On the Uniqueness of Ideality Factor and Voltage Exponent of

Nov 12, 2014 - Our model predictions are supported by experimental results on solar cells fabricated at five different laboratories using different ma...
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On the Uniqueness of Ideality Factor and Voltage Exponent of Perovskite-Based Solar Cells Sumanshu Agarwal,*,† Madhu Seetharaman,‡ Naresh K. Kumawat,§ Anand S. Subbiah,† Shaibal K. Sarkar,† Dinesh Kabra,§ Manoj A. G. Namboothiry,‡ and Pradeep R. Nair*,∥ †

Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695016, Kerala, India § Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India ∥ Department of Electrical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India ‡

S Supporting Information *

ABSTRACT: Perovskite-based solar cells have attracted much recent research interest with efficiency approaching 20%. While various combinations of material parameters and processing conditions are attempted for improved performance, there is still a lack of understanding in terms of the basic device physics and functional parameters that control the efficiency. Here we show that perovskite-based solar cells have two universal features: an ideality factor close to two and a space-charge-limited current regime. Through detailed numerical modeling, we identify the mechanisms that lead to these universal features. Our model predictions are supported by experimental results on solar cells fabricated at five different laboratories using different materials and processing conditions. Indeed, this work unravels the fundamental operation principle of perovskite-based solar cells, suggests ways to improve the eventual performance, and serves as a benchmark to which experimental results from various laboratories can be compared. SECTION: Energy Conversion and Storage; Energy and Charge Transport

T

role of various parameters on eventual performance. Indeed, there has been significant discussion among the community on the possible effect of ferroelectric properties (and large dielectric constant17) of perovskites on the solar cell performance. While it is well known that the principle of superposition may not hold good for many classes of solar cells including perovskites, it is extremely important to develop a detailed understanding of the dark IV characteristics. This knowledge is crucial to further explore the light IV characteristics and to develop appropriate methodologies to predict panel-level performances so that the eventual promises and prospects of this technology could be quantitatively evaluated. In this context, here we provide a comprehensive analysis on the dark characteristics of these solar cells. Through experiments and detailed numerical simulations, we show that: (A) The dark current is dominated by carrier recombination in perovskite with an ideality factor close to two (low bias regime). (B) The high bias current is limited by space-charge effects. Curiously, through detailed simulations, we also find that the combination of dark ideality factor of two and space-chargelimited (SCL) transport is a unique scenario in terms of the

he search for a low-cost alternative for conventional photovoltaic devices has resulted in an increased research activity on organic and sensitized solar cells. Despite worldwide efforts, the reported efficiencies are still not good enough to challenge the inorganic-based (i.e., silicon) conventional photovoltaic industry. However, recent reports on perovskitebased solar cells are particularly encouraging as efficiencies approaching 20% were reported even on planar structures.1,2 As shown in Figure 1a, the active layer in such solar cells is a perovskite compound (mostly organic−inorganic halides1,3−5) that is sandwiched between electron transport layer (ETL) and hole transport layer (HTL). Literature reports indicate that such perovskites are good light absorbers, resulting in efficient generation of electron−hole pairs (exciton binding energies are comparable to thermal energy6−8). The generated electrons and holes are then transported to their respective electrodes, selectively, via ETL and HTL. Following the initial exciting results, different research groups have explored various types of perovskites by changing the halide group,5,9,10 and large carrier diffusion lengths were reported.11 Different chemical processes for fabrication were also reported for such solar cells,12−16 with varying success levels. Despite these exciting developments, a detailed understanding on the essential device physics that control the operation of perovskite-based solar cells is still lacking. As a result, most of the community is unaware about the functional © XXXX American Chemical Society

Received: October 11, 2014 Accepted: November 12, 2014

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possible range of material parameters. Specifically, these universal features suggest that the low-frequency relative permittivity of perovskites is similar to that of HTL, in contrast with the recent reports on giant dielectric constants.17 Indeed, this study explores the essential device physics that control the dark IV features of perovskite-based solar cells and provides a set of benchmark results or theoretical expectations to which experimental data from various laboratories can be compared and contrasted. Such a consolidation of theoretical insights with broad experimental trends is helpful in identifying and further optimizing the functional parameters that govern the landscape of this rapidly evolving field of perovskite solar cell research. Table 1 provides the details of the experimental devices used in this study. Specifically, these devices were fabricated in different laboratories (Oxford University1 vs EPFL18 vs three different laboratories at IISER TVM and IIT Bombay) and show a huge heterogeneity in terms of processing (e.g., coevaporation vs spin coating vs dip coating), ETL (TiO2 vs PCBM), perovskite (CH3NH3PbI3‑xClx vs CH3NH3PbI3), HTL (Spiro-MeOTAD vs P3HT vs PEDOT:PSS), device architecture (mesoporous vs planar), layer thicknesses, electrodes and, most importantly, have varying efficiencies (i.e., ranging from 1

Figure 1. Band level alignment in perovskite-based solar cell. (a) Schematic of perovskite solar cell with energy levels of different materials. Energy band diagram (simulation result) of the device under equilibrium is shown in panel b.

Table 1. Details of the Perovskite-Based Solar Cells Used in This Studya cell structure literature results

Cell A: structure: planar; source: Oxford University1

Cell B: structure: mesoporous; source: EPFL18

fabrication method spin-coating co-evaporation spin-coating

JSC 21.5 VOC 1.07 FF 67

front contact: FTO ETL (mesoporous): TiO2 perovskite

spin-coating

JSC 20

spin coating followed by dip coating spin-coating thermal evaporation

VOC 0.98

HTL: spiro-MeOTAD back contact: Au experimental results (this work)

Cell C: structure: planar; source: Dept. of Physics, IITB

Cell D: structure: planar; source: School of Physics, IISER TVM

front contact: ITO HTL: PEDOT:PSS (50 nm) perovskite (330 nm) ETL: PCBM (50 nm) back contact: Ag front contact: FTO ETL (compact): TiO2 (110 nm) perovskite (210 nm) HTL: P3HT (110 nm) back contact: Ag

Cell E: structure: planar; source: Dept. of Energy Science and Engineering, IITB

performance

front contact: FTO ETL (compact): TiO2 perovskite (330 nm) HTL: spiro-MeOTAD (400 nm) back contact: Ag

front contact: FTO ETL (compact): TiO2 (100 nm) perovskite (400 nm) HTL: spiro-MeOTAD (70 nm) back contact: Ag

sputtered spin-coating spin coating spin-coating thermal evaporation sputtering spin-coating

efficiency

15.4

13.3

FF 68

JSC 15.36 VOC 0.74 FF 42

4.8

JSC 12.56

spin coating spin-coating thermal evaporation

VOC 0.66 FF 36

spin-coating

JSC 7.1

thermal co-evaporation spin-coating

VOC 0.66 FF 30

3

1.4

thermal evaporation

a

Unit for JSC is mA/cm2, VOC is in V, while FF and efficiency are in %. Perovskite material used in all the cells was CH3NH3PbI3−xClx, except for Cell B, which was CH3NH3PbI3. 4116

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recombination (with B = 1 × 10−10 cm3 s−1, intrinsic perovskite material) indicate that the dark characteristics are dominated by SRH recombination. This justifies the assumption of SRH as the dominant recombination mechanism. The ETL (225 nm thick) properties closely match those of TiO2,26 while the HTL (200 nm thick) properties are adapted from spiro-MeOTAD.27 Both ETL and HTL are treated as recombination/generation free. Electrode work functions are assumed to be 4.2 and 4.95 eV for front contact (FC) and back contact (BC), respectively. We note that a variety of different materials are used as ETL and HTL for perovskite-based solar cells (see refs 1 and 18 and Table 1), with many of them being organic semiconductors (may be intentionally or unintentionally doped) or metal oxides with high conductivities. Hence the appropriate choice of material parameters like doping density is very crucial from a theoretical perspective. Here we first discuss the simulation results under the assumption that all materials are intrinsic in nature (however, the carrier concentration in ETL/HTL could still be significant due to contact injection; see energy band diagram in Figure 1b). We also assume that the static relative permittivity for ETL is 170 (close to reported results for TiO226), that for HTL is 5 (similar to reported results for SpiroMeOTAD28), and that for perovskite is 5. As mentioned, this simplified set of parameters serves as benchmark to explore the origin of experimentally observed ideality factor and high bias voltage exponent. Later, we also report numerical simulation results for a broad range of material parameters like doping density and dielectric constants to test the validity of model assumptions. The energy band diagram in Figure 1b provides important insights regarding the expected dark IV features of perovskitebased solar cells. Under dark conditions, the steady state current in such a device could be due to three components: (a) electron transport from FC to BC, (b) hole transport from BC to FC, and (c) electron−hole recombination in the perovskite layer (here we ignore carrier recombination at material interfaces like ETL/perovskite and perovskite/HTL). However, the presence of a large electron barrier at the perovskite/HTL interface (see Figure 1b) prevents any significant electron transport toward the BC, thus ruling out option (a). Similarly, the large hole barrier present at the ETL/perovskite interface prevents any significant hole transport toward the FC, thus negating the possibility of (b). Indeed, our simulation results indicate that there is negligible over-the-barrier transport of either type of carriers between the contact electrodes, i.e. FC and BC. (See section III of the Supporting Information.) Note that classical theory on solid state diodes predicts that either (a) or (b) could result (i.e., over the barrier transport) in a diode ideality factor of 1, while (c) could result in an ideality factor of 2, if the recombination is dominated by SRH mechanism.22 (See section IV of Supporting Information for theoretical analysis of the expected ideality factors.) Figure 3a shows the simulated dark IV characteristics (semilog plot on left y axis) and we observe that the diode ideality factor is 2, as predicted by our analysis. The current in the device can be limited through transport/ recombination in three different layers, as follows: (a) electron transport through ETL, (b) hole transport through HTL, and (c) the rate of carrier recombination in perovskite. In low to moderate bias regime, carrier transport through ETL and HTL is sufficiently high and current is limited by recombination rate in perovskite layer. At high applied bias, I−V characteristics in Figure 3a indicate an apparent saturation from the exponential

to 15%). Figure 2 shows the experimental dark IV characteristics of the cells listed in Table 1. (Fabrication details are provided in section I of the Supporting Information.) Curiously, Figure 2a indicates that all cells show an ideality factor (η) close to two, despite the fact that many of them show nonohmic shunt behavior at low biases.19 (See section II of the Supporting Information for details of extraction of ideality factors.) In addition, panel b of the same Figure shows linearity in √J (J is the current density) versus applied bias (V). Note that while Ohm’s law indicates that J ∝ V, the generalized space-charge transport20 indicates that J ∝ Vn, where n, the voltage exponent, is ≥2. Hence, our experimental trends shown in Figure 2b indicate that space-charge effects dominate the transport at high bias regime. To explore the origin of the universal features in the dark IV characteristics of perovskite-based solar cells, we performed self-consistent numerical simulation of continuity and Poisson’s equations.21,22 The device structure and the energy level alignments of various materials are shown in Figure 1a. The properties of perovskite material are similar to that of the reported values for CH3NH3PbI3−xClx (band gap 1.55 eV2,23). Shockley−Read−Hall (SRH) is assumed to be the dominant carrier recombination mechanism in perovskite. We assumed a carrier lifetime of 2.73 × 10−7 s, which along with the mobility 2 cm2/Vs gives a carrier diffusion length of 1180 nm, close to the experimentally reported values in literature.11,24 We would like to mention that recent literature reports high photoluminescence (PL) quantum efficiency for perovskite24,25 and indicates that the radiative recombination coefficient (B) is on the order of 1 × 10−10 cm3 s−1. Our detailed numerical simulations with both SRH (carrier lifetime of 2.73 × 10−7 s) and radiative

Figure 2. Experimental I−V characteristics (normalized) of perovskitebased solar cells (see Table 1 for detailed description of cell structure). (a) Semilog plot of J−V characteristics. (b) √J versus V plot. For better visualization, the voltage axis has been shifted for some cells, and the corresponding shifts are Cell A 0.2 V, Cell B 0.6 V. 4117

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Figure 3. I−V characteristics of simulated perovskite solar cell. Semilog plot, on the left y axis in panel a, shows ideality factor of 2 in the low bias regime. √J versus applied bias is plotted on the right y axis and indicates space-charge-limited transport at high bias regime. Potential drop across different layers is shown in panel b to identify the region that controls the space-charge-limited transport (electron and hole mobility values in cm2/ Vs for different materials are μ(ETL) = 0.017, 2.11, μ(HTL) = 1.64, 4 × 10−5, μ(perovskite) = 2, 2).

permittivities, 5 and 100. For each case, we consider various combinations of doping densities (see the caption of Figure 4), with the HTL being either intrinsic or p-type doped, while the perovskite is considered as either intrinsic or n-type doped (with all other parameters being the same as the case discussed in Figure 3). Interestingly, we find that the unique combination of η ≈ 2 and n ≈ 2 is possible only if the perovskite dielectric constant is low (i.e., similar to that of HTL), and both the perovskite and HTL are either intrinsic or low doped. Note that for each of the cases shown in Figure 4, the observed ideality factor directly follows from basic semiconductor device physics. For example, if the perovskite is heavily doped (n-type) and the HTL is also heavily doped (p-type), the scenario is very similar to that of the conventional P−N junction diode (with negligible over-the-barrier transport due to the band discontinuity). This results in an ideality factor of two, as expected. On the contrary, if the perovskite is heavily doped and the HTL is low doped, the entire applied bias will be dropped across the HTL, resulting in η ≈ 1, also observed in simulations. (Refer to section IV of the Supporting Information for theoretical analysis on the ideality factors.) The variation in the voltage exponent, n, can also be understood in simple terms. For heavy doping in HTL, high bias current is dominated by drift of majority carriers, and a variation as per Ohm’s law is expected with n ≈ 1. For intrinsic or low-doped HTL, space charges are significant that lead to n ≈ 2, as observed in our experimental results. Using symmetry arguments, we find that if one uses a heavily doped HTL (say PEDOT:PSS as in cell C of our study), the same conclusions would hold for the variation of material parameters in ETL and perovskite. (Similar arguments could be extended to the scenario of perovskite being p-type-doped as well.) For the devices used in this study, the perovskite was not intentionally doped. For cells D and E, the HTL was undoped, and for cell C, the ETL (PCBM) was undoped. Hence the experimentally reported universal features are indeed consistent with the choice of material parameters used in this study. Furthermore, our preliminary simulations suggest that diode ideality factor of two will be observed even for mesoporous structures in the absence of significant voltage drops across ETL/HTL. Indeed, we find the same trend in the reported experimental data (Cell B, see Table 1 and Figure 2). However, we note that it is possible for a device to exhibit an ideality factor that is different

increase observed in the low bias regime. This might be due to SCL transport through either ETL or HTL or both.29 To test this hypothesis, √Jdark versus applied bias is plotted in the same Figure (Figure 3a). A linear characteristic is observed in the high bias regime, thus confirming SCL current. (For details, see section V of the Supporting Information.) However, it is still not clear whether this feature is due to the SCL transport in ETL or HTL. To ascertain the same, the incremental potential drop across different layers is plotted in Figure 3b. We find that most of the applied bias is dropped across the perovskite layer at low bias regimes, thus resulting in SRH recombinationinduced ideality factor of 2.22 (See section IV of the Supporting Information for theoretical analysis on the observed ideality factors.) The potential drop across the perovskite saturates under high bias regimes, while the drop across ETL is negligible under all bias conditions (due to its large dielectric constant, also see Figure 3 of Supporting Information). Now it is evident that under high bias conditions most of the additional applied bias drops across HTL alone. This observation indicates that it is indeed the SCL current in HTL that controls the device characteristics under high bias regime (also supported through other arguments provided later in the discussion on the Role of HTL Mobility). Similar space-charge effects could be observed if the high bias transport is controlled by ETL as well (for example, the cell C uses PEDOT:PSS as HTL and PCBM as ETL). In fact an experimental observation of n = 2 indicates only the presence of space-charge effects, and it could be in ETL or HTL. (High carrier mobility in perovskites usually negates the possibility of any space-charge effects in the perovskite layer.) Uniqueness of the Universal Features. The simulation results shown in Figure 2 were based on the assumption that the materials are intrinsic in nature and indicate two strong trends: (a) η ≈ 2 in low bias regime and n ≈ 2 in high bias regime. However, as previously mentioned, the exact doping conditions of many of the reported experimental devices are either unknown or poorly characterized. Similarly, there exist some conflicting reports on relative permittivity of perovskites. Hence, to test the claims of universality of η ≈ 2 and n ≈ 2, we performed extensive simulations over a broad range of material parameters, and the results are summarized in Figure 4. Here we assume that ETL is heavily doped (n type, 1018 cm−3). For the perovskite, we consider two different relative 4118

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Figure 4. Dependence of ideality factor (η) and voltage exponent (n) on HTL and perovskite properties. The ETL is assumed to be heavily doped and HTL relative permittivity is assumed to be 5. It is evident that the unique observation of η ≈ 2 and n ≈ 2 can be obtained only when the HTL and perovskite are either intrinsic or low-doped in nature with perovskite dielectric constant being similar to that of the HTL. If any of these conditions are not met, then we observe that either the voltage exponent or the ideality factor will not be 2. Here L indicates a doping density of 1 × 1014 cm−3, H indicates a doping density of 1 × 1018 cm−3, and I indicates that the material is intrinsic.

dielectric constant of perovskites obtained through impedance spectroscopy measurements.17 This is clearly a topic that requires further research, and our results (Figure 4) indicate that experimental claims of extremely large dielectric constants for perovskite should also be supported by corresponding experimental observation of ideality factor and voltage exponents. This additional check could indeed lead to better understanding of the device physics. Role of Carrier Lifetime on Performance. The model results can be used to obtain quantitative information about the carrier lifetime (τ) and hence the eventual performance of the solar cells. Detailed balance under open circuit conditions indicates that the photogeneration rate (G) should be equal to the recombination rate, R. For the E-B diagram shown in Figure 1b with SRH recombination,22 we have R ≈ ni exp(qVOC/2kT)/2τ, where ni is the intrinsic carrier concentration in perovskite, VOC is the open-circuit potential of the cell, and kT/q is the thermal voltage. Accordingly, we find that the VOC of the cells should scale logarithmically with the generation rate and the carrier lifetime as

from two for the following conditions other than listed in Figure 4: (a) significant over-the-barrier transport could result in ideality factors closer to 1 (this is due to nonideal blocking effects of ETL/HTL, see Figure 1b), (b) significant voltage drop in ETL/HTL could result in an ideality factor larger than two (this is similar to the series resistance effect), and (c) parasitic shunt effects (could result in ideality factor larger than two), nonideal contact properties, trap-limited transport in various layers, radiative process being the dominant carrier recombination mechanism in perovskite (this could result in an ideality factor closer to 1), and so on. In addition, the voltage exponent will asymptotically reach 1 if any series resistance effects dominate the device performance. We would also like to mention that transient effects could result in some interesting observations in dark IV characteristics, similar to those reported for light IV characteristics,30 which needs to be explored further. Relative Permittivity of Perovskites. The analysis and simulation results shown in Figure 4 support the universal features of dark IV characteristics of perovskite-based solar cells: (a) The low bias regime should exhibit a diode ideality factor of two and (b) the high bias regime is due to SCL transport. Interestingly, our simulations also indicate that the ideality factor will be 1 if the relative permittivity of perovskite is on the order of 100 (or more, as suggested by recent reports17) for all cases except when the HTL is heavily doped (see Figure 4, the section for high dielectric constant of perovskites). These interesting results can be understood as followsthe potential drop across any region is affected by the relative permittivity and the profile of space charge (Poisson’s equation, ∇2ϕ = ρ/εrε0). Hence, if the perovskite dielectric constant is large (say, εr = 1000), it is expected that the band bending in the same region would be much smaller than the case illustrated in Figure 1b. Under such conditions, the entire applied bias will be dropped across the HTL layer, with negligible potential drop in the perovskite layer, resulting in an ideality factor of one. (See Figure 4 of the Supporting Information for a comparison of E-B diagrams). If the HTL is also heavily doped, then the band bending will be across the perovskite, resulting in an ideality factor close to 2. However, as previously discussed and shown in Figure 4, a highly doped HTL will always show a voltage exponent of one. (Also see section IV of the Supporting Information.) Hence, the unique experimental observation of η ≈ 2 and n ≈ 2 indicates a significant potential drop across the perovskite layer and hence does not support the recent reports on giant

VOC =

2kT ⎛ 2Gτ ⎞ ln⎜ ⎟ q ⎝ ni ⎠

(1)

Equation 1 indicates that VOC versus light intensity (in a semilog plot) shows a slope of 2kT/q if the perovskite is intrinsic and SRH is the dominant recombination mechanism. A similar analysis indicates that VOC versus light intensity shows a slope of kT/q if perovskite is heavily doped (with SRH as dominant recombination mechanism) or if the radiative process is the dominant carrier recombination mechanism (regardless of perovskite doping). Hence the slope of VOC versus light intensity is an important characterization tool that gives valuable information on the dominant recombination mechanism in the device.31 It can also give valuable insight into the relative magnitude of perovskite doping, if any. Recently, Bi et al.32 reported the variation of VOC versus light intensity with slope close to 2kT/q, thus further validating the model predictions (and also the assumption of intrinsic properties for perovskite and SRH as the dominant recombination mechanism at low injection levels). Equation 1 also indicates that it is very crucial to improve carrier lifetimes to achieve better efficiency. Role of HTL Mobility. Table 1 and Figure 2b indicate that SCL transport is observed for all devices despite the fact that 4119

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different materials are used for HTL (or ETL). To validate the robustness of the model predictions on SCL transport, we performed simulations for a wide range of HTL thicknesses and hole mobilities. SCL transport was observed in all I−V characteristics. The back-extracted effective mobility (from the slope of √J versus V curve, refer to section VI of the Supporting Information for details) from simulated IV characteristics is plotted in Figure 5a for different HTL thicknesses. We note that for large HTL thickness the extracted mobility is very close to the HTL mobility used in simulation, thus confirming model predictions. For small HTL thickness, the extracted mobility deviates from the HTL mobility (by a factor of two) indicating that the carrier transport in other layers is also significant. Furthermore, the back-extracted mobilities from the experimental data (provided in Figure 2) are plotted in Figure 5b. The extracted values are well within the range of reported mobilities for the corresponding materials.27,28,33−36 This is significant as literature reports much higher values for perovskite mobilities (>1 cm2/Vs11,37), thus indicating that the SCL behavior in these devices is not caused by charge transport in perovskite layer. We note that SCL behavior could also arise due to transport limitations in ETL as well, and the proposed method can be used to extract effective mobilities for such cases also (e.g. Cell C of this study). Figure 5b and the efficiencies provided in Table 1 allow us to draw definite conclusions on the role of ETL/HTL mobility on device performance. It is evident that better ETL/HTL mobility yields better performance (mainly through better FF; see Table 1). Hence, we identify that carrier lifetime in

perovskite (see eq 1) and ETL/HTL mobilities are the two most important parameters that control performance, and further research should focus on improving these material parameters for better efficiency. To summarize, here we showed, for the first time, that the dark IV characteristics of perovskite-based solar cells exhibit certain universal features. Through detailed numerical modeling we identified the underlying physics behind these universal features. In addition, we also provided extensive experimental datafrom champion cells reported in literature to our own devicesthat confirm the model predictions. Our results are of broad significance to the community as they provide a unique benchmark to which experimental results from various laboratories could be compared. Furthermore, we identify the key functional parameters that limit performance, discuss the role of characterization schemes, and elucidate on the broad applicability of these theoretical predictions.

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ASSOCIATED CONTENT

S Supporting Information *

(a) Device fabrication details, (b) ideality factor extraction for experimental devices, (c) simulation results to show that the terminal current is dictated by recombination in perovskite layer, (d) detailed theory on ideality factors and voltage exponents to support the numerical simulation results, (e) ideality factor and voltage exponent extraction for simulation results, and (f) extraction of mobility using Mott−Gurney relation. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*S.A.: E-mail: [email protected]. *P.R.N.: E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This paper is based on work partially supported by the Solar Energy Research Institute for India and the United States (SERIIUS), funded jointly by the U.S. Department of Energy (under subcontract DE-AC36-08GO28308) and the Govt. of India’s Department of Science and Technology (under subcontract IUSSTF/JCERDC-SERIIUS/2012). The authors also acknowledge the Center of Excellence in Nanoelectronics (CEN) and National Center for Photovoltaic Research and Education (NCPRE), IIT Bombay for computational, device fabrication, and characterization facilities. M.A.G.N. acknowledges funding from Department of Science and Technology (DST/TM/SERI/2k11/73(G)), Solar Energy Research Initiative project, Ministry of Human Resource Development, and Govt. of India.

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Figure 5. Effective mobility extraction from IV data (from the high bias regime, using Mott−Gurney relation29). Panel a shows the extracted mobility for simulated cells for various HTL thicknesses (d) with other parameters kept the same. Panel b shows extracted mobility values for experimental results shown in Figure 2. The extracted mobility values are in the expected range of hole mobilities in HTL (as PEDOT:PSS is heavily doped, ETL thickness was used for Cell C and extracted mobility is electron mobility in ETL) and are much smaller than the reported carrier mobility in perovskite (shown by the dotted lines).

REFERENCES

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The Journal of Physical Chemistry Letters

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dx.doi.org/10.1021/jz5021636 | J. Phys. Chem. Lett. 2014, 5, 4115−4121