Supporting Information for Effect of Cation Rotation on Charge ...
Supporting Information for
Effect of Cation Rotation on Charge Dynamics in Hybrid Lead Halide Perovskites María C. Gélvez-Rueda1, Duyen H. Cao2, Sameer Patwardhan2, Nicolas Renaud1, Constantinos C. Stoumpos2, George C. Schatz2, Joseph T. Hupp2,3, Omar K. Farha2,4, Tom J. Savenije1, Mercouri G. Kanatzidis2,3, and Ferdinand C. Grozema1 1
Delft University of Technology, Delft, 2628BL, The Netherlands. 2
3
Northwestern University, Evanston, IL 60208, United States.
Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, United States 4
Department of Chemistry, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
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Bulk materials
Figure S1. Photograph of CH3NH3PbX3 (X = I, Br, Cl) powder materials Characterization of CH3NH3PbX3 (X= I, Br, Cl) and mixed CH3NH3PbI3-xBrx perovskites
Figure S2. XRD patterns of CH3NH3PbX3 and CH3NH3PbI3-xBrx
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Figure S3. SEM image of polycrystalline CH3NH3PbI3 bulk material
Figure S4. Optical bandgaps of powder materials of CH3NH3PbX3 perovskites Charge carrier properties of MAPbCl3 determined by PR-TRMC
Figure S5 Conductivity transients and mobility for CH3NH3PbCl3(c) at different temperatures. The mobility of MAPbCl3 (~0.07 cm2V-1s-1) is one order of magnitude lower than the mobility of the other perovskites (~2 cm2V-1s-1). In addition, the mobility and half-lifetime temperature trends for MAPbCl3 are unclear. As the temperature decreases, the mobility
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seems to increase following band-like transport while the half-lifetime remains constant. But after the β/γ phase transition both carrier mobility and lifetime drop. In order to rationalize this much lower mobility, we performed Density Functional Theory (DFT) calculations of the electronic structure of MAPbX3 (X=I, Br, Cl) (see Figure S6 and Table S1). Similar to other DFT calculations1, the effective masses of electrons and holes in all compounds were found to be rather similar. As a consequence, DFT calculations do not show a fundamental reason for this behavior. The lower mobility of MAPbCl3 may be caused by possible defects (diffusion of halide ions as interstitial defects)2-3 not seen in XRD measurements. However, why chloride diffusion in MAPbCl3 would affect more the mobility of the charges than Iodine or Bromine diffusion in MAPbI3 and MAPbBr3 is still unclear. A detailed study of the activation energy for halogen migration in MAPbX3 (X=I, Br, Cl) perovskites is out of the scope of this paper.
Figure S6. Band structure calculation of (CH3NH3)PbX3 (X=I, Br, Cl) perovskites
Table S1. Effective mass of charge carriers of CH3NH3PbX3 (X=I, Br, Cl) perovskites MAPbI3 m1 m2 m3 m⇤
hole -0.129 -0.172 -0.189 -0.159
elec 0.841 0.767 0.139 0.310
MAPbBr3 hole elec -0.148 1.034 -0.181 0.891 -0.190 0.112 -0.171 0.272 m⇤ = 3
✓
1 1 1 + + m1 m2 m3
◆
MAPbCl3 hole elec -0.187 2.411 -0.213 1.582 -0.246 0.107 -0.213 0.289 1
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Mobility of CH3NH3PbX3 (X= I, Br, Cl) and mixed CH3NH3PbI3-xBrx perovskites
Figure S7. Charge carrier mobilities of CH3NH3PbX3 (X=I, Br, Cl) and mixed CH3NH3PbI3-xBrx perovskites as a function of temperature Mobility of CsPbBr3
Figure S8. Charge carriers mobility and half-lifetime of CsPbBr3 as a function of temperature.
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Charge carrier dynamics model Based on previous analogous models4-5 and the experimental data, the model designed includes the following processes: •
Generation of charge carriers (1),
•
Second order bimolecular recombination (radiative recombination function of the amount of charges created) (2),
•
Second order charge trapping with a limited amount of traps (trap filling is a function of the amount of traps available) (3), and
•
Second order recombination with trapped charges (4).
Figure S9. Schematic charge carriers’ dynamics model
The concentration of charge carriers (electrons in the conduction band, holes in the valence band), and filled traps in time are determined as function of rates at which the processes previously mentioned occur. The generation rate (k1) is function of the irradiation dose (D), the pair formation energy (Ep) and the perovskite density in the PR-TRMC sample holder. A schematic representation of the different rates in the model is shown in Figure S10.
Figure S10. Schematic recombination rates on the charge carriers’ dynamics model
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The differential equations that describe this system of rate processes are listed below. They describe the variation in time of the electron concentration in the valence band (nh), in the conduction band (ne) and in trap states (nT). A finite concentration of trap states (Nt) is defined in the system. The generation profile (Gp) is limited by the electron pulse length and represents the total amount of charge in the pulse. Gp is nonzero only for the duration of the (rectangular) excitation pulse. In addition, the system is assumed to be fully homogeneous in concentration. This means that every charge carrier experiences the same rate dynamics. 𝑑𝑛! = −𝐺! 𝑡 𝑘! + 𝑘! 𝑛! 𝑛! + 𝑘! 𝑛 ! 𝑛! 𝑑𝑡 𝑑𝑛! = 𝐺! 𝑡 𝑘! − 𝑘! 𝑛! 𝑛! − 𝑘! 𝑛! 𝑑𝑡
𝑁! − 𝑛 !
𝑑𝑛 ! = 𝑘! 𝑛! 𝑑𝑡
𝑁! − 𝑛 !
− 𝑘! 𝑛 ! 𝑛!
Finally, knowing the electron and hole concentrations in time, the change in conductivity in time was calculated defining the mobility of electrons and holes separately according to Equation 1. The mobilities defined in the model are different from the sum of the mobilities experimentally determined by PR-TRMC since it is possible to discriminate between the positive and negative charges. This feature was included in the model in order to obtain more information regarding the charge carrier dynamics. The kinetic scheme implemented is a set of coupled differential equations, where only the electrons in the conduction band and holes in the valence band contribute to the pulse induced change in conductivity. We find that for each sample a unique set of kinetic parameters is able to reproduce all PRTRMC transients with different initial concentration of charges (different pulse lengths). ∆𝜎 = 𝑒 𝑛! 𝜇! + 𝑛! 𝜇! Equation 1
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References 1. Berdiyorov, G. R.; El-Mellouhi, F.; Madjet, M. E.; Alharbi, F. H.; Peeters, F. M.; Kais, S., Effect of Halide-Mixing on the Electronic Transport Properties of Organometallic Perovskites. Sol Energ Mat Sol C 2016, 148, 2-10. 2. Hoke, E. T.; Slotcavage, D. J.; Dohner, E. R.; Bowring, A. R.; Karunadasa, H. I.; McGehee, M. D., Reversible Photo-Induced Trap Formation in Mixed-Halide Hybrid Perovskites for Photovoltaics. Chem Sci 2015, 6, 613-617. 3. Eames, C.; Frost, J. M.; Barnes, P. R. F.; O'Regan, B. C.; Walsh, A.; Islam, M. S., Ionic Transport in Hybrid Lead Iodide Perovskite Solar Cells. Nat Commun 2015, 6. 4. Hutter, E. M.; Eperon, G. E.; Stranks, S. D.; Savenije, T. J., Charge Carriers in Planar and Meso-Structured Organic-Inorganic Perovskites: Mobilities, Lifetimes, and Concentrations of Trap States. J Phys Chem Lett 2015, 6, 3082-3090. 5. Stranks, S. D.; Burlakov, V. M.; Leijtens, T.; Ball, J. M.; Goriely, A.; Snaith, H. J., Recombination Kinetics in Organic-Inorganic Perovskites: Excitons, Free Charge, and Subgap States. Physical Review Applied 2014, 2.
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Effect of Cation Rotation on Charge Dynamics in Hybrid Lead Halide Perovskites María C. Gélvez-Rueda1, Duyen H. Cao2, Sameer Patwardhan2, Nicolas Renaud1, Constantinos C. Stoumpos2, George C. Schatz2, Joseph T. Hupp2,3, Omar K. Farha2,4, Tom J. Savenije1, Mercouri G. Kanatzidis2,3, and Ferdinand C. Grozema1 1
Delft University of Technology, Delft, 2628BL, The Netherlands. 2
3
Northwestern University, Evanston, IL 60208, United States.
Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, United States 4
Department of Chemistry, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
S1
Bulk materials
Figure S1. Photograph of CH3NH3PbX3 (X = I, Br, Cl) powder materials Characterization of CH3NH3PbX3 (X= I, Br, Cl) and mixed CH3NH3PbI3-xBrx perovskites
Figure S2. XRD patterns of CH3NH3PbX3 and CH3NH3PbI3-xBrx
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Figure S3. SEM image of polycrystalline CH3NH3PbI3 bulk material
Figure S4. Optical bandgaps of powder materials of CH3NH3PbX3 perovskites Charge carrier properties of MAPbCl3 determined by PR-TRMC
Figure S5 Conductivity transients and mobility for CH3NH3PbCl3(c) at different temperatures. The mobility of MAPbCl3 (~0.07 cm2V-1s-1) is one order of magnitude lower than the mobility of the other perovskites (~2 cm2V-1s-1). In addition, the mobility and half-lifetime temperature trends for MAPbCl3 are unclear. As the temperature decreases, the mobility
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seems to increase following band-like transport while the half-lifetime remains constant. But after the β/γ phase transition both carrier mobility and lifetime drop. In order to rationalize this much lower mobility, we performed Density Functional Theory (DFT) calculations of the electronic structure of MAPbX3 (X=I, Br, Cl) (see Figure S6 and Table S1). Similar to other DFT calculations1, the effective masses of electrons and holes in all compounds were found to be rather similar. As a consequence, DFT calculations do not show a fundamental reason for this behavior. The lower mobility of MAPbCl3 may be caused by possible defects (diffusion of halide ions as interstitial defects)2-3 not seen in XRD measurements. However, why chloride diffusion in MAPbCl3 would affect more the mobility of the charges than Iodine or Bromine diffusion in MAPbI3 and MAPbBr3 is still unclear. A detailed study of the activation energy for halogen migration in MAPbX3 (X=I, Br, Cl) perovskites is out of the scope of this paper.
Figure S6. Band structure calculation of (CH3NH3)PbX3 (X=I, Br, Cl) perovskites
Table S1. Effective mass of charge carriers of CH3NH3PbX3 (X=I, Br, Cl) perovskites MAPbI3 m1 m2 m3 m⇤
hole -0.129 -0.172 -0.189 -0.159
elec 0.841 0.767 0.139 0.310
MAPbBr3 hole elec -0.148 1.034 -0.181 0.891 -0.190 0.112 -0.171 0.272 m⇤ = 3
✓
1 1 1 + + m1 m2 m3
◆
MAPbCl3 hole elec -0.187 2.411 -0.213 1.582 -0.246 0.107 -0.213 0.289 1
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Mobility of CH3NH3PbX3 (X= I, Br, Cl) and mixed CH3NH3PbI3-xBrx perovskites
Figure S7. Charge carrier mobilities of CH3NH3PbX3 (X=I, Br, Cl) and mixed CH3NH3PbI3-xBrx perovskites as a function of temperature Mobility of CsPbBr3
Figure S8. Charge carriers mobility and half-lifetime of CsPbBr3 as a function of temperature.
S5
Charge carrier dynamics model Based on previous analogous models4-5 and the experimental data, the model designed includes the following processes: •
Generation of charge carriers (1),
•
Second order bimolecular recombination (radiative recombination function of the amount of charges created) (2),
•
Second order charge trapping with a limited amount of traps (trap filling is a function of the amount of traps available) (3), and
•
Second order recombination with trapped charges (4).
Figure S9. Schematic charge carriers’ dynamics model
The concentration of charge carriers (electrons in the conduction band, holes in the valence band), and filled traps in time are determined as function of rates at which the processes previously mentioned occur. The generation rate (k1) is function of the irradiation dose (D), the pair formation energy (Ep) and the perovskite density in the PR-TRMC sample holder. A schematic representation of the different rates in the model is shown in Figure S10.
Figure S10. Schematic recombination rates on the charge carriers’ dynamics model
S6
The differential equations that describe this system of rate processes are listed below. They describe the variation in time of the electron concentration in the valence band (nh), in the conduction band (ne) and in trap states (nT). A finite concentration of trap states (Nt) is defined in the system. The generation profile (Gp) is limited by the electron pulse length and represents the total amount of charge in the pulse. Gp is nonzero only for the duration of the (rectangular) excitation pulse. In addition, the system is assumed to be fully homogeneous in concentration. This means that every charge carrier experiences the same rate dynamics. 𝑑𝑛! = −𝐺! 𝑡 𝑘! + 𝑘! 𝑛! 𝑛! + 𝑘! 𝑛 ! 𝑛! 𝑑𝑡 𝑑𝑛! = 𝐺! 𝑡 𝑘! − 𝑘! 𝑛! 𝑛! − 𝑘! 𝑛! 𝑑𝑡
𝑁! − 𝑛 !
𝑑𝑛 ! = 𝑘! 𝑛! 𝑑𝑡
𝑁! − 𝑛 !
− 𝑘! 𝑛 ! 𝑛!
Finally, knowing the electron and hole concentrations in time, the change in conductivity in time was calculated defining the mobility of electrons and holes separately according to Equation 1. The mobilities defined in the model are different from the sum of the mobilities experimentally determined by PR-TRMC since it is possible to discriminate between the positive and negative charges. This feature was included in the model in order to obtain more information regarding the charge carrier dynamics. The kinetic scheme implemented is a set of coupled differential equations, where only the electrons in the conduction band and holes in the valence band contribute to the pulse induced change in conductivity. We find that for each sample a unique set of kinetic parameters is able to reproduce all PRTRMC transients with different initial concentration of charges (different pulse lengths). ∆𝜎 = 𝑒 𝑛! 𝜇! + 𝑛! 𝜇! Equation 1
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References 1. Berdiyorov, G. R.; El-Mellouhi, F.; Madjet, M. E.; Alharbi, F. H.; Peeters, F. M.; Kais, S., Effect of Halide-Mixing on the Electronic Transport Properties of Organometallic Perovskites. Sol Energ Mat Sol C 2016, 148, 2-10. 2. Hoke, E. T.; Slotcavage, D. J.; Dohner, E. R.; Bowring, A. R.; Karunadasa, H. I.; McGehee, M. D., Reversible Photo-Induced Trap Formation in Mixed-Halide Hybrid Perovskites for Photovoltaics. Chem Sci 2015, 6, 613-617. 3. Eames, C.; Frost, J. M.; Barnes, P. R. F.; O'Regan, B. C.; Walsh, A.; Islam, M. S., Ionic Transport in Hybrid Lead Iodide Perovskite Solar Cells. Nat Commun 2015, 6. 4. Hutter, E. M.; Eperon, G. E.; Stranks, S. D.; Savenije, T. J., Charge Carriers in Planar and Meso-Structured Organic-Inorganic Perovskites: Mobilities, Lifetimes, and Concentrations of Trap States. J Phys Chem Lett 2015, 6, 3082-3090. 5. Stranks, S. D.; Burlakov, V. M.; Leijtens, T.; Ball, J. M.; Goriely, A.; Snaith, H. J., Recombination Kinetics in Organic-Inorganic Perovskites: Excitons, Free Charge, and Subgap States. Physical Review Applied 2014, 2.
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