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/

Transcript

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

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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
   

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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
   

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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
   

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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
   

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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
   

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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
   

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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 –
   

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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.
   

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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.
    

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

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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
    

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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
    

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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.
    

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

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

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

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18. (HSE06 Singleshots on PBEsol Structures)
    

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

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20. View Slide

21. View Slide

22. View Slide

23. View Slide

24. (HSE06 Singleshots on PBEsol Structures)
    

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

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26. SQS; Ag-Bi CN = 9
    

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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.
    

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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.
    

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

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