Model for the Prediction of the Lifetime and Energy Yield of Methyl

Subscriber access provided by UNIV AUTONOMA DE COAHUILA UADEC

Energy, Environmental, and Catalysis Applications

Model for the Prediction of the Lifetime and Energy Yield of Methyl Ammonium Lead Iodide Perovskite Solar Cells at Elevated Temperatures João Pedro Bastos, Griet Uytterhoeven, Weiming Qiu, Ulrich Wilhelm Paetzold, David Cheyns, Supriya Surana, Javier Rivas, Manoj Jaysankar, Wenya Song, Tom Aernouts, Jef Poortmans, and Robert Gehlhaar ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b00923 • Publication Date (Web): 18 Apr 2019 Downloaded from http://pubs.acs.org on April 18, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 14 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

ACS Applied Materials & Interfaces

Model for the Prediction of the Lifetime and Energy Yield of Methyl Ammonium Lead Iodide Perovskite Solar Cells at Elevated Temperatures João P. Bastos,*†‡ Griet Uytterhoeven,† Weiming Qiu,† Ulrich W. Paetzold,†⟘ David Cheyns,† Supriya Surana,†§ Javier Rivas,‖ Manoj Jaysankar,†‡ Wenya Song,†‡ Tom Aernouts,† Jef Poortmans†‡# and Robert Gehlhaar† † Imec

- part of Solliance, Kapeldreef 75, 3001 Heverlee, Belgium of Electrical Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001, Leuven, Belgium ⟘ Institute of Microstructure Technology, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Karlsruhe, Germany § Department Physics, Katholieke Universiteit Leuven, Celestijnenlaan 200d, B-3001, Leuven, Belgium ‖ Faculty of Science, University La Laguna, 38200 San Cristóbal de La Laguna, Spain # Institute for Materials Research & IMEC-associated lab IMOMEC, Hasselt University, Wetenschapspark 1, B-3590 Diepenbeek, Belgium ‡ Department

KEYWORDS: Perovskite Solar Cells, Stability, Degradation, High temperature, Lifetime, Energy yield, Methyl Ammonium Lead Iodide ABSTRACT: With the realization of highly efficient perovskite solar cells, the long-term stability of these devices is the key challenge hindering their commercialization. In this work, we study the temperature dependent stability of perovskite solar cells and develop a model capable of predicting the lifetime and energy yield of perovskite solar cells outdoors. This model results from the measurement of the kinetics governing the degradation of perovskite solar cells at elevated temperatures. The individual analysis of all the key current-voltage parameters allows for the prediction of the device performance under thermal stress with high precision. An extrapolation of the device lifetime at various European locations based on historical weather data illustrates the relation between the laboratory data and real-world applications. Finally, the understanding of the degradation mechanisms affecting perovskite solar cells allows to define and implement strategies to enhance the thermal stability of perovskite solar cells.

INTRODUCTION The rapid increase of the power conversion efficiency (PCE) of perovskite solar cells (PSC) makes this thin-film technology a promising candidate for future low-cost solar energy harvesting. However, the limited lifetime of these devices hinders their large-scale uptake and economical breakthrough. To improve the stability, extensive research was directed towards understanding the stability limitations of state-of-the-art devices. Recent results show that the losses in performance caused by light-soaking at room temperature are recoverable,1,2 but that the losses caused by elevated temperatures alone3–5 or by lightsoaking at elevated temperatures1,6 are not. Therefore, thermal stress is a significant source of degradation to PSC and understanding the degradation mechanisms it triggers is essential to improve the lifetime of these devices.

Previous work studying the effects of thermal stress of PSC focused mostly on identifying novel materials and processes to enhance the stability of the devices, or on studying the degradation mechanisms. Proving that a new material can extend the lifetime of a devices at elevated temperatures demonstrates a pathway for stability improvement,7–10 but provides limited information about the reasons for this increased lifetime. Understanding the degradation mechanism allows for the development of specific solutions that can effectively prevent the degradation. For the case of methyl ammonium lead iodide (MAPI)-based PSC, the most commonly studied perovskite absorber material, the degradation mechanisms are usually associated with either MAPI or the hole transport layer (HTL). MAPI decomposes via the breakdown of the organic cation by two simultaneous reactions: eq. 1, which is dominant,5,11 and eq. 2, which is

ACS Paragon Plus Environment

ACS Applied Materials & Interfaces 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

Page 2 of 14

Figure 1 - Evolution of the device parameters of devices stored isothermally at 23 °C, 50 °C, 63 °C and 85 °C in N2: a) PCE; b) Jsc; c) Voc and d) FF.

thermodynamically favored but kinetically hindered.12 The activation energy of this decomposition reaction is reported to be 1.24-1.54 eV in non-reactive atmospheres.13,14 𝐶𝐻3 𝑁𝐻3 𝑃𝑏𝐼3 (𝑠) → 𝑃𝑏𝐼2 (𝑠) + 𝐶𝐻3 𝑁𝐻2 (𝑔) + 𝐻𝐼(𝑔) (𝑒𝑞. 1) 𝐶𝐻3 𝑁𝐻3 𝑃𝑏𝐼3 (𝑠) → 𝑃𝑏𝐼2 (𝑠) + 𝑁𝐻3 (𝑔) + 𝐶𝐻3 𝐼(𝑔) (𝑒𝑞. 2) The thermal degradation associated with the most common HTL, 2, 2', 7, 7' – Tetrakis [N, N-di(4methoxyphenyl)amino] - 9, 9'-spirobifluorene (spiroMeOTAD), is related to the additives of the layer. A pure spiro-MeOTAD layer is stable up to its intrinsic glass transition temperature (Tg) of 124 °C, which should render this layer stable up to that temperature. However, the cosolvent 4-tert-Butylpyridine (tBP) which is added to increase the solubility of the dopant Bis(trifluoromethane)sulfonimide lithium salt (LiTFSI),15 acts as a plasticizer, reducing the Tg of spiro-MeOTAD from 124 °C to 72 °C.16 Heating devices above the Tg of spiroMeOTAD leads to crystallization, which reduces the performance of the devices.4,16,17 Furthermore, heating at 120 °C results in voids in the spiro-MeOTAD layers with both LiTFSI and tBP, but not in spiro-MeOTAD layers with only one of the additives, or in neat films.18 Thus, temperatures higher than 70 °C induce multiple failure mechanisms on spiro-MeOTAD layers.

One alternative to spiro-MeOTAD is Poly [bis (4-phenyl) (2,4,6-trimethylphenyl) amine] (PTAA), a polymer with a chemical structure similar to spiro-MeOTAD. The Tg of PTAA (94 °C) is lower than that of spiro-MeOTAD, but since PTAA requires a smaller amount of LiTFSI than spiroMeOTAD, less tBP is added. As a consequence, replacing spiro-MeOTAD by PTAA should increase the thermal stability of MAPI-based devices. The key challenge ahead is to understand the degradation mechanisms triggered by thermal stress, quantify their related losses and kinetics, and produce a model that can predict the lifetime and energy yield of PSC based on weather data. In this work, we examine the impact of thermal stress on each key current-voltage parameter and quantify the losses associated with each degradation mechanism. More specifically, we extract the activation energy and pre-exponential factors governing the kinetics of each degradation mechanism and describe the losses by a function. Based on the functions derived for each parameter, we can derive a model that describes the PCE degradation of the devices over time. This description of the PCE as a function of temperature and time permits an estimate of the lifetime and energy yield of devices in a given location through the utilization of historical weather data. Furthermore, the understanding of all the degradation mechanisms enables the development of new strategies to enhance the lifetime of perovskite solar cells.

2 ACS Paragon Plus Environment

Page 3 of 14 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


RESULTS AND DISCUSSION Selection of the Most Stable Hole Transport Layer Firstly, we compare the thermal stability of devices with the two different HTLs: spiro-MeOTAD and PTAA, to select the most stable device structure. The devices are fabricated on glass substrates with pre-patterned Indium Tin Oxide (ITO) layer as transparent electrode in the following layer sequence: e-beam TiO2 as electron transport layer, MAPI as photo-active layer, a HTL, and Au as reflective contact. The PCE of nine devices with each HTL is 12.1 ± 1.1 % for PTAA and 12.5 ± 0.7 % for spiro-MeOTAD (see Table S-1 for more details). The devices with the two different HTLs are compared side-by-side by storing them in N2, in the dark, at 85 °C in between measurements. The PCE of devices with spiro-MeOTAD decreases faster than the PCE of devices with PTAA (Figure S-1a). The cause for the faster PCE reduction of the devices with spiroMeOTAD is the additional reduction of fill factor (FF) compared with the devices with PTAA (Figure S-1b). The better stability at elevated temperatures of devices with PTAA is expected due to the smaller amount of the plasticizer tBP added to PTAA. Therefore, the study of the intrinsic stability continues with the more thermally stable structure: ITO / TiO2 / MAPI / PTAA / Au. For a more detailed study a new batch of devices with PTAA as HTL is prepared and stored in N2, in the dark, and at constant temperatures: 23 °C, 50 °C, 63 °C or 85 °C, only removed from the heating plates for measurements at predetermined times (Figure 1). Two sets of at least nine devices were tested at each temperature, and the average initial PCE of the 78 devices is 11.4 ± 0.8 % (see Table S-2 for more details). Devices stored at temperatures up to 63 °C present minor losses of PCE, associated with reductions of the open-circuit voltage (Voc) and fill factor (FF). Devices stored at 85 °C show an increased loss of PCE, which can be accounted by a reduction of the short-circuit current density (Jsc). The causes for the performance reduction are analyzed in more detail in dedicated sections for each parameter. Investigation of the Degradation Mechanisms and Quantification of its Impact and Kinetics In this section the degradation mechanisms triggered by elevated temperatures are investigated for each device parameter. Then the losses and kinetics associated with each degradation mechanism are quantified. These investigations serve as the base for the model to estimate the loss of performance of devices in isothermal conditions. The Reduction of the Short-Circuit Current Density The reduction of Jsc in devices stored at 85 °C is accompanied by a color change in the sample, which acquires a more yellow appearance with time (Figure S-2a). This change in appearance indicates that MAPI degrades progressively with PbI2 staying behind while the organic components volatilize.7 The color change is caused by a reduction in absorption of the devices in the range of MAPI (450-800 nm, Figure S-2b) and the absorption spectrum

becomes more similar to that of devices with PbI2 as the active layer (ITO / TiO2 / PbI2 / PTAA / Au, Figure S-2b). To better understand the chemical transformations of MAPI, ITO / TiO2 / MAPI layer stacks are either stored at 23 °C or 100 °C for 100 h in N2, in the dark, and then measured by Time-of-Flight Secondary Ion Mass Spectroscopy (ToFSIMS). The thermally stressed stacks exhibit yellow coloration and only low counts of the of methyl ammonium ion (CH3NH3+). This contrasts with the reference pristine stack, which has a strong methyl ammonium ion signal (Figure S-2c). Therefore, absorption and ToF-SIMS measurements confirm that the loss of Jsc is caused by the loss of methyl ammonium, the cation of MAPI, as described by eqs. 1 and 2. To continue the study of Jsc reduction, the Jsc values are corrected and normalized (Figure S-3). The reduction of Jsc is caused by the reduction of the charge-generating phase, i.e. the fraction of MAPI, because charge collection is barely affected (Figure 1d shows negligible FF losses even for devices at 85 °C). Therefore, the Jsc can be directly related to the charge-generating phase, i.e. MAPI, by: 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝐽𝑠𝑐 (𝑡) = 𝛿(𝑡) = 1 − 𝜑(𝑡)

(𝑒𝑞. 3)

where δ is the fraction of MAPI and φ is the fraction of PbI2. The Jsc of the devices stored at 85 °C follows a ‘s-shaped’, or sigmoidal, curve and provides an indication of the mechanism behind the degradation. During a solid-state reaction, like MAPI decomposition, the fraction of the original phase can be described by a set of general functions.19–21 For diffusion driven reactions, the fraction of the original phase diminishes with a single decay over time, while in autocatalytic reactions, and in reactions involving the nucleation and growth of a new phase, the fraction of the original phase follows a sigmoidal curved over time. The sigmoidal shape of the Jsc curve readily dismisses the hypothesis that MAPI degradation is driven by the simple diffusion of methyl ammonium (CH3NH3), or its decomposition products, from the device. Moreover, the degradation reaction is not auto-catalytic (eqs. 1 and 2). Consequently, the best hypothesis is that the degradation of MAPI is driven by the nucleation and growth of a new phase, PbI2. The Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation was developed to describe the nucleation and growth of a new phase from the original phase and was already utilized to describe the degradation of MAPI into PbI2 in humid air.22 Thus, we fit the normalized Jsc curves with the JMAK equation: 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝐽𝑠𝑐 (𝑡) = 𝛿(𝑡) = 𝑒 (−𝑘𝐽𝑀𝐴𝐾×𝑡

𝑛𝐽𝑀𝐴𝐾 )

(𝑒𝑞. 4)

where nJMAK is the JMAK exponent, and kJMAK is the JMAK reaction rate. Unlike most reaction rates, the kJMAK is a complex rate constant of the nth order, hence the unit is t-n. The higher reactional order of kJMAK incorporates both the nucleation and the growth reactions, which can themselves have an order higher than one. The Jsc curves of devices



Page 4 of 14

Figure 2 – Extraction of the parameters governing of the Jsc reduction: a) Overlay of experimental data (solid line and error margin) and fits with the JMAK functions with nJMAK =3.2 (dashed lines); b) Calculation of the activation energy and attempt rate from the reaction rates (grey line) obtained from the fits with the JMAK functions with nJMAK =3.2 of the Jsc degradation at different temperatures (black circles).

tested at different temperatures are simultaneously fitted with a fixed nJMAK. The lowest sum of residuals from the simultaneous fits, and therefore the best fit, are obtained with nJMAK = 3.2 (Figure 2a and S-4a). The activation energy (Ea,MAPI) and attempt rate (AMAPI, with units t-n) of the reaction can be extracted from the kJMAK at different temperatures, since they are related through the Arrhenius equation:

𝑘𝐽𝑀𝐴𝐾 (𝑇) = 𝐴𝑀𝐴𝑃𝐼 × 𝑒

𝐸𝑎,𝑀𝐴𝑃𝐼 (− ) 𝑘𝐵 𝑇

(𝑒𝑞. 5)

where kB is the Boltzmann constant (8.62.10−5 eV K-1) and T is the absolute temperature (K). From the plot of the 1/(kBT) vs log(kJMAK) the Ea,MAPI and AMAPI are extracted from the slope and intercept with the y axis, respectively (Figure 2b). The degradation of the MAPI in devices has an Ea,MAPI = 1.83 eV, and an AJMAK = 4.8 x 1016 h-3.2. This Ea,MAPI is larger than previous reports (by 0.29-0.59 eV) and this difference can be due to the utilization of different atmosphere (N2 in this work vs vacuum13), MAPI configuration (film in device in this work vs powder14), experimental method (isothermal measurements in this work vs ramped profile14) or experimental errors. Based on the extracted values, the evolution of Jsc over time in isothermal conditions can be represented by:

degradation on-set with the values obtained by TGA. We note that only the values of the degradation on-set can be directly compared, because eq. 7 describes the fraction of existing MAPI and TGA measures the remaining sample weight. This implies that right after the loss of the organic components there will be no MAPI according to eq. 7, but 74 wt% of the initial mass is still left as PbI2 in the TGA measurement. The prediction of the on-set degradation of MAPI based on the JMAK equation and the Ea,MAPI and AMAPI is 290 °C (Figure 3), which is about 10% lower than the reports based on TGA.11 The reasonable description of MAPI degradation both in isothermal and temperature ramp conditions by eq. 6 utilizing the derived Ea,MAPI and AMAPI validates the use of this equation. Moreover, these results explain the seemingly conflicting observations of on-set of degradation temperatures below 100 °C in isothermal tests3,4 and of approximately 300 °C in TGA measurements.11,23 This large difference is explained by the relatively high Ea,MAPI that coupled with the fast ramp rates utilized in TGA measurements leads to high on-sets for degradation (see figure S-5 for the dependence of the on-set of temperature on the temperature ramp and Ea). 𝛿(𝑡, 𝑇) 𝑑𝛿 𝑑𝑇 = × = 𝑑𝑡 𝑑𝑇 𝑑𝑡 (−A ×𝑡 𝑛 ×𝑒 A × 𝑡 𝑛 × 𝐸𝑎 (− × 𝑒 𝑘𝐵 × 𝑇 2

𝐸 (−𝑘 𝑎 ) 𝐸𝑎 𝐵×𝑇 − ) 𝑘𝐵 ×𝑇

)×

𝑑𝑇 𝑑𝑡

(𝑒𝑞. 7)

𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝐽𝑠𝑐 (𝑡, 𝑇) = 𝛿(𝑡, 𝑇) = (−𝐴𝑀𝐴𝑃𝐼 ×𝑒

𝑒

𝐸𝑎,𝑀𝐴𝑃𝐼 (− 𝑘 𝑇 ) 𝑛 𝐵 ×𝑡 𝐽𝑀𝐴𝐾 )

(𝑒𝑞. 6)

As this model is supposed to be a general description for the degradation of MAPI, we compare its prediction for a ramped temperature profile with thermogravimetric analysis (TGA) measurements. For this, we calculate the partial derivative of eq. 6 with respect to time (eq. 7), utilize the derived Ea,MAPI and AMAPI, the ramp rate typically utilized in TGA measurements (10 °C/min)11 and compare the

Moreover, we note that our suggestion that MAPI degrades by nucleation and growth of PbI2 agrees with the observation of ‘islands’ of a new phase appearing on MAPI upon its decomposition.24,25 To gain a better understanding about the location and process for the nucleation and growth of PbI2, we simulate this process for different conditions (see Figure S-6 for more details). The simulations indicate that the nucleation of PbI 2 is best described by nucleation at a constant rate at the edges of the active area (Figure S-7). This insight from the simulation is


Page 5 of 14 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


Figure 3 - Prediction of the MAPI degradation under ramped temperature conditions similar to TGA. The plot is based on eq. 7, the extracted Ea,MAPI and AMAPI, and a ramp rate of 10 °C/min.

Figure 4 - Fitting of the initial Voc reduction caused by oxygen desorption: a) fits (dashed lines) with an exponential decay with a fixed asymptote; b) activation energy and attempt rate derived from the fits; c) comparison between the experimental values (solid lines) and the equation derived (dashed lines) to describe the progression of the Voc; d) Voc values after removal of the exponential fit.

in good agreement with the pictures of the substrates captured during the experiment (Figure S-2a). The pictures show an initial conversion of MAPI into PbI2 in areas without gold contact, i.e., outside the active area, and then a progression of the yellow areas into the active area. The extracted data also suggests additional information about the degradation mechanism. Fractional nJMAK are associated with either diffusion-controlled growth, or distributions of sizes or shapes of reactant particles.21 The

recipe used to produce the samples results in MAPI films composed of crystals with uniform shapes and sizes.26 Consequently, the reason for the fractional exponent should be the diffusion-controlled growth of PbI2. This hypothesis is plausible, because the degradation reaction of MAPI produces gaseous products that need to diffuse out for the reaction to proceed (in agreement with the results of section 2.5).9,13 Moreover, this hypothesis could also explain the higher Ea,MAPI derived in this work.



Page 6 of 14

Figure 5 – The Voc recovery is associated with PbI2 passivation of MAPI: a) Fitting of Voc decay as a function of φ; b) Experimental values with new equation to describe the Voc recovery.

In summary, eq. 6 provides a rational description of the evolution of Jsc over time. This description has two major implications: firstly, there is no lower temperature threshold for the degradation of MAPI in devices. This degradation happens rather progressively, according to the Ea,MAPI and AMAPI values and the extent of the degradation depends on the thermal history of the device; secondly, the extracted Ea,MAPI and AMAPI values imply that MAPI devices will degrade, even for mild operation conditions. The Reduction of the Open-Circuit Voltage The evolution of Voc for devices stored at 85 °C is dictated by three mechanisms: Voc first decreases in the very first hours, then increases, reaching a maximum at 350 h, and finally decreases again (Figure 1c). These behaviors indicate that thermal stress induces two degradation, and one recovery, mechanisms that affect Voc. We relate the initial Voc decrease to the desorption of molecular oxygen that passivates the MAPI during airexposure of the device. We observe a lower Voc in devices without air-exposure during fabrication compared to Voc of air-exposed devices (Figure S-8a). The higher Voc is only related to the exposure of MAPI to air and not to the doping of HTL, because devices in which MAPI was exposed to air before HTL deposition have a Voc as high as devices with the standard recipe (Figure S-8a). These observations are in line with the reports of molecular oxygen quickly adsorbing into MAPI27 and passivating it.28–30 Therefore, the higher Voc of air-exposed devices must be due to passivation of MAPI by molecular oxygen. Moreover, when the air-doped devices are stored in N2 at room temperature, their Voc progressively decreases to the value of the devices that were not air-doped (Figure S-8b). This decrease of Voc suggests that oxygen desorbs from MAPI in an atmosphere with low oxygen partial pressures. Desorption of molecular oxygen from MAPI is a first order reaction (a reaction depends only on the concentration of one reactant), as it can be seen from the reaction: 𝑂2 (𝑎𝑑𝑠) → 𝑂2 (𝑔). For a first order reaction the concentration of a reactant over time is described by a mono-exponential decay.31 Thus, in line with the hypothesis that the initial Voc decrease is caused by

desorption of molecular oxygen, we fit the initial reduction of the Voc with an exponential function of the form: 𝑉𝑜𝑐 (𝑡) = 𝑉𝑜𝑐,∞ + ∆𝑉𝑜𝑐,𝑜𝑥𝑦 𝑒 −𝑘𝑉𝑜𝑐,𝑜𝑥𝑦×𝑡 [𝑉]

(𝑒𝑞. 8)

where Voc,∞ is the asymptotic value, ΔVoc,oxy the extra opencircuit voltage provided by oxygen passivation, and kVoc,oxy the rate of the exponential decay (Figure 4a). The activation energy (Ea,oxy) and attempt rate (Aoxy) for Voc,oxy decay are calculated from the rate constants (Figure 4b), like for Jsc. The ΔVoc,oxy has Ea,oxy = 0.79 eV and Aoxy = 3.0×1010 h-1 (Figure 4c). This activation energy closely matches the 0.72 eV obtained by density functional theory (DFT) calculations for the adsorption of oxygen on positively charged iodide vacancies on the {001} planes of MAPI.30 The adsorption of oxygen on positively charged iodide vacancies is a reasonable hypothesis, because positively charged iodide vacancies are expected to exist spontaneously at room temperature in the dark32 and to be created by electric fields applied to MAPI.33 Moreover, adsorption of oxygen on iodide vacancies has already been suggested due to the similarity in size of oxygen and iodide.27 The additional energy compared to the DFT calculations can be related to the additional step of diffusion through the HTL and contact. The fits associated with oxygen desorption are subsequently subtracted from the Voc curves to increase the visibility of the remaining trends (Figure 4d). The modified data evidence an increase of Voc for the devices stored at 63 °C and 85 °C. These are also the only storage temperatures at which the devices present a sizeable reduction of Jsc. Side-by-side comparison of the variation Voc and Jsc shows that similar losses of Jsc result in the similar gains of Voc (Figure S-9). These observations indicate that the increase in Voc is linked to the conversion of MAPI into PbI2. Small amounts of PbI2 have been suggested to passivate MAPI and other perovskites.34,35 In one of the reports, an increase in Voc of 0.05-0.06 V was attributed to PbI2 passivation,35 very similar to the 0.07 V increase we observe for a 6 % reduction of Jsc. Moreover, Matsumoto et al. also reported a Voc increase of 0.06-0.07 V after a Jsc


Page 7 of 14 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


Figure 6 - Second Voc decay is related to the reduction of Jsc: a) Voc decay shows expected dependence on Jsc; b) Experimental Voc values vs the more complete Voc description.

reduction caused by MAPI degradation.36 Thus, the relation between the PbI2 fraction (φ = 1-δ = 1- normalized Jsc) and Voc increase is parameterized with an exponential function (Figure 5a). This exponential function converges to 0.07 V (Voc,PbI2) and has a decay constant (kPbI2) of 25. The ‘PbI2 fraction’, φ, is substituted by the equation describing Jsc (eq. 5), according to φ = 1- normalized Jsc. This additional Voc component is added to eq. 8 resulting in a more complete description of the Voc (Figure 5b). Further conversion of MAPI into PbI2 reduces the Voc of the devices. The impact of decreased carrier generation is clear for samples stored at 85 °C, for which a Jsc reduction larger than 6% (or a conversion of more than 6% of MAPI into PbI2) results in a second reduction of Voc (Figure S-10). The relation between the loss of Jsc and reduction of Voc is established by rearranging the photo-diode equation as a function of Voc: ∆𝑉𝑂𝐶,𝑙𝑜𝑠𝑠 (𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝐽𝑠𝑐 ) = 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝐽𝑠𝑐 𝑛 ∙ 𝑉𝑡 ∙ ln ( ) [𝑉] 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝐽𝑠𝑐,𝑖𝑛𝑖𝑡𝑖𝑎𝑙

(𝑒𝑞. 9)

where n is the ideality factor of the diode, Vt the thermal voltage, the normalized Jsc at a given time is given by eq. 6, and normalized Jsc,initial, is 1. A good match with the data is achieved by including the corresponding values of n = 2.3, Vt = 0.028 V (the equilibrium temperature in the solar simulator is 50 °C) (Figure 6a). This component is then added to the description of Voc reduction. To be compatible with the description of the normalized Jsc, we also normalize the full description of the Voc over time, with Voc,t=0 being the initial Voc value:

𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑉𝑜𝑐 (𝑡, 𝑇) = (𝑉𝑜𝑐,∞ + ∆𝑉𝑜𝑐,𝑜𝑥𝑖 × 𝑒

−𝐴𝑉𝑜𝑐,𝑜𝑥𝑖 ×𝑒

𝐸𝑎,𝑜𝑥𝑖 (− ) 𝑘𝐵 𝑇

×𝑡

+

))

−

𝐸𝑎,𝑀𝐴𝑃𝐼 (− ) 𝑘𝐵 𝑇 𝑛 𝐴𝑀𝐴𝑃𝐼 ×𝑒 ×𝑡 𝐽𝑀𝐴𝐾

−𝑘𝑃𝑏𝐼2 × 1−𝑒 (

∆𝑉𝑜𝑐,𝑃𝑏𝐼2 − ∆𝑉𝑜𝑐,𝑃𝑏𝐼2 × 𝑒 ( 𝑛 × 𝑉𝑡 × (𝐴𝑀𝐴𝑃𝐼 ×

)

( 𝐸𝑎,𝑀𝐴𝑃𝐼 (− ) 𝑘𝐵 𝑇 𝑒

× 𝑡 𝑛𝐽𝑀𝐴𝐾 ))/𝑉𝑜𝑐,𝑡=0

The three mechanisms that impact Voc are explained and parametrized. The first decay of Voc of 0.10 V is due to desorption of oxygen from MAPI. Then a recovery of 0.07 V is observed when 6 % of MAPI is converted into PbI2, which passivates the remaining MAPI. A further loss of MAPI reduces the Jsc and causes a loss of Voc. The Reduction of the Fill Factor The FF of all devices presents a reduction of 10% that is mostly independent of the storage temperature of the devices. For temperatures below 85 °C the FF reduction happens in the initial 10 h and saturates, while for the devices at 85 °C the reduction happens in two stages and appears to stabilize. An approximate description of the progress of the FF of the devices at different temperatures is obtained by the fit with a mono-exponential decay, where FF∞ is the asymptotic value of FF, ΔFF is the excess of FF and kFF is the decay rate. The average of the extracted values are: FF∞ = 63.3, ΔFF = 6.2 and kFF =0.1 h-1(Figure S-11). Again, for compatibility, we normalize the FF to the initial value, FFt=0: 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝐹𝐹(𝑡) = (𝐹𝐹∞ + ∆𝐹𝐹𝑒 (−𝑘𝐹𝐹×𝑡) )⁄𝐹𝐹𝑡=0 (𝑒𝑞. 11)

Reduction of the Power Conversion Efficiency and Calculation of Device Lifetimes and Energy Yield The normalized PCE can be obtained through the product of the normalized device parameters Jsc, Voc and FF. Based on the equations derived above, the normalized PCE is


(𝑒𝑞. 10)


Page 8 of 14

Figure 7 – Good agreement between the experimental PCE values (solid lines) and the derived equations (dashed lines), for devices stored at: a) 23 °C; b) 50 °C; c) 63 °C; d) 85 °C. For all temperatures except 23 °C each solid line is the average of two substrates with minimum of nine working cells.

described in eq. 12. This equation agrees qualitatively and quantitively with the measured values, mostly falling within experimental error. Therefore, the equation can be utilized to estimate the PCE of a device after a certain time at a fixed temperature. For instance, the lifetime of a device (usually defined at the time to reach 80 % of the initial efficiency, t80) can be easily estimated graphically and the graphs in Figure 7 illustrate that t80 is reached within 1000 h at all storage temperatures. Interestingly, the fast initial PCE loss is due to the quick decays of the FF and Voc, although the largest losses in the long term are caused by the Jsc reduction. If the burn-in caused by FF and Voc is disregarded, the devices are stable for more than 1000 h at temperatures up to 63 °C. 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑃𝐶𝐸(𝑡, 𝑇) = 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝐽𝑠𝑐 (𝑡, 𝑇) × 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑉𝑜𝑐 (𝑡, 𝑇) × 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝐹𝐹(𝑡)

with good precision based on the air temperature (T0 [K]) and solar irradiance (Psun [W m−2]), even in quickly varying weather conditions.37 Here, to simplify the calculations we utilize a steady-state equation that considers thermal equilibrium is determined by radiative emission (see the Supporting Information for the derivation): 1

𝑇𝑑𝑒𝑣 =

(𝑇04

4 1 − 𝑃𝐶𝐸 + ∙ 𝑃𝑠𝑢𝑛 ) [𝐾] 2 ∙ 𝜎𝐵

(𝑒𝑞. 13)

where 𝜎𝐵 is the Stefan-Boltzmann constant (5.7×10−8 W m−2 K−4). We utilize eqs. 12 and 13 to estimate the device lifetime and energy yield at 87 European locations based on historical weather data (Figure 8) and assuming an initial (𝑒𝑞. 12) PCE of 15%. The weather data consists of hourly information about T0 and Psun (global irradiation) for

The equation derived for the PCE can be extended to dynamic weather conditions to estimate lifetimes and energy yields. For this, we assume that the degradation rate at each moment depends on the degradation state of the device (i.e. its PCE at that moment) and its temperature. Recently, we demonstrated that the temperature of a device, Tdev in [K], in outdoor conditions can be estimated


Page 9 of 14 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


Figure 8 - Data derived from the model for 87 locations in Europe based on historical weather data (from 1st of January 2005 to 1st of January 2006): a) t80; b) total energy produced in the time to reach t80; c) normalized PCE after the considered period; d) total energy generated during the considered period.

devices tilted at 45 ˚facing south. We further account for the reduction of PCE caused by operation at elevated temperatures.38 This approach offers a practical method to determine an upper limit for the lifetime and energy yield of encapsulated perovskite devices under realistic temperature-induced stress. It should be noted that lightinduced stress is another key degradation mechanism for encapsulated perovskite devices, which is not discussed here. Lifetime estimates based solely on light-stress should consider day-night cycles, because continuous light-soaking causes excessive degradation.1 However, typical day-night cycles have a reversible component that is irregular39 and therefore difficult to account for. More importantly, estimates based on day-night light cycles at 25 °C would significantly overestimate the lifetime and energy yield as it neglects the substantial impact of elevated temperatures during light-soaking.1 We note that the mechanisms we consider in this model should also be active in the case of light-soaking at elevated temperatures and could play a determining role. This hypothesis is supported by the observation of similar PCE degradation trends for triple-cation devices stressed at elevated temperature under 1 sun illumination.1 Therefore, this model can potentially be refined by deriving the Ea and A of devices light-soaked at different temperatures, as the combination of temperature and light accelerates the

degradation rate compared with either mono-stress condition.1,24 Improving the Thermal Stability of Perovskites Solar Cells The loss of performance in MAPI-based devices in the long-term is driven by the Jsc reduction. This reduction happens because the gas products from MAPI degradation are not contained, thereby moving the equilibrium towards the products (see eqs. 1 and 2). Hence, preventing the outgassing of degradation products of MAPI should inhibit, or at least delay, the reaction. One way to reduce this outgassing is through the addition of a gas barrier. This hypothesis is tested by comparing the response under thermal stress of: partial stacks (ITO / TiO2 / MAPI) completed after 350 h of with PTAA and Au, with normal devices (ITO / TiO2 / MAPI / PTAA / Au), and devices with additional 150 nm of MoO3 evaporated on top of them (ITO / TiO2 / MAPI / PTAA / Au / MoO3). The devices with MoO3 present a slower Jsc reduction, and consequently a slower PCE reduction at 85 °C, while partial stacks degraded the fastest (Figure 9a). Other groups have also reported an increase of thermal stability through the addition of an oxide layer as a diffusion barrier.9,40 This approach of adding an oxide as a gas barrier is an easy method to



Page 10 of 14

Figure 9 - The thermal stability of devices can be improved by: a) Adding a gas barrier layer like MoO3 to the stack; b) Replacing MAPI with more stable perovskite like CsFA. No significant difference in the PCE of devices with CsFA either completed at once or up to CsFA stored at 85 °C for 1000 h and then completed.

increase the limited thermal stability of MAPI-based devices. Another approach to increase the thermal stability of perovskite devices is to replace the MAPI by a perovskite that is more thermally stable. Substitution of methylammonium by other cations, like formamidinium (FA) and Cs, increases the thermal stability of perovskites.24,40,41 Perovskites with both Cs and FA (CsFA) have better thermal stability than MAPI, as demonstrated by stacks of ITO / TiO2 / CsFA stored at 85 °C for 1000 h and only then completed, and which have practically the same efficiencies as devices readily fabricated (Figure 9b). This higher stability seems to be related to the higher activation energy for the thermal degradation of CsFA perovskites (0.66 eV)42 compared with MAPI (0.51 eV)14 in comparable atmospheres.

CONCLUSIONS Multiple degradation mechanisms are outlined for MAPIbased devices under thermal stress. Overall these findings demonstrate that MAPI-based devices without packaging or barriers will degrade irreversibly at elevated temperatures that can be easily reached outdoors. The reduction of Jsc is caused by nucleation and growth of the PbI2 from MAPI. The activation energy and attempt rate of the nucleation and growth of PbI2 in fully working devices are determined. The derived values demonstrate that degradation is inevitable, even in mild outdoor conditions. Simulations of the process suggest that the nucleation of PbI2 happens progressively and starts at the edges of the contact covered area. Changes of the Voc have multiple causes: an initial reduction is observed for devices at all temperatures and is related to the desorption of oxygen from the surfaces of MAPI. The activation energy and attempt rate for the desorption of oxygen indicate that the devices will lose 0.1 V of Voc even in mild outdoor conditions. Part of the Voc can be recovered through PbI2 passivation of MAPI, if some MAPI decomposes into PbI2. Finally, if a large amount of MAPI

decomposes into PbI2 less charges will be generated (lower Jsc), causing an irreversible reduction of the Voc. The FF of the devices presents a small decrease at all temperatures. Due to the small variation the mechanism behind the reduction of FF is not investigated. The description of the evolution of all device parameters permits a good description of PCE as a function of time at a constant temperature. Furthermore, the temperature of the device in operational conditions can be calculated from the environment temperature and incident sun power. This temperature can then be used to calculate the PCE reduction of the device during a certain time step. The model presented in this work offers a practical method to determine an upper limit for the lifetime and energy yield of well encapsulated perovskite devices subjected to outdoor stresses. Moreover, this model demonstrates that estimations of device lifetime based on fittings of the PCE reduction with a single exponential decay might lead to severe overestimations, especially if the device is stressed at low temperatures. Finally, based on the degradation mechanisms identified we demonstrate two alternatives to improve the thermal stability of perovskite solar cells.

EXPERIMENTAL METHODS Device Fabrication: The glass substrates with patterned ITO electrodes were purchased from Colorado Concept Coatings. The ITO coated glass was cleaned with ultrasonic baths of detergent, deionized water, acetone, and isopropanol each for 10 minutes, and then transferred into an Angstrom Engineering evaporation system, equipped with an electron beam source. The TiO2 pellets purchased from Prof. Feierabend GmbH were reactive electron beam evaporated at a rate of 1 Å/s onto ITO substrates, using a partial O2 pressure of 1.7 × 10-4 Torr during the deposition, to maintain the stoichiometry of the film. To make the perovskite precursor solution, PbCl2 (purchased from Sigma–Aldrich) was mixed with and CH3NH3I (purchased from Lumtec) with a molar ratio of 1:3 in N,N-


Page 11 of 14 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


dimethylformamid (DMF). The precursor solution was stirred at room temperature for 10 minutes, and then spin coated at 3000 rpm for 60 s onto the TiO2 layer. The obtained films were annealed on a hot plate at 90 °C in nitrogen for 1 hour to form a perovskite crystal structure. After that, the hole transport layer, either 80 mg/ml spiroOMeTAD solution doped with 17.5 µl of lithium bis(trifluoromethanesulfonyl) imide (LiTFSI 520 mg/ml in acetonitrile) and 28.5 µl of 4-tert-butylpyridine (tBP), or 10 mg/ml of PTAA doped with 5 µl (TBP) and 10 µl of LiTFSI solution (170 mg Lithium bistrifluoromethanesulphonimidate /1 ml acetonitrile) was spin-coated onto the perovskite films. All of the spin-coating processes mentioned above were performed in an N 2 filled glove box. The perovskite films coated were then exposed to air overnight if the HTL was spiro-OMeTAD, or for 2 hours if the HTL was PTAA, for oxygen doping. The devices were completed by depositing the electrodes onto the HTL through shadow masks, defining an active area of 0.13 cm 2. The 100 nm of Au were evaporated in an Angstrom Engineering evaporation system at a base pressure of 10-4 Pa and evaporation rate of 1 A/s. Device Characterization and Ageing: The photovoltaic characteristics were measured with a Keithley 2602A in four-wire configuration under an Abet xenon arc lamp with 100 mW cm−2 intensity and AM1.5G spectrum. The intensity of the lamp was calibrated with an ISE Fraunhofer certified Si photodiode. The devices were measured from forward to reverse bias with a scan speed of 1 V/s. The devices were kept in N2 in the dark and the temperature of the samples was set by a heating plate calibrated with a thermometer and an infra-red calibration tool. The transmission and reflectance were measured with a photospectrometer setup (Bentham PVE300) by illuminating the solar cell with a modulated monochromatic light (Xe and quartz halogen lamps). The Time-of-Flight Secondary Ion Mass Spectroscopy (ToF-SIMS) measurements was conducted using a TOFSIMS V spectrometer (ION-TOF GmbH, Münster, Germany) equipped with a 30 keV liquid metal ion gun (LMIG) operating with bismuth primary ions as analysis beam and Ar GCIB as sputter gun. Depth profiles were acquired using Ar GCIB of 2.5 eV/atoms on a square area of 450 x 450 µm2. Spectra were acquired in static mode (primary ion fluence < 1012 ions·cm−2), in order to preserve the molecular information, using Bi3+ on a square area of 150 x 150 µm2. During analysis, charging of the surface was prevented by applying charge compensation using lowenergy electron flood gun. Spectral interpretation was carried out using Surface Lab software v6.7 (ION-TOF GmbH, Münster, Germany).

Corresponding Author * [email protected].

ACKNOWLEDGMENT The authors would also like to gratefully acknowledge Solliance for the financial support, the Initiating and Networking funding of the Helmholtz Association (HYIG of U. Paetzold). This research has received (partial) funding from the Flemish Government–Department of Economics, Science and Innovation. The authors also thank T. Merckx, A. Hadipour and. L. Rakocevic, for the fruitful discussions.

REFERENCES (1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

ASSOCIATED CONTENT Supporting Information. Experimental, Stability at Elevated Temperatures with Different Hole Transport Layers, Characterization of the Effects of Elevated Temperatures on the Devices, Jsc Reduction, Simulation of the Jsc reduction, Voc Reduction, FF Reduction.

AUTHOR INFORMATION

(9)

(10)

11

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 (1), 61–67. https://doi.org/10.1038/s41560-017-0060-5. Khenkin, M. V.; K. M., A.; Visoly-Fisher, I.; Galagan, Y.; Di Giacomo, F.; Patil, B. R.; Sherafatipour, G.; Turkovic, V.; Rubahn, H.-G.; Madsen, M.; Merckx, T.; Uytterhoeven, G.; Bastos, J. P. A.; Aernouts, T.; Brunetti, F.; Lira-Cantu, M.; Katz, E. A. Reconsidering Figures of Merit for Performance and Stability of Perovskite Photovoltaics. Energy Environ. Sci. 2018. https://doi.org/10.1039/C7EE02956J. Conings, B.; Drijkoningen, J.; Gauquelin, N.; Babayigit, A.; D’Haen, J.; D’Olieslaeger, L.; Ethirajan, A.; Verbeeck, J.; Manca, J.; Mosconi, E.; Angelis, F. De; Boyen, H.-G. Intrinsic Thermal Instability of Methylammonium Lead Trihalide Perovskite. Adv. Energy Mater. 2015, 5 (15), 1500477. https://doi.org/10.1002/aenm.201500477. Sheikh, A. D.; Munir, R.; Haque, M. A.; Bera, A.; Hu, W.; Shaikh, P.; Amassian, A.; Wu, T. Effects of High Temperature and Thermal Cycling on the Performance of Perovskite Solar Cells: Acceleration of Charge Recombination and Deterioration of Charge Extraction. ACS Appl. Mater. Interfaces 2017, 9 (40), 35018–35029. https://doi.org/10.1021/acsami.7b11250. Huang, W.; Sadhu, S.; Ptasinska, S. Heat- and Gas-Induced Transformation in CH 3 NH 3 PbI 3 Perovskites and Its Effect on the Efficiency of Solar Cells. Chem. Mater. 2017, 29 (19), 8478–8485. https://doi.org/10.1021/acs.chemmater.7b03243. Bastos, J. P.; Paetzold, U. W.; Gehlhaar, R.; Qiu, W.; Cheyns, D.; Surana, S.; Spampinato, V.; Aernouts, T.; Poortmans, J. LightInduced Degradation of Perovskite Solar Cells: The Influence of 4-Tert-Butyl Pyridine and Gold. Adv. Energy Mater. 2018, 8 (23), 1800554. https://doi.org/10.1002/aenm.201800554. Habisreutinger, S. N.; Leijtens, T.; Eperon, G. E.; Stranks, S. D.; Nicholas, R. J.; Snaith, H. J. Carbon Nanotube/Polymer Composites as a Highly Stable Hole Collection Layer in Perovskite Solar Cells. Nano Lett. 2014, 14 (10), 5561–5568. https://doi.org/10.1021/nl501982b. Bush, K. A.; Bailie, C. D.; Chen, Y.; Bowring, A. R.; Wang, W.; Ma, W.; Leijtens, T.; Moghadam, F.; McGehee, M. D. Thermal and Environmental Stability of Semi-Transparent Perovskite Solar Cells for Tandems Enabled by a Solution-Processed Nanoparticle Buffer Layer and Sputtered ITO Electrode. Adv. Mater. 2016, 28 (20), 3937–3943. https://doi.org/10.1002/adma.201505279. Zhao, J.; Brinkmann, K. O.; Hu, T.; Pourdavoud, N.; Becker, T.; Gahlmann, T.; Heiderhoff, R.; Polywka, A.; Görrn, P.; Chen, Y.; Cheng, B.; Riedl, T. Self-Encapsulating Thermostable and AirResilient Semitransparent Perovskite Solar Cells. Adv. Energy Mater. 2017, 7 (14), 1602599. https://doi.org/10.1002/aenm.201602599. Xu, B.; Zhu, Z.; Zhang, J.; Liu, H.; Chueh, C. C.; Li, X.; Jen, A. K. Y. 4-Tert-Butylpyridine Free Organic Hole Transporting

ACS Paragon Plus Environment


(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19) (20)

(21)

(22) (23)

(24)

(25)

Materials for Stable and Efficient Planar Perovskite Solar Cells. Adv. Energy Mater. 2017, 7 (19), 1–10. https://doi.org/10.1002/aenm.201700683. Dualeh, A.; Gao, P.; Seok, S. Il; Nazeeruddin, M. K.; Grätzel, M. Thermal Behavior of Methylammonium Lead-Trihalide Perovskite Photovoltaic Light Harvesters. Chem. Mater. 2014, 26 (21), 6160–6164. https://doi.org/10.1021/cm502468k. Latini, A.; Gigli, G.; Ciccioli, A. A Study on the Nature of the Thermal Decomposition of Methylammonium Lead Iodide Perovskite, CH 3 NH 3 PbI 3 : An Attempt to Rationalise Contradictory Experimental Results. Sustain. Energy Fuels 2017, 1 (6), 1351–1357. https://doi.org/10.1039/C7SE00114B. Smecca, E.; Numata, Y.; Deretzis, I.; Pellegrino, G.; Boninelli, S.; Miyasaka, T.; La Magna, A.; Alberti, A. Stability of SolutionProcessed MAPbI 3 and FAPbI 3 Layers. Phys. Chem. Chem. Phys. 2016, 18 (19), 13413–13422. https://doi.org/10.1039/C6CP00721J. Yu, X.; Qin, Y.; Peng, Q. Probe Decomposition of Methylammonium Lead Iodide Perovskite in N 2 and O 2 by in Situ Infrared Spectroscopy. J. Phys. Chem. A 2017, 121 (6), 1169–1174. https://doi.org/10.1021/acs.jpca.6b12170. Krüger, J.; Plass, R.; Cevey, L.; Piccirelli, M.; Grätzel, M.; Bach, U. High Efficiency Solid-State Photovoltaic Device Due to Inhibition of Interface Charge Recombination. Appl. Phys. Lett. 2001, 79 (13), 2085–2087. https://doi.org/10.1063/1.1406148. Malinauskas, T.; Tomkute-Luksiene, D.; Sens, R. R.; Daskeviciene, M.; Send, R.; Wonneberger, H.; Jankauskas, V.; Bruder, I.; Getautis, V. Enhancing Thermal Stability and Lifetime of Solid-State Dye-Sensitized Solar Cells via Molecular Engineering of the Hole-Transporting Material Spiro-OMeTAD. ACS Appl. Mater. Interfaces 2015, 7 (21), 11107–11116. https://doi.org/10.1021/am5090385. Zhao, X.; Kim, H.-S.; Seo, J.-Y.; Park, N.-G. Effect of Selective Contacts on the Thermal Stability of Perovskite Solar Cells. ACS Appl. Mater. Interfaces 2017, 9 (8), 7148–7153. https://doi.org/10.1021/acsami.6b15673. Jena, A. K.; Ikegami, M.; Miyasaka, T. Severe Morphological Deformation of Spiro-OMeTAD in (CH 3 NH 3 )PbI 3 Solar Cells at High Temperature. ACS Energy Lett. 2017, 2 (8), 1760–1761. https://doi.org/10.1021/acsenergylett.7b00582. Khawam, A.; Flanagan, D. R. Solid-State Kinetic Models: Basics and Mathematical Fundamentals. J. Phys. Chem. B 2006, 110 (35), 17315–17328. https://doi.org/10.1021/jp062746a. Burnham, A. K. Introduction to Chemical Kinetics. In Global Chemical Kinetics of Fossil Fuels; Springer International Publishing: Cham, 2017; pp 25–74. https://doi.org/10.1007/978-3-319-49634-4_2. Galway, A. K.; Brown, M. E. Chapter 3 Kinetic Models for Solid State Reactions. In Thermal Decomposition of Ionic Solids: chemical properties and reactivities of ionic crystalline phases; 1999; Vol. 86, pp 75–115. https://doi.org/10.1016/S01676881(99)80004-4. Tran, C. D. T.; Liu, Y.; Thibau, E. S.; Llanos, A.; Lu, Z.-H. Stability of Organometal Perovskites with Organic Overlayers. AIP Adv. 2015, 5 (8), 087185. https://doi.org/10.1063/1.4930082. Baikie, T.; Fang, Y.; Kadro, J. M.; Schreyer, M.; Wei, F.; Mhaisalkar, S. G.; Graetzel, M.; White, T. J. Synthesis and Crystal Chemistry of the Hybrid Perovskite (CH3NH3)PbI3 for Solid-State Sensitised Solar Cell Applications. J. Mater. Chem. A 2013, 1 (18), 5628. https://doi.org/10.1039/c3ta10518k. Akbulatov, A. F.; Luchkin, S. Y.; Frolova, L. A.; Dremova, N. N.; Gerasimov, K. L.; Zhidkov, I. S.; Anokhin, D. V.; Kurmaev, E. Z.; Stevenson, K. J.; Troshin, P. A. Probing the Intrinsic Thermal and Photochemical Stability of Hybrid and Inorganic Lead Halide Perovskites. J. Phys. Chem. Lett. 2017, 8 (6), 1211– 1218. https://doi.org/10.1021/acs.jpclett.6b03026. Kim, T. W.; Shibayama, N.; Cojocaru, L.; Uchida, S.; Kondo, T.; Segawa, H. Real-Time In Situ Observation of Microstructural

(26)

(27)

(28)

(29)

(30)

(31) (32)

(33)

(34)

(35)

(36)

(37)

(38)

(39)

Page 12 of 14

Change in Organometal Halide Perovskite Induced by Thermal Degradation. Adv. Funct. Mater. 2018, 28 (42), 1804039. https://doi.org/10.1002/adfm.201804039. Qiu, W.; Paetzold, U. W.; Gehlhaar, R.; Smirnov, V.; Boyen, H.G.; Tait, J. G.; Conings, B.; Zhang, W.; Nielsen, C. B.; McCulloch, I.; Froyen, L.; Heremans, P.; Cheyns, D. An Electron Beam Evaporated TiO 2 Layer for High Efficiency Planar Perovskite Solar Cells on Flexible Polyethylene Terephthalate Substrates. J. Mater. Chem. A 2015, 3 (45), 22824–22829. https://doi.org/10.1039/C5TA07515G. Aristidou, N.; Eames, C.; Sanchez-Molina, I.; Bu, X.; Kosco, J.; Islam, M. S.; Haque, S. A. Fast Oxygen Diffusion and Iodide Defects Mediate Oxygen-Induced Degradation of Perovskite Solar Cells. Nat. Commun. 2017, 8 (May), 15218. https://doi.org/10.1038/ncomms15218. Motti, S. G.; Gandini, M.; Barker, A. J.; Ball, J. M.; Srimath Kandada, A. R.; Petrozza, A. Photoinduced Emissive Trap States in Lead Halide Perovskite Semiconductors. ACS Energy Lett. 2016, 1 (4), 726–730. https://doi.org/10.1021/acsenergylett.6b00355. Tian, Y.; Peter, M.; Unger, E.; Abdellah, M.; Zheng, K.; Pullerits, T.; Yartsev, A.; Sundström, V.; Scheblykin, I. G. Mechanistic Insights into Perovskite Photoluminescence Enhancement: Light Curing with Oxygen Can Boost Yield Thousandfold. Phys. Chem. Chem. Phys. 2015, 17 (38), 24978–24987. https://doi.org/10.1039/C5CP04410C. Brenes, R.; Eames, C.; Bulović, V.; Islam, M. S.; Stranks, S. D. The Impact of Atmosphere on the Local Luminescence Properties of Metal Halide Perovskite Grains. Adv. Mater. 2018, 30 (15), 1706208. https://doi.org/10.1002/adma.201706208. OpenStax. Chemistry. Walsh, A.; Scanlon, D. O.; Chen, S.; Gong, X. G.; Wei, S.-H. SelfRegulation Mechanism for Charged Point Defects in Hybrid Halide Perovskites. Angew. Chemie Int. Ed. 2015, 54 (6), 1791–1794. https://doi.org/10.1002/anie.201409740. Senocrate, A.; Moudrakovski, I.; Kim, G. Y.; Yang, T.-Y.; Gregori, G.; Grätzel, M.; Maier, J. The Nature of Ion Conduction in Methylammonium Lead Iodide: A Multimethod Approach. Angew. Chemie Int. Ed. 2017, 56 (27), 7755–7759. https://doi.org/10.1002/anie.201701724. Chen, Q.; Zhou, H.; Song, T.-B.; Luo, S.; Hong, Z.; Duan, H.-S.; Dou, L.; Liu, Y.; Yang, Y. Controllable Self-Induced Passivation of Hybrid Lead Iodide Perovskites toward High Performance Solar Cells. Nano Lett. 2014, 14 (7), 4158–4163. https://doi.org/10.1021/nl501838y. Lee, Y. H.; Luo, J.; Son, M.-K.; Gao, P.; Cho, K. T.; Seo, J.; Zakeeruddin, S. M.; Grätzel, M.; Nazeeruddin, M. K. Enhanced Charge Collection with Passivation Layers in Perovskite Solar Cells. Adv. Mater. 2016, 28 (20), 3966–3972. https://doi.org/10.1002/adma.201505140. Matsumoto, F.; Vorpahl, S. M.; Banks, J. Q.; Sengupta, E.; Ginger, D. S. Photodecomposition and Morphology Evolution of Organometal Halide Perovskite Solar Cells. J. Phys. Chem. C 2015, 119 (36), 20810–20816. https://doi.org/10.1021/acs.jpcc.5b06269. Gehlhaar, R.; Merckx, T.; Qiu, W.; Aernouts, T. Outdoor Measurement and Modeling of Perovskite Module Temperatures. Glob. Challenges 2018, 2 (7), 1800008. https://doi.org/10.1002/gch2.201800008. Jacobsson, T. J.; Tress, W.; Correa-Baena, J.-P.; Edvinsson, T.; Hagfeldt, A. Room Temperature as a Goldilocks Environment for CH 3 NH 3 PbI 3 Perovskite Solar Cells: The Importance of Temperature on Device Performance. J. Phys. Chem. C 2016, 120 (21), 11382–11393. https://doi.org/10.1021/acs.jpcc.6b02858. Khenkin, M. V.; K. M., A.; Visoly-Fisher, I.; Kolusheva, S.; Galagan, Y.; Di Giacomo, F.; Vukovic, O.; Patil, B. R.; Sherafatipour, G.; Turkovic, V.; Rubahn, H.-G.; Madsen, M.; Mazanik, A. V.; Katz, E. A. Dynamics of Photoinduced Degradation of Perovskite Photovoltaics: From Reversible to Irreversible Processes. ACS Appl. Energy Mater. 2018, 1 (2),


Page 13 of 14 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

(40)

(41)

(42)

ACS Applied Materials & Interfaces 799–806. https://doi.org/10.1021/acsaem.7b00256. Bush, K. A.; Palmstrom, A. F.; Yu, Z. J.; Boccard, M.; Cheacharoen, R.; Mailoa, J. P.; McMeekin, D. P.; Hoye, R. L. Z.; Bailie, C. D.; Leijtens, T.; Peters, I. M.; Minichetti, M. C.; Rolston, N.; Prasanna, R.; Sofia, S.; Harwood, D.; Ma, W.; Moghadam, F.; et al. 23.6%-Efficient Monolithic Perovskite/Silicon Tandem Solar Cells with Improved Stability. Nat. Energy 2017, 2 (4), 17009. https://doi.org/10.1038/nenergy.2017.9. Hanusch, F. C.; Wiesenmayer, E.; Mankel, E.; Binek, A.; Angloher, P.; Fraunhofer, C.; Giesbrecht, N.; Feckl, J. M.; Jaegermann, W.; Johrendt, D.; Bein, T.; Docampo, P. Efficient Planar Heterojunction Perovskite Solar Cells Based on Formamidinium Lead Bromide. J. Phys. Chem. Lett. 2014, 5 (16), 2791–2795. https://doi.org/10.1021/jz501237m. Tan, W.; Bowring, A. R.; Meng, A. C.; McGehee, M. D.; McIntyre, P. C. Thermal Stability of Mixed Cation Metal Halide Perovskites in Air. ACS Appl. Mater. Interfaces 2018, 10 (6), 5485–5491. https://doi.org/10.1021/acsami.7b15263.



TABLE OF CONTENS


Page 14 of 14

Model for the Prediction of the Lifetime and Energy Yield of Methyl

Recommend Documents