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)
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)
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?
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
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):
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
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
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
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
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
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
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
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
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
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
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
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)
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
19. Defect Calculation Workflow 19 Host primitive cell Goyal et al, Comp Mater Sci 2017
20. Defect Calculation Workflow 20 Host primitive cell Goyal et al, Comp Mater Sci 2017
21. Defect Calculation Workflow 21
22. Defect Calculation Workflow 22
23. Defect Calculation Workflow 23
24. Defect Calculation Workflow 24
25. Defect Calculation Workflow 25
26. Defect Calculation Workflow 26
27. Defect Calculation Workflow 27 ➡ Energy ➡ Concentration ➡ Transition Level ➡ Deep/Shallow ➡ Doping ➡ Carrier capture ➡ Diffusion ➡ …
29. Metal-metal dimers possible for vacancies in semiconductors: Lany & Zunger Phys Rev Lett 2004 Lany & Zunger Phys Rev B 2005
30. Metal-metal dimers possible for vacancies in semiconductors: Lany & Zunger Phys Rev Lett 2004 Lany & Zunger Phys Rev B 2005
31. Metal-metal dimers possible for vacancies in semiconductors: Lany & Zunger Phys Rev Lett 2004 Lany & Zunger Phys Rev B 2005
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
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
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
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
36. Defect Calculation Workflow 36
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 ➡ …
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
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 ➡ …
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
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
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
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
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
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
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
47. 11 relaxations with 𝚪-only sampling (Spin-Unpolarised for simplicity) ShakeNBreak
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
49. Acknowledgements Profs David Scanlon & Aron Walsh Irea Mosquera-Lois
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
51. Cation Disorder: Optical Properties (AgBiS2 ) 51
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
53. XRD Theory: Expt: 2θ ⬆ 2θ ⬆ Cation Disorder: Control via Annealing
54. XRD Theory: Expt: XPS Theory: Expt: 2θ ⬆ 2θ ⬆ EBi 5d ⬇ EBi 5d ⬇ Cation Disorder: Control via Annealing
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