At each pressure point, a reference transmission spectrum was collected using the ... Bandgap of FAPbI3 at ambient pressure condition (1 atm). a, collected ...
Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2016.
Supporting Information for Adv. Funct. Mater., DOI: 10.1002/adfm.201604208
Pressure-Induced Bandgap Optimization in Lead-Based Perovskites with Prolonged Carrier Lifetime and Ambient Retainability Gang Liu,* Lingping Kong, Jue Gong, Wenge Yang, Hokwang Mao,* Qingyang Hu, Zhenxian Liu, Richard D. Schaller, Dongzhou Zhang, and Tao Xu*
Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2016.
Supporting Information Pressure-induced Bandgap Optimization in Lead-based Perovskites with Prolonged Carrier Lifetime and Ambient Retainability Gang Liu, Lingping Kong, Jue Gong, Wenge Yang, Ho-kwang Mao, Qingyang Hu, Zhenxian Liu, Richard D. Schaller, Dongzhou Zhang, and Tao Xu
Contents: Supplementary Note: Band gap determination via Tauc plots. Supplementary Figures S1-S16. Supplementary Tables S1-S4. References.
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Supplementary Note: Band gap determination via Tauc plots. Optical absorption measurements have been conducted as a function of pressure for FAPbI3 at various pressures. At each pressure point, a reference transmission spectrum was collected using the silicon oil sample before measuring transmission and then was used to determine a baseline. Supplementary Fig. S1 gives the transmission spectrum of silicon oil measured from 450 nm to 1100 nm at ambient pressure. Clearly, no absorption onset has been observed thus the determination of bandgap of FAPbI3 cannot be affected by the signal of silicon oil. Supplementary Fig. S2(a) shows the transmission spectra of the silicon oil (I0(E)) and FAPbI3 sample (IS(E)) at ambient pressure condition. The transmittance spectrum of FAPbI3 sample can be obtained by1
T ( E) I S ( E) / I 0 ( E) .
(S-1)
Then, the absorbance spectrum of FAPbI3 sample can be derived by1
( E)d log(T ( E)) log( I S ( E) / I 0 ( E)) .
(S-2)
Here, α is absorbance coefficient; d is the sample thickness; T(E) is the transmittance as a function of energy. Supplementary Fig. S2(b) shows the transmittance spectrum of FAPbI3 at ambient condition. The nature of the bandgap can be estimated by examining Tauc plots as2-4
( dhv)2 hv
(S-3)
( dhv)1/2 hv
(S-4)
and
for direct bandgap and indirect bandgap, respectively. Then, the magnitude of bandgap (Eg) can be given by extrapolating the linear portion of the Tauc plot to the baseline. Better linear fits were obtained for the direct bandgap Tauc plots for both FAPbI3 at all pressures. Supplementary Fig. S2(c) gives the direct bandgap magnitude of 1.489 eV at ambient pressure for FAPbI3. 2
Supplementary Figure S1. Collected transmission spectrum of the silicon oil at ambient condition (1 atm). The signal from detector will not affect the bandgap determination.
Supplementary Figure S2. Bandgap of FAPbI3 at ambient pressure condition (1 atm). a, collected transmission spectra of the silicon oil background and FAPbI3 sample (in the oil) at 1 atm. Blue line: silicon oil (background); orange line: FAPbI 3 in silicon oil b, the transmittance spectrum of FAPbI3. c, Tauc plots for FAPbI3. Bandgap magnitude was determined to be 1.489 eV with direct nature.
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Supplementary Figure S3. Bandgap of FAPbI3 in compression from 0.1 GPa to 2.1 GPa.
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Supplementary Figure S4. High-resolution synchrotron XRD pattern measured at 0.4 GPa for as-prepared FAPbI3 sample. The crystal structure can be well fitted using trigonal α-FAPbI3 structure with P3m1 space group symmetry, as evidenced by relative small fitting errors (Rp =1.05%; Rwp =1.55%). Blue open circle: experimental data; red line: calculated result; black line: difference between raw data and refinement; green bar: Bragg bars for P3m1 space group. Rietveld refinements of XRD patterns were accomplished using GSAS program. First, fit the background by running powpref followed by genles action in GSAS interface. Then, a profile-fitting procedure was applied to refine cell parameters and search space group. In this work, we use the ambient structure as the initial structure for all high pressure structure refinements. The final Rietveld refinement including cell parameters and atomic positions were performed to obtain the detailed structural information. The quality of the fitting between the experimental and calculated profile is assessed by the various R parameters including Rp and Rwp.
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Supplementary Figure S5. Charge density of FAPbI3 with P3m1 structures (up: 1 bar; down: 2.1 GPa). Compared to the low pressure structure (1 bar), the case at 2.1 GPa has more electronic charge density overlapping between the Pb and I atoms. Symbols: purple spheres: I atoms, grey atoms: Pb atoms.
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Supplementary Figure S6. Density of states (DOS) of FAPbI3 with a structure of P3m1 at 1 bar.
Supplementary Figure S7. Density of states (DOS) of FAPbI3 with a structure of P3m1 at 0.7 GPa.
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Supplementary Figure S8. Density of states (DOS) of FAPbI3 with a structure of P3m1 at 1.4 GPa.
Supplementary Figure S9. Calculated electronic band structure of FAPbI3 at 1 bar. A direct band gap of 1.62 (0.03) eV was observed, slightly wider than experimental result (1.49 eV).
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Supplementary Figure S10. Calculated electronic band structure of FAPbI3 at 2.1 GPa. A direct band gap of 1.38 (0.03) eV was observed.
Supplementary Figure S11. Calculated pressure-driven bandgap evolution of FAPbI3. Obvious bandgap narrowing was observed, agreeing well with the in-situ high pressure optical experiments.
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Supplementary Figure S12. Optical of FAPbI3 in compression from 2.8 GPa to 7.1 GPa. At 2.8 GPa (a) and 3.4 GPa (b), bandgap magnitude was determined to be 1.362 eV and 1.671 eV, respectively. At 7.1 GPa (c), from the absorbance spectrum, no clear onset can be observed.
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Supplementary Figure S13. Determination of bulk modulus of MAPbI3. by fitting experimental
data
with
the
Birch
relation
V 7 V 5 V 2 3 3 P(V ) B0 [( 0 ) 3 ( 0 ) 3 ]{1+ ( B ' 4)[( 0 ) 3 1]} ,5 where we assume B’=4, the bulk 2 V V 4 V modulus K0 of MAPbI3 was estimated to be 13.6(5) GPa. The structural data of MAPbI 3 are collected from Ref. S6.
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Supplementary Figure S14. Schematic of MA group in compression. Under pressures, CN bond length decreases. Blue ball: C; Yellow ball: N; grey ball: H.
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Supplementary Figure S15. Schematic of FA group in compression. Under pressures, C-N bond length decreases. Besides, N-C=N bond angle decreases, allowing flexible space needed for achieving high compressibility. Blue ball: C; Yellow ball: N; grey ball: H.
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Supplementary Figure S16. Optical micrographs of FAPbI3 in a diamond anvil cell at various pressures (in compression). At 6.0 GPa, the sample becomes red, indicating FAPbI3 cannot totally absorb red light. Thus, the bandgap widening is suggested.
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Supplementary Table S1. Refined lattice parameters for FAPbI3 derived from synchrotron high resolution powder x-ray diffraction at room temperature and various pressures (in compression). Pressure Crystal system Space group
Lattice parameters (Å)
Rp; Rwp
1 atm
Trigonal
P3m1
a = b = 9.000(1); c = 11.073(4)
1.17%; 2.42%
0.4 GPa
Trigonal
P3m1
a = b = 8.791(3); c = 11.057(6)
1.05%; 1.55%
0.7 GPa
Trigonal
P3m1
a = b = 8.726(3); c = 11.044(3)
1.12%; 1.77%
1.0 GPa
Trigonal
P3m1
a = b = 8.691(5); c = 10.978(6)
1.11%; 1.91%
1.3 GPa
Trigonal
P3m1
a = b = 8.617(3); c = 10.895(5)
1.33%; 2.37%
1.7 GPa
Trigonal
P3m1
a = b = 8.571(6); c = 10.832(5)
1.22%; 2.14%
2.0 GPa
Trigonal
P3m1
a = b = 8.551(3); c = 10.784(4)
1.15%; 1.55%
Supplementary Table S2. Bond angles for FAPbI3 derived from synchrotron high resolution powder x-ray diffraction at room temperature and various pressures (in compression). Pressure
Pb2-I1-Pb3 (degrees)
Pb1-I2-Pb2 (degrees)
Pb3-I3-Pb1 (degrees)
1 atm
179.80(8)
179.80(10)
179.88(9)
0.4 GPa
179.95(6)
179.88(10)
179.92(7)
0.7 GPa
179.79(9)
179.86(8)
179.89(6)
1.0 GPa
179.81(11)
179.87(8)
179.87(9)
1.3 GPa
179.85(12)
179.91(7)
179.90(7)
1.7 GPa
179.79(9)
179.86(10)
179.88(9)
2.0 GPa
179.79(8)
179.86(10)
179.88(9)
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Supplementary Table S3. Bond lengths for FAPbI3 derived from synchrotron high resolution powder x-ray diffraction at room temperature and various pressures (in compression). Pressure
Pb1-I2 (Å)
Pb1-I3 (Å)
Pb2-I1 (Å)
Pb2-I2 (Å)
Pb3-I1 (Å)
Pb3-I3 (Å)
1 atm
3.1838(13)
3.1921(11)
3.1828(9)
3.1898(16)
3.1927(11)
3.1798(12)
0.4 GPa
3.1333(15)
3.1413(14)
3.1325(13)
3.1391(18)
3.1419(13)
3.1294(15)
0.7 GPa
3.1193(14)
3.1272(13)
3.1184(10)
3.1250(17)
3.1278(12)
3.1154(12)
1.0 GPa
3.1023(15)
3.1102(17)
3.1015(12)
3.1080(15)
3.1108(14)
3.0984(14)
1.3 GPa
3.0769(14)
3.0847(13)
3.0761(13)
3.0825(14)
3.0853(12)
3.0731(15)
1.7 GPa
3.0600(15)
3.0678(13)
3.0592(12)
3.0656(15)
3.0683(14)
3.0562(19)
2.0 GPa
3.0506(14)
3.0584(13)
3.0498(12)
3.0562(14)
3.0590(12)
3.0468(12)
Supplementary Table S4. Time constants for the biexponential decay observed in the PL dynamics for the first 900 ns following photoexcitation of FAPbI3 polycrystals as a function of pressure (Fitting function: I PL t Iint [ exp t / 1 exp t / 2 ] I 0 ). Pressure
α
β
1 †
2 †
‡
1 atm
0.40167
0.59982
125±3 ns
25±1 ns
65.14 ns
0.3 GPa
0.37096
0.62057
180±3 ns
31±1 ns
85.68 ns
0.8 GPa
0.34267
0.64731
202±5 ns
32±1 ns
89.83 ns
1.7 GPa
0.31863
0.67554
284±7 ns
34±1 ns
113.31 ns
2.4 GPa
0.40040
0.59707
133±3 ns
24±1 ns
68.57 ns
†
Errors are derived from the fitting function.
‡
represents the mean lifetime, which can be calculated by
16
12 22 . 1 2
References S1. Jaffe, A., Lin, Y., Mao, W. L. & Karunadasa, H. I. Pressure-induced conductivity and yellow-to-black piezochromism in a layered Cu–Cl hybrid perovskite. J. Am. Chem. Soc. 137, 1673-1678 (2015). S2. Tauc, J. Optical properties and electronic structure of amorphous Ge and Si. Mater. Res. Bull. 3, 37-46 (1968). S3. Fox, M. Optical Properties of Solids, Oxford University Press, Oxford (2010). S4. Strobel, T. A. et al. High-pressure study of silane to 150 GPa. Phys. Rev. B 83, 144102 (2011). S5. Birch, F. Finite Elastic Strain of Cubic Crystals. Phy Rev 71, 809-824 (1947). S6. Capitani, F. et al. High-pressure behavior of methylammonium lead iodide (MAPbI 3) hybrid perovskite. J. Appl. Phys. 119, 185901 (2016).
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