Thermal decomposition kinetics of FAPbI3 thin films

Thermal Decomposition Kinetics of FAPbI3Thin Films Thomas Burwig and Karl Heinze Martin Luther University Halle-Wittenberg, Von-Danckelmann-Platz 3, 06120 Halle (Saale), Germany∗ Paul Pistor Martin Luther University Halle-Wittenberg, Von-Danckelmann-Platz 3, 06120 Halle (Saale), Germany∗and Universidad Pablo de Olavide, Carretera de Utrera 1, 41013 Sevilla, Spain† (Dated: May 3, 2022) In the realm of organic-inorganic-hybrid metal-halide perovskites, FAPbI3is seeing increasing attention as a potentially more stable alternative to MAPbI3. To add to our previous work, where we studied the reaction kinetics of the thermal decomposition of MAPbI3, here we analyze the compositional change and crystal phase evolution during the thermal decomposition of FAPbI3thin films. To this end, we prepare the perovskite using thermal co-evaporation and monitor the growth and thermal decomposition in vacuum with an in-situ X-ray diffraction setup. The experimental procedure has been carried out via three approaches: producing a partially decomposed sample with the help of a graded temperature profile, using a temperature ramp and a set of isothermal decomposition experiments. From this data we analyze and calculate the stoichiometry and phase change, the activation energy Eand the frequency factor Aof the thermal decomposition process, in addition to the thermal expansion coefficient during heating. We compare our results to the ones obtained for MAPbI3thin films by the same experimental method, confirming the enhanced thermal stability of FAPbI3. INTRODUCTION Since the first successful demonstration of metal-halide perovskites as photoabsorbers in 2009,[1] this organicinorganic semiconductor family has gained a lot of interest for a variety of applications, which, besides photovoltaics, include high energy photon detectors,[2, 3] LEDs[4–7] and lasers.[8] In all of these applications, metal-halide perovskites, such as the prototypical methyl ammonium lead iodide (MAPbI3) and derivatives based on Cs, formamidinium (FA), Sn, Br or Cl, have shown significant potential for enabling efficient, low-cost optoelectronic devices. The most significant drawback of these perovskite-based devices, however, is their lack of stability towards a variety of environmental factors such as heat, moisture or UV illumination.[9] In this work we will focus on thermal stability aspects and the decomposition kinetics of the perovskite absorber formamidinium lead iodide FAPbI3, complementing our previous work on MAPbI3.[10] Solar cells can reach up to 85 °C under operating conditions[11] and, in contrast to moisture-related degradation, thermal decomposition cannot be alleviated by encapsulation. Therefore it is vital to understand the thermal decomposition pathways and kinetics for these materials in view of any application where the material is subjected to heat. For the workhorse material MAPbI3 it has become clear that severe degradation may occur at comparatively low temperatures (close to the operating conditions of solar cells), while the exact onset of degradation is still a matter of dispute.[12] This is even more the case for the recently strongly investigated perovskite FAPbI3, where less stability studies are available. As Zhang et al. point out, the observed decomposition depends significantly on the chosen temperature regime, as isothermal experiments usually found decompositions at much lower temperatures than ramp experiments.[12] Our earlier results on the thermal stability of MAPbI3, using a temperature ramp, showed a 50 % decomposition at 230 °C[13] and Dualeh et al. found an onset of the decomposition of MAPbI3at 234 °C, again using a temperature ramp[14]. In contrast to this, Kim et al. have found a detectable decomposition of MAPbI3at 80 °C after 1 h.[15] This conflict is an example for one of several problems which impede the formation of a complete and clear picture of the degradation mechanisms in current research: I) As already noted, the choice of temperature regime significantly affects results. II) Degradation studies of completed solar cells often report only the decline in performance over time for a given temperature, lacking substantial information on the exact degree of decomposition. III) Many studies analyzing perovskite decomposition only report the degree of decomposition for one set of time and temperature, which does not allow for the extraction of kinetic parameters. This can also lead to difficulties when comparing the results of different research groups, especially when different conditions (e.g. different temperatures) are chosen for the trials. IV) Materials with different morphologies (single crystal, powder, thin film) can be expected to degrade differently.[16] V) The synthesis method can play a significant role in the stability of the resulting material. For example, solvent residues that remain after wet chemical preparation can decrease the stability.[17] VI) The history of the investigated samples cannot be excluded as a factor for their stability. Samples that have been exposed to air (and thus to moisture, light, etc.) can reasonably 2 be expected to show a different decomposition behavior. VII) When temporarily exposing the samples to environmental factors, such as ambient air or light, these factors are often difficult to precisely quantify or are often not seen as “report-worthy” by the researchers. It is for these reasons that in the current study we explicitly investigate thin films with properties similar to those applied in solar cells (e.g. thickness), that were prepared solvent-free in vacuum by co-evaporation and investigated in situ within the vacuum chamber without air exposure at any time. In the past, we have reported the synthesis, phase evolution and thermal decomposition of a variety of different perovskite thin films that were prepared by co-evaporation in vacuum and studied via temperature ramp experiments with in situ X-ray diffraction (XRD) analysis. The materials studied so far include MAPbI3, MAPbBr3, MAPbCl3,[13] CsPbI3, CsPbBr3,[18] and also the double perovskite Cs2AgBiBr6.[19, 20] To add to this list, FAPbI3will be studied in this work. While single temperature ramp experiments give a general idea of the thermal stability limits of a material and allow for a qualitative comparison of different materials, for a more detailed and general view of the decomposition kinetics, sets of iso-thermal measurements or sets of different temperature ramps are needed. In a previous work, we elaborated on the kinetics of the thermal decomposition of MAPbI3in detail, by determining the kinetic triplet of this reaction. This consist of the activation energy E, the frequency factor Aand the reaction model f(α), where αis the extent of reaction.[10] These kinetic parameters allow for a generalization of the decomposition behavior over a larger temperature range and for more meaningful comparisons to other experiments. It has been shown by a large number of studies, that the major limiting component for the thermal stability of MAPbI3is the organic MA molecule.[13, 18, 21–30] Therefore, we study the impact of exchanging the MA molecule with FA to see how this modification influences the thermal stability of the resulting material. Solar cells that use FAPbI3absorber layers have been shown to be more resilient towards temperature[31] and moisture,[32] which makes this material a promising object of study. To our knowledge, there are three research groups that have investigated the reaction kinetics of the thermal decomposition of FAPbI3: Juarez-Perez et al. used a wet-chemically prepared powder in vacuum and He atmosphere.[33] Pool et al. used spin coated thin films that were annealed under N2atmosphere.[34] Luongo et al. prepared a powder via dry grinding of the precursors and heated the samples up in Ar and He.[35] All of these trials use multiple temperature ramps to determine the kinetic data of the reaction and none of them use preparation methods that are likely candidates for use in industrial applications. Our goal is to complement these findings with isothermally acquired data on co-evaporated thin films. The different preparation methods, experimental parameters and resulting values for Eand Aare compiled in Tab. III. In order to be comparable to our previous experiments on the MA based perovskites,[13] we first prepare FAPbI3 in high vacuum via co-evaporation of FAI and PbI2. With an in situ X-ray diffraction setup, we are able to monitor the crystallization and phase evolution of the thin films at any time of the experiment. Afterwards, without breaking the vacuum, we perform three sets of decomposition measurements. First, a sample is decomposed using a temperature ramp in order to determine the general temperature range where a measurable decomposition is to be expected. In addition, we decompose FAPbI3thin films using a set of isothermal experiments in the temperature range between 230 °C and 290 °C. From this data we calculate the activation energy Eand the frequency factor Afor this process. The data is first analyzed under the assumption of a first order model, where the rate constants kare determined by fitting an exponential decay onto the data. Then a more general approach is used, where the data is tested against a variety of different reaction models. Finally, we partially decompose a FAPbI3sample by applying a temperature gradient over the length of sample, enabling us to investigate the morphology and stoichiometry changes during the decomposition via scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX). THEORY FAPbI3Crystal Structure Similarly to CsPbI3, FAPbI3is a polymorph and can exist in different crystal phases at room temperature. The black, photoactive αphase has a band gap of 1.48 eV[31] and is sometimes identified with a cubic symmetry (Pm3m,a=b=c= 6.3620(8)  A)[36], while other reports assign a trigonal symmetry (P3m1, a=b= 8.9817(13)  A, c = 11.006(2)  A)[37]. The δ phase is photo inactive, orange in appearance, has a band gap of 2.14 eV[38] and has a hexagonal crystal structure (P63mc,a=b= 8.6603(14)  A, c= 7.9022(6)  A)[37]. The αphase is stable for temperatures above 130 °C, while at lower temperatures the perovskite will gradually transform into the δphase, even in an inert gas atmosphere.[38, 39] A partial exchange of FA with MA[39] or of I with Br[40] has been shown to increase the stability of the photoactive αphase under ambient conditions. 3 Reaction Kinetics In general, the extent of conversion αof a reaction changes over the time taccording to the following formula [41]: dα dt=k(T)·f(α) (1) Here, Tis the absolute temperature, kis the reaction rate and f(α) is the reaction model. αis defined as being 0 at the start of the reaction and 1 at the end. The data presented in this work is tested against the same models as the MAPbI3samples in our previous work in Ref. [10]. The complete list of tested reaction models can be found in the supporting information. The reaction rate k(T) is defined as [41]: k(T) = A·exp −E RT (2) Where Ris the universal gas constant, Eis the activation energy and Ais the pre-exponential factor. In principle, the kinetic parameters of a thermal decomposition reaction can be determined by a single temperature ramp experiment. However, as has been explained by Vyazovkin et al., an experiment that uses a temperature ramp changes Tand αsimultaneously, which leads to a very high uncertainty in any determined kinetic parameters. If only a single temperature ramp experiment is used, this makes the results next to unusable.[41] For this reason, we use four isothermal experiments with different temperatures to determine the kinetic parameters for the degradation. For the first evaluation approach, we assumed the reaction model to be of first order, where an equation of the form y=ae−kx (3) is fitted onto the data. Then ln kis plotted over 1/T for each isothermal experiment. An equivalent form of Eq. 2 is: ln k= ln A−E RT (4) This has the same structure as the equation: y=m+nx (5) Therefore, a linear fit of the data for y= ln kover x= 1/T can then be identified with this equation, which allows the calculation of ln A=mand E=−nR. The second evaluation methodology used to analyze the kinetic data was a model fitting approach which includes a variety of common reaction models. For this, different integrated reaction models g(α) are used, where g(α) follows from the reaction model f(α) by integration [41]: g(α) = Zα 0 [f(α)]−1(6) g(α) gives a unit-less measure for the time it takes for the reaction to achieve a certain extend of conversion and, in this way, it relates the time twith the reaction rate k(T) [41]: g(α) = k(T)·t(7) A plot of g(α) over tcan be linearly fitted to yield a value for k(T). Then, similarly to the first approach, ln kcan then be plotted over 1/T and the kinetic parameters can be determined using an Arrhenius fit. In our analysis, the peak area evolution of certain characteristic XRD peaks is assumed to be proportional to the amount of a given material within the film. The validity of this assumption has been discussed at length in our previous work,[10] and we only summarize the main points here. Besides a decomposition of the material, there are two main effects that could reduce the area of the detected peaks: A layer of product (PbI2) covers the film and reduces the detected X-ray intensity: To calculate the absorption Bof a layer of PbI2with linear attenuation coefficient µ, coverage cand thickness dwhen hit by X-rays with an incidence angle of θ, one can use the following formula: B=c·1−e−µx(8) where x= 2 ·d/ sin θis the distance the X-rays travel through the film. To make an assessment as to the value of these parameters, the SEM images of the partial decomposition experiment, which are shown in Fig. 4 and Fig. 5, can be helpful to consider. Fig. 5 dshows an image with material contrast and, as can be seen there, the PbI2does not form a solid layer on top of the perovskite, but has a coverage of roughly 50 %. The cross sectional image in Fig. 4 dindicates a PbI2thickness of around 100 nm. The attenuation coefficient of PbI2for X-rays with an energy of 8.04 keV is 1556.51 cm−1.[42] With the above mentioned values this would lead to an absorption of B= 4.4 %. This in itself can be considered negligible. While it is difficult to assess which extent of conversion corresponds to the SEM images, there is no PbI2at the beginning, therefore at α= 0 the absorption is be B= 0 %. Since the evaluation of the isothermal experiments focuses on the first half of the decomposition, the impact of the PbI2absorption should be very limited. Additionally, the results for Eand Athat were based on the declining FAPbI3peak were very similar to the ones obtained from the growing PbI2peak, and since the PbI2is formed above the perovskite, the results based on the PbI2peak should not be affected at all by this phenomenon. A recrystallization or reorientation of the material: There is the known transition from the δphase to the αphase of FAPbI3at around 130 °C.[38, 39] As can be seen in the colormap in Fig. 2 by the change in relative peak intensities, the FAPbI3film does respond to the 4 increasing temperature by recrystallizing/changing the preferential orientation of the crystal grains. To limit the effect of this on the results of the isothermal decomposition experiments, an intermediate temperature at 160 °C was held for at least 20 min, before heating to the respective isothermal decomposition. It is also of note that the results for Eand Athat used the growing PbI2peak as their basis where similar to the values obtained from studying the declining FAPbI3peak. Since the growing PbI2peak should not be influenced by a recrystallization of the FAPbI3educt, this is a good indication that this phenomenon has no major impact on our results. We would like to insert a short comment on an ongoing dispute concerning the interpretation of solid state decomposition analysis. When using the Arrhenius approach to determine the reaction kinetics of a decomposition reaction from the solid state, it is of note, that the applicability of the Arrhenius equation to this class of reactions is, at this point, a contentious topic. This has to do with the fact that the base assumptions behind the Arrhenius model pertain to the theory of gases and liquids: The atoms, ions or molecules in the reactant species move freely with a kinetic energy that is proportional to the temperature of the substance. If a collision with an energy of at least Eoccurs, it leads to a reaction. The frequency factor Adescribes how often these collisions happen and the term of the MaxwellBoltzmann distribution (exp −E RT , see Eq. 2) gives the relative fraction of collisions that occur with an energy of at least E. Further restrictions as to which collisions lead to a reaction – such as requiring the collisions of specific bonds – are usually incorporated into the frequency factor.[43] According to Garn, the energies within solids are too equally spread out to allow for the application of Maxwell-Boltzmann statistics and thus there exists no distinct activated species.[44] This violates one of the central assumptions of the Arrhenius model and immediately raises the question, what an empirically determined activation energy from a conventional Arrhenius plot actually signifies. A recent discussion of the current state of the theory of solid state decomposition is given in Ref. [45]. A promising contribution to this topic was made by L’vov, who developed the theory of congruent dissociative volatilization (CDV) that aims to close this explanatory gap. His theory is derived in detail in the references [46], [47] and [48]. This theory retains the validity of the empiric relation described by Eq. 4, but here the activation energy Eis assigned to the molar enthalpy ∆rH◦ T/ν, thus relating the empirically determined value Eto an actual physical property of the studied material. Just as important, it gives a theoretical foundation to the application of the Arrhenius relation. Additionally, it provides an explanation for the often observed “compensation effect”, where similar experiments on the same substance lead to disparate results for Aand Ethat, however, follow the relation ln A=aE +b. The CDV theory proposes the following model reaction for solid state decompositions: R(s/l)↔S(g) + V(g)→S(s) + V(g) (9) Here, a reactant R(liquid or gas) first reacts into two gaseous products, one of which volatile (V), that remains a gas, and one non-volatile (S), that subsequently condenses to form a solid. When applied to the thermal decomposition of FAPbI3(ignoring any further decomposition of the FAI component) the equation is: FAPbI3(s)↔PbI2(g) + FAI(g)→PbI2(s) + FAI(g) (10) Such a re-condensation of PbI2would explain the very high crystallinity of the reaction product, as it was observed in our experiments. In our current work, we are unable to add significant further insight into the applicability of the CDV theory. However, for completeness we mention it here in order to offer an alternative physical interpretation for the commonly extracted activation energies. Independent from the above discussion on their physical interpretation, the experimental data presented in this work and the kinetic parameters extracted in the following sections allow to determine the temperature dependence of the degradation kinetics of FAPbI3in an empirical way, enabling the comparison with MAPbI3and the prediction of the degree of decomposition for a given set of time and temperature. EXPERIMENTAL DETAILS The sample preparation and post-treatment took place within a high vacuum chamber under a base pressure of 2×10−5mbar. The FAPbI3thin films were deposited using thermal co-evaporation of the precursors PbI2at 350 °C and FAI at 195 °C from Al2O3crucibles. The pressure within the chamber increased to 7 ×10−5mbar during the deposition of the films, mostly due to the evaporation of FAI. The target sample thickness was around 310 nm with an average growth rate of 0.13  A s−1. After the preparation, without interrupting the vacuum, the samples were heated via radiative heat from a carbon heating element at the back of the sample holder. During the whole process, including growth and annealing, the samples were observed using an in-situ XRD system. The system had a fixed source-sample-detector geometry during the whole process and recorded 1 measurement every 60 s. The X-ray source was made of Cu and a Ni filter was used to reduce the strength of the Cu kβreflexes. The detector was composed of three Dectris Mythen 1 K modules, that together cover a 2θrange of 28°. More information about the preparation and analysis apparatus can be found in Ref. [13]. In line with previous experiments, we first exposed a freshly deposited FAPbI3layer to a temperature ramp of 5 of 3.6 K min−1, starting at room temperature, to investigate the phase evolution and to determine the onset of decomposition. For the isothermal experiments, the samples were heated to either 230 °C, 250 °C, 270 °C or 290 °C. In order to ensure that the initial FAPbI3thin film was completely in the photo-active αphase and in order to avoid recrystallization effects observed at lower temperatures, an intermediate temperature step of at 160 °C for at least 20 min was introduced prior to applying the actual isothermal decomposition temperature. For the preparation of the partially decomposed sample, half of the sample was covered by a stainless steel plate, partially shielding the sample from the heater. This cover was applied after the FAPbI3deposition, in a nitrogen filled glovebox attached to the deposition chamber, therefore ensuring that the sample would not come into contact with ambient air. The decomposition process kept the sample at 250 °C for 50 min. Due to the shield, the sample was effectively exposed to a temperature gradient over its length. RESULTS Growth To grow the perovskite, FAI and PbI2have been thermally co-evaporated in a high vacuum chamber. More details on the growth conditions can be found in the Experimental Details section. A colormap representation of the growth process is shown in Fig. 1. The XRD peaks that became detectable upon the formation of the perovskite correspond well to either the black αphase or the yellow δphase of FAPbI3. The peaks of the αphase have been indexed using the PDF reference 00-069-0999 and the δphase peaks have been indexed according to Han et al.’s work in Ref. [38]. The visible peaks of the αphase are: (100) [13.92°], (110) [19.70°], (111) [24.51°], (200) [28.00°], (210) [31.39°]. From the δphase, the following peaks are detected: (002) [22.39°], (021) [25.36°], (¯ 122) [30.52°], (004) [32.80°]. Additionally, the (¯ 130) peak of the δphase might exist, but is overlayed by the (210) peak of the αphase. The δphase vanished after heating the samples to 160 °C for twenty minutes and only the α phase remained. Temperature Ramp Experiment To identify any phase changes that might occur during annealing, a freshly prepared film was subjected to a temperature ramp. Below 160 °C, for the peaks assigned to the α-FAPbI3phase no decomposition but only a recrystallization was observed, which manifested in variations of the relative peak intensities. For temperatures above FIG. 1. Colormap of the growth of the FAPbI3perovskite that was used in the isothermal decomposition experiment at 290 °C. Every column of pixels corresponds to one XRD scan and the color indicates the number of counts received at the respective angle. The bottom graph shows the temperatures of the crucibles, the opening and closing times of the shutters and the chamber pressure. The XRD peaks are labeled by phase and miller index. 230 °C, the intensities of the perovskite peaks rapidly decrease until disappearing above approximately 270 °C, as can be observed in Fig. 2. In parallel to the decomposition of FAPbI3, PbI2is formed. For temperatures above 290 °C, the PbI2decomposes and some metallic lead is detected. It is of note that with this experimental setup we cannot detect organic (and possibly volatile) decomposition products and as such we cannot make a comment as to whether the decomposition is driven by the dissociation of the FA molecule itself, as is the case for MAPbI3, or whether the FA molecule stays intact during the decomposition. However, in works by Juarez-Perez et al. the FA decomposition products HCN and NH3 have been detected during the thermal decomposition of FAPbI3and FAPbBr3.[33] Since the positions of the XRD peaks directly depend on the lattice constant of the analyzed material, their shift upon heating with a temperature ramp allows for the calculation of the thermal expansion coefficient of a material. Fig. 3 shows the change of the lattice constant in relation to the temperature together with a linear fit of the data, as calculated from the (200) peak. αLwas also calculated from the positions of the (100), (110), (111), and (210) FAPbI3peaks in the XRD pattern for each scan. Since most of these other peaks were only faintly visible or not very sharp, a weighted average was taken 6 FIG. 2. Colormap of the temperature ramp experiment of the thermal decomposition of FAPbI3. The top graph shows the integrated intensity of the (200) and (210) peaks of the α phase and the bottom graph shows the sample’s temperature. An additional peak detected at 20°for this deposition run was identified with contamination of the Kapton window and is labeled with an asterisk in the graph. Notably, the (110) peak of the αphase overlays this peak for a time before the perovskite fully disappears. 300 350 400 450 500 6 . 0 6 . 1 6 . 2 6 . 3 6 . 4 6 . 5 a L i n e a r F i t a [ Å ] T [ K ] F i t F o r m u l a : y = m * x + n m = 3 . 1 3 2 E - 4 ± 1 . 0 0 3 E - 5 n = 6.152 ± 0.004 FIG. 3. Dependence of the lattice constant aon the temperature Ttogether with a linear fit over the data. ahas been calculated using the position of the (200) FAPbI3peak. TABLE I. EDX measurements of different positions in Fig. 4. The values are given as the amount of I atoms per one Pb atom, which is the [I]/[Pb] ratio, also referred to here as IP. For FAPbI3the expected IP is 3 and for PbI2it is 2. Position I per Pb (IP) A3.2 D2.9 G2.1 and the result was αL= 48.08 ±1.32 ×10−6K−1. The results for the separate peaks can be found in the supporting information. Due to the deviations in the results for the different peaks, we would estimate the actual relative uncertainty of the end result to be closer to 10 %, resulting in a final value of αL= 48 ±5×10−6K−1. This value for the linear thermal expansion coefficient for FAPbI3is higher than the value we obtained, using the same method, for MAPbI3thin films in Ref. [13], which is 36 ±1×10−6K−1. Partial Decomposition - SEM/EDX analysis As described in the section on the Experimental Details, one sample was partially decomposed by applying a temperature gradient over its surface. One sample was taken out of the vacuum chamber prior to annealing, serving as an untreated reference sample. The sample turned orange upon exposure to ambient air, which indicates the transition from the αto the δphase. This untreated sample was analyzed with a scanning electron microscope (SEM) in this state. The resulting images are shown in Fig. 5 (aand b). The images were taken by two detectors (consecutively, not simultaneously): an Everhart-Thornley secondary electron detector (ET-SE) and an in-lens secondary electron detector (IL-SE). The ET-SE image (a), shows a smooth layer with full coverage and particles of roughly 300 nm in average size. The ILSE image (b), which provides a higher material contrast, suggests a very homogeneous layer without any visible secondary phases. The succession of SEM images shown in Fig. 4 provides an insight into the progress of the reaction and the resulting morphology change on a microscopic scale. Going from left to right (lower to higher annealing temperature), the sample first shows only very small signs of decomposition while the decomposition gets more pronounced towards the right side. Image Ais an exception to this, because the metal rail that blocked the thermal radiation let some heat through on the leftmost side. Because of this, the part of the sample which is least decomposed is shown in images Band C. Some rifts are already visible at these positions while the layer still covers most of the sample. At point D, roughly in the middle 7 of the sample, some pores and voids appear. The cross section shows a declining layer thickness and hints at flat platelets forming at the top of the layer. Their characteristic form suggests a hexagonal crystal structure, as expected for the decomposition product PbI2, that was detected with XRD. Fig. 5 (cand d) shows the same spot of the image with a larger magnification and, in addition to the ET-SE image, also shows an IL-SE image. Due to the higher material contrast of the IL-SE image, two clearly distinct phases are visible. The brighter part of the image with the hexagonal platelet structures is assigned to PbI2, as indicated above. The slightly darkened spot in the middle is likely an artifact of the IL-SE system, as those detectors can sometimes lead to a small dark area at the center of the image. Overall, this image gives the impression that FAPbI3(in dark) is overlayed by the brighter PbI2, consistent with the cross section image of Din Fig. 4, indicating the formation of a PbI2top layer. The next image (E) shows an increase in porousness and the PbI2platelets are now clearly visible in the cross section. This is also the part of the sample where, in the photo, the dark perovskite area gives way to the yellow PbI2. In image F, which in the photo is already completely yellow, the layer coverage has decreased significantly. The pores from before have now started forming elongated ridges. On position Gthe sample exhibits a very low surface coverage and what remains of the layer is highly furrowed. The cross section underlines this by showing a layer that has significantly lost in thickness and looks more like a loose scattering of material, rather than a solid layer. EDX measurements of the [I]/[Pb] ratio (IP) taken on positions A,Dand G, which are shown in Tab. I, are consistent with these visual observations. Positions Aand D’s IPs are close to the value expected for FAPbI3(IP ≈3), while the results for position Gindicate that PbI2is formed (IP ≈2), which is consistent with the expectations. Isothermal Decomposition - First Order Approach To calculate the kinetic parameters of the thermal decomposition reaction, a set of isothermal decomposition experiments has been conducted at temperatures of 230 °C, 250 °C, 270 °C and 290 °C. In the first experiment at 230 °C the area of the perovskite peaks declined by only 50 % over 3.5 h. An overview of the results is depicted in Fig. 6. The sample annealed at 250 °C showed recrystallization prior to decomposition: After the final temperature of 250 °C was reached, the (111) and (200) peaks gained notably in intensity over several minutes before declining. The (210) peak did not exhibit this behavior. After the initial increase, the following decline of the (111) and (200) peaks was far more rapid than that of the (210) peak. In consequence, the initial recrystallization might lead to an overestimation of the subsequent TABLE II. Results of the first order approach for the (210) FAPbI3peak and the (001) PbI2peak. The result that was obtained by averaging the kvalues of these two peaks for each temperature is denoted as “AVG”. Peak E[kJ/mol] ln A[s−1] (210) FAPbI3169.1±3.6 30.6±0.9 (001) PbI2159.1±2.9 28.5±0.7 AVG 165.3±4.9 29.9±1.2 intensity decay and reaction rate k, when considering merely the (111) and (200) peaks. For these reasons, the evaluation is focused on the decline of the FAPbI3 (210) peak. Since the decomposition of FAPbI3results in a crystalline PbI2layer, the formation of this reaction product also constitutes an indicator for the progress of the decomposition reaction and is decoupled from any recrystallization effects occurring in the FAPbI3layer. Therefore, the rise of the PbI2(001) peaks is used as a second variable for the calculation of the reaction rate k. For better comparability with the declining peak areas of the FAPbI3reflexes, the peak areas aof the PbI2reflexes are given as (1 −a) in Fig. 7. In order to determine a first estimate for the the reaction rate k, the data points were fitted using the exponential equation of Eq. 3. Since the exact beginning of the decomposition can be difficult to determine, the first 4 to 5 data points were ignored and the fit was conducted down to a normalized peak area aof 0.3. This is possible because for a first order decay, the speed of the reaction does not depend on the extent of the reaction. The 250 °C process does not fit this exponential decay as well as the others, but the fit range was chosen by the same criteria for consistency. The process using 230 °C is the only exception to this, since the area of the perovskite peaks only dropped to 50 % during the course of the experiment. However, since it showed a very consistent exponential decay, the result is quite insensitive to the choice of the fit range. After obtaining a value for kfor each experiment, ln khas been plotted over 1/T to achieve an Arrhenius-type plot, which is depicted in Fig. 8 for the (210) peak of FAPbI3and the (001) peak of PbI2, as well as the plot resulting from averaging over the kvalues for the (210) FAPbI3peak and the (001) PbI2peak. The exponential fits shown in Fig. 7 provide a statistical error σfor each value of kand these errors have been used in the Arrhenius fits to weigh the data according to wi= 1/σi. The resulting fit for the averaged values of kyielded values for the activation energy E= 165.3±4.9 kJ mol−1and the pre-exponential factor ln A= 29.9±1.2. The results of these evaluations are summarized in Tab. II. 8 Model Fitting Approach Our work on MAPbI3(Ref. [10]) showed the difficulty to determine a specific reaction model from our data. In addition, the obtained Eand Avalues did not significantly deviate from the ones obtained from the manual first order fitting method. We made a similar comparison with the same set of reaction models for the data on FAPbI3obtained here. The outcome was similar to the MAPbI3case, as the linearity of the g(α) over tplot (a rough measure for how well a model fits the reaction) and the values for Eand Awere similar for many of the models. The specific results for all models are included in the supporting information. The evaluation of the (210) FAPbI3peak with the different reaction models resulted in values of E≈150 ±24 kJ mol−1and ln A= 26 ±5, while the (001) PbI2peak yielded E≈160 ±16 kJ mol−1 and ln A= 28 ±4. Compensation Effect Just as in our previous work, we again found that the results of the various methods and reaction models follow a line with the form ln A=a E +b(11) The ln Aover Edata is plotted in Fig. 9. This behavior is generally known as the compensation effect, which refers to the phenomenon that similar experiments on the decomposition of a material can lead to a significant spread of Eand ln Avalues, while those values are coupled by a linear dependence. The line described by Eq. 11 implies that there is a temperature Tat which these processes agree on a specific turnover ratio k. From the values of aand bone can calculate these values for Tand k: T=1 R a (12) ln k=b(13) A linear fit of the data presented in Fig. 9 gave values of a= 0.243 ±0.022 and b=−10.453 ±3.553, which results in a temperature of agreement of T= 222 ±45 °C and a corresponding turnover ratio of ln k= 10.453 ±3.553. L’vov’s theory of CDV explains the compensation effect with the buildup of product gases in the reactor, that influence the values for Eand Aaccording to Eq. 11. Unfortunately, since all our experiments were conducted in high vacuum, this explanation does not apply to our case. A more likely explanation is the simple fact that, because the evaluations used the same experimental data, their results need to agree on the overall turnover ratio to some degree, but the specific values for Eand Aare more sensitive to small deviations in the data and the choice of the evaluation method. When comparing the results of our work with the other works mentioned in Tab. III, the results of Luongo et al. are close to the linear fit line shown in Fig. 9, hinting at an overall similar rate of decomposition. DISCUSSION The activation energy of the thermal decomposition of FAPbI3that has been determined in this work (E= 165 kJ mol−1) is significantly larger than that which has been determined for MAPbI3(E= 110 kJ mol−1) in our previous work.[10] However, it needs to be stressed that this does not by itself indicate a higher thermal stability, i.e. a lower rate of thermal decomposition at any given temperature. To make such an assessment, the rate constant Aneeds to be taken into account as well. According to Eq. 2, the activation energy Edetermines how k changes with a change in temperature T, while the rate constant Ais a scalar factor onto the exponential term that, especially in the field of solid state decompositions, can vary by many orders of magnitude between different processes.[49] To get an understanding of how the values for Eand A, taken together, translate into the thermal stability of a material, one can use Eq. 2 to calculate k(T). Fig. 10 shows the calculated k(T) relation for FAPbI3and MAPbI3(with Eand Ataken from Ref. [10]), together with the experimentally determined values for k. The figure also shows the temperature difference between k(T) of MAPbI3and k(T) of FAPbI3for a given rate k. From this it can be estimated that the start of the decomposition of FAPbI3is shifted upwards by about 45 °C when compared to MAPbI3, while the temperature difference between the two curves becomes smaller as the temperature increases. Overall, the results confirm the higher thermal stability of FAPbI3when compared to MAPbI3. While Fig. 10 implies an upwards shift of the temperature of thermal decomposition by only roughly 45 °C, the increased stability becomes more apparent when looking at the predicted decomposition behavior at lower temperatures. In our work on MAPbI3[10] we calculated the time in which the perovskite would decompose by 20 % to α= 0.2 at 85 °C and the result was 2800 h (around 120 d). For FAPbI3to decompose to the same extent at 85 °C, it would take roughly 8 000 000 h (around 900 years). A similar calculation stated that for MAPbI3to not decompose by more than 20 % within 1 h it would need to be stored below 180 °C. In the case of FAPbI3this temperature would be 230 °C. Zhang et al. note that, compared to MA, FA is a larger molecule with a smaller dipole moment and, in perovskites, has a larger bonding strength to the halides, which reduces halide ion migration and explains the higher stability commonly observed with FA-based perovskites.[50, 51] 9 TABLE III. Comparison of the results and experimental methods of this work with the works of Juarez-Perez et al.,[33] Pool et al.[34] and Luongo et al.[35] The results of Luongo et al. are divided into three parts. A: In situ XRD of the whole decomposition process; B: Differential scanning calorimetry (DSC) of the first decomposition step; C: DSC of the second decomposition step. Source E[kJ/mol] ln A[s−1] Configuration Preparation Atmosphere T-regime Measured Value This work 165.3±4.9 29.9±1.2 Thin film Co-evaporation Vacuum Isothermal Time-resolved XRD [33] 115 ±3 6.9±0.2 Powder Solution + Mortar Vacuum & He Ramp TGA [34] 96.5±13.1 7.260 ±0.007 Thin Film Spin-coating N2Ramp Time-resolved XRD [35] A 112 ±9 14.8±2.0 Powder Grinding of precursors He Ramp Time-resolved XRD [35] B 205 ±20 - Powder Grinding of precursors Ar Ramp DSC [35] C 410 ±20 - Powder Grinding of precursors Ar Ramp DSC CONCLUSIONS In conclusion, we have determined the kinetic parameters for the thermal decomposition of co-evaporated FAPbI3thin films, deriving an activation energy of E= 165.3±4.9 kJ mol−1and a pre-exponential factor of ln A= 29.9±1.2. The data indicates that the onset of decomposition occurs at higher temperatures compared to MAPbI3, which confirms the higher thermal stability of the FA-based perovskite. The temperature ramp experiment indicated the start of the decomposition of FAPbI3to occur at roughly 230 °C, which is in good agreement with what would be expected from the determined values for Eand A. The linear expansion coefficient was determined to be αL= 50.17 ±1.61 ×10−6K−1and a value of αV= 152.25 ±4.85 ×10−6K−1was determined for the volumetric expansion coefficient. The SEM analysis of the partially decomposed sample indicated a decomposition that started from the top of the layer, forming PbI2, and progressed through the whole layer while significantly reducing its surface coverage. SUPPORTING INFORMATION AVAILABLE Supporting Information include all results of the model fitting approach. CONFLICTS OF INTEREST There are no conflicts of interest to disclose. ACKNOWLEDGMENTS We gratefully acknowledge the financial support from the German Federal Ministry of Research and Education (BMBF) under contract number 03EK3570B (StrukturSolar II). ∗[email protected] †[email protected] [1] A. Kojima, K. Teshima, Y. Shirai, and T. Miyasaka, Organometal halide perovskites as visible-light sensitizers for photovoltaic cells, Journal of the American Chemical Society 131, 6050 (2009). [2] Y. C. Kim, K. H. Kim, D.-Y. Son, D.-N. Jeong, J.-Y. Seo, Y. S. Choi, I. T. Han, S. Y. Lee, and N.-G. Park, Printable organometallic perovskite enables large-area, low-dose x-ray imaging, Nature 550, 87 (2017). [3] H. Wei and J. Huang, Halide lead perovskites for ionizing radiation detection, Nature Communications 10, 10.1038/s41467-019-08981-w (2019). [4] Q. Shan, J. Song, Y. Zou, J. Li, L. Xu, J. Xue, Y. Dong, B. Han, J. Chen, and H. 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Pistor, Reaction kinetics of the thermal decomposition of MAPbI3 thin films, Physical Review Materials 5, 065405 (2021). 16 90 100 110 120 130 140 150 160 170 5 1 0 1 5 2 0 2 5 3 0 F i r s t O r d e r ( 2 1 0 ) ( 0 0 1 ) P b I 2 A V G M o d e l F i t t i n g F A P b I 3 P 2 P b I 2 A 2 L i n e a r F i t F i r s t O r d e r & M o d e l F i t t i n g L i t e r a t u r e J u a r e z - P e r e z P o o l L u o n g o l n ( A ) E [ k J / m o l ] FIG. 9. The results of this work depicted as an ln Aover E plot, together with the results of Juarez-Perez et al.,[33] Pool et al.[34] and Luongo et al.[35] The linear fit is indicated by the dashed line. 150 200 250 300 0 1x103 2x103 3x103 4x103 M A P b I 3 E x p e r i m e n t a l F A P b I 3 E x p e r i m e n t a l M A P b I 3 C a l c u l a t e d F A P b I 3 C a l c u l a t e d k [ 1 / s ] T [ ° C ] 2 6 ° C 3 3 ° C 3 8 ° C 4 5 ° C FIG. 10. Comparison of how the rate constant of the thermal decomposition kdepends on the temperature Tfor MAPbI3 (data taken from our earlier work in Ref. [10]) and FAPbI3 (data taken from this work). The circles represent the kvalues obtained from the measurements and the dotted lines are calculations using Eq. 2, with E= 110.5 kJ mol−1 and ln A= 19.3 for MAPbI3and E= 165.3 kJ mol−1and ln A= 29.9 in the case of FAPbI3. The arrows show the difference in temperature between the two calculated curves for the same value of k.