 7, 13137– 13141.

(17)

Wheeler, S.; Bryant, D.; Troughton, J.; Kirchartz, T.; Watson, T. M.; Nelson, J.; Durrant, J. R. Transient Optoelectronic Analysis of the Impact of Material Energetics and Recombination Kinetics upon the Open-Circuit Voltage of Hybrid Perovskite Solar Cells. J. Phys. Chem. C 2017, 121, 13496–13506.

(18)

Correa-Baena, J.-P.; Turren-Cruz, S.-H.; Tress, W.; Hagfeldt, A.; Aranda, C.; Shooshtari, L.; Bisquert, J.; Guerrero, A. Changes from Bulk to Surface Recombination Mechanisms between Pristine and Cycled Perovskite Solar Cells. ACS Energy Lett. 2017, 2, 681–688.

(19)

Pockett, A.; Carnie, M. J. Ionic Influences on Recombination in Perovskite Solar Cells. ACS Energy Lett. 2017, 2, 1683–1689.

(20)

Walter, D.; Fell, A.; Wu, Y.; Duong, T.; Barugkin, C.; Wu, N.; White, T. P.; Weber, K. Transient Photovoltage in Perovskite Solar Cells: Interaction of Trap-Mediated Recombination and Migration of Multiple Ionic Species. J. Phys. Chem. C 2018, 122, 11270–11281.

(21)

Calado, P.; Telford, A. M.; Bryant, D.; Li, X.; Nelson, J.; O’Regan, B. C.; Barnes, P. R. F. Evidence for Ion Migration in Hybrid Perovskite Solar Cells with Minimal Hysteresis. Nat. Commun. 2016, 7, 13831.



(22)

Zarazua, I.; Han, G.; Boix, P. P.; Mhaisalkar, S.; Fabregat-Santiago, F.; Mora-Seró, I.; Bisquert, J.; Garcia-Belmonte, G. Surface Recombination and Collection Efficiency in Perovskite Solar Cells from Impedance Analysis. J. Phys. Chem. Lett. 2016, 7, 5105– 5113.

(23)

Pockett, A.; Eperon, G.; Sakai, N.; Snaith, H.; Peter, L. M.; Cameron, P. J. Microseconds, Milliseconds and Seconds: Deconvoluting the Dynamic Behaviour of Planar Perovskite Solar Cells. Phys. Chem. Chem. Phys. 2017, 19, 5959–5970.

(24)

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, 2390–2394.

(25)

Zarazua, I.; Bisquert, J.; Garcia-Belmonte, G. G. Light-Induced Space-Charge Accumulation Zone as Photovoltaic Mechanism in Perovskite Solar Cells. J. Phys. Chem. Lett. 2016, 7, 525–528.

(26)

Wang, Q. Fast Voltage Decay in Perovskite Solar Cells Caused by Depolarization of Perovskite Layer. J. Phys. Chem. C 2018, 122, 4822–4827.

(27)

Guerrero, A.; Garcia-Belmonte, G.; Mora-Sero, I.; Bisquert, J.; Kang, Y. S.; Jacobsson, T. J.; Correa-Baena, J. P.; Hagfeldt, A. Properties of Contact and Bulk Impedances in Hybrid Lead Halide Perovskite Solar Cells Including Inductive Loop Elements. J. Phys. Chem. C 2016, 120, 8023–8032.

(28)

Pockett, A.; Eperon, G. E.; Peltola, T.; Snaith, H. J.; Walker, A.; Peter, L. M.; Cameron, P. J. Characterization of Planar Lead Halide Perovskite Solar Cells by Impedance Spectroscopy, Open-Circuit Photovoltage Decay, and Intensity-Modulated Photovoltage/Photocurrent Spectroscopy. J. Phys. Chem. C 2015, 119, 3456–3465.


Page 40 of 53

Page 41 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(29)

Liu, Y.; Renna, L. A.; Thompson, H. B.; Page, Z. A.; Emrick, T.; Barnes, M. D.; Bag, M.; Venkataraman, D.; Russell, T. P. Role of Ionic Functional Groups on Ion Transport at Perovskite Interfaces. Adv. Energy Mater. 2017, 7, 1701235.

(30)

Smith, E. C.; Ellis, C. L. C.; Javaid, H.; Renna, L. A.; Liu, Y.; Russell, T. P.; Bag, M.; Venkataraman, D. Interplay Between Ion Transport, Applied Bias and Degradation under Illumination in Hybrid Perovskite p-i-n Devices. J. Phys. Chem. C 2018, 122, 13986−13994.

(31)

Kim, G. Y.; Senocrate, A.; Yang, T.; Gregori, G.; Grätzel, M.; Maier, J. Large Tunable Photoeffect on Ion Conduction in Halide Perovskites and Implications for Photodecomposition. Nat. Mater. 2018, 17, 445–449.

(32)

Colella, S.; Todaro, M.; Masi, S.; Listorti, A.; Altamura, D.; Caliandro, R.; Giannini, C.; Carignani, E.; Geppi, M.; Meggiolaro, D.; et al. Light-Induced Formation of Pb 3+ Paramagnetic Species in Lead Halide Perovskites. ACS Energy Lett. 2018, 1840–1847.

(33)

Xing, J.; Wang, Q.; Dong, Q.; Yuan, Y.; Fang, Y.; Huang, J. Ultrafast Ion Migration in Hybrid Perovskite Polycrystalline Thin Films under Light and Suppression in Single Crystals. Phys. Chem. Chem. Phys. 2016, 18, 30484–30490.

(34)

Whalley, L. D.; Crespo-Otero, R.; Walsh, A. H-Center and V-Center Defects in Hybrid Halide Perovskites. ACS Energy Lett. 2017, 2, 2713–2714.

(35)

Mosconi, E.; Meggiolaro, D.; Snaith, H. J.; Stranks, S. D.; De Angelis, F. LightInduced Annihilation of Frenkel Defects in Organo-Lead Halide Perovskites. Energy Environ. Sci. 2016, 9, 3180–3187.



(36)

Ghahremanirad, E.; Bou, A.; Olyaee, S.; Bisquert, J. Inductive Loop in the Impedance Response of Perovskite Solar Cells Explained by Surface Polarization Model. J. Phys. Chem. Lett. 2017, 8, 1402–1406.

(37)

Raga, S. R.; Qi, Y. The Effect of Impurities on the Impedance Spectroscopy Response of CH3NH3PbI3 Perovskite Solar Cells. J. Phys. Chem. C 2016, 120, 28519–28526.

(38)

Miyano, K.; Tripathi, N.; Yanagida, M.; Shirai, Y. Lead Halide Perovskite Photovoltaic as a Model P-i-n Diode. Acc. Chem. Res. 2016, 49, 303–310.

(39)

Kim, H.-S.; Mora-Sero, I.; Gonzalez-Pedro, V.; Fabregat-Santiago, F.; Juarez-Perez, E. J.; Park, N.-G.; Bisquert, J. Mechanism of Carrier Accumulation in Perovskite ThinAbsorber Solar Cells. Nat. Commun. 2013, 4, 2242.

(40)

Gonzalez-Pedro, V.; Juarez-Perez, E. J.; Arsyad, W. S.; Barea, E. M.; FabregatSantiago, F.; Mora-Sero, I.; Bisquert, J. General Working Principles of CH3NH3PbX3 Perovskite Solar Cells. Nano Lett. 2014, 14, 888–893.

(41)

Li, Y.; Ding, B.; Chu, Q. Q.; Yang, G. J.; Wang, M.; Li, C. X.; Li, C. J. Ultra-High Open-Circuit Voltage of Perovskite Solar Cells Induced by Nucleation Thermodynamics on Rough Substrates. Sci. Rep. 2017, 7, 1–10.

(42)

Ameen, S.; Shaheer Akhtar, M.; Seo, H.-K.; Nazeeruddin, M. K.; Shin, H.-S. Towards Design of Metal Oxide Free Perovskite Solar Cell Paradigm: Materials Processing and Enhanced Device Performance. Chem. Eng. J. 2015, 281, 599–605.

(43)

Chavhan, S.; Miguel, O.; Grande, H.-J.; Gonzalez-Pedro, V.; Sánchez, R. S.; Barea, E. M.; Mora-Seró, I.; Tena-Zaera, R. Organo-Metal Halide Perovskite-Based Solar Cells with CuSCN as the Inorganic Hole Selective Contact. J. Mater. Chem. A 2014, 2, 12754–12760.


Page 42 of 53

Page 43 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(44)

Ameen, S.; Akhtar, M. S.; Seo, H. K.; Nazeeruddin, M. K.; Shin, H. S. An Insight into Atmospheric Plasma Jet Modified ZnO Quantum Dots Thin Film for Flexible Perovskite Solar Cell: Optoelectronic Transient and Charge Trapping Studies. J. Phys. Chem. C 2015, 119, 10379–10390.

(45)

Yadav, P.; Alotaibi, M. H.; Arora, N.; Dar, M. I.; Zakeeruddin, S. M.; Grätzel, M. Influence of the Nature of A Cation on Dynamics of Charge Transfer Processes in Perovskite Solar Cells. Adv. Funct. Mater. 2017, 28, 1706073.

(46)

Bag, M.; Renna, L. A.; Adhikari, R. Y.; Karak, S.; Liu, F.; Lahti, P. M.; Russell, T. P.; Tuominen, M. T.; Venkataraman, D. Kinetics of Ion Transport in Perovskite Active Layers and Its Implications for Active Layer Stability. J. Am. Chem. Soc. 2015, 137, 13130–13137.

(47)

Miyano, K.; Yanagida, M.; Tripathi, N.; Shirai, Y. Hysteresis, Stability, and Ion Migration in Lead Halide Perovskite Photovoltaics. J. Phys. Chem. Lett. 2016, 7, 2240–2245.

(48)

Bisquert, J. Theory of the Impedance of Electron Diffusion and Recombinantion in a Thin Layer. J. Phys. Chem. B 2002, 106, 325–333.

(49)

Chen, X.; Shirai, Y.; Yanagida, M.; Miyano, K. Photocarrier Dynamics in PerovskiteBased Solar Cells Revealed by Intensity-Modulated Photovoltage Spectroscopy. Phys. Chem. Chem. Phys. 2018, 20, 17918–17926.

(50)

Kovalenko, A.; Pospisil, J.; Krajcovic, J.; Weiter, M.; Guerrero, A.; Garcia-Belmonte, G. Interface Inductive Currents and Carrier Injection in Hybrid Perovskite Single Crystals. Appl. Phys. Lett. 2017, 111, 1–5.



(51)

Eames, C.; Frost, J. M.; Barnes, P. R. F.; O’Regan, B. C.; Walsh, A.; Islam, M. S. Ionic Transport in Hybrid Lead Iodide Perovskite Solar Cells. Nat. Commun. 2015, 6, 7497.

(52)

Weber, S.; Hermes, I. M.; Turren Cruz, S. H.; Gort, C.; W. Bergmann, V.; Gilson, L.; Hagfeldt, A.; Grätzel, M.; Tress, W.; Berger, R. How the Formation of Interfacial Charge Causes Hysteresis in Perovskite Solar Cells. Energy Environ. Sci. 2018, 11, 2404–2413.

(53)

Peng, W.; Aranda, C.; Bakr, O. M.; Garcia-Belmonte, G.; Bisquert, J.; Guerrero, A. Quantification of Ionic Diffusion in Lead Halide Perovskite Single Crystals. ACS Energy Lett. 2018, 3, 1477–1481.

(54)

Li, W.; Liu, J.; Bai, F. Q.; Zhang, H. X.; Prezhdo, O. V. Hole Trapping by Iodine Interstitial Defects Decreases Free Carrier Losses in Perovskite Solar Cells: A TimeDomain Ab Initio Study. ACS Energy Lett. 2017, 2, 1270–1278.

(55)

Lopez-Varo, P.; Jiménez-Tejada, J. A.; García-Rosell, M.; Ravishankar, S.; GarciaBelmonte, G.; Bisquert, J.; Almora, O. Device Physics of Hybrid Perovskite Solar Cells: Theory and Experiment. Adv. Energy Mater. 2018, 8, 1702772.

(56)

Sarker, S.; Ahammad, A. J. S.; Seo, H. W.; Kim, D. M. Review Article: Electrochemical Impedance Spectra of Dye-Sensitized Solar Cells : Fundamentals and Spreadsheet Calculation. Int. J. Photoenergy 2014, 2014, 851705.

(57)

Vicente, N.; Garcia-Belmonte, G. Organohalide Perovskites Are Fast Ionic Conductors. Adv. Energy Mater. 2017, 7, 1700710.

(58)

Yu, H.; Zhang, Q.; Han, C.; Zhu, X.; Sun, X.; Yang, Q.; Yang, H.; Deng, L.; Zhao, F.; Wang, K.; et al. Improving Photovoltaic Performance of Inverted Planar Structure


Page 44 of 53

Page 45 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Perovskite Solar Cells via Introducing Photogenerated Dipoles in the Electron Transport Layer. Org. Electron. 2018, 63, 137–142. (59)

Randles, J. E. B. Kinetics of Rapide Electrode Applications. Discuss. Faraday Soc. 1947, 34, 355–358.

(60)

Ho, C. Application of A-C Techniques to the Study of Lithium Diffusion in Tungsten Trioxide Thin Films. J. Electrochem. Soc. 1980, 127, 343–350.

(61)

Contreras-Bernal, L.; Salado, M.; Todinova, A.; Calio, L.; Ahmad, S.; Idígoras, J.; Anta, J. A. Origin and Whereabouts of Recombination in Perovskite Solar Cells. J. Phys. Chem. C 2017, 121, 9705–9713.

(62)

García-Rosell, M.; Bou, A.; Jiménez-Tejada, J. A.; Bisquert, J.; Lopez-Varo, P. Analysis of the Influence of Selective Contact Heterojunctions on the Performance of Perovskite Solar Cells. J. Phys. Chem. C 2018, 122, 13920–13925.

(63)

Yuan, Y.; Wang, Q.; Shao, Y.; Lu, H.; Li, T.; Gruverman, A.; Huang, J. Electric-FieldDriven Reversible Conversion between Methylammonium Lead Triiodide Perovskites and Lead Iodide at Elevated Temperatures. Adv. Energy Mater. 2016, 6, 1501803.

(64)

Yuan, Y.; Chae, J.; Shao, Y.; Wang, Q.; Xiao, Z.; Centrone, A.; Huang, J. Photovoltaic Switching Mechanism in Lateral Structure Hybrid Perovskite Solar Cells. Adv. Energy Mater. 2015, 5, 1500615.



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Anode

V = 0.85 V P = 15.4 mW/cm2

Electrons

(c)

Density

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28


q

Holes

ZW, Dissipa�on at the boundary.

q

migration Perovskite

Mobile ICathode

(d)


q

q

ZG, Dissipa�on inside the bulk with ﬁxed life�me.

q

q q

q

q q


(a) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

(b)

Page 50 of 53

W

W


Page 51 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Power density 2 (μW/cm ) = 0 4.62 15.4 46.2 154 462 1540 4620 15400 46200 123000

Bias = 0.9 V


Bias = 0 V

Bias = 0.6 V

Bias = 0.7 V

Bias = 0.8 V

Bias = 0.75 V

Bias = 0.8 V

Bias = 0.95 V

Bias = 1 V ACS Paragon Plus Environment

Bias = 1.05 V

(a) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(c)

(b)


L (nH cm2) Rs (Ohm cm2)

(d)


Re (Ohm cm2 ) Exponen�al ﬁt Cb (nF/cm2)

Page 52 of 53

Page 53 of 53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24


Cb (nF cm-2) Rct0 (Ohm cm2) Aw0 (Ohm cm2 mW-1 s-0.5) ACS Paragon Plus Environment

Effect of Light and Voltage on Electrochemical Impedance

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