Supporting Information. Ultralong Radiative States in Hybrid Perovskite Crystals: Compositions for Submillimeter Diffusion Lengths

Transcription

1 Supporting Information Ultralong Radiative States in Hybrid Perovskite Crystals: Compositions for Submillimeter Diffusion Lengths Erkki Alarousu, 1 Ahmed M. El-Zohry, 1 Jun Yin, 1 Ayan A. Zhumekenov, 1 Chen Yang, 1 Esra Alhabshi, 2 Issam Gereige, 2 Ahmed AlSaggaf, 2 Anton V. Malko, 3 Osman M. Bakr, 1,4 * and Omar F. Mohammed 1, * 1 KAUST Solar Center, King Abdullah University of Science and Technology, Division of Physical Sciences and Engineering, Thuwal , Kingdom of Saudi Arabia 2 Saudi Aramco Research & Development Center, Dhahran 31311, Kingdom of Saudi Arabia 3 Department of Physics, the University of Texas at Dallas, Richardson, TX, 75080, USA 4 KAUST Catalysis Center, King Abdullah University of Science and Technology (KAUST), Thuwal , Saudi Arabia Corresponding Author osman.bakr@kaust.edu.sa and omar.abdelsaboor@kaust.edu.sa S1

2 Materials and Methods Lead bromide ( 98%), lead iodide (99.999% trace metal basis), DMF (anhydrous, 99.8%) and GBL ( 99%) were purchased from Sigma Aldrich. FABr, MABr, FAI and MAI were purchased from Dyesol Ltd (Australia). All salts and solvents were used as received without any further purification. FAPbBr 3, FAPbI 3, MAPbBr 3 and MAPbI 3 perovskite single crystals were grown by inverse temperature crystallization (ITC) following previously reported procedures. 1-2 The XRD, SEM, optical images, and I- V measurements of the studies single crystals can be found in our previous work. 2-5 The streak camera setup has been described previously in details, using the laser repetition rate of 1kHz. 4 Computational Methods The density functional theory (DFT) calculations were carried out by using PWSCF code as implemented in the Quantum ESPRESSO (QE) package. 6 The generalized gradient approximation (GGA) of Perdew- Burke-Ernzerhof (PBE) exchange-correlation functional with ultrasoft pseudopotentials were used. The plane-wave basis set cutoffs of the wavefunctions and the charge density were set at 50 and 300 Ry, respectively. A uniform grid of k-mesh in the Brillouin zone was employed to optimize the crystal structures and obtain the electronic band structures for FAPbBr 3 and FAPbI 3. The van der Waals functional vdw-df2, 7-8 which self-consistently accounts for dispersion effects, was also used for the structural optimizations. The optimized crystal parameters of cubic phase for FAPbBr 3 and FAPbI 3 are: a = 6.31 Å, b = 6.08 Å, c = 6.23 Å and a = 6.69 Å, b = 6.50 Å, c = 6.60 Å, respectively. A supercell containing 324 atoms was used for the defect calculations, and the Brillouin zone was sampled by the Γ point. The atomic positions of FAPbBr 3 and FAPbI 3 supercells with defects were fully relaxed until the supercell with forces on each atom less than 1 ev/å. The defect formation energies, ΔH(α,q), for the supercells containing the relax defect α at charge state q can be determined by: ΔH(α, q) = E(α, q) E(host) + n i (E i + μ i ) + q(e VBM (host) + E F ) where E(α, q) is the total energy of the supercell containing the defect, and E(host) is the total energy of the host supercell without a defect. μ i is the chemical potential of constituent i referenced to elemental solid or molecule with energy E i. Here, the µ FA is referred to a quasi-bcc artificial structure constituent of formamidinium, the µ Br or µ I is referred to Br 2 or I 2 solid phase with a Cmca symmetry, the µ Pb is referred to the fcc Pb solid phase. E VBM (host) is the valence band maximum (VBM) of perfect supercell and E F is the Fermi energy measured from VBM. The n i is the number of atoms taken out of the supercell to form S2

3 the defects, and q is the number of electrons transferred from the supercell to the Fermi reservoirs in forming the defective supercell. In the equilibrium growth conditions, the chemical potential μ i should satisfy the following equations to avoid the formation of second phases such as FAX, PbX 2 (X=Br or I), and elemental solids 9 : μ FA + μ Pb + 3μ X = ΔH(FAPbX 3 ) = 6.44 ev (FAPbBr 3 ); 4.92 ev (FAPbI 3 ) μ Pb + 2μ X < ΔH(PbX 2 ) = 3.25 ev (FAPbBr 3 ); 2.43 ev (FAPbI 3 ) μ FA + μ X < ΔH(FAX) = 3.01 ev (FAPbBr 3 ); 2.59eV (FAPbI 3 ) μ FA < 0 ev, μ X < 0 ev, μ Pb < 0 ev where ΔH(FAPbX 3 ) (X=Br or I) is the formation enthalpy of FAPbX 3 defined as the total energy difference ΔH(FAPbX 3 ) = E(FAPbX 3 )-E(FA)-E(Pb)-3E(X), ΔH(PbX 2 ) is the formation enthalpy of PbX 2 defined as the total energy difference ΔH(PbX 2 ) = E(PbX 2 )-E(Pb)-2E(X), and ΔH(FAX) is the formation enthalpy of FAX defined as the total energy difference ΔH(FAX) = E(FAX)-E(FA)-E(X). Here the cubic NaCl structure was used for FAX containing 4 formulas; an orthorhombic structure for PbBr 2 ; a layered hexagonal structure for PbI 2. Our DFT calculations show that the decompose energy for cubic FAPbBr 3 and FAPbI 3 is only ~0.10 ev. Consequently, defect formation energies are not well defined under equilibrium growth conditions because under no chemical potential conditions both FAPbBr 3 and FAPbI 3 are stable compounds under equilibrium growth conditions. Thus, we consider the growth under non-equilibrium conditions in the main text. Table S1. Comparison of reported lifetimes for single crystals of perovskite materials. Material Technique Lifetime References MAPbI 3 Streak Camera 83 ns MAPbI 3 Transient photovoltage 82 µs MAPbBr 3 Transient reflectance 31 ns MAPbBr 3 Single photon counting 1.2 µs FAPbI 3 Single photon counting 0.48 µs S3

4 Table S2. Fitting values for PL kinetic traces of FAPbBr 3 at different excitation densities. Times are in microseconds and amplitudes (A) are in percent. The photo-generated carriers by 2P at low excitation fluence are calculated as described previously. 15 Fluence (µj.cm -2 ) Photo-generated Carriers (10 11 cm -3 ) τ 1 (µs) (A %) τ 2 (µs) (A %) (46) 65 (54) (56) 65 (44) (57) 65 (43) (56) 65 (44) (59) 65 (41) 1 FAPbBr 3 emission decay vs. excitation fluence values in ( J/cm Time ( s) Figure S1. Emission kinetic decays of FAPbBr 3 single crystal at different pump fluences. S4

5 0.8 Emission Time µj/cm µj/cm 2 Fitting Fitting Wavelength (nm) Figure S2. Extracted emission spectra of FAPbBr 3 at time zero upon changing excitation fluence. 0.8 Emission Time Zero After µj/cm µj/cm Wavelength (nm) Figure S3. Extracted emission spectra of FAPbBr 3 at time zero after re-absorption correction upon changing excitation power. S5

6 0.8 Emission Time µj/cm 2 Before correction After correction Difference Wavelength (nm) Figure S4. Difference Emission Spectra before and after re-absorption correction for FAPbBr 3 crystal. FAPbBr 3 emission µj/cm nm Time ( s) Figure S5. Emission kinetic decays of FAPbBr 3 at two different wavelengths. S6

7 MAPbBr 3 s (68 %) s (32 %) 2-exp fit Time ( s) Figure S6. Emission kinetic decay of MAPbBr 3 excited by 2p, 820 nm. FAPbI 3 1 = 0.74 µs (43%) 2 = 4.33 µs (57%) 0.5 MAPbI 3 1 = 7 µs (6%) 2 = 0.43 µs (94%) 2-exp fit Time (µs) Figure S7. Emission kinetic decay of FAPbI 3 and MAPbI 3 excited by 2p, 940 nm. S7

8 Figure S8. Optimized crystal structures of FAPbBr 3 supercell with (a) Br and (b) FA vacancy and FAPbI 3 supercell with (c) I and (d) FA vacancy. S8

9 Normalized Absorption and Emission Normalized Absorption and Emission MAPbBr 3 FAPbBr MAPbI FAPbI Wavelength (nm) Wavelength (nm) Figure S9. Steady-state absorption (black solid line) and emission (red dotted line) measurements for the studied single crystals. S9

10 References (1) Saidaminov, M. I.; Abdelhady, A. L.; Maculan, G.; Bakr, O. M. Retrograde Solubility of Formamidinium and Methylammonium Lead Halide Perovskites Enabling Rapid Single Crystal Growth. Chem. Comm. 2015, 51, (2) Saidaminov, M. I.; Abdelhady, A. L.; Murali, B.; Alarousu, E.; Burlakov, V. M.; Peng, W.; Dursun, I.; Wang, L. F.; He, Y.; Maculan, G., et al. High-Quality Bulk Hybrid Perovskite Single Crystals within Minutes by Inverse Temperature Crystallization. Nat. Commun. 2015, 6, (3) 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, (4) Sarmah, S. P.; Burlakov, V. M.; Yengel, E.; Murali, B.; Alarousu, E.; El-Zohry, A. M.; Yang, C.; Alias, M. S.; Zhumekenov, A. A.; Saidaminov, M. I., et al. Double Charged Surface Layers in Lead Halide Perovskite Crystals. Nano Lett. 2017, 17, (5) Shi, D.; Adinolfi, V.; Comin, R.; Yuan, M.; Alarousu, E.; Buin, A.; Chen, Y.; Hoogland, S.; Rothenberger, A.; Katsiev, K. Low Trap-State Density and Long Carrier Diffusion in Organolead Trihalide Perovskite Single Crystals. Science 2015, 347, (6) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I., et al. Quantum Espresso: A Modular and Open- Source Software Project for Quantum Simulations of Materials. J. Phys.: Condens. Matter 2009, 21, (7) Berland, K.; Cooper, V. R.; Lee, K.; Schroder, E.; Thonhauser, T.; Hyldgaard, P.; Lundqvist, B. I. Van Der Waals Forces in Density Functional Theory: A Review of the vdw-df Method. Rep. Prog. Phys. 2015, 78, (8) Langreth, D. C.; Lundqvist, B. I.; Chakarova-Kack, S. D.; Cooper, V. R.; Dion, M.; Hyldgaard, P.; Kelkkanen, A.; Kleis, J.; Kong, L. Z.; Li, S., et al. A Density Functional for Sparse Matter. J Phys-Condens. Mat. 2009, (9) Yin, W. J.; Shi, T. T.; Yan, Y. F. Unusual Defect Physics in CH 3 NH 3 PbI 3 Perovskite Solar Cell Absorber. Appl. Phys. Lett. 2014, 104, S10

11 (10) Fang, H. H.; Raissa, R.; Abdu-Aguye, M.; Adjokatse, S.; Blake, G. R.; Even, J.; Loi, M. A. Photophysics of Organic-Inorganic Hybrid Lead Iodide Perovskite Single Crystals. Adv. Funct. Mater. 2015, 25, (11) Dong, Q.; Fang, Y.; Shao, Y.; Mulligan, P.; Qiu, J.; Cao, L.; Huang, J. Electron-Hole Diffusion Lengths > 175 μm in Solution-Grown CH 3 NH 3 PbI 3 Single Crystals. Science 2015, 347, (12) Yang, Y.; Yan, Y.; Yang, M. J.; Choi, S.; Zhu, K.; Luther, J. M.; Beard, M. C. Low Surface Recombination Velocity in Solution-Grown CH 3 NH 3 PbBr 3 Perovskite Single Crystal. Nat. Commun. 2015, 6, (13) Fang, Y.; Wei, H.; Dong, Q.; Huang, J. Quantification of Re-Absorption and Re-Emission Processes to Determine Photon Recycling Efficiency in Perovskite Single Crystals. Nat. Commun. 2017, 8, (14) Han, Q. F.; Bae, S. H.; Sun, P. Y.; Hsieh, Y. T.; Yang, Y.; Rim, Y. S.; Zhao, H. X.; Chen, Q.; Shi, W. Z.; Li, G., et al. Single Crystal Formamidinium Lead Iodide (FAPbI 3 ): Insight into the Structural, Optical, and Electrical Properties. Adv. Mater. 2016, 28, (15) Niesner, D.; Schuster, O.; Wilhelm, M.; Levchuk, I.; Osvet, A.; Shrestha, S.; Batentschuk, M.; Brabec, C.; Fauster, T., Temperature-dependent optical spectra of single-crystal (CH 3 NH 3 )PbBr 3 cleaved in ultrahigh vacuum. Phys. Rev. B 2017, 95, S11