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Vacancy-Ordered Perovskites Cs₂(Sn/Ti)X₆: Alloying, Optoelectronic, Stability & Defect Properties

Vacancy-Ordered Perovskites Cs₂(Sn/Ti)X₆: Alloying, Optoelectronic, Stability & Defect Properties

Slides for an invited talk on Tin & Titanium Vacancy-Ordered Halide Perovskites (Cs₂MX₆; M = Sn, Ti; X = I, Br, Cl)(Cs₂SnI₆, Cs₂SnBr₆, Cs₂SnCl₆, Cs₂TiI₆, Cs₂TiBr₆, Cs₂TiCl₆) at MRS Spring 2023, San Francisco – discussing our results on alloying the cation site, optoelectronic properties, excitons, stability and defects; in collaboration with Shanti Liga and Gerasimos Konstantatos at ICFO, Barcelona.

Papers discussed available here (open-access):
https://pubs.acs.org/doi/full/10.1021/acs.jpclett.2c02436
(Perovskite-inspired materials review): https://iopscience.iop.org/article/10.1088/1361-6528/abcf6d
Shanti's paper on Cs₂TiBr₆ stabilization: https://doi.org/10.1039/D3CC00581J
A preprint on our cation-alloying work should be out soon! 🤞

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

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

Seán R. Kavanagh

May 02, 2023
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  1. 1
    02/05/2023
    [email protected]
    Tin & Titanium Vacancy-Ordered Halide
    Perovskites: Cs2
    (Sn/Ti)X6
    Seán R. Kavanagh*, Shanti M. Liga,
    Christopher N. Savory, Gerasimos
    Konstantatos, Aron Walsh & David O. Scanlon*

    View full-size slide

  2. 2
    02/05/2023
    [email protected]
    Tin & Titanium Vacancy-Ordered Halide
    Perovskites: Cs2
    (Sn/Ti)X6
    Seán R. Kavanagh*, Shanti M. Liga,
    Christopher N. Savory, Gerasimos
    Konstantatos, Aron Walsh & David O. Scanlon*

    View full-size slide

  3. 3
    ‘Perovskite-Inspired’
    Materials?
    Y.-T. Huang, S.R. Kavanagh, D.O. Scanlon, A. Walsh, and R.L.Z. Hoye, Nanotechnology 32, 132004 (2021)
    R.L.Z. Hoye et al. Chem Mater 29, 1964 (2017)
    S.R. Kavanagh, C.N. Savory, D.O. Scanlon, and A. Walsh, Materials Horizons 8, 2709 (2021)

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  4. 4
    Y.-T. Huang, S.R. Kavanagh, D.O. Scanlon, A. Walsh, and R.L.Z. Hoye, Nanotechnology 32, 132004 (2021)
    R.L.Z. Hoye et al. Chem Mater 29, 1964 (2017)
    S.R. Kavanagh, C.N. Savory, D.O. Scanlon, and A. Walsh, Materials Horizons 8, 2709 (2021)
    Alternative Crystal Structures but Chemically-Similar:
    -> Cations with filled (semi-)valence orbitals
    Sb2
    Se3
    & Sb2
    S3
    :
    X. Wang, Z. Li, S.R. Kavanagh et al. Phys. Chem. Chem. Phys. 2022
    X. Wang, A.M. Ganose, S.R. Kavanagh et al. ACS Energy Lett. 2022
    X. Wang, S.R. Kavanagh et al. Under Review at Phys Rev Lett
    Sn2
    SbS2
    I3
    :
    S.R. Kavanagh et al. Materials Horizons 2021
    A. Nicolson, S. R. Kavanagh et al. Under Review at J. Am. Chem. Soc.
    AgBiS2
    & NaBiS2
    :
    S. R. Kavanagh‡ & Y. Wang‡ et al. Nature Photonics 2022
    S. R. Kavanagh‡ & Y. Huang‡ et al. Nature Communications 2022
    Cu2
    SiSe3
    :
    A. Nicolson, S.R. Kavanagh et al. Under Review at ACS Energy Lett.
    Also BiOI, SbSeI, Cu2
    GeSe3

    ‘Perovskite-Inspired’
    Materials?
    Perovskite Structure:
    AI
    2
    BIBIIIX6
    : Cs2
    AgBiBr6
    & Cs2
    AgSbBr6
    :
    A. H. Slavney et al. J. Am. Chem. Soc. 2016
    S. R. Kavanagh‡ & Z. Li‡ et al. J. Mater. Chem. A, 2020
    AI
    2
    BIVX6
    : Cs2
    TiX6
    & Cs2
    SnX6
    :
    M. Chen et al. Joule, 2018
    S. R. Kavanagh et al. J. Phys. Chem. Lett., 2022
    S. R. Kavanagh‡ & S. M. Liga‡ et al. In Submission
    AI
    3
    BIII
    2
    X9
    : Cs3
    Bi2
    Br9
    :
    B.-B. Yu et al. J. Mater. Chem. A, 2019
    C. J. Krajewska, S. R. Kavanagh et al. Chem. Sci., 2021

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  5. 6
    • M4+: Sn4+, Te4+, Ge4+, Ti4+, Zr4+, Hf4+
    • Isolated MX6
    octahedra
    • Non-toxic
    • Fully-oxidised cations: Stability ⬆
    • Solution synthesis (nanocrystals / thin films)
    • Best solar cell performance of η = 3.3% for Cs2
    TiBr6
    (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
    MIVX6
    ≋ A(00/MIV)X3
    Perovskite-Inspired: Vacancy-Ordered (Double) Perovskites

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  6. 7
    Cs2
    MX6
    – Crystal Structure AI
    2
    MIVX6
    ≋ A(00/MIV)X3

    View full-size slide

  7. 8
    Cs2
    MX6
    – Crystal Structure AI
    2
    MIVX6
    ≋ A(00/MIV)X3

    View full-size slide

  8. 9
    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%
    aExp
    (Å) 10.36 10.77 11.64 10.24 10.68 11.50
    ΔEg
    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
    vacancy-ordered A4
    MX6
    )
    Improved agreement with experiment ✅
    Bandgap decrease ⬇
    Hybrid DFT = HSE06+SOC a(Cl) < a(Br) < a(I) a(Sn) > a(Ti)

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  9. 10
    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.
    AIMIIX3
    ➡ AI
    2
    MIVX6
    Cs2
    SnI6
    • Disperse Sn s – X p interactions
    • Low me (CBM)
    for Cs2
    SnX6
    Symmetry-forbidden Symmetry-allowed

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  10. 11
    Cs2
    MX6
    – Electronic Structure
    Cs2
    SnI6

    View full-size slide

  11. 12
    Cs2
    MX6
    – Electronic Structure
    AIMIIX3
    ➡ AI
    2
    MIVX6
    • 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 Cs2
    TiX6
    Cs2
    TiI6
    Symmetry-forbidden Symmetry-allowed

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  12. 13
    Cs2
    MX6
    – Electronic Structure
    Cs2
    TiI6

    View full-size slide

  13. 14
    Cs2
    MX6
    – Electronic Structure
    Cs2
    SnCl6
    Cs2
    SnBr6
    Cs2
    SnI6
    Cs2
    TiCl6
    Cs2
    TiBr6
    Cs2
    TiI6
    Eg, Optical
    (Hybrid DFT; eV) 4.5 2.9 1.2 4.0 3.0 1.9
    Eg, 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 Cs2
    SnX6
    • Severe overestimation of experimental bandgap by DFT for Cs2
    TiX6
    Eg
    (Cl) > Eg
    (Br) > Eg
    (I)
    Bandgap overestimation for Cs2
    TiX6
    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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  14. 15
    Cs2
    TiX6
    – Electronic Structure (Reminder)
    Cs2
    TiI6

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  15. 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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  16. 17
    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).

    View full-size slide

  17. 18
    Cs2
    MX6
    – Electronic Structure

    View full-size slide

  18. Cs2
    MX6
    – Electronic Structure

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  19. 20
    Cs2
    MX6
    – Electronic Structure
    Cs2
    TiI6
    Cs2
    SnI6
    Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975

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  20. Cs2
    MX6
    – Ultra-Strong Excitons
    Ultra-strong exciton binding despite relatively low
    electronic bandgaps.
    -> Similar results obtained with vertex-corrected GŴ
    (courtesy of Dr. Chris Savory)
    -> Calculation parameters triple-checked
    Similar results reported:
    Cucco, Katan, Even, Kepenekian, Volonakis
    ACS Mater Lett 2023
    Bhumla, Jain, Sheoran, Bhattacharya
    J Phys Chem Lett 2023
    Zhang, Gao, Cruz, Sun, Zhang, Zhao
    arXiv:2211.05323
    Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975

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  21. Cs2
    MX6
    – Ultra-Strong Excitons
    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?
    -> Similar results obtained with vertex-corrected GŴ
    (courtesy of Dr. Chris Savory)
    -> Calculation parameters triple-checked
    Similar results reported:
    Cucco, Katan, Even, Kepenekian, Volonakis
    ACS Mater Lett 2023
    Bhumla, Jain, Sheoran, Bhattacharya
    J Phys Chem Lett 2023
    Zhang, Gao, Cruz, Sun, Zhang, Zhao
    arXiv:2211.05323
    Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975

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  22. Cs2
    SnX6
    = Mostly stable under air,
    thermal, water & photo stresses.
    X = I (Cs2
    SnI6
    ) shows some very slow
    decomposition in air.
    X = Br, Cl ➡ Stable in (humid) air.
    23
    Cs2
    MX6
    – Stability
    Saporov et al. Chem Mater 2016

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  23. Cs2
    TiX6
    :
    X = I: Unstable in air.
    X = Br: Stable under heat and light.
    Stability in air?
    • 1Chen et al. Joule 2018 ➡ Thin films, stable in humid air
    • 2Kong et al. J. Mater. Chem. C 2019 ➡ Powder, slight decomposition in humid air
    • 3Euvrard et al. J. Mater. Chem. A 2020 ➡ Powder, decomposition in humid air (~20h)
    • 4Grandhi et al. Nanomaterials 2021 ➡ Nanocrystal films, slow decomposition in air (~1 wk)
    X = Cl: Very slow decomposition in air (~1-2% over 2 weeks).2,4
    24
    Cs2
    MX6
    – Stability Cs2
    TiBr6
    Cs2
    TiI6

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  24. Intrinsic Thermodynamic Stability
    Cs2
    SnI6
    Cs2
    SnBr6
    Cs2
    SnCl6
    Cs2
    TiI6
    Cs2
    TiBr6
    Cs2
    TiCl6
    Hybrid DFT + vdW
    Decomposition Energy (eV)
    +56 meV +129 meV +174 meV +75 meV +120 meV +162 meV
    25
    • Positive decompositions energies ➡
    Thermodynamically stable in each case, as
    witnessed experimentally (stable in inert
    atmospheres)
    • Van der Waal’s dispersion interactions found to
    be significant in stabilizing Cs2
    MX6
    :
    Cs2
    SnI6
    Cs2
    TiI6
    Hybrid DFT
    Decomposition Energy (eV)
    +14 meV +51 meV
    Hybrid DFT + vdW
    Decomposition Energy (eV)
    +56 meV +75 meV
    Increasing stability as X: I -> Br -> Cl

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  25. External Decomposition in Oxygen/Water
    • O2
    decomposition significantly more favourable for M = Ti as expected (strong stability of TiO2
    )
    • O2
    decomposition less favoured as X -> I, Br, Cl.
    Note: Reaction kinetics ignored here.
    Reactants Products ΔH (eV)
    Cs2
    SnI6
    + O2
    SnO2
    + 2CsI + 4I(s)
    -2.43
    Cs2
    SnBr6
    + O2
    SnO2
    + 2CsBr + 2Br2(l)
    -0.10
    Cs2
    SnCl6
    + O2
    SnO2
    + 2CsCl + 2Cl2(g)
    +0.82
    Reactants Products ΔH (eV)
    Cs2
    TiI6
    + O2
    TiO2
    + 2CsI3
    + 4I(s)
    -4.90
    Cs2
    TiBr6
    + O2
    TiO2
    + 2CsBr + 2Br2(l)
    -1.70
    Cs2
    TiCl6
    + O2
    TiO2
    + 2CsCl + 2Cl2(g)
    -0.38
    Aqueous Decomposition: Cs2
    MX6
    + H2
    O ➡ MO2
    + 2 CsX + 4HX(g)
    Gaseous product (4HX(g)
    ) means reaction energy ΔE is a function of pHX
    (i.e. environment-dependent)

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  26. • Experimentally, Cs2
    MX6
    found to be
    hygroscopic and to exhibit
    accelerated decomposition under
    humid oxygen atmospheres.
    • Calculations find aqueous
    decomposition to be
    thermodynamically favoured under
    certain HX(g)
    partial pressure ranges.
    • Additionally, potential
    kinetic/catalytic effect from surface
    hydration.
    O2
    /H2
    O Decomposition
    27
    Humid Air Dessicated Air
    E.G: Cs2
    (Ti0.4
    Sn0.6
    )Br6

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  27. Cs2
    MX6
    Stability: Conclusions
    • Cs2
    SnX6
    far more stable than Cs2
    TiX6
    in ambient atmospheres.
    • However Cs2
    TiX6
    is interesting because:
    • Ultra-strong Frenkel excitons ➡ Playground to study associated physical
    phenomena
    • Initially, promising photovoltaic performance (diminished by identification of
    strong excitons however)
    • Non-linear optics: Only known third-harmonic generation (THG) active lead-
    free perovskite, thanks to centrosymmetric crystal structure.1
    • Can we alloy Sn/Ti to tune stability and optical/electronic properties?
    28
    1Grandhi et al. Nanomaterials 2021

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  28. Special Quasirandom Structures (SQS) with
    hybrid DFT including spin-orbit coupling
    29
    Cs2
    (Snx
    Ti1-x
    )X6

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  29. 30
    d(Ti – X) in Cs2
    (Snx
    Ti1-x
    )X6
    ≃ d(Ti – X) in Cs2
    TiX6
    d(Sn – X) in Cs2
    (Snx
    Ti1-x
    )X6
    ≃ d(Sn – X) in Cs2
    SnX6
    Cs2
    (Snx
    Ti1-x
    )X6
    Consistent behaviour across all X = I, Br, Cl
    HSE06+SOC+vdW

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  30. 31
    Cs2
    (Snx
    Ti1-x
    )X6
    : Optical Properties
    Cs2
    (Snx
    Ti1-x
    )I6
    Cs2
    (Snx
    Ti1-x
    )Br6
    Quasiparticle spectrum with hybrid DFT + SOC ➡ negligible hybridization/mixing

    View full-size slide

  31. Experiment
    32
    Cs2
    (Snx
    Ti1-x
    )X6
    : Optical Properties
    Theory
    (Linear sum of endpoint excitonic spectra)

    View full-size slide

  32. Energy-lowering reconstructions prevalent in a wide
    & diverse range of materials/defects.
    33
    Importance of Defect Structure
    Searching!
    More details in Thursday morning’s talk:
    EL04.05.02: Symmetry-Breaking and
    Reconstruction at Point Defects in Perovskites
    April 13, 9-9.15 AM
    shakenbreak.readthedocs.io
    1. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* npj Comp Mater 2023
    2. Mannodi-Kanakkithodi Nature Physics 2023
    3. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* J. Open Source Software 2022
    4. Mosquera-Lois & Kavanagh*, Matter 2021
    5. Kavanagh, Walsh, Scanlon ACS Energy Lett 2021
    6. Kavanagh*, Scanlon, Walsh, Freysoldt; Faraday Discussions 2022
    Cs2
    TiI6
    :
    Large energy lowering of ΔE: -0.4 – -2.5 eV for
    many native defects:
    • VTi
    0, VTi
    -1, VTi
    -2, VTi
    -3, VTi
    -4 (all VTi
    charge states)
    • Ii
    0, Ii
    -1
    • ICs
    0, ICs
    -1, ICs
    -2
    • TiCs
    0, TiCs
    +1, TiCs
    +2,
    TiCs
    +3
    • ITi
    0, ITi
    -1
    • TiI
    +2, TiI
    +5
    • Csi
    +1

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  33. VTi
    -4 – Fully-ionised Titanium Vacancy
    Unperturbed; Slightly contracted octahedron ShakeNBreak: Iodine trimer; ΔE = -0.8 eV

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  34. VTi
    -1
    Unperturbed; distorted contracted octahedron ShakeNBreak: double Iodine trimer; ΔE = -1.1 eV

    View full-size slide

  35. VTi
    -1
    Unperturbed; distorted contracted octahedron ShakeNBreak: double Iodine trimer; ΔE = -1.1 eV

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  36. VTi
    0 – Neutral Titanium Vacancy
    Unperturbed; distorted contracted octahedron ShakeNBreak: effective ITi
    + VI
    complex -> ΔE = -1.6 eV

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  37. TiCs
    +3 – Fully-ionised Titanium-on-Caesium
    Unperturbed; Ti-Ti bond within
    Iodine octahedron
    ShakeNBreak: Ti split, one goes to vacant octahedral
    site near missing caesium -> ΔE = -2.5 eV

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  38. TiI
    +5 – Fully-ionised Titanium-on-Iodine
    Unperturbed; Ti-Ti bond, distorted octahedron ShakeNBreak: off-centred Ti to vacant octahedral site
    -> ΔE = -2 eV

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  39. TiI
    +5 – Fully-ionised Titanium-on-Iodine
    Unperturbed; Ti-Ti bond, distorted octahedron ShakeNBreak: off-centred Ti to vacant octahedral site
    -> ΔE = -2 eV

    View full-size slide

  40. TiI
    +5 – Fully-ionised Titanium-on-Iodine
    Unperturbed; Ti-Ti bond, distorted octahedron ShakeNBreak: off-centred Ti to vacant octahedral site
    -> ΔE = -2 eV

    View full-size slide

  41. Energy-lowering reconstructions prevalent in a wide
    & diverse range of materials/defects.
    42
    Importance of Defect Structure
    Searching!
    More details in Thursday morning’s talk:
    EL04.05.02: Symmetry-Breaking and
    Reconstruction at Point Defects in Perovskites
    April 13, 9-9.15 AM
    shakenbreak.readthedocs.io
    1. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* npj Comp Mater 2023
    2. Mannodi-Kanakkithodi Nature Physics 2023
    3. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* J. Open Source Software 2022
    4. Mosquera-Lois & Kavanagh*, Matter 2021
    5. Kavanagh, Walsh, Scanlon ACS Energy Lett 2021
    6. Kavanagh*, Scanlon, Walsh, Freysoldt; Faraday Discussions 2022
    Cs2
    TiI6
    :
    Large energy lowering of ΔE: -0.4 – -2.5 eV for
    many native defects, due to:
    • Multinary composition
    • Reduced crystal symmetry
    • Space to distort / ‘open’ crystal structure
    • Presence of ionic & covalent bonding

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  42. Conclusions
    Highly localised, isolated MX6
    octahedra yield ‘molecular salt’ behaviour
    Ultra-strong Frenkel excitonic binding (Eb
    ~ 1 eV) in Cs2
    MX6
    (where M = d0 cation), resolving longstanding discrepancies
    between theory and experiment.
    Symmetry-breaking and reconstruction rampant for defects in
    Cs2
    MX6
    Other exciting applications for these unusual materials with
    strong exciton binding, extremely weak inter-octahedral
    interactions and facile mixing? Quantum defects?...

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  43. Acknowledgements
    Shanti Liga &
    Prof G. Konstantatos
    Profs Aron Walsh & David O. Scanlon
    @Kavanagh_Sean_
    [email protected]
    Kavanagh et al. ‘Frenkel Excitons in Vacancy-
    Ordered Titanium Halide Perovskites (Cs2
    TiX6
    )’
    J. Phys. Chem. Lett. 2022, 13, 10965–10975
    Liga‡ & Kavanagh‡ et al. In Submission

    View full-size slide

  44. 45
    Cs2
    (Snx
    Ti1-x
    )X6
    : Optical Properties
    Cs2
    (Snx
    Ti1-x
    )I6
    Cs2
    (Snx
    Ti1-x
    )Br6
    Quasiparticle spectrum with hybrid DFT + SOC ➡ negligible hybridization/mixing

    View full-size slide

  45. Experiment
    46
    Cs2
    (Snx
    Ti1-x
    )X6
    : Optical Properties
    Theory
    (Linear sum of endpoint excitonic spectra)

    View full-size slide