Symmetry-Breaking at Defects in Perovskites

Slides for my talk 'Symmetry-Breaking & Reconstruction at Defects in Perovskites' at MRS Spring 2023, San Francisco – discussing the issue of global optimisation for defects in solids, its particular relevance & importance for perovskites, and our work (ShakeNBreak) on tackling this issue.

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

ShakeNBreak website: https://shakenbreak.readthedocs.io/en/latest/

Our general defect calculation package doped is available here: https://github.com/SMTG-UCL/doped

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

Other references:
Matter Preview of Defect Structure Searching: https://www.sciencedirect.com/science/article/pii/S2590238521002733
Metastable defects : https://doi.org/10.1039/D2FD00043A
Recombination at V_Cd in CdTe (case study): https://pubs.acs.org/doi/abs/10.1021/acsenergylett.1c00380

Transcript

1. Standard defect supercell relaxation Seán R. Kavanagh‡ & Irea Mosquera-Lois,‡ Aron Walsh, David O. Scanlon MRS Spring 2023 Symmetry-Breaking & Reconstruction at Defects in Perovskites
2. Standard defect supercell relaxation Seán R. Kavanagh‡ & Irea Mosquera-Lois,‡ Aron Walsh, David O. Scanlon MRS Spring 2023 Symmetry-Breaking & Reconstruction at Defects in Perovskites
3. Defect Calculation Workflow 3 Host primitive cell Goyal et al, Comp Mater Sci 2017
4. Defect Calculation Workflow 4 Host primitive cell Goyal et al, Comp Mater Sci 2017
5. Defect Calculation Workflow 5
6. Defect Calculation Workflow 6
7. Defect Calculation Workflow 7
8. Defect Calculation Workflow 8
9. Defect Calculation Workflow 9
10. Defect Calculation Workflow 10
11. Defect Calculation Workflow 11 ➡ Energy ➡ Concentration ➡ Transition Level ➡ Deep/Shallow ➡ Doping ➡ Carrier capture ➡ Diffusion ➡ …
12. VCd in CdTe
13. Metal-metal dimers possible for vacancies in semiconductors: Lany & Zunger Phys Rev Lett 2004 Lany & Zunger Phys Rev B 2005 VCd in CdTe
14. Metal-metal dimers possible for vacancies in semiconductors: Lany & Zunger Phys Rev Lett 2004 Lany & Zunger Phys Rev B 2005 VCd in CdTe
15. Metal-metal dimers possible for vacancies in semiconductors: Lany & Zunger Phys Rev Lett 2004 Lany & Zunger Phys Rev B 2005 VCd in CdTe
16. VCd in CdTe Tei in CdTe Standard Relaxation ShakeNBreak (Our Method) Kavanagh*, Scanlon, Walsh, Freysoldt Faraday Discussions 2022
17. 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 VCd in CdTe
18. 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 VCd in CdTe
19. Potentially the Wrong Defect! Mosquera-Lois & Kavanagh* Matter 2021 Kavanagh, Walsh, Scanlon ACS Energy Lett 2021 Mosquera-Lois‡ & Kavanagh‡*, Walsh and Scanlon* npj Comput Mater 2023 Standard defect supercell relaxation
20. 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 Mosquera-Lois‡ & Kavanagh‡*, Walsh and Scanlon* npj Comput Mater 2023
21. Defect Calculation Workflow 21
22. How Important/Prevalent is This? Very Literature Examples (reconstructions found serendipitously or through manual searching): • Gallium vacancies, migration and compensation in Ga2 O3 1 • Catalytic activity (divalent metal dopants in CeO2 )2 • CdTe solar cell performance3,4 • Defect absorption / bandgap lowering (Sn-doped Cs3 Bi2 Br9 )5 • Persistent Photoconductivity in Si, GaAs DX centres1,6 • Oxide polarons (in BiVO4 )7 • Colour centres and deep anion vacancies in II-VI compounds8 1. Varley et al J. Phys.: Condens. Matter 2011 2. Kehoe, Scanlon, Watson, Chem Mater 2011 3. Kavanagh, Walsh, Scanlon ACS Energy Lett 2021 4. Kavanagh*, Scanlon, Walsh, Freysoldt Faraday Discussions 2022 5. Krajewska, Kavanagh et al. Chem Sci 2021 6. Du & Zhang Phys Rev B 2005 7. Osterbacka, Ambrosio, Wiktor J Phys Chem C 2022 8. Lany & Zunger Phys Rev Lett 2004 Inaccurate Structure ➡ Inaccurate Formation Energy ➡ Inaccurate: ➡ Energy ➡ Concentration ➡ Transition Level ➡ Deep/Shallow ➡ Doping ➡ Carrier capture ➡ Diffusion ➡ …
23. ShakeNBreak: Summary • 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 aid the accuracy of defect calculations 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
24. Indicators of Defect Reconstructions & Metastability • Multinary composition • Reduced crystal symmetry • Space to distort / ‘open’ crystal structures • Mixed ionic/covalent bonding • Dynamic structure (i.e. more complex PES)
25. Case Study: Double Perovskites (A2 BIBIIIX6 ) Cs2 AgBiBr6 Large energy lowering of ΔE: -0.1 – -2.75 eV for many antisite defects e.g.
26. Case Study: Double Perovskites (A2 BIBIIIX6 ) • AgCs 0, AgCs +1 (all AgCs charge states) • BiCs 0, BiCs +1, BiCs +2 (all BiCs charge states) • BrCs 0 • CsAg -1, CsAg 0, CsAg +1 (all CsAg charge states) • BiAg 0, BiAg +1 • BiAg -2, BiAg -1, BrAg 0 (all BrAg charge states) • AgBi -2 • BrBi 0, BrBi -1, BrBi -2, BrBi -3, BrBi -4 (all BrBi charge states) • AgBr 0, AgBr +1, AgBr +2 (all AgBr charge states) • BiBr 0, BiBr +1, BiBr +2, BiBr +3, BiBr +4, BiBr +5 (all BiBr charge states) • CsBr 0, CsBr +1, CsBr +2 (all CsBr charge states) Cs2 AgBiBr6 Large energy lowering of ΔE: -0.1 – -2.75 eV for many antisite defects
27. BiCs 0 – Neutral Bismuth-on-Caesium Unperturbed; 2 Bi-Br bonds, slightly distorted octahedra ShakeNBreak: tetra-coordinated Bi-Br, off-centred Ag -> ΔE = -1.25 eV
28. BiCs 0 – Neutral Bismuth-on-Caesium Unperturbed; 2 Bi-Br bonds, slightly distorted octahedra ShakeNBreak: tetra-coordinated Bi-Br, off-centred Ag -> ΔE = -1.25 eV
29. BiCs 0 – Neutral Bismuth-on-Caesium Unperturbed; 2 Bi-Br bonds, slightly distorted octahedra ShakeNBreak (metastable): similar tetra-coordinated Bi-Br (square planar), off-centred Ag -> ΔE = -1.1 eV
30. BrAg -2 – Fully-ionised Bromine-on-Silver Unperturbed; 2 elongated Br-Br bonds, undistorted octahedra ShakeNBreak: BrAg displaces from octahedron centre, gives 7-fold coordinated Bi and off-centred Ag -> ΔE = -1.5 eV
31. BiAg 0 – Neutral Bismuth-on-Silver Unperturbed; Bi-Br octahedron replacing Ag-Br, minimal distortion ShakeNBreak: Tetragonal elongation of BiAg octahedron -> square-planar coordination, displaced Ag -> ΔE = -0.35 eV
32. Case Study: Vacancy-Ordered Perovskites (A2 BIVX6 ) AI 2 MIVX6 ≋ A(00/MIV)X3 Kavanagh et al. ‘Frenkel Excitons in Vacancy- Ordered Titanium Halide Perovskites (Cs2 TiX6 )’ J. Phys. Chem. Lett. 2022, 13, 10965–10975 Kavanagh‡ & Liga‡ et al. In Submission Cs2 TiI6 Large energy lowering of ΔE: -0.4 – -2.5 eV for many native defects: • VTi 0, VTi -1, VTi -2, VTi -3, VTi -4 (all VTi charge states) • Ii 0, Ii -1 (all Ii charge states) • Csi +1 • ICs 0, ICs -1, ICs -2 (all ICs charge states) • TiCs 0, TiCs +1, TiCs +2, TiCs +3 (all TiCs charge states) • ITi 0, ITi -1 • TiI +2, TiI +5
33. VTi -4 – Fully-ionised Titanium Vacancy Unperturbed; Slightly contracted octahedron ShakeNBreak: Iodine trimer; ΔE = -0.8 eV
34. VTi -1 Unperturbed; distorted contracted octahedron ShakeNBreak: double Iodine trimer; ΔE = -1.1 eV
35. VTi -1 Unperturbed; distorted contracted octahedron ShakeNBreak: double Iodine trimer; ΔE = -1.1 eV
36. VTi 0 – Neutral Titanium Vacancy Unperturbed; distorted contracted octahedron ShakeNBreak: effective ITi + VI complex -> ΔE = -1.6 eV
37. TiCs +3 – Fully-ionised Titanium-on-Caesium Unperturbed; Ti-Ti bond within Iodine octahedron ShakeNBreak: Ti split, one goes to vacant octahedral site near missing caesium -> ΔE = -2.5 eV
38. TiI +5 – Fully-ionised Titanium-on-Iodine Unperturbed; Ti-Ti bond, distorted octahedron ShakeNBreak: off-centred Ti to vacant octahedral site -> ΔE = -2 eV
39. TiI +5 – Fully-ionised Titanium-on-Iodine Unperturbed; Ti-Ti bond, distorted octahedron ShakeNBreak: off-centred Ti to vacant octahedral site -> ΔE = -2 eV
40. TiI +5 – Fully-ionised Titanium-on-Iodine Unperturbed; Ti-Ti bond, distorted octahedron ShakeNBreak: off-centred Ti to vacant octahedral site -> ΔE = -2 eV
41. What about polarons / self-trapped excitons? A4 MIIX6 : ➡ High thermal sensitivity of PL lifetimes ➡ Ultra-high spatial and thermal resolution devices (for remote thermography) MII = Pb, Sn 1. Yakunin, S. et al. Nature Materials 2019 2. B. Kang & K. Biswas J. Phys. Chem. Lett. 2018
42. Previous calculations (unperturbed relaxations) predict tetragonal contracted octahedron for self-trapped exciton structure. Unperturbed; Tetragonally-Contracted Octahedron ShakeNBreak; Tetragonally-Expanded Octahedron ΔE ~ -0.4 (MII = Pb, Sn)
43. Does it matter? Thanks to Dr. Youngkwang Jung @ Cambridge for the figure! Initial octahedron structure
44. Energy-lowering reconstructions prevalent in a wide & diverse range of materials/defects. 44 Importance of Defect Structure Searching! 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 Particularly strong for perovskites, due to: • Multinary composition • Reduced crystal symmetry • Space to distort / ‘open’ crystal structures • Presence of ionic & covalent bonding • Dynamic crystal structure
45. Studies using ShakeNBreak (and finding lower energy defect structures): • X. Wang, S. R. Kavanagh, D. O. Scanlon, A. Walsh; Under Review at Phys Rev Lett (arXiv: 2302.04901) • C. Krajewska, S. R. Kavanagh et al. Chem Sci 2021 • S. R. Kavanagh*, D. O. Scanlon, A. Walsh, C. Freysoldt Faraday Discussions 2022 • J. Cen et al; J. Mater. Chem. A (Accepted) 2023 • J. Willis, Q. Zhou et al. In preparation. • Y. T. Huang & S. R. Kavanagh et al. Nature Communications 2022 • A. Nicolson et al; Under Review at J. Am. Chem. Soc. (ChemRxiv: 10.26434/chemrxiv-2023-7454p) • Y. Kumagai et al; In submission • A. Samli et al;. In preparation Acknowledgements Profs David Scanlon & Aron Walsh Irea Mosquera-Lois @Kavanagh_Sean_
47. Standard Relaxation (Metastable) Example: Vacancies in Sb2 Se3 /Sb2 S3 Reveals rare 4-electron negative-U behavior and ultra- strong self-compensation in Sb2 S3 & Sb2 Se3 Difference in predicted VSb concentration = 1021 Our Method (Ground-state) Wang, Kavanagh, Scanlon, Walsh; ‘Four-electron Negative-U Vacancy Defects in Antimony Selenide’ Under Review (arXiv: 2302.04901) Do we expect this behaviour in perovskites?
48. 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 2023 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 5. Kavanagh*, Scanlon, Walsh, Freysoldt; Faraday Discussions 2022
49. How Important is This? Very VCd -1 VCd 0 h+ e- Our Method (Ground-state) Standard Relaxation (Metastable) h+ capture e– capture h+ capture e– capture Kavanagh, Walsh, Scanlon ACS Energy Lett 2021 Inaccurate Structure ➡ Inaccurate Formation Energy ➡ Inaccurate: ➡ Energy ➡ Concentration ➡ Transition Level ➡ Deep/Shallow ➡ Doping ➡ Carrier capture ➡ Diffusion ➡ …
50. Why isn’t this an issue for bulk structure prediction? Good initial guesses from experimental databases, starting us close to the global minimum For unknown crystal structure prediction, this is a huge avenue of research Ø PES exploration But defects are unknown structures! No database of known defect structures Ø Efficient structure-searching techniques required