Cation Disorder in ABZ₂ Chalcogenide Photovoltaics (NaBiS₂ & AgBiS₂) and Symmetry Breaking at Defects

Slides from my talk on 'Cation Disorder on Solar Cell Performance in ABZ₂ Materials (NaBiS₂ & AgBiS₂)' at the MRS Fall 2022 conference in Boston (modified for the CDT-ACM Christmas Party 2022, with additional slides on symmetry-breaking at defects in solids).
Papers mentioned are here:
AgBiS2: https://www.nature.com/articles/s41566-021-00950-4
NaBiS2 (open-access): https://www.nature.com/articles/s41467-022-32669-3
Symmetry-breaking defects:
https://pubs.acs.org/doi/abs/10.1021/acsenergylett.1c00380
https://pubs.rsc.org/en/content/articlehtml/2022/fd/d2fd00043a
https://www.sciencedirect.com/science/article/pii/S2590238521002733
https://arxiv.org/abs/2207.09862
https://shakenbreak.readthedocs.io/

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. 1
   02/01/2023
   Defects and Disorder in
   Semiconductor Materials
   Seán Kavanagh
   Profs: David O. Scanlon & Aron Walsh
   sean.kavanagh.19@ucl.ac.uk
   (University College London & Imperial College London)
   

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2. 2
   02/01/2023
   Part 1:
   Cation Disorder in ABZ2
   Materials
   (NaBiS2
   & AgBiS2
   )
   Seán Kavanagh
   Profs: David O. Scanlon & Aron Walsh
   sean.kavanagh.19@ucl.ac.uk
   (University College London & Imperial College London)
   

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3. Heard about Perovskites?
   3
   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)
   I. Mosquera-Lois and S.R. Kavanagh, Matter 4, 2602 (2021)
   ‘Perovskite-Inspired’
   Materials?
   

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4. 4
   ABZ2
   – ‘Perovskite-Inspired’
   • AI,BIII = Metal cations, Z = Chalcogen (S, Se)
   • Rocksalt crystal structure (𝐹𝑚#
   3𝑚) with AI/BIII cation disorder
   • MX6
   octahedra -> Similar to perovskite motif
   • Close-packed and cation disorder:
   • (Pseudo-)Direct and low bandgaps
   • Lower effective masses1
   • Metal-chalcogen bonds: Stability ⬆
   • Nanocrystal solution synthesis
   AI/BIII
   Z
   1. Y.-T. Huang, S. R. Kavanagh, D. O. Scanlon, A. Walsh and R. L. Z. Hoye, Nanotechnology, 2021, 32, 132004
   

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5. Modelling Disorder – A Challenge for Theory
   Special Quasirandom Structures (SQS)
   g(r)supercell
   ≃ g(r)random
   • Snapshot of total disorder
   Structural Enumeration:
   • Generate all (440) symmetry-inequivalent cation
   arrangements within a 32-atom supercell.
   • Calculate structures, energies, optical & scattering
   properties
   • Correlate with PV performance
   5
   Total
   Disorder
   (𝐹𝑚#
   3𝑚):
   Total Order (𝑅#
   3𝑚):
   

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6. Cation Disorder: Optical Properties (AgBiS2
   )
   6
   (Hybrid DFT)
   Collaborators:
   Dr. Yongjie Wang, Dr. Ignasi
   Burgués-Ceballos, Prof.
   Gerasimos Konstantatos (ICFO)
   Y. Wang‡ & S. R. Kavanagh‡, I. Burgués-Ceballos; A. Walsh, D.O. Scanlon, G. Konstantatos Nature Photonics 2022 16, 235
   

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7. Homogeneous near-random (SQS) disorder:
   Cation Disorder: Optical Properties (AgBiS2
   )
   Inhomogeneous (clustered) disorder: (2 examples)
   Y. Wang‡ & S. R. Kavanagh‡, I. Burgués-Ceballos; A. Walsh, D.O. Scanlon, G. Konstantatos Nature Photonics 2022 16, 235
   

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8. Cation Disorder:
   Control via Annealing
   Collaborators:
   Dr. Yongjie Wang, Dr. Ignasi
   Burgués-Ceballos, Prof.
   Gerasimos Konstantatos (ICFO)
   Y. Wang‡ & S. R. Kavanagh‡, I. Burgués-Ceballos; A. Walsh, D.O. Scanlon, G. Konstantatos Nature Photonics 2022 16, 235
   

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9. Cation Disorder:
   Control via Annealing
   Collaborators:
   Dr. Yongjie Wang, Dr. Ignasi
   Burgués-Ceballos, Prof.
   Gerasimos Konstantatos (ICFO)
   Y. Wang‡ & S. R. Kavanagh‡, I. Burgués-Ceballos; A. Walsh, D.O. Scanlon, G. Konstantatos Nature Photonics 2022 16, 235
   

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10. XRD
    Theory:
    Expt:
    XPS
    Theory:
    Expt:
    TEM
    Theory:
    Expt:
    2θ ⬆
    2θ ⬆
    EBi 5d
    ⬇
    EBi 5d
    ⬇
    aAgBiS₂
    ⬇
    aAgBiS₂
    ⬇
    Cation Disorder: Control via Annealing
    Collaborators:
    Dr. Yongjie Wang, Dr. Ignasi Burgués-Ceballos,
    Prof. Gerasimos Konstantatos (ICFO)
    Y. Wang‡ & S. R. Kavanagh‡, I. Burgués-Ceballos; A. Walsh, D.O. Scanlon, G. Konstantatos Nature Photonics 2022 16, 235
    

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11. AgBiS2
    :
    • Highest absorption coefficient ⍺ of any
    currently-studied PV material
    • Highest efficiency of any Bismuth-based
    solar material
    BiSI BiI3
    Bi2
    S3
    MA3
    Bi2
    I9
    Cs3
    Bi2
    I9
    Cs2
    AgBiBr6
    AgBi2
    I7
    Ag2
    Bi2
    I9
    AgBiS2
    0
    2
    4
    6
    8
    10
    PV Efficiency (%)
    Bi-Based PV
    • Solar cells with record-breaking efficiencies η > 9%,
    using an ultrathin 30 nm absorber (previous η = 6%)
    • Control of atomic disorder facilitates major absorption
    enhancement, allowing high-efficiency ultrathin devices
    Collaborators:
    Dr. Yongjie Wang, Dr. Ignasi
    Burgués-Ceballos, Prof.
    Gerasimos Konstantatos (ICFO)
    Y. Wang‡ & S. R. Kavanagh‡, I. Burgués-Ceballos; A. Walsh, D.O. Scanlon, G. Konstantatos Nature Photonics 2022 16, 235
    

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12. What about NaBiS2
    ?
    AI/BIII
    Z
    Strong absorption ➡ high potential efficiency in ultrathin cells
    Collaborators:
    Y-T. Huang, Prof. R.L.Z. Hoye
    (Oxford) I. Levine, T. Unold (HZB),
    L. M. Herz, S. M. Stranks
    (Cambridge)
    Y.T. Huang‡ & S. R. Kavanagh‡ et al. Nature Communications 2022 13 (1), 1-13
    

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13. Z
    ➡ Calculations reveal trap levels above VBM, at Na-rich pockets
    Y.T. Huang‡ & S. R. Kavanagh‡ et al. Nature Communications 2022 13 (1), 1-13
    Collaborators:
    Y-T. Huang, Prof. R.L.Z. Hoye
    (Oxford) I. Levine, T. Unold (HZB),
    L. M. Herz, S. M. Stranks
    (Cambridge)
    In-gap states can kill PV performance1,2
    1. Kavanagh, Scanlon, Walsh ACS Energy Lett 2021
    2. Kavanagh, Scanlon, Walsh, Freysoldt Faraday Discussions 2022
    

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14. What causes the localised states?
    Na+ = Empty valence shell (s0), Ag+ = Filled shell (d10s0) -> ‘defect-tolerant’1
    ➡ Spectator ion, flat non-bonding VBM
    AI/BIII
    Z
    ➡ Calculations reveal trap levels above VBM, at Na-rich pockets
    1. Y.-T. Huang, S. R. Kavanagh, D. O. Scanlon, A. Walsh and R. L. Z. Hoye, Nanotechnology, 2021, 32, 132004
    

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15. Na+ = Empty valence shell (s0)
    ➡ Spectator ion, flat non-bonding
    VBM
    ➡ Trap levels above VBM, at Na-
    rich pockets
    Cation Disorder in NaBiS2
    : Electronic Properties
    

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16. Trap levels above VBM, at Na-rich pockets
    Cation Disorder in NaBiS2
    : Electronic Properties
    ➡ Ultrafast carrier trapping (𝛕 ~ ps),
    followed by slow decay (𝛕 ~ μs),
    confirmed by pump-probe measurements
    ➡Record efficiency η = 0.6%
    𝛕short
    = 34 ps
    𝛕long
    ~ 6 μs
    

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17. NaBiS2
    : Y.T. Huang‡ & S. R. Kavanagh‡ et al. Nature Communications 2022 13 (1), 1-13
    AgBiS2
    : Y. Wang‡ & S. R. Kavanagh‡, I. Burgués-Ceballos; A. Walsh, D.O. Scanlon, G. Konstantatos Nature Photonics 2022 16, 235
    Key Takeaways & Acknowledgements
    @Kavanagh_Sean_
    Profs David O. Scanlon & Aron Walsh
    (‡ = co-first-authors)
    Disorder = Powerful tool for materials design
    Both the nature of the disorder and the underlying orbital chemistry
    are key considerations for intelligent disorder engineering!
    Collaborators:
    Dr. Y. Wang, Prof. G. Konstantatos
    (ICFO Barcelona, Spain)
    Y-T. Huang, Prof. R. L. Z. Hoye (Oxford), Dr.
    I. Levine, Prof. T. Unold (HZB), Prof L. Herz,
    Prof. S. M. Stranks (Cambridge)
    

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18. 18
    02/01/2023
    Standard defect supercell relaxation
    Seán R. Kavanagh‡ & Irea Mosquera-Lois,‡
    Aron Walsh, David O. Scanlon
    Part 2: Identifying the Ground State
    Structures of Point Defects in Solids
    

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19. Defect Calculation Workflow
    19
    Host primitive cell
    Goyal et al, Comp Mater Sci 2017
    

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20. Defect Calculation Workflow
    20
    Host primitive cell
    Goyal et al, Comp Mater Sci 2017
    

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21. Defect Calculation Workflow
    21
    

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22. Defect Calculation Workflow
    22
    

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23. Defect Calculation Workflow
    23
    

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24. Defect Calculation Workflow
    24
    

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25. Defect Calculation Workflow
    25
    

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26. Defect Calculation Workflow
    26
    

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27. Defect Calculation Workflow
    27
    ➡ Energy
    ➡ Concentration
    ➡ Transition Level
    ➡ Deep/Shallow
    ➡ Doping
    ➡ Carrier capture
    ➡ Diffusion
    ➡ …
    

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28. View Slide

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

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

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

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32. 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
    

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33. 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
    

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34. Potentially the Wrong Defect!
    Mosquera-Lois & Kavanagh, Matter 2021
    Kavanagh, Walsh, Scanlon ACS Energy Lett 2021
    Mosquera-Lois‡ & Kavanagh‡, Walsh, Scanlon, npj Comp Mater 2022
    Standard defect supercell relaxation
    

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35. 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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36. Defect Calculation Workflow
    36
    

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37. 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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38. How Important is This? Very
    Standard Relaxation (Metastable)
    Our Method
    (Ground-state)
    ΔE ~ 2 eV
    NV(Sb)
    (Ground-state) / (Metastable) = 1021
    Example: VSb
    in Sb2
    Se3
    /Sb2
    S3
    Qualitatively alters transition levels, deep/shallow &
    carrier recombination for VSb
    in Sb2
    S3
    & Sb2
    Se3
    Mosquera-Lois‡ & Kavanagh‡, Walsh, Scanlon, npj Comp Mater 2022
    

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39. How Important/Prevalent is This? Very
    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, npj Comp Mater 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
    Inaccurate Structure ➡ Inaccurate Formation Energy ➡
    Inaccurate:
    ➡ Energy
    ➡ Concentration
    ➡ Transition Level
    ➡ Deep/Shallow
    ➡ Doping
    ➡ Carrier capture
    ➡ Diffusion
    ➡ …
    

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40. Structure Searching Strategies
    1. Electron attractor method
    2. Random sampling
    3. Evolutionary Algorithm
    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
    Different hyperparameter choices ➡
    ➡ Good for polaronic defects (but only polaronic defects)
    ➡ Will eventually find the ground-state (may take >100s calculations)
    ➡ Can be enhanced with ML models
    

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41. Structure Searching Strategies
    1. Electron attractor method
    2. Random sampling
    3. Evolutionary Algorithm
    Different hyperparameter choices ➡
    ➡ Good for polaronic defects (but only polaronic defects)
    ➡ Guaranteed to find the ground-state, eventually…
    ➡ Can be enhanced with ML models
    ➡ Significant manual effort (setup & hyperparameter tuning)
    ➡ Inefficient
    ➡ Require many calculations so typically only possible
    with lower levels of theory (which often give incorrect
    defect structures)
    ➡ Infeasible for typical full
    defect studies
    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
    

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42. 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 2022
    Mosquera-Lois‡ & Kavanagh‡, Walsh, Scanlon;
    J. Open Source Software 2022
    

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

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

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45. 11 relaxations with 𝚪-only sampling
    ShakeNBreak
    Mosquera-Lois‡ & Kavanagh‡, Walsh, Scanlon; npj Comp Mater 2022
    Mosquera-Lois‡ & Kavanagh‡, Walsh, Scanlon; J. Open Source Software 2022
    

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46. 11 relaxations with 𝚪-only sampling
    ShakeNBreak
    Mosquera-Lois‡ & Kavanagh‡, Walsh, Scanlon; npj Comp Mater 2022
    Mosquera-Lois‡ & Kavanagh‡, Walsh, Scanlon; J. Open Source Software 2022
    

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47. 11 relaxations with 𝚪-only sampling
    (Spin-Unpolarised for simplicity)
    ShakeNBreak
    

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48. 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.1,2
    Efficient (<10% computational cost of full defect study)
    Automated & user-friendly (Python API & CLI; only one or
    two lines of code), trivially parallel…
    ShakeNBreak
    1. Mosquera-Lois‡ & Kavanagh‡, Walsh, Scanlon; npj Comp Mater 2022
    2. Mosquera-Lois‡ & Kavanagh‡, Walsh, Scanlon; J. Open Source Software 2022
    3. Alkauskas et al. Phys. Rev. B, 2016
    4. Kavanagh, Scanlon, Walsh, Freysoldt; Faraday Discussions 2022
    

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49. Acknowledgements
    Profs David Scanlon & Aron Walsh
    Irea Mosquera-Lois
    

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50. 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 2022
    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
    

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51. Cation Disorder: Optical Properties (AgBiS2
    )
    51
    

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52. Cation Disorder: Optical Properties (AgBiS2
    )
    52
    Collaborators:
    Dr. Yongjie Wang,
    Dr. Ignasi Burgués-
    Ceballos, Prof.
    Gerasimos
    Konstantatos
    (ICFO)
    Y. Wang‡ & S. R. Kavanagh‡, I. Burgués-Ceballos; A. Walsh, D.O. Scanlon, G. Konstantatos Nature Photonics 2022 16, 235
    

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53. XRD
    Theory:
    Expt:
    2θ ⬆
    2θ ⬆
    Cation Disorder: Control via Annealing
    

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54. XRD
    Theory:
    Expt:
    XPS
    Theory:
    Expt:
    2θ ⬆
    2θ ⬆
    EBi 5d
    ⬇
    EBi 5d
    ⬇
    Cation Disorder: Control via Annealing
    

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55. Heard about Perovskites?
    55
    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)
    I. Mosquera-Lois and S.R. Kavanagh, Matter 4, 2602 (2021)
    • Cheap
    • Efficient
    • Solution-processable (quick and cheap
    manufacturing)
    • Tunable (single-junction & tandem application)
    But:
    • Toxic (Pb)
    • Stability Concerns
    

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