Impact of Defects on Solar Cell Performance in Selenium

Slides for my talk on modelling defects in selenium and their impact on solar cell performance at MRS Spring 2023, San Francisco.

YouTube video recording: https://youtu.be/ZPobC2cS2KY

Hopefully a preprint on this work will be out soon! 🤞

References:
ShakeNBreak website: https://shakenbreak.readthedocs.io/en/latest/
Our general defect calculation package doped is available here: https://github.com/SMTG-UCL/doped

See the referenced paper from Rasmus Nielsen on Se solar cells here: https://doi.org/10.1039/D2TA07729A

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

Transcript

1. 1
   02/05/2023
   Impact of Defects on Solar Cell
   Performance in Selenium
   Seán Kavanagh
   Profs: David O. Scanlon & Aron Walsh
   sean.kavanagh.19@ucl.ac.uk
   (University College London & Imperial College London) Y.-T. Huang, S. R. Kavanagh, D.O. Scanlon, A. Walsh,
   R.L.Z. Hoye, Nanotechnology 32, 132004 (2021)
   

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2. 2
   02/05/2023
   Impact of Defects on Solar Cell
   Performance in Selenium
   Seán Kavanagh
   Profs: David O. Scanlon & Aron Walsh
   sean.kavanagh.19@ucl.ac.uk
   (University College London & Imperial College London) Y.-T. Huang, S. R. Kavanagh, D.O. Scanlon, A. Walsh,
   R.L.Z. Hoye, Nanotechnology 32, 132004 (2021)
   

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3. Why Selenium?
   • First material used for photovoltaic (PV) solar cells, in 1883 (η < 1%).
   • Researchers then moved on to c-Si, CdTe, CZTS/CIGS, perovskites...
   • Recent surge in interest after decades of neglect, following Todorov
   et al. record efficiency η = 6.5% in 2017.
   • Low-temperature solution-growth & processing, “simple” chemistry,
   chain-like structure could yield benign grain boundaries.
   • Wide-bandgap (~1.9 eV) suitable for single-junction or tandem PV.
   3
   

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4. Se PV Efficiency: Limiting Factor?
   4
   2Nielsen et al. J Mater Chem A 2022
   Record Efficiency:1
   η = 6.5% with Voc
   = 969 mV
   Theoretical max η ~ 24% (detailed balance limit)
   Record Voc
   2 = 991 mV
   Eg
   (Se, direct) = 1.95 eV
   ➡ Voc
   deficit > 600 mV, suggesting non-radiative
   recombination at defects to be the key
   contributing factor.
   1Todorov et al. Nat. Commun. 2017
   

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5. Selenium: Bulk Properties
   5
   Strong inter-chain vdW
   dispersion interactions
   ~10% volume decrease when
   including vdW effects
   Theory (Hybrid DFT
   + vdW)
   Experiment
   Direction a,b c a,b c
   Lattice Parameter (Å) 4.34 4.96 4.37 4.95
   Volume (Å3) 81.1 81.9
   εionic
   0.63 0.94 0.461 0.621
   ε∞ (optical)
   6.71 10.28 6.971 11.621
   Esurface
   (J/m2) 0.18 0.1752
   1Danielewicz & Coleman Appl. Opt, 1974
   210.1016/0022-3093(71)90004-4
   

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6. Selenium: Bulk Properties
   6
   Se p
   Direct band gap Eg, dir
   = 1.83 eV (Expt: 1.95 eV)1
   Indirect gap Eg, indir
   = 1.71 eV (Expt: 1.85 eV)2
   ➡ Partial contribution to Voc
   deficit from indirect gap
   1Nielsen et al. J Mater Chem A 2022
   2Moreth Phys Rev Lett 1979
   CBM:
   VBM:
   Theory = HSE06+vdW+SOC
   

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7. Defect Calculation Workflow
   7
   Host primitive cell
   Goyal et al, Comp Mater Sci 2017
   

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8. Defect Calculation Workflow
   8
   Host primitive cell
   Goyal et al, Comp Mater Sci 2017
   

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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
    

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13. Defect Calculation Workflow
    13
    

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14. Defect Calculation Workflow
    14
    

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15. Defect Calculation Workflow
    15
    ➡ Energy
    ➡ Concentration
    ➡ Transition Level
    ➡ Deep/Shallow
    ➡ Doping
    ➡ Carrier capture
    ➡ Diffusion
    ➡ …
    

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16. Computational Defect Thermodynamics
    VBM CBM
    D+1
    D0
    D-1
    Fermi Level E
    F
    (eV)
    Formation Energy ΔH
    X,q
    (eV)
    ε(+1/0) ε(0/-1)
    E
    F
    VBM
    CBM
    ε(+1/0)
    ε(0/-1)
    Kavanagh*, Scanlon, Walsh, Freysoldt Faraday Discussions 2022
    

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17. Intrinsic Defect Formation Energy Diagram
    17
    Sei
    0 = Dominant, lowest energy native defect
    • Electrically benign
    • Neutral across most of the bandgap, with a
    negative-U (0/-2) level just below the CBM.
    0
    -1
    -2
    0
    -2
    +1
    Calculated with doped (GitHub.com/SMTG-UCL/doped)
    & ShakeNBreak (shakenbreak.readthedocs.io), using VASP
    

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18. Why is Sei
    0 so low energy?
    Split-interstitial motif:
    Sei
    0 joins Se chain which
    twists to accommodate.
    ➡ Low-energy & no
    dangling bonds
    -> stays neutral.
    18
    

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19. Intrinsic Defect Formation Energy Diagram
    19
    0
    -1
    -2
    0
    -2
    +1
    Calculated with doped (GitHub.com/SMTG-UCL/doped)
    & ShakeNBreak (shakenbreak.readthedocs.io), using VASP
    VSe
    (0/-1)
    VSe
    (+1/0)
    VSe
    (-1/-2)
    VSe
    -> Moderate formation energy, expect
    low but non-negligible concentrations.
    • Multiple in-gap defect levels, which could
    be active for carrier recombination.
    

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20. Vacancy Defects (VSe
    )
    +1:
    Terminated +
    Bridging Chain
    0* (ΔE = 27 meV):
    ‘Self-healed’
    Chain
    0 and -1:
    Two Terminated
    Chains
    -2:
    Elongated Bonds; ‘Self-
    healed’ + Bridging
    

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21. Intrinsic Defect Formation Energy Diagram
    21
    0
    -1
    -2
    0
    -2
    +1
    Calculated with py-sc-fermi
    = EF
    Anneal Temperature = 300K
    Fermi level (EF
    ) determined by charge neutrality condition: p + ND
    + = n + NA
    –
    

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22. 22
    0
    -1
    -2
    0
    -2
    +1
    = EF
    Intrinsic Defect Formation Energy Diagram
    Anneal Temperature = 463 K (190℃)
    Calculated with py-sc-fermi
    Fermi level (EF
    ) determined by charge neutrality condition: p + ND
    + = n + NA
    –
    

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23. 23
    0
    -1
    -2
    0
    -2
    +1
    = EF
    Intrinsic Defect Formation Energy Diagram
    Anneal Temperature = 1000K
    Calculated with py-sc-fermi
    Fermi level (EF
    ) determined by charge neutrality condition: p + ND
    + = n + NA
    –
    

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24. 24
    • Se without impurities -> insulating/weakly p-type
    • Large p-type doping window
    • High sensitivity to p-type impurities
    • n-type doping not possible
    • But experiment1 sees ~1016 holes/cm-3…
    1Nielsen et al. J Mater Chem A 2022
    0
    -1
    -2
    0
    -2
    +1
    Calculated with doped (GitHub.com/SMTG-UCL/doped)
    & ShakeNBreak (shakenbreak.readthedocs.io), using VASP
    = EF
    Sei
    VSe
    Anneal Temperature = 463 K (190℃)
    

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25. What Else is In There?
    Potential impurities:
    • Halogens are common impurities in chalcogenide materials, often
    present in supplier precursors ➡ F, Cl, Br
    • Typically grown on Tellurium substrates ➡ Te
    • Typically annealed in air to aid crystallization ➡ O
    • Hydrogen is a very common impurity in materials ➡ H
    • Sulfur present in precursors, can bond easily with Se ➡ S
    25
    • Experiment1 sees ~1016 holes/cm-3…
    • Not from intrinsic defects
    

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26. 26
    Substitutions: XSe
    Interstitials: Xi
    F
    Cl
    Br
    H
    O
    S
    Te
    Calculated with doped (GitHub.com/SMTG-UCL/doped)
    & ShakeNBreak (shakenbreak.readthedocs.io) Using dopant-rich chemical potential limits
    Halogens
    Chalcogens
    Hydrogen
    

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27. VSe
    +1:
    Terminated +
    Bridging Chain
    Stable Positive Halogen Interstitials?
    Fi
    +1:
    Two Bridging Chains
    + Se-F Bond
    Fi
    -1:
    Intercalated F-1 ion
    

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28. Energy-lowering reconstructions prevalent in a wide
    & diverse range of materials/defects.
    Selenium no different:
    Large energy lowering of ΔE: 0.1 – 1.1 eV (avg. ~0.6 eV)
    for:
    • VSe
    0
    • FSe
    -1, BrSe
    -1, ClSe
    -1
    • Fi
    0, Fi
    +1
    • Bri
    0, Bri
    +1
    • Cli
    0, Cli
    +1
    • Si
    0, Si
    -1, Hi
    -1, Oi
    -1, Tei
    -1… 28
    e.g. Si
    0
    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
    

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29. 0.0 0.8 1.6
    Fermi Level (eV)
    0.0
    0.5
    1.0
    1.5
    Formation Energy (eV)
    Sei
    VSe
    Fi
    29
    • Fluorine interstitials could increase hole
    concentrations slightly, but still <1013 cm-3
    • Experiment sees ~1016 holes/cm-3…
    Calculated with doped (GitHub.com/SMTG-UCL/doped)
    & ShakeNBreak (shakenbreak.readthedocs.io), using VASP
    = EF
    Anneal Temperature = 463 K (190℃)
    0.0
    0.5
    1.0
    1.5 Sei
    VSe
    Fi
    

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30. Conclusions & Future Steps
    • Self-interstitials are neutral and benign for recombination, but Se
    vacancies could capture charge carriers.
    • ➡ Explicitly calculate non-radiative recombination rates of Vse
    • ➡ Devise passivation strategies; out-of-equilibrium Se over-pressures? Fermi
    level control during growth/annealing?
    • Hydrogen/halogens/chalcogens do not seem to be the cause of p-
    type doping in Selenium. Se chains show strong valence alternation
    & re-bonding to self-compensate.
    • ➡ Pnictogens (N, P, As) perhaps? Chalcogen substitutions are low energy,
    pnictogens could also substitute and be under-valent (-> negatively-charged)
    30
    

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31. Acknowledgements
    31
    @Kavanagh_Sean_
    sean.kavanagh.19@ucl.ac.uk
    Rasmus Nielsen @ DTU Physics
    -> Growing & characterizing
    Selenium thin-films for PV
    Talk Friday morning:
    EN04.14.02: The Renaissance
    of Selenium Thin-Film Solar
    Cells; April 14, 8.45-9 AM
    Profs David Scanlon & Aron Walsh
    Alp Samli
    Intrinsic:
    

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32. Other Results:
    Band Alignment
    Lower VBM compared
    to Sb2
    Se3
    as expected
    (anti-bonding Sb s – Se
    p interaction in Sb2
    Se3
    gives raised VBM)
    32
    

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33. Other results:
    • Interestingly, PBEsol seems to perform terribly for this material, with or
    without D3 vdW dispersion correction. Gives lattice parameter errors
    ~8%, HSE06-on-PBEsol structure gives a bandgap underestimated by
    50% compared to HSE06-on-HSE06 or experiment, and the ionic
    dielectric is off by an order of magnitude (again compared to HSE06 or
    experiment which match) due to the severely underestimated interchain
    distances (which makes a big difference to inter-chain interactions)
    • PBE does better, but still not great (checked against Materials Project
    PBE results). Errors of around 3-4% in the lattice parameters both with
    and without D3 (overestimates a,b without D3, underestimates with D3).
    • Dispersion-corrected hybrid DFT (HSE06+D3) is very accurate for the
    bulk properties of Se on the other hand; gives lattice parameters
    matching experiment to 1%, closely matches the experimental bandgap
    (ΔEg
    <0.1 eV), matches the experimental dielectric screening (both ionic
    and electronic contributions) very well…
    33
    

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