Frenkel Excitons in Vacancy-ordered Titanium Halide Perovskites (Cs₂TiX₆)

Slides from my talk on 'Frenkel Excitons in Vacancy-ordered Titanium Halide Perovskites (Cs₂TiX₆)' at the MRS Fall 2022 conference in Boston.

Papers discussed available here (open-access):
https://pubs.acs.org/doi/full/10.1021/acs.jpclett.2c02436

Questions welcome! For other computational photovoltaics, defects and disorder talks, have a look at my YouTube channel!
https://www.youtube.com/SeanRKavanagh

If you're interested in this work, you can check out our recent review on these and other perovskite-inspired materials:
https://iopscience.iop.org/article/10.1088/1361-6528/abcf6d

For more info about me and my research articles see:
https://seankavanagh.com

Transcript

1. 2 02/01/2023 Seán R. Kavanagh, Christopher N. Savory, Shanti M. Liga, Gerasimos Konstantatos, Aron Walsh & David O. Scanlon sean.kavanagh.19@ucl.ac.uk J. Phys. Chem. Lett. 2022, 13, 10965–10975 Frenkel Excitons in Vacancy-Ordered Titanium Halide Perovskites (Cs2 TiX6 )
2. AIMIIX 3 AI 2 MIVX 6 ≋ A(00/MIV)X 3 Cation Substitution Perovskite-Inspired: Vacancy-Ordered (Double) Perovskites 1. Y.-T. Huang, S. R. Kavanagh, D. O. Scanlon, A. Walsh and R. L. Z. Hoye, Nanotechnology, (2021), 32, 132004. 2. Z. Li‡ & S. R. Kavanagh‡ et al. J. Mater. Chem. A, (2020), 8, 21780–21788. 3. C. J. Krajewska, S. R. Kavanagh, L. Zhang, D. J. Kubicki, K. Dey, K. Gałkowski, C. P. Grey, S. D. Stranks, A. Walsh, D. O. Scanlon and R. G. Palgrave, Chem. Sci., (2021), 12, 14686–14699.
3. 4 • M4+: Sn4+, Te4+, Ge4+, Ti4+, Zr4+, Hf4+ • Isolated MX6 octahedra • Non-toxic • Fully-oxidised cations: Stability ⬆ • Solution synthesis (nanocrystals / thin films) • Current best solar cell performance of η = 3.3% for Cs2TiI6 (best non-Sn lead-free perovskite efficiency)2 1. Y.-T. Huang, S. R. Kavanagh, D. O. Scanlon, A. Walsh and R. L. Z. Hoye, Nanotechnology, (2021), 32, 132004. 2. M. Chen, M.-G. Ju, A. D. Carl, Y. Zong, R. L. Grimm, J. Gu, X. C. Zeng, Y. Zhou and N. P. Padture, Joule, (2018), 2, 558–570. AI 2 MIVX 6 ≋ A(00/MIV)X 3 Perovskite-Inspired: Vacancy-Ordered (Double) Perovskites
4. 5 Cs2 MX6 – Crystal Structure
5. 6 Cs2 MX6 – Crystal Structure Cs2 SnCl6 Cs2 SnBr6 Cs2 SnI6 Cs2 TiCl6 Cs2 TiBr6 Cs2 TiI6 Δa (Hybrid DFT) +2.8% +3.5% +2.7% +2.6% +2.9% +2.3% Δa (Hybrid DFT + vdW) -0.4% +0.1% -0.9% -0.6% -0.6% -1.5% a Exp (Å) 10.36 10.77 11.64 10.24 10.68 11.50 ΔE g w/vdW (eV) -0.14 -0.23 -0.31 -0.04 -0.08 -0.15 Strong dispersion (vdW) interactions between ’molecular’ MX6 octahedra (also for related A4MX6) Improved agreement with experiment ✅ Bandgap decrease ⬇ Hybrid DFT = HSE06+SOC a(Cl) < a(Br) < a(I) a(Sn) > a(Ti)
6. 7 Cs2 MX6 – Electronic Structure • Filled (d10/s2) ➡ empty (d0/s0) cation subshells • Non-bonding (rather than anti- bonding) VBM, with weaker dispersion & heavier hole masses. AIMIIX 3 ➡ AI 2 MIVX 6 Cs2SnI6 • Disperse Sn s – X p interactions • Low me (CBM) for Cs2SnX6 Symmetry-forbidden Symmetry-allowed
7. 8 Cs2 MX6 – Electronic Structure Cs2 SnI6
8. 9 Cs2 MX6 – Electronic Structure AIMIIX 3 ➡ AI 2 MIVX 6 • Filled (d10/s2) ➡ empty (d0/s0) cation subshells • Non-bonding (rather than anti- bonding) VBM, with weaker dispersion & heavier hole masses. • Weak Ti d – X p interactions • Flat Ti d CBM • Heavy me (CBM) for Cs2TiX6 Cs2TiI6 Symmetry-forbidden Symmetry-allowed
9. 10 Cs2 MX6 – Electronic Structure Cs2 TiI6
10. 11 Cs2 MX6 – Electronic Structure Cs2SnCl6 Cs2SnBr6 Cs2SnI6 Cs2TiCl6 Cs2TiBr6 Cs2TiI6 E g, Optical (Hybrid DFT; eV) 4.5 2.9 1.2 4.0 3.0 1.9 E g, Optical (Experiment; eV) 4.4-4.9 2.7-3.3 1.25-1.3 2.8-3.4 1.8-2.3 1.0-1.2 Hybrid DFT = HSE06+SOC+vdW • Agreement with experiment for Cs2SnX6 • Severe overestimation of experimental bandgap by DFT for Cs2TiX6 Eg(Cl) > Eg(Br) > Eg(I) Bandgap overestimation for Cs2TiX6 witnessed across the literature: Chen, M. et al. Joule 2, 558–570 (2018). Ju, M.-G. et al. ACS Energy Lett. 3, 297–304 (2018). Kong, D. et al. J. Mater. Chem. C 8, 1591–1597 (2020). Euvrard, J., Wang, X., Li, T., Yan, Y. & Mitzi, D. B. J. Mater. Chem. A 8, 4049–4054 (2020). Mahmood, Q. et al. Materials Science in Semiconductor Processing 137, 106180 (2022). Li, W., Zhu, S., Zhao, Y. & Qiu, Y. Journal of Solid State Chemistry 284, 121213 (2020). Cucco, B. et al. Appl. Phys. Lett. 119, 181903 (2021). …
11. 12 Cs2 TiX6 – Electronic Structure (Reminder) Cs2 TiI6
12. Cs2 TiX6 – Electronic Structure GW ➡ Worse bandgap overestimation (as found by Cucco at al.1) GW+BSE ➡ Excellent agreement! 1. Cucco, B. et al. Appl. Phys. Lett. 119, 181903 (2021).
13. 14 Cs2 TiX6 – Electronic Structure GW ➡ Worse bandgap overestimation (as found by Cucco at al.1) GW+BSE ➡ Excellent agreement! 1. Cucco, B. et al. Appl. Phys. Lett. 119, 181903 (2021).
14. 15 Cs2 MX6 – Electronic Structure
15. Cs2 MX6 – Electronic Structure
16. 17 Cs2 MX6 – Electronic Structure Cs2 TiI6 Cs2 SnI6 Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975
17. Cs2 MX6 – Remaining Questions 1. B. Cunningham, M. Gruening, D. Pashov and M. van Schilfgaarde, arXiv:2106.05759 [cond-mat], (2021). 2. S. Acharya, D. Pashov, A. N. Rudenko, M. Rösner, M. van Schilfgaarde and M. I. Katsnelson, npj Comput. Mater., (2021), 7, 208. Suspiciously large GW quasiparticle bandgaps, and thus exciton binding… Underscreening of electron interactions in GW1,2 could result from localized orbitals and large vacant space Checked: • Functional choice (PBE+GW vs HSE+GW) • Pseudopotential choice • GW & BSE convergence (empty bands, frequency gridpoints…) Dielectric Screening: Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975
18. Cs2 MX6 – Remaining Questions 1. B. Cunningham, M. Gruening, D. Pashov and M. van Schilfgaarde, arXiv:2106.05759 [cond-mat], (2021). 2. S. Acharya, D. Pashov, A. N. Rudenko, M. Rösner, M. van Schilfgaarde and M. I. Katsnelson, npj Comput. Mater., (2021), 7, 208. Suspiciously large GW quasiparticle bandgaps, and thus exciton binding… Underscreening of electron interactions in GW1,2 could result from localized orbitals and large vacant space Checked: • Functional choice (PBE+GW vs HSE+GW) • Pseudopotential choice • GW & BSE convergence (empty bands, frequency gridpoints…) Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975 Similar results reported: Cucco, Katan, Even, Kepenekian, Volonakis arXiv:2210.14081 (Accepted ACS Mater Lett) Zhang, Gao, Cruz, Sun, Zhang, Zhao arXiv:2211.05323 Bhumla, Jain, Sheoran, Bhattacharya arXiv:2209.08559
19. Cs2 MX6 – Remaining Questions Cs 2 TiI 6 Cs 2 SnI 6 Cs 2 TiI 6 Cs 2 TiBr 6 Cs 2 TiI 6 Cs 2 TiBr 6 Cs 2 TiCl 6 Cs 2 TiI 6 Cs 2 TiBr 6 Cs 2 TiCl 6 Y. K. Jung, S. Kim, Y-C. Kim, A. Walsh J. Phys. Chem. Lett. 2021 12 (34), 8447–8452
20. Cs 2 SnI 6 Cs 2 SnBr 6 Cs 2 SnCl 6 Cs 2 SnI 6 Cs 2 SnBr 6 Cs 2 SnI 6 Cs 2 SnBr 6 Cs 2 SnCl 6 Cs 2 TiI 6 Cs 2 SnI 6 Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975 Cs2 MX6 – Remaining Questions
21. Conclusions Highly localised, isolated MX6 octahedra yield ‘molecular salt’ behaviour Substitution of Sn4+ -> Ti4+ gives qualitatively different optical behaviour • Severe DFT overestimation of Cs2TiX6 bandgaps; qualitatively incorrect Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975 Strong excitonic binding in Cs2 MX6 (M = d0 cation), resolving longstanding discrepancies between theory and experiment. Are the ultra-strong predicted Eex (GW+BSE) true consequences of the localised octahedra, or residual GW errors?
22. Acknowledgements Shanti Liga & Prof G. Konstantatos Profs Aron Walsh & David O. Scanlon @Kavanagh_Sean_ sean.kavanagh.19@ucl.ac.uk Kavanagh et al. ‘Frenkel Excitons in Vacancy-Ordered Titanium Halide Perovskites (Cs2 TiX6 )’ J. Phys. Chem. Lett. 2022, 13, 10965–10975
23. 25 Cs2 MX6 – Crystal Structure
24. Cs2 MX6 – Remaining GW Issues • Severe underscreening of e-h interactions due to correlated, localized d orbitals and significant vacant space in these materials ➡ true challenge for theory. • Excitonic effects explain the origin of experiment- theory discrepancies and bring absorption spectra into excellent agreement, but quantitative bandgap prediction remains elusive. Acharya, S. et al. Importance of charge self-consistency in first-principles description of strongly correlated systems. npj Comput Mater 7, 208 (December 2021). Cunningham, B., Gruening, M., Pashov, D. & van Schilfgaarde, M. Quasiparticle Self consistent GW with ladder diagrams in W. arXiv:2106.05759 [cond-mat] (2021).