Hydrogen-like Wannier–Mott Excitons in Single Crystal of

Hydrogen-like Wannier−Mott Excitons in Single Crystal of Methylammonium Lead Bromide Perovskite Jenya Tilchin,† Dmitry N. Dirin,‡,§ Georgy I. Maikov,† Aldona Sashchiuk,† Maksym V. Kovalenko,‡,§ and Efrat Lifshitz*,† †

Schulich Faculty of Chemistry, Russell Berrie Nanotechnology Institute, Solid State Institute, Technion, Haifa 32000, Israel Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 1, Zurich CH-8093, Switzerland § Empa − Swiss Federal Laboratories for Materials Science and Technology, Ü berlandstrasse 129, Dübendorf CH-8600, Switzerland ‡

S Supporting Information *

ABSTRACT: A thorough investigation of exciton properties in bulk CH3NH3PbBr3 perovskite single crystals was carried out by recording the reflectance, steady-state and transient photoluminescence spectra of submicron volumes across the crystal. The study included an examination of the spectra profiles at various temperatures and laser excitation fluencies. The results resolved the first and second hydrogen-like Wannier−Mott exciton transitions at low temperatures, from which the ground-state exciton’s binding energy of 15.33 meV and Bohr radius of ∼4.38 nm were derived. Furthermore, the photoluminescence temperature dependence suggested dominance of delayed exciton emission at elevated temperatures, originating from detrapping of carriers from shallow traps or/and from retrapping of electron−hole pairs into exciton states. The study revealed knowledge about several currently controversial issues that have an impact on functionality of perovskite materials in optoelectronic devices. KEYWORDS: hydrogen-like transitions, exciton binding energy, perovskites, lead halides, single crystals, photophysics

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perovskites’ stability. Indeed, it is known that perovskite materials undergo structural phase transitions on application of external stimuli (e.g., temperature27 or pressure28). For example MAPbBr3 has cubic cell structure at room temperature, tetragonal between 145 and 237 K and orthorhombic phase at lower temperatures.29 The phase transitions involve tilting of octahedra.30 The reader is referred to recent reviews31−33 summarizing the crystalline properties and their influence on the physical properties of the AMX3 materials. Chemical and photochemical instability of the AMX3 has been reported often for thin film samples. By including alloying or hybrid structures, positive prospects to overcome the instability exist.34 The electronic band structure of AMX3 encompasses the [PbX6] units: The valence band is composed of Pb(6s) and I(5p) or Br(4p) antibonding states. The conduction band is mainly compiled from the antibonding Pb(6p)−I(5p) interactions with a small contribution from I(5s) or Br(4s) atomic orbitals.35,36 The AMX3 are known as direct band gap semiconductors, with extrema at the R[111] Brillouin point. Previous theoretical reports35,37 indicated the occurrence of

he halide perovskites have elicited substantial interest since the 1960s1−3 due to their unusual physical properties, combining efficient optical transitions and high carrier mobility. Dormant interest has been revived due to groundbreaking discoveries of the perovskites’ usefulness in photovoltaic cells, with power conversion efficiencies rivaling other technologies based on organic, Si, CdTe, CIGS and GaAs materials.4−8 Moreover, these materials demonstrate high performance in optoelectronic applications such as light emitting diodes,9 lasers,10,11 photodetectors12,13 and show future prospects for single photon source14 and spin electronics.15,16 The renaissance of the halide perovskites also initiated a vast amount of fundamental studies with efforts to unravel the underlying physics controlling the unique performance of these materials and to grow high-quality organometallic lead trihalides single crystals12,17−24 and colloidal nanocrystals.25,26 Trihalide perovskites, such as AMX3 (A = Cs1+, methylammonium [MA], formamidinium [FA]; M = Pb, Ga, In; X = I, Cl, Br), have recently received extensive attention. They are composed of interconnected MX6−4 octahedral units; the “A” charge balancing specie occupies cages created by 12 halide atoms within the octahedral network. One of the major concerns for practical application is associated with the © 2016 American Chemical Society

Received: April 24, 2016 Accepted: June 1, 2016 Published: June 1, 2016 6363

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microphotoluminescence (μ-PL) spectrum. The μ-PL enabled examination of spatially different spots across the sample. The detected spectra showed intensity and spectral stability when monitored at various temperatures (see Figure S2, SI) excluding the involvement of an Auger process, as reported in perovskite nanocrystals or polycrystalline films.50 Typical μ-PL spectrum (red line) and corresponding reflectance curve (blue line) of MAPbBr3 recorded at 10 K, are shown in Figure 1a; enlargement of high energy sides of the

strong spin−orbit coupling at the conduction band, as expected from materials consisting of a heavy metal such as Pb, leading to formation of split-off states. Accordingly, the valence and conduction band-edges each have an angular momentum J = 1/ 2, i.e., the allowed band-edge absorbance is related to the ±1/2 ↔ ±1/2 transitions. Furthermore, crystal field symmetry and exchange interaction induce additional tuning, although the consequent influence of these surplus interactions are not discussed further in the current study.38 In general, the perovskites demonstrate long-range ambipolar (with nearly the same effective mass for the electron and hole) transport characteristics,39,40 as well as strong band-edge oscillator strength,41 justifying the considerable interest in those material for optoelectronic applications. Pillars that define the photophysical properties of these perovskites and may control practical applications, are related to the questions whether photon absorption induces a direct formation of free-carriers or excitons species.42 If excitons are created, what are their binding energies? Some reports affirm values of the exciton binding energy (Ebinding ) in bromine-based X materials in the 30−40 meV range.38,43,44 Others reported the values of 35−50 meV3,38,42 in iodine-based material or incompatible values of 5−15 meV.37,45,46 Moreover, a conflict arises in the determination of the dielectric screening, from the infinite to the static regime or in-between these limits.47 The source of ferroelectricity, frequently found in AMX3, and the accompanying influence on the photophysics or spin-physics are also left as questions.15,48 Despite the diligent efforts, there are contradicting opinions in the literature regarding the fundamental properties mentioned, and further work is required to reconcile the conflicts. The current work concentrates on the singlecrystalline form of MAPbBr3 in order to differentiate between the intrinsic photophysics and effects of surfaces and grain boundaries. The study includes investigating steady-state exciton transitions (reflectance and emission) and emission decay times at various temperatures. The results resolved n1 (1S) and n2 (2S) hydrogen-like Wannier−Mott exciton transitions in the reflectance and in the photoluminescence spectra, both with relatively small binding energies (up to ∼15.33 meV) and effective Bohr radius (down to ∼4.38 nm), enabling dissociation into free carriers at room temperature. Furthermore, the study supplies an analysis of the band gap temperature dependence in terms of a two-oscillator model and suggests the mechanisms that govern the band gap changes. In addition, the study suggests the major contribution of a delayed fluorescence in the exciton emission. It is worth noting that the investigation of the localized three-dimensional Wannier−Mott excitons in the present study serves as a model that can be rescaled for the study of excitons in low dimensional perovskite materials (nanocrystals, platelets or thin films).

Figure 1. (a) Reflectance (blue line) and μ-PL spectra (red line) recorded at 10 K. The top inset is a schematic presentation of hydrogen-like Wannier−Mott excitonic states. The inset beyond the reflectance spectrum presented the zoom into the high energy side of the main transition line in the energy range from 2.258 to 2.279 eV. (b) Power dependent spectra recorded at 4.5 and 20 K. Inset: Schematics of a free exciton and a donor−acceptor (D−A) pair recombination path.

RESULTS AND DISCUSSION A solution-grown bulk single crystal of MAPbBr3 with dimensions of 3 × 3 × 2 mm was prepared using a procedure similar to ref 17 with a slight modification, as described in the Supporting Information (SI). The optical experimental setup is given in the Methods section below. In the framework of the optical setup, the excitation beam was focused on to a ∼ 0.5 μm spot and penetrated through a similar depth; hence, the detection volume was compatible with the reported threedimensional free-carriers diffusion length.49 The emission from such a confined volume is referred in the following text as

spectra are shown in the bottom inset. Additional μ-PL spectra, recorded at 4.5 K, are provided in the SI, Figure S3. They show similar excitonic signatures to that shown in Figure 1a. The reflectance curve in Figure 1a is dominated by dispersive signals (labeled n1 and n2), accompanied by an emission line (centered at ∼2.2478 eV) ascribed to an exciton emission (PL1, see below). The reflectance curve has been fitted to the real part of a linear susceptibility according to Kramers−Kronig 6364

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ACS Nano ⎛ Ej − E + iγj ⎞ relation,51,52 R(E) = R j Re⎜ γ 2 + (E − E )2 ⎟, where, Rj, Ej, and γj j ⎠ ⎝ j (for j = 1, 2) are the amplitude, resonance energy and broadening parameter, respectively. The reflectance fit is shown in Figure 1a by the black dashed curve, revealing exciton transitions at E1 ∼ 2.2558 eV (n1) and E2 ∼ 2.2673 eV (n2). The spectral signatures in the reflectance curve are similar to hydrogen-like Wannier−Mott excitons, resembling features observed in the absorption curve of bulk GaAs53 and in the reflectance curve of bulk GaN.51,54 While GaN experiences the influence of an hexagonal crystal field, pronounced as a lift of angular momentum degeneracy (into heavy and light hole)51,54 in the valence band-edge, the orthorhombic MAPbBr3 bulk single crystal lacks such a degeneracy; spin−orbit coupling isolated the valence band-edge by opening an extremely large gap (>100 meV) between the band-edge and remote states, however the band-edge extrema are composed solely of the Kramers doublets.15,37 Thus, the association of n1 and n2 to a split off pairs is excluded. Plots of energy shift of E1 and E2 with the increase in the temperature are discussed at length below, concealing typical exciton behavior in both n1 and n2 transitions; thus, their association to hydrogen-like transitions is the most probable explanation. Coexistence of phases at the lowest temperatures, as proposed before in thin films with grain boundaries,55 can be excluded here as well, due to a similarity of excitonic features when monitoring a large submicron volumes across the sample of a high crystalline quality. A hydrogen-like exciton transition energy is related to the band-edge (Eg) and exciton binding (Ebinding ) energies via the X relation, En = Eg − Ebinding /n2, when n = 1, 2, 3, ..., ∞, and thus, X the values Eg = 2.2711 eV and Ebinding = 15.33 meV were X derived. A related energy cascade scheme is shown in the top inset in Figure 1a. Further, the crystal’s dielectric constant (ε) and the excitons’ Bohr radius (rn, n = 1, 2) can be emanated from the variables found so far, using the relations μ/m ε EXbinding = 2 0 Ry(H ) and rn = μ / m n2aB, respectively, where ε

binding energy for a ground state exciton elucidates the high charge mobility and long diffusion length found at room temperature.18,19,57 The μ-PL spectrum shown in Figure 1a includes a dominant band labeled PL1, centered at EPL1∼ 2.2478 eV, and a few subsidiary bands below and above energy of PL1. The sharpness of the PL1 band and the temperature induced shift in accordance with the n1 reflectance feature (discussed at length below), suggest its assignment to a ground state hydrogen-like exciton. The wide and weak band at the low energy side is assigned later to a donor−acceptor recombination and is labeled D−A. At the high energy side, two weak pumps are visualized, centered at 2.2566 eV and at 2.2646 eV; the first is shifted from the excitation energy by ∼3943 cm−1 and retains this shift nearly throughout the entire temperature profile examined in this study. An independent measure of the RAMAN spectrum (see Figure S4, SI) showed the existence of a vibrational resonance at 3926 cm−1 compatible with the weak pump at the high energy slop of the PL1 band. More significantly, the higher energy bump, labeled PL2 in Figure 1a, showed an energy shift similar to that of PL1, which could be resolved only up to 20K due to phonon broadening (see discussion below), assigning it to the second (or excited state) hydrogen-like exciton. The exciton lines, PL1 and PL2 are Stokes shifted from n1 and n2 transitions by EStokes ∼ 8.00 meV 1 ∼ 2.70 meV, respectively (at 10K). A Stokes shift is and EStokes 2 related to a variation in chemical bond (or an electron−hole distance) at the excited state thus, the inequality EStokes < EStokes 2 1 arises from the difference in the corresponding exciton radius (when r1 < r2). The Stokes shift typically refers to a threedimensional free-exciton in direct band gap semiconductors,58 although it might also be related to an exciton bound to an extremely shallow trap or to a self-trapped exciton.59 In case of a bound exciton, its energy may be shifted by a few meV from that of the free-exciton, but it also should show a sharp-peak appearance. Since it is hard to make a distinction in the current case, PL1 and PL2 are referred here by a general term, exciton. Figure 1b presents evolution of μ-PL spectra with increasing excitation power from P0 to 100P0 (P0 = 0.15 W/cm2) recorded at 4.5 K (bottom) and 20 K (top), when each curve was normalized in reference to the most intense band. At the lowest temperature, the exciton intensity grows linearly with the increase of the pumping power. The D−A band did not gain intensity with the increase of the laser power, and instead showed a weight shift to a higher energy. The broad nature is characteristic of a collection of recombination events between electron−hole pairs with distribution of distances. On an increase of the pumping power, population of all sites increases, however, close-by pairs recombine faster, viz., their recombination is more pronounced, while far-apart pairs with a slow recombination process eventually becomes saturated, pronounced as a reduction of intensity at the lowest energy side.60,61 The saturation effect with an increase of illumination fluency excludes consideration of multiple exciton formation.62−64 In addition, the contribution of coexistence of hightemperature phase can be excluded as well, due to signatures of a sharp structural phase transition way above the measured temperature of the spectrum shown in Figure 1b. Although, the intensity of the D−A band is relatively small with respect to that of the exciton, even a diluted amount of trapping site can have an influence on the exciton dynamics and these processes require further investigations (see below).

0

μ is the exciton reduced mass (0.13m038), m0 is a free electron rest mass, Ry(H) = 13.6 eV is the hydrogen atom ground state energy and aB is the Bohr radius of the hydrogen atom. The expression of Ebinding provides the value of ε = 10.75. In the X present case Ebinding is nearly equal to the value of the optical X phonon of 15.87 meV (see measurements below). Equality of this kind commonly known to dictate a dielectric constant with interpolated value between the static and infinite values.47 The infinite value was reported to be ∼6.5,3,38 the static constant of iodide analogues was found to be ∼21,56 while the constant derived here possesses an intermediate value between extreme points. Knowing the value of ε, rn were found to be, r1 = 4.38 nm and r2 = 17.53 nm, where r1 is considered as the bulk Bohr radius (aB*) of a ground-state exciton. is in striking contrast to previously The value of Ebinding X reported values which merged between 30 to 50 meV,38,43,44 but it is in close agreement with values (15−20 meV) found in iodine-analogue compounds in references.37,45 The discrepancies may stem from the fact that many previous studies measured thin films of polycrystalline materials with grain boundaries and overall two-dimensional morphology, while the present study characterized a three-dimensional bulk exciton. Due to the anisotropy in two-dimensional materials, the binding energy anticipated to be 3−4 times larger than that of three-dimensional structures.47 In any event, relatively small

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Figure 2. Temperature dependence of the reflectance (a) and normalized μ-PL (b) spectra. (c) The exemplar μ-PL spectrum recorded at 60 K (blue line) and the corresponding calculated thermally induced phonon broadening due to the change in phonon states occupation (red dashed line). The schematic presents the changes in phonon occupation number.

Figure 3a shows the temperature dependence of E1 (green squares), E2 (green open diamonds), EPL1 (red circles) and EPL2

The detuned energy of a D−A recombination band with respect to the band gap energy is given by the expression, ΔED−A = Eg − (ED + EA) + e2/4πε0εR, where ED/A is an energy of donor/acceptor site and R is a distance between these sites. The round bracket in this equation describes the total energy depth of the donor and acceptor states, while the last term describes the screening effect dependence of the D−A mutual distance, R. At low excitation power an assumption can be made that R → ∞, and detuning from Eg then reduces to ED + EA. In the spectra shown in Figure 1b, at 20 K the entire D−A band is shifted from EPL1 by approximately 30 ± 10 meV. Without further knowledge, we can assume a nearly symmetric detuning from corresponding band-edges, each by ∼15 meV. Recent theoretical work, which calculated the formation energy of various different defect sites, suggested the existence of typical shallow defects such as Pb2+ and Br− vacancies (VPb+2, VBr−) or Pb−Br antisites.65 The existence of VPb+2 was detected by electron spin resonance.66 VPb+2 and VBr− were shown to exist in analogous PbI2 layered materials, using optically detected magnetic resonance and seem to act as acceptor and donor trapping states, respectively.61 Reflectance and normalized μ-PL spectra recorded at various temperatures are shown in Figure 2a and 2b, respectively. An enlargement of n2 spectral region of reflectance and μ-PL spectra are shown Figure S5, SI. When the temperature is raised, the n1 dispersion broadens due to thermally induced interaction with phonons, and can no longer be resolved at T > 130 K (see corresponding cyan curve in Figure 2a). Comparison of the μ-PL spectra recorded at various temperatures (see Figure 2b) reveals an appearance of an asymmetric shoulder at the high-energy side of PL1 band at T < 80 K. This shoulder presumably originates from a recombination from remote states (e.g., exciton or free carriers at energies ≥ n2), activated due to a cross between them and the thermally populated phonon states coupled to the n1 electronic potential. In order to validate this assumption, Figure 2c presents exemplar μ-PL spectrum recorded at 60 K (blue curve) in comparison with calculated phonon state occupation curve (red curve) which was generated according to the Maxwell− Boltzmann distribution.67 The red curve was simulated using, dN/N ∼ E1/2 exp (−ΔE/kBT) dΔE, considering ΔE = E − EPL1 as the detuned energy from EPL1. A scheme of dN/N is shown in the inset of Figure 2c.

Figure 3. (a) Temperature dependence of n1 (E1, green squares) and n2 (E2, green empty diamond) absorption energy; theoretical fit of eq 2 to E1(T) (black dashed line); energy of PL1 (EPL1, red circles) and PL2 (EPL2, red open triangles) emission bands. (b) Energy correction to E1(T) due to electron coupling to acoustic and optic phonon branches. (c) RAMAN scattering spectrum measured with nonpolarized 632.8 nm excitation at 4.5 K.

(red open triangles), extracted from the data presented in Figure 2a and 2b. The plot of EPL1(T) exhibits sudden jumps around 165 K, 175 and 220 K,27 associated with structural phase transitions, as mentioned in the Introduction. Further details about the phase transformation are shown in Figure S6 (SI); however, the discussion here is solely concerned with the orthorhombic phase 70 K. Extrapolation of the phonon dispersion curves to the zero-temperature does show unexpected nonzero contribution, which was found also in other places, and was associated with a zero-point motion of a crystal.72 In any event, the phonon modes were further verified by recording the RAMAN spectrum at 4.5 K, as shown in Figure 3c. This RAMAN spectrum includes a longitudinal optical (LO) phonon centered at ∼127 cm−1 (3.82 THz), which is in good agreement with the fitted value, ωBr = 127.2 cm−1 (3.83 THz) given above. In order to decipher exciton recombination dynamic, the transient-PL (tr-PL) spectra of an isolated exciton band were recorded at various temperatures. The PL1 exciton band was separated from all other emission events by a tunable band-pass filter, with an optical window of ±7 meV around EPL1 at any temperature. Figure 4a shows representative tr-PL curves recorded at 20 K (green) and 100 K (brown), given by a log−log presentation, and a decay of the excitation laser (black). The tr-PL curves are characterized by sudden intensity

(1)

where nj , q ⃗ is a number of phonons at a j branch with wave vector q⃗ that follows Bose distribution for bosons, as nj , q ⃗ = (exp(ℏωj , q ⃗ /kBT ) − 1)−1, where (ωj , q ⃗ ) is the angular frequency of a phonon mode. The first term in eq 1 describes the change in Eg (T) due to the thermal lattice expansion (∂V/ ∂T), when ∂Eg/∂V is the expansion coefficient, to be here as temperature independent parameter at a fixed structural phase 175 μm in SolutionGrown CH3NH3PbI3 Single Crystals. Science 2015, 347, 967−970. (20) Dang, Y.; Liu, Y.; Sun, Y.; Yuan, D.; Liu, X.; Lu, W.; Liu, G.; Xia, H.; Tao, X. Bulk Crystal Growth of Hybrid Perovskite Material CH3NH3PbI3. CrystEngComm 2015, 17, 665−670. (21) Maculan, G.; Sheikh, A. D.; Abdelhady, A. L.; Saidaminov, M. I.; Haque, M. A.; Murali, B.; Alarousu, E.; Mohammed, O. F.; Wu, T.; Bakr, O. M. CH3NH3PbCl3 Single Crystals: Inverse Temperature Crystallization and Visible-Blind UV-Photodetector. J. Phys. Chem. Lett. 2015, 6, 3781−3786. (22) Stoumpos, C. C.; Malliakas, C. D.; Peters, J. A.; Liu, Z.; Sebastian, M.; Im, J.; Chasapis, T. C.; Wibowo, A. C.; Chung, D. Y.; Freeman, A. J.; Wessels, B. W.; Kanatzidis, M. G. Crystal Growth of the Perovskite Semiconductor CsPbBr3: A New Material for HighEnergy Radiation Detection. Cryst. Growth Des. 2013, 13, 2722−2727. (23) Yang, Y.; Yan, Y.; Yang, M.; Choi, S.; Zhu, K.; Luther, J. M.; Beard, M. C. Low Surface Recombination Velocity in Solution-Grown CH3NH3PbBr3 Perovskite Single Crystal. Nat. Commun. 2015, 6, 7961. (24) Manser, J. S.; Saidaminov, M. I.; Christians, J. A.; Bakr, O. M.; Kamat, P. V. Making and Breaking of Lead Halide Perovskites. Acc. Chem. Res. 2016, 49, 330−338. (25) Dirin, D. N.; Dreyfuss, S.; Bodnarchuk, M. I.; Nedelcu, G.; Papagiorgis, P.; Itskos, G.; Kovalenko, M. V. Lead Halide Perovskites and Other Metal Halide Complexes as Inorganic Capping Ligands for Colloidal Nanocrystals. J. Am. Chem. Soc. 2014, 136, 6550−6553. (26) Nedelcu, G.; Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Grotevent, M. J.; Kovalenko, M. V. Fast Anion-Exchange in Highly Luminescent Nanocrystals of Cesium Lead Halide Perovskites (CsPbX3, X = Cl, Br, I). Nano Lett. 2015, 15, 5635−5640. (27) Onoda-Yamamuro, N.; Matsuo, T.; Suga, H. Calorimetric and IR Spectroscopic Studies of Phase Transitions in Methylammonium Trihalogenoplumbates (II). J. Phys. Chem. Solids 1990, 51, 1383−1395. (28) Gesi, K. Effect of Hydrostatic Pressure on the Structural Phase Transitions in CH3NH3PbX3 (X = Cl, Br, I). Ferroelectrics 1997, 203, 249−268. (29) Poglitsch, A.; Weber, D. Dynamic Disorder in Methylammonium Trihalogenoplumbates (II) Observed by Millimeter-Wave Spectroscopy. J. Chem. Phys. 1987, 87, 6373−6378. (30) Stoumpos, C. C.; Kanatzidis, M. G. The Renaissance of Halide Perovskites and Their Evolution as Emerging Semiconductors. Acc. Chem. Res. 2015, 48, 2791−2802. (31) Brittman, S.; Adhyaksa, G. W. P.; Garnett, E. C. The Expanding World of Hybrid Perovskites: Materials Properties and Emerging Applications. MRS Commun. 2015, 5, 7−26. (32) Hsiao, Y.-C.; Wu, T.; Li, M.; Liu, Q.; Qin, W.; Hu, B. Fundamental Physics Behind High-Efficiency Organo-Metal Halide Perovskite Solar Cells. J. Mater. Chem. A 2015, 3, 15372−15385. (33) Chen, Q.; De Marco, N.; Yang, Y.; Song, T.-B.; Chen, C.-C.; Zhao, H.; Hong, Z.; Zhou, H. Under the Spotlight: The Organic− Inorganic Hybrid Halide Perovskite for Optoelectronic Applications. Nano Today 2015, 10, 355−396. (34) Du, M. H. Efficient Carrier Transport in Halide Perovskites: Theoretical Perspectives. J. Mater. Chem. A 2014, 2, 9091−9098. (35) Umebayashi, T.; Asai, K.; Kondo, T.; Nakao, A. Electronic Structures of Lead Iodide Based Low-Dimensional Crystals. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 67, 155405. (36) Brandt, R. E.; Stevanović, V.; Ginley, D. S.; Buonassisi, T. Identifying Defect-Tolerant Semiconductors with High MinorityCarrier Lifetimes: Beyond Hybrid Lead Halide Perovskites. MRS Commun. 2015, 5, 265−275. (37) Even, J.; Pedesseau, L.; Katan, C. Analysis of Multivalley and Multibandgap Absorption and Enhancement of Free Carriers Related to Exciton Screening in Hybrid Perovskites. J. Phys. Chem. C 2014, 118, 11566−11572.

No. 914/15), the Israel Science Foundation, Bikura (Project No. 1508/14) and excellence center FTA (Project No. 872967). M.V.K. acknowledges financial support from European Union via FP7 (ERC Starting Grant (NANOSOLID, GA No. 306733). E.L. and M.V.K. acknowledge the Horizon 2020 ETN PHONSI project.

REFERENCES (1) Moller, C. K. Crystal Structure and Photoconductivity of Caesium Plumbohalides. Nature 1958, 182, 1436−1436. (2) Ishihara, T. Optical Properties of PbI-Based Perovskite Structures. J. Lumin. 1994, 60−61, 269−274. (3) Hirasawa, M.; Ishihara, T.; Goto, T.; Uchida, K.; Miura, N. Magnetoabsorption of the Lowest Exciton in Perovskite-Type Compound CH3NH3PbI3. Phys. B 1994, 201, 427−430. (4) Zhou, H.; Chen, Q.; Li, G.; Luo, S.; Song, T.-B.; Duan, H.-S.; Hong, Z.; You, J.; Liu, Y.; Yang, Y. Interface Engineering of Highly Efficient Perovskite Solar Cells. Science 2014, 345, 542−546. (5) Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131, 6050−6051. (6) Lee, M. M.; Teuscher, J.; Miyasaka, T.; Murakami, T. N.; Snaith, H. J. Efficient Hybrid Solar Cells Based on Meso-Superstructured Organometal Halide Perovskites. Science 2012, 338, 643−647. (7) Kim, H.-S.; Lee, C.-R.; Im, J.-H.; Lee, K.-B.; Moehl, T.; Marchioro, A.; Moon, S.-J.; Humphry-Baker, R.; Yum, J.-H.; Moser, J. E.; Gratzel, M.; Park, N.-G. Lead Iodide Perovskite Sensitized AllSolid-State Submicron Thin Film Mesoscopic Solar Cell with Efficiency Exceeding 9%. Sci. Rep. 2012, 2, 591. (8) Jeon, N. J.; Noh, J. H.; Yang, W. S.; Kim, Y. C.; Ryu, S.; Seo, J.; Seok, S. I. Compositional Engineering of Perovskite Materials for High-Performance Solar Cells. Nature 2015, 517, 476−480. (9) Mitzi, D. B.; Chondroudis, K.; Kagan, C. R. Organic-Inorganic Electronics. IBM J. Res. Dev. 2001, 45, 29−45. (10) Yakunin, S.; Protesescu, L.; Krieg, F.; Bodnarchuk, M. I.; Nedelcu, G.; Humer, M.; De Luca, G.; Fiebig, M.; Heiss, W.; Kovalenko, M. V. Low-Threshold Amplified Spontaneous Emission and Lasing from Colloidal Nanocrystals of Caesium Lead Halide Perovskites. Nat. Commun. 2015, 6, 8056. (11) Zhu, H.; Fu, Y.; Meng, F.; Wu, X.; Gong, Z.; Ding, Q.; Gustafsson, M. V.; Trinh, M. T.; Jin, S.; Zhu, X. Y. Lead Halide Perovskite Nanowire Lasers with Low Lasing Thresholds and High Quality Factors. Nat. Mater. 2015, 14, 636−642. (12) Fang, Y.; Dong, Q.; Shao, Y.; Yuan, Y.; Huang, J. Highly Narrowband Perovskite Single-Crystal Photodetectors Enabled by Surface-Charge Recombination. Nat. Photonics 2015, 9, 679−686. (13) Sutherland, B. R.; Johnston, A. K.; Ip, A. H.; Xu, J.; Adinolfi, V.; Kanjanaboos, P.; Sargent, E. H. Sensitive, Fast, and Stable Perovskite Photodetectors Exploiting Interface Engineering. ACS Photonics 2015, 2, 1117−1123. (14) Park, Y.-S.; Guo, S.; Makarov, N. S.; Klimov, V. I. Room Temperature Single-Photon Emission from Individual Perovskite Quantum Dots. ACS Nano 2015, 9, 10386−10393. (15) Kepenekian, M.; Robles, R.; Katan, C.; Sapori, D.; Pedesseau, L.; Even, J. Rashba and Dresselhaus Effects in Hybrid Organic−Inorganic Perovskites: From Basics to Devices. ACS Nano 2015, 9, 11557− 11567. (16) Zheng, F.; Tan, L. Z.; Liu, S.; Rappe, A. M. Rashba Spin−Orbit Coupling Enhanced Carrier Lifetime in CH3NH3PbI3. Nano Lett. 2015, 15, 7794−7800. (17) Saidaminov, M. I.; Abdelhady, A. L.; Murali, B.; Alarousu, E.; Burlakov, V. M.; Peng, W.; Dursun, I.; Wang, L.; He, Y.; Maculan, G.; Goriely, A.; Wu, T.; Mohammed, O. F.; Bark, O. M. High-Quality Bulk Hybrid Perovskite Single Crystals Within Minutes by Inverse Temperature Crystallization. Nat. Commun. 2015, 6, 7586. (18) Shi, D.; Adinolfi, V.; Comin, R.; Yuan, M.; Alarousu, E.; Buin, A.; Chen, Y.; Hoogland, S.; Rothenberger, A.; Katsiev, K.; Losovyj, Y.; Zhang, X.; Dowben, P. A.; Mohammed, O. F.; Sargent, E. H.; Bark, O. 6369

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ACS Nano (38) Tanaka, K.; Takahashi, T.; Ban, T.; Kondo, T.; Uchida, K.; Miura, N. Comparative Study on the Excitons in Lead-Halide-Based Perovskite-Type Crystals CH3NH3PbBr3 CH3NH3PbI3. Solid State Commun. 2003, 127, 619−623. (39) Heo, J. H.; Im, S. H.; Noh, J. H.; Mandal, T. N.; Lim, C.-S.; Chang, J. A.; Lee, Y. H.; Kim, H.-J.; Sarkar, A.; Nazeeruddin, Md. K.; Gratzel, M.; Seok, S. I. Efficient Inorganic-Organic Hybrid Heterojunction Solar Cells Sontaining Perovskite Compound and Polymeric Hole Conductors. Nat. Photonics 2013, 7, 486−491. (40) Giorgi, G.; Fujisawa, J.-I.; Segawa, H.; Yamashita, K. Small Photocarrier Effective Masses Featuring Ambipolar Transport in Methylammonium Lead Iodide Perovskite: A Density Functional Analysis. J. Phys. Chem. Lett. 2013, 4, 4213−4216. (41) Deschler, F.; Price, M.; Pathak, S.; Klintberg, L. E.; Jarausch, D.D.; Higler, R.; Hüttner, S.; Leijtens, T.; Stranks, S. D.; Snaith, H. J.; Atature, M.; Phillips, R. T.; Friend, R. H. High Photoluminescence Efficiency and Optically Pumped Lasing in Solution-Processed Mixed Halide Perovskite Semiconductors. J. Phys. Chem. Lett. 2014, 5, 1421− 1426. (42) D’Innocenzo, V.; Grancini, G.; Alcocer, M. J. P.; Kandada, A. R. S.; Stranks, S. D.; Lee, M. M.; Lanzani, G.; Snaith, H. J.; Petrozza, A. Excitons versus Free Charges in Organo-Lead Tri-Halide Perovskites. Nat. Commun. 2014, 5, 3586. (43) Yang, Y.; Yang, M.; Li, Z.; Crisp, R.; Zhu, K.; Beard, M. C. Comparison of Recombination Dynamics in CH3NH3PbBr3 and CH3NH3PbI3 Perovskite Films: Influence of Exciton Binding Energy. J. Phys. Chem. Lett. 2015, 6, 4688−4692. (44) Kunugita, H.; Hashimoto, T.; Kiyota, Y.; Udagawa, Y.; Takeoka, Y.; Nakamura, Y.; Sano, J.; Matsushita, T.; Kondo, T.; Miyasaka, T.; Ema, K. Excitonic Feature in Hybrid Perovskite CH3NH3PbBr3 Single Crystals. Chem. Lett. 2015, 44, 852−854. (45) Miyata, A.; Mitioglu, A.; Plochocka, P.; Portugall, O.; Wang, J. T.-W.; Stranks, S. D.; Snaith, H. J.; Nicholas, R. J. Direct Measurement of the Exciton Binding Energy and Effective Masses for Charge Carriers in Organic-Inorganic Tri-Halide Perovskites. Nat. Phys. 2015, 11, 582−587. (46) Yang, Y.; Ostrowski, D. P.; France, R. M.; Zhu, K.; van de Lagemaat, J.; Luther, J. M.; Beard, M. C. Observation of a Hot-Phonon Bottleneck in Lead-Iodide Perovskites. Nat. Photonics 2016, 10, 53− 59. (47) Klingshirn, C. F. Chapter 9: Excitons, Biexcitons and Trions. In Semiconductor Optics, 4th ed.; Klingshirn, C. F., Ed.; Springer-Verlag: Berlin, 2012; pp 249−271. (48) Liao, W.-Q.; Zhang, Y.; Hu, C.-L.; Mao, J.-G.; Ye, H.-Y.; Li, P.F.; Huang, S. D.; Xiong, R.-G. A Lead-Halide Perovskite Molecular Ferroelectric Semiconductor. Nat. Commun. 2015, 6, 7338. (49) Luo, S.; Daoud, W. A. Recent Progress in Organic-Inorganic Halide Perovskite Solar Cells: Mechanisms and Material Design. J. Mater. Chem. A 2015, 3, 8992−9010. (50) Wen, X.; Ho-Baillie, A.; Huang, S.; Sheng, R.; Chen, S.; Ko, H.C.; Green, M. A. Mobile Charge-Induced Fluorescence Intermittency in Methylammonium Lead Bromide Perovskite. Nano Lett. 2015, 15, 4644−4649. (51) Korona, K. P.; Wysmolek, A.; Pakula, K.; Stepniewski, R.; Baranowski, J. M.; Grzegory, I.; Lucznik, B.; Wróblewski, M.; Porowski, S. Exciton Region Reflectance of Homoepitaxial GaN Layers. Appl. Phys. Lett. 1996, 69, 788−790. (52) Boyd, R. W. Chapter 3: Quantum-Mechanical Theory of the Nonlinear Optical Susceptibility. In Nonlinear Opt., 3rd ed.; Academic Press: Burlington, 2008; pp 135−206. (53) Weisbuch, C.; Benisty, H.; Houdré, R. Overview of Fundamentals and Applications of Electrons, Excitons and Photons in Confined Structures. J. Lumin. 2000, 85, 271−293. (54) Skromme, B. J. Optical and Magneto-Optical Characterization of Heteroepitaxial Gallium Nitride. Mater. Sci. Eng., B 1997, 50, 117− 125. (55) Wehrenfennig, C.; Liu, M.; Snaith, H. J.; Johnston, M. B.; Herz, L. M. Charge Carrier Recombination Channels in the Low-

Temperature Phase of Organic-Inorganic Lead Halide Perovskite Thin Films. APL Mater. 2014, 2, 081513. (56) Brivio, F.; Walker, A. B.; Walsh, A. Structural and Electronic Properties of Hybrid Perovskites for High-Efficiency Thin-Film Photovoltaics from First-Principles. APL Mater. 2013, 1, 042111. (57) Tian, W.; Zhao, C.; Leng, J.; Cui, R.; Jin, S. Visualizing Carrier Diffusion in Individual Single-Crystal Organolead Halide Perovskite Nanowires and Nanoplates. J. Am. Chem. Soc. 2015, 137, 12458− 12461. (58) Ullrich, B.; Singh, A. K.; Barik, P.; Xi, H.; Bhowmick, M. Inherent Photoluminescence Stokes Shift in GaAs. Opt. Lett. 2015, 40, 2580−2583. (59) Williams, R. T.; Song, K. S. The Self-Trapped Exciton. J. Phys. Chem. Solids 1990, 51, 679−716. (60) Kong, W.; Ye, Z.; Qi, Z.; Zhang, B.; Wang, M.; Rahimi-Iman, A.; Wu, H. Characterization of an Abnormal Photoluminescence Behavior upon Crystal-Phase Transition of Perovskite CH3NH3PbI3. Phys. Chem. Chem. Phys. 2015, 17, 16405−16411. (61) Lifshitz, E.; Yassen, M.; Bykov, L.; Dag, I. Continuous Photoluminescence, Time Resolved Photoluminescence and Optically Detected Magnetic Resonance Measurements of PbI2 NanometerSized Particles, Embedded in SiO2 Films. J. Lumin. 1996, 70, 421−434. (62) Osovsky, R.; Cheskis, D.; Kloper, V.; Sashchiuk, A.; Kroner, M.; Lifshitz, E. Continuous-Wave Pumping of Multiexciton Bands in the Photoluminescence Spectrum of a Single CdTe-CdSe Core-Shell Colloidal Quantum Dot. Phys. Rev. Lett. 2009, 102, 197401. (63) Htoon, H.; Malko, A. V.; Bussian, D.; Vela, J.; Chen, Y.; Hollingsworth, J. A.; Klimov, V. I. Highly Emissive Multiexcitons in Steady-State Photoluminescence of Individual ″Giant″ CdSe/CdS Core/Shell Nanocrystals. Nano Lett. 2010, 10, 2401−2407. (64) Tilchin, J.; Rabouw, F. T.; Isarov, M.; Vaxenburg, R.; Van DijkMoes, R. J. A.; Lifshitz, E.; Vanmaekelbergh, D. Quantum Confinement Regimes in CdTe Nanocrystals Probed by Single Dot Spectroscopy: From Strong Confinement to the Bulk Limit. ACS Nano 2015, 9, 7840−7845. (65) Buin, A.; Comin, R.; Xu, J.; Ip, A. H.; Sargent, E. H. HalideDependent Electronic Structure of Organo-Lead Perovskite Materials. Chem. Mater. 2015, 27, 4405−4412. (66) Shkrob, I. A.; Marin, T. W. Charge Trapping in Photovoltaically Active Perovskites and Related Halogenoplumbate Compounds. J. Phys. Chem. Lett. 2014, 5, 1066−1071. (67) Gross, E. F.; Permogorov, S. A.; Razbirin, B. S. Annihilation of Excitons and Exciton-Phonon Interaction. Sov. Phys. Usp. 1971, 14, 104. (68) Lian, H. J.; Yang, A.; Thewalt, M. L. W.; Lauck, R.; Cardona, M. Effects of Sulfur Isotopic Composition on the Band Gap of PbS. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 233202. (69) Kent, P. R. C.; Zunger, A. Carrier Localization and the Origin of Luminescence in Cubic InGaN Alloys. Appl. Phys. Lett. 2001, 79, 1977−1979. (70) Yu, C.; Chen, Z. J.; Wang, J.; Pfenninger, W.; Vockic, N.; Kenney, J. T.; Shum, K. Temperature Dependence of the Band Gap of Perovskite Semiconductor Compound CsSnI3. J. Appl. Phys. 2011, 110, 063526. (71) Dey, P.; Paul, J.; Bylsma, J.; Karaiskaj, D.; Luther, J. M.; Beard, M. C.; Romero, A. H. Origin of the Temperature Dependence of the Band Gap of PbS and PbSe Quantum Dots. Solid State Commun. 2013, 165, 49−54. (72) Göbel, A.; Ruf, T.; Cardona, M.; Lin, C. T.; Wrzesinski, J.; Steube, M.; Reimann, K.; Merle, J. C.; Joucla, M. Effects of the Isotopic Composition on the Fundamental Gap of CuCl. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 15183−15190. (73) Hennion, B.; Prevot, B.; Krauzman, M.; Pick, R. M.; Dorner, B. Neutron Scattering of the TO Phonon in CuCl at 5K. J. Phys. C: Solid State Phys. 1979, 12, 1609. (74) Kawai, H.; Giorgi, G.; Marini, A.; Yamashita, K. The Mechanism of Slow Hot-Hole Cooling in Lead-Iodide Perovskite: First-Principles Calculation on Carrier Lifetime from Electron−Phonon Interaction. Nano Lett. 2015, 15, 3103−3108. 6370

DOI: 10.1021/acsnano.6b02734 ACS Nano 2016, 10, 6363−6371

Article

ACS Nano (75) Nomura, S.; Kobayashi, T. Exciton−LO-phonon Couplings in Spherical Semiconductor Microcrystallites. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 1305−1316. (76) Wu, X.; Trinh, M. T.; Niesner, D.; Zhu, H.; Norman, Z.; Owen, J. S.; Yaffe, O.; Kudisch, B. J.; Zhu, X. Y. Trap States in Lead Iodide Perovskites. J. Am. Chem. Soc. 2015, 137, 2089−2096. (77) Boyd, R. W. Chapter 6: Nonlinear Optics in the Two-Level Approximation. In Nonlinear Opt., 3rd ed.; Academic Press: Burlington, 2008; pp 277−328. (78) Yang, H.; Xie, X. S. Probing Single-Molecule Dynamics Photon by Photon. J. Chem. Phys. 2002, 117, 10965−10979. (79) Kuno, M.; Fromm, D. P.; Hamann, H. F.; Gallagher, A.; Nesbitt, D. J. Nonexponential ″Blinking″ Kinetics of Single CdSe Quantum Dots: A Universal Power Law Behavior. J. Chem. Phys. 2000, 112, 3117−3120. (80) Mülken, O.; Blumen, A. Coherent Exciton Dynamics and Trapping in Topologically Disordered Systems. Phys. E 2010, 42, 576−579. (81) Mülken, O.; Blumen, A.; Amthor, T.; Giese, C.; Reetz-Lamour, M.; Weidemüller, M. Survival Probabilities in Coherent Exciton Transfer with Trapping. Phys. Rev. Lett. 2007, 99, 090601. (82) Rabouw, F. T.; Kamp, M.; van Dijk-Moes, R. J. A.; Gamelin, D. R.; Koenderink, A. F.; Meijerink, A.; Vanmaekelbergh, D. Delayed Exciton Emission and its Relation to Blinking in CdSe Quantum Dots. Nano Lett. 2015, 15, 7718−7725. (83) Stranks, S. D.; Burlakov, V. M.; Leijtens, T.; Ball, J. M.; Goriely, A.; Snaith, H. J. Recombination Kinetics in Organic-Inorganic Perovskites: Excitons, Free Charge, and Subgap States. Phys. Rev. Appl. 2014, 2, 034007. (84) Marcus, R. A.; Sutin, N. Electron Transfers in Chemistry and Biology. Biochim. Biophys. Acta, Rev. Bioenerg. 1985, 811, 265−322. (85) Sheng, R.; Wen, X.; Huang, S.; Hao, X.; Chen, S.; Jiang, Y.; Deng, X.; Green, M. A.; Ho-Baillie, A. W. Y. Photoluminescence Characterisations of a Dynamic Aging Process of Organic-Inorganic CH3NH3PbBr3 Perovskite. Nanoscale 2016, 8, 1926−1931. (86) Zhang, M.; Yu, H.; Lyu, M.; Wang, Q.; Yun, J.-H.; Wang, L. Composition-Dependent Photoluminescence Intensity and Prolonged Recombination Lifetime of Perovskite CH3NH3PbBr3-xClx Films. Chem. Commun. 2014, 50, 11727−11730. (87) He, H.; Yu, Q.; Li, H.; Li, J.; Si, J.; Jin, Y.; Wang, N.; Wang, J.; He, J.; Wang, X.; Zang, Y.; Ye, Z. Exciton Localization in SolutionProcessed Organolead Trihalide Perovskites. Nat. Commun. 2016, 7, 10896.

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