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Cation disorder engineering yields AgBiS2 nanocrystals with enhanced optical absorption for efficient ultrathin solar cells

Cation disorder engineering yields AgBiS2 nanocrystals with enhanced optical absorption for efficient ultrathin solar cells

Presentation given at the 'Modelling Club' meeting between the Walsh (Imperial College), Scanlon (UCL) and Morgan (Bath) research groups, on the theoretical investigations behind the paper 'Cation disorder engineering yields AgBiS2 nanocrystals with enhanced optical absorption for efficient ultrathin solar cells'; link: https://www.nature.com/articles/s41566-021-00950-4

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

Seán R. Kavanagh

March 04, 2022
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  1. Modelling Club Meeting
    28/06/21
    Efficiency Improvement via Enhanced
    Absorption in AgBiS2
    Nanocrystal Solar
    Cells
    Seán Kavanagh

    View Slide

  2. AgBiS2
    :
    - Two polymorphs: Trigonal (𝑅"
    3𝑚) & Disordered
    Rocksalt (𝐹𝑚"
    3𝑚).
    - 𝑅"
    3𝑚 thermodynamically favoured at room
    temperature,1-3 but cubic phase (𝐹𝑚"
    3𝑚)
    kinetically stabilised during nanocrystal synthesis.
    - Bandgap range: 1 – 2 eV, depending on
    synthesis conditions (-> phase and nanocrystal
    size).
    1. Guin et al. Chem. Mater. 2013, 7.
    2. Viñes et al. Phys. Rev. B 2016, 94 (23), 235203.
    3. This work.
    S Ag/Bi

    View Slide

  3. Previous AgBiS2
    world record efficiency: 6.3%. ICFO Annealed Samples -> 8.8%, certified
    10 20 30 40 50 60 70 80
    200C
    150C
    28 nm
    47 nm
    100C
    6.2 nm
    w/o TA
    4.2 nm
    2Theta
    Schapbachite
    AgBiS
    2

    View Slide

  4. Computational Strategy
    1. Model disordered rocksalt AgBiS2
    (𝐹𝑚"
    3𝑚), using the Special Quasirandom
    Structure (SQS) approach, via ATAT.
    • Calculate electronic & optical properties and compare with (𝑅"
    3𝑚)
    phase; i.e. (Cation) Order vs Disorder

    View Slide

  5. SQS supercells arrange atoms to match the radial correlation
    functions of a perfect, infinite random structure, allowing
    disordered phases to be modelled using periodic DFT, at
    modest supercell size.
    Special Quasirandom Structures (SQS)
    Ordered, Trigonal (𝑅"
    3𝑚)
    Disordered,
    Cubic (𝐹𝑚"
    3𝑚)
    1. Zunger, A.; Wei, S.-H.; Ferreira, L. G.; Bernard, J. E. Special Quasirandom Structures. Phys. Rev. Lett. 1990, 65 (3), 353–356.
    2. van de Walle, A.; Asta, M.; Ceder, G. The Alloy Theoretic Automated Toolkit: A User Guide. Calphad 2002, 26 (4), 539–553.
    S Ag/Bi

    View Slide

  6. SQS supercells arrange atoms to match the radial correlation
    functions of a perfect, infinite random structure, allowing
    disordered phases to be modelled using periodic DFT, at
    modest supercell size.
    Special Quasirandom Structures (SQS)
    Ordered, Trigonal (𝑅"
    3𝑚)
    Disordered,
    Cubic (𝐹𝑚"
    3𝑚)
    1. Zunger, A.; Wei, S.-H.; Ferreira, L. G.; Bernard, J. E. Special Quasirandom Structures. Phys. Rev. Lett. 1990, 65 (3), 353–356.
    2. van de Walle, A.; Asta, M.; Ceder, G. The Alloy Theoretic Automated Toolkit: A User Guide. Calphad 2002, 26 (4), 539–553.
    Ag/Bi
    S

    View Slide

  7. SQS supercells arrange atoms to match the radial correlation
    functions of a perfect, infinite random structure, allowing
    disordered phases to be modelled using periodic DFT, at
    modest supercell size.
    Special Quasirandom Structures (SQS)
    Disordered,
    Cubic (𝐹𝑚"
    3𝑚)
    1. Zunger, A.; Wei, S.-H.; Ferreira, L. G.; Bernard, J. E. Special Quasirandom Structures. Phys. Rev. Lett. 1990, 65 (3), 353–356.
    2. van de Walle, A.; Asta, M.; Ceder, G. The Alloy Theoretic Automated Toolkit: A User Guide. Calphad 2002, 26 (4), 539–553.
    SQS, Cations Only:
    Ag/Bi
    S

    View Slide

  8. Order (𝑅"
    3𝑚) vs Disorder (𝐹𝑚"
    3𝑚; SQS)
    a (Å) Δa
    𝐹𝑚#
    3𝑚
    PBEsol 5.56 -1.6%
    HSE06 5.67 +0.3%
    Experiment 5.65 –
    𝑅#
    3𝑚
    PBEsol 6.68 -2.3%
    HSE06 6.79 -0.8%
    Experiment 6.84 –

    View Slide

  9. Order (𝑅"
    3𝑚) vs Disorder (𝐹𝑚"
    3𝑚; SQS)
    a (Å) Δa
    𝐹𝑚#
    3𝑚
    PBEsol 5.56 -1.6%
    HSE06 5.67 +0.3%
    Experiment 5.65 –
    𝑅#
    3𝑚
    PBEsol 6.68 -2.3%
    HSE06 6.79 -0.8%
    Experiment 6.84 –
    Ag-S (Å) Bi-S (Å)
    𝐹𝑚#
    3𝑚
    PBEsol 2.74 2.82
    HSE06 2.84 2.82
    Experiment 2.82 2.82
    𝑅#
    3𝑚
    PBEsol 2.72 2.83
    HSE06 2.81 2.83
    Experiment 2.87 - Δ 2.87 + Δ
    Δ unresolved experimentally
    Park, J.-S.; Kim, S.; Hood, S. N.; Walsh, A. Open-Circuit Voltage Deficit in Cu2
    ZnSnS4
    Solar Cells by Interface Bandgap Narrowing. Applied Physics Letters 2018, 113 (21), 212103.
    Ag-S and Bi-S distances (‘bond lengths’)
    are remarkably similar.
    –> Amenable to cation disorder.

    View Slide

  10. Affected by kinetic (growth conditions etc.) and ligand effects, however.
    Under the regular solution approximation, the Gibbs free energy (𝛥𝐺) is given as:
    𝛥𝐺 = 𝛥𝐻 − 𝑇𝛥𝑆!"#$%&'()*%"#)+
    𝛥𝑆!"#$%&'()*%"#)+
    = −𝑁𝑘,
    (𝑥 ln 𝑥 − (1 − 𝑥) ln(1 − 𝑥)), x = 0.5 for (Ag0.5
    Bi0.5
    S)2
    ΔH Order/Disorder
    (meV/atom)
    (Bulk) Thermodynamic
    Transition Temperature (K)
    PBEsol 33.1 1110
    HSE06+SOC (PBEsol-relaxed) 20.7 690
    RPA (PBEsol-relaxed) 22.9 770
    HSE06+SOC (HSE06-relaxed) 17.4 580
    Experiment 500-6201,2
    1. Geller, S.; Wernick, J. H. Acta Cryst 1959, 12 (1), 46–54. 2. Guin, S. N.; Biswas, K. Chem. Mater. 2013, 7.

    View Slide

  11. 𝑹(
    𝟑𝒎
    Indirect:
    0.85 eV
    Direct:
    1.56 eV
    Direct:
    0.69 eV
    𝐅𝐦(
    𝟑𝒎 (SQS)
    Ag
    Bi
    S

    View Slide

  12. Order (𝑅"
    3𝑚) vs Disorder (𝐹𝑚"
    3𝑚; SQS)
    0.0 0.5 1.0 1.5 2.0 2.5 3.0
    Energy (eV)
    0
    1
    2
    3
    4
    5
    Absorption Coefficient α (cm−1)
    1e5
    Fm3m (SQS)
    R3m

    View Slide

  13. Computational Strategy
    1. Model disordered rocksalt AgBiS2
    (𝐹𝑚"
    3𝑚), using the Special Quasirandom
    Structure (SQS) approach, via ATAT.
    • Calculate electronic & optical properties and compare with (𝑅"
    3𝑚)
    phase; i.e. (Cation) Order vs Disorder

    View Slide

  14. Computational Strategy
    1. Model disordered rocksalt AgBiS2
    (𝐹𝑚"
    3𝑚), using the Special Quasirandom
    Structure (SQS) approach, via ATAT.
    • Calculate electronic & optical properties and compare with (𝑅"
    3𝑚)
    phase; i.e. (Cation) Order vs Disorder
    2. Use Jonathan Skelton’s Transformer to enumerate all symmetry-
    inequivalent configurations (cation site orderings) within the 32-atom SQS
    supercell -> 440 structures.
    - Relax and calculate energies with PBEsol.
    - Analyse thermodynamics and optical/electronic trends.

    View Slide

  15. Alternatives: bsym, enumlib (in pymatgen), SOD
    S Ag/Bi
    “Transformer is a Python library
    for transforming structures by
    performing atomic substitutions”

    View Slide

  16. Alternatives: bsym, enumlib (in pymatgen), SOD
    S Ag/Bi
    𝑅"
    3𝑚

    View Slide

  17. Alternatives: bsym, enumlib (in pymatgen), SOD
    S Ag/Bi

    View Slide

  18. (HSE06 Singleshots on PBEsol Structures)

    View Slide

  19. Inhomogeneous disorder
    (Ag-rich and Bi-rich regions)
    Homogeneous (random)
    cation disorder
    (Partial) cation order

    View Slide

  20. View Slide

  21. View Slide

  22. View Slide

  23. View Slide

  24. (HSE06 Singleshots on PBEsol Structures)

    View Slide

  25. Ag-Bi CN = 7 Ag-Bi CN = 5.5

    View Slide

  26. SQS; Ag-Bi CN = 9

    View Slide

  27. Conclusions
    (Partial) inhomogeneous cation disorder (local
    Ag-rich and Bi-rich regions) present initially
    -> Thermalisation / homogenisation via
    annealing, transforming to homogeneous
    disorder (SQS), alongside nanocrystal
    growth.
    Favourable orbital-mixing & greater
    delocalisation of band extrema, alongside size
    effects
    -> Enhanced optical absorption and thus
    improved solar efficiencies.

    View Slide

  28. Experiment SQS
    400 800 1200
    Wavelength (nm)
    0
    2.0 × 105
    4.0 × 105
    6.0 × 105
    8.0 × 105
    1.0 × 106
    Absorption (cm−1)
    Expt. Gap
    S. L. Diedenhofen, M. Bernechea, K. M. Felter, F. C. Grozema and L.
    D. A. Siebbeles, Solar RRL, 2019, 3, 1900075.

    View Slide

  29. Experiment SQS
    600 1200 1800
    Wavelength (nm)
    0
    1.0 × 105
    2.0 × 105
    3.0 × 105
    4.0 × 105
    Absorption (cm−1)

    View Slide