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Dephasing and quantum beating of excitons in methyl ammonium lead iodide perovskite nanoplatelets Bernhard Johann Bohn, Thomas Simon, Moritz Gramlich, Alexander Florian Richter, Lakshminarayana Polavarapu, Alexander S. Urban, and Jochen Feldmann ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b01292 • Publication Date (Web): 29 Nov 2017 Downloaded from http://pubs.acs.org on November 30, 2017

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ACS Photonics

Dephasing and quantum beating of excitons in methylammonium lead iodide perovskite nanoplatelets Bernhard J. Bohn1,2,*, Thomas Simon1,2, Moritz Gramlich1,2, Alexander F. Richter1,2, Lakshminarayana Polavarapu1,2, Alexander S. Urban1,2,*, and Jochen Feldmann1,2,* 1 Chair for Photonics and Optoelectronics, Department of Physics and Center for NanoScience (CeNS), Ludwig-Maximilians-Universität (LMU), Amalienstraße 54, 80799 Munich, Germany 2 Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 Munich, Germany

Keywords: perovskite nanocrystals, exciton dephasing time, exciton binding energy, temperature-dependent absorption spectroscopy, four-wave mixing, quantum beat spectroscopy

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Perovskite nanocrystals have emerged as an interesting material for light-emitting and other optoelectronic applications. Excitons are known to play an important role in determining the optical properties of these nanocrystals and their energetic levels as well as quantization properties have been extensively explored. Despite this, there are still many aspects of perovskites that are still not well known, e.g. the homogeneous and inhomogeneous linewidths of the energetic transitions, quantities that cannot be directly extracted by linear absorption optical spectroscopy on nanocrystal ensembles. Here, we present temperature-dependent absorption and four-wave mixing (FWM) experiments on thick methylammonium lead iodide (MAPI) perovskite nanoplatelets exhibiting bulk-like absorption and emission spectra. Dephasing times T2 of excitons are determined to lie in the range of several hundreds of femtoseconds at low temperatures. This value enables us to distinguish between the homogeneous and inhomogeneous contribution to the total broadening of the excitonic transitions. These turn out to be predominantly inhomogeneously broadened at low temperatures and homogeneously broadened at room temperature. Furthermore, we find excitonic quantum beats, which allow for the determination of the exciton binding energy and we extract EB = 25±2 meV in the low temperature regime, in good agreement with other reports.


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Lead halide perovskites have gained in importance as promising candidates for the realization of low-cost high-efficiency solar cells as well as other optoelectronic devices such as LEDs, lasers or photodetectors.1-2 While many of the initial studies focused on thin perovskite films, new reports have shown that perovskite nanocrystals (NCs) have a great potential especially for light-emitting applications due to a large spectral tunability and high emission quantum yields.3-4 Various synthesis methods have been used to control the composition and the morphology of these NCs and all-inorganic as well as hybrid organic-inorganic platelets3, cubes5-6 and wires7 have been reported. Despite the very different geometries, many of these NCs exhibit bulk-like optical properties, as seen in absorption and photoluminescence (PL) spectra. This is due to the fact that quantum confinement effects only play a role in NCs whose size in at least one dimension approaches the exciton Bohr radius, which in halide perovskites, turns out to be quite small and depends strongly on the composition.8 Thus, only the thinnest NCs show strong quantum confinement effects, in form of blue-shifted absorption onsets and greatly enhanced exciton binding energies.3 Due to the novelty of this material and its intricate nature, some of the fundamental properties of halide perovskites are still not well known, for example, studies rarely distinguish between the homogeneous and inhomogeneous linewidths of excitons in such structures; additionally there are large discrepancies in reported values of the exciton binding energy.9 One of the reasons for this is that inhomogeneous broadening effects in ensembles of these nanocrystals significantly smear out the energetic features, rendering their distinction partially impossible. Especially for light emission applications based on these materials it is a question of interest whether the observed broadening is mainly homogeneous or inhomogeneous in nature.10


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A powerful technique to measure homogeneous linewidths is transient four-wave mixing (FWM) which enables their determination from the directly measured dephasing times T2 (coherence lifetimes) of the respective transistions.11-13 Extensive FWM studies have been performed on quantum well heterostructures, where long exciton dephasing times in the picosecond range have been reported.14 Recently, March et al. applied FWM with a spectrally resolved detection scheme and focused on the resolved energy levels in methylammonium lead iodide (MAPI) perovskite films.15 With this method, they were able to distinguish between free and defect-bound excitons.16 FWM is a versatile method and can also be used to examine energy levels by means of quantum beat spectroscopy (QBS). This technique enables a determination of the spacing of energetic levels hidden below the inhomogeneous broadening of a material.17-18 Exciton binding energies in InGaAs/GaAs heterostructures were measured by QBS17, however, this technique has not yet been applied to perovskite materials. In this work, we apply temperature-dependent absorption spectroscopy and transient FWM on MAPI nanoplatelets (NPls) in order to shed light on the coherent properties of excitons in these structures. We focus on the homogeneous and inhomogeneous linewidths of the excitonic transitions by measuring their dephasing times T2. We also show that excitonic wave packets can be generated if the spectral width of the excitation pulses is broad enough to encompass bound excitonic and continuum state transitions. In this way, the excited transitions generate quantum beats in their FWM signal and enable a different approach to obtain the exciton binding energy EB of the material.


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MAPI perovskite NPls were prepared according to the synthesis developed by Hintermayr et al. (see Methods section for details on the synthesis and sample preparation).3 The NPls used here have thicknesses in the range of 20 - 100 nm with varying lateral dimensions of up to 500 nm. Previously, it was shown that NPls of these dimensions exhibit bulk-like behavior.3 At low temperatures optical spectra exhibit clear excitonic features, however, due to the small exciton Bohr radius in this material quantum confinement effects only play a minor role in such samples.3-5 A diluted NPl solution was spin-coated onto a silicon substrate, which was then imaged using scanning electron microscopy (SEM). As shown in Figure 1a the NPls, which exhibit a wide range of thicknesses and lateral dimensions, tend to form small aggregates on the substrate. For this reason, an investigation of individual NPls is not possible and optical properties must be experimentally derived from an ensemble. This ensemble exhibits inhomogeneous broadening effects mainly due to size dispersion and different shapes of the NPls.

Figure 1. (a) SEM image of a small aggregate of MAPI NPls on a substrate. (b) Experimentally measured absorption spectrum of a MAPI NPl ensemble at 175 K. (c) Theoretical model of the electronic energy levels in perovskite crystals in the two-particle picture: ground state, excitonic levels (1s, 2s, 2p …) and continuum onset at the band gap energy EG. The difference between EG and the 1s excitonic state E1s is the exciton binding energy EB.


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Additionally, inhomogeneous broadening can also originate from impurities, strain inhomogeneities or different local electric and magnetic fields in the NPls.19-20 Therefore, we expect that inhomogeneous broadening contributes considerably to the total broadening of transitions in the linear absorption spectra of these materials. Figure 1b shows an example of an inhomogeneously broadened spectrum recorded at 175 K, where the transitions are spectrally broadened and for which it is not possible to determine the exact energy levels underneath the broadened spectrum. Generally, as for any semiconductor material, excited electrons and holes in perovskite crystals can exist either as electron-hole continuum states, or bound together through Coulomb interaction in an excitonic state.21 The energy required to generate a free electron-hole pair through photon absorption is given by the band gap energy EG. Electrons and holes bound as excitons with radii far larger than the lattice constant of the material are known as Wannier-Mott excitons and studies have shown that this applies for MAPI perovskite materials.22-23 This type of exciton is treated in analogy to the hydrogen model and has discrete energy levels at = −

∗ 1 = − (1) 8ℎ

below EG (see Figure 1c) where ∗ is the reduced mass of the electron-hole system and stands for the dielectric function of the material.9 The energy difference between the band gap and the excitonic ground state (1s, n = 1) represents the exciton binding energy EB = EG – E1s. In an ideal case as illustrated in Figure 2a, the linear absorption spectrum of one single perovskite NPl displays sharp features, enabling a precise determination of the individual energetic levels, the exciton binding energy EB, and of the homogeneous broadening Γhom. However, in an ensemble of NPls the absorption spectrum can differ for each NPl leading to a distribution of optical transitions, and thus to inhomogeneous broadening (see Figure 2b). The


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combined signal of these NPls is strongly broadened with the total width of the excitonic features given by Γtotal = Γhom + Γinhom, rendering Γhom inaccessible. In the case depicted here the continuum onset can no longer be clearly defined and information on the 2s state and the binding energy EB of the exciton is lost.

Figure 2. (a) Scheme for the absorption spectrum of one single bulk-like NPl where the homogeneous broadening of the Lorentzian-shaped excitonic peaks is given by Γhom (dark blue). The excitonic levels (1s, 2s) and the continuum onset are well separated and easily distinguishable. However, in the measurements an ensemble of many NPls is examined simultaneously and thus a Gaussian-shaped inhomogeneous broadening Γinhom of the transitions occurs (shown in red for the 1s level). (b) In accordance with this Gaussian distribution (red) individual NPls show different absorption spectra due to varying size, shape and surrounding (dark blue lines). In the resulting total absorbance spectrum (black solid line) this causes broadened excitonic transitions as well as a broadened continuum onset. The total broadening of the excitonic transition is then given by Γtotal = Γhom + Γinhom.

As mentioned above, the inhomogeneous broadening mainly stems from the size distribution and the varying shape of the NPls in the ensemble, thus, it can be assumed to be a temperatureindependent quantity Γinhom. On the other hand, the homogeneous broadening of the optical


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transitions are determined by dephasing processes such as exciton-phonon scattering.24 Consequently, the homogeneous linewidth is expected to strongly depend on the temperature of the sample, Γhom(T). The temperature dependence of linear absorption spectra can provide much information on the electronic energy levels of the perovskite platelets and the total broadening of the spectral features. To investigate this, we deposited the NPls on a sapphire substrate, placed it inside a liquid helium cryostat (see Methods section for a detailed description of the setup) and recorded temperature-dependent absorption spectra (see Figure 3a). At room temperature, all excitonic features are completely invisible due to linewidth broadening. As the temperature of the system is reduced, the absorption edge redshifts, a generally observed feature of lead halide perovskites, which is purported to be due to the p-type character of the conduction band.25 Additionally, the absorption onset becomes progressively steeper due to the decreasing homogeneous broadening, and below 200 K the 1s exciton peak becomes distinguishable at the absorption edge. Around 150 K, there is a sharp jump of the absorption onset to higher energies. This is the signature of the phase transition of bulk MAPI from a tetragonal to an orthorhombic crystal structure and is known to occur around 150 K, confirming the bulk-like nature of the NPls used here.26 A further reduction of the temperature leads to an increasingly pronounced excitonic absorption peak, which again redshifts, as for temperatures above the phase transition temperature. The Elliott model27 can be applied to extract the exciton binding energy using the data of the absorption onset. For MAPI, values in the range 15-30 meV have been reported for the low temperature orthorhombic phase,28-29 generally agreeing that EB increases with decreasing temperature.9 The difficulty in applying this technique to MAPI crystals lies in the fact that the exciton binding energy is relatively small in comparison to the broadening of the levels and thus


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especially at high temperatures the 1s excitonic level and the band gap onset are not spectrally resolved, which can lead to fitting ambiguities.30 Also, as shown in Figure 3a, at high temperatures this interference of the 1s excitonic level and the nearby continuum onset makes it difficult to obtain the total broadening of the 1s level, Γtotal(T), using the absorption data. However, at temperatures below 200 K, where the 1s exciton peak is distinguishable, the low energy side of the peak in the absorbance data is used to extract the full width at half maximum (FWHM) of the 1s energy level as a function of temperature T. This is shown in Figure 3b and represents the total broadening, Γtotal(T), of the 1s exciton transition. As discussed in the following we find that the absorption data can be explained best by using a model which determines the scattering with longitudinal optical (LO) phonons as the dominant mechanism for the temperature-induced broadening. This agrees with a study by Wright et al.31 who investigated the electron-phonon coupling in MAPI films using temperature-dependent photoluminescence measurements. Consequently, the total broadening of the 1s exciton can be described via Γ () = Γ + /[exp ( /$ ) − 1]

(2)

with Γ0 = Γtotal(0 K), the Fröhlich coupling constant, γLO, and the average LO phonon energy, ELO. The coupling to acoustic phonons was also modelled, but the fit to the data is nearly independent of this part. Evaluating the data of Figure 3b, we obtain Γ0 = 24±1 meV, γLO = 95±28 meV and ELO = 21±3 meV for the MAPI NPls (dashed black line). These values agree well with those from previous publications, for example with the ones reported by Wu et al. who obtained γLO = 92±24 meV and ELO = 25±5 meV by measuring the excitonic photoluminescence of MAPI films.32


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Interestingly, the data also shows that Γtotal(T) does not seem to be strongly affected by the phase transition just below 150 K. The trend of the total broadening Γtotal(T) reducing with decreasing temperature continues at this transition without a noticeable discontinuity at the phase transition temperature. This suggests that the exciton-phonon scattering rates are similar for the two crystal structures around this temperature.

Figure 3. (a) Experimental temperature-dependent absorption spectra of MAPI perovskite NPls for temperatures between 25 K and 295 K. The peak of the 1s exciton experiences a redshift when decreasing the temperature and around 150 K the transition from the tetragonal to the orthorhombic phase occurs. (b) Total broadening of the 1s exciton level Γtotal (FWHM of the absorption edge for T ≤ 200 K) as function of the temperature T taken from the data in (a) and denoted by crosses. A theoretical model (black dashed line) considering optical phonons as the dominant reason for the temperature-dependent broadening is fit to the data.31 Using the dephasing time T2 at 25 K obtained from the four-wave mixing experiments, the homogeneous broadening at this temperature is calculated Γhom(25 K) = 2ħ / T2(25 K) = 1.7±0.1 meV and the value of Γinhom = 22±1 meV can be assigned to the temperature-independent inhomogeneous broadening. Thus for each temperature one can distinguish between the homogeneous and inhomogeneous contribution to the total broadening of the excitonic level Γtotal(T).


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By applying linear absorption spectroscopy on the MAPI NPls, we have already gained information on two of the main quantities of the 1s excitonic energy level, namely the energetic position E1s(T ≤ 200 K) and the total broadening versus temperature Γtotal(T ≤ 200 K), however, the values of Γinhom as well as Γhom(T) cannot be assigned yet (compare to Figure 2b, even at 0 K Γinhom is smaller than the total broadening Γtotal). This problem can be solved by directly measuring the dephasing time T2 and using the relation Γhom = 2ħ / T2 to calculate the homogeneous linewidth.12 The dephasing time T2 of the 1s exciton transition is the time it takes for the coherently excited polarization to lose its coherence. This is e.g. lost due to scattering events with other charge carriers or phonons.24 As such, T2 is not a material constant, as it depends on the excitation density and the temperature of the sample. Lower excitation densities and lower temperatures are expected to lead to less scattering, consequently lengthening the dephasing time T2. Here the technique of four-wave mixing (FWM) with a time integrated detection scheme is applied to measure T2 directly.18, 24 For the FWM experiments, the output of a tunable optical parametric amplifier (OPA) is split into two beams (pulse length ~115 fs, wave vectors at focus k1 and k2), which are focused on the MAPI NPls with a controlled time delay τ (see Figure 4a). FWM generates a photon echo that is emitted in the directions 2k2 – k1 and 2k1 – k2, which can be detected by a photodiode connected to a lock-in amplifier.33 For each pulse delay τ the time integrated FWM signal of the sample is recorded (see Methods section for details on the FWM setup). Both pulses have a Gaussian shaped spectrum in frequency with a FWHM of around 27 meV for the wavelengths used in the FWM measurements. As shown in Figure 4b their central position can be shifted by tuning the OPA, so that either (i) only the 1s exciton, (iv) only the free electron-hole pair transitions of the continuum, or (ii) & (iii) both are excited at the same time. Depending on which of these


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excitation variants is chosen, the resulting FWM curves appear very different (see Figure 4c). In order to minimize the scattering in the sample and thereby increase the dephasing time to make the fast processes resolvable, all measurements have been performed at a low temperature of 25 K and an excitation density of ~1017 cm-3.

Figure 4. (a) Experimental setup for time integrated four-wave mixing (FWM). Both pulses are focused through a lens (L) on the perovskite NPls (P) on the substrate (S) inside the cryostat. The signal at 2k2 – k1 is measured as a function of the time delay between the two pulses τ. (b) Absorption spectrum of MAPI NPls from Figure 3a at 25 K with excitonic peak and continuum (top panel). The panel below shows shifted spectra of the excitation pulses to allow for: (i) only 1s exciton excitation, (ii) & (iii) simultaneous excitation of excitons and free electron-hole pair transitions, or (iv) excitation of free electron-hole pair transitions. (c) Resulting FWM decay curves for these excitation spectra for a charge carrier density of ~1017 cm-3 at a temperature of T = 25 K: (i) The exponentially decaying signal provides the dephasing time T2 = 800±20 fs for the 1s exciton. (ii) In this case the excitation pulse spectrally overlaps slightly with the continuum transitions, thus an exciton wave packet is generated. With this small overlap the beating only occurs as a shoulder in the decaying FWM signal. (iii) When the spectrum of the excitation pulse overlaps with the 1s exciton and the continuum transitions to a similar extent these transitions are


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excited simultaneously. The beating behavior reaches its maximum at a central excitation wavelength of 735 nm when quantum beats with a periodicity of TB = 165±10 fs can be observed. The exciton binding energy of the MAPI NPls can be extracted via EB = h/TB = 25±2 meV. (iv) The dephasing for the free electron-hole pair transition is too fast to be resolved by the used laser pulses.

The first panel in Figure 4c shows the case (i) where only the 1s exciton is excited and the loss of coherence of this energetic transition is observed. By fitting the exponential decay of the signal, one obtains a decay time of τdecay = 200 fs. This decay time is related to the dephasing time via T2 = g·τdecay with g = 2 for a homogeneously broadened sample and g = 4 for a generally inhomogeneous sample.18,

34

An estimate for both values shows that the homogeneous

broadening is less than or equal to 3.4 meV, which is far less than the total broadening of 24 meV obtained from the linear absorption spectra. The standard deviation σ of the Gaussianshaped total broadening Γtotal (FWHM) can be calculated via σ = Γ /'8 ln(2) = 10.2 and

for

Γhom < σ the broadening is referred to as inhomogeneous broadening.35 This shows that the sample is predominantly inhomogeneously broadened at low temperatures and g = 4 applies here, which confirms that the recorded signal is actually a photon echo.34 This results in a dephasing time of T2 = 800±20 fs for the 1s exciton of MAPI NPls. Consequently, the homogenous broadening at 25 K is given by Γhom(25 K) = 2ħ / T2(25 K) = 1.7±0.1 meV, which enables us to also determine the temperature-independent inhomogeneous broadening evaluating the absorption data, Γinhom = 22±1 meV (see red dashed line in Figure 3b). Using the theoretical model of Equation (2) the homogeneous broadening of the 1s exciton at room temperature can be estimated to be around 70 meV, i.e. the exciton dephasing time at room temperature is only T2 ≈ 20 fs. This value is far shorter than the pulse length of the OPA used, showing that at room


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temperature no FWM signal should be resolvable. With this excitation at the low energy side of the excitonic peak it is likely that the less present defect-bound excitons are observed as well. For these excitons one expects less scattering, thus slightly longer dephasing times, which is the reason why the slope of the decay in panel (i) of Figure 4c is not explicitly monoexponential.36 These results agree with March et al. who observed free and defect-bound excitons in MAPI films at 10 K.16 As shown in Figure 4b, when increasing the photon energy of the OPA to the corresponding wavelengths of 750 nm and 735 nm, i.e. case (ii) & (iii), the 1s exciton and continuum transitions can be coherently excited at the same time, if the spectral width of the pulse is broad enough to cover both transitions. In the second panel (ii) the excitation pulse overlaps spectrally only slightly with the continuum transitions and still mainly excites the 1s exciton. In comparison to case (i) with the pure excitation of the 1s exciton a shoulder appears in the FWM signal. This suggests that exciton wave packets are generated in which the excited transitions interfere with each other. The excitation at even higher energies with a central wavelength of 735 nm confirms this assumption and proves that the picture of exciton wave packets holds true for the coherent transition dynamics in perovskite NPls. In this case depicted in panel (iii) in Figure 4c the central wavelength of the excitation pulse at 735 nm is chosen in a way that the 1s exciton and continuum transition are excited to a similar extent. Here we observe a quantum beating behavior with a clear signal drop between the first two peaks, which cannot be seen in case (i). This implies that the excitation pulse is actually broad enough to generate an excitonic wave packet and quantum beat spectroscopy (QBS) can be conducted to gain information on the energy spacing of the excited transitions. This beating signal enables us to measure the time between the 0 fs delay position and the first beat after the main peak, TB = 165±10 fs, where the transitions of


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the 1s exciton and the continuum transitions interfere constructively.17 The exciton binding energy EB at this low temperature is given by the difference of these two mentioned transition levels E1s and EG, thus can be directly calculated via EG – E1s = EB = h / TB = 25±2 meV. This value fits in the range of other reported values of 2-50 meV for MAPI, which were obtained using several different techniques.9 This highlights the strength of this approach using QBS especially for inhomogeneously broadened materials with low binding energies, since this technique is not influenced by the inhomogeneous broadening effects of a sample. EB and TB are inversely proportional to each other, so materials with low binding energies will exhibit long beating times TB, which are significantly easier to detect experimentally. Another advantage of this technique is that the energy spacing is measured directly as a difference of two transitions, rendering an error-prone assumption of the absolute band gap position unnecessary. As mentioned above, the Elliott model can be used to extract exciton binding energies from linear absorption data.9 This is practical for cases where the inhomogeneous broadening does not hinder the distinction of the 1s transition from the continuum. In the easiest case, when both the 1s and the 2s level can be determined directly from the absorption data, the exciton binding energy can simply be calculated via EB = 4/3 (E2s - E1s), where E1s and E2s are the positions of the two lowest excitonic levels. Summing up, this means that QBS offers a suitable technique for the calculation of small binding energies and supplements the Elliott model in cases where the energy levels are difficult to distinguish in linear absorption spectroscopy due to inhomogeneous broadening. The plot of the fourth panel (iv) in Figure 4c indicates that even at low temperatures the dephasing of the free electron-hole pair transitions is too fast to perform a reasonable data deconvolution to obtain T2.


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In summary, we have analyzed the excitonic energy levels and transition linewidths of MAPI nanoplatelet ensembles that experience inhomogeneous broadening. In temperature-dependent absorption measurements we determine the total broadening of the 1s excitonic level Γtotal(T), which does not seem to be affected by the crystal phase transition from the orthorhombic to the tetragonal phase at 150 K. A theoretical model considering optical phonons as the main source for the scattering of the excitons has been applied to extract the Fröhlich coupling constant, γLO = 95±28 meV, and the average LO phonon energy ELO = 21±3 meV. Using this information, FWM experiments on the 1s exciton are conducted and exciton dephasing times are extracted in the range of several hundreds of femtoseconds for a temperature of 25 K and an excitation density in the range of ~1017 cm-3. This way we are able to calculate how the total broadening of the excitonic level is made up of a temperature-independent inhomogeneous contribution of Γinhom = 22±1 meV and a temperature-dependent homogenous part Γhom(T), which is below 2 meV at 5 K and approximately 70 meV at room temperature. These values would lead to exciton dephasing times of the MAPI perovskite NPls far below 100 fs at room temperature. Additionally, we show how FWM can be used for quantum beat spectroscopy, offering an alternative approach for obtaining the exciton binding energy EB of the perovskite nanocrystals. For the MAPI NPl sample we extract a value of 25±2 meV in the low temperature phase at 25 K, well in the range of recently reported values obtained through many other techniques. This proof of concept study shows the versatility of FWM as a powerful technique for measuring the homogeneous broadening of an ensemble of various nanocrystals and in the case of QBS also as a way to determine exciton binding energies, provided that the excitation spectrum is broad enough to excite an excitonic wave packet, i.e. multiple transitions simultaneously. This paves the way for


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further studies on other perovskite compositions and morphologies or different materials such as hybrid nanostructures. METHODS Synthesis of perovskite nanoplatelets and sample preparation. All chemicals were purchased from Sigma-Aldrich and used as received. The methylammonium lead iodide (CH3NH3PbI3, MAPbI3 or MAPI) nanoplatelets (NPls) were prepared using a slightly modified ligand-assisted ultrasonication approach similar to our previously reported method.3 Methylammonium iodide (CH3NH3I or MAI, 0.16 mmol) and lead iodide (PbI2) precursor powders were dispersed in a mixture of 10 ml of toluene, 0.3 ml of oleylamine and 0.3 ml of octanoic acid. The mixture was sonicated for 30 min to obtain nanoplatelets and the formation of NPls can be observed by the change in color of the dispersion from transparent via orange/brown to black. Directly after the ultrasonication the dispersion was centrifuged and the sediment was redispersed in toluene to remove the excess of ligands which would otherwise destroy the NPls with time. This dispersion is now stable for months. For all of our optical measurements double side-polished sapphire was used as a substrate, since especially at low temperatures its thermal conductivity is several orders of magnitude higher than that of fused silica. The dispersion containing the perovskite NPls was drop casted on the substrate and the total thickness of the deposited NPl layer was around 300 nm (measured with a Dektak profilometer). Absorption measurements. The temperature-dependent absorption spectra were recorded using a Xenon lamp as a light source with a broad spectrum that covers the whole visible range. The sample on the sapphire substrate was mounted inside a PID temperature-controlled cryostat and the transmitted radiant flux Φt(λ) was spectrally resolved and recorded using a spectrometer (SpectraPro SP2300, Princeton Instruments) and a coupled CCD (PIXIS 400 eXcelon, Princeton


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Instruments). For the calculation of the spectral absorbance OD(λ) = log10 (Φr(λ) / Φt(λ)) an empty sapphire substrate at room temperature was used to record the reference spectrum Φr(λ). The lamp illuminates a spot on the sample with a diameter of 5 mm, thus the absorbance of an ensemble of single NPls is measured, and for each spectrum the signal is integrated and averaged for 120 seconds. Four-wave mixing. Degenerate transient four-wave mixing (FWM) with a time integrated detection scheme18 is applied to measure the exciton dephasing time T2 and the exciton binding energy EB. A Ti:Sapphire amplifier system (Libra-HE, Coherent) in combination with an optical parametric amplifier (OPerA-Solo, Light Conversion) provides the laser excitation pulses with tunable wavelength and a repetition rate of 1 kHz. In order to keep the group delay dispersion low, i.e. the pulse duration short, the amount and thickness of transmissive optical elements in the setup was minimized and an optical autocorrelator (pulseCheck, A·P·E) supported by dispersion simulations was used to determine the pulse length at the sample of around 115 fs. A spectrometer provided the information about the excitation spectrum at the sample position (see Figure 4b). The linear polarization of the laser is set to be vertical, so that behind the 50:50 beamsplitter both laser pulses have a parallel polarization and after being focused through the same lens (f = 200 mm) coincide in the sample in s-polarization. A beam profiler controlled the spatial overlap in the focal spot and a linear stage was applied to adjust the temporal overlap or delay between the two pulses. The time delay τ = 0 fs represents the exact temporal overlap of the two pulses in the sample, for τ < 0 fs pulse #1 hits the sample before pulse #2 and for τ > 0 fs it is the other way around. In order to accurately define this 0 fs position the FWM signals in the direction of 2k2 – k1 and 2k1 – k2 were compared since they have to be symmetric in relation to the position τ = 0 fs. The sample itself is mounted in a liquid helium cryostat to enable


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measurements at low temperatures down to around 25 K. Behind the sample the diffracted beam at 2k2 – k1 was detected by a photodetector (see Figure 4a). A chopper system was synchronized to the laser and modulated the two laser beams with different frequencies in order to use a lockin amplifier (SR830, Stanford Research Systems) to detect the signal of the photodetector at the difference of these frequencies to make sure that the measured signal is actually the FWM signal generated by both pulses and not only scattered light of one pulse. A LabView program controlled the essential devices in the setup and recorded the data.

Author Information: *

Corresponding authors:

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[email protected] Declaration of competing financial interests: All authors declare no competing financial interests. Acknowledgements: We would like to thank Prof. Richard Phillips for fruitful discussions. This work was supported by the Bavarian State Ministry of Science, Research, and Arts through the grant “Solar Technologies go Hybrid (SolTech)”, by LMU Munich‘s Institutional Strategy LMUexcellent within the framework of the German Excellence Initiative (A.S.U), by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement COMPASS No. 691185, and by the Alexander von Humboldt-Stiftung (L.P.).


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References: 1. Green, M. A.; Ho-Baillie, A.; Snaith, H. J. The emergence of perovskite solar cells. Nat. Photonics 2014, 8 (7), 506-514. 2. Li, G. R.; Price, M.; Deschler, F. Research Update: Challenges for high-efficiency hybrid lead-halide perovskite LEDs and the path towards electrically pumped lasing. APL Mater. 2016, 4 (9), 091507. 3. Hintermayr, V. A.; Richter, A. F.; Ehrat, F.; Doblinger, M.; Vanderlinden, W.; Sichert, J. A.; Tong, Y.; Polavarapu, L.; Feldmann, J.; Urban, A. S. Tuning the Optical Properties of Perovskite Nanoplatelets through Composition and Thickness by Ligand-Assisted Exfoliation. Adv. Mater. 2016, 28 (43), 9478-9485. 4. Sichert, J. A.; Tong, Y.; Mutz, N.; Vollmer, M.; Fischer, S.; Milowska, K. Z.; Garcia Cortadella, R.; Nickel, B.; Cardenas-Daw, C.; Stolarczyk, J. K.; Urban, A. S.; Feldmann, J. Quantum Size Effect in Organometal Halide Perovskite Nanoplatelets. Nano Lett. 2015, 15 (10), 6521-7. 5. Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Krieg, F.; Caputo, R.; Hendon, C. H.; Yang, R. X.; Walsh, A.; Kovalenko, M. V. Nanocrystals of Cesium Lead Halide Perovskites (CsPbX(3), X = Cl, Br, and I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut. Nano Lett. 2015, 15 (6), 3692-6. 6. Tong, Y.; Bladt, E.; Ayguler, M. F.; Manzi, A.; Milowska, K. Z.; Hintermayr, V. A.; Docampo, P.; Bals, S.; Urban, A. S.; Polavarapu, L.; Feldmann, J. Highly Luminescent Cesium Lead Halide Perovskite Nanocrystals with Tunable Composition and Thickness by Ultrasonication. Angew. Chem., Int. Ed. 2016, 55 (44), 13887-13892. 7. Im, J. H.; Luo, J.; Franckevicius, M.; Pellet, N.; Gao, P.; Moehl, T.; Zakeeruddin, S. M.; Nazeeruddin, M. K.; Gratzel, M.; Park, N. G. Nanowire perovskite solar cell. Nano Lett. 2015, 15 (3), 2120-6. 8. Physical Chemistry Chemical PhysicsButkus, J.; Vashishtha, P.; Chen, K.; Gallaher, J. K.; Prasad, S. K. K.; Metin, D. Z.; Laufersky, G.; Gaston, N.; Halpert, J. E.; Hodgkiss, J. M. The Evolution of Quantum Confinement in CsPbBr3 Perovskite Nanocrystals. Chem. Mater. 2017, 29 (8), 3644-3652. 9. Herz, L. M. Charge-Carrier Dynamics in Organic-Inorganic Metal Halide Perovskites. Annu. Rev. Phys. Chem. 2016, 67, 65-89. 10. Feldmann, J.; Peter, G.; Gobel, E. O.; Dawson, P.; Moore, K.; Foxon, C.; Elliott, R. J. Linewidth Dependence of Radiative Exciton Lifetimes in Quantum-Wells. Phys. Rev. Lett. 1987, 59 (20), 2337-2340. 11. Ye, P.; Shen, Y. Transient four-wave mixing and coherent transient optical phenomena. Phys. Rev. A 1982, 25 (4), 2183.


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12. Albrecht, T. F.; Sandmann, J. H. H.; Cundiff, S. T.; Feldmann, J.; Stolz, W.; Gobel, E. O. Femtosecond Degenerate 4-Wave-Mixing on Unstrained (Inga)as/Inp Multiple-Quantum-Wells Using an Optical Parametric Oscillator. Solid-State Electron. 1994, 37 (4-6), 1327-1331. 13. Davis, J. A.; Wathen, J. J.; Blanchet, V.; Phillips, R. T. Time-resolved four-wave-mixing spectroscopy of excitons in a single quantum well. Phys. Rev. B 2007, 75 (3), 035317. 14. Koch, M.; Weber, D.; Feldmann, J.; Gobel, E. O.; Meier, T.; Schulze, A.; Thomas, P.; Schmitt-Rink, S.; Ploog, K. Subpicosecond photon-echo spectroscopy on GaAs/AlAs shortperiod superlattices. Phys. Rev. B 1993, 47 (3), 1532-1539. 15. March, S. A.; Riley, D. B.; Clegg, C.; Webber, D.; Liu, X.; Dobrowolska, M.; Furdyna, J. K.; Hill, I. G.; Hall, K. C. Four-wave mixing in perovskite photovoltaic materials reveals long dephasing times and weaker many-body interactions than GaAs. ACS Photonics 2017, 4 (6), 1515-1521. 16. March, S. A.; Clegg, C.; Riley, D. B.; Webber, D.; Hill, I. G.; Hall, K. C. Simultaneous observation of free and defect-bound excitons in CH3NH3PbI3 using four-wave mixing spectroscopy. Sci. Rep. 2016, 6, 39139. 17. Feldmann, J.; Meier, T.; von Plessen, G.; Koch, M.; Gobel, E. O.; Thomas, P.; Bacher, G.; Hartmann, C.; Schweizer, H.; Schafer, W.; Nickel, H. Coherent dynamics of excitonic wave packets. Phys Rev Lett 1993, 70 (20), 3027-3030. 18. Koch, M.; von Plessen, G.; Feldmann, J.; Gobel, E. O. Excitonic quantum beats in semiconductor quantum-well structures. Chem. Phys. 1996, 210 (1-2), 367-388. 19. Alivisatos, A. P.; Harris, A. L.; Levinos, N. J.; Steigerwald, M. L.; Brus, L. E. Electronic states of semiconductor clusters: Homogeneous and inhomogeneous broadening of the optical spectrum. J. Chem. Phys. 1988, 89 (7), 4001-4011. 20. Perret, N.; Morris, D.; Franchomme-Fossé, L.; Côté, R.; Fafard, S.; Aimez, V.; Beauvais, J. Origin of the inhomogenous broadening and alloy intermixing in InAs/GaAs self-assembled quantum dots. Phys. Rev. B 2000, 62 (8), 5092-5099. 21. D'Innocenzo, V.; Grancini, G.; Alcocer, M. J.; Kandada, A. R.; 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. 22. 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. 23. Tanaka, K.; Takahashi, T.; Ban, T.; Kondo, T.; Uchida, K.; Miura, N. Comparative study on the excitons in lead-halide-based perovskite-type crystals CH 3 NH 3 PbBr 3 CH 3 NH 3 PbI 3. Solid State Commun. 2003, 127 (9), 619-623. 24. Moody, G.; Dass, C. K.; Hao, K.; Chen, C. H.; Li, L. J.; Singh, A.; Tran, K.; Clark, G.; Xu, X. D.; Berghauser, G.; Malic, E.; Knorr, A.; Li, X. Q. Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides. Nat. Commun. 2015, 6, 8315. 25. Manser, J. S.; Christians, J. A.; Kamat, P. V. Intriguing Optoelectronic Properties of Metal Halide Perovskites. Chem. Rev. 2016, 116 (21), 12956-13008. 26. Li, D.; Wang, G.; Cheng, H. C.; Chen, C. Y.; Wu, H.; Liu, Y.; Huang, Y.; Duan, X. Sizedependent phase transition in methylammonium lead iodide perovskite microplate crystals. Nat. Commun. 2016, 7, 11330. 27. Elliott, R. Intensity of optical absorption by excitons. Phys. Rev. 1957, 108 (6), 1384.


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28. 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 (22), 11566-11572. 29. Yamada, Y.; Nakamura, T.; Endo, M.; Wakamiya, A.; Kanemitsu, Y. Photoelectronic Responses in Solution-Processed Perovskite CH3NH3PbI3 Solar Cells Studied by Photoluminescence and Photoabsorption Spectroscopy. IEEE J. Photovoltaics 2015, 5 (1), 401405. 30. 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 (22), 4566-72. 31. Wright, A. D.; Verdi, C.; Milot, R. L.; Eperon, G. E.; Perez-Osorio, M. A.; Snaith, H. J.; Giustino, F.; Johnston, M. B.; Herz, L. M. Electron-phonon coupling in hybrid lead halide perovskites. Nat. Commun. 2016, 7, 11755. 32. Wu, K.; Bera, A.; Ma, C.; Du, Y.; Yang, Y.; Li, L.; Wu, T. Temperature-dependent excitonic photoluminescence of hybrid organometal halide perovskite films. Phys. Chem. Chem. Phys. 2014, 16 (41), 22476-22481. 33. Cho, M.; Scherer, N. F.; Fleming, G. R.; Mukamel, S. Photon echoes and related four‐ wave‐mixing spectroscopies using phase‐locked pulses. J. Chem. Phys. 1992, 96 (8), 5618-5629. 34. Yajima, T.; Taira, Y. Spatial optical parametric coupling of picosecond light pulses and transverse relaxation effect in resonant media. J. Phys. Soc. Jpn. 1979, 47 (5), 1620-1626. 35. Naeem, A.; Masia, F.; Christodoulou, S.; Moreels, I.; Borri, P.; Langbein, W. Giant exciton oscillator strength and radiatively limited dephasing in two-dimensional platelets. Phys. Rev. B 2015, 91 (12), 121302. 36. Lummer, B.; Heitz, R.; Kutzer, V.; Wagner, J. M.; Hoffmann, A.; Broser, I. Dephasing of Acceptor-Bound Excitons in Ii-Vi Semiconductors. Physica Status Solidi B: Basic Solid State Physics 1995, 188 (1), 493-505.

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TOC 39x19mm (300 x 300 DPI)


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Figure 1. (a) SEM image of a small aggregate of MAPI NPls on a substrate. (b) Experimentally measured absorption spectrum of a MAPI NPl ensemble at 175 K. (c) Theoretical model of the electronic energy levels in perovskite crystals in the two-particle picture: ground state, excitonic levels (1s, 2s, 2p …) and continuum onset at the band gap energy EG. The difference between EG and the 1s excitonic state E1s is the exciton binding energy EB. 51x14mm (300 x 300 DPI)


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Figure 2. (a) Scheme for the absorption spectrum of one single bulk-like NPl where the homogeneous broadening of the Lorentzian-shaped excitonic peaks is given by Γhom (dark blue). The excitonic levels (1s, 2s) and the continuum onset are well separated and easily distinguishable. However, in the measurements an ensemble of many NPls is examined simultaneously and thus a Gaussian-shaped inhomogeneous broadening Γinhom of the transitions occurs (shown in red for the 1s level). (b) In accordance with this Gaussian distribution (red) individual NPls show different absorption spectra due to varying size, shape and surrounding (dark blue lines). In the resulting total absorbance spectrum (black solid line) this causes broadened excitonic transitions as well as a broadened continuum onset. The total broadening of the excitonic transition is then given by Γtotal = Γhom + Γinhom. 82x82mm (300 x 300 DPI)


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Figure 3. (a) Experimental temperature-dependent absorption spectra of MAPI perovskite NPls for temperatures between 25 K and 295 K. The peak of the 1s exciton experiences a redshift when decreasing the temperature and around 150 K the transition from the tetragonal to the orthorhombic phase occurs. (b) Total broadening of the 1s exciton level Γtotal (FWHM of the absorption edge for T ≤ 200 K) as function of the temperature T taken from the data in (a) and denoted by crosses. A theoretical model (black dashed line) considering optical phonons as the dominant reason for the temperature-dependent broadening is fit to the data.31 Using the dephasing time T2 at 25 K obtained from the four-wave mixing experiments, the homogeneous broadening at this temperature is calculated Γhom(25 K) = 2ħ / T2(25 K) = 1.7±0.1 meV and the value of Γinhom = 22±1 meV can be assigned to the temperature-independent inhomogeneous broadening. Thus for each temperature one can distinguish between the homogeneous and inhomogeneous contribution to the total broadening of the excitonic level Γtotal(T). 97x115mm (300 x 300 DPI)


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Figure 4. (a) Experimental setup for time integrated four-wave mixing (FWM). Both pulses are focused through a lens (L) on the perovskite NPls (P) on the substrate (S) inside the cryostat. The signal at 2k2 – k1 is measured as a function of the time delay between the two pulses τ. (b) Absorption spectrum of MAPI NPls from Figure 3a at 25 K with excitonic peak and continuum (top panel). The panel below shows shifted spectra of the excitation pulses to allow for: (i) only 1s exciton excitation, (ii) & (iii) simultaneous excitation of excitons and free electron-hole pair transitions, or (iv) excitation of free electron-hole pair transitions. (c) Resulting FWM decay curves for these excitation spectra for a charge carrier density of ~1017 cm-3 at a temperature of T = 25 K: (i) The exponentially decaying signal provides the dephasing time T2 = 800±20 fs for the 1s exciton. (ii) In this case the excitation pulse spectrally overlaps slightly with the continuum transitions, thus an exciton wave packet is generated. With this small overlap the beating only occurs as a shoulder in the decaying FWM signal. (iii) When the spectrum of the excitation pulse overlaps with the 1s exciton and the continuum transitions to a similar extent these transitions are excited simultaneously. The beating behavior reaches its maximum at a central excitation wavelength of 735 nm when quantum beats with a periodicity of TB = 165±10 fs can be observed. The exciton binding energy of the MAPI NPls can be extracted via EB = h/TB = 25±2 meV. (iv) The dephasing for the free electron-hole pair transition is too fast to be resolved by the used laser pulses. 109x67mm (300 x 300 DPI)


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