ShakeNBreak: Symmetry-Breaking and Reconstruction at Defects in Solids

Pre-recording of my talk 'Symmetry-Breaking and Reconstruction at Defects in Solids' at APS March 2023 in Las Vegas, USA – discussing the issue of global optimisation for defects in solids, its importance and our work (ShakeNBreak) on tackling this issue.

Talk recording on YouTube: https://youtu.be/aqXlyLofLSU

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

For other talks on YouTube, have a look at my channel!
For other research articles see:
https://bit.ly/3pBMxOG

Slides for my talks can be found here:
https://speakerdeck.com/kavanase

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
   APS March 2023
   I. Mosquera-Lois‡ & S. R. Kavanagh‡*, A. Walsh and D. O. Scanlon*,
   npj Comput Mater, 2023, 9, 1–11
   Identifying the Ground State
   Structures of Point Defects in Solids
   

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2. Standard defect supercell relaxation
   Identifying the Ground State
   Structures of Point Defects in Solids
   Seán R. Kavanagh‡ & Irea Mosquera-Lois,‡
   Aron Walsh, David O. Scanlon
   APS March 2023
   I. Mosquera-Lois‡ & S. R. Kavanagh‡*, A. Walsh and D. O. Scanlon*,
   npj Comput Mater, 2023, 9, 1–11
   

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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)
    

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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 is This?
    Kavanagh*, Scanlon, Walsh, Freysoldt Faraday Discussions 2022
    Inaccurate Structure ➡ Inaccurate Formation Energy ➡ Inaccurate:
    ➡ Energy
    ➡ Concentration
    ➡ Transition Level
    ➡ Deep/Shallow
    ➡ Doping
    ➡ Carrier capture
    ➡ Diffusion
    ➡ …
    

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23. How Important is This? Very
    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 at Phys Rev Lett (arXiv: 2302.04901)
    

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24. How Important/Prevalent is This? Very
    Further Examples:
    • Gallium vacancies, migration and compensation in Ga2
    O3
    1
    • Catalytic activity (divalent metal dopants in CeO2
    )2
    • CdTe solar cell performance3
    • Defect absorption / bandgap lowering (Sn-doped Cs3
    Bi2
    Br9
    )4
    • Persistent Photoconductivity in Si, GaAs DX centres1,5
    • Oxide polarons (in BiVO4
    )6
    • Colour centres and deep anion vacancies in II-VI compounds7
    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. Krajewska, Kavanagh et al. Chem Sci 2021
    5. Du & Zhang Phys Rev B 2005
    6. Osterbacka, Ambrosio, Wiktor J Phys Chem C 2022
    7. 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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25. Structure Searching Strategies
    1. Electron attractor method
    2. Random sampling
    3. Evolutionary Algorithm
    ➡ Good for polaronic defects (but only polaronic defects)
    ➡ Guaranteed to find the ground-state, eventually…
    ➡ Can be enhanced with ML models
    Pham & Deskins, J Chem Theory Comp 2021
    Huang, M. et al. J. Semicond 2022
    Pickard & Needs. Phys Rev Lett 2006
    Morris, Pickard, Needs. Phys Rev B 2008
    Morris, Pickard, Needs. Phys Rev B 2009
    Arrigoni & Madsen npj Comp Mater 2021
    ➡ Significant manual effort (setup & hyperparameter tuning)
    ➡ Inefficient
    ➡ Require many calculations so typically only possible
    with cheap inaccurate levels of theory (semi-local DFT)
    ➡ Infeasible for typical full defect studies
    Further details in: Mosquera-Lois‡ & Kavanagh‡*, Walsh and Scanlon* npj Comput Mater 2023
    

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26. Our Method: ShakeNBreak
    Idea: Leverage the localised “molecule-in-a-solid”
    behaviour of point defects:
    • Chemically-guided neighbour bond distortions:
    No. distorted bonds = Δ{Valence Electrons}
    • Stretch/compress neighbour bonds (±60% range)
    ➡ Distortion mesh of trial structures
    • ‘Rattle’: Add small random displacements to break
    symmetry and aid location of global minimum
    • Relax
    Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon*; npj Comp Mater 2023
    Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon*; J. Open Source Software 2022
    

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27. ShakeNBreak
    11 relaxations with 𝚪-only sampling
    Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* npj Comp Mater 2023
    Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* J. Open Source Software 2022
    

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28. ShakeNBreak
    11 relaxations with 𝚪-only sampling
    Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* npj Comp Mater 2023
    Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* J. Open Source Software 2022
    

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29. 11 relaxations with 𝚪-only sampling
    ShakeNBreak
    Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* npj Comp Mater 2023
    Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* J. Open Source Software 2022
    

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30. 11 relaxations with 𝚪-only sampling
    ShakeNBreak
    Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* npj Comp Mater 2023
    Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon* J. Open Source Software 2022
    

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31. 11 relaxations with 𝚪-only sampling
    (Spin-Unpolarised for simplicity)
    ShakeNBreak
    :
    

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32. Successfully reproduces all previously-reported cases (so far!)
    (Benchmarks: Si, CdTe, GaAs, CeO2
    , ZnO…)
    Energy-lowering reconstructions identified in a diverse
    range of materials & defects
    (Sb2
    S3
    /Sb2
    Se3
    , In2
    O3
    , TiO2
    , Si, CdTe, GaAs, CeO2
    , ZnO)
    Can locate low-energy metastable structures
    ➡ Important for diffusion (transition states) and carrier
    recombination.3-5
    Efficient (<10% computational cost of full defect study)
    Automated & super user-friendly (Python API or CLI),
    trivially parallel…
    ShakeNBreak
    1. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon*; npj Comp Mater 2023
    2. Mosquera-Lois‡ & Kavanagh‡*, Walsh, Scanlon*; J. Open Source Software 2022
    3. Alkauskas et al. Phys. Rev. B, 2016
    4. Kavanagh, Walsh, Scanlon ACS Energy Lett 2021
    5. Kavanagh*, Scanlon, Walsh, Freysoldt; Faraday Discussions 2022
    :
    

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33. Sneak Preview:
    Slide Credit: Aron Walsh (Defects Seminar/Invited Talks 2023)
    Example: VO
    +1 in Na2
    TiSiO5
    Collaboration w/Prof. Yu Kumagai @
    Tohoku University, Japan
    High-throughput search for symmetry-
    breaking at oxygen vacancies
    >200 oxides calculated so far
    Empirically, symmetry-breaking
    particularly likely with:
    - Multinary composition
    - Reduced crystal symmetry
    - Mixed ionic/covalent bonding
    (i.e. more complex potential energy
    surface, as expected)
    

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34. Acknowledgements
    Profs David Scanlon & Aron Walsh
    Irea Mosquera-Lois
    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
    • S. R. Kavanagh*, D. O. Scanlon, A. Walsh, C. Freysoldt Faraday Discussions
    • J. Cen et al; Under Review at J. Mater. Chem. A, (ChemRxiv: 10.26434/chemrxiv-2023-nk8lr)
    • J. Willis, Q. Zhou et al. In preparation.
    • Y. T. Huang & S. R. Kavanagh et al. Nature Communications
    • A. Nicolson et al; In preparation – ChemRxiv next week!
    • Y. Kumagai et al; In submission
    • A. Samli et al;. In preparation
    

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35. 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
    Catch me at Tuesday’s poster session for more discussion!
    

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36. 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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37. 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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38. 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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39. Parameter Testing
    Tip of the iceberg…
    

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40. View Slide