ShakeNBreak: Identifying Ground-State Defect Structures (SMTG Group Meeting Sept 2022)

Presentation for the Scanlon (SMTG) group meeting, September 2022.

Code docs here: https://shakenbreak.readthedocs.io/en/latest/
Preprint here: https://arxiv.org/abs/2207.09862

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

For other research articles and updates, check out my website at:
https://seankavanagh.com/

Transcript

1. 1
   17/09/2022
   Shaking and Breaking
   Seán Kavanagh
   SMTG Group Meeting 15/09/22
   

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2. 2
   17/09/2022
   Shaking and Breaking
   Seán Kavanagh
   SMTG Group Meeting 15/09/22
   

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3. Outline
   • Introduction
   • Example cases
   • Outlook
   • Ongoing development: Pymatgen breaking changes & extra
   user-friendly
   3
   

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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
   Host primitive cell
   Goyal et al, Comp Mater Sci 2017
   

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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
    

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12. Defect Calculation Workflow
    12
    ➡ Energy
    ➡ Concentration
    ➡ Transition Level
    ➡ Deep/Shallow
    ➡ Doping
    ➡ Carrier capture
    ➡ Diffusion
    ➡ …
    

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13. Defect Calculation Workflow
    13
    

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14. Potentially the Wrong Defect!
    Mosquera-Lois & Kavanagh, Matter 2021
    Mosquera-Lois, Kavanagh, Walsh, Scanlon, arXiv 2022
    Standard defect supercell relaxation
    

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15. 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
    

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16. How Prevalent is This? Very
    Standard defect supercell relaxation
    Qualitatively alters transition levels, deep/shallow &
    carrier recombination for VCd
    in CdTe
    Kavanagh, Walsh, Scanlon ACS Energy Lett 2021
    

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17. Defect Calculation Workflow
    17
    

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18. How Important is This? Very
    Incorrect:
    ➡ Energy
    ➡ Concentration
    ➡ Transition Level
    ➡ Deep/Shallow
    ➡ Doping
    ➡ Carrier capture
    ➡ Diffusion
    ➡ …
    Incorrect Structure ➡ Incorrect Formation Energy ➡
    Standard Relaxation (Metastable)
    ShakeNBreak
    (Ground-state)
    ΔE ~ 2 eV
    NV(Sb)
    (Ground-state) / NV(Sb)
    (Metastable) = 1021
    Example: VSb
    in Sb2
    Se3
    /Sb2
    S3
    

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19. How Important is This? Very
    Incorrect:
    ➡ Energy
    ➡ Concentration
    ➡ Transition Level
    ➡ Deep/Shallow
    ➡ Doping
    ➡ Carrier capture
    ➡ Diffusion
    ➡ …
    Incorrect Structure ➡ Incorrect Formation Energy ➡
    VCd
    -1
    VCd
    0
    VCd
    -1
    h+
    e-
    ShakeNBreak
    (Ground-state)
    Standard Relaxation
    (Metastable)
    h+ capture
    e– capture
    h+ capture
    e– capture
    

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20. How Important/Prevalent is This? Very
    Incorrect:
    ➡ Energy
    ➡ Concentration
    ➡ Transition Level
    ➡ Deep/Shallow
    ➡ Doping
    ➡ Carrier capture
    ➡ Diffusion
    ➡ …
    Incorrect Structure ➡ Incorrect Formation Energy ➡
    Further Examples:
    • Doping / Charge Compensation in Sb2
    S3
    & Sb2
    Se3
    1
    • Catalytic activity (divalent metal dopants in CeO2
    )1,2
    • 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. Mosquera-Lois, Kavanagh, Walsh, Scanlon, arXiv 2022
    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
    

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21. Structure Searching Strategies
    1. Electron attractor method
    2. Random sampling
    3. Evolutionary Algorithm
    • Replace defect atom with
    more/less electronegative
    species to trap charge
    • Relax
    • Replace original atom
    • Relax
    Pham & Deskins, J Chem Theory Comp 2021
    

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22. Structure Searching Strategies
    1. Electron attractor method
    2. Random sampling
    3. Evolutionary Algorithm
    • Replace defect atom with
    more/less electronegative
    species to trap charge
    • Relax
    • Replace original atom
    • Relax
    • Works well for polaronic defects
    • Only works for polaronic defects
    • Requires manual effort
    • Requires intuition / prior knowledge of the polaron site
    • Biases toward one specific defect structure (polaron), which may
    not be the ground-state (as observed for e.g. VCd
    , VSb,
    VIn
    …)
    Pham & Deskins, J Chem Theory Comp 2021
    

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23. Structure Searching Strategies
    1. Electron attractor method
    2. Random sampling
    3. Evolutionary Algorithm
    • Generate wide range of trial
    structures by randomly placing
    atoms around defect site
    • (With minimum distance constraints)
    • Relax
    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
    

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24. Structure Searching Strategies
    1. Electron attractor method
    2. Random sampling
    3. Evolutionary Algorithm
    • Generate wide range of trial
    structures by randomly placing
    atoms around defect site
    • With some minimum distance
    constraints
    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
    • Will find the ground state if you test enough structures,
    for each defect
    • Requires manual effort
    • Inefficient; requires many calculations so typically only
    possible with lower levels of theory (which often give
    incorrect defect structures)
    Ø Infeasible for typical full defect studies
    

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25. Structure Searching Strategies
    1. Electron attractor method
    2. Random sampling
    3. Evolutionary Algorithm
    Similar idea:
    • Generate trial structures from
    displacements around defect site
    • Calculate forces and energies
    • Mutate (-> new structures from
    evolutionary algorithm)
    • Repeat until convergence Arrigoni & Madsen npj Comp Mater 2021
    Different hyperparameter choices ➡
    

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26. Structure Searching Strategies
    1. Electron attractor method
    2. Random sampling
    3. Evolutionary Algorithm
    Similar idea:
    • Generate trial structures from
    displacements around defect site
    • Calculate forces and energies
    • Mutate (-> new structures from
    evolutionary algorithm)
    • Repeat until convergence Arrigoni & Madsen npj Comp Mater 2021
    • Powerful method for identifying defect ground-state and
    metastable structures
    • Can be enhanced with ML models
    • Requires manual effort (hyperparameter tuning for each
    defect species)
    • Inefficient; requires many calculations so typically only
    possible with lower levels of theory (which often give
    incorrect defect structures)
    Ø Infeasible for typical full defect studies
    

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27. ShakeNBreak
    Idea: Leverage the localised “molecule-in-a-solid”
    behaviour of point defects:
    • Chemically-guided neighbour bond distortions:
    No. distorted bonds = ΔNo. Electrons
    • Stretch/compress neighbour bonds (+/-50% range)
    ➡ Distortion mesh of trial structures
    • ‘Rattle’: Add small random displacements to break
    symmetry and aid location of global minimum
    • Relax
    

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28. ShakeNBreak
    11 relaxations with 𝚪-only sampling
    

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29. ShakeNBreak
    11 relaxations with 𝚪-only sampling
    

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30. 11 relaxations with 𝚪-only sampling
    ShakeNBreak
    

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31. 11 relaxations with 𝚪-only sampling
    ShakeNBreak
    

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32. Distortion Factor
    11 relaxations with 𝚪-only sampling
    (Spin-Unpolarised for simplicity)
    ShakeNBreak
    

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33. Success with all known cases so far
    (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
    Efficient (<10% computational cost of full defect study)
    Automated & user-friendly (Python API & CLI; only one or
    two lines of code), trivially parallel…
    Distortion Factor
    ShakeNBreak
    

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34. Other Example Cases So Far
    • Kat -> Defects in Y2
    Ti2
    O5
    S2
    , >0.2 eV energy lowering in >15% of cases
    • Adair -> VSi
    in Cu2
    SiSe3
    and others
    • Jiayi -> Defects in LMNO
    • Xinwei (Walsh group) -> Many energy-lowering distortions and metastable
    configurations in Sb2
    Se3
    and Sb2
    S3
    • Zhenzhu (Walsh group) -> Defects in BaZrS3
    • Se -> Lower energy Sei
    • BiOI -> Loweer energy BiI
    • Disordered NaBiS2
    -> Lower energy VNa
    34
    

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35. Looking Forward
    • Materials with hard bonds can require
    adjusting of rattle magnitude. Simple
    to adjust, but can we identify this
    beforehand?
    35
    • With low-symmetry systems, we often have many metastable
    configurations. SnB will give a good best guess of the groundstate
    structure (certainly better than an unperturbed relaxation),
    especially with the catch-all re-run step, but could we be more
    exhaustive?
    

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36. • With low-symmetry systems, we often have many metastable
    configurations. SnB will give a good best guess of the groundstate
    structure (certainly better than an unperturbed relaxation),
    especially with the catch-all re-run step, but could we be more
    exhaustive?
    (Machine-Learned) Force-field approach?
    From standard SnB workflow:
    • ~10 relaxations with ~100 ionic steps per defect (hybrid DFT, Γ-point)
    • VASP MD MLFF uses ~100 reference structures (with energies & forces)…
    • But doesn’t featurise charge state; doesn’t know if it’s looking at VSe
    0, VSe
    -1, VSe
    +1…
    ➡ Could test every possible distortion, identify groundstate & all metastable configurations with (near-)total confidence
    

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37. Ongoing Development: Pymatgen
    37
    

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38. Ongoing Development:
    Identify a defect from a
    defect supercell?
    38
    

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39. 39
    Ongoing Development:
    Identify a defect from a
    defect supercell?
    Harder than it initially seems…
    Need to:
    1. Determine what type of defect is present, based on stoichiometry
    2. Determine where exactly the defect is
    

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42. Conclusions
    42
    • Obtaining the correct defect structure is important!
    • Energy-lowering reconstructions prevalent in a wide & diverse range of
    materials/defects.
    • Particularly common for materials:
    • With mixed ionic-covalent bonding; soft, polarisable, anharmonic
    bonds; low crystal symmetry and/or multinary composition
    ➡ Dimer formation & rebonding
    • Ionic systems where:
    • Defects/dopants introduce large distortions or yield Jahn-
    Teller/crystal-field effects
    • Polarons form
    ShakeNBreak = our method to combat this and aid the accuracy of defect calculations
    

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43. Acknowledgements
    

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44. Acknowledgements
    

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46. 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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48. Unperturbed
    48
    

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49. Unperturbed
    49
    

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50. ShakeNBreak
    50
    

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51. ShakeNBreak
    51
    

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52. ShakeNBreak
    52
    

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53. ShakeNBreak
    53
    

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54. Unperturbed
    54
    

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55. Unperturbed
    55
    

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56. ShakeNBreak
    56
    

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57. ShakeNBreak
    57
    

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58. ShakeNBreak
    58
    

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59. ShakeNBreak
    59
    

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60. ShakeNBreak
    60
    Groundstate baby!
    

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