Anisotropy of Thermal Diffusivity in Lead Halide Perovskite Layers

Article Cite This: J. Phys. Chem. C 2019, 123, 14914−14920

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Anisotropy of Thermal Diffusivity in Lead Halide Perovskite Layers Revealed by Thermal Grating Technique P. Š cǎ jev,† R. Aleksieju̅nas,*,† S. Terakawa,‡,∥ C. Qin,‡,∥ T. Fujihara,⊥ T. Matsushima,‡,§,∥ C. Adachi,‡,§,∥ and S. Juršeṅ as† †

Institute of Photonics and Nanotechnology, Vilnius University, Sauletekio Ave. 3, Vilnius LT-10257, Lithuania Center for Organic Photonics and Electronics Research (OPERA) and §International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi, Fukuoka 819-0395, Japan ∥ Adachi Molecular Exciton Engineering Project, Japan Science and Technology Agency (JST), ERATO, 744 Motooka, Nishi, Fukuoka 819-0395, Japan ⊥ Innovative Organic Device Laboratory, Institute of Systems, Information Technologies and Nanotechnologies (ISIT), Fukuoka Industry-Academia Symphonicity (FiaS), 2-110, 4-1 Kyudai-shinmachi, Nishi, Fukuoka 819-0388, Japan

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‡

S Supporting Information *

ABSTRACT: Heat management of optoelectronic devices is of critical significance in lead halide perovskites due to the intrinsically low thermal conductivity of this material. Despite its importance, thermal conductivity remains understudied, particularly in polycrystalline perovskite layers with different halides. Here, we employ a novel method for investigation of thermal properties in perovskite layers, which is based on a light-induced transient diffraction grating technique. We demonstrate the applicability of thermal grating technique by determining in an all-optical way the thermo-optic coefficient, speed of sound, and thermal conductivity in vapor-deposited polycrystalline layers of MAPbX3 (X = Cl, Br, I), MAPbBr2I, and MAPbCl2Br perovskites. We reveal the spatial anisotropy of thermal conductivity, which is noticeably lower in the direction along the layer surface (0.2−0.5 W/(m K)) if compared to that across the layer (0.3−1.1 W/(m K)). Finally, we demonstrate that for both directions the thermal conductivity scales linearly with the average speed of sound in the perovskite layers.

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INTRODUCTION Lead halide perovskites (MAPbX3) earned their fame mostly as an efficient and potentially cheap material for solar cells.1 Recent advances, however, encouraged to consider them for a much wider range of applications, including light-emitting or even laser diodes.2−4 These photonic devices operate at high drive currents resulting in a considerable amount of heat that must be dissipated. Heat management turns out to be of critical importance in perovskite devices due to their intrinsically low thermal conductivity.5 Heating of a photonic device is detrimental in itself; for lead halide perovskites, it is especially destructive due to their thermal instability6 since heat promotes the evolution of volatile organic species and formation of lead halides.7 Therefore, there is a necessity in a detailed understanding of heat transport in perovskites and methods to investigate them. Despite its practical importance, the heat transport in perovskites has been studied much less than, e.g., charge carrier transport and is not fully understood yet. Two important questions are related to the role of compositional structure and phonon scattering at the grain boundaries in polycrystalline perovskite layers. Indeed, it is desirable to use low-cost and scalable deposition methods, but they are known to yield the polycrystalline perovskite layers.8 It is intuitive to expect then that thermal conductivity κ in these layers should decrease due © 2019 American Chemical Society

to phonon scattering at grain boundaries; however, the experimental studies dealing with thermal conductivity in polycrystalline perovskites still are few, whereas the majority of published works are devoted to MAPbI3 single crystals. Even for lead iodide crystals, the reported κ values are somewhat scattered depending on the measurement technique and individual sample: κ = 0.14 W/(m K) was obtained in crystal platelets by microphotoluminescence technique,9 κ = 0.3−0.42 W/(m K) was measured in single crystals by flash method,10,11 and κ = 0.5 W/(m K) using the thermocouples attached to the investigated layers.5 As to the role of the compositional structure, two recent studies addressed the dependence of κ on halide X in MAPbX3 single crystals: ultralow values within the range κ = 0.3−0.73 W/(m K) were reported independently on halides, with general tendency of κ increasing from −I3 to −Br3 to −Cl3.11,12 Both latter studies concluded that low thermal conductivity in lead halide perovskites has an intrinsic nature determined by low acoustic speed in soft material and strong phonon−phonon scattering due to lattice vibration anharmonicity. This conclusion was further supported by calculations using the equilibrium molecular dynamics.13 Resonant Received: March 11, 2019 Revised: May 25, 2019 Published: May 28, 2019 14914

DOI: 10.1021/acs.jpcc.9b02288 J. Phys. Chem. C 2019, 123, 14914−14920

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The Journal of Physical Chemistry C Table 1. Parameters of the Perovskite Layersa sample MAPbI3 MAPbBr2I MAPbBr3 MAPbCl2Br MAPbCl3

thickness (nm) 600 480 500 460 500

(1100) ± 50 (1300) ± 50 ± 50

grain size (nm)

pump wavelength (nm)

αpump (105 cm−1)

Eg (eV)

τ0PL (ns)

± ± ± ± ±

527 527 527 351 351

1.2 0.77 0.66 1.2 1.2

1.65 1.96 2.36 2.42 3.11

0.5 8 0.6 0.11 0.15

100 150 160 140 130

50 50 50 50 50

a

Numbers in parenthesis correspond to thicker layers.

for comparison. The average grain size in the samples was 130−160 nm; only in the MAPbI3 layer, the grains were smaller of ∼100 nm size. The values of absorption coefficient at the pump wavelength αpump, band gap EG, and the carrier lifetime (determined from photoluminescence decay) τ0PL are used as determined in the previous work.19 Thermal Diffraction Grating Measurements. We use the LITG technique for determination of the thermal diffusion coefficient, thermo-optic coefficient, and the average speed of sound in the lead halide perovskite layers of different compositions. This versatile pump−probe type method is based on measuring the diffraction efficiency of a probe beam on a periodically modulated refractive index n, which is created by exposing the sample to the interference field of light.20 In this work, we exploit the fact that there are several physical mechanisms causing the modulation of refractive index and they appear on distinctly different time scales. Initially, the refractive index is altered proportionally to the density of photogenerated excess carriers; this regime becomes increasingly popular for determination of carrier diffusion coefficient in perovskites.18,19,21,22 The upper limit for the decay time of free carrier grating is set by the excess carrier lifetime, which in highly excited perovskite layers is on the order of up to tens of nanoseconds.18,19 We note that there are multiple reports of very long carrier lifetimes, up to the microsecond scale;23,24 however, such a long lifetime is characteristic for low carrier densities when carrier transport is strongly influenced by carrier localization processes. The second stage of LITG decay takes place on a considerably longer time scale, where the refractive index is modulated due to thermo-optic effect by periodical temperature variation; we refer to this stage as thermal (diffraction) grating.20 The heating of the sample occurs in the illuminated areas due to nonradiative carrier recombination. The thermal grating decays with characteristic time τG due to (i) thermal diffusion along the grating vector (parallel to the sample surface) and (ii) thermal diffusion toward the substrate with characteristic times τD and τTh. The grating decay time τG can be expressed as20

scattering was argued to be of lesser importance, at least at room temperature,12,14,15 in contrast to what had been proposed before.5 The impact of layer polycrystallinity remains even less clear. In several studies, κ was measured in polycrystalline MAPbX3 samples with X = I, Br, and Cl, but the obtained values strikingly resembled those in single crystals with the corresponding halide.5,14,16 All of these measurements, however, were carried out on samples prepared by the hot pressing procedure, which resulted in laterally large grains of dimensions on the micron scale. Elbaz et al. concluded that ∼70% of phonons determining the thermal conductivity have mean free path below 100 nm in organic−inorganic perovskites,12 suggesting that thermal conductivity should not be affected in the layers with large grains as in the mentioned studies. A possible impact of grain boundary scattering was proposed by Guo et al., who demonstrated that the thermal conductivity is larger at the layer surface than that deeper in the sample (0.5 vs 0.3 W/(m K)), probably due to the increasing lateral dimensions of grains when going further away from the substrate.17 In this paper, we present a new method of measuring the thermal properties of perovskite layers by employing the lightinduced transient grating (LITG) technique. We upgraded the setup that was used to study the carrier transport in perovskite layers18,19 by expanding the probe delay time up to several microseconds, which allowed the observation of thermal diffraction grating dynamics. We used thermal grating technique then to obtain in an all-optical manner the thermo-optic coefficient, average speed of sound, and thermal diffusivity in vapor-deposited polycrystalline MAPbX3 layers with different halides and much smaller crystallite size. We reveal the anisotropy of thermal diffusivity, which noticeably differs in directions parallel and perpendicular to the layer surface. We discuss the possible reasons for this anisotropy in terms of phonon scattering at grain boundaries of nonspherical and spatially oriented crystallites. We demonstrate that in both directions the thermal conductivity scales linearly with the average speed of sound in the layer.

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EXPERIMENTAL METHODS Materials. MAPbI3, MAPbBr3, MAPbCl3, and two mixed halide perovskite MAPbBr2I, MAPbCl2Br polycrystalline layers of smooth surfaces and different band gaps were vapordeposited on fused silica (FS) substrates. For the detailed description of sample growth procedures, please refer to our earlier work.19 The parameters of the layers that are used in the current study are provided in Table 1. The thickness and average grain size of perovskite layers were determined from scanning electron microscopy (SEM) images shown in the Supporting Information (Figure S1). The layer thickness in the main set varied from 460 to 600 nm; we also included two thicker layers of MAPbI3 and MAPbBr3 (1100 and 1300 nm)

4π 2DTh 1 1 1 1 = + = + τG τTh τD τTh Λ2

(1)

where Λ is the period of thermal grating and DTh is the thermal diffusion coefficient. DTh is related to thermal conductivity κ as DTh = κ/ρCp, where ρ and Cp are the material density and heat capacity, respectively. By measuring a set of decay transients for several different Λ values, one can determine DTh, according to eq 1. This method has been shown as a suitable tool for thermal diffusion investigation in both bulk materials and layers on a substrate;25 we used it previously to determine the thermo-optic coefficient in SiC.26 14915


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The Journal of Physical Chemistry C Finally, the heating of the lattice results in the additional mechanism of refractive index modulation due to the local changes in material density. As a result, the spatially periodic thermal grating gives rise to the traveling acoustic wave that can be seen in LITG kinetics as periodic decoration of otherwise continuous decay. From the period of these oscillations, the speed of sound can be determined in various materials,20 as it was demonstrated explicitly for 4H-SiC.26 In this work, we used 10 ps duration pulses from an Nd-YLF laser at 527 or 351 nm wavelength to record the transient in a sample. The pump wavelength for a given layer was chosen so that the quanta energy would exceed the band gap of the studied perovskite material. The diameter of pump beams was 750 ± 20 μm, whereas the pump energy fluences were 1.1 mJ/ cm2 for 351 nm and 1.9−2.5 mJ/cm2 for 527 nm excitations. The transient grating was monitored by diffraction of an electronically delayed probe pulse at 1064 nm that was delivered by a 10 ns duration Nd-YAG laser (the probe beam diameter was 200 ± 30 μm). The period Λ of the transient grating was varied between 1.9, 2.3, 2.9, 3.8, and 7.8 μm, using the holographic beam splitters of different periods and a telescope that projected the image of the splitters onto the sample surface.

Figure 1. Absolute values of thermo-optic coefficient as a function of the perovskite band gap EG. The solid line shows the fit according to eq 3 with the free fitting parameters A = (4.2 ± 0.3) × 10−5 K−1, B = (2.4 ± 0.2) × 10−5 eV/K, and Γ = 0.0134 eV.

B(EG − E) dn =A+ dT (EG − E)2 + Γ 2

where E = 1.1654 eV is the photon energy of the probe beam; A, B, and Γ are the free fitting parameters, with A representing the thermo-optic coefficient value far below the band gap; and Γ is the damping constant. The solid line in Figure 1 shows the fit to eq 3 with the fitting coefficient values of A = (4.2 ± 0.3) × 10−5 K−1, B = (2.4 ± 0.2) × 10−5 eV K−1, and Γ = 0.0134 eV. We note that qualitatively similar dependencies of n on temperature and wavelength are assumed for all perovskites, which is feasible since the induced temperature modulation is small and the difference EG − E is large for all investigated perovskites. The calculated dependence of the thermo-optic coefficient on band gap is shown by the solid line in Figure 1. To compare the obtained values to published data, we estimated the thermo-optic coefficient value dn/dT = −(0.8 ± 0.3) × 10−4 K−1 at E = 1.1654 eV using the ellipsometry results obtained at several temperatures in MAPbI3.29 This is in fair agreement with our value of −(0.9 ± 0.1) × 10−4 K−1. Please note that the thermo-optic coefficient is negative in perovskites since their band gap decreases with temperature, contrary to conventional semiconductors. In addition, we applied the thermal grating technique to measure the thermooptic coefficient in CdTe where the reference data is more readily available. Our value of 1.8 × 10−4 K−1 was in good agreement with the published one of 2.0 × 10−4 K−1;30 we used CpCdTe = 0.209 J/(g K) and ρCdTe = 5.86 g/cm3.31 Speed of Sound. To determine the speed of sound in the perovskite layers, we used an intense excitation at 351 nm wavelength, which ensured rapid local heating of the lattice and resulted in the appearance of acoustic waves and oscillations in the initial parts of thermal grating transients (Figure 2). The oscillating parts of LITG transients were fitted to the following relation26

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RESULTS AND DISCUSSION Thermo-Optic Coefficient. We begin with the determination of the thermo-optic coefficient dn/dT in the perovskite layers with different halides. As it is shown in ref 26, the diffraction efficiency η(t), which is measured experimentally as the ratio between the intensities of diffracted and transmitted parts of the probe, for a thermal grating can be expressed in the following form η(t ) =

dn π · I0(1 − e−αpump·d) ·e−t / τG dT Cpρλprobe

(2)

where λprobe is the probe wavelength, I0 is the energy fluence of the pump beam, and d is the layer thickness. The Cp values were taken from ref 27 and are shown in Table 2. Since we did Table 2. Speed of Sound Measured by LITG Method in Perovskite Layers sample

vT (m/s)

vL (m/s)

vava (m/s)

Vavb (m/s)

MAPbI3 MAPbBr2I MAPbBr3 MAPbCl2Br MAPbCl3

1292 1603 1676 1788 2104

1603 2163 2480 2385 3020

1404 1790 1944 1987 2397

1390

(3)

1717 2194

a

The estimated experimental error of speed of sound does not exceed 50 m/s. bThe average values of sound speed reported by Elbaz et al.12

ij ij 2πt yz i yy zz + A sinjjj 2πt zzzzzzz η(t ) = Ajjjje−t/ τG + A1 sinjjj 2 z j j T z j T zzz k 1 { k 2 {{ k

not find any data on Cp in mixed halide perovskites, it was obtained by interpolation between the corresponding single halide perovskite values according to the molar halide composition. The thermo-optic coefficient values calculated from the measured η(t) using eq 2 are shown in Figure 1 as a function of the band gap of the perovskite. As can be seen, dn/dT decreases with EG from 0.92 to 0.5 K−1 within the investigated range. This dependence fits well to the model proposed by Ziang et al.,28 which we modify assuming a single resonance at EG

2

(4)

where the first term describes the exponential decay of thermal grating according to eq 1, whereas the second and third terms account for oscillatory component caused by transverse and longitudinal phonons, respectively; A stands for the corresponding amplitudes; and T stands for periods of these components. A and T served as free parameters to fit the data in Figure 2 to eq 4. From the obtained oscillation periods T, we calculated the sound speed for transverse vT = Λ/T1 and 14916


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The Journal of Physical Chemistry C

diffraction efficiency transients for different grating period values in MAPbBr3; the decay kinetics in other samples looks similar. The time constant of grating decay τG decreases for smaller periods, indicating the contribution of heat diffusion. Note that in this study we investigate the processes much slower than free carrier recombination. As it was already mentioned, the lifetime of free carriers reaches up to ∼10 ns in these layers, as determined from the time-resolved PL measurements (see Table 1). To illustrate the rate of free carrier recombination, we show in Figure 3b the transient of differential transmission, whose signal amplitude is proportional to free carrier density. To additionally confirm that the investigated LITG dynamics is not affected by free carrier recombination, we measured the decay kinetics for different excitation energy fluencies. Figure 3b shows that while the LITG signal amplitude scales with excitation squared (see the inset), the grating decay time remains independent of excitation. This fact excludes the impact of free carrier recombination, where the recombination rate at given carrier densities should increase with excitation due to band-to-band and Auger recombination.32 The decay time constants τG were used to build the plots of 1/τG against 1/Λ2 (Figure 3c) and to determine the thermal diffusion coefficient DTh and the characteristic time τTh according to eq 1; the obtained values are listed in Table 3. We attribute the period-independent term 1/τTh to the rate of heat transport toward the substrate serving as a heat sink. This assumption is supported by the values of τTh, which are larger for thicker layers (see Table 3, numbers in parenthesis for MAPbI3 and MAPbBr3), since the phonon travel distance is longer.

Figure 2. Initial parts of LITG transients under strong 351 nm excitation and Λ = 0.93 μm grating period in the perovskite layers. The dots show the experimental data, and the lines show the calculated decay transients according to eq 4. The oscillations mark the contribution of the photoacoustic effect.

longitudinal vL = Λ/T2 sound waves. The average sound speed vav was calculated as A v + A 2 vL vav = 1 T A1 + A 2 (5) In Table 2, we list the measured transverse, longitudinal, and average sound velocities in our samples. While we could not find any data for mixed perovskites, the speed of sound obtained by LITG in MAPbX3 (X = Cl, Br, I) is in reasonable agreement with that obtained using the elastic modulus values measured by nanoindentation experiments.12 Thermal Diffusivity. Now, we apply the thermal diffraction gratings to investigate heat dynamics in the perovskite layers. To determine the thermal diffusivity and thermal conductivity in the samples, we recorded the transient gratings for various grating periods Λ. Figure 3a shows the

Figure 3. (a) Diffraction efficiency transients recorded in MAPbBr3 at free different grating periods Λ. The solid lines indicate the decay traces modeled using eq 7. (b) Diffraction efficiency transients recorded in MAPbBr3 at one fixed grating period and different excitation energy fluencies. The numbers near the transients indicate the excitation energy fluencies and time constants of grating decay. Inset: the dependence of the peak diffraction efficiency value vs excitation energy fluence. The number shows the slope of the dependence in log−log representation. (c) Grating decay rate 1/τG as a function of 1/Λ2. The solid lines show the modeled D∥. Open points show data for two thicker layers. 14917


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The Journal of Physical Chemistry C Table 3. Thermal Properties of Perovskite Layersa sample

ρ (g/cm3)

Cp (J/(g K))

dn/dT (10−4 K−1)

DTh (10−3 cm2/s)

τTh (ns)

D∥ (10−3 cm2/s)

D⊥ (10−3 cm2/s)

κ∥ (W/(m K))

κ⊥ (W/(m K))

MAPbI3 MAPbBr2I MAPbBr3 MAPbCl2Br MAPbCl3

4.16 3.932 3.818 3.387 3.171

0.306 0.337 0.355 0.436 0.492

0.93 0.76 0.65 0.59 0.53

1.6 (1.6) 3.0 3.2 (2.6) 3.4 3.9

2470 (3950) 920 1440 (9000) 910 703

1.5 (1.5) 2.6 2.9 (2.5) 3.0 3.5

2.2 (2.1) 4.0 3.5 (3.7) 4.8 6.0

0.19 (0.19) 0.34 0.39 (0.34) 0.44 0.5

0.28 (0.27) 0.52 0.47 (0.5) 0.71 1.1

a

Numbers in parenthesis correspond to the thicker layers

i

(10) k { and the value z0 ≈ 30 nm was used. Fused silica (FS) parameters used in the modeling are the following: CpFS = 0.74 J/(g K), ρFS = 2.2 g/cm3, DThFS = 8.2 × 10−3 cm2/s, and dn/ dT(FS) = 9 × 10−6 K−1.33,34 The described model provided a good agreement between the calculated and measured dynamics of thermal grating (the calculated transients for MAPbBr3 are shown by solid lines in Figure 3a) and allowed for estimation of the heat diffusion coefficient in directions parallel and perpendicular to the sample surface. As can be seen in Table 3, DTh and D∥ values are rather close. This fact leads to the conclusion that the standard procedure of diffusion coefficient determination from eq 1 can be used for estimation of heat diffusivity and thermal conductivity of a perovskite layer with good precision. More thorough analysis, however, allows for some further insights into the role of crystallite grains in thermal conductivity of perovskite layers. The values of D∥, D⊥, κ∥, and κ⊥ obtained from modeling are listed in Table 3, whereas Figure 4 shows the calculated κ∥ and

dΔT (x , y , z) = ∇·(D(x , y , z)∇ΔT (x , y , z)) dt + G (x , y , z , t )

y

∫ jjjj ∂D∂(zz) zzzzdz = D⊥substrate − D⊥perovskite

To better describe the heat transport under our experimental conditions, we adopted the model of heat diffusion supplemented with periodic heat generation term20

(6)

where ∇ is the differential operator, G(x,y,z,t) = (P(x,y,z,t)αpump)/(ρCp) is the temperature generation function, and P(x,y,z,t) is the photoexcitation power, related to the excitation energy fluence as ∫ P(x,y,z,t)dt = I(x,y,z). In a thin perovskite layer deposited on a silica substrate and photoexcited by a periodic interference pattern, it is reasonable to assume that temperature gradients are formed along two perpendicular directions, one along the grating vector (in our case, along the layer surface) and the other perpendicular to the surface or along the direction toward the substrate; we denote these two directions as x and z, respectively. We denote the diffusion coefficient components as Dx = Dy = D∥(z) (diffusion coefficient along the surface) and Dz = D⊥(z) (diffusion coefficient across the surface). We assume D∥(z) being constant in the (x, y) plane, but both diffusivity components change toward the substrate. Under these assumptions, eq 6 is transformed into the following form ∂ 2ΔT (x , z , t ) ∂ΔT (x , z , t ) = D (z ) ∂t ∂x 2 2 ∂ ΔT (x , z , t ) + D⊥(z) ∂z 2 ∂D (z)∂ΔT (x , z , t ) + ⊥ + G (x , z , t ) ∂z ∂z (7)

Figure 4. Dependence of thermal conductivity on the average speed of sound for the directions parallel (κ∥ navy symbols) and perpendicular (κ⊥ olive symbols) to the layer surface. The solid lines show the linear fits.

with initial spatial distribution ΔT(x,z)

i i 2πx zyyzz zzz exp( −αz), z < d , ΔT0 ΔT (x , z) = ΔT0jjj1 + cosjjj k Λ {{ k I0·αpump = ρCp (8)

κ⊥ values as functions of the average sound speed (Table 2). Several conclusions can be drawn by analyzing the data in Figure 4. First of all, the thermal conductivity in the studied polycrystalline layers is small (0.2−1.1 W/(m K)) and fits reasonably well within the limits reported by other authors. However, a clear spatial anisotropy of thermal conductivity can be seen, which is 1.5−2.2 times higher in the direction perpendicular to the surface than that along the surface. Finally, the measured thermal conductivity increases linearly with the speed of sound in the layers for both directions. The latter result agrees well with that reported by Elbaz et al., where it was proposed that the mean free path of acoustic phonons is similar in all MAPbX3 perovskites and the differences in heat

D⊥(z) is expected to be inhomogeneous near the substrate, continuously transforming from D⊥perovskite to D⊥substrate, which is taken into account in eq 7 by the derivative ∂D⊥(z)/∂z. We assume this derivative to have a sharp Gaussian shape ij (z − d)2 yz (D⊥ substrate − D⊥ perovskite) ∂D⊥(z) zz expjjj− = zz 2 j ∂z π ·z 0 z 0 k {

(9)

The integration constant in eq 9 was chosen such that 14918


The Journal of Physical Chemistry C

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conductivity result mainly from the variations in the speed of sound.12 Thus, we show that linear dependence applies to the grained layers as well. We attribute the spatial anisotropy of κ to the influence of crystallite grains on heat conductivity, which we believe can be 2-fold. First, the difference in κ values may originate from the nonequal scattering rates of acoustic phonons at grain boundaries, due to the nonspherical shape of the grains. SEM images (see the Supporting Information, Figure S1) show the grainy character of the layers, with the mean grain size within 100−160 nm range (see Table 1). A closer inspection reveals that grains at least in some layers are not spherical but rather prolongated toward the substrate. As a result, the mean distance between the grain boundaries across the sample is generally larger than that along the surface and considerably exceeds 100 nm. It was predicted that only the grains of dimensions of around 100 nm or less effectively participate in phonon scattering because the majority of phonons have the mean free path below 100 nm.12 Therefore, the phonons traveling toward the substrate might experience less scattering, which leads to higher heat conductivity. We also note that phonons traveling along the surface can experience additional scattering due to surface roughness, which might be the reason behind the lowest κ value in iodide films. Second, XRD spectra (Supporting Information, Figure S2) suggest a high level of orientational ordering of crystallites in some layers (−PbCl3, −PbBr2I). Therefore, the anisotropy of κ in part can be related to differences of sound speed along the different crystallographic directions, as it was shown by numerical simulations for single MAPbX3 crystals.11

AUTHOR INFORMATION

Corresponding Author

*E-mail: ramunas.aleksiejunas@ff.vu.lt. ORCID

P. Š čajev: 0000-0001-9588-0570 R. Aleksieju̅nas: 0000-0002-9093-2252 C. Adachi: 0000-0001-6117-9604 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Vilnius University team acknowledges the financial support provided by the Research Council of Lithuania under the project no. S-MIP-17-71. Additionally, this work was supported by the Japan Science and Technology Agency (JST), ERATO, Adachi Molecular Exciton Engineering Project (grant number JPMJER1305), JSPS KAKENHI (grant numbers JP15K14149 and JP16H04192), and The Canon Foundation.

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REFERENCES

(1) Green, M. A.; Ho-Baillie, A.; Snaith, H. J. The Emergence of Perovskite Solar Cells. Nat. Photonics 2014, 8, 506−514. (2) Stranks, S. D.; Snaith, H. J. Metal-Halide Perovskites for Photovoltaic and Light-Emitting Devices. Nat. Nanotechnol. 2015, 10, 391−402. (3) Sutherland, B. R.; Sargent, E. H. Perovskite Photonic Sources. Nat. Photonics 2016, 10, 295−302. (4) Tan, Z.-K.; Moghaddam, R. S.; Lai, M. L.; Docampo, P.; Higler, R.; Deschler, F.; Price, M.; Sadhanala, A.; Pazos, L. M.; Credgington, D.; et al. Bright Light-Emitting Diodes Based on Organometal Halide Perovskite. Nat. Nanotechnol. 2014, 9, 687−692. (5) Pisoni, A.; Jaćimović, J.; Barišić, O. S.; Spina, M.; Gaál, R.; Forró, L.; Horváth, E. Ultra-Low Thermal Conductivity in OrganicInorganic Hybrid Perovskite CH3NH3PbI3. J. Phys. Chem. Lett. 2014, 5, 2488−2492. (6) Leijtens, T.; Eperon, G. E.; Noel, N. K.; Habisreutinger, S. N.; Petrozza, A.; Snaith, H. J. Stability of Metal Halide Perovskite Solar Cells. Adv. Energy Mater. 2015, 5, No. 1500963. (7) Leijtens, T.; Bush, K.; Cheacharoen, R.; Beal, R.; Bowring, A.; McGehee, M. D. Towards Enabling Stable Lead Halide Perovskite Solar Cells; Interplay between Structural, Environmental, and Thermal Stability. J. Mater. Chem. A 2017, 5, 11483−11500. (8) Li, Z.; Klein, T. R.; Kim, D. H.; Yang, M.; Berry, J. J.; Van Hest, M. F. A. M.; Zhu, K. Scalable Fabrication of Perovskite Solar Cells. Nat. Rev. Mater. 2018, 3, No. 18017. (9) Shen, C.; Du, W.; Wu, Z.; Xing, J.; Ha, S. T.; Shang, Q.; Xu, W.; Xiong, Q.; Liu, X.; Zhang, Q. Thermal Conductivity of Suspended Single Crystal CH3NH3PbI3 Platelets at Room Temperature. Nanoscale 2017, 9, 8281−8287. (10) Ye, T.; Wang, X.; Li, X.; Yan, A. Q.; Ramakrishna, S.; Xu, J. Ultra-High Seebeck Coefficient and Low Thermal Conductivity of a Centimeter-Sized Perovskite Single Crystal Acquired by a Modified Fast Growth Method. J. Mater. Chem. C 2017, 5, 1255−1260. (11) Ge, C.; Hu, M.; Wu, P.; Tan, Q.; Chen, Z.; Wang, Y.; Shi, J.; Feng, J. Ultralow Thermal Conductivity and Ultrahigh Thermal Expansion of Single-Crystal Organic-Inorganic Hybrid Perovskite CH3NH3PbX3(X = Cl, Br, I). J. Phys. Chem. C 2018, 122, 15973− 15978. (12) Elbaz, G. A.; Ong, W. L.; Doud, E. A.; Kim, P.; Paley, D. W.; Roy, X.; Malen, J. A. Phonon Speed, Not Scattering, Differentiates Thermal Transport in Lead Halide Perovskites. Nano Lett. 2017, 17, 5734−5739. (13) Wang, M.; Lin, S. Anisotropic and Ultralow Phonon Thermal Transport in Organic−Inorganic Hybrid Perovskites: Atomistic Insights into Solar Cell Thermal Management and Thermoelectric

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CONCLUSIONS In this work, we applied a novel method of thermal grating to study the heat transport properties in polycrystalline vapordeposited MAPbX3 and mixed perovskite layers. This method can be attractive as it allows determining in an all-optical way the material parameters like thermo-optic coefficient, speed of sound, and thermal conductivity. We reveal the anisotropy of thermal conductivity, which is 1.5−2.2 times higher across the layer than that along the surface. We speculate that this difference can be related to phonon scattering at grain boundaries, which is different in mentioned directions due to the nonspherical shape of crystallites in the layers; also, the orientation of crystallites within the layer can play a role due to different sound speeds along different crystallographic directions. Finally, we show by independent measurements that thermal conductivity scales linearly with the speed of sound, which varies in perovskites with different halides, confirming that the speed of sound is the reason behind different thermal conductivities in organic−inorganic lead halide perovskite layers. The results of the anisotropy of thermal transport can be especially important for designing the active regions of grained perovskite high-power light-emitting and laser diodes.

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b02288. Cross-sectional SEM images of the investigated layers (Figure S1); XRD patterns of the investigated layers (Figure S2) (PDF) 14919


Article

The Journal of Physical Chemistry C Energy Conversion Efficiency. Adv. Funct. Mater. 2016, 26, 5297− 5306. (14) Kovalsky, A.; Wang, L.; Marek, G. T.; Burda, C.; Dyck, J. S. Thermal Conductivity of CH3NH3PbI3 and CsPbI3: Measuring the Effect of the Methylammonium Ion on Phonon Scattering. J. Phys. Chem. C 2017, 121, 3228−3233. (15) Qian, X.; Gu, X.; Yang, R. Lattice Thermal Conductivity of Organic-Inorganic Hybrid Perovskite CH3NH3PbI3. Appl. Phys. Lett. 2016, 108, No. 063902. (16) Heiderhoff, R.; Haeger, T.; Pourdavoud, N.; Hu, T.; Al-Khafaji, M.; Mayer, A.; Chen, Y.; Scheer, H. C.; Riedl, T. Thermal Conductivity of Methylammonium Lead Halide Perovskite Single Crystals and Thin Films: A Comparative Study. J. Phys. Chem. C 2017, 121, 28306−28311. (17) Guo, Z.; Yoon, S. J.; Manser, J. S.; Kamat, P. V.; Luo, T. Structural Phase- and Degradation-Dependent Thermal Conductivity of CH3NH3PbI3Perovskite Thin Films. J. Phys. Chem. C 2016, 120, 6394−6401. (18) Scajev, P.; Qin, C.; Aleksiejunas, R.; Baronas, P.; Miasojedovas, S.; Fujihara, T.; Matsushima, T.; Adachi, C.; Jursenas, S. Diffusion Enhancement in Highly Excited MAPbI3 Perovskite Layers with Additives. J. Phys. Chem. Lett. 2018, 9, 3167−3172. (19) Š čajev, P.; Aleksiejunas, R.; Miasojedovas, S.; Nargelas, S.; Inoue, M.; Qin, C.; Matsushima, T.; Adachi, C.; Jursenas, S. Two Regimes of Carrier Diffusion in Vapor Deposited Lead-Halide Perovskites. J. Phys. Chem. C 2017, 121, 21600−21609. (20) Eichler, H. J.; Gunter, P.; Pohl, D. W. Laser-Induced Dynamic Grattings; Springer-Verlag: NY, 1986. (21) Webber, D.; Clegg, C.; Mason, A. W.; March, S. A.; Hill, I. G.; Hall, K. C. Carrier Diffusion in Thin-Film CH3NH3PbI3 Perovskite Measured Using Four-Wave Mixing. Appl. Phys. Lett. 2017, 111, No. 121905. (22) Arias, D. H.; Moore, D. T.; Van De Lagemaat, J.; Johnson, J. C. Direct Measurements of Carrier Transport in Polycrystalline Methylammonium Lead Iodide Perovskite Films with Transient Grating Spectroscopy. J. Phys. Chem. Lett. 2018, 9, 5710−5717. (23) Han, Q.; Bai, Y.; Liu, J.; Du, K.; Li, T.; Ji, D.; Zhou, Y.; Cao, C.; Shin, D.; Ding, J.; et al. Additive Engineering for High-Performance Room-Temperature-Processed Perovskite Absorbers with MicronSize Grains and Microsecond-Range Carrier Lifetimes. Energy Environ. Sci. 2017, 10, 2365−2371. (24) Johnston, M. B.; Herz, L. M. Hybrid Perovskites for Photovoltaics: Charge-Carrier Recombination, Diffusion, and Radiative Efficiencies. Acc. Chem. Res. 2016, 49, 146−154. (25) Käding, O. W.; Skurk, H.; Maznev, A. A.; Matthias, E. Transient Thermal Gratings at Surfaces for Thermal Characterization of Bulk Materials and Thin Films. Appl. Phys. A: Mater. Sci. Process. 1995, 61, 253−261. (26) Š čajev, P.; Jarašiunas, K. Application of a Time-Resolved FourWave Mixing Technique for the Determination of Thermal Properties of 4H-SiC Crystals. J. Phys. D: Appl. Phys. 2009, 42, No. 055413. (27) Knop, O.; Wasylishen, R. E.; White, M. A.; Cameron, T. S.; Oort, M. J. M. Van. Alkylammonium Lead Halides. Part 2. CH3NH3PbX3 (X = Cl, Br, I) Perovskites: Cuboctahedral Halide Cages with Isotropic Cation Reorientation. Can. J. Chem. 1990, 68, 412−422. (28) Ziang, X.; Shifeng, L.; Laixiang, Q.; Shuping, P.; Wei, W.; Yu, Y.; Li, Y.; Zhijian, C.; Shufeng, W.; Honglin, D.; et al. Refractive Index and Extinction Coefficient of CH3NH3PbI3 Studied by Spectroscopic Ellipsometry. Opt. Mater. Express 2015, 5, 29−43. (29) Jiang, Y.; Soufiani, A. M.; Gentle, A.; Huang, F.; Ho-Baillie, A.; Green, M. A. Temperature Dependent Optical Properties of CH3NH3PbI3 Perovskite by Spectroscopic Ellipsometry. Appl. Phys. Lett. 2016, 108, No. 061905. (30) Hlídek, P.; Bok, J.; Franc, J.; Grill, R. Refractive Index of CdTe: Spectral and Temperature Dependence. J. Appl. Phys. 2001, 90, 1672−1674. (31) Palmer, D. W. www.semiconductors.co.uk (accessed April 25, 2019).

(32) Saba, M.; Quochi, F.; Mura, A.; Bongiovanni, G. Excited State Properties of Hybrid Perovskites. Acc. Chem. Res. 2016, 49, 166−173. (33) http://accuratus.com/fused.html (accessed April 25, 2019). (34) Leviton, D. B.; Frey, B. J. Temperature-Dependent Absolute Refractive Index Measurements of Synthetic Fused Silica. In Optomechanical Technologies for Astronomy; International Society for Optics and Photonics, 2006; p 62732K.

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Anisotropy of Thermal Diffusivity in Lead Halide Perovskite Layers

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