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
   )
   

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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.
   

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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
   

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4. 5
   Cs2
   MX6
   – Crystal Structure
   

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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)
   

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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
   

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7. 8
   Cs2
   MX6
   – Electronic Structure
   Cs2
   SnI6
   

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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
   

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9. 10
   Cs2
   MX6
   – Electronic Structure
   Cs2
   TiI6
   

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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).
    …
    

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11. 12
    Cs2
    TiX6
    – Electronic Structure (Reminder)
    Cs2
    TiI6
    

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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).
    

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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).
    

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14. 15
    Cs2
    MX6
    – Electronic Structure
    

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15. Cs2
    MX6
    – Electronic Structure
    

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16. 17
    Cs2
    MX6
    – Electronic Structure
    Cs2
    TiI6
    Cs2
    SnI6
    Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975
    

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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
    

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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
    

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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
    

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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
    

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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?
    

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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
    

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23. 25
    Cs2
    MX6
    – Crystal Structure
    

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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).
    

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