Cation-Induced Band-Gap Tuning in Organohalide Perovskites ...
Cation-Induced Band-Gap Tuning in Organohalide Perovskites: Interplay of Spin-Orbit Coupling and Octahedra Tilting Anna Amat,a Edoardo Mosconi,a,* Enrico Ronca,a,b Claudio Quarti,a Paolo Umari,c,d Md. K. Nazeeruddin,e Michael Grätzel,e Filippo De Angelis a,* a
Computational Laboratory for Hybrid/Organic Photovoltaics (CLHYO), CNR-ISTM, Via Elce di Sotto 8, I-06123, Perugia, Italy.
b
Department of Chemistry, Biochemistry and Biotechnologies, University of Perugia, Via Elce di Sotto 8, I-06123, Perugia, Italy.
c
Dipartimento di Fisica e Astronomia, Università di Padova, via Marzolo 8, I-35131 Padova, Italy. d
CNR-IOM DEMOCRITOS, Theory@Elettra Group, c/o Sincrotrone Trieste, Area Science Park, Basovizza, I-34012 Trieste, Italy. e
Laboratory of Photonics and Interfaces, Institute of Chemical Science and Engineering, E P F L, CH-1015 Lausanne, Switzerland email: [email protected], [email protected]
SUPPORTING INFORMATION
Figure S1. Top: Normalized absorption spectra for FAPbI3, MAPbI3 and CsPbI3, along with estimated optical-absorption onsets. Adapted from Eperon, G. E.; Stranks, S. D.; Menelaou, C.; Johnston, M. B.; Herz, L. M.; Snaith, H. J. Formamidinium lead trihalide: a broadly tunable perovskite for efficient planar heterojunction solar cells. Energy Environ. Sci. 2014, 7, 982-988. Bottom: Comparison of the optical absorption spectra of MAPbI3 and FAPbI3 (absorbance multiplied by 4). Redrawn from the data of Pellet, N.; Gao, P.; Gregori, G.; Yang, T.-Y.; Nazeeruddin, M. K.; Maier, J.; Grätzel, M. Mixed-Organic-Cation Perovskite Photovoltaics for Enhanced Solar-Light Harvesting. Angew. Chem. Int. Ed. 2014, 53, 3151-3157.
Figure S2. Optimized structure of the tetragonal 1-MA system, compared with X-ray data for the Pb-I distances from Stoumpos, C. C.; Malliakas, C. D.; Kanatzidis, M. G. Inorg. Chem. 2013, 52, 9019-9038. Notice the calculated alternate long-short-long Pb-I bonds, nicely matching the typical non centrosymmetric I4/cm space group experimental data.
Figure S3. SOC – SR band-gap differences as a function of the α dihedral . The best quadratic fit is y = -0.0003x2 -0.0012x + 1.2754 with R2 = 0.9997.
Table S1. Calculated effective masses for holes (mh) and electrons (me) by SOC-DFT for the CsPbI3 model as a function of the α angle and for structures 1-MA and 2-FA. α mh
0
5
10
15
20
25
30
1-MA
2-FA
Γ-M
0.17
0.17
0.18
0.19
0.21
0.23
0.26
0.30
0.24
Γ -Z
0.23
0.23
0.23
0.23
0.23
0.35
0.35
0.44
0.43
Γ -X
0.14
0.14
0.15
0.16
0.18
0.20
0.24
0.22
0.19
Γ -A
0.15
0.15
0.16
0.17
0.18
0.20
0.22
0.24
0.22
Γ -R
0.14
0.14
0.15
0.15
0.17
0.18
0.20
0.20
0.19
Avg.
0.17
0.17
0.17
0.18
0.19
0.23
0.25
0.28
0.25
α
me
0
5
10
15
20
25
30
1-MA
2-FA
Γ -M
0.13
0.13
0.14
0.15
0.17
0.20
0.24
0.16
0.17
Γ -Z
0.16
0.16
0.17
0.17
0.17
0.24
0.23
0.26
0.26
Γ -X
0.11
0.12
0.12
0.13
0.15
0.18
0.22
0.16
0.15
Γ -A
0.12
0.12
0.13
0.13
0.15
0.17
0.19
0.14
0.15
Γ -R
0.11
0.11
0.12
0.12
0.14
0.15
0.17
0.14
0.14
Avg.
0.13
0.13
0.13
0.14
0.15
0.19
0.21
0.17
0.17
Figure S4. SR-GW calculated absorption spectra for 1-MA (blue) and 2-FA (brown); joint DOS for 1-MA (red) and 2-FA (magenta); and the ratio between the absorption coefficient and the joint DOS for 1-MA (green) and 2-FA (light blue). The dashed vertical line signals the calculated band-gap region.
Figure S5. Comparison of SOC-GW calculated band structure for MAPbI3 (A, blue lines) and MASnI3 (B, red lines) along the directions Γ (0,0,0) → M (0.5, 0.5,0); Γ → Z (0,0,0.5); Γ → X (0,0.5,0); Γ → A (0.5,0.5,0.5); Γ → R (0,0.5,0.5). Redrawn from the data published in Umari, P.; Mosconi, E.; De Angelis, F. Sci. Rep. 2014, 4, 4467.
Notice the smaller band splitting along the Γ → M direction in MASnI3 compared to MAPbI3.
Computational Laboratory for Hybrid/Organic Photovoltaics (CLHYO), CNR-ISTM, Via Elce di Sotto 8, I-06123, Perugia, Italy.
b
Department of Chemistry, Biochemistry and Biotechnologies, University of Perugia, Via Elce di Sotto 8, I-06123, Perugia, Italy.
c
Dipartimento di Fisica e Astronomia, Università di Padova, via Marzolo 8, I-35131 Padova, Italy. d
CNR-IOM DEMOCRITOS, Theory@Elettra Group, c/o Sincrotrone Trieste, Area Science Park, Basovizza, I-34012 Trieste, Italy. e
Laboratory of Photonics and Interfaces, Institute of Chemical Science and Engineering, E P F L, CH-1015 Lausanne, Switzerland email: [email protected], [email protected]
SUPPORTING INFORMATION
Figure S1. Top: Normalized absorption spectra for FAPbI3, MAPbI3 and CsPbI3, along with estimated optical-absorption onsets. Adapted from Eperon, G. E.; Stranks, S. D.; Menelaou, C.; Johnston, M. B.; Herz, L. M.; Snaith, H. J. Formamidinium lead trihalide: a broadly tunable perovskite for efficient planar heterojunction solar cells. Energy Environ. Sci. 2014, 7, 982-988. Bottom: Comparison of the optical absorption spectra of MAPbI3 and FAPbI3 (absorbance multiplied by 4). Redrawn from the data of Pellet, N.; Gao, P.; Gregori, G.; Yang, T.-Y.; Nazeeruddin, M. K.; Maier, J.; Grätzel, M. Mixed-Organic-Cation Perovskite Photovoltaics for Enhanced Solar-Light Harvesting. Angew. Chem. Int. Ed. 2014, 53, 3151-3157.
Figure S2. Optimized structure of the tetragonal 1-MA system, compared with X-ray data for the Pb-I distances from Stoumpos, C. C.; Malliakas, C. D.; Kanatzidis, M. G. Inorg. Chem. 2013, 52, 9019-9038. Notice the calculated alternate long-short-long Pb-I bonds, nicely matching the typical non centrosymmetric I4/cm space group experimental data.
Figure S3. SOC – SR band-gap differences as a function of the α dihedral . The best quadratic fit is y = -0.0003x2 -0.0012x + 1.2754 with R2 = 0.9997.
Table S1. Calculated effective masses for holes (mh) and electrons (me) by SOC-DFT for the CsPbI3 model as a function of the α angle and for structures 1-MA and 2-FA. α mh
0
5
10
15
20
25
30
1-MA
2-FA
Γ-M
0.17
0.17
0.18
0.19
0.21
0.23
0.26
0.30
0.24
Γ -Z
0.23
0.23
0.23
0.23
0.23
0.35
0.35
0.44
0.43
Γ -X
0.14
0.14
0.15
0.16
0.18
0.20
0.24
0.22
0.19
Γ -A
0.15
0.15
0.16
0.17
0.18
0.20
0.22
0.24
0.22
Γ -R
0.14
0.14
0.15
0.15
0.17
0.18
0.20
0.20
0.19
Avg.
0.17
0.17
0.17
0.18
0.19
0.23
0.25
0.28
0.25
α
me
0
5
10
15
20
25
30
1-MA
2-FA
Γ -M
0.13
0.13
0.14
0.15
0.17
0.20
0.24
0.16
0.17
Γ -Z
0.16
0.16
0.17
0.17
0.17
0.24
0.23
0.26
0.26
Γ -X
0.11
0.12
0.12
0.13
0.15
0.18
0.22
0.16
0.15
Γ -A
0.12
0.12
0.13
0.13
0.15
0.17
0.19
0.14
0.15
Γ -R
0.11
0.11
0.12
0.12
0.14
0.15
0.17
0.14
0.14
Avg.
0.13
0.13
0.13
0.14
0.15
0.19
0.21
0.17
0.17
Figure S4. SR-GW calculated absorption spectra for 1-MA (blue) and 2-FA (brown); joint DOS for 1-MA (red) and 2-FA (magenta); and the ratio between the absorption coefficient and the joint DOS for 1-MA (green) and 2-FA (light blue). The dashed vertical line signals the calculated band-gap region.
Figure S5. Comparison of SOC-GW calculated band structure for MAPbI3 (A, blue lines) and MASnI3 (B, red lines) along the directions Γ (0,0,0) → M (0.5, 0.5,0); Γ → Z (0,0,0.5); Γ → X (0,0.5,0); Γ → A (0.5,0.5,0.5); Γ → R (0,0.5,0.5). Redrawn from the data published in Umari, P.; Mosconi, E.; De Angelis, F. Sci. Rep. 2014, 4, 4467.
Notice the smaller band splitting along the Γ → M direction in MASnI3 compared to MAPbI3.
