Symmetry-Breaking at Defects in Perovskites

Slides for my talk 'Symmetry-Breaking & Reconstruction at Defects in Perovskites' at MRS Spring 2023, San Francisco – discussing the issue of global optimisation for defects in solids, its particular relevance & importance for perovskites, and our work (ShakeNBreak) on tackling this issue.

YouTube video recording: https://youtu.be/yzevtGjGALI

ShakeNBreak website: https://shakenbreak.readthedocs.io/en/latest/

Our general defect calculation package doped is available here: https://github.com/SMTG-UCL/doped

See our open-access papers on defect structure-searching here:
https://www.nature.com/articles/s41524-023-00973-1
https://joss.theoj.org/papers/10.21105/joss.04817
https://www.nature.com/articles/s41567-023-02049-9

Questions welcome! For other computational photovoltaics, defects and disorder talks, have a look at my YouTube channel!
https://www.youtube.com/SeanRKavanagh
For other research articles see:
https://bit.ly/3pBMxOG

Other references:
Matter Preview of Defect Structure Searching: https://www.sciencedirect.com/science/article/pii/S2590238521002733
Metastable defects : https://doi.org/10.1039/D2FD00043A
Recombination at V_Cd in CdTe (case study): https://pubs.acs.org/doi/abs/10.1021/acsenergylett.1c00380

Transcript

1. Standard defect supercell relaxation
   Seán R. Kavanagh‡ & Irea Mosquera-Lois,‡
   Aron Walsh, David O. Scanlon
   MRS Spring 2023
   Symmetry-Breaking & Reconstruction at
   Defects in Perovskites
   

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2. Standard defect supercell relaxation
   Seán R. Kavanagh‡ & Irea Mosquera-Lois,‡
   Aron Walsh, David O. Scanlon
   MRS Spring 2023
   Symmetry-Breaking & Reconstruction at
   Defects in Perovskites
   

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3. Defect Calculation Workflow
   3
   Host primitive cell
   Goyal et al, Comp Mater Sci 2017
   

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4. Defect Calculation Workflow
   4
   Host primitive cell
   Goyal et al, Comp Mater Sci 2017
   

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5. Defect Calculation Workflow
   5
   

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6. Defect Calculation Workflow
   6
   

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7. Defect Calculation Workflow
   7
   

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8. Defect Calculation Workflow
   8
   

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9. Defect Calculation Workflow
   9
   

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10. Defect Calculation Workflow
    10
    

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11. Defect Calculation Workflow
    11
    ➡ Energy
    ➡ Concentration
    ➡ Transition Level
    ➡ Deep/Shallow
    ➡ Doping
    ➡ Carrier capture
    ➡ Diffusion
    ➡ …
    

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12. VCd
    in CdTe
    

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13. Metal-metal dimers possible for vacancies in semiconductors:
    Lany & Zunger Phys Rev Lett 2004
    Lany & Zunger Phys Rev B 2005
    VCd
    in CdTe
    

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14. Metal-metal dimers possible for vacancies in semiconductors:
    Lany & Zunger Phys Rev Lett 2004
    Lany & Zunger Phys Rev B 2005
    VCd
    in CdTe
    

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15. Metal-metal dimers possible for vacancies in semiconductors:
    Lany & Zunger Phys Rev Lett 2004
    Lany & Zunger Phys Rev B 2005
    VCd
    in CdTe
    

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16. VCd
    in CdTe Tei
    in CdTe
    Standard Relaxation
    ShakeNBreak
    (Our Method)
    Kavanagh*, Scanlon, Walsh, Freysoldt
    Faraday Discussions 2022
    

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17. Metal-metal dimers possible for vacancies in semiconductors:
    Lany & Zunger Phys Rev Lett 2004
    Lany & Zunger Phys Rev B 2005
    Kavanagh, Walsh, Scanlon
    ACS Energy Lett 2021
    VCd
    in CdTe
    

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18. Metal-metal dimers possible for vacancies in semiconductors:
    Lany & Zunger Phys Rev Lett 2004
    Lany & Zunger Phys Rev B 2005
    Kavanagh, Walsh, Scanlon
    ACS Energy Lett 2021
    VCd
    in CdTe
    

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19. Potentially the Wrong Defect!
    Mosquera-Lois & Kavanagh* Matter 2021
    Kavanagh, Walsh, Scanlon ACS Energy Lett 2021
    Mosquera-Lois‡ & Kavanagh‡*, Walsh and Scanlon*
    npj Comput Mater 2023
    Standard defect supercell relaxation
    

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20. How Prevalent is This?
    Tested on a diverse range of materials: Si, CdTe, GaAs, Sb2
    S3
    , Sb2
    Se3
    , CeO2
    , In2
    O3
    , ZnO, anatase-TiO2
    Energy-lowering reconstructions, missed by standard relaxations, found in every material studied
    Mosquera-Lois‡ & Kavanagh‡*, Walsh and Scanlon* npj Comput Mater 2023
    

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21. Defect Calculation Workflow
    21
    

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22. How Important/Prevalent is This? Very
    Literature Examples (reconstructions found serendipitously or
    through manual searching):
    • Gallium vacancies, migration and compensation in Ga2
    O3
    1
    • Catalytic activity (divalent metal dopants in CeO2
    )2
    • CdTe solar cell performance3,4
    • Defect absorption / bandgap lowering (Sn-doped Cs3
    Bi2
    Br9
    )5
    • Persistent Photoconductivity in Si, GaAs DX centres1,6
    • Oxide polarons (in BiVO4
    )7
    • Colour centres and deep anion vacancies in II-VI compounds8
    1. Varley et al J. Phys.: Condens. Matter 2011
    2. Kehoe, Scanlon, Watson, Chem Mater 2011
    3. Kavanagh, Walsh, Scanlon ACS Energy Lett 2021
    4. Kavanagh*, Scanlon, Walsh, Freysoldt Faraday Discussions 2022
    5. Krajewska, Kavanagh et al. Chem Sci 2021
    6. Du & Zhang Phys Rev B 2005
    7. Osterbacka, Ambrosio, Wiktor J Phys Chem C 2022
    8. Lany & Zunger Phys Rev Lett 2004
    Inaccurate Structure ➡ Inaccurate Formation Energy ➡
    Inaccurate:
    ➡ Energy
    ➡ Concentration
    ➡ Transition Level
    ➡ Deep/Shallow
    ➡ Doping
    ➡ Carrier capture
    ➡ Diffusion
    ➡ …
    

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23. ShakeNBreak: Summary
    • Obtaining the correct defect structure
    is important!
    • Our current procedure for defect
    calculations is incomplete
    • Energy-lowering reconstructions
    prevalent in a wide & diverse
    range of materials/defects.
    • ShakeNBreak = easily-implemented
    method to combat this and aid the
    accuracy of defect calculations
    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
    

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24. Indicators of Defect Reconstructions &
    Metastability
    • Multinary composition
    • Reduced crystal symmetry
    • Space to distort / ‘open’ crystal structures
    • Mixed ionic/covalent bonding
    • Dynamic structure
    (i.e. more complex PES)
    

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25. Case Study: Double Perovskites (A2
    BIBIIIX6
    )
    Cs2
    AgBiBr6
    Large energy lowering of ΔE: -0.1 – -2.75 eV for many antisite defects
    e.g.
    

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26. Case Study: Double Perovskites (A2
    BIBIIIX6
    )
    • AgCs
    0, AgCs
    +1 (all AgCs
    charge states)
    • BiCs
    0, BiCs
    +1, BiCs
    +2 (all BiCs
    charge states)
    • BrCs
    0
    • CsAg
    -1, CsAg
    0, CsAg
    +1 (all CsAg
    charge states)
    • BiAg
    0, BiAg
    +1
    • BiAg
    -2, BiAg
    -1, BrAg
    0 (all BrAg
    charge states)
    • AgBi
    -2
    • BrBi
    0, BrBi
    -1, BrBi
    -2, BrBi
    -3, BrBi
    -4 (all BrBi
    charge
    states)
    • AgBr
    0, AgBr
    +1, AgBr
    +2 (all AgBr
    charge states)
    • BiBr
    0, BiBr
    +1, BiBr
    +2, BiBr
    +3, BiBr
    +4, BiBr
    +5 (all BiBr
    charge states)
    • CsBr
    0, CsBr
    +1, CsBr
    +2 (all CsBr
    charge states)
    Cs2
    AgBiBr6
    Large energy lowering of ΔE: -0.1 – -2.75 eV for many antisite defects
    

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27. BiCs
    0 – Neutral Bismuth-on-Caesium
    Unperturbed; 2 Bi-Br bonds, slightly distorted
    octahedra
    ShakeNBreak: tetra-coordinated Bi-Br, off-centred Ag
    -> ΔE = -1.25 eV
    

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28. BiCs
    0 – Neutral Bismuth-on-Caesium
    Unperturbed; 2 Bi-Br bonds, slightly distorted
    octahedra
    ShakeNBreak: tetra-coordinated Bi-Br, off-centred Ag
    -> ΔE = -1.25 eV
    

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29. BiCs
    0 – Neutral Bismuth-on-Caesium
    Unperturbed; 2 Bi-Br bonds, slightly distorted
    octahedra
    ShakeNBreak (metastable): similar tetra-coordinated
    Bi-Br (square planar), off-centred Ag -> ΔE = -1.1 eV
    

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30. BrAg
    -2 – Fully-ionised Bromine-on-Silver
    Unperturbed; 2 elongated Br-Br bonds,
    undistorted octahedra
    ShakeNBreak: BrAg
    displaces from octahedron centre, gives
    7-fold coordinated Bi and off-centred Ag -> ΔE = -1.5 eV
    

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31. BiAg
    0 – Neutral Bismuth-on-Silver
    Unperturbed; Bi-Br octahedron replacing
    Ag-Br, minimal distortion
    ShakeNBreak: Tetragonal elongation of BiAg
    octahedron ->
    square-planar coordination, displaced Ag -> ΔE = -0.35 eV
    

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32. Case Study: Vacancy-Ordered Perovskites (A2
    BIVX6
    )
    AI
    2
    MIVX6
    ≋ A(00/MIV)X3
    Kavanagh et al. ‘Frenkel Excitons in Vacancy-
    Ordered Titanium Halide Perovskites (Cs2
    TiX6
    )’
    J. Phys. Chem. Lett. 2022, 13, 10965–10975
    Kavanagh‡ & Liga‡ et al. In Submission
    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 (all Ii
    charge states)
    • Csi
    +1
    • ICs
    0, ICs
    -1, ICs
    -2 (all ICs
    charge states)
    • TiCs
    0, TiCs
    +1, TiCs
    +2, TiCs
    +3 (all TiCs
    charge states)
    • ITi
    0, ITi
    -1
    • TiI
    +2, TiI
    +5
    

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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
    

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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
    

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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
    

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41. What about polarons / self-trapped excitons?
    A4
    MIIX6
    :
    ➡ High thermal sensitivity of PL lifetimes
    ➡ Ultra-high spatial and thermal resolution
    devices (for remote thermography)
    MII = Pb, Sn
    1. Yakunin, S. et al. Nature Materials 2019
    2. B. Kang & K. Biswas J. Phys. Chem. Lett. 2018
    

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42. Previous calculations (unperturbed relaxations) predict tetragonal contracted
    octahedron for self-trapped exciton structure.
    Unperturbed; Tetragonally-Contracted Octahedron ShakeNBreak; Tetragonally-Expanded Octahedron
    ΔE ~ -0.4 (MII = Pb, Sn)
    

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43. Does it matter?
    Thanks to Dr. Youngkwang Jung @ Cambridge for the figure!
    Initial octahedron structure
    

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44. Energy-lowering reconstructions prevalent in
    a wide & diverse range of materials/defects.
    44
    Importance of Defect Structure
    Searching!
    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
    Particularly strong for perovskites, due to:
    • Multinary composition
    • Reduced crystal symmetry
    • Space to distort / ‘open’ crystal structures
    • Presence of ionic & covalent bonding
    • Dynamic crystal structure
    

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45. Studies using ShakeNBreak (and finding lower energy defect structures):
    • X. Wang, S. R. Kavanagh, D. O. Scanlon, A. Walsh; Under Review at Phys Rev Lett (arXiv: 2302.04901)
    • C. Krajewska, S. R. Kavanagh et al. Chem Sci 2021
    • S. R. Kavanagh*, D. O. Scanlon, A. Walsh, C. Freysoldt Faraday Discussions 2022
    • J. Cen et al; J. Mater. Chem. A (Accepted) 2023
    • J. Willis, Q. Zhou et al. In preparation.
    • Y. T. Huang & S. R. Kavanagh et al. Nature Communications 2022
    • A. Nicolson et al; Under Review at J. Am. Chem. Soc. (ChemRxiv: 10.26434/chemrxiv-2023-7454p)
    • Y. Kumagai et al; In submission
    • A. Samli et al;. In preparation
    Acknowledgements
    Profs David Scanlon & Aron Walsh
    Irea Mosquera-Lois
    @Kavanagh_Sean_
    

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46. View Slide

47. Standard Relaxation
    (Metastable)
    Example: Vacancies in Sb2
    Se3
    /Sb2
    S3
    Reveals rare 4-electron negative-U behavior and ultra-
    strong self-compensation in Sb2
    S3
    & Sb2
    Se3
    Difference in predicted VSb
    concentration = 1021
    Our Method
    (Ground-state)
    Wang, Kavanagh, Scanlon, Walsh;
    ‘Four-electron Negative-U Vacancy Defects in Antimony Selenide’
    Under Review (arXiv: 2302.04901)
    Do we expect this behaviour in perovskites?
    

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48. Key Takeaways
    • Obtaining the correct defect structure
    is important!
    • Our current procedure for defect
    calculations is incomplete
    • Energy-lowering reconstructions
    prevalent in a wide & diverse
    range of materials/defects.
    • ShakeNBreak = easily-implemented
    method to combat this and ensure the
    accuracy of defect calculations
    @Kavanagh_Sean_ sean.kavanagh.19@ucl.ac.uk
    1. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* npj Comp Mater 2023
    2. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* J. Open Source Software 2022
    3. Mosquera-Lois & Kavanagh*, Matter 2021
    4. Kavanagh, Walsh, Scanlon ACS Energy Lett 2021
    5. Kavanagh*, Scanlon, Walsh, Freysoldt; Faraday Discussions 2022
    

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49. How Important is This? Very
    VCd
    -1
    VCd
    0
    h+ e-
    Our Method
    (Ground-state)
    Standard Relaxation
    (Metastable)
    h+ capture
    e– capture
    h+ capture
    e– capture
    Kavanagh, Walsh, Scanlon
    ACS Energy Lett 2021
    Inaccurate Structure ➡ Inaccurate Formation Energy ➡
    Inaccurate:
    ➡ Energy
    ➡ Concentration
    ➡ Transition Level
    ➡ Deep/Shallow
    ➡ Doping
    ➡ Carrier capture
    ➡ Diffusion
    ➡ …
    

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50. Why isn’t this an issue for bulk structure prediction?
    Good initial guesses from experimental databases, starting us close to the global minimum
    For unknown crystal structure prediction,
    this is a huge avenue of research
    Ø PES exploration
    But defects are unknown structures!
    No database of known defect structures
    Ø Efficient structure-searching techniques
    required
    

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51. View Slide