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Impact of Layer Thickness on the Charge Carrier and Spin Coherence Lifetime in 2D Layered Perovskite Single Crystals Xihan Chen, Haipeng Lu, Zhen Li, Yaxin Zhai, Paul F. Ndione, Joseph J. Berry, Kai Zhu, Ye Yang, and Matthew C. Beard ACS Energy Lett., Just Accepted Manuscript • Publication Date (Web): 28 Aug 2018 Downloaded from http://pubs.acs.org on August 28, 2018

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ACS Energy Letters

Impact of Layer Thickness on the Charge Carrier and Spin Coherence Lifetime in 2D Layered Perovskite Single Crystals Xihan Chen┼, Haipeng Lu┼, Zhen Li, Yaxin Zhai, Paul Ndione, Joseph J. Berry, Kai Zhu, Ye Yang* and Matthew C. Beard* ┼

These two authors contribute equally

Chemical and Nano Science Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States Corresponding Author Ye Yang* [email protected] Matthew C. Beard* [email protected]

ABSTRACT Here we report the charge carrier recombination rate and spin-coherence lifetimes in single crystals of 2D Ruddlesden-Popper perovskites PEA2PbI4·(MAPbI3)n−1 (PEA, phenethylammonium; MA, methylammonium; n = 1, 2, 3, 4). Layer thickness dependent charge carrier recombination rates are observed with the fastest rates for n = 1 due to the large exciton binding energy and the slowest rates for n = 2. Room temperature spin-coherence times also show a nonmonotonic layer thickness dependence with an increasing spin-coherence lifetime with increasing layer thickness from n = 1 to n = 4, followed by a decrease in lifetime from n = 4 to ∞. The longest coherence lifetime of ~7 ps is observed in the n = 4 sample. Our results are consistent with two contributions; Rashba-splitting increases the spin-coherence lifetime going from the n = ∞ to the layered systems, while phonon-scattering which increases for smaller layers decreases the spin-coherence lifetime. The interplay between these two factors contributes to the layer thickness dependence.

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Recently, 2-dimensional (2D) lead-halide based perovskite layered systems are attracting attention. Compared to their 3D counterpart, 2D systems offer greater tunability1 and stability,2 making them candidates for high-performance optoelectronic applications.3-5 In addition, there is a growing interest in exploring the lead-halide perovskite family for optospintronics6-10.The presence of lead and iodide induces a large spin-orbit coupling (SOC) which in the presence of structural inversion asymmetry lifts the spin-degeneracy of the conduction and valance bands.11 2D perovskites self-assemble into natural “quantum-well” structures that break the symmetry of the 3D system, therefore, they have come into focus11-12 as a means to enhance the Rashba-effect and increase their potential for optospintronic applications.12 Recently, Zhai et. al. reported a ‘giant’ Rashba splitting in a 2D perovskite system.11 Here, we elucidate how the room temperature spin-coherence lifetimes and overall carrier dynamics depend upon layer thickness. We study and compare the charge carrier recombination and spin-coherence dynamics in single crystals of two-dimensional (2D) hybrid perovskites PEA2PbI4·(MAPbI3)n−1 (PEA, phenethylammonium; MA, methylammonium; n = 1, 2, 3, 4 using transient reflection (TR) spectroscopy.13 Single crystals are studied to avoid samples that contain mixtures of different layers (n’s) typically found in thin film samples. In addition, single crystal studies permit isolation and differentiation of the different n’s and therefore can elucidate the role of layer thickness. The carrier dynamics are measured by following the exciton bleach kinetics. While the spin-coherence dynamics are measured using circularly polarized pump and probe pulses.


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Figure 1. (A) Linear extinction coefficient and (B) XRD pattern of exfoliated 2D hybrid perovskite PEA2PbI4· (MAPbI3)n−1 single crystals. The cartoon in (B) shows the layered crystal structure. The red wiggled line represents PEA, the blue dots represents MA ion and the black square with orange dots represent PbI64- octahedral. Single

Crystal

Characterization.

Single

crystals

of

2D

hybrid

perovskite

PEA2PbI4·(MAPbI3)n−1 (n = 1, 2, 3, 4) are grown from modified methods described by Stoumpos et. al,14 (see Methods section). To expose a clean reflective surface for the subsequent optical measurements, the single crystals are exfoliated using scotch tape methods. The exfoliated single crystals are between 20-100 µm thick. The linear extinction coefficient (Fig. 1A) and refractive index (Fig. S1) of the single crystals are determined from ellipsometry measurements. The extinction coefficient maximum (exciton transition energy) decreases from 2.4 eV to 1.9 eV with increasing layer thickness (higher n-number), indicating a decrease in the quantum confinement, consistent with previous literature reports.15-16 The crystal structures of 2D single crystals are characterized by X-ray diffraction (XRD) (Fig. 1B). The XRD patterns are consistent with previously reported 2D crystal structure of PEA2PbI4·(MAPbI3)n−1 (n = 1, 2, 3, 4)16. The indexing confirms an in-plane orientation of the PbI6 sheets along the exfoliated surface as shown in the Fig. 1B cartoon.


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Figure 2. Normalized Transient reflection spectra (A) and the associated Kramers-Kronig transformed spectra (B) of 2D hybrid perovskite PEA2PbI4·(MAPbI3)n−1 single crystals. Transient reflection kinetics of 2D hybrid perovskite PEA2PbI4· (MAPbI3)n−1 single crystals under various pump fluences. The kinetics of (C) n = 1 was recorded at 2.45 eV. The kinetics of (D) n = 2 recorded at 2.25 eV. The kinetics of (E) n = 3 was recorded at 2.05 eV. And the kinetics of (F) n = 4 was recorded at 1.9 eV. The black-solid lines in the graph are the fits to the kinetic traces according to the carrier recombination model. Total Carrier Dynamics. Transient reflection (TR) measurements17-18 are carried out for all n = 1 − 4 exfoliated single crystals using a broadband probe with energy from 1.6 – 2.8 eV and monochromatic pump at 2.5 eV. Fig. 2A shows representative transient reflectance spectra at 10 ps after photo excitation. The spectra display a positive and negative feature near the exciton transition energy and a broad negative feature above the exciton energy. A Kramers-Kronig


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transformation is applied to the transient reflectance spectra (Fig. 2B) so as to extract the change in absorbance (Δ) within the probing region of the reflected light. The Δ transient spectra show a photoinduced bleach centered at 2.45, 2.2, 2.05 and 1.9 eV for n = 1 – 4 respectively, which coincides with the exciton peak position determined from their respective extinction coefficient measurements (Fig. 1A). Therefore, we assign the TR spectral features as a bleach of excitonic absorption due to either phase-space filling by free carriers and/or state-filling due to the presence of excitons.13,

19

The broad photo-induced absorption above the bandgap is

attributed to bandgap renormalization, but is not relevant for these measurements.19 Since bleaching of the excitonic transition can occur equally for free-carriers and excitons, the kinetics of the TR-spectra, reflects the total carrier dynamics (exciton and free-charges). Since the TR measurements are sensitive to surface carriers,20 we ensure that carrier diffusion away from the crystal surface is not the primary cause of the TR signal decay (as in the case of bulk perovskite samples)13, 20 by changing the excitation wavelength. The kinetics appear invariant under different pump energies (Fig. S2). Therefore, the main cause for TR signal decay is carrier recombination.(See Fig. S2 for detailed analysis) The initial carrier concentration ( ) is determined by the ratio of absorbed pump photon fluence to the pump photon penetration depth. The probing depth in reflection is much smaller than the pump penetration depth such that carrier distribution in the probing volume can be treated as uniform. The detailed calculation of carrier density, pump penetration depth and probing depth are provided in the Supporting Information. In the current study, varies by more than an order of magnitude, and within such a range, the signal amplitudes (−Δ / at delay of 2 ps shown in Fig. S3) are proportional to for all four samples, Δ / = ⋅ (constant b is the slope of the linear fit, Fig. S3). Therefore, the kinetics for the different pump fluences directly represent the carrier recombination dynamics for different initial injected carrier densities, (Fig. 2C – 2F). Carrier dynamics in semiconductors are typically described by the following equation:

(1) () = − ∙ () − ∙ () − ∙ () () is the carrier density at a pump-probe delay of t, , and denote the monomolecular, bimolecular, and trimolecular recombination rate constants. The first order recombination rate constants are determined by measuring the response from very low pump fluence where higher order recombination contributions are negligible (Fig. S4). We apply numerical integration of eq.


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1 to simultaneously model all the kinetic traces for each sample where only and are set as global free fitting parameters. The fitted rate constants are listed in Table 1. Table 1. List of carrier recombination rate constants for 2D hybrid perovskite PEA2PbI4·(MAPbI3)n−1 single crystals. and are obtained from global fitting of TR kinetics for different excitation fluences.

( )

( )

( )

n=1

0.71 ± 0.10

27.06 ± 4.15 × 10

27.68 ± 5.05 × 10(

n=2

0.10 ± 0.05

2.88 ± 0.51 × 10

0.79 ± 0.21 × 10(

n=3

0.23 ± 0.06

4.42 ± 0.62 × 10

2.36 ± 0.55 × 10(

n=4

0.22 ± 0.04

4.80 ± 0.70 × 10

1.84 ± 0.50 × 10(

Typically, monomolecular recombination is generally assigned to defect recombination and can reflect the sample quality (defect density, grain boundaries, etc.). While bi- and trimolecular recombination reflects intrinsic recombination channels (radiative and Auger recombination).21 However, such facile assignments are complicated by the presence of both excitons and free-charge carriers and the varying exciton binding energy within the samples.(see Fig. S1 for exciton binding energy estimation) In the n = 1 sample mostly excitons are formed, while for the n = 4 case mostly free-charges are initially formed. For n = 2 and 3, free-carriers are initially formed followed by exciton formation. With this in mind we can make some interesting observations. First, the monomolecular recombination is faster in all of the single crystal layered systems compared to that typically found in single crystals of MAPbI3.20 Second, the trend in the various rate constants for the different layer thicknesses is the same irrespective of the rate constant. All of rate constants are the largest for the n = 1 sample, while they are the smallest for n = 2 and nearly identical for n = 3 and 4. The large rate constants for n = 1 can likely be attributed to the large exciton binding energy. Previous reports22-24 find that the exciton binding energy can be as high as ~ 0.5 eV, and we estimate a binding energy of 480 meV for these samples (Fig. S1b). Furthermore, the photoexcitation wavelength is tuned to the exciton


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resonance. Therefore, for n = 1, exciton recombination plays a major role. The monomolecular rate for the n = 1 case can be a mixture of radiative geminate recombination and defect recombination. In contrast, for the n = 2 through 4, as our pump energy is at least 0.3 eV above the bandgap, a large portion of free charge carriers are produced, for example, Gelvez-Rueda et.al find that over 80% of the excitations produce free-charge carriers for n = 2, 3 and 4 for 2D BA2PbI4·(MAPbI3)n−1.22 In the PEA systems we are studying, we expect similar behavior and we don’t expect to resolve exciton formation or decay to free-carrier dynamics in these studies, since the TR measurements are sensitive to the presence of both free-carriers and excitons. If the bimolecular rate constant consists mainly of radiative events then we would expect that the trend in the rates would follow the binding energy times the bandgap.21 However, since the binding energy and the bandgap are larger for the n = 2 case compared to the n = 3 and 4 we conclude that some non-radiative component contributes to the bimolecular rate. For n = 3 to 4 systems, the measured and coefficient are very similar to the ones measured in 3D films.21 Accounting for the fact the absorption coefficient (Fig. 1A) averages over both the organic and inorganic wells, while the photogenerated carriers reside within the inorganic wells (and thus the effective concentration within the wells is higher) reduces the effective rate constants (see Table S1) but the trends are the same. For the case of n=1, the term only becomes important at very high carrier densities (~4x10-18cm-3), with a 5 times higher effective carrier density. At these high carrier densities the Coulomb interaction is screened and the resulting exciton population can be significantly reduced with an increase in the free-carrier concentration, thus the term can likely be assigned to the typical Auger three-particle process. The recombination rate constants we observed have established the potential use of 2D layered perovskite as optoelectronic materials. For n = 1, due to the fast carrier recombination rate and large exciton binding energy, photo generated charge carriers will recombine before they can be extracted for useful work. For n = 2, 3 and 4, the slower recombination rates enable the charge carrier to be extracted prior to recombination. More importantly, the addition of organic PEA layer can passivate the surface that reduce the number of traps and prevent moisture ingress, making them great candidate for solar cell applications.


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Figure 3. (A) Illustration of spin dynamics measurement. A circularly polarized pump (+ , or + ) with photon energy resonant with or above the exciton resonance can generate carriers with polarized total angular momentum that selectively bleach the exciton |.1/ or |−1/ resonance due to phase-space filling. Thus, the total angular momentum coherence lifetimes of carriers can be measured by probing the kinetics of the corresponding exciton bleach. The pump pulse is resonant with the lower energy side of the exciton resonance to minimize the effect of phonon mediated carrier cooling. (B) Representative spin coherence lifetime for n = 4 single crystal. The decay traces are normalized at 20 ps (C) The dynamics of spin coherence plotted as + , - + for n = 1, 4 and ∞ perovskites. The dashed red line represents the single exponential fit to the spin coherence dynamics (D) Lifetime of spins in excited states for n = 1 – 4 and 3D MAPbI3 single crystals. The blue shaded region indicates potential influence of Rashba effect. The red shaded region indicates phonon effect on the spin coherence lifetime. Spin-coherence dynamics. To explore the spin-coherence dynamics in 2D perovskite n = 1 – 4 and 3D MAPbI3 single crystals (Fig. 3), we measure the exciton bleach kinetics by TR spectroscopy with circularly polarized pump and probe pulses. (Fig. 3A) Pump + , has angular momentum of |+1> and generates an exciton in |+1> state, while pump + does the opposite. The probe + , pulse selectively detects the change of exciton |.1/ state. The flip of a spin will simultaneously lead to a decay of the + , bleach and a formation of the + bleach. The decay and formation kinetics merge at the half-way point between their respective initial amplitudes, indicating that the initially polarized spin population has depolarized. Fig. 3B shows the decay


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dynamics of n = 4 single crystal. Additional decay dynamics can be found in Fig. S5. To quantitatively determine the spin-coherence time, we plot the difference of + , and + bleach (Fig. 3C for n = 1, 4 and ∞ perovskites). The dashed red line indicates a single exponential fit. Additional analysis for n = 2 and 3 can be found in Fig. S6, and the characteristic spin-coherence time τ is plotted in Fig. 4D and lengthens from ~0.3 ps in n = 1 sample to ~7 ps in n = 4 samples at room temperature, interestingly, the coherence time shortens to 1.5 ps for n = ∞ (3D) MAPbI3 (Fig. 3D).


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Figure 4. THz spectra and temperature dependent photoluminescence linewidth of 2D hybrid perovskite PEA2PbI4·(MAPbI3)n−1 single crystals. (A) n = 1 (B) n = 2 (C) n = 3 (D) n = 4. The vertical grey line indicates the fitted peak frequency.


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There are several factors that can contribute to the interesting observed trend in spincoherence lifetime. First, the breaking of symmetry in 2D layered quantum well structure can induce a stronger Rashba-splitting compared to 3D structure.6,

11, 25

Rashba-splitting,26

originating from spin-orbit coupling and the breaking of inversion symmetry, induces an additional barrier to spin flipping since |.1/ and |−1/ are in different momentum valleys. In the systems we are measuring, reducing the dimensionality from 3D to 2D should result in a variation in the asymmetry resulting in a larger Rashba-splitting. In fact, Zhai et. al measure a ‘giant’ Rashba-splitting for the n = 1 2D system,11-12 suggesting that as n decreases the Rashba splitting increases as the number of PbI6 layers decreases. This trend is represented by the blue shaded region in Fig. 3D labelled Rashba and is likely responsible for the increased spincoherence lifetime from 1.5 ps for the 3D case to 7 ps for the n = 4 sample. There are several mechanisms explored in the literature for spin-coherence in semiconductor systems.27 Phonon scattering can depolarize the spins through Elliot-Yafet (EY) mechanism at room temperature.27-28 Stronger phonon scattering can lead to a faster spin randomization.29 To explore, we measured the phonon frequency with time-domain Terahertz (TD-THz) spectroscopy30 and temperature dependent photoluminescence linewidth (Fig. 4). For THz results, two observations can be made. First, two phonon modes are observed with frequency close to 1 and 2 THz, very close to the transverse optical (TO) and longitudinal optical (LO) phonon frequency measured for 3D MAPbI3.30-32 Second, the phonon frequency shifts and the phonon spectra broaden with decreasing layer thickness. For n = 1, the phonon frequencies are significantly shifted to lower frequency with TO shifted to ~ 0.8 THz and LO shifted to ~ 1.6 THz. The frequency shift is also accompanied by a significant broadening of the phonon spectrum (see Table S2 for best-fit parameters). The origin for the frequency shift and spectral broadening is unknown and needs further investigation. However, our results are consistent with the labile nature of these systems as predicted from first principles calculations on the 3D systems.33 Studies34-35 have shown that phonon broadening can be partially attributed to anharmonic phonon–phonon coupling that increases phonon scattering rates. The measured PL linewidth has a dependence on temperature. (Fig.4 and Fig. S7) The temperature dependent width Γ can be approximately written as 0 = 0 . 123 4 . 156 56 (4) . 1789 :

; < 31 =< >

,

where 0 represents intrinsic line width, γac is the acoustic phonon coupling term,


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156 is the optical phonon coupling term and 1789 is the impurity term (will not be discussed here). 56 (4) is the occupational number of phonons and can be written as 56 (4) =

.

;@A ? =< >

For the perovskite samples measured here, B56 is close to 1.9 THz, much smaller than the thermal energy of 6.3 THz at room temperature. 56 (4) can be approximately written as

C< D E@A

.

Therefore, Γ can be approximately written as 0 = 0 . 14 with γ proportional to electron phonon coupling. By fitting the temperature dependent linewidth, γ can be obtained. From the fitting results, we observe a very large γ of 0.25 for n = 1 sample. γ decreases with increasing n number and is the smallest for n = 4, indicating decreased electron-phonon coupling for increasing n number, which is consistent with other 2D perovskite systems.29 With an increased rate of phonon-scattering for the smaller number of layers, spins depolarize faster. This trend is represented by the red shaded region in Fig. 3D. These two counteracting factors thus play a role in the observed trend in spin-coherence lifetimes and the trend can be explained as follows. In 2D systems, the breaking of symmetry induced larger splitting of spin degenerate band and increases the spin lifetime compared to the 3D system. In the meantime, due to the increased phonon scattering process from n = 4 to n = 1, the spin lifetime decreases again with decreasing layer thickness. The interplay between these two factors gives the longest spin coherence lifetime in the n = 4 intermediate structure. Similar trends in the room temperature coherence dynamics have been observed in III-V quantum well structures (decreased spin coherence lifetime within decreasing well-width).36-37 In these cases the spin-coherence is governed by the D’yakonov-Perel (DP) mechanism. We rule out the DP mechanism for our samples because the carrier mobility within the wells is low and the phonon-scattering rate is high, therefore the EY mechanism is more likely the cause for the spin to lose coherence. In summary, we investigate the carrier recombination rate for 2D hybrid perovskite PEA2PbI4·(MAPbI3)n−1 single crystals using TR spectroscopy. Our results indicate that the recombination rate constants in the n = 1 sample is ~ 3 times larger than that in n = 2, 3, 4 sample owing to the larger exciton binding energy, making it not suitable for solar cell applications but could be suitable for light emitting applications. We have also studied the spin-coherence kinetics as a function of layered thickness in 2D hybrid perovskite single crystals. Compared


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with their 3D counterpart, the breaking of symmetry in the 2D samples results in a longer spincoherence lifetime. However, the reduced dimensionality is accompanied with a strong phonon scattering. These counteracting effects lead to the longest room temperature spin-coherence lifetime of 7 ps in the n = 4 layered system.

ASSOCIATED CONTENT Supporting Information. Experimental Methods, Refractive index n, Exicton binding energy estimation, penetration depth calculation, carrier concentration calculation, signal amplitude versus carrier density, low fluence TR measurements, Recombination rate table, spin coherence dynamics, the phonon frequencies table and temperature dependent PL spectra. NOTES The authors declare no competing financial interest. ACKNOWLEDGEMENT We gratefully acknowledge support from the Center for Hybrid Organic Inorganic Semiconductors for Energy (CHOISE) an Energy Frontier Research Center funded by the Office of Basic Energy Sciences, Office of Science within the US Department of Energy through contract number DE-AC36-08G028308. Initial spin-coherence lifetime measurements were performed with funding through an LDRD project. The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes. References (1) Cao, D. H.; Stoumpos, C. C.; Farha, O. K.; Hupp, J. T.; Kanatzidis, M. G. 2D Homologous Perovskites as Light-Absorbing Materials for Solar Cell Applications. J. Am. Chem. Soc. 2015, 137 (24), 7843-7850. (2) Smith, I. C.; Hoke, E. T.; Solis-Ibarra, D.; McGehee, M. D.; Karunadasa, H. I. A Layered Hybrid Perovskite Solar‐Cell Absorber with Enhanced Moisture Stability. Angew. Chem., Int. Ed. 2014, 53 (42), 11232-11235. (3) Rodríguez-Romero, J.; Hames, B. C.; Mora-Seró, I.; Barea, E. M. Conjugated Organic Cations to Improve the Optoelectronic Properties of 2D/3D Perovskites. ACS Energy Lett. 2017, 2 (9), 1969-1970. (4) Lin, H.; Zhou, C.; Tian, Y.; Siegrist, T.; Ma, B. Low-Dimensional Organometal Halide Perovskites. ACS Energy Lett. 2018, 3 (1), 54-62. (5) Venkatesan, N. R.; Labram, J. G.; Chabinyc, M. L. Charge-Carrier Dynamics and Crystalline Texture of Layered Ruddlesden–Popper Hybrid Lead Iodide Perovskite Thin Films. ACS Energy Lett. 2018, 3 (2), 380-386.


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(6) 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 (14), 3362-3370. (7) 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. (8) 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. (9) Li, J.; Haney, P. M. Optical Spintronics in Organic-Inorganic Perovskite Photovoltaics. Phys. Rev. B 2016, 93 (15), 155432. (10) Chen, X.; Lu, H.; Yang, Y.; Beard, M. C. Excitonic Effects in Methylammonium Lead Halide Perovskites. J.Phys.Chem. Lett 2018, 9 (10), 2595-2603. (11) Zhai, Y.; Baniya, S.; Zhang, C.; Li, J.; Haney, P.; Sheng, C.-X.; Ehrenfreund, E.; Vardeny, Z. V. Giant Rashba Splitting in 2D Organic-Inorganic Halide Perovskites Measured by Transient Spectroscopies. Sci. Adv. 2017, 3 (7), 1700704. (12) 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 (6), 1600477. (13) Yang, Y.; Yan, Y.; Yang, M. J.; 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, 7961-7961. (14) Stoumpos, C. C.; Cao, D. H.; Clark, D. J.; Young, J.; Rondinelli, J. M.; Jang, J. I.; Hupp, J. T.; Kanatzidis, M. G. Ruddlesden–Popper Hybrid Lead Iodide Perovskite 2D Homologous Semiconductors. Chem. Mater. 2016, 28 (8), 2852-2867. (15) Blancon, J.-C. et al. Extremely Efficient Internal Exciton Dissociation Through Edge States in Layered 2D Perovskites. Science 2017, 355 (6331), 1288-1292. (16) Peng, W.; Yin, J.; Ho, K.-T.; Ouellette, O.; De Bastiani, M.; Murali, B.; El Tall, O.; Shen, C.; Miao, X.; Pan, J. Ultralow Self-Doping in Two-dimensional Hybrid Perovskite Single Crystals. Nano Lett. 2017, 17 (8), 4759-4767. (17) 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 (30), 10632-10639. (18) 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 (5), 1830-1841. (19) 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 2015, 10, 53. (20) Yang, Y.; Yang, M.; Moore, David T.; Yan, Y.; Miller, Elisa M.; Zhu, K.; Beard, Matthew C. Top and Bottom Surfaces Limit Carrier Lifetime in Lead Iodide Perovskite Films. Nat. Energy 2017, 2, 16207. (21) Yang, Y.; Yang, M. J.; 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 (23), 4688-4692.


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ACS Energy Letters

(22) Gélvez-Rueda, M. C.; Hutter, E. M.; Cao, D. H.; Renaud, N.; Stoumpos, C. C.; Hupp, J. T.; Savenije, T. J.; Kanatzidis, M. G.; Grozema, F. C. Interconversion between Free Charges and Bound Excitons in 2D Hybrid Lead Halide Perovskites. J. Phys. Chem. C 2017, 121 (47), 2656626574. (23) Tanaka, K.; Takahashi, T.; Kondo, T.; Umebayashi, T.; Asai, K.; Ema, K. Image Charge Effect on Two-dimensional Excitons in an Inorganic-Organic Quantum-well Crystal. Phys. Rev. B 2005, 71 (4), 045312. (24) Yaffe, O.; Chernikov, A.; Norman, Z. M.; Zhong, Y.; Velauthapillai, A.; van der Zande, A.; Owen, J. S.; Heinz, T. F. Excitons in Ultrathin Organic-Inorganic Perovskite Crystals. Phys. Rev. B 2015, 92 (4), 045414. (25) Stranks, S. D.; Plochocka, P. The Influence of the Rashba Effect. Nat. Mater. 2018, 17 (5), 381-382. (26) Rashba, E. I. Semiconductors with a Loop of Extrema. J. Electron. Spectrosc. Relat. Phenom. 2015, 201, 4-5. (27) Žutić, I.; Fabian, J.; Das Sarma, S. Spintronics: Fundamentals and Applications. Rev. Mod. Phys. 2004, 76 (2), 323-410. (28) 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 (3), 1553-1558. (29) Guo, Z.; Wu, X.; Zhu, T.; Zhu, X.; Huang, L. Electron–Phonon Scattering in Atomically Thin 2D Perovskites. ACS nano 2016, 10 (11), 9992-9998. (30) La-o-vorakiat, C. et al.. Phonon Mode Transformation Across the Orthohombic– Tetragonal Phase Transition in a Lead Iodide Perovskite CH3NH3PbI3: A Terahertz TimeDomain Spectroscopy Approach. J. Phys.Chem. Lett. 2016, 7 (1), 1-6. (31) Wright, A. D.; Verdi, C.; Milot, R. L.; Eperon, G. E.; Pérez-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) Sendner, M. et al. Optical Phonons in Methylammonium Lead Halide Perovskites and Implications for Charge Transport. Mater. Horizons 2016, 3 (6), 613-620. (33) Brivio, F.; Frost, J. M.; Skelton, J. M.; Jackson, A. J.; Weber, O. J.; Weller, M. T.; Goñi, A. R.; Leguy, A. M. A.; Barnes, P. R. F.; Walsh, A. Lattice Dynamics and Vibrational Spectra of the Orthorhombic, Tetragonal, and Cubic Phases of Methylammonium Lead Iodide. Phys. Rev. B 2015, 92 (14), 144308. (34) Delaire, O. et al. Giant Anharmonic Phonon Scattering in PbTe. Nat. Mater. 2011, 10, 614. (35) Overy, A. R.; Simonov, A.; Chater, P. A.; Tucker, M. G.; Goodwin, A. L. Phonon Broadening from Supercell Lattice Dynamics: Random and Correlated Disorder. Phys. Status Solidi B 2017, 254 (4), 1600586. (36) Tackeuchi, A.; Nishikawa, Y.; Wada, O. Room‐temperature Electron Spin Dynamics in GaAs/AlGaAs Quantum Wells. Appl. Phys. Lett. 1996, 68 (6), 797-799. (37) Tackeuchi, A.; Wada, O.; Nishikawa, Y. Electron Spin Relaxation in InGaAs/InP Multiple-Quantum Wells. Appl. Phys. Lett. 1997, 70 (9), 1131-1133.


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Impact of Layer Thickness on the Charge Carrier ... - ACS Publications

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