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Letter

Ultralong Radiative States in Hybrid Perovskite Crystals: Compositions for Sub-Millimeter Diffusion Lengths Erkki Alarousu, Ahmed M. El-Zohry, Jun Yin, Ayan A. Zhumekenov, Chen Yang, Esra Elhabshi, Issam Gereige, Ahmed Alsaggaf, Anton V. Malko, Osman M. Bakr, and Omar F. Mohammed J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b01922 • Publication Date (Web): 29 Aug 2017 Downloaded from http://pubs.acs.org on August 31, 2017

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The Journal of Physical Chemistry Letters

Ultralong Radiative States in Hybrid Perovskite Crystals: Compositions for Sub-millimeter Diffusion Lengths Erkki Alarousu,1 Ahmed M. El-Zohry,1 Jun Yin,1 Ayan A. Zhumekenov,1 Chen Yang,1 Esra Elhabshi,2 Issam Gereige,2 Ahmed AlSaggaf ,2 Anton V. Malko,3 Osman M. Bakr,1,4* and Omar F. Mohammed1,* 1

KAUST Solar Center, King Abdullah University of Science and Technology, Division of Physical Sciences and Engineering, Thuwal 23955-6900, Kingdom of Saudi Arabia

2

Saudi Aramco Research & Development Center, Dhahran 31311, Kingdom of Saudi Arabia 3

4

Department of Physics, the University of Texas at Dallas, Richardson, TX, 75080, USA

KAUST Catalysis Center, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia

Corresponding Author Email: [email protected] and [email protected]

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ABSTRACT

Organic-inorganic hybrid perovskite materials have recently evolved into the leading candidate solution-processed semiconductor for solar cells due to their combination of desirable optical and charge transport properties. Chief among these properties is the long carrier diffusion length, which is essential to optimizing the device architecture and performance. Herein, we used timeresolved photoluminescence (at low excitation fluence, 10.59 µJ·cm-2 upon two-photon excitation) which is the most accurate and direct approach to measure the radiative charge carrier lifetime and diffusion lengths. Lifetimes of about 72 and 4.3 µs for FAPbBr3 and FAPbI3 perovskite single crystals have been recorded, presenting the longest radiative carrier lifetimes reported to date for perovskite materials. Subsequently, carrier diffusion lengths of 107.2 and 19.7 µm are obtained. In addition, we demonstrate the key role of the organic cation units in modulating the carrier lifetime and its diffusion lengths, in which the defect formation energies for FA cations are much higher than those with the MA ones.

TOC GRAPHICS


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Organic-inorganic hybrid perovskites have captivated the attention of the photovoltaic research community due to a rare combination of optoelectronic and materials processing properties such as: long carrier diffusion lengths, tunable optical band gaps, compatibility with low-temperature fabrication methods, and low exciton binding energy, which leads to efficient exciton dissociation and charge collection in solar cell devices.1-4 Recently, organic-inorganic perovskite-based solar cells achieved a remarkable certified photoconversion efficiency (PCE) of 22.1%.5 The ability to manipulate carrier diffusion lengths in perovskite materials via judicious variation of compositional parameters is of a fundamental importance to the design of such high performance solar cell devices. Several measurements recently reported using reliable techniques such as time-resolved fluorescence and transient absorption spectroscopies3, 6 have shown carrier diffusion lengths in tri-iodine perovskite films exceeding sub-micrometer (µm) distances. On the other hand, more indirect methods such as time-resolved microwave conductance (TRMC) and steady-state photoconductance decay measurements tend to report hundreds of µm carrier diffusion lengths.7, 8

In addition, it has been found that the lifetimes of the perovskite single crystals are dramatically

varied and strongly depend on the excitation energy, light penetration depth (surface vs. bulk) and pump fluence9 (a summary of some recently reported lifetimes of various hybrid organic– inorganic perovskite single crystals, measured with different techniques, is presented in Table S1). To clarify these disparities, we performed a time-resolved photoluminescence (PL) study by directly observing radiative carrier lifetimes of the fresh perovskite single crystals using a streak camera through two-photon (2p) excitations and ultralow-excitation fluence. These experimental conditions minimize the influence of surface recombination including carrier trapping, and avoid the higher order non-radiative processes such as non-radiative Auger recombination. PL lifetimes


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of ca. 72 and 4.3 µs for FAPbBr3 and FAPbI3 perovskites single crystals have been recorded, respectively, presenting the longest radiative carrier lifetimes reported to date for perovskite materials. Moreover, carrier diffusion lengths of 107.2 and 19.7 µm have been obtained, representing also the longest carrier diffusion lengths in perovskites directly deduced from radiative carrier lifetimes. Additionally, by performing Density Functional Theory (DFT) calculations, we evaluate the impact of the defect formation for the organic cations and halides on the radiative carrier lifetimes.

Figure 1. 2D-pseudo color transient emission map for FAPbBr3 single crystal, excited by 2p, 820 nm, at low excitation fluence of 10.59 µJ·cm-2. The extracted kinetic trace with the biexponential fit are in the inset figure. The extracted spectra at different time slots are shown to the right hand side.


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Commonly, the used above bandgap photoexcitation of perovskites mostly obtains information about the carrier dynamics at the surface layers with a thickness determined by the penetration depth of the light, typically at the sub-µm distances.10 Recently, it was shown that perovskite single crystals have two kinds of layers, which are surface layer (a thickness of ca. 200-300 nm) and bulk layers. The surface layer behaves very different from that of bulk layers in terms of carrier lifetime and the number of trap states.10-12 To avoid this limitation, 2p excitation is used to generate PL almost throughout the entire sample depth due to the long optical penetration depth (ca. hundreds of micrometers), mainly reflecting the carrier dynamics within the bulk of the single crystal.13-16 Previously, it was argued that 2p excitation was not accurate to extract the carrier diffusion lengths due to the influence of photon recycling and re-absorption effects.14,

15, 17-19

However, more recent reports confirm that accurate measurements of the

diffusion lengths with 2p excitation could be obtained14, 20 for low PL quantum yield (PLQY) samples where contribution of photon recycling is negligible.16,

21

To accurately resolve this

issue, we conducted picosecond (ps) time-resolved PL experiments using 2p excitation at 820 nm for FAPbBr3 (FA stands for formamidinium) single crystal as seen in Figure 1. The measurements were conducted at different fluences varying from 10.59 µJ·cm-2 to 31.77 µJ·cm-2 (see Table S2). The volume density of photo-generated carriers following 2p excitation was calculated using the nonlinear absorption coefficient of perovskite single crystal.22 Generally, the extracted spectra at different times for FAPbBr3 (Figure 1), and FAPbI3 (Figure 2) show negligible PL shift with time due to absence of ion redistribution or migration at the crystal bulks.10 The PL emission decay at each excitation density was fitted by a bi-exponential function, providing fast and slow lifetimes, which is consistent with the literature for such observation.14 The inset of Figure 1 shows the PL decay at the low excitation fluence with two


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lifetimes of ca. 17 and ca. 72 µs. For statistical purposes and to minimize the degree of fluctuations between different measurements, we conducted a global fit with fixed lifetime parameters for a range of excitation densities. We were able to fit all kinetics with two lifetimes of ca. 12 µs and 65 µs as shown in Table S2, attesting to the uniformity of the extracted lifetimes. It is worth mentioning that penetration depth decreases as the fluence of 2p excitation increases. So it is intuitive to assume that the increase in amplitude for the short-lifetime component as the fluence increase (see Table S2 of the Supporting Information) can be attributed to the surface layer domain with large amount of traps. Thus, the faster lifetime component has been attributed to the Shockley-Read-Hall recombination process that is due to presence of the surface non-radiative defects (see Figure S1).23

Figure 2. 2D-pseudo color transient emission map for FAPbI3 single crystal, excited by 2p, 940 nm. The extracted kinetic trace with the bi-exponential fit are in the inset figure. The extracted spectra at different time slots are shown to the right hand side.


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The extracted PL spectra for FAPbBr3 at time zero show a blue shift of the emission maxima from 577.5 nm to 571.5 nm upon increase of excitation fluence from 10.59 µJ·cm-2 to 31.77 µJ·cm-2 (see Figure S2). This shift is attributed to the re-absorption effect that is present upon different penetration depth of the 2p laser excitation. After correction for the re-absorption10, this shift is minimized to be ca. 1.5 nm (see Figure S3). The 1.5 nm shift between corrected emission spectra in Figure S4, can be attributed to the presence of a defect layer similar to what was observed for red mercuric iodide single crystal using 2p excitation.24 Note that the negative portion of the difference spectrum in Figure S4 is due to that the corrected emission spectrum. Accordingly, we could distinguish the time-resolved PL stemming from charge recombination processes from the effects of photon recycling (see Figure S4). Therefore, two kinetic traces at the two extreme sides of the transient emission spectra of FAPbBr3 were extracted and compared to investigate the influence of the re-absorption process on the recombination lifetime. The two kinetic traces at 558 and 600 nm present similar exponential decay, which exclude any significant influence of re-absorption on the intrinsic diffusion length of photo-generated carriers (see Figure S5). Thus, the longer lifetime of ca. 72 µs is attributable to the intrinsic emissive lifetime of the charge recombination process, representing the longest radiative carrier lifetime reported to date for fresh perovskite materials at low excitation fluence. It is worth pointing out that age and the quality of the crystal as well as the excitation fluence can significantly influence the carrier lifetimes.9, 10, 25 Notably, the carrier recombination between photo-generated carriers and traps present inside the single crystal dominates due to low fluence (10-30 µJ·cm-2) used in our measurements.26 However, due to the minority of traps present inside the crystals bulk, the photo-generated carriers diffuse until meeting each other and show luminescence with long


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lifetime. In other words, since the bulk is almost a trap free-zone, the photo-generated charges even at low fluence undergoes bimolecular radiative recombination which arises from direct band-to-band electron−hole recombination. To explore the impact of the organic cation and halide on the radiative carrier recombination dynamics in perovskites, we also studied single crystals of MAPbBr3 (MA stands for methyl ammonium), FAPbI3, and MAPbI3 under the same excitation conditions. The steady state measurements of these single crystals are shown in Figure S9 of the Supporting Information. Note that we have almost zero absorption contribution at 940 nm for the iodide crystals. In this case, the contribution from 1p excitation at 940 nm is negligible. Interestingly, we found that the longest PL lifetime observed for MAPbBr3 single crystal (see Figure S6) was 2.0 µs, demonstrating the importance and the impact of organic cations on the radiative carrier recombination of these single crystals.9 On the other hand we recorded longest PL lifetimes of 4.3 µs (shown in Figure 2) and 0.43 µs for FAPbI3 and MAPbI3 single crystals, respectively, which are over an order of magnitude shorter than the lifetimes of MAPbBr3 and FAPbBr3 single crystals, respectively (see Figure S7). This observation clearly indicates that the halides with different defects activation energy can significantly impact the radiative carrier recombination dynamics as well (vide infra). Carrier diffusion lengths can be estimated from the low fluence PL lifetimes and previously established values of carrier mobility (µ)9 using the following relation: 𝑘𝐵 𝑇 𝐿𝐷 = √ × 𝜇𝜏 𝑒

(1)

where kB is Boltzman’s constant, T is temperature in kelvin, and e is the electron charge. Unlike lifetimes, carrier mobility values for single crystals have by and large been consistently reported within the same order. Thus, typical mobilities of 62 cm2·V−1·s−1 for FAPbBr3 and 35


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cm2·V−1·s−1 for FAPbI3, when combined with their respective lifetimes (72 µs for FAPbBr3 and 4.3 µs for FAPbI3)27 yield carrier diffusion lengths of 107 µm and 19.7 µm, respectively, which are so far the largest carrier diffusion lengths in perovskites obtained from direct radiative charge carrier lifetime measurements. It should be noted that our method here provides the most accurate and direct approach to measure carrier diffusion lengths (unlike the indirect and less reliable methods such as time-resolved microwave conductance (TRMC) and steady-state photoconductance decay measurements which tend to report hundreds of µm carrier diffusion lengths It is worth mentioning that the carrier mobility values (FAPbBr3: 62 cm2·V−1·s−1 and FAPbI3: 35 cm2·V−1·s−1) used herein for estimating the diffusion length are consistent with other recently reported values. Thus, the diffusion length value is mainly dependent on the radiative lifetime in our case. Given the large differences between the lifetimes (and consequently carrier diffusion lengths) between FAPbBr3 and FAPbI3, we sought to understand the role of halides in those large variations. The long radiative lifetime of hybrid perovskite single crystals can be attributed to one or a combination of the following factors: the presence of ferroelectric domains28, the formation of large polarons resulting from cations reorientations (protecting the charge carriers from carrier-carrier scattering)29, 30, and the indirect-band recombination due to strong spin-orbit couplings.31 However, the last factor can be excluded for explaining the different radiative recombination rates between FAPbBr3 and FAPbI3 since these two crystals have the same cubic symmetry.9,

31

Moreover, these hybrid perovskites have the same degree of electron-phonon

coupling strength.32 Therefore, to understand the large variation of charge diffusion lengths between the various investigated single crystals, we performed density functional theory (DFT)


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calculations on defects energy formation in these crystals, which become the dominant scattering path for reducing the charge carrier diffusion length.

Figure 3. The defect formation energies of FA and halogen (Br or I) vacancies as functions of electron Fermi levels under three different conditions for FAPbBr3: (a) µBr = 0 eV, µFA = -3.27 eV, µPb = -3.16 eV, (b) µBr = -0.79 eV, µFA = -2.46 eV, µPb = -1.60 eV, and (c) µBr = -1.67 eV, µFA = -1.43 eV, µPb = 0 eV; and for FAPbI3: (a) µI = 0 eV, µFA = -2.39eV, µPb = -2.54 eV, (b) µI = -0.63 eV, µFA = -1.78 eV, µPb = -1.24 eV, and (c) µI = -1.16 eV, µFA = -1.43 eV, µPb = 0 eV.

Here, we considered the dominant vacancy defects (i.e. VMA and VX, X=Br or I) and chosen three chemical potential points, A, B, and C, to represent different growth environments that might lead to structural defects: A refers to a Br(I)-rich/Pb-poor condition, C refers a Br(I)poor/Pb-rich condition, and B is in the middle between A and C and corresponds to a moderate growth condition. Figure 3 shows the formation energy of the considered vacancy defects as a


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function of Fermi level at the three chemical potentials and Table 1 lists the formation energies of these vacancy defects. The optimized supercell structures with vacancy defects are shown in Figure S8 of the Supporting Information. Under Br(I)-rich/Pb-poor condition (A point), VFA in both FAPbBr3 and FAPbI3 has the lowest formation energy of 0.16 and 0.19 eV, respectively, which becomes the dominant defect. At B and C points, the dominant defect is also VFA, but the formation energy increases to 0.65 and 1.68 eV for FAPbBr3 and 0.41 and 0.77 eV for FAPbI3.

Table 1. The calculated formation energies (in eV) of FA and halogen (Br or I) vacancies for FAPbBr3 and FAPbI3 at the three chosen chemical potential points A, B and C at zero point Fermi Energies. VFA

VFA

VBr

VI

(FAPbBr3)

(FAPbI3)

(FAPbBr3)

(FAPbI3)

A

0.16

0.19

2.74

1.39

B

0.65

0.41

3.53

0.76

C

1.68

0.77

4.41

0.23

Therefore, the VFA defect concentration in the Br (I)-poor is much smaller than that in the Br(I)-rich condition. On the other hand, under Br(I)-poor condition, VI become the dominant defect for FAPbI3, with a formation energy of 0.23 eV. In all three conditions, VBr in FAPbBr3 has a much larger formation energies (> 2 eV) than V I in FAPbI3, indicating that FAPbBr3 has much lower halogen defect concentration than FAPbI3 (see Table 1). Also, by comparing the experimental results with the theoretical ones, case B and C are more appropriate to illustrate the differences measured in diffusion lengths between FAPbBr3 and FAPbI3. Thus, FAPbBr3 should


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intrinsically have rather low non-radiative recombination rate due to lower vacancy defect concentration, which will decrease the charge carrier-defects scattering and thus increase the charge carrier diffusion length. In conclusion, lifetimes of 71.8 and 4.33 µs for FAPbBr3 and FAPbI3 perovskites single crystals have been recorded upon 2p excitation, respectively, representing the longest radiative carrier lifetime reported to date for perovskite materials. More importantly, sub-millimeter and tens of µm carrier diffusion length for FAPbBr3 and FAPbI3 perovskites single crystals was extracted, representing the longest carrier diffusion lengths measured directly from radiative carrier recombination. This long carrier diffusion length especially in FAPbBr3 single crystal is attributed to the high defects formation energy as illustrated by the DFT calculations. These findings provide not only the most reliable carrier diffusion lengths for perovskite single crystal, but perhaps more importantly demonstrate the key role of the cation units and halide ion in modulating carrier lifetime and diffusion lengths in perovskites.

ASSOCIATED CONTENT ACKNOWLEDGMENT The authors gratefully acknowledge funding support from KAUST, Technology Innovation Center for Solid-State Lighting at KAUST. A.M. gratefully acknowledges the support from CRDF Global. Supporting Information. List of materials and instruments used, computational details, tables of reported lifetimes for perovskite, fitting parameters; figures of kinetic traces and extracted emission spectra for the perovskite single crystals.


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AUTHOR INFORMATION Notes The authors declare no competing financial interests. REFERENCES (1) Grätzel, M. The Light and Shade of Perovskite Solar Cells. Nat. Mater. 2014, 13, 838-842. (2) Bisquert, J.; Qi, Y. B.; Ma, T. L.; Yan, Y. F. Advances and Obstacles on Perovskite Solar Cell Research from Material Properties to Photovoltaic Function. ACS Energy Lett. 2017, 2, 520523. (3) 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. (4) Gonzalez-Pedro, V.; Juarez-Perez, E. J.; Arsyad, W. S.; Barea, E. M.; Fabregat-Santiago, F.; Mora-Sero, I.; Bisquert, J. General Working Principles of CH3NH3PbX3 Perovskite Solar Cells. Nano Lett. 2014, 14, 888-893. (5) National Renewable Energy Laboratory. Research Cell Record Efficiency Chart. https://www.nrel.gov/pv/assets/images/efficiency-chart.png (accessed Augest 1st, 2017). (6) Simpson, M. J.; Doughty, B.; Yang, B.; Xiao, K.; Ma, Y.-Z. Imaging Electronic Trap States in Perovskite Thin Films with Combined Fluorescence and Femtosecond Transient Absorption Microscopy. J. Phys. Chem. Lett. 2016, 7, 1725-1731. (7) Dong, Q.; Fang, Y.; Shao, Y.; Mulligan, P.; Qiu, J.; Cao, L.; Huang, J. Electron-Hole Diffusion Lengths > 175 μm in Solution-Grown CH3NH3PbI3 Single Crystals. Science 2015, 347, 967-970. (8) Bi, Y.; Hutter, E. M.; Fang, Y. J.; Dong, Q. F.; Huang, J. S.; Savenije, T. J. Charge Carrier Lifetimes Exceeding 15 µs in Methylammonium Lead Iodide Single Crystals. J. Phys. Chem. Lett. 2016, 7, 923-928. (9) Zhumekenov, A. A.; Saidaminov, M. I.; Haque, M. A.; Alarousu, E.; Sarmah, S. P.; Murali, B.; Dursun, I.; Miao, X.-H.; Abdelhady, A. L.; Wu, T., et al. Formamidinium Lead Halide Perovskite Crystals with Unprecedented Long Carrier Dynamics and Diffusion Length. ACS Energy Lett. 2016, 1, 32-37.


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Ultralong Radiative States in Hybrid Perovskite ... - ACS Publications

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