Polar Fluctuations in Metal Halide Perovskites Uncovered by Acoustic Phonon Anomalies Peijun Guo,† Yi Xia,† Jue Gong,‡ Constantinos C. Stoumpos,§ Kyle M. McCall,§ Grant C. B. Alexander,§ Zhiyuan Ma,∥ Hua Zhou,∥ David J. Gosztola,† John B. Ketterson,⊥ Mercouri G. Kanatzidis,§ Tao Xu,‡ Maria K. Y. Chan,† and Richard D. Schaller*,†,§ †
Center for Nanoscale Materials, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, United States Department of Chemistry and Biochemistry, Northern Illinois University, DeKalb, Illinois 60115, United States § Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States ∥ Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, United States ⊥ Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States ‡
S Supporting Information *
ABSTRACT: Solution-processable metal halide perovskites (MHPs) offer great promise for efficient light-harvesting and -emitting devices because of their long carrier lifetime and superior carrier transport properties. Similar to traditional oxide perovskites, MHPs exhibit strong dynamic disorders that may further impact their electronic properties. Here we investigate the coherent acoustic phonons of inorganic and organic−inorganic (hybrid) MHP single crystals (CsPbCl3, MAPbCl3, CsPbBr3, MAPbBr3, FAPbBr3, MAPbI3, and FAPbI3) using pump−probe reflection spectroscopy. We show significant phonon softening in the cubic phase of all compositions close to the cubic-to-tetragonal phase transition temperature. Such phonon softening in conjunction with strong acoustic damping is attributed to pretransitional polar fluctuations. Comparison of MHPs with different compositions show that the degree of pretransitional fluctuations is correlated with the size rather than the dipole moment of the A-site cations, and further with the size of the anions. of fluctuating symmetry-breaking domains in the cubic phase of both all-inorganic and hybrid MHPs, which involve cooperative motions of the A-site cations and the lead halide frameworks. Compared to the all-inorganic MHPs, the reorientations of the dipolar organic A-site cations in hybrid MHPs strongly couple to the lead halide framework and may further contribute to a polar behavior.25 An improved understanding of the dynamic structural fluctuations with a potential impact on the energetic landscape and optoelectronic properties is thus crucial to the further improvement of MHP-based technologies. Here, using transient reflection spectroscopy, we study the coherent acoustic phonons (CAPs) of lead-based single-crystal MHPs with a variety of A-site cations (methylammonium or MA, formamidinium or FA, and Cs) and halide anions (Cl, Br, and I) over a wide range of temperatures traversing all accessible phases. We observe anomalous CAP velocities for both the inorganic and hybrid MHPs in the cubic phase near (and above) the cubic-to-tetragonal (C−T) phase transition
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etal halide perovskites (MHPs) are emerging materials for low-cost solar cells with efficiencies now exceeding 22%.1 Despite being solution processed, MHPs exhibit excellent optoelectronic properties including tunable band gaps, large absorption coefficients, long carrier lifetimes and modestly high mobility.2 The success of MHPs in the related fields of photovoltaics3 and light emission4 and detection5 has motivated widespread research efforts aimed at improved understanding of their fundamental optical and electronic properties.6,7 The most well-studied MHP for photovoltaics, namely methylammonium lead iodide (MAPbI3), adopts a tetragonal structure at room temperature and hence may potentially exhibit ferroelectricity, which was proposed as a possible mechanism to bolster charge separation and suppress carrier recombination. However, the existence of such macroscopic polar order in MAPbI3 is still controversial.7−18 Relatedly, MHPs such as MAPbBr3, FAPbBr3, and FAPbI3 have been reported to exhibit long carrier lifetimes of several microseconds that are comparable to that of MAPbI3,19,20 yet they occupy a pseudocubic structure near room temperature where macroscopic ferroelectricity is unexpected. Recent inelastic X-ray scattering21−23 and lowfrequency Raman spectroscopy24 measurements show evidence © XXXX American Chemical Society
Received: August 24, 2017 Accepted: September 22, 2017
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DOI: 10.1021/acsenergylett.7b00790 ACS Energy Lett. 2017, 2, 2463−2469
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Figure 1. Transient spectral maps of MAPbBr3 and MAPbI3 single crystals at 295 K. (a) ΔR/R map of MAPbBr3 in the visible range (pump fluence was 0.21 mJ·cm−2). (b) Fourier transform of the ΔR/R map shown in panel a. (c) ΔR/R map of MAPbI3 in the NIR range (pump fluence was 0.25 mJ·cm−2). (d) Fourier transform of the ΔR/R map shown in panel c. Scale bars shown in panels a and c are defined as ΔR/R (1 × 10−3).
temperature (i.e., pretransitional), denoted as TC−T. These irregularities in CAP velocities in conjunction with strong acoustic damping near TC−T reveal polar fluctuations in the cubic phase. Temperature-dependent phonon calculations further confirm that the anomalous CAP velocities cannot arise from the strong anharmonicity and large atomic displacements in these “soft” perovskite materials but can result only from local fluctuations. Comparative studies show that the degree of pretransitional fluctuations increases with the size of the anion and is further correlated with the size, rather than the dipole moment, of the A-site cation. The MAPbCl3, MAPbBr3, FAPbBr3, MAPbI3, and FAPbI3 single crystals were solution-grown based on reported methods; the CsPbCl3 and CsPbBr3 crystals were grown via the vertical Bridgman method.26−28 Single-crystal X-ray diffraction results are shown in Figure S1. For transient reflection measurements, we used 350 nm (above band gap) pump and visible or nearinfrared (NIR) probe at nearly normal incidence on the (001) facets of CsPbCl3, MAPbCl3, MAPbBr3, and FAPbBr3 (with pseudocubic structures at 295 K), (010) facet of CsPbBr3 (with an orthorhombic structure at 295 K), (100) facet of MAPbI3 (with a tetragonal structure at 295 K), and (011) facet of FAPbI3 (with a cubic structure at 295 K). Figure 1a shows the transient spectral map for MAPbBr3 taken at 295 K; the colorcoded quantity, ΔR/R, is defined as [R(t) − R0]/R0 where R0 is the reflection without pumping and R(t) with pumping (at delay time t). Figure 1a reveals oscillations of the probe intensity in the below band gap range. The wavelengthdependent oscillation frequency signifies the generation and propagation of CAPs,29 which yield successive constructive and destructive interferences of the probe pulse upon reflection both by the crystal surface and by the propagating stress-pulse that induces a local index modulation within the crystal. Fourier decomposition of Figure 1a, as displayed in Figure 1b, distills the oscillation frequency (denoted as f), which is related to the probe wavelength λ by f = 2vn/λ, with v being the CAP velocity and n being the wavelength-dependent refractive index. The
CAPs are launched by impulsive lattice heating from hot carriers,30 as we found pumping with below band gap photons cannot generate the probe oscillations. The oscillations are observed for below band gap probe wavelengths only, because of the large penetration depth of such photons necessary for generating interferences; this is to be compared to the fewhundred-nanometer penetration depth of the pump where lattice heating takes place.31 Relatedly, pump illumination has negligible influence on the temperature of the probed region, consistent with a pump fluence independent probe oscillation frequency (not shown here). Because the lowest band gap of all examined crystals is 1.4−1.5 eV (for FAPbI3), in the subsequent measurements we adopted a NIR probe covering wavelengths from 850 to 1200 nm. Figure 1c shows the ΔR/R map for MAPbI3 measured at 295 K. Here, the Fourier decomposition in time, as presented in Figure 1d, reveals two distinct frequencies; the high and low frequencies are attributed to the longitudinal and transverse acoustic phonons (LAP and TAP), respectively, due to their different group velocities. Along the [100] direction of tetragonal MAPbI3 crystal with I4cm symmetry, the one LAP velocity and two TAP velocities are vLAP = (c11/ρ)1/2, vTAP,1 = (c44/ρ)1/2, and vTAP,2 = [(c44+c66)/ 2ρ]1/2, respectively, where cij denotes the elastic moduli and ρ is the mass density. Here we observe only one TAP frequency, indicating that either c44 ≈ c66 (in which case the system behaves more isotropic) or one TAP is associated with small shear strain that cannot be captured by our transient reflection measurements. Besides MAPbI3, all the other crystals exhibit a single oscillation frequency (see Figures S2 and S3), which we assign to the LAP because of the stronger index modulation parallel to the direction of probe light resulting from the compressive strain. We note that TAP mode is often not strongly manifested in transient reflection measurements, owing to the weak lattice dilation (associated with the shear strain) and with it a weak index modulation along the propagation direction of light. For MAPbBr3 and MAPbCl3, the LAP velocity along the [001] direction is vLAP = (c11/ρ)1/2. 2464
DOI: 10.1021/acsenergylett.7b00790 ACS Energy Lett. 2017, 2, 2463−2469
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ACS Energy Letters From the equation f = 2vn/λ, the LAP velocities can be calculated using the oscillation frequency (f) at each probed wavelength in conjunction with the corresponding refractive index (n). Figure 2a presents the LAP velocities of MAPbX3 (X
with temperature. Figure 3 shows that all the single crystals display an increasing vLAP (and vTAP of MAPbI3 as shown Figure S4) with decreasing temperature in the tetragonal and orthorhombic phases, except for CsPbBr3 which seems to exhibit an opposite trend in a small region close to the tetragonal-to-orthorhombic (T−O) phase change temperature, TT−O. The increase of vLAP (and hence the elasticity) with decreasing temperature follows the normal anharmonic behavior, which yields lattice contraction and with it stronger atomic bonding. However, except for FAPbBr3, a decrease of vLAP is observed for all crystals upon cooling in the cubic phase when approaching TC−T, signifying a substantial softening of the zone-center acoustic phonon. Although the TC−T for FAPbBr3 has not been reported, based on its pseudocubic symmetry at room temperature20 and a TT−O of 150−160 K,34 we expect its TC−T to lie in the range of 290−160 K. As shown in Figure 3e, a nearly constant LAP velocity in the range from 190 to 260 K is observed for FAPbBr3, indicating that acoustic softening is still present and cancels out normal anharmonic effect, but it is weaker than that in other compositions. The discontinuous change of frequency with temperature near the T−O phase transition temperature observed for MAPbCl3, MAPbI3, and likely CsPbBr3 can be attributed to an incommensurately modulated structure35,36 and/or to domain formation due to sudden changes in the lattice parameters at the phase transition.37 Note that for MAPbBr3, the reflection of probe suddenly changed from specular to diffuse at TT−O, below which no acoustic phonon signature was observed. We note that MHPs exhibit positive linear thermal expansion coefficients (denoted as α) in all the phases (including the cubic phase). (1) The α of MAPbI3 is 1.95 × 10−4 K−1 in the cubic phase and 2.66 × 10−4 K−1 in the tetragonal phase.37 (2) The α values of CsPbCl3 and CsPbBr3 are 3.09 × 10−5 K−1 and 3.01 × 10−5 K−1 in the respective cubic phases, as reported elsewhere.38,39 (3) We measured the α of MAPbCl3 (3.17 × 10−5 K−1) and MAPbBr3 (2.52 × 10−5 K−1) in the cubic phases from low-temperature X-ray diffraction experiments (see Figure S5). The normal lattice anharmonicity is expected to yield an increase of elasticity (and vLAP) when approaching TC−T from
Figure 2. Acoustic phonon velocities in MAPbX3 (X = Cl, Br, and I). (a) Phonon velocities calculated at each wavelength using the equation f = 2vn/λ. (b) Mean values and standard deviations of the phonon velocities plotted in panel a.
= Cl, Br, I) calculated at each wavelength (using literaturereported refractive indices31) based on the frequency plots shown in Figures 1b,d and S3 with the mean values and standard deviations plotted in Figure 2b. We found that an increase of the anion size (Cl → Br → I) leads to a decrease of the LAP velocity, consistent with a decreasing bond strength between the Pb and anions. The calculated elastic moduli with the same trend are further shown in Table S1. In perovskites, a phase transition is intimately associated with anomalous behaviors of various physical quantities.32 To examine the variation of LAP velocity around phase transitions, we performed temperature-dependent transient reflection measurements. The temperature-dependent LAP frequencies at a fixed probe wavelength are shown in Figure 3. Note that although the variation of LAP frequency can arise from a temperature-dependent refractive index (because f = 2vn/λ), the thermal-optic coefficient (dn/dT) is typically between 10−6 and 10−5 K−1;33 hence, the relative frequency shift of LAP with temperature with an observed magnitude on the order of 10−4 K−1 (within each phase) is dominated by the change of vLAP
Figure 3. Temperature-dependent frequencies of the probe oscillations for MHP single crystals. (a−f) Temperature dependence of the probe oscillation frequencies of CsPbCl3, MAPbCl3, CsPbBr3, MAPbBr3, FAPbBr3, and MAPbI3. The LAP frequencies were calculated from ΔR/R kinetics at 935 nm for all the crystals except CsPbBr3 for which ΔR/R kinetics at 895 nm was used (due to better signal-to-noise ratio). The vertical dashed lines mark the phase transitions; C, T, and O indicate cubic, tetragonal, and orthorhombic phases, respectively. 2465
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Figure 4. Calculated phonon band structures for CsPbCl3 and CsPbBr3. Calculated phonon dispersions at 0 K (black) in (a) CsPbCl3 and in (d) CsPbBr3; at temperature slightly above TC−T for (a, b) CsPbCl3 (at 350 K, cyan) and (d, e) CsPbBr3 (425 K, cyan); at elevated temperature for (b) CsPbCl3 (at 450 K, red) and (e) CsPbBr3 (at 525 K, red). (c, f) Calculated group velocities for the lowest-lying three phonon branches at 350 K for CsPbCl3 and at 425 K for CsPbBr3 (cyan), and at 450 K for CsPbCl3 and at 525 K for CsPbBr3 (red). Insets show the group velocities along the [001] direction near the Brillouin zone center.
above. This is further investigated by first-principles phonondispersion calculations of the cubic CsPbCl3 and CsPbBr3. As shown in Figure 4a,d, the 0 K phonon dispersion diagram contains many modes with imaginary frequencies, indicating an unstable cubic phase at low temperatures (consistent with an observed lower symmetry). At an intermediate temperature above TC−T (Figure 4a,d), the cubic phase is stabilized (no imaginary modes), and the phonon dispersions are renormalized for the low-lying optical modes (softened) and acoustic modes (hardened). Further increasing the temperature by 100 K (Figure 4b,e) leads to slight softening of the high-frequency optical modes and hardening of the low-frequency optical modes near the zone-center. For the acoustic modes, we computed vLAP along the [001] direction (Figure 4c,f) using the obtained phonon dispersions without any imaginary modes. The renormalized phonon dispersions reflect all higher-order phonon−phonon interactions including the fourth-order interatomic force constants (IFCs) that stabilize the octahedral rotation and the remaining higher-order terms, which can become important given the large atomic displacements (see Tables S2 and S3). However, the computed vLAP decreases slightly upon heating in both compositions, which follows an anharmonic behavior. As such, the observed “acoustic anomaly” close to TC−T does not arise from interatomic interactions but can be explained by local order parameter fluctuations that are not captured by first-principles calculations. Note that well above TC−T the normal anharmonic behavior (i.e., acoustic hardening upon cooling) is recovered in CsPbCl3, MAPbCl3, MAPbBr3, and FAPbBr3 (Figure 3); this is not the case for CsPbBr3 and MAPbI3. In particular, we found that CsPbBr3 became unstable at around 600 K (190 K above the TC−T) as evident from an irreversible color change of the crystal, but still the vLAP reaches a plateau near 600 K, suggesting a vanishing of acoustic softening. For MAPbI3, the loss of acoustic phonon signatures may arise from a strong absorption of acoustic waves, as we found the probe oscillations were fully recovered even
after measurements at 390 K, indicative of no permanent damage. Acoustic anomalies have been observed in relaxor ferroelectrics,40 in which fluctuating polar nanoregions (also called dynamic precursor microregions) are formed in the cubic phase at the so-called Burns temperature. The fluctuating polar clusters arising from symmetry-breaking displacements couple with strain and result in a softening of the elasticity that is proportional to the mean square of the polarization, Δc ∝ −⟨P2⟩.41 Although relaxors frequently exhibit C−T phase transitions of some second-order character, even in prototypical oxide perovskites such as BaTiO3 with a well-known first-order C−T phase transition, acoustic softening was observed and was associated with the off-center displacement of Ti cations along the eight equivalent [111] directions in the cubic phase near TC−T.42 Hence, the pretransitional acoustic softening in perovskites need not result from a second-order phase transition but necessarily implies dynamic disorders. For hybrid MHPs, diffraction and calorimetric measurements confirmed that the C−T transition is first-order.21,37,43 Low-frequency Raman scattering experiments on CsPbBr3 and MAPbBr3 reveal that local polar fluctuations in the cubic phases arise from headto-head motions of the A-site cation along the [100] directions, which are intrinsic to the lead halide framework regardless of the dipole moment of the A-site cation.24,44 Here our temperature-dependent measurements show that the Csbased MHPs exhibit the strongest phonon softening with onset temperatures 150−200 K above TC−T, whereas MA-based MHPs show weaker phonon softening whose onset temperatures are reduced to 80−120 K above TC−T, and FAPbBr3 shows the weakest acoustic softening compared to CsPbBr3 and MAPbBr3. Hence for the bromides, the strength of acoustic softening increases along the line of FA+ → MA+ → Cs+, which does not correlate with their relative strength of dipole moment (MA+ > FA+ > Cs+) but rather their relative size (FA+ > MA+ > Cs+). We hypothesize that the dynamic motion of the cations is 2466
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Figure 5. Temperature-dependent ΔR/R kinetic traces for MHP single crystals. (a−f) Temperature-dependent ΔR/R kinetics at 935 nm for all the crystals except CsPbBr3 (c), for which ΔR/R kinetics at 895 nm was plotted. Adjacent curves are vertically shifted for clarify of presentation; higher-lying curves are for higher temperatures.
scatter the acoustic waves. Note that no obvious acoustic damping is observed for FAPbBr3, which is consistent with the lack of strong acoustic softening shown in Figure 3. The disappearance of the acoustic anomaly (Figure 3) together with the recovery of long-lived probe oscillations below TC−T (Figure 5) indicates freezing of the fluctuation upon the C− T phase transition. In conclusion, we performed temperature-dependent CAP measurements on various MHP single crystals and observed pretransitional acoustic softening near TC−T arising from polar fluctuations for both all-inorganic and hybrid MHPs. The strong damping (i.e., shorter mean free path) and reduced group velocities of the heat-carrying acoustic phonons are expected to result in reduced thermal conductivities near TC−T, especially for MHPs with small A-site cations and large anions. Our measurement is also in line with the work by Pisoni et al.,46 in which resonant scattering owing to cation disorder was considered as a contributing factor to the low thermal conductivity of MHPs. Although the inferred fluctuating lattice disorder may alter the electronic structures of MHPs and contribute to a longer carrier lifetime,47−50 the observed rank in the degree of acoustic softening, and possibly polar fluctuations for the bromides (FAPbBr3 < MAPbBr3 < CsPbBr3) is opposite to that in previously reported carrier lifetimes (FAPbBr3 > MAPbBr3 > CsPbBr3).20,51 However, detailed defect configurations and trap densities in these different bromides may play a significant role in the measured carrier lifetimes.52 Further work will focus on correlating the observed dynamic structural disorders to the intrinsic optoelectronic properties of MHPs.
more constrained with an increasing cation size, which in turn suppresses the pretransitional structural fluctuations. This is also supported by our measurements on FAPbI3 (shown in Figure S6), which, although exhibiting a different series of phase transitions with reported hysterisis,45 still shows acoustic phonon softening (manifested as a flat region in the frequency−temperature plot shown in Figure S6c) that is weaker than that in MAPbI3. Suppression of the dynamic disorder due to size effect is also reflected by comparing MAPbX3 of different anions (X = Cl, Br, I). We find that increasing the anion size results in a stronger acoustic softening per degree change of temperature, with df/dT ∼ 3.0 × 10−3 GHz·K−1 for X = Cl, to df/dT ∼ 9.3 × 10−3 GHz·K−1 for X = Br, and to df/dT ∼ 14 × 10−3 GHz·K−1 for X = I, averaged over the temperature range in which acoustic softening is observed. As a result, the degree of pretransitional structural fluctuations is determined by the relative size of the A-site cation with respect to the size of the Pb−X octahedron. We also note that the onset temperature (∼200 K) of the acoustic hardening below the acoustic softening regime for FAPbBr3 likely suggests a lower C−T phase change temperature compared to MAPbBr3 (∼240 K). Hence, an increasing cation size (for APbBr3 with A = Cs → MA → FA), or a decreasing anion size (for MAPbX3 with X = I → Br → Cl), gives rise to a more rigid perovskite scaffold and an accompanying lower C−T transition temperature, because the cubic phase is more stable and can persist over a broader temperature range. Besides the elastic softening (which is a static behavior), the ΔR/R kinetics (used to construct Figure 3) shown in Figure 5 further demonstrate strong acoustic attenuation manifested as fewer distinct oscillation periods at temperatures around TC−T (shown in red) for CsPbCl3, MAPbCl3, CsPbBr3, and MAPbBr3. For MAPbI3, the probe oscillations become less well-defined above TC−T possibly owing to strong damping. The observed Landau−Khalatnikov-type damping of LAPs arises from strong polar fluctuations near TC−T. Qualitatively, the fluctuating polar domains with characteristic sizes smaller than acoustic phonon wavelengths exert random stresses that
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsenergylett.7b00790. Experimental methods and additional transient reflection, X-ray diffraction, and first-principles calculation results (PDF) 2467
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected];
[email protected]. ORCID
Peijun Guo: 0000-0001-5732-7061 Constantinos C. Stoumpos: 0000-0001-8396-9578 Kyle M. McCall: 0000-0001-8628-3811 Mercouri G. Kanatzidis: 0000-0003-2037-4168 Tao Xu: 0000-0002-3343-7263 Maria K. Y. Chan: 0000-0003-0922-1363 Richard D. Schaller: 0000-0001-9696-8830 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The work was performed at the Center for Nanoscale Materials, a U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences User Facility under Contract No. DE-AC02-06CH11357. T.X. acknowledges financial support from the U.S. National Science Foundation (CBET1150617). Work at Northwestern University was supported by Grant SC0012541 from the U.S. Department of Energy, Office of Science (samples synthesis, purification and characterization). Use of the Advanced Photon Source, an Office of Science user facility, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. We thank Dr. Benjamin T. Diroll and Dr. Matthew E. Sykes for assistance in transient absorption measurements.
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