Excitonic Effects in Methylammonium Lead Halide Perovskites - The

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Excitonic Effects in Methylammonium Lead Halide Perovskites Xihan Chen, Haipeng Lu, Ye Yang, and Matthew C. Beard J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00526 • Publication Date (Web): 01 May 2018 Downloaded from http://pubs.acs.org on May 1, 2018

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The Journal of Physical Chemistry Letters

Excitonic Effects in Methylammonium Lead Halide Perovskites Xihan Chen, Haipeng Lu, Ye Yang, Matthew C. Beard Chemistry and Nanoscience Center, National Renewable Energy Laboratory, Golden, CO, 80401 TOC Graphic

Abstract The exciton binding energy in methylammonium lead iodide (MAPbI3) is about 10 meV, around 1/3 of the available thermal energy (kBT ~ 26 meV) at room temperature. Thus exciton populations are not stable at room temperature at moderate photoexcited carrier denisties. However, excitonic resonances dominate the absorption onset. Furthermore, these resonances determine the transient absorbance and transient reflectance spectra. The exciton binding energy is a reflection of the Coulomb interaction energy between photoinduced negatively charged electrons which are lifted from the valence band to the conduction band, leaving a positively charged hole behind. As such it serves as a marker for the strength of electron/hole interactions and impacts a variety of phenomena, such as, absorption, radiative recombination, and Auger recombination. In this Perspective, we discuss the role of excitons and excitonic resonances in the optical properties of lead-halide perovskite semiconductors. Finally, we discuss how the strong light-matter interactions induces an optical stark effect splitting the doubly spin degenerate ground exciton states and is easily observed at room temperature. Lead-halide perovskites represent an intriguing class of solution-deposited semiconductors with great potential for opto-electronic applications. Recent interest in these systems stems from their performance in solar cells, with the highest certified power conversion efficiency of a polycrystalline lead-halide perovskite thin-film solar cell approaching 23%, exceeding that of solar cells fabricated from multicrystalline silicon and CdTe.1 Studies have attributed this success in solar cells to their photophysical properties such as strong light absorption, long charge-carrier diffusion lengths2-5 and low intrinsic surface recombination6-12. Lead-halide perovskite systems have also shown promise in other optoelectronic applications such as lasers13-16, light-emitting diodes17-20, photodetectors21-24 and optospintronics25-28. In contrast to the rapid progress in solar cells, the aforementioned opto-electronics are more or

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less still lingering at the stage of “proof-of-concept” and require deeper understanding of their optoelectronic properties. In this Perspective, we describe how excitonic effects modulate the opto-electroic behavior in the prototypical methylammonium lead iodide (MAPbI3) perovskite semiconductor. Absorption of photons in semiconductors lifts electrons out of the valence band into the conduction band generating free-charge carriers, i.e. – negatively-charged electrons in the conduction band and positively-charged holes in the valance band. Coulombic interactions between the photo-excited electron and hole give rise to ‘excitonic effects’ that modulate the opto-electronic behavior of semiconductors. It is important to note that the linear absorption strength of any particular optical resonance does not indicate the presence of excited states but rather the strength of the light-matter coupling at that resonance frequency.29 Excitons are fundamental quasi-particles that form bound electron-hole pairs due to the Coloumb interaction. At room temperature and under 1-sun illumination intensity very few excitons exist in thin films of MAPbI3 reflecting an exciton binding energy that is only ~10 meV, much smaller than the available thermal energy. However, excitonic effects play an important role in defining the optical properties, which will be discussed in the following order. (1) Exciton resonances dominate the bandedge absorption onset; (2) the transient absorption (TA) and transient reflection (TR) spectra are dominated by bleaching of the excitonic resonance; (3) the bi- and tri-molecular carrier recombination exhibit dependence on the exciton binding energy because they are modulated by the same Coulomb interaction; (4) the bandedge exciton states can be entangled with photons via the optical stark effect; (5) exciton bleach dynamics under circullary-polarized excitation can follow the total angular momentum depolarization dynamics of carriers.

Figure 1. Exciton absorption in direct band gap semiconductors. (A) Schematic diagram of bound (excitons) and ionized (free-carriers) electron-hole pair energy levels. The vertical and horizontal axes correspond to the energy () and the electron-hole center-of-mass momentum ( ). The origin point (0,0) indicates the ground state with zero energy and zero momentum. The blue parabolic curves and the shaded region represent the kinetic energy bands of the exciton states and continuum free-carrier states, respectively. The green arrow indicates the optical transition for a photon with energy and ACS Paragon Plus Environment

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momentum . Since the momentum, , of photon is very small only those states along the = 0 axis are optically allowed producing the descrite exciton lines in the absorption spectrum. The gap between the lowest exciton state and bottom of continuum is defined as exciton binding energy, . (B) Hypothetical bandedge absorption spectrum according to eq. 4. The lowest three exciton states are resolved (with arbitrary broadening). The exciton states merge continuously into the continuum at the bandedge. The energy difference between the first exciton peak and free carrier absorption edge corresponds to the exciton binding energy. The red curve represents the free carrier absorption spectrum in the absence of excitonic effect. Lower plot is an expanision of the upper plot.

Excitons are generally ascribed to two categories, Frankel and Wannier. The former are tightly bound electron-hole pairs with small Bohr radii and usually exist in wide-gap semiconductors and organic materials with small dielectric constants, while the latter are weakly bound and mostly found in semiconductors with large dielectric constants. In the case of the lead-halide perovskite semiconductors, we only consider Wannier excitons. Similar to any two-particle problem, the exciton Schrodinger equation can be solved by separating the motion of the electron-hole pair into center-of-mass motion and electron-hole relative motion.30-31 Considering the center-of-mass motion, the exciton is treated as a neutral particle freely moving inside the semiconductor, and the kinetic energy from this center-of-mass motion, , is given by, (1) = 2 where is the sum of electron and hole effective masses, and is the sum of electron and hole momentum, resulting in a parabolic energy dispersion curve (blue curves, Fig. 1a) in a twoparticle diagram. On the other hand, the relative electron-hole motion is determined by the Coulomb potential, which resembles the relative electron-proton motion in a hydrogen atom. Thus, the relative motion part (Wannier equation) is mathematically equivalent to the Schrodinger equation for the hydrogen atom, with quantized energy eigenvalues: 1 (2) = − where is exciton Rydberg energy; is the principle quantum number. The negative sign in eq. 2 indicates that formation of an exciton bound state releases energy. The total energy of excitons is expressed as: 1 (3) = + + ≈ + − 2 where is the band gap energy. As increases, the exciton energy approaches the continuum (Fig. 1A, shaded area). The energy difference between the lowest energy exciton state and lowest conduction band continuum state is equal to , also defined as the exciton binding energy. Note that these equations define the available exciton states and their energies but not the optical transitions.


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Optical transitions from the ground state to exciton states significantly modify the absorption spectrum, particularly below and near the bandedge. To conserve both energy and momentum, optical transitions to exciton states are only allowed when the photon and exciton dispersion curves (green arrow and blue parabolas, Fig. 1A, respectively) intersect. It should be noted that the green arrow in Fig. 1A exaggerates the photon momentum, and the real intersection must be much closer to the vertical axis, where ≈ 0, and thus according to eq. 3, the exciton resonances are only observed for photon energies below the bandgap energy (Fig. 2A). Note that both exciton and free-carrier states (shaded region in Fig. 1A), exist for ≠ 0 but those states cannot be populated by light absorption. Photon energies that are greater than the bandgap only produce occupation of free-carrier states. Furthermore, the optical resonances require both angular momentum and parity to be conserved. To satisfy these requirements, only the transitions to exciton states with =0 (s-like states) are allowed for semiconductors with p-like conduction band and s-like valence band, such as II-VI and III-V semiconductors, as well as, the opposite (p-like conduction band and s-like valence band), as the case for lead-halide perovskite semiconductors.31 Applying these selection rules and taking into account absorption into transitions to free-carrier states, the bandedge absorption spectrum can be described by the Elliott equation:31-32 4 4' '( ) (4) = !"# − $ ∙ &

∙ 2# − + ⁄ $8 . + / 1 *+ℎ'- 567

where the frequency dependence of is approximated as a constant and related to the interband transition matrix element, is the photon energy, "# − $ is the Heaviside step

function, - is defined as9 /# − $, and 2 denotes a delta function. The first term

describes the absorption of continuum states and the second term is for the series of optically allowed exciton resonances. A prototypical bandedge absorption spectrum is sketched in Fig. 1B by substituting arbitrary parameters into eq. 4 and introducing arbitrary line broadening. In this hypothetical case, the first three exciton peaks (denoted as 1S, 2S and 3S) are resolved below the continuum edge. However, all excitonic transitions contribute near the bandedge and even though their amplitudes decrease as increases, the absorption over a small energy range reaches a consant and merges into the continuum at the bandedge. In the absence of excitonic effects, the free-carrier absorption spectrum would be proportional to the square root of energy (red curve, Fig. 1B) and right at the bandgap energy the density of states goes to zero. However, this is not the case in the presence of Coulomb interactions and leads to a step-like band edge absorption. We can simplify the first term in Eq. 4 for photon energies at or near the bandedge to, 7⁄ (5) 2' # = $ = α< ∙

= −


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where, < ,is the absorption coefficient in the absence of Coulombic effects. Since < varies as = − ? the absorption coefficient mathematically approaches a constant value at the bandedge.

Figure 2. Steady-state and transient spectra of lead-halide perovskites. (A) Absorption coefficient as function of energy for MAPbBr3 (blue-traces) and MAPbI3 films (red-traces). The band edge absorption for both samples are modeled by the Elliott equation (grey-traces). The cyan and green-traces correspond to the components arising from exciton and free-carrier resonances, respectively. (B) Typical transient absorption(TA) spectra of lead-halide perovskite thin films. The transient spectrum of MAPbI3 is truncated at 2.3 eV here. (C) Typical transient reflection (TR) spectra of the MAPbBr3 and MAPbI3 perovskite single crystals. The transient spectra are all recorded at 10 ps delay with low excitation intensities. This figure is adpted from ref 33 with perimission from American Chemical Society and ref 6 and 8 with permission from Nature Publishing Group.

Elliott’s formula (eq. 4) can successfully deconvolve the bandedge absorption into exciton and continuum contributions (Fig. 2A). Such an analysis has been done for methylammonium lead-bromide (MAPbBr3) and MAPbI3, including for single crystals and polycrystalline films. The exciton binding energies are determined to be ~10 meV and ~40 meV for MAPbI3 and MAPbBr3, respectively, with values that slightly vary from sample-to-sample.6, 8, 26, 33-37 Compared with the serial exciton peaks expected in the ideal case (Fig. 1B), only one exciton peak is resolved because of the relatively small exciton binding energy and large spectral broadening. The spectral-broadening for these samples is due in large part to phonon scattering, which is confirmed by temperature dependent absorption spectra. As the temperature is lowered, the 1S-exciton resonance and free-carrier absorption become


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spectrally isolated and the exciton resonance sharpens.34, 38 To further illustrate the impact of the exitonic effect on the absorption spectum we compare MAPbI3 and MAPbBr3 to that of GaAs39 by dividing the absorption coefficient, , by the respective exciton binding energy and then plotting vs. the photon energy divided by the respective bandgap energy (Fig 3). Represented in this fashion the intensity is propotional to the intraband matrix element, and we find that the lead-halide perovskite semiconductors exhibit similar behavior to that found in GaAs. The bandedge states for both GaAs and the lead halide perovskites arise from p and s atomic orbitals (although inverted from one another) therefore it is not surprising the intraband matrix elements are similar. As the photon energy increases, Elliott’s model deviates from the experimental data due to non-parabolicity of the bands, as well as, contributions from higher energy bands. The binding energies for the lead halide peroskites are similar to those found in III-V semiconductors (Fig. 3B compares the binding enegy vs. the bandgap for a variety of semiconductors).31 Again, we find that the dependence of the binding energy indicates similarity between the Pb-halide system and III-V semiconductors.

Figure 3. A. Comparison of bandedge absorption for GaAs (ref. 39), MAPbI3 (Red), MAPbBr3 (Blue). B. Binding energy of range of semiconductors vs. the bandgap (data from Ref. 31) of the semiconductor. Blue squares are for MAPbI3 and MAPbBr3.

An experimental complication with using Eq. 4 to extract the exciton binding energy occurs when the binding energy is small in comparison to the linewidth broadening (as in the case here for MAPbI3).35 In this case, the exciton linewidth merges with the continuum and the spectral decomposition presented above can be problematic. In this case, it’s useful to use modulation spectrosocpies that are able to further deconvolve the the exciton and free-carrier contributions.40 Here we show that both transient absorption (TA) and transient reflectance (TR) can enable extraction of the binding energy because they modulate the excitonic linewidth


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and not the continuum. As detailed in our previous paper, the TA-bleach is dominated by reduction of the exciton resonance due to phase-space filling, rather than by bleaching of the continuum states (state-filling), under low and moderate excitation intensity.37State-filling of exction transitions bleaches the exciton resonance intensity due to the presence of exctions (as in the case of quantum dots41). However, as discussed above excitons are not photoexcited when the photon energy exceeds the bandgap and excitons in MAPbI3, even when they are created initially, should be thermally ionized into free carriers at room temperature.38 Nevertheless, the exciton resonance is clearly bleached even in the absence of actual excitons. This paradox can be explained by the phase-space filling phenomena.37 Briefly, in phase-space exciton states are built from a linear combination of conduction and valence band free-carrier states. The exciton resonance strength includes the interband transition matrix element ( , in eq. 4). Thus, the presence of free-carriers can reduce the strength of interband transitions (state-filling) as well as the exciton resonance (phase-space filling) because of the exclusion principle.42-45 We find that the spectral width and peak-position of the TA-bleach for both samples (Fig. 2B) coincide with those of the exciton resonance, and not the continuum band, in the corresponding steady-state absorption spectra. Near the bandedge, bleaching of contiunnum states is offset by a photoinduced absorption that occurs due to bandgap renormalization. The presence of free-carriers can also reduce the exciton binding energy due to increased dielectric screening and thus, the exciton resonance can also be reduced by the presence of free-carriers due to the reduction in binding energy (see eq. 4). However this should be negligible for low excitation intensity.42-43 High excitation intensities can also introduce additional spectral broadening, which is not important for low excitation intensity.37 In contrast to the single peak in the TA-spectra, a pair of negative and positive features near the bandedge is observed in the TR-spectra. The features are anti-symmetric about the exciton resonance energy (Fig. 2C). The TR-spectra are related to the TA-spectra through a Kramers-Kronig transformation and we find that the TR anti-symmetric peaks also originate from bleaching of exciton resonance.6, 8 Given that there is spectral overlap in the linear absorption spectrum between the exciton resonance and free-carrier absorption for MAPbI3, modelling the linear and transient-spectra simultaneously can greatly reduce the uncertainty of the spectral decomposition and determine the exciton binding energy more accurately.33 Except under extremely high excitation intensity,37, 46 the TA-bleach and TR anti-symmetric peaks are linearly proportional to the photo-induced carrier density8, 33 as phase-space filling exhibits a linear dependence on the carrier density.42-43, 47-49 Therefore, the carrier dynamics in the bulk (TA) and near the surface (TR) can be monitored by measuring the kinetics of TAbleach and TR anti-symmetric peaks.


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Table 1. List of carrier recombination rate constants for MAPbBr3 and MAPbI3 films. The rate constant of B and C represent the bi- and tri-molecular recombination rate constant, respectively.33

ABCD EFG

HBCI EFG

MAPbBr3

4.9 ± 0.2 × 10-10

13.5 ± 0.3 × 10-28

MAPbI3

1.5 ± 0.1 × 10-10

3.4 ± 0.1 × 10-28

Under low excitation intensity, monomolecular recombination dominates the carrier lifetime, and usually it occurs with assistance of defects which are generally assigned either to the bulk (point defects and grain boundaries), or exposed surfaces. The monomolecular recombination is most important when considering photovoltaic applications because PV devices operate under low excitation intensities such that the steady state carrier densities are in the range of 1015 to 1016 cm-3. The defect density is usually controlled by extrinsic factors, and in this sense the monomolecular rate constant (J-coefficient) should vary from film-to-film depending on how the samples are prepared. When considering the carrier lifetime in these low carrier concentration regimes, carrier diffusion must also be considered. In the case of thin films, diffusion of carriers to the surfaces followed by surface recombination can dominate the carrier lifetimes, and thus, surface recombination must be taken into consideration. Furthermore, when the excitation energy is varied, carriers can be generated close to or further from the surface and thereby modulate the measured carrier lifetimes. By considering surface and bulk recombination as well as diffusion of carriers to the surfaces we find a general rule of thumb: if the measured carrier lifetime is shorter than ~0.5 µs then that likely indicates the carrier lifetimes are limited by surface recombination, while if the measured carrier lifetime is greater ~0.5 µs then that indicates carrier lifetimes are limited by bulk recombination.6 As the excitation intensity increases, bi- and tri-molecular recombination events begin to dominate the carrier lifetime. Since these are governed by the same Coulomb interaction the trends in bi- and tri-molecular should also reflect the trends in exciton binding energy. The bimolecular recombination rate constants (K-coefficient) for both MAPbBr3 and MAPbI3 films are in line with values of the K-coefficient for other direct band gap semiconductors (~10-9–10-10 cm3s-1). Therefore, we can attribute the bimolecular recombination to radiative recombination. Note that the value of B-coefficient for MAPbI3 implies that the radiative lifetime would be ~ 6 µs at 1-Sun intenstity (~ 1015 cm-3). For semiconductors, the K-coefficient is proportional to the product of the optical transition energy (approximated as ) and the absorption coefficient at the optical transition energy, # = $.50-52 As shown in Fig. 2A, the ratio of # = $ for MAPbBr3 to that for MAPbI3 is approximately 3.1, which is primarily determined by the ratio of exciton binding energies. Taking into account the ratio of between two samples, the ratio of K-coefficient for MAPbBr3 to that for MAPbI3 is around 4.5, qualitatively consistent with experimental data (Table 1) that indicates this ratio is 3.3. Since the absorption is enhanced by the Coulomb attraction due to the excitonic effect, the radiative rate is also enhanced


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accordingly by the same affect. This estimation further confirms that in lead-halide perovskites the radiative recombination is responsible for the bi-molecular recombination. The tri-molecular recombination is intuitively attributed to three-particle Auger recombination, and its rate constant (referred to as L-coefficient) is also listed in Table 1. We find that the L-coefficient MAPbBr3 is larger than that for MAPbI3 by factor of ~4; the larger exciton binding energy can also partially account for the enhancement of its L-coefficient. Due to the Coulomb interaction, a carrier attracts the opposite charge to its vicinity and repels those with the identical charges, so the otherwise homogeneous carrier distribution in space, actually displays microscopic inhomogeneity. As a result, the possibility of a carrier finding two other carriers with opposite charges at the same location is increased, and thus Auger recombination will be enhanced. This Coulomb-enhanced Auger recombination has been theoretically investigated and experimentally confirmed in silicon, and the enhancement factor is a threeparticle (eeh or ehh) correlation factor, ?M .53-54 To simplify the correlation function, ?M can be approximated as the product of two correlation factors, ?N ∙ ? , where ?N is the electron-hole correlation factor, and ? describes the correlation between an incoming electron/hole and an already correlated electron-hole pair.55 Unfortunately, it is difficult to quantify ?N and ? . However, ?N is also the radiative recombination enhancement factor,55 and therefore is proportional to the exciton binding energy. Given the neutral entity of the correlated electronhole pair, ? is expected to be smaller than ?N because of screening. Thus, ?N (MAPbBr3)/ ?N (MAPbI3) can be estimated as 3.1 according to the ratio of exciton binding energies between these two materials, while the ratio of ?N ∙ ? is likely to fall in the range from 3.1 to 9.5 (3.1×3.1). The measured ratio of L-coefficients between these two lead halide perovskites is determined to be 4, closer to the lower boundary of the ratio of Coulomb enhancement factor. The different energy band gaps can be another factor that affects the L-coefficients. Because momentum conservation during the Auger process can be satisfied more easily in a narrower band gap semiconductor, the C-coefficient has been found to increase with decreasing .56 Therefore, in contrast to the Coulomb enhancement, the momentum conservation requirement decreases the ratio of L coefficient for MAPbBr3 compared to that for MAPbI3, which may explain the overestimation of the L-coefficient ratio based solely on Coulomb enhancement. Apparently, more rigorous analysis is required to quantitatively rationalize the difference in L-coefficients between the different lead-halide perovskites. Another interesting observation that is worth consideration, is that the L-coefficient in lead halide perovskites is at least 2 order-of-magnitude larger than that found in GaAs (L~10F1Q RST * F7)56 and Si (L~10F17 RST * F7)54, 57, two important semiconductors for solar cells. The of MAPbI3 is similar to that of both GaAs and Si, and in particular, MAPbI3 and GaAs possess many similar photophysical properties. A fundamental understanding of difference in


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L-coefficient between these materials could be of importance to applications that require higher carrier density such as LEDs and lasers.

Figure 4. Optical Stark effect (OSE) in MAPbI3 films. (A) Exciton state energy shift due to OSE. The diagram shows energy levels of ground state (|0V) and the two-fold degenerate exciton states (|W1V). These quantum states are labeled by azimuthal quantum number of the total angular momentum. The interaction of the exciton state and a photon shifts the exciton state towards higher energy and is governed by optical selection rules. The doubling degenerate exciton state can be lifted by the OSE. (B) TA spectra recorded during OSE. The pump and probe pulses are circularly polarized, and the polarization notation is described in main text. The spectra are recorded at zero pump-probe delay (∆Y = 0 Z*). The pump photon energy is 1.55 eV with a detuning ∆ of 81 meV. The probe is a white-light continuum with photon energy from 2.76 eV to 1.55 eV. The black curves are the fitting functions described by eq. 6 in main text. This figure is adapted from ref 26 with permission from Nature Publishing Group.

In this section, we will focus on another type of exciton-photon interaction; the optical Stark effect (OSE). The consequence of the OSE is the entanglement of the exciton state with a non-resonant pump photon, and this light-matter interaction only persists as long as the photon field is present.58-60 Unlike absorption, OSE is not associated with carrier or exciton generation. As shown in Fig. 4A, when the pump-photon energy () is lower than the exciton transition energy (Q ), a mixed exciton-photon state results with energy that is shifted toward higher energies. Applying a perturbation to the exciton-photon interaction in a two-level system, the energy shift (2 ) can be expressed as61: [Q\ 〈^〉 (6) 2 =

∆

where μQa is the transition dipole moment, 〈F〉 is the time-averaged electric field of the pump light, and ∆ is the detuning of the photon frequency, , from Q . Since 〈^〉 is proportional to pump light intensity, 2 should be linear with increasing pump intensity. OSE is implicitly


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governed by optical selection rules through μQa , and thus a large exction absorption, implying large μQa , is a prerequisite of a strong OSE. For MAPbI3, the bright exciton state has two-fold of degeneracy, denoted by the azimuthal quantum number of the total angular momentum |W1V (Fig. 4A). According to the optical selection rules, using circularly polarized pump-light can selectively interact with one of the degenerate exciton states. For example, non-resonant circularly polarized pump with angular momentum quantum number of +1, referred to as c +, can only interact with an exciton state with angular momentum |+1V while leaving the other |−1V exction state unperturbed. TA spectroscopy can monitor the energy shift via an induced spectral change ∆J. As 2 ≪ Q , ∆J can be approximately described by the following equation26: 1 eJ (7) ∆J = −

2 e

∙ 2

where J is the steady state absorption spectrum (Fig. 2), and a positive (negative) 2 indicates blue (red) shift of the spectrum. Eq. 7 suggests that the profile of ∆J resembles the first derivative of the absorption spectra, while the amplitude of the ∆J linearly depends on the pump intensity via eq. 6. ∆J spectra recorded at zero pump-probe delay are shown in Fig. 4B for two pump-probe polarization configurations. For a c + pump, a c + probe detects a spectral change while a c − probe shows no spectral change. The TA-spectra are then modeled by eq. 7, and the best fits finds 2 for the exciton state |+1V as 1.1 meV. To simulate ∆J, the first derivative of the exciton absorption spectrum (deconvolvd from the linear absorption using eq. 4), rather than use of the total absorption spectrum is needed. Thus, the OSE opperates on exciton states and not on the continuum. A strong OSE has also been observed at room temperature in two-dimensional lead-halide perovskite layers.62

Figure 5. Total angular momentum depolarization dynamics probed by the TA exciton state bleach kinetics. The polarized exciton state bleach kinetics for (A) MAPbI3 film, (B) MAPbBr3 film and (C) MAPbBr3 single crystal. The kinetic traces are labeled by the pump-proble polarization configuration. The black curves are the single-exponential fittings. In panel A, the fast component of the blue curve due to the OSE is not shown.


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A circularly polarized pump (c + or c −) with photon energy resonant with or above the exciton resonance can generate carriers with polarized total angular momentum that selectively bleach the exciton |+1V or |−1V resonance due to phase-space filling. Thus, the total angular momentum depolarization (referred to here as spin-depoloarization) of carriers can be measured by probing the kinetics of the corresponding exciton bleach. Because phonon mediated carrier-cooling can efficiently depolarize the carrier’s angular momentum, we have excluded this effect by tuning our pump pulse to be resonant with the lower energy side of the exciton resonance. The exciton resonance bleach kinetics for MAPbBr3 and MAPbI3 samples (Fig. 5) are measured by TA spectroscopy with circularly polarized pump and probe pulses. Pump c + exclusively bleaches the absorption of the exciton |+1V state, and the probe c + and c − selectively detects the bleach of exciton |+1V and |−1V state, respectively. The spin depolarization will lead to a decay of |+1V bleach and a formation of |−1V bleach simultaneously, which is justified by the similar decay and formation time constants extracted from single exponential decay (black curves, Fig. 5). The decay and formation kinetics merge at the half-way point between their respective initial amplitudes, indicating that the spin of carriers are completely depolarized at this stage. Our results indicate that the spin depolarization in MAPbI3 is twice as fast as that in MAPbBr3. The scattering with defects or grain boundaries through Elliot-Yafet (EY) mechanism has been inferred as the primary cause of the depolarization.63 However, we compare the spin depolarization dynamics between single crystals of MAPbBr3 and a polycrystalline film (Fig. 5B and 5C). The single crystal sample should have fewer grain boundaries and fewer bulk defects than the polycrystalline films. Our results suggest no significant difference in spin depolarization time between these two samples, implying that scattering with defects or grain boundaries may not be the major depolarization channel. Recently, the lifetime of exciton spin polarization has been determined to be longer than 1 ns in lead-halide perovskite films at the temperature of 4 K, under which condition most phonons are frozen out, yet the phonon scattering via EY mechanism still could not satisfactorily describe the experimental data.27 Therefore, further investigations are needed to explore the cause of the fast spin depolarization. In this letter, we have discussed the excitonic effect in methyammonium lead-halide perovskite semiconductors. The Coulomb interaction plays an important role in defining their photophysical properties and can influence optoelectronic applications. We have shown that the lead-halide perovskite system behaves as a direct bandgap semiconductor with particular similarities to III-V semiconductors. As pointed out in this letter, more theoretical or experimental investigations should be conducted to quatitatively examine the excitonic effect on radiative and Auger recombination, on photon-matter entanglement and on spindepolarization. From the material aspect, learning how to control excitonic effects by adjusting


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the composition, structure, morphology and tuning of quantum confinement should be fruitful avenues for exploration. Acknowledgments: We gratefully acknowledge support through the Division of Chemical Sciences, Geosciences and Biosciences, Office of Basic Energy Sciences, Office of Science within the US Department of Energy through contract number DE-AC36-08G028308. Spin-depolarization measurements were performed with funding through an LDRD project. We acknowledge helpful disscusions with Jao van de Lagemaat, Joseph Berry, Joseph Luther, and Kai Zhu.

References: 1. NREL. https://www.nrel.gov/pv/assets/images/efficiency-chart.png (accessed January 2018). 2. Dong, Q.; Fang, Y.; Shao, Y.; Mulligan, P.; Qiu, J.; Cao, L.; Huang, J. Electron-hole diffusion lengths > 175 um in solution-grown CH3NH3PbI3 single crystals. Science 2015, 347, 967-970. 3. 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. 4. 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. 5. Tian, W.; Zhao, C.; Leng, J.; Cui, R.; Jin, S. Visualizing Carrier Diffusion in Individual SingleCrystal Organolead Halide Perovskite Nanowires and Nanoplates. J. Am. Chem. Soc. 2015, 137, 12458-12461. 6. Yang, Y.; Yang, M.; Moore, David T.; Yan, Y.; Miller, E. M.; Zhu, K.; Beard, M. C. Top and bottom surfaces limit carrier lifetime in lead iodide perovskite films. Nat. Energy 2017, 2, 16207. 7. Yang, M.; Zeng, Y.; Li, Z.; Kim, D. H.; Jiang, C. S.; van de Lagemaat, J.; Zhu, K. Do grain boundaries dominate non-radiative recombination in CH3NH3PbI3 perovskite thin films? Phys. Chem. Chem. Phys. 2017, 19, 5043-5050. 8. 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. 9. Wu, B.; Nguyen, H. T.; Ku, Z.; Han, G.; Giovanni, D.; Mathews, N.; Fan, H. J.; Sum, T. C. Discerning the Surface and Bulk Recombination Kinetics of Organic-Inorganic Halide Perovskite Single Crystals. Adv. Energy Mater. 2016, 6, 1600551. 10. Fang, H.-H.; Adjokatse, S.; Wei, H.; Yang, J.; Blake, G. R.; Huang, J.; Even, J.; Loi, M. A. Ultrahigh sensitivity of methylammonium lead tribromide perovskite single crystals to environmental gases. Sci. Adv. 2016, 2, e1600534. 11. Zhu, H.; Trinh, M. T.; Wang, J.; Fu, Y.; Joshi, P. P.; Miyata, K.; Jin, S.; Zhu, X. Y. Organic Cations Might Not Be Essential to the Remarkable Properties of Band Edge Carriers in Lead Halide Perovskites. Adv. Mater. 2017, 29, 1603072.


13


Page 14 of 17

12. Wei, H.; Fang, Y.; Mulligan, P.; Chuirazzi, W.; Fang, H.-H.; Wang, C.; Ecker, B. R.; Gao, Y.; Loi, M. A.; Cao, L.; Huang, J. Sensitive X-ray detectors made of methylammonium lead tribromide perovskite single crystals. Nat. Photonics 2016, 10, 333-339. 13. 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. 14. 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. 15. Deschler, F.; Price, M.; Pathak, S.; Klintberg, L. E.; Jarausch, D.-D.; Higler, R.; Hüttner, S.; Leijtens, T.; Stranks, S. D.; Snaith, H. J.; et al. High Photoluminescence Efficiency and Optically Pumped Lasing in Solution-Processed Mixed Halide Perovskite Semiconductors. J. Phys. Chem. Lett. 2014, 5, 1421-1426. 16. 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. 17. Yao, E.-P.; Yang, Z.; Meng, L.; Sun, P.; Dong, S.; Yang, Y.; Yang, Y. High-Brightness Blue and White LEDs based on Inorganic Perovskite Nanocrystals and their Composites. Adv. Mater. 2017, 29, 1606859. 18. Zhang, L.; Yang, X.; Jiang, Q.; Wang, P.; Yin, Z.; Zhang, X.; Tan, H.; Yang, Y.; Wei, M.; Sutherland, B. R.; Sargent, E. H.; You, J. Ultra-bright and highly efficient inorganic based perovskite light-emitting diodes. Nat. Commun. 2017, 8, 15640. 19. Kim, Y.-H.; Cho, H.; Lee, T.-W. Metal halide perovskite light emitters. Proc. Natl. Acad. Sci. 2016, 113, 11694-11702. 20. 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 (CsPbX3, X = Cl, Br, and I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut. Nano Lett. 2015, 15, 3692-3696. 21. Guo, Y.; Liu, C.; Tanaka, H.; Nakamura, E. Air-Stable and Solution-Processable Perovskite Photodetectors for Solar-Blind UV and Visible Light. J. Phys. Chem. Lett. 2015, 6, 535-539. 22. Lee, Y.; Kwon, J.; Hwang, E.; Ra, C.-H.; Yoo, W. J.; Ahn, J.-H.; Park, J. H.; Cho, J. H. HighPerformance Perovskite–Graphene Hybrid Photodetector. Adv. Mater. 2015, 27, 41-46. 23. Fang, Y.; Dong, Q.; Shao, Y.; Yuan, Y.; Huang, J. Highly narrowband perovskite singlecrystal photodetectors enabled by surface-charge recombination. Nat. Photonics 2015, 9, 679686. 24. Yakunin, S.; Dirin, D. N.; Shynkarenko, Y.; Morad, V.; Cherniukh, I.; Nazarenko, O.; Kreil, D.; Nauser, T.; Kovalenko, M. V. Detection of gamma photons using solution-grown single crystals of hybrid lead halide perovskites. Nat. Photonics 2016, 10, 585-589. 25. Kepenekian, M.; Even, J. Rashba and Dresselhaus Couplings in Halide Perovskites: Accomplishments and Opportunities for Spintronics and Spin–Orbitronics. J. Phys. Chem. Lett. 2017, 8, 3362-3370.


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Page 15 of 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


26. Yang, Y.; Yang, M.; Zhu, K.; Johnson, J. C.; Berry, J. J.; van de Lagemaat, J.; Beard, M. C. Large polarization-dependent exciton optical Stark effect in lead iodide perovskites. Nat. Commun. 2016, 7, 12613. 27. Odenthal, P.; Talmadge, W.; Gundlach, N.; Wang, R.; Zhang, C.; Sun, D.; Yu, Z.-G.; Valy Vardeny, Z.; Li, Y. S. Spin-polarized exciton quantum beating in hybrid organic–inorganic perovskites. Nat. Phys. 2017, 13, 894-899. 28. Li, J.; Haney, P. M. Optical spintronics in organic-inorganic perovskite photovoltaics. Phys. Rev. B 2016, 93, 155432. 29. Bernath, P. F. Spectra of Atoms and Molecules. Oxford University Press: 2005. 30. Yu, P. Y.; Cardona, M. Fundamentals of Semiconductors. 4 ed.; Springer-Verlag Berlin Heidelberg: 2010; p. 775. 31. Peyghambarian, N.; Koch, S. W.; Mysyrowicz, A. Introduction to Semiconductor Optics. Prentice-Hall, Inc.: 1993; p. 485. 32. Elliott, R. J. Intensity of Optical Absorption by Excitons. Phys. Rev. 1957, 108, 1384-1389. 33. 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. 34. Davies, C. L.; Filip, M. R.; Patel, J. B.; Crothers, T. W.; Verdi, C.; Wright, A. D.; Milot, R. L.; Giustino, F.; Johnston, M. B.; Herz, L. M. Bimolecular recombination in methylammonium lead triiodide perovskite is an inverse absorption process. Nat. Commun. 2018, 9, 293. 35. Sestu, N.; Cadelano, M.; Sarritzu, V.; Chen, F.; Marongiu, D.; Piras, R.; Mainas, M.; Quochi, F.; Saba, M.; Mura, A.; et al. Absorption F-Sum Rule for the Exciton Binding Energy in Methylammonium Lead Halide Perovskites. J. Phys. Chem. Lett. 2015, 6, 4566-4572. 36. Saba, M.; Cadelano, M.; Marongiu, D.; Chen, F.; Sarritzu, V.; Sestu, N.; Figus, C.; Aresti, M.; Piras, R.; Lehmann, A. G.; et al. Correlated electron-hole plasma in organometal perovskites. Nat. Commun. 2014, 5, 5049. 37. 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. 38. 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. 39. Adachi, S. Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlxGa1−xAs, and In1−xGaxAsyP1−y. J. Appl. Phys. 1989, 66, 6030-6040. 40. Ziffer, M. E.; Mohammed, J. C.; Ginger, D. S. Electroabsorption Spectroscopy Measurements of the Exciton Binding Energy, Electron–Hole Reduced Effective Mass, and Band Gap in the Perovskite CH3NH3PbI3. ACS Photonics 2016, 3, 1060-1068. 41. Klimov, V. I. Spectral and dynamical properties of multilexcitons in semiconductor nanocrystals. Annu. Rev. Phys. Chem. 2007, 58, 635-673. 42. Schmitt-Rink, S.; Chemla, D. S.; Miller, D. A. B. Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures. Phys. Rev. B 1985, 32, 6601-6609. 43. Huang, D.; Chyi, J.-I.; Morkoç, H. Carrier effects on the excitonic absorption in GaAs quantum-well structures: Phase-space filling. Phys. Rev. B 1990, 42, 5147-5153.


15


Page 16 of 17

44. Hunsche, S.; Leo, K.; Kurz, H.; Köhler, K. Exciton absorption saturation by phase-space filling: Influence of carrier temperature and density. Phys. Rev. B 1994, 49, 16565-16568. 45. Calcagnile, L.; Rinaldi, R.; Prete, P.; Stevens, C. J.; Cingolani, R.; Vanzetti, L.; Sorba, L.; Franciosi, A. Free-carrier effects on the excitonic absorption of n-type modulation-doped Zn1xCdxSe/ZnSe multiple quantum wells. Phys. Rev. B 1995, 52, 17248-17253. 46. Manser, J. S.; Kamat, P. V. Band filling with free charge carriers in organometal halide perovskites. Nat. Photonics 2014, 8, 737-743. 47. Yang, Y.; Gu, J.; Young, J. L.; Miller, E. M.; Turner, J. A.; Neale, N. R.; Beard, M. C. Semiconductor interfacial carrier dynamics via photoinduced electric fields. Science 2015, 350, 1061-1065. 48. Chen, X.; Choing, S. N.; Aschaffenburg, D. J.; Pemmaraju, C. D.; Prendergast, D.; Cuk, T. The Formation Time of Ti-O(*) and Ti-O(*)-Ti Radicals at the n-SrTiO3/Aqueous Interface during Photocatalytic Water Oxidation. J. Am. Chem. Soc. 2017, 139, 1830-1841. 49. Waegele, M. M.; Chen, X.; Herlihy, D. M.; Cuk, T. How surface potential determines the kinetics of the first hole transfer of photocatalytic water oxidation. J. Am. Chem. Soc. 2014, 136, 10632-10639. 50. van Roosbroeck, W.; Shockley, W. Photon-Radiative Recombination of Electrons and Holes in Germanium. Phys. Rev. 1954, 94, 1558-1560. 51. Lasher, G.; Stern, F. Spontaneous and Stimulated Recombination Radiation in Semiconductors. Phys. Rev. 1964, 133, A553-A563. 52. Dmitriev, A.; Oruzheinikov, A. The rate of radiative recombination in the nitride semiconductors and alloys. J. Appl. Phys. 1999, 86, 3241-3246. 53. Hangleiter, A.; Häcker, R. Enhancement of band-to-band Auger recombination by electron-hole correlations. Phys. Rev. Lett. 1990, 65, 215-218. 54. Altermatt, P. P.; Schmidt, J.; Heiser, G.; Aberle, A. G. Assessment and parameterisation of Coulomb-enhanced Auger recombination coefficients in lowly injected crystalline silicon. J. Appl. Phys. 1997, 82, 4938-4944. 55. Hangleiter, A. Recombination of correlated electron-hole pairs in two-dimensional semiconductors. Phys. Rev. B 1993, 48, 9146-9149. 56. Charache, G. W.; Baldasaro, P. F.; Danielson, L. R.; DePoy, D. M.; Freeman, M. J.; Wang, C. A.; Choi, H. K.; Garbuzov, D. Z.; Martinelli, R. U.; Khalfin, V.; et al. InGaAsSb thermophotovoltaic diode: Physics evaluation. J. Appl. Phys. 1999, 85, 2247-2252. 57. Dziewior, J.; Schmid, W. Auger coefficients for highly doped and highly excited silicon. Appl. Phys. Lett. 1977, 31, 346-348. 58. Scully, M. O.; Zubairy, M. S. Quantum Optics. Cambridge University Press: 1997. 59. Von Lehmen, A.; Chemla, D. S.; Heritage, J. P.; Zucker, J. E. Optical Stark effect on excitons in GaAs quantum wells. Opt. Lett. 1986, 11, 609-611. 60. Mysyrowicz, A.; Hulin, D.; Antonetti, A.; Migus, A.; Masselink, W. T.; Morkoç, H. "Dressed Excitons" in a Multiple-Quantum-Well Structure: Evidence for an Optical Stark Effect with Femtosecond Response Time. Phys. Rev. Lett. 1986, 56, 2748-2751. 61. Combescot, M. Optical Stark effect of the exciton. II. Polarization effects and exciton splitting. Phys. Rev. B 1990, 41, 3517-3533.


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62. Giovanni, D.; Chong, W. K.; Dewi, H. A.; Thirumal, K.; Neogi, I.; Ramesh, R.; Mhaisalkar, S.; Mathews, N.; Sum, T. C. Tunable room-temperature spin-selective optical Stark effect in solution-processed layered halide perovskites. Sci. Adv. 2016, 2, e1600477. 63. Giovanni, D.; Ma, H.; Chua, J.; Grätzel, M.; Ramesh, R.; Mhaisalkar, S.; Mathews, N.; Sum, T. C. Highly Spin-Polarized Carrier Dynamics and Ultralarge Photoinduced Magnetization in CH3NH3PbI3 Perovskite Thin Films. Nano Lett. 2015, 15, 1553-1558.


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Excitonic Effects in Methylammonium Lead Halide Perovskites - The

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