Lead Halide Perovskite Photovoltaic as a Model p ... - ACS Publications

Jan 12, 2016 - CONSPECTUS: The lead halide perovskite photovoltaic cells, especially the iodide compound. CH3NH3PbI3 family, exhibited enormous progre...
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Lead Halide Perovskite Photovoltaic as a Model p−i−n Diode Published as part of the Accounts of Chemical Research special issue “Lead Halide Perovskites for Solar Energy Conversion”. Kenjiro Miyano,*,† Neeti Tripathi,† Masatoshi Yanagida,†,‡ and Yasuhiro Shirai†,‡ †

Global Research Center for Environment and Energy based on Nanomaterials Science (GREEN), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan ‡ Photovoltaic Materials Unit, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan CONSPECTUS: The lead halide perovskite photovoltaic cells, especially the iodide compound CH3NH3PbI3 family, exhibited enormous progress in the energy conversion efficiency in the past few years. Although the first attempt to use the perovskite was as a sensitizer in a dye-sensitized solar cell, it has been recognized at the early stage of the development that the working of the perovskite photovoltaics is akin to that of the inorganic thin film solar cells. In fact, theoretically perovskite is always treated as an ordinary direct band gap semiconductor and hence the perovskite photovoltaics as a p−i−n diode. Despite this recognition, research effort along this line of thought is still in pieces and incomplete. Different measurements have been applied to different types of devices (different not only in the materials but also in the cell structures), making it difficult to have a coherent picture. To make the situation worse, the perovskite photovoltaics have been plagued by the irreproducible optoelectronic properties, most notably the sweep direction dependent current−voltage relationship, the hysteresis problem. Under such circumstances, it is naturally very difficult to analyze the data. Therefore, we set out to make hysteresis-free samples and apply time-tested models and numerical tools developed in the field of inorganic semiconductors. A series of electrical measurements have been performed on one type of CH3NH3PbI3 photovoltaic cells, in which a special attention was paid to ensure that their electronic reproducibility was better than the fitting error in the numerical analysis. The data can be quantitatively explained in terms of the established models of inorganic semiconductors: current/ voltage relationship can be very well described by a two-diode model, while impedance spectroscopy revealed the presence of a thick intrinsic layer with the help of a numerical solver, SCAPS, developed for thin film solar cell analysis. These results point to that CH3NH3PbI3 is an ideal intrinsic semiconductor, which happens to be very robust against accidental doping, and that the perovskite photovoltaic cell is in fact a model p−i−n diode. The analytical methods and diagnostic tools available in the inorganic semiconductor PV cells are useful and should be fully exploited in the effort of improving the efficiency. One outstanding question is why the perovskite stays intrinsic. Considering the defects and impurities that must abound in the perovskite layers formed by the spin-coating process, for example, there must be physicochemical mechanism keeping it from being doped. This may be related to the special band structure making up the band gap in this ionic solid. Understanding the mechanism may open a door for the wider utility of this class of solid.

1. INTRODUCTION A quick look at the “Best Research-Cell Efficiencies”1 provided by NREL (National Renewable Energy Laboratory) shows that the pace of the improvement of the energy conversion efficiency of perovskite cells (the latest entry in the chart) is the fastest in photovoltaic (PV) research history. This fact alone is amazing. More surprising though is that the progress has been achieved via simple film spreading techniques, spincoating, dip-coating, and so on. Historically, this class of materials has been the subject of solid state chemistry or solid state physics, where single crystals are the norm of the sample form. Layered variants have been studied in the search for properties similar to those associated with the superconducting CuO2 planes2 or in the interest of the strong binding energy of excitons as a consequence of the lower dimension.3 Other standard solid state properties such as the effective mass of carriers have also been studied in crystals.4 © XXXX American Chemical Society

Therefore, the proposal of using perovskite as a sensitizer in the DSSC structure5 and the ensuing big boom of the perovskite researches6 took us by surprise. The use of mesoporous substrates, for example, was foreign to those familiar with the ordinary inorganic solar cells. In order to understand the science behind the perovskite PVs, we set out to apply traditional inorganic semiconductor point of view and try to see how far we can go. In this Account, we would like to show that this line of thought led us to conclude that the perovskite solar cells are surprisingly simple p−i−n diodes. The closest cousin is inorganic thin-film PVs. Of course, this is nothing new. In the early stage of development, this was noticed and its similarity to the inorganic thin film PVs has been pointed out.7 Received: September 25, 2015

A

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Accounts of Chemical Research Here, however, we go one step further and make the analogy quantitative by exploiting many time-tested models and powerful tools available in inorganic semiconductor research. In particular, a simulating software developed in thin-film PVs turns out to be very useful to have a semiquantitative understanding of the intrinsic character of the perovskite layer, as will be described below. There remains one outstanding problem though: we do not know why it can be a simple p−i−n diode despite the defects and impurities, which must be present in numerous numbers in the perovskite layer considering the structure and the fabrication process. This may be a hint that there is a class of useful semiconductor materials robust against impurities and defects. Understanding the apparent self-passivation mechanism must have profound impact.

Figure 1. Cross-sectional SEM micrograph of a sample cell.

spin-coating CH3NH3I (two-step interdiffusion method). Care was taken so that the film is tightly packed and retains a smooth surface after each step. Unfortunately, there is a limit in the thickness of good quality films fabricated with this method. This is one of the limiting factors of the performance of our cells, in which the incident photons are not fully utilized. Several methods to alleviate the difficulty are under consideration.

2. BACKGROUND CONSIDERATIONS AND CELL FABRICATION 2.1. Band Structure

The earlier band structure calculation,8 simple (for example, spin−orbit interaction was not taken into account) but elucidating enough, tells us that a perovskite crystal of the formula APbI3 is a semiconductor with a direct band gap at the Γ point when the crystal is tetragonal. The valence band (VB) has the character of Pb 6s−I 5p hybridization, and the conduction band (CB) Pb 6p−I 6s hybridization. The bonding is highly ionic, and it is interesting that both bands are formed by antibonding of atomic orbitals. A recent calculation with spin−orbit interaction9 indicates that the Pb p-orbital in the CB spin splits, reducing the band gap close to the observed 1.55 eV. The arrangement of s-character VB and spin-split p-character CB resembles the band structure of GaAs with the CB and VB interchanged. The optical transition occurs between s and p symmetry, which provides very strong oscillator strength resulting in the absorbance in the range of 104−105 cm−1. It is to be noted that the band gap and the absorbance are similar to the values of GaAs, which give us high hope to realize high efficiency single-junction solar cells as has been proven in GaAs (28.8%).1

3. ELECTRONIC CHRACTERIZATION 3.1. Hysteresis10

In order to perform detailed electronic measurements, the cells must be electronically stable and reproducible. Especially, the hysteresis-free operation as illustrated in Figure 2 is essential for

2.2. Cell Design

With a GaAs-like material, one can design a PV cell in the form of either p−n, p−i−n, or even Schottky junction. However, due to the lack of information on doping CH3NH3PbI3 (MAPI), we are left with only one choice, a p−i−n structure. This is nothing new, of course. One aspect of the cell to which we paid our attention was to use a planar structure in spite of the demonstrated better efficiencies by the cells with mesoporous electrode. With a mesoporous electrode, we cannot easily define the profile of the electrostatic potential and the carrier density distribution. The planar electrode is essential to ensure the applicability of a simple one-dimensional (1D) driftdiffusion analysis developed in the thin-film PV research.

Figure 2. J/V curves demonstrating hysteresis-free properties. The curves are obtained with both sweep directions (arrows) at different sweep rates (legend).

2.3. Cell Fabrication

quantitative analysis. The two-step interdiffusion method turns out to be effective in avoiding the hysteresis.12 It is not clear which aspect in our fabrication method is effective in achieving the hysteresis-free samples. It could be that the excess amount of CH3NH3I ensures the stoichiometric reaction with the underlying PbI2, while unreacted CH3NH3I is easily removed during a low temperature annealing. The ionic motion is suspected as the source of hysteresis,13 and stoichiometry may be important to avoid it. It has been pointed out that PCBM

The facile method to form planar PV cells is to use spin-coating throughout. There are many candidate materials for the p- and n-layers, many of which have been developed previously for the organic solar cells. Among them, we adopted the structure11 shown in Figure 1: the p-layer is PEDOT:PSS (poly(3,4ethylenedioxythiophene):poly(styrenesulfonate), and the nlayer is PC61BM (phenyl-C61-butyric-acid-methyl ester). The MAPI layer is formed by spin-coating PbI2 layer followed by B

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In Figure 4, we show the fitting results with the diode equations for the single-diode and two-diode models using the

penetrates into MAPI and passivates the surface and intergrain defect sites, thereby reducing the hysteresis.14 This may not apply to our case because we observe hysteresis-free operation with an additional hole blocking layer on MAPI that blocks PCBM penetration (data not shown). 3.2. Diode Equation

The most fundamental equation that describes the diode action is the diode equation,15 ⎤ V + JR s ⎡ q(V + JR s) J(V ) = Jphoto − J0 exp⎢ − 1⎥ − R sh ⎦ ⎣ nkBT (1)

Here the meanings of the symbols are as follows: J is the current density measured at the cell electrodes, V is the voltage measured across the cell, Jphoto is the photogenerated current density, J0 is the reverse saturation current density, q is the elementary charge, Rs is the series resistance, Rsh is the shunt resistance, kB is the Boltzmann constant, T is the absolute temperature, and n is the ideality factor. The ideality factor contains information on the carrier recombination. In our previous attempt,16 we found that n ∼ 1.3 independent of the efficiency of the cell (10.5−11.5%) and concluded that n may not be a good indicator of the loss mechanism. We also tried to apply a two-diode model (described below) and found that the quality of the fit was worse and discarded the model in those earlier cases. As we improved the fabrication technique, a different picture emerged. The two-diode model now represents the data much better. The two-diode model is expressed by eq 1 with the diode part replaced by ⎡ q(V + JR s) ⎤ ⎡ q(V + JR s) ⎤ −J01 exp⎢ ⎥ − J02 exp⎢ ⎥ kBT ⎣ 2kBT ⎦ ⎦ ⎣

Figure 4. Fit of the diode equations to the J/V data. Filled circles are data in the dark, and open circles are data under AM1.5 illumination. Red lines are fitting curves using the two-diode model. Blue lines (solid and dashed) are fitting curves using the single-diode model. The blue dashed lines are the fitting to the data without constraints, while the blue solid line is the fitting to the dark data using parameter set consistent to the one used to fit the data under illumination.

J/V curves of a 15.1% efficiency cell. The fitting procedure is described in a previous publication;16 that is, the sum of the relative errors was minimized. The fitting results using the twodiode model are shown in red curves. No constraints were imposed among the fitting parameters, and the relative error is less than 1%. The fitting results using the single-diode model are shown in blue curves. The blue dashed curves are fitting to the data without constraints to the fitting parameters. The goodness of the fit is as good as the ones with the twoparameter model. Especially, the fits to the data under illumination with both models are indistinguishable. However, the fitting parameters thus obtained in the single-diode model are internally inconsistent. The parameters are J0 = 1.78 × 10−17 A/cm2 and n = 1.07 under illumination, and J0 = 1.98 × 10−18 A/cm2 and n = 1.00 in the dark. Both parameters differ considerably. If we impose n = 1.07, the fit to the data in the dark turns out to be J0 = 1.16−17 A/cm2, much closer to the fit to the data under illumination but the quality of the fit is unacceptable as is shown in the blue solid curve in Figure 4. On the other hand, the fitting parameters for the two-diode model obtained in two illumination conditions agree reasonably well as shown in Table 1. The fitting turned out to be very tight, that is, the error minimum is very deep and narrow in the parameter space, suggesting that the obtained fitting parameters are physically meaningful. In Table 1 are also shown typical parameters for GaAs p−i−n diode.18 Considering that the band gap difference between GaAs and MAPI is about 0.1 eV, J01

(2)

This model is based on the assumption that there are two recombination paths, one is through the band-to-band transition (the first term, n = 1) and another through the ingap recombination centers (the second term, n = 2, is the Shockley−Read−Hall mechanism17). The equivalent circuit for the two-diode model is shown in Figure 3a.

Table 1. Fitting Parameters for the Two-Diode Model MAPI (dark) 2

J01 (A/cm ) J02 (A/cm2) Rsh (Ω cm2) Rs (Ω cm2)

Figure 3. Equivalent circuits for the analysis of the electronic properties. (a) Two-diode model, (b) for the impedance spectroscopy analysis of a cell in the dark, and (c) for the impedance spectroscopy analysis of a cell under light illumination. C

−18

1.6 × 10 8.9 × 10−12 1.7 × 104 3.75

MAPI (sun) −18

1.8 × 10 8.7 × 10−12 2.1 × 104 3.51

GaAs 6.3 × 10−18 9.2 × 10−11 105 0.42

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Accounts of Chemical Research values for MAPI are larger than expected (one would expect a factor of exp(0.1/0.026) ∼ 45 difference in a naive picture). Nonetheless, all in all, they compare reasonably well quantitatively. 3.3. Impedance Spectroscopy

Following the confirmation of reasonable DC electronic behavior, we proceed to examine the AC behavior. In inorganic semiconductors, the temperature dependent admittance spectroscopy at high frequencies has been traditionally employed in order to detect the deep trap levels.19 This technique has been also applied to perovskite PV cells as well providing the trap energy levels.20 However, we use here impedance spectroscopy (IS) instead because we need information on low frequency capacitance which we can compare with the numerical simulation directly (see below). There have been many perovskite IS studies,21 of course, but the ones with the explicit p−i−n diode picture are few.22 We performed IS in the dark, under various light illumination conditions, and at varying bias voltages. The frequency range was 0.1−1 MHz and the amplitude of the modulation AC voltage was 10 mV. As reported earlier,16 the Nyquist plot in the dark is a semicircle, whereas the plot under light illumination splits into two semicircles in the high and low frequency ranges, respectively, and the low frequency circle is considerably flattened. We will examine the bias dependent behavior of these plots in more detail. Because the Nyquist plot in the dark can be fitted with a semicircle, the equivalent circuit is a parallel RC circuit depicted in Figure 3b. The fitting parameters were obtained by searching the combination of Rs, Rv, and C, that minimizes the sum of the differences between the data and calculated impedance values,

Figure 5. Nyquist plot of a sample in the dark at the bias voltage of (a) 0.1 V and (b) 0.8 V. Circles are data, and lines are fit using the equivalent circuit Figure 3b.

n

min ∑ |Zdata(ωi) − Zcalc(ωi)| i=1

(3)

where Z is the complex impedance. The absolute value in eq 3 is the error between the data and calculated impedance at a frequency ωi expressed in terms of the distance between the two points in the complex (Real(Z), Imaginary(Z)) plane. Typical fitting results are shown in Figure 5. The quality of fitting depends on the bias voltage. As is obvious in Figure 5a, the error at low bias voltage can be considerably large. The fitting above 0.5 V is reasonable although there is a low frequency component not taken into account with the equivalent circuit (Figure 5b, downward arrow. We will come back to this additional component later.). The bias voltage dependence of the two parameters, RV and C, are shown in Figure 6; the latter is plotted as 1/C2 (the Mott−Schottky plot) for later discussion. Note that plotted are the raw data not normalized by the cell area (about 0.4 cm2) for the ease of comparison. In Figure 6a, RV is plotted with the differential resistance of the DC J/V curve, dV/dJ. They differ considerably below 0.5 V. The differential resistance is too large so that the low frequency data contain very large noise and the fitting is not fully reliable. This is especially so at 0 V. Thus, we do not show IS data points for 0 V. Instead, as a reference, RV and 1/ C2 values measured with an LCR meter at 1 kHz are shown in Figure 6. Despite the uncertainty, however, it is clear that the bias voltage dependence of the capacitance is very small. This point will be discussed later. The Nyquist plot under light illumination is analyzed using the model shown in Figure 3c. Here the impedance expressed

Figure 6. Bias dependence of RV (circles) and the differential resistance dV/dJ (line) (a) and C expressed in 1/C2 (b). Filled circles at V = 0 V in both (a) and (b) were measured with an LCR meter.

as Ztrap represents the flattened semicircle component. We assume that its frequency dependence is of the form Ztrap = Zt /{1 + (iωτ )α }

(4)

The subscript “trap” implies that the impedance is governed by the trapping-detrapping process, whose typical time constant is τ, and α is an indicator of the width of the distribution of the trapping time. We hastily add, however, that there is no a priori reason to assume the particular form, eq 4. This is just a proposal to describe an intermittent phenomenon. Various forms of equations have been proposed for this purpose both in the time and frequency domains berore.23 We have no definite recipes at the moment to choose one out of many possibilities. Equation 4 is a phenomenological form that happens to reproduce our data remarkably well throughout various illumination intensities and bias voltages as shown below. Some fitting results are shown in Figure 7. The light source is a laser diode operated at 650 nm. The light intensity is adjusted to be 31 mW/cm2 on the cell surface. In order to show the quality of the fit, the real and imaginary parts of the error, Zdata(ω) − Zcalc(ω), for Figure 7a are presented in Figure 7a-1 as a function of frequency. The fitting is good except for the D

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Figure 8. Bias voltage dependent parameters of the equivalent circuit shown in Figure 3c. (a) Total resistance Rs + RV + Zt at zero frequency (circles) and the differential resistance of the J/V curve, dV/dJ (line), (b) RV (circles) and Zt (diamonds), (c) α, the exponent, (d) τ, the time constant, and (e) Mott−Schottky plot (1/C2 vs bias voltage).

Figure 7. Nyquist plot of a sample under light illumination at the bias voltage of (a) 0.4 V, (b) 0.7 V, and (c) 0.8 V. The circles are data and lines are fit. (a-1) Error Zdata(ω) − Zcalcu(ω) at each frequency f = ω/ 2π. Real part is in red, and imaginary part in blue.

data at the lowest frequencies where the noise is large. (Note the frequency increases to the right in Figure 7a-1 but to the left in Figure 7a.) Throughout the entire bias voltage, one model (Figure 3c) can reproduce the data very well. From the fitting parameters, we can extract the bias dependent parameters as shown in Figure 8. There are two notable features in Figure 8. The trapping-detrapping contribution diminishes rapidly around 0.6 V. The related parameters Zt, α, and τ all shift toward nonessential (i.e., of ordinary resistive character) values; Zt → constant, α → 1, and τ → constant. C is constant up to a certain bias voltage and starts to diverge (1/C2 diminishes), which seems to coincide with the disappearance of trapping-detrapping behavior. A linear Mott−Schottky plot is a textbook example of a p−n junction.24 Clearly, this does not apply to both Figures 6b and 8e. Qualitatively, the behavior of Figure 8e is in agreement with what we expect for a p−i−n diode with a completely depleted iregion at zero bias voltage. The built-in potential pushes the electrons and holes toward the respective electrodes at the short-circuit condition. As the forward bias voltage increases, the diffusion current penetrates into the i-region, which brings the quasi-Fermi level closer to the band edge causing further increase in the carrier density. The process is highly nonlinear. Up to a point, the penetration is insignificant and the capacitance is hardly affected. Beyond a certain point, the nonlinearity sets in. The positive feedback quickly pushes the carriers into the insulating region. The thinning of the

insulating region results in the diverging capacitance. Due to the nonlinearity, in order to understand the behavior quantitatively, we have to resort to numerical means, which can handle the carrier density and quasi Fermi energy selfconsistently. 3.4. Numerical Simulation

Since our cells are simple planar, a 1D simulation should suffice. We used SCAPS program.25 In short, SCAPS (solar cell capacitance simulator) is a 1D numerical solver for solar cells using the drift-diffusion model. The Poisson equation and the continuity equations for electrons and holes are solved selfconsistently by iteration. Various recombination pathways are incorporated. Because of the exponential dependence between the chemical potentials and the free carrier densities, the problem is highly nonlinear, especially in the nondoped region. This makes a stark contrast to the case in p−n junctions, in which a linearizing approximation is allowed and an analytical solution exists.24 The program was originally developed to simulate thin-film PV cells. Our simulation is based on the band diagram shown in Figure 9, where the perovskite layer is assumed to be nondoped. HOMO levels of PEDOT:PSS, MAPI, and PCBM and the Fermi levels of Ag and ITO were measured with a photoelectron spectrometer (Riken Keiki, AC-3). LUMO levels are calculated using the published value.26 However, many parameters are not exactly known to us. For example, the E

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nm) is adjusted to arrive at the exact agreement with the observed capacitance at zero bias voltage in Figure 10b. The essential feature of our observation that the plateau extends to the bias voltage just before the J/V curve takes off is reproduced well. The subsequent behavior is also similar to Figure 8e. The more extended flat region for the data in the dark is reasonable because of less free carriers to fill the i-region. We believe that this is a solid piece of evidence that the perovskite layer acts as an intrinsic semiconductor. As noted above, a more elaborate simulation is required for the interpretation of the bias dependent behavior of the parameters related to Ztrap. It should be pointed out that nonlinear Mott−Schottky plots have been observed before.27 However, we believe that the overall bias dependence, plateau, and steep slope are reproduced in one model for the first time in a perovskite cell.

Figure 9. Band diagrams used for numerical simulation, SCAPS.

mobilities, carrier densities, and so forth of PEDOT:PSS and PCBM depend much on the sample preparation. Other parameters, such as the density of states of MAPI, have to be taken from numerical calculations. Instead of going through detailed scrutiny of all of these parameters, we used a set of parameters which are somewhat arbitrary but reasonable. Because we are interested only in the capacitance as a function of the bias voltage semiquantitatively at the moment, we expect that we do not make gross errors by choosing somewhat inaccurate numbers here. The recombination processes were also left blank. Of course, this approximation is not allowed if we were to analyze the photoactivated trap behavior, which we hope to address in future works. The simulated J/V and 1/C2 vs bias voltage is plotted in Figure 10 together with the measured

3.5. Crossover Phenomenon

One property frequently observed in thin-film PVs is the “crossover” behavior.28 This is a phenomenon that the J/V curve in the dark crosses those under illumination. It is clear that J/V curves with different Jphoto should not cross: a common set of (J, V) does not satisfy eq 1 with different Jphotos simultaneously. Thus, an additional mechanism not taken into consideration in eq 1 must be present. In the thin-film PV research, the origin is attributed to the interface trap states, which are photoactivated and provide extra charged layer.28 This layer counteracts part of the built-in potential resulting in the reduction of the apparent bias voltage. Because eq 1 is an implicit function of J, the J/V curves with two different Jphotos are not simple lateral translation of each other. However, near the crossover point with similar values of J, the two curves must be similar and the comparison of the two by lateral translation is meaningful. We found that this is indeed the case in our cells. In Figure 11a, we show the J/V curves, which we used in Figure 3, in a linear scale. Although not very distinct, the crossover is clear in the expanded view shown in the inset. This is better illustrated if we plot the difference, J(V)illum − J(V)dark, (Figure 11b, blue line). Without the potential loss, the difference should be just Jphoto, a constant. The constant difference current is in fact recovered if we shift the J(V)illum upward by 80 mV and subtract J(V)dark (Figure 11b, red line). 80 mV potential loss corresponds to the efficiency loss by 1.2%, a significant figure. If this photoactivated trap site is at the interface, it is likely to be located at the PEDOT:PSS/MAPI interface because the effect is pronounced under monochromatic illumination far above the band gap, at which, transmission measurements show that the light does not

Figure 10. Simulated J/V curve and 1/C2 vs V using the band model in Figure 9. (a) In the dark and (b) under light illumination of 30 mW/cm2.

data, Figures 6b and 8e. The relative dielectric constant of 25 and cell area of 0.4 cm2 are used, and the film thickness (∼275

Figure 11. (a) Crossover of J/V curves measured in the dark (red) and under AM 1.5 illumination (blue), respectively. Inset is an expanded view near the crossover point. (b) Difference, Jillum − Jdark. Using the raw data (blue) and by shifting Jillum upward by 80 mV (red). F

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The band structure in which both VB and CB are formed by antibonding may be one clue. In a homopolar semiconductor, Si, for example, the VB is made of bonding orbitals while CB is made of antibonding orbitals. The nonbonding level lies just in the middle of the energy gap, which is a very efficient recombination center and is detrimental to the efficient photocarrier separation. This is not applicable to perovskite. Detailed studies show that the electronic levels associated with various defects do not lie deep inside the gap of the bulk30 or at the surface.31 This may explain the low bulk recombination rate (Table 1, J02). Another interesting theoretical proposal is that the compositional defects are of Schottky type, meaning that although the number of ionic vacancies are numerous, the overall stoichiometry is maintained and no effective doping occurs.32 This is in accordance with our observation that the perovskite layer appears to be a good intrinsic semiconductor. The robustness of perovskite against unfavorable defects and impurities deserves special attention, because this may point to the possibility of a class of electronic materials with highly desirable properties.

reach the rear side (MAPI/PCBM interface) of the perovskite layer. The photoactivated ion motion is also a possibility.29 Indepth study on the crossover phenomena is underway. 3.6. Trapping−Detrapping

With the possible photoactivated trap sites, the origin of the extra semicircle in Nyquist plot under optical illumination is clear. The frequency dependent impedance follows the filling and emptying processes of these sites. This supports the proposed equivalent circuit, Figure 3c as well, because the two elements, RV and Ztrap, are electronically in series but spatially distinct in the space between the two electrodes. Figure 8b−d shows that the trapping−detrapping process is insensitive to the bias voltage change up to a point followed by a rapid decrease in effectiveness. This could be understood as follows: at low bias voltage, the trapping−detrapping process is governed by the combination of the optical trap generation rate and the carrier density (the carriers fill the traps). The former should be proportional to the light intensity and the latter again to the light intensity because the carriers present at the interface at low bias voltage is mainly the majority carriers generated by light and swept to the electrode by the built-in potential. As the bias voltage increases, the diffusion current of minority carriers reach the electrode on the opposite side. The density of minority carries at the interface must be much larger than photon density and minority carriers effectively empty the traps. We now have ordinary carrier recombination mediated by defect sites rather than the trapping-detrapping. The low frequency flattened semicircle now becomes an ordinary semicircle (α = 1). Although the contribution of this component to the entire transport process diminishes, it persists to higher bias voltage. At this stage, photoexcitation is no longer relevant and the equivalent circuit consists of the series connection of the bulk resistive element and the interface resistive element with its own capacitance. In close inspection, we do have a hint of extra low frequency contribution in the Nyquist plot in the dark at higher bias voltage as well (cf., Figure 5b, arrow). Thus, the Nyquist plots at various light illumination levels and bias voltages all appear to converge into a simple coherent picture at the phenomenological level. It should be noted that the diminishing depletion region (diverging capacitance, Figure 8e) and the diminishing trapping−detrapping behavior (Figure 8b−d) have quite similar bias voltage dependence: both are the consequences of the increasing diffusion current. Thus, the data all appear to be consistent with the proposed model and we should be able to uncover the underlying physical processes responsible for eq 4 with various modulation and time-resolved spectroscopic means.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

This work was funded by MEXT under the Program for Development of Environmental Technology using Nanotechnology (GREEN). Notes

The authors declare no competing financial interest. Biographies Kenjiro Miyano is a professor emeritus of University of Tokyo and fellow at National Institute for Materials Science (NIMS). He received BEng from University of Tokyo, Ph.D. from Northwestern University. After spending 2 years at UC Berkeley as a postdoc, he joined Argonne National Lab. He then moved to Tohoku University as an associate professor and to University of Tokyo, where he was a professor in Applied Physics Department until 2012. His research interest is in optical properties of condensed matter. Neeti Tripathi received her Ph.D. degree in physics from University of Delhi, India in 2013. She then worked as postdoctoral researcher at National Institute of Advanced Industrial Science and Technology (AIST), Japan from 2013 to 2014. Currently she is working as a postdoctoral fellow at NIMS. Her research focus is to develop new materials and methods for photovoltaic applications and device fabrications. Masatoshi Yanagida is a principal researcher at NIMS. He received his Ph.D. in 1998 at Hokkaido University. He also worked in Japan Society for the Promotion of Science (JSPS) research fellowships for young scientists from 1995 to 1998. He worked at AIST from 1998 to 2008, and focused on the development of sensitizers and the tandem structure of DSSCs. His current research interests include the mechanism of carrier transport of lead halide perovskite solar cells and DSSCs.

4. CONCLUSIONS AND OUTSTANDING QUESTION By showing quantitative agreement with the well-established concepts and equations in the inorganic semiconductor research, we believe that our assertion that the perovskite PV cell is a model p−i−n diode is upheld. However, there is one outstanding question; we know that the perovskite films formed by spin-coating method must contain enormous amount of structural defects and impurities. Although, we compared the perovskite with GaAs, a PV cell made with GaAs with similar amount of defects and impurities would not work at all. Perovskite is not only a model intrinsic semiconductor but also an ideal intrinsic semiconductor.

Yasuhiro Shirai received his BS degree in electrical engineering while working for Nippon Avionics Co., Ltd in 1993−2000. He was also an exchange student from 1997 to 1998 at University of Kansas, where he studied chemistry and electrical engineering. He received his Ph.D. from Rice University in 2006. Between 2007 and 2010, he carried out G

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Accounts of Chemical Research

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ICYS postdoctoral fellow at NIMS and later became a research staff. He is currently a senior researcher at NIMS and his research has focused on design and synthesis of photovoltaic materials and device fabrications.

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ACKNOWLEDGMENTS

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REFERENCES

We thank Prof. Marc Burgelman for the use of SCAPS. K.M. is indebted to Prof. J.-F. Guillemoles for his kind instruction for using SCAPS.

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DOI: 10.1021/acs.accounts.5b00436 Acc. Chem. Res. XXXX, XXX, XXX−XXX