Thermal Conductivity of CH3NH3PbI3 and CsPbI3 - ACS Publications

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Thermal Conductivity of CHNHPbI and CsPbI: Measuring the Effect of the Methylammonium Ion on Phonon Scattering Anton Kovalsky, Lili Wang, Gage T. Marek, Clemens Burda, and Jeffrey S. Dyck J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12231 • Publication Date (Web): 19 Jan 2017 Downloaded from http://pubs.acs.org on January 22, 2017

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The Journal of Physical Chemistry C 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.

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The Journal of Physical Chemistry

Thermal Conductivity of CH3NH3PbI3 and CsPbI3: Measuring the Effect of the Methylammonium Ion on Phonon Scattering

Anton Kovalsky,1 Lili Wang, 1 Gage T. Marek,2 Clemens Burda,*,1 and Jeffrey S. Dyck*,2 1

Department of Chemistry, Case Western Reserve University, Cleveland, OH 44106 2

John Carroll University, Department of Physics, University Heights, OH 44118

ABSTRACT: Temperature-dependent thermal conductivity in the range between 7K and 300K was measured for CH3NH3PbI3 and CsPbI3, and compared to a Debye model via the Callaway method. Thermal conductivity was found to be extremely low across the whole temperature range for both materials, with CH3NH3PbI3 lower than CsPbI3. Fitting analysis showed that a resonant phonon scattering term can account for the difference in thermal transport behavior between the perovskite with a methylammonium (MA) ion versus a single cesium atom in the cationic A site of the lattice. The resonant frequency associated with this term is in the range of ~15-30 cm-1, pointing to the rotational degree of freedom of the organic ion. Analysis of the temperature dependence of the possible phonon scattering mechanisms showed that thermal conductivity of both CH3NH3PbI3 and CsPbI3 perovskites was dominated by Umklapp scattering at room temperature, and the rotation of the organic cation may be responsible for suppressing the thermal conductivity of CH3NH3PbI3 in comparison with CsPbI3, particularly at low temperatures, ~25K. This work presents the first determination of temperature-dependent thermal conductivity of CsPbI3.

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I.

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Introduction Organic-inorganic hybrid perovskites have attracted much attention because of their

unique photoelectric properties for potential uses in photovoltaic solar cells1–3, achieving certified efficiency of >20% so far.4 In recent years, tremendous effort has been put forth to improve the performance of perovskite-based solar cells by investigating the fundamental mechanisms of carrier transport.5–7 This progress has made these hybrid perovskites strong potential candidate materials for next generation photovoltaics. 12–17 Thermal transport properties of perovskites provide insight into the fundamental phonon physics of these materials. Herein, we explore the effect of methylammonium (MA)– an organic cation occupying the A site in the ABX3 lattice – on phonon scattering. The underlying mechanisms are shown to differ from the behavior of perovskite with a single cesium cation, possibly due to the MA’s additional rotational degrees of freedom. While it is known14 that it is the structure of the edge-connected BX6 octahedra that is primarily responsible for the electronic band structure of perovskite, the cation at the A-sites is expected to influence the thermal properties. In this study, the contribution of resonant scattering due to the MA ion is investigated by analyzing thermal conductivity data according to the Debye model using the Callaway method15 for calculating the thermal conductivity with a combined scattering time constant. Our results show that a resonant scattering term may be important in accounting for the difference in thermal transport behavior between a perovskite with MA ions, compared with cesium ions at its A-sites. Thermal properties of hybrid perovskites, such as their Seebeck coefficient, thermal diffusivity, and heat capacity16 have been investigated previously, and the link between thermal


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conductivity and perovskite-based solar cell efficiency has also been studied.17 Pisoni et al.18 reported the temperature-dependent thermal conductivity of CH3NH3PbI3, which was only 0.5 (W/(K*m)) at room temperature. In that work, the authors compare temperature-dependent thermal conductivity of a polycrystalline sample of CH3NH3PbI3 with a monocrystalline sample of the same compound, and show that both samples’ thermal behavior can be modeled using a resonant scattering term, and that according to their model, resonant scattering plays an important role in thermal transport, while grain boundary scattering plays only a minor role. This was a surprising finding regarding the effect of grain boundaries on energy transport, considering grain size is known to play an important role in perovskite-based photovoltaic device performance.19 It is important to note that Pisoni et al. obtained their polycrystalline sample by growing the monocrystal and then crushing it and pressing the resulting powder into a pellet. The crystallinity obtained by such a top-down procedure may be inherently different from that found in perovskite solar cells, where bottom-up crystal growth and engineering of crystallinity is critical. In solar cells, grain sizes are typically on the submicron scale.20 A time-domain thermoreflectance study of the thermal conductivity of spun-cast CH3NH3PbI3 films on various substrates was carried out by Guo et al17 wherein the authors modeled the thermal conductivity by accounting only for grain boundary-, point defect-, and Umklapp-related phonon scattering, omitting the potential contribution of resonant scattering. Guo et al were careful to point out that theirs was an in situ experiment that analyzed the thermal behavior of thin film perovskite cast onto substrates that mimic their environment in a solar cell. In contrast to their pump-probe laserbased measurement, conventional steady state thermal conductivity measurements, as done in our work, may be important for understanding the fundamental thermal physics in this material.


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In this study, we isolate and quantify the effect of methylammonium (MA) by comparing the thermal conductivity of CH3NH3PbI3 with that of CsPbI3, providing a quantitative determination of the difference in thermal conductivity in the MA-based material versus the Csbased one. We also provide, to the best of our knowledge, the first thermal conductivity measurements of CsPbI3 in this temperature range. We obtain our samples by drying and annealing a thin film from precursor solution in order to mimic the morphology of perovskite thin films. Our experimental results show that similarly processed MA-based and Cs-based perovskites have distinct but similar thermal behaviors, and we use modeling to deduce whether the suppressed thermal conductivity of CH3NH3PbI3 relative to CsPbI3 should be attributed to the cation’s molecular motion, or to the difference in grain size inherent to thin films of the MAbased perovskite. II.

Methods

CH3NH3PbI3 was prepared by synthesizing CH3NH3I from CH3NH2 (40 wt%, in water, Sigma) and HI (48 wt%, in water, Sigma) and mixing it with equimolar amounts of PbI2 powder (99 %, Fisher) in anhydrous N’N-dimethylformamide (DMF, water content < 50 ppm). This solution was dried in a vacuum oven and then heated under Ar atmosphere to 100oC. CsPbI3 was prepared in a similar fashion, with CsI in place of CH3NH3I, and by heating the dried powder under Ar flow to 350oC. Since the approach of making pellets from similarly dried powders is both reasonably simple and made for a robust comparison between the samples, this approach was chosen for our work. The powders were ground and pressed into 7.6 mm x 2.5 mm x 2.5 mm pellets, using a precision-cut steel die (General Precision Corporation). The pressure during pressing was 1.62 MPa, and was held for 30 minutes at room temperature. The density of the pressed pellets,


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relative to full density, was 91% for CsPbI3 and 97% for MAPbI3. The effect of porosity was taken into account for the thermal conductivity. All powders were characterized for phase purity via X-ray diffraction (XRD) analysis (Phillips Xpert). Pellets were also broken up after thermal measurements and grain sizes were determined with scanning electron microscopy (Phenom ProX). Figure S1 presents the XRD spectra at room temperature. MAPbI3 experiences a phase transition at 161K. Because the MAPbI3 low temperature phase is structurally similar to the CsPbI3 phase, only the data in the range from low temperature to the phase transition (7K-150K) was used in applying the theoretical analysis described herein. Thermal conductivity as a function of temperature was measured by the longitudinal steady state technique (schematic in Figure S2) in a closed-cycle helium cryostat at pressure below 10-5 torr. Fine (25 µm diameter) chromel-constantan differential thermocouples were used to determine the temperature difference across the sample, while a miniature strain gage mounted to the free end of the sample was used to generate temperature gradients of ~ 1% of the sample temperature. The sample was attached to the copper heat sink, and the thermocouples were attached to the sample, with Stycast FT2850. The effects of radiation losses near room temperature have been minimized with near ideal sample length and cross-section and the use of a radiation shield. III.

Results and Discussion Figure 1 shows the temperature dependence of the thermal conductivities for

CH3NH3PbI3 and CsPbI3 perovskites. A correction to the raw data has been made to account for the porosity of each sample. We employ the expression,21


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1+ β P    1− P 

κ fully dense = κ measured 

(1)

1.6 CsPbI3

Thermal Conductivity (W/(m*K))

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CsPbI3 (radiative loss corrected)

1.4

CH3NH3PbI3 CH3NH3PbI3 (radiative loss corrected)

1.2 1.0 0.8 0.6 0.4 0.2 0

50

100

150

200

250

300

Temperature (K)

Figure. 1. Temperature-dependent thermal conductivities for CH3NH3PbI3 and CsPbI3. Dotted lines represent corrections to the data after estimated heat losses due to radiation are removed.

where P is the porosity obtained by dividing experimental density of each pellet by the bulk density of the material, and β is a parameter related to the pore shape, which is taken here as β = 2, as has been done previously for similar porous samples.21 Our data on CH3NH3PbI3 matches well with the polycrystal data of ref. [17]. Relative to CH3NH3PbI3, the CsPbI3 perovskite has only a modestly higher thermal conductivity at room temperature, and the difference becomes greater upon cooling to low temperature. A small discontinuity in the thermal conductivity data is observed for CH3NH3PbI3 at ~161K, the temperature of the reported22 orthorhombic-tetragonal phase transition temperature. Upon this phase transition, our data indicate that thermal conductivity undergoes a small reduction, about 10%, in going from the orthorhombic to the


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tetragonal phase. Pisoni et al reported a similar kink in temperature-dependent thermal conductivity, albeit without a significant step down. By contrast, Guo et al. showed a much greater jump in thermal conductivity across this phase transition in their perovskite film on a Si substrate, but not when the perovskite film was on a mesoporous Al2O3 substrate. Guo et al.suggested that the reduction in thermal conductivity must thus be intrinsic to the neat film on Si. They further rationalize the difference between their observation and that of Pisoni’s polycrystalline sample by pointing out that the crushed-and-compressed polycrystalline powder pellet would not contain any preferentially oriented grains, whereas the perovskite film spun-cast onto a silicon substrate would experience preferentially oriented order, and thus that the observed jump in thermal conductivity may be related to an emergent quality of the perovskite-on-Si film. Our observation of the jump in a similarly ground-and-compressed bulk polycrystalline pellet suggests that a reduction in thermal conductivity in going from orthorhombic to tetragonal perovskite is intrinsic to the perovskite itself. The absence of the jump in Guo et al.’s perovskiteon-Al2O3 may be a result of the mesoporous alumina scaffold obscuring the change. Emissive heat loss causes thermal conductivity to be overestimated above 150 K. Therefore, a correction (shown as dotted lines in Figure 1) is applied to this data in the usual manner,23 noting that power from the heater is lost to the surroundings, P = σsb*ε*A [(Tsample)4 – (Tsurroundings)4], where σsb is the Stefan-Boltzmann constant, ε is the sample surface emissivity, and A is the exposed surface area. The dashed lines in Figure 1 are generated using ε = 0.8 for both materials. In the theoretical analysis below, we restrict the model fits to T below the phase transition of CH3NH3PbI3 since the radiation loss correction is very small in this temperature range and, moreover, the two samples share the orthorhombic crystal structure.


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In an attempt to clarify the precise role of the MA ion in limiting the thermal conductivity, we start by considering the difference between the MA and Cs cations. The Cs ion has no internal degrees of freedom (e.g., rotational), thus CsPbI3 is simpler to analyze from the standpoint of phonon scattering. In general, the total thermal conductivity may have contributions from both the lattice (acoustic phonons) and the charge carriers. However since the electrical conductivity is very low for CH3NH3PbI3 (0.1 MΩ-1*cm-1)24, one can ignore the electronic term, leaving only the contribution of the lattice thermal conductivity, . The contribution of electronic thermal conductivity of the CsPbI3 is equally ignored.25 The temperature dependence of the lattice thermal conductivity can be expressed by the Debye model as:

k k T  κ L (T ) = B2  B  2π ν  h 

3 θT

∫ τc 0

y 4e y dy (e y − 1) 2

(2)

where is the Boltzmann constant, = ⁄ with being the Debye temperature and n the number of atoms per primitive unit cell, C is the combined (including all relevant interactions) ℏ

phonon scattering time constant, =

is a dimensionless parameter with being the phonon

frequency, and v is the speed of sound, which was estimated from the relation:

kθ ν= B h

 2N  6π  V  

−1 3

(3)

where N/V is the number of atoms per unit volume.


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1

CsPbI3 - experiment CH3NH3PbI3 - experiment CsPbI3 3-mechanism fit (eq. 4) CH3NH3PbI3 3-mechanism fit (eq. 4) CH3NH3PbI3 2-mechanism fit (eq. 5) CH3NH3PbI3 4-mechanism fit (eq. 6)

10

100

Temperature (K)

Figure. 2. Thermal conductivities of CH3NH3PbI3 and CsPbI3 on a logarithmic scale, with solid lines representing model fitting with a 3-mechanism approach, and dotted lines representing modified approaches containing a resonant term for the CH3NH3PbI3. Only experimental data from 7K to 150K was fitted, so as to avoid complication due to the phase transition of CH3NH3PbI3 at ~161K and the unavoidable contribution of radiation effects on the data which are not negligible at higher temperatures.

We start with an analysis of CsPbI3, which we expect to be simpler, free of any phonon scattering due to internal degrees of freedom of MA. In this case, the combined scattering time is taken as:

τ c −1 =

−θ v + Aω 4 + Bω 2Te 3T d

(4)

where d is the average crystal grain size, and A and B are temperature independent coefficients. These terms represent grain boundary scattering, point defect scattering, and Umklapp scattering, respectively. The value of for CsPbI3 is not known, so we use the value = 120 K known for CH3NH3PbI3.16 This approximation is justified based on the similarities of the average atomic masses and lattice parameters of the two related materials.26 We use n = 5, and obtain an excellent agreement to the experimental data as shown in Figure 2, with fitting parameters shown in Table 1. The coefficient associated with Umklapp scattering term in τ C can be expressed as:


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hγ 2 B= M θν 2

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(5)

We explore the same theoretical approach for CH3NH3PbI3, with the results also shown in Figure 2 and Table 1. We again choose n = 5, which treats the MA ion as a point mass. In this scattering model, there is no allowance for resonant scattering due to rotations of the MA ion. Although the fitted values for d appear to be low relative to the average feature size seen under SEM (Figure S3), which shows a range of grain sizes between sub-micron to several microns, the fitted value of d for CH3NH3PbI3 is lower than that of CsPbI3, which is in qualitative agreement with the SEM images. Further, the point defect and Umklapp scattering prefactors, A and B are quite similar between the two compounds, which is reasonable. It appears that there may not be any need to invoke an additional scattering mechanism to account for the thermal conductivity for CH3NH3PbI3 given the good fit of the model to the data (Figure 2, solid black line, CH3NH3PbI3 3-mechanism fit). In particular, this approach to the modeling suggests that the difference in the behavior of the thermal conductivity between CsPbI3 and CH3NH3PbI3 can be accounted for by distinct differences in grain size. According to their results, Pisoni et al.18 suggested that resonant scattering by MA plays a large role in thermal conductivity of this material, whereas grain boundary scattering plays a minor role. The modeling results discussed above would not support this conclusion, though the fitted value of d may be too low suggesting an additional scattering mode is required. To explore the maximum effect that the internal degrees of freedom that the MA ion could have on the thermal conductivity, we modify the combined scattering constant in the same way as Pisoni et al, to account exclusively for Umklapp and resonant scattering, obtaining:


10

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−1

τ c = Bω Te 2

−θ

3T

ω 2ω0 2 +C 2 (ω − ω0 2 ) 2

(6)

where the last term on the right accounts for resonant scattering at a resonant frequency ω0 and an additional temperature independent constant C. The results for this fitting method can be seen in the third row of Table 1 and the dotted line in Figure 2. Notably, the resonant frequency obtained by fitting this model to the experimental data matches closely with the value of 42K published by Pisoni.18 In order for these two scattering mechanisms to be dominant over grain boundary and point defect related scattering, the implication is that d is greater than 20 µm according to our analysis. While this assumption may be valid for Pisoni’s monocrystalline sample preparation, our grain sizes are much smaller, as seen in the SEM images (Figure S3). Further, the upper limit on the point defect scattering prefactor A is 3×10-42 s, a value two orders of magnitude smaller than the fitted value in the CsPbI3 sample prepared by the same technique, which may additionally undermine this approach. Thus far, we have considered the two extreme theoretical scenarios – one in which there is no grain boundary/point defect scattering, which seems physically unlikely for our material, and one in which there is no resonant scattering, which is plausible according to the fit, but does not necessarily disprove the occurrence of resonant scattering. In reality, the correct picture of phonon scattering in CH3NH3PbI3 is likely between these two extremes.

To apply a model that takes into account all four relevant phonon scattering mechanisms, we take the following approach. Here, the combined scattering time relevant to Equation (2) is

τ c −1 =

−θ ω 2ω 2 v + Aω 4 + Bω 2Te 3T + C 2 0 2 2 d (ω − ω0 )

(7)


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Table 1. Fitting parameters from different approaches to thermal conductivity modeling A

B

d

C

ω0

(s × 10-40)

(K/s × 10-17)

(nm)

(-)

(K)

CsPbI3

1.8

6.2

270

--

--

MAPbI3

1.7

6.3

62

--

--

MAPbI3

--

5.8

--

1.1×1011

41

MAPbI3

1.8

6.2

270

3.8×108

18

We wish to avoid 5 free parameters in our model fitting to the data, so we postulate that the key difference between the Cs-based and MA-based material is purely the additional resonant scattering on the A-site due to the MA molecule. This leads us to take as fixed constants the A, B, and d values from the CsPbI3 fitting approach above, leaving only C and ω0 as free parameters. The results of this 4-mechanism, 2-free-parameter fitting approach is shown by the dashed black line in Figure 2 and the strength of the fit is nearly indiscernible from those of the two extreme approaches considered above. Moreover, the grain size d used in this approach is more appropriate to our samples. We conclude thus far that the difference observed in the thermal conductivity of CH3NH3PbI3 compared to CsPbI3 samples can be plausibly accounted for either by difference in grain sizes or by the additional resonant scattering mechanism hypothesized for the MAcontaining perovskite, and likely a combination of both. However, the resonant frequency extracted from these approaches (20 – 40 K, or 15 – 30 cm-1) can reasonably be assigned to a weakly hindered rotation of the molecule within its inorganic cage – a free rotation would be in the range of 1-10 cm-1 while hindered rotations have frequencies from tens to hundreds of wavenumbers.27 Furthermore, this result is in good agreement with reported ultrafast 2D


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vibrational spectroscopy measurements that reveal a distinct cationic librational motion on the picosecond timescale.28 Our modeling results suggest that the extremely low thermal conductivity in CH3NH3PbI3 can be understood to be limited by the combination of phonons scattering on point defects, grain boundaries, other phonons, and resonant excitations of the MA ion. A key question we wish to address is the relative importance of each scattering mechanism at various temperatures, particularly the dominant

scattering mechanism and relative importance of the resonant

scattering mechanism near room temperature where devices based on this material would operate. To clarify this, we extrapolate our fitting results to room temperature and consider the effect of each separate mechanism on the total thermal conductivity individually. Firstly, our scenario above based on Equation (2) and (4) shows that the minimum effect of resonant scattering is in fact none at all. The maximum contribution is explored in Figure 3a where the solid black line represents the temperature dependence of the model fit according to Equation (5) up to room temperature. Setting C = 0 “turns off” the resonant scattering term, leaving only the Umklapp scattering term (blue dashed line in Figure 3a). This illustrates how resonant scattering with a resonant frequency of 41 K has the largest effect at very low temperature, and a much smaller effect at room temperature. On the other hand, the model with only resonant scattering (setting B = 0; red/orange dashed line) results in a thermal conductivity that rises much more significantly at room temperature. Therefore, we can qualitatively see that the dominant phonon scattering effect at room temperature is phonon-phonon scattering. It is in fact the lattice framework that is the primary reason for the ultra-low thermal conductivity in our material at room temperature, and the details of what is on the A-site is a secondary consideration. In comparison to CsPbI3, we see a very similar Umklapp term pre-factor, B, in Table 1 which


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supports this conclusion. Figure 3b shows a similar analysis on the full 4-mechanism approach. Here, the solid black line represents the model using fitting parameters related to Equation (6) (as in Figure 3b), and extrapolated to room temperature. Now, one can see that the very low thermal conductivity at low temperature is primarily accounted for with a combination of grain boundary and point defect scattering. 10

2-Mechanism model Umklapp off Res. scat. off

(a) 10

1


100


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(b) 1

4-mechanism model Grain boun. off Pt. def. off Umklapp off Res. scat. off

0.1 0.1 10

100

10

Temperature (K)

100

Temperature (K)

Figure. 3. Room-temperature-extrapolated (a) 4-mechanism model and (b) 2-mechanism model showing the temperature dependence of each phonon scattering mechanism by silencing the respective term for grain boundary scattering, point defect scattering, Umklapp scattering, and MA-ion-related resonant scattering.

At room temperature, the most important mechanism is again Umklapp scattering. In this most realistic 4-mechanism approach, the resonant scattering from the MA ion is relatively minimal at room temperature. The analysis in Figure 3 highlights the fact that although the resonant phonon scattering associated with hindered rotations of the MA ion on the perovskite A-site is likely a factor limiting the thermal conductivity at low temperature, its relative importance at room temperature is quite small relative to the intrinsic Umklapp phonon-phonon scattering determined primarily


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by the perovskite cage structure. At low temperature, however, the relative importance of grain boundary and point defect scattering must be more significant, and researchers exploring thermal conductivity in this range have to thoroughly address the morphology of all samples. Obviously, the thermal properties depend strongly on sample preparation, and comparison of different thermal data, even for the same chemical compound, should be made with particular care. IV.

Summary

In conclusion, temperature-dependent thermal conductivities are measured for two polycrystalline perovskite compounds, CH3NH3PbI3 and CsPbI3, grown from precursor solutions. This is to the best of our knowledge the first report of thermal conductivity data on CsPbI3. Further, a comparison of the data to a model of lattice thermal conductivity based on the Debye model is presented. The thermal conductivity on both materials is extremely low over the entire temperature range studied. While the difference in thermal conductivity between the two compounds is large at temperatures around 40K, the difference is rather small at room temperature, and our model presents the temperature dependence and relative contribution for the various phonon scattering mechanisms. In the case of CsPbI3, the predicted29 low thermal conductivity can be feasibly understood in terms of phonons scattering on other phonons (Umklapp), point defects, and grain boundaries. For CH3NH3PbI3, the inclusion of a resonant scattering term appears to be necessary in order to understand the data. Interestingly, the difference between thermal conductivity in the MA-containing vs. the Cs-containing samples over the entire temperature range studied could be accounted for by addition of a resonant scattering term to the combined phonon scattering time with a resonance frequency of ~15 – 30 cm-1, which can reasonably be attributed to a hindered rotation. However, at room temperature,


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our results show that for both compounds, the dominant phonon scattering mechanism is Umklapp scattering. In particular, we wish to highlight that while the MA ion in CH3NH3PbI3 induces phonon scattering that impacts the thermal conductivity at low temperature, its affect at room temperature in our samples is small. ASSOCIATED CONTENT See supporting information for X-ray diffraction (XRD) and scanning electron microscopy (SEM) characterization of CH3NH3PbI3 and CsPbI3 and for schematic of measurement setup. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION

Corresponding Author Prof. Clemens Burda, [email protected], 216.368.5918

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT The authors would like to thank Prof. Yixin Zhao (Shanghai Jiao Tong University) for teaching us the synthesis and for additional discussions about perovskites. The authors also thank Case Western Reserve University for supporting the research. REFERENCES

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Thermal Conductivity of CH3NH3PbI3 and CsPbI3 - ACS Publications

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