Excited State Properties of Hybrid Perovskites - Accounts of Chemical

Article pubs.acs.org/accounts

Excited State Properties of Hybrid Perovskites Published as part of the Accounts of Chemical Research special issue “Lead Halide Perovskites for Solar Energy Conversion”. Michele Saba, Francesco Quochi, Andrea Mura, and Giovanni Bongiovanni* Dipartimento di Fisica, Università degli Studi di Cagliari, I-09042 Monserrato, Italy CONSPECTUS: Metal halide perovskites have come to the attention of the scientific community for the progress achieved in solar light conversion. Energy sustainability is one of the priorities of our society, and materials advancements resulting in low-cost but efficient solar cells and large-area lighting devices represent a major goal for applied research. From a basic point of view, perovskites are an exotic class of hybrid materials combining some merits of organic and inorganic semiconductors: large optical absorption, large mobilities, and tunable band gap together with the possibility to be processed in solution. When a novel class of promising semiconductors comes into the limelight, lively discussions ensue on the photophysics of band-edge excitations, because just the states close to the band edge are entailed in energy/charge transport and light emission. This was the case several decades ago for III−V semiconductors, it has been up to 10 years ago for organics, and it is currently the case for perovskites. Our aim in this Account is to rationalize the body of experimental evidence on perovskite photophysics in a coherent theoretical framework, borrowing from the knowledge acquired over the years in materials optoelectronics. A crucial question is whether photon absorption leads to a population of unbound, conductive free charges or instead excitons, neutral and insulating bound states created by Coulomb interaction just below the energy of the band gap. We first focus on the experimental estimates of the exciton binding energy (Eb): at room temperature, Eb is comparable to the thermal energy kBT in MAPbI3 and increases up to values 2−3kBT in wide band gap MAPbBr3 and MAPbCl3. Statistical considerations predict that these values, even though comparable to or larger than thermal energy, let free carriers prevail over bound excitons for all levels of excitation densities relevant for devices. The analysis of photophysics evidence confirms that all hybrid halide perovskites behave as f ree-charge semiconductors. Thanks to such property, in combination with band gap energies covering the entire solar spectrum, perovskites represent a promising materials platform for highly efficient, single and multijunction solar cells. Concerning the use of perovskites as color-tunable materials in light emitting devices, free-charges are not the preferred species, as they recombine radiatively through a bimolecular process that is inefficient at the charge-injection levels typical of LED operation. Strategies to overcome this limit, and thus extend the use of perovskite materials beyond solar energy conversion, could be borrowed from inorganic semiconductor optoelectronics and include the fabrication of nanostructures with reduced dimensionality to alter the electronic density of states, as well as engineering composite materials.

1. INTRODUCTION Electronic states near the band gap determine key processes for optoelectronic devices, such as charge transport and light emission. It is therefore not surprising that the investigation of the electronic excitations near the optical absorption edge is of paramount importance in the modern science of semiconductors and is often at the center of the scientific debate when a novel class of promising materials captures the attention of the scientific community. Two kinds of photoexcitations are possible for direct band gap semiconductors near the band edge: free electron−hole pairs and bound excitons. Which of the two prevails is dependent upon the magnitude of the Coulomb attraction between positively charged holes and negatively charged electrons, screened by the dielectric properties of the materials. The exciton binding energy provides a measure of such correlation and is the main parameter that determines the balance between the populations of the two species. The two © XXXX American Chemical Society

limiting cases are represented by (i) free-carrier materials, such as low-gap III−V semiconductors, where the exciton binding energy is few meV and at room temperature the excited states is almost exclusively populated by free carriers, while excitons, described by the hydrogenic Wannier theory and having a radius much larger than the crystal unit cell, only appear at cryogenic temperatures; (ii) excitonic materials, such as conjugated organic semiconductors, where the so-called Frenkel excitons prevail, localized in a single molecule and with binding energies measured in hundreds of meV. The excited state properties are very different for the two types of materials, with profound consequences for applications. A gas of free electron−hole pairs is conductive, while a gas of bound excitons is insulating; as a consequence, in solar cells based on free-carrier materials the internal electric field of Received: September 30, 2015

A

DOI: 10.1021/acs.accounts.5b00445 Acc. Chem. Res. XXXX, XXX, XXX−XXX

Article

Accounts of Chemical Research a homojunction is sufficient to create a directional charge flow, while organic solar cells need heterojuctions to split neutral excitons. Free carriers are usually associated with large diffusion lengths and wide energy bands; on the contrary, excitons diffuse typically by hopping and only for few nm distances before recombining. Excitons can emit light efficiently even at low densities, while electron−hole pairs recombine through a bimolecular process, which is efficient at high densities, but inefficient at low densities. Concerning lead halide perovskites, the rapid progress in solar cell performances has shadowed a lack of consensus on some of the basic photophysics phenomena. Perovskites represent a class of semiconductors with binding energies intermediate between the Frenkel and Wannier extremes and it is not clear a priori whether they are excitonic or free carrier materials. Some of the work published in literature assume that lead halide perovskites are similar to molecular semiconductors, where photon absorption creates an exciton, localized in a single molecule; others approach perovskites as III−V inorganic semiconductors, assuming that most photoexcitations are free carriers. Conflicting reports have been published on the value of the exciton binding energy for the most studied materials, namely methylammonium lead bromide (MAPbBr3) and iodide (MAPbI3); as an example, reported values for MAPbI3 range from 2 to 55 meV,1−16 representing an intriguing puzzle. Similar uncertainty reigns in determining the radiative efficiency and trap recombination rates. We review here the debate on perovskite photophysics, rationalizing the experimental evidence in the single coherent theoretical framework that as been successfully established in III−V semiconductors. Understanding the photophysics processes naturally presents consequences on the potential and limitations of perovskite materials for use in solar cells, LEDs, and lasers, as well as materials improvements that may boost applications.

Figure 1. (a) Absorption (continuous line) and continuous-wave luminescence (dotted line) spectra of a MAPbI3 film (thickness, 800 nm) recorded at 300 and 170 K. (b, c) Continuous black lines are theoretical fits to the experimental absorption spectra at 170 and 300 K; dotted lines are exciton contributions to absorption, and shortdashed (long-dashed) lines are continuum contributions with (without) the inclusion of Coulomb interactions. Exciton binding energy: 25 ± 3 meV. Reproduced with permission from ref 17. Copyright 2014 Macmillan Publishers Limited.

energy Eb, the energy gap Eg, and the squared transition dipole moment μcv2: α(ℏω) ∝ μcv

+

2. ABSORPTION SPECTRUM AND EXCITON BINDING ENERGY We start by discussing the optical response of MAPbI3, as for this compound progress in preparation and film processing, together with the large body of experimental findings, allows outlining a first coherent picture of the photophysics. Photoluminescence and absorbance spectra, representative of the optical response near the energy gap, are reported in Figure 1a. MAPbI3 crystallizes in the tetragonal crystal phase for temperatures between 162 and 330 K.1 At ambient temperature, the exciton optical transition is vaguely distinguishable as a broad shoulder at 1.65 eV. Lowering the sample temperature down to 170 K reduces line broadening, the visibility of the excitonic peak increases, while the magnitude of the free carrier absorption on the high-energy side remains almost unaffected by temperature (discounting the little offset variation). The photoluminescence spectrum, once corrected for self-absorption, results to be almost resonant with the excitonic resonance, denoting the intrinsic origin of the emitting species, without noticeable contributions from defects. The analysis of the band-edge absorption provides direct information on bound exciton states, on free carriers, and on the actual role played by Coulomb interaction. The Elliott theory represents the simplest analytical approach to describe absorption spectrum near the energy band gap in direct semiconductors;18 in such framework, the absorption coefficient α(ℏω) is described as a function of the exciton binding

2

⎡ 2E E b ⎢∑ 3b δ(ℏω − Enb) ⎢ n n ⎣

θ(ℏω − Eg ) ⎤ ⎥ −2π ℏωE−bE ⎥ ⎦ g 1−e

(1)

There are three main effects of the electron−hole Coulomb interaction on the absorption spectrum of eq 1: (i) the introduction of the excitonic transitions with energies Ebn = Eg − (Eb/n2) (first term in RHS), (ii) the modification of the spectral dependence of the band-to-band absorption (described by the second term in RHS), no more represented by the simple square root dependence of the valence-to-conduction joint density of states, (E − Eg)1/2; (iii) the dependence of the overall absorption coefficient and of the relative contributions of the two terms on Eb. Figure 1b and c shows the theoretical absorption coefficient α(ℏω), convoluted with a secant hyperbolic function to simulate line broadening, together with the simulated single contributions of bound excitons and the free carrier continuum. Parameters were chosen to fit experimental spectra at 170 and 300 K, resulting in Eb = 25 meV as best fit value.1 Photon absorption by free carriers (short-dashed line) gives a plateau on the high-energy side of the excitonic resonance. The modification of the absorption by free electron−hole pairs induced by Coulomb interaction can be appreciated by comparing the two theoretical curves computed, respectively, with the interaction switched on and off: the absorption coefficient of free carries is appreciably enhanced by Coulomb interaction, being over a factor of 2 larger than that one calculated for noninteracting electron−hole pairs (Eb = 0) in a wide spectral window above the band gap. B


Article

Accounts of Chemical Research The ability to extract a value for Eb by fitting the Elliott formula to absorption spectra relies on the fact that the exciton and continuum contributions have different dependences on Eb: the excitonic contribution scales as Eb3/2, while the continuum only as Eb1/2; for growing values of Eb therefore the exciton peak becomes better resolved and has an absorption value higher than the neighboring continuum plateau. In our laboratory, the size and shape of the absorption coefficient due to band-to-band transitions was not observed to depend on lattice temperature in the tetragonal phase of MAPbI3 films, as shown in Figure 1a. Accordingly, least-squares fitting the Elliot formula to experimental absorption spectra did not find any dependence of the binding energy on temperature. MAPbI3 absorption spectra as a function of temperature published in ref 19 and readapted in Figure 2 confirm that the

Sn, Ge), and halide anion (I, Br and Cl).7,22 The band gap of tin halide perovskites falls in the near-infrared and does not show perceivable evidence of excitonic enhancement at the absorption band-edge, indicating a negligible exciton binding energy.23−26 Mixed lead halide perovskites, with Br or Cl anions (MaPbBr3‑xClx), represent the part of the perovskite family matching the green and blue part of the visible spectrum.6 As expected, wider band gap materials display a more pronounced excitonic resonance, even at room temperature (see Figure 3, bottom panel). We extracted values for the

Figure 2. Absorption spectra of MAPbI3 as a function of temperature were readapted from ref 19. In order to better compare the magnitude of the continuum contributions, the zero in the horizontal axis was chosen for each curve at the exciton resonance. Published data were extracted from the pdf files through the CurveSnap software, freely available online.

Figure 3. Absorption spectra for lead halide perovskites (top panel) with respective fits based on Elliott formula (back lines); measurements are at room temperature. The bottom panel shows the exciton binding energy extracted from the fit as a function of the energy bandgap of the respective materials. Data for MAPbCl3 were extracted from ref 6 using CurveSnap.

absorption in the continuum only marginally depends on temperature even for T < 150 K, when MAPbI3 crystallizes in the orthorhombic crystal phase of MAPbI3 and optical spectra evidence a well spectrally resolved excitonic peak. In the framework of the Elliott theory, the fact that the continuum absorption does not change with temperature means that Eb is approximately constant.16 This argument bypasses the main limitation of fitting procedures, which become unreliable when the line width Γ is comparable or even larger than Eb, as it is not possible to resolve the exciton and continuum contributions. Conversely, other research groups found a collapse of the exciton binding energies for increasing temperature14,15,20,21 yielding a very small value, Eb ∼ 6 meV or even less at room temperature, the origin of which was attributed to screening effects induced by methylammonium ion rotations. We remark that significant deviations from the prediction of the Elliott theory (Eb ∼ 25 ± 3 meV) could only arise from failures of the effective mass approximation, which could be expected for high binding energies, and thus more likely for wider band gap perovskites. Tuning of the energy band gap to cover the entire solar spectrum and colors of interest for lighting devices can be achieved by a suitable choice of the organic cation (e.g., methylamonium or formamidinium), divalent metal cation (Pb,

exciton binding energies much larger than thermal energy, 64 meV for MaPbBr3 and 69 meV for MaPbCl3 (≈ 2−3kBT), by fitting absorption spectra extracted from ref 6 via the Elliott formula.

3. PHOTOEXCITATION DYNAMICS The strong band edge absorption spectrum, the small exciton binding energies, the small effective exciton mass (0.1me),15 and the high carrier mobility27−31 show that MAPbI3 films behave as a direct semiconductor with a small energy band gap.32 It is therefore instructive to use the knowledge acquired for III−V inorganic semiconductors along the last 30 years as reference for the relaxation dynamics of photoexcitations in perovskite films. We show in Figure 4 a schematic description of the basic photophysical processes expected in a semiconductor with small exciton binding energy. The upper left panel refers to ultrafast spectroscopy experiments under pulsed excitation; the dispersion diagrams represent free carriers (left), with absorption described by the continuum terms in eq 1 and occurring for electron and holes with opposite total momenta, and the 1s exciton (right), with absorption described by the first term in eq 1 and possible only for zero momentum. Photon absorption with quantum energy well above the exciton resonance can create (i) an electron−hole pair with total momentum q ≃ 0 or (ii) an exciton with momentum q ≠ 0 C


Article

Accounts of Chemical Research

kBT), namely, materials in which neutral excitons are the room temperature photoexcitations (such as in organic semiconductors), and “free-charge” semiconductors (Eb < kBT), with Coulomb-correlated, but unbound, electrons and holes being the dominant photoexcitations at ambient conditions (such as inorganic semiconductors). The class of hybrid perovskites would therefore encompass both types of materials, with MAPbI3 marking the divide between them. However, simply comparing the binding and thermal energies is not the right approach for two-particle states (free charges) coupled to single-particle bound states (excitons), and leads to order-ofmagnitude wrong estimates of ncar/nex. One has instead to account for that fact that the probability of an electron and a hole being uncorrelated scales as the joint density of the two particles (i.e., the product of the density of each species), ncar2, while the probability of finding a bound exciton scales linearly as nex. As a consequence, the relevant statistics is dictated by the Saha’s equation: ⎛ μ kBT ⎞3/2 ncar 2 = neq (T ) = ⎜ X 2 ⎟ e−E b / kBT nex ⎝ 2π ℏ ⎠

Figure 4. Scheme for the photoexcitation dynamics described in the text. At time t = 0, free carriers are predominantly excited, while the geminate, direct creation of excitons is not favored. Free carriers then may relax, if enough time is given, to equilibrium with the exciton population as predicted by the Saha equation. CB, VB, and GS stand for conduction band, valence band, and electron−hole pair ground state, respectively. It has to be noted that excitons and free carriers cannot be pictured in the same dispersion graph, as excitons need a single-particle diagram, while free carriers need a two-body diagram.

(2)

2neq(T) represents the value of the crossover density for which electron−hole pair and exciton densities are equal (ncar = nex = neq); below such density, free carriers prevail, and above it excitons are the majority. Predictions of Saha’s equation for thermal equilibrium were first discussed by Petrozza et al.19 We elaborate in Figure 5 the

(geminate exciton formation).33 In semiconductors with highly delocalized electron wave functions, the cross section for the formation of geminate excitons is, however, negligible owing to the fact that this second-order process requires the coherent absorption/emission of a phonon of wavevector q during the electron−hole correlation time, which is extremely short at room temperature (fs time scale).33 Given the analogy in electronic structure between perovskites and III−V semiconductor, one has to assume that photoexcitation in perovskites results in a hot gas of unbound free carriers. After injections, free carriers quickly thermalize via very efficient carrier−carrier scattering; excess energy is lost through optical and acoustical phonon emission. At room temperature, thermal equilibrium with lattice is achieved in a very short time, typically in the picosecond time scale. The right panel illustrates the reaction processes e + h ↔ X, leading to the equilibrium exciton (nex) and carrier (ncar) densities at temperature T. The initial formation rate e + h → X is proportional to the carrier density, knn = Cncar2. C was measured as a function of both carrier density and temperature in III−V quantum wells,34−36 while a theoretical assessment, which takes into account the actual quantum dynamics of this process in the context of delocalized carriers, was provided by Piermarocchi et al.33 C represents the inorganic analogous of the Langevin constant (kL = (e/εεr)μ, with μ being the carrier mobility) for the rate of bimolecular exciton formation from carriers pairs, derived for organics in the framework of a classical kinetics model. The next step is to estimate what relative fractions of excitons and free carriers to expect at equilibrium and how do they depend on Eb. The statistics of a gas with two allowed levels split in energy by Eb, would suggest using the simple relation (ncar/nex) = e−(Eb/kBT). In other words, the ambient thermal energy kBT would represent the boundary for the exciton binding energy to distinguish “excitonic” semiconductors (Eb >

Figure 5. Exciton fraction calculated according to the Saha equilibrium condition as a function of exciton binding energy and excited state density. Temperature for the calculation is 300 K.

exciton and free carriers phase diagram, that is, the fraction of excitons nex/n as a function of the total excited population density n and the exciton binding energy Eb, assuming 300 K as temperature. For a fixed Eb, the relative population of excitons increases for increasing n as the reaction e + h ↔ X favors the bimolecular process of exciton formation. However, the maximum carrier injection levels achievable under solar light illumination are around 1015 cm−3. In this range of excitations and at room temperature, thermal equilibrium implies that free carriers represent the large majority of photoexcitations even for binding energies as large as 150 meV and thus for all threedimensional hybrid ABX3 perovskites studied up to now. In the following, we show the extent to which this photophysical picture applies to experimental data for perovD


Article

Accounts of Chemical Research skites. Thermalization of the electron−hole populations to the lattice temperature (T = 300 K) was experimentally demonstrated in ref 37, where plasma temperatures as a function of time after excitation were extracted by fitting the high energy tail of time-gated photoluminescence spectra with an e−(E/kBT) exponential function. Experimental evidence that free charges are the dominant species even at excitation densities higher than 1015 cm−3 have been recently given by means of transient photoluminescence, differential transmission experiments and transient THz spectroscopy.17,19,28,29,38−41 We briefly comment two basic optical experiments. Figure 6 shows that the photolumines-

Figure 7. Plot of the normalized PL intensity at time zero after pulsed laser excitation versus the square of the transient differential transmission signal amplitude (also at time zero) in a CH3NH3PbI3−xClx film and in a working solar cell (device) based on the same perovskite materials. Reproduced with permission from ref 38. Copyright 2014 American Chemical Society.

Far from population inversion, direct radiative recombination of carriers is also a bimolecular process R = krn2. The bimolecular decay constant, kr = 2.6 × 10−10 cm3 s−1, was directly assessed from the semiconductor absorption coefficient via the so-called Kubo−Martin−Schwinger relation.17 This estimate represents a median value with respect to those ones extracted from the dynamics of free carriers, investigated by means of transient spectroscopy.40 The knowledge of kr allows a reliable estimate of the photoexcitation radiative lifetime, τr ≳ (1/krns) = 4 μs, at densities of interest for solar energy conversion, namely for n ≲ 1015 cm−3. This long radiative lifetime suggest that carrier recombination should be dominated by trap-mediated recombinations (known as Shockley−Read−Hall recombination in the solar cell community) in the solar cell or LED operating regime, unless samples of exceptional high quality are employed. This scenario is supported by the results of time-resolved spectroscopy. Figure 8 shows the transient photoluminescence signal. At low excitations, the decay is nearly exponential, indicating a monomolecular recombination decay induced by charge trapping. Increasing the injection level, the decay becomes faster due to the increasing importance of the bimolecular radiative recombination of the electron−hole pairs, and at very high densities, due to the growing relevance of Auger processes, scaling as n3. The light emission quantum yield (QY), extrapolated from the time integrated photoluminescence intensity and excitation pulse fluence, fully confirmed this analysis. The QY grows linearly, then saturates and at very high excitation (n > 1018 cm−3) decreases. The increase of the QY with pulse fluence results from the increase of the bimolecular radiative recombination rate. When radiative recombination becomes faster than trapping for n > 1017 cm−3, the QY saturates at values not far from unity because the majority of electron−hole pairs decays emitting a photon. If the photoexcited population is further increased, n > 1018 cm−3, Auger processes dominate, causing the decrease of the QY. A comprehensive quantitative analysis of all the photoluminescence results was self-consistently given, which allowed us to estimate an Auger coefficient of 2−4 × 10−28 cm6 s−1 and a monomolecular charge lifetime of ∼10 ns. This latter depends

Figure 6. Photoluminescence emission intensity estimated at time t = 0 after excitation (PL0) as a function of laser pulse fluence. The quadratic dependence is shown by the dotted lines as a guide for eyes. Relative values for the two materials are arbitrary.

cence intensity PL0, emitted in a short temporal window of a few tens of picoseconds following a femtosecond laser excitation, scales as the square of the optically injected carriers, as expected for the bimolecular recombination of the electron− hole plasma.17 This experiment proved that just after excitation (≈ 50 ps) the exciton population was negligible. Remarkably, the quadratic dependence of PL0 is also observed in the wide band gap perovskite MAPbBr3, where Eb ≈ 60 eV ≫ kBT, representing a more severe test for the prediction of Saha equation, thus bringing an other piece of evidence that all hybrid halide perovskites behaves under illumination as f reecharge semiconductors. In a different experiment, both the transients of the differential transmission signal (ΔT/T)(t), which integrated over the exciton resonance can be assumed proportional to n, and the photoluminescence intensity PL(t) were measured in a wide temporal range.38 Figure 7 shows that PL(t) scales linearly with [(ΔT/T)(t)]2, implying that the photoluminescence intensity decays as n(t)2 in the time range nanosecond to microsecond. From the two experiments, we can safely conclude that free carriers are the dominant species at any time after excitation, in agreement with Saha’s equation. E


Article


Figure 8. (a) Transient photoluminescence signal for a MAPbI3 sample as a function of the injected electron−hole pair density at the film surface. Straight lines in the semilogarithmic plot represent an exponential fit to the initial decay of the photoluminescence signal. Photoluminescence was excited by 150 fs long laser pulses with a repetition rate of 1 kHz and 3.18 eV photon energy. Injected carrier densities, from top to bottom: 1.2 × 1019, 3.9 × 1018, 1.2 × 1018, and 1.9 × 1017 cm−3. (b) Time-integrated photoluminescence signals and emission quantum yield for the same MAPbI3 sample as a function of the injected carrier density (laser pulse fluence is on the top axis). Readapted with permission from ref 17. Copyright 2014 Macmillan Publishers Limited.

on trap density, which is a film-dependent quantity. Values close to 1 μs were recently reported in films of very high quality.38,42 These values, although exceptionally long, are not sufficient to guarantee that the carrier recombination in solar cells under working condition is radiative-limited (τr ≳ 4 μs). It should be noted that disorder might also affect the value of the Auger coefficient, as localization of photoexcitations in traps or potential minima may lead to a local increase in the excitation density, causing faster Auger recombination.

diffusion lengths, combined with the processability in solution at low temperature, represent an unusual mixture of favorable properties that make this class of semiconductors a novel material platform for highly efficient, single and multijunction solar cells. The coherent interpretation of perovskite photophysics as free-charge semiconductors helps understanding the evolution of solar cells, from the initial architectures based on mesoscopic titania and bulk heterojunctions, that assumed organic solar cells as a model, to the present prevalence of bilayer, planar structures, analogue to standard inorganic photovoltaics. Concerning light emission, the bimolecular recombination of free carriers means that the radiative recombination rate increases linearly with density; as a consequence, a density window exists in which radiative recombination is the dominant channel. Such window, 1017−1018 cm−3, includes the density needed to reach population inversion, and therefore, perovskites may be successfully employed for efficient lasers and optical amplifiers.37,38,43−46 Concerning LEDs instead, optical emission may occur at low densities, when radiative recombination is slower than recombination through traps, with a corresponding very low radiative quantum yield.47,48 A strategy therefore is needed to increase light emission efficiency. A boost to LED performances may come from increasing the exciton binding energy with confinement strategies. A possible strategy, suggested by GaN technology for LEDs, could be a suitable introduction of lowdimension (2d, 1d, and 0d) perovskites2,7,22,49 in a bulk perovskite matrix, as that one recently realized (dots-inperovskite-matrix) based on an intriguing solution-processed version of the heteroepitaxial technique of crystal growth.50

4. CONCLUSION AND OUTLOOK We have critically reviewed recent optical experiments on the photophysics of band edge electronic excitations (neutral excitons and free electrons and holes), determining the basic working mechanisms of optoelectronic devices. Optical spectroscopy has provided an estimate of the binding energy of excitons: at room temperature, Eb is small, probably vanishing for near-infrared perovskites (MASnI3), it becomes comparable to kBT in MAPbI3, and it increases to values far exceeding thermal energy (2−3 kBT) in wide band gap MAPbBr3 and MAPbCl3. Such binding energies are large enough to provide a significant enhancement of the absorption coefficient close and well above the band gap, thanks to the attractive Coulomb interaction between electrons and holes; on the other hand, Eb ≤ 150 meV can be considered low enough to let free carriers prevail over bound excitons at room temperature for all excited state densities relevant for optoelectronic applications. This latter conclusion, arising from basic statistical considerations and checked experimentally in wide band gap perovskites, implies that hybrid halide perovskites with a three-dimensional crystal structure should all belong to the class of f ree-charge semiconductors. The high absorption coefficient, the possibility of tuning the band gap energy across the whole solar spectrum, the free-charge character of the photoexcitations, and their long F


Article


■

(11) Löper, P.; Stuckelberger, M.; Niesen, B.; Werner, J.; Filipič, M.; Moon, S.-J.; Yum, J.-H.; Topič, M.; De Wolf, S.; Ballif, C. Complex Refractive Index Spectra of CH3NH3PbI3 Perovskite Thin Films Determined by Spectroscopic Ellipsometry and Spectrophotometry. J. Phys. Chem. Lett. 2015, 6, 66−71. (12) Jiang, Y.; Green, M. A.; Sheng, R.; Ho-Baillie, A. Room Temperature Optical Properties of Organic−Inorganic Lead Halide Perovskites. Sol. Energy Mater. Sol. Cells 2015, 137, 253−257. (13) 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. (14) Kim, H.-S.; Im, S. H.; Park, N.-G. Organolead Halide Perovskite: New Horizons in Solar Cell Research. J. Phys. Chem. C 2014, 118, 5615−5625. (15) 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. (16) Sestu, N.; Cadelano, M.; Sarritzu, V.; Chen, F.; Marongiu, D.; Piras, R.; Mainas, M.; Quochi, F.; Saba, M.; Mura, A.; Bongiovanni, G. Absorption F-Sum Rule for the Exciton Binding Energy in Methylammonium Lead Halide Perovskites. J. Phys. Chem. Lett. 2015, 6, 4566−4572. (17) Saba, M.; Cadelano, M.; Marongiu, D.; Chen, F.; Sarritzu, V.; Sestu, N.; Figus, C.; Aresti, M.; Piras, R.; Lehmann, A. G.; Cannas, C.; Musinu, A.; Quochi, F.; Mura, A.; Bongiovanni, G. Correlated Electron−Hole Plasma in Organometal Perovskites. Nat. Commun. 2014, 5, 5049. (18) Elliott, R. Intensity of Optical Absorption by Excitons. Phys. Rev. 1957, 108, 1384−1389. (19) 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. (20) 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. (21) Bakulin, A. A.; Selig, O.; Bakker, H. J.; Rezus, Y. L. A.; Müller, C.; Glaser, T.; Lovrinčić, R.; Sun, Z.; Chen, Z.; Walsh, A.; Frost, J. M.; Jansen, T. L. C. Real-Time Observation of Organic Cation Reorientation in Methylammonium Lead Iodide Perovskites. J. Phys. Chem. Lett. 2015, 6, 3663−3669. (22) Stoumpos, C. C.; Kanatzidis, M. G. The Renaissance of Halide Perovskites and Their Evolution as Emerging Semiconductors. Acc. Chem. Res. 2015, 48, 2791−2802. (23) Mitzi, D. B.; Feild, C. A.; Harrison, W.; Guloy, A. M. Conducting Tin Halides with a Layered Organic-Based Perovskite Structure. Nature 1994, 369, 467−469. (24) Yamada, K.; Nakada, K.; Takeuchi, Y.; Nawa, K.; Yamane, Y. Tunable Perovskite Semiconductor CH3NH3SnX3 (X: Cl, Br, or I) Characterized by X-Ray and DTA. Bull. Chem. Soc. Jpn. 2011, 84, 926− 932. (25) Stoumpos, C. C.; Malliakas, C. D.; Kanatzidis, M. G. Semiconducting Tin and Lead Iodide Perovskites with Organic Cations: Phase Transitions, High Mobilities, and Near-Infrared Photoluminescent Properties. Inorg. Chem. 2013, 52, 9019−9038. (26) Noel, N. K.; Stranks, S. D.; Abate, A.; Wehrenfennig, C.; Guarnera, S.; Haghighirad, A.-A.; Sadhanala, A.; Eperon, G. E.; Pathak, S. K.; Johnston, M. B.; Petrozza, A.; Herz, L. M.; Snaith, H. J. LeadFree Organic-Inorganic Tin Halide Perovskites for Photovoltaic Applications. Energy Environ. Sci. 2014, 7, 3061−3068. (27) Wehrenfennig, C.; Liu, M.; Snaith, H. J.; Johnston, M. B.; Herz, L. M. Charge-Carrier Dynamics in Vapour-Deposited Films of the Organolead Halide Perovskite CH3NH3PbI3−XClX. Energy Environ. Sci. 2014, 7, 2269.

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Notes

The authors declare no competing financial interest. Biographies Michele Saba holds a Ph.D. from EPFL (2001), has been a postdoc at MIT, and is currently associate professor in condensed matter physics at the Università di Cagliari. Francesco Quochi holds a Ph.D. from EPFL (1999), has been a postdoc at Bell Labs, Lucent Technologies, and is currently associate professor in condensed matter physics at the Università di Cagliari. Andrea Mura is associate professor in condensed matter physics at the Università di Cagliari and vice director of the Physics Department. Giovanni Bongiovanni is full professor in condensed matter physics at the Università di Cagliari and director of the Physics Department.

■

ACKNOWLEDGMENTS The authors thank the Regione Autonoma della Sardegna for financial support through L.R. 7/2007, “Progetti di ricerca di base e orientata”, Project Nos. CRP-18353, CRP-18013, and CRP- 24978.

■

REFERENCES

(1) Hirasawa, M.; Ishihara, T.; Goto, T.; Uchida, K.; Miura, N. Magnetoabsorption of the Lowest Exciton in Perovskite-Type Compound (CH3NH3)PbI3. Phys. B 1994, 201, 427−430. (2) Koutselas, I. B.; Ducasse, L.; Papavassiliou, G. C. Electronic Properties of Three- and Low-Dimensional Semiconducting Materials with Pb Halide and Sn Halide Units. J. Phys.: Condens. Matter 1996, 8, 1217−1227. (3) 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. (4) Lin, Q.; Armin, A.; Nagiri, R. C. R.; Burn, P. L.; Meredith, P. Electro-Optics of Perovskite Solar Cells. Nat. Photonics 2014, 9, 106− 112. (5) Savenije, T. J.; Ponseca, C. S., Jr.; Kunneman, L.; Abdellah, M.; Zheng, K.; Tian, Y.; Zhu, Q.; Canton, S. E.; Scheblykin, I. G.; Pullerits, T.; Yartsev, A.; Sundströ m, V. Thermally Activated Exciton Dissociation and Recombination Control the Carrier Dynamics in Organometal Halide Perovskite. J. Phys. Chem. Lett. 2014, 5, 2189− 2194. (6) Comin, R.; Walters, G.; Thibau, E. S.; Voznyy, O.; Lu, Z.-H.; Sargent, E. H. Structural, Optical, and Electronic Studies of WideBandgap Lead Halide Perovskites. J. Mater. Chem. C 2015, 3, 8839− 8843. (7) Sum, T. C.; Chen, S.; Xing, G.; Liu, X.; Wu, B. Energetics and Dynamics in Organic− Inorganic Halide Perovskite Photovoltaics and Light Emitters. Nanotechnology 2015, 26, 342001. (8) Zheng, K.; Zhu, Q.; Abdellah, M.; Messing, M. E.; Zhang, W.; Generalov, A.; Niu, Y.; Ribaud, L.; Canton, S. E.; Pullerits, T. Exciton Binding Energy and the Nature of Emissive States in Organometal Halide Perovskites. J. Phys. Chem. Lett. 2015, 6, 2969−2975. (9) Grancini, G.; Srimath Kandada, A. R.; Frost, J. M.; Barker, A. J.; De Bastiani, M.; Gandini, M.; Marras, S.; Lanzani, G.; Walsh, A.; Petrozza, A. Role of Microstructure in the Electron−Hole Interaction of Hybrid Lead Halide Perovskites. Nat. Photonics 2015, 9, 695−701. (10) Poglitsch, A.; Weber, D. Dynamic Disorder in Methylammoniumtrihalogenoplumbates (II) Observed by Millimeter-Wave Spectroscopy. J. Chem. Phys. 1987, 87, 6373−6378. G


Article

Accounts of Chemical Research (28) Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J. P.; Leijtens, T.; Herz, L. M.; Petrozza, A.; Snaith, H. J. Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in an Organometal Trihalide Perovskite Absorber. Science 2013, 342, 341− 344. (29) Xing, G.; Mathews, N.; Sun, S.; Lim, S. S.; Lam, Y. M.; Grätzel, M.; Mhaisalkar, S.; Sum, T. C. Long-Range Balanced Electron- and Hole-Transport Lengths in Organic-Inorganic Ch3NH3PbI3. Science 2013, 342, 344−347. (30) 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.; Bakr, O. M. Low Trap-State Density and Long Carrier Diffusion in Organolead Trihalide Perovskite Single Crystals. Science 2015, 347, 519−522. (31) Ponseca, C. S., Jr.; Savenije, T. J.; Abdellah, M.; Zheng, K.; Yartsev, A.; Pascher, T.; Harlang, T.; Chabera, P.; Pullerits, T.; Stepanov, A.; Wolf, J.-P.; Sundströ m, V. Organometal Halide Perovskite Solar Cell Materials Rationalized: Ultrafast Charge Generation, High and Microsecond-Long Balanced Mobilities, and Slow Recombination. J. Am. Chem. Soc. 2014, 136, 5189−5192. (32) Filippetti, A.; Delugas, P.; Mattoni, A. Radiative Recombination and Photoconversion of Methylammonium Lead Iodide Perovskite by First Principles: Properties of an Inorganic Semiconductor Within a Hybrid Body. J. Phys. Chem. C 2014, 118, 24843−24853. (33) Piermarocchi, C.; Tassone, F.; Savona, V.; Quattropani, A.; Schwendimann, P. Exciton Formation Rates in GaAs/AlXGa1−XAs Quantum Wells. Phys. Rev. B: Condens. Matter Mater. Phys. 1997, 55, 1333−1336. (34) Deveaud, B.; Kappei, L.; Berney, J.; Morier-Genoud, F.; Portella-Oberli, M. T.; Szczytko, J.; Piermarocchi, C. Excitonic Effects in the Luminescence of Quantum Wells. Chem. Phys. 2005, 318, 104− 117. (35) Kaindl, R. A.; Carnahan, M. A.; Hägele, D.; Lövenich, R.; Chemla, D. S. Ultrafast Terahertz Probes of Transient Conducting and Insulating Phases in an Electron-Hole Gas. Nature 2003, 423, 734− 738. (36) Chemla, D. S.; Shah, J. Many-Body and Correlation Effects in Semiconductors. Nature 2001, 411, 549−557. (37) Cadelano, M.; Sarritzu, V.; Sestu, N.; Marongiu, D.; Chen, F.; Piras, R.; Corpino, R.; Carbonaro, C. M.; Quochi, F.; Saba, M.; Mura, A.; Bongiovanni, G. Can Trihalide Lead Perovskites Support Continuous Wave Lasing? Adv. Opt. Mater. 2015, 3, 1557−1564. (38) Deschler, F.; Price, M.; Pathak, S.; Klintberg, L. E.; Jarausch, D.D.; Higler, R.; Hüttner, S.; Leijtens, T.; Stranks, S. D.; Snaith, H. J.; Atatüre, 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. (39) Manser, J. S.; Kamat, P. V. Band Filling with Free Charge Carriers in Organometal Halide Perovskites. Nat. Photonics 2014, 8, 737−743. (40) Wehrenfennig, C.; Liu, M.; Snaith, H. J.; Johnston, M. B.; Herz, L. M. Charge Carrier Recombination Channels in the LowTemperature Phase of Organic-Inorganic Lead Halide Perovskite Thin Films. APL Mater. 2014, 2, 081513. (41) Fang, H.-H.; Raissa, R.; Abdu-Aguye, M.; Adjokatse, S.; Blake, G. R.; Even, J.; Loi, M. A. Photophysics of Organic−Inorganic Hybrid Lead Iodide Perovskite Single Crystals. Adv. Funct. Mater. 2015, 25, 2378−2385. (42) Wehrenfennig, C.; Eperon, G. E.; Johnston, M. B.; Snaith, H. J.; Herz, L. M. High Charge Carrier Mobilities and Lifetimes in Organolead Trihalide Perovskites. Adv. Mater. 2014, 26, 1584−1589. (43) Sutherland, B. R.; Hoogland, S.; Adachi, M. M.; Wong, C. T. O.; Sargent, E. H. Conformal Organohalide Perovskites Enable Lasing on Spherical Resonators. ACS Nano 2014, 8, 10947−10952. (44) 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.

(45) Xing, G.; Mathews, N.; Lim, S. S.; Yantara, N.; Liu, X.; Sabba, D.; Grätzel, M.; Mhaisalkar, S.; Sum, T. C. Low-Temperature Solution-Processed Wavelength-Tunable Perovskites for Lasing. Nat. Mater. 2014, 13, 476−480. (46) Dhanker, R.; Brigeman, A. N.; Larsen, A. V.; Stewart, R. J.; Asbury, J. B.; Giebink, N. C. Random Lasing in Organo-Lead Halide Perovskite Microcrystal Networks. Appl. Phys. Lett. 2014, 105, 151112. (47) Jaramillo-Quintero, O. A.; Sanchez, R. S.; Rincón, M.; MoraSeró, I. Bright Visible-Infrared Light Emitting Diodes Based on Hybrid Halide Perovskite with Spiro-OMeTAD as a Hole-Injecting Layer. J. Phys. Chem. Lett. 2015, 6, 1883−1890. (48) Tan, Z.-K.; Moghaddam, R. S.; Lai, M. L.; Docampo, P.; Higler, R.; Deschler, F.; Price, M.; Sadhanala, A.; Pazos, L. M.; Credgington, D.; Hanusch, F.; Bein, T.; Snaith, H. J.; Friend, R. H. Bright LightEmitting Diodes Based on Organometal Halide Perovskite. Nat. Nanotechnol. 2014, 9, 687−692. (49) Dou, L.; Wong, A. B.; Yu, Y.; Lai, M.; Kornienko, N.; Eaton, S. W.; Fu, A.; Bischak, C. G.; Ma, J.; Ding, T.; Ginsberg, N. S.; Wang, L.W.; Alivisatos, A. P.; Yang, P. Atomically Thin Two-Dimensional Organic-Inorganic Hybrid Perovskites. Science 2015, 349, 1518−1521. (50) Ning, Z.; Gong, X.; Comin, R.; Walters, G.; Fan, F.; Voznyy, O.; Yassitepe, E.; Buin, A.; Hoogland, S.; Sargent, E. H. Quantum-Dot-inPerovskite Solids. Nature 2015, 523, 324−328.

H


Excited State Properties of Hybrid Perovskites - Accounts of Chemical

Recommend Documents