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

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Transcript

1. Modelling Club Meeting 28/06/21 Efficiency Improvement via Enhanced Absorption in AgBiS2 Nanocrystal Solar Cells Seán Kavanagh
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
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
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
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
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
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
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 –
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.
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.
11. 𝑹( 𝟑𝒎 Indirect: 0.85 eV Direct: 1.56 eV Direct: 0.69 eV 𝐅𝐦( 𝟑𝒎 (SQS) Ag Bi S
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
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
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.
15. Alternatives: bsym, enumlib (in pymatgen), SOD S Ag/Bi “Transformer is a Python library for transforming structures by performing atomic substitutions”
16. Alternatives: bsym, enumlib (in pymatgen), SOD S Ag/Bi 𝑅" 3𝑚
17. Alternatives: bsym, enumlib (in pymatgen), SOD S Ag/Bi
18. (HSE06 Singleshots on PBEsol Structures)
19. Inhomogeneous disorder (Ag-rich and Bi-rich regions) Homogeneous (random) cation disorder (Partial) cation order
24. (HSE06 Singleshots on PBEsol Structures)
25. Ag-Bi CN = 7 Ag-Bi CN = 5.5
26. SQS; Ag-Bi CN = 9
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.
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.
29. Experiment SQS 600 1200 1800 Wavelength (nm) 0 1.0 × 105 2.0 × 105 3.0 × 105 4.0 × 105 Absorption (cm−1)