Modelling Energy Surfaces of Defects in Solids (APS Metropolis Talk)

'Modelling Energy Surfaces of Defects in Solids' talk at APS March 2025 in Anaheim, for the Metropolis Award.

Presentation recording: https://youtu.be/FvnpAtPFhXc

Google Scholar for References: https://scholar.google.com/citations?user=P-7ICrQAAAAJ&hl=en
Website: https://seankavanagh.com/

Transcript

1. Modelling Energy Surfaces of Defects in Solids Seán R. Kavanagh, Environmental Fellow @ Harvard
2. Modelling Energy Surfaces of Defects in Solids Seán R. Kavanagh, Environmental Fellow @ Harvard
3. Outline 1. Metastability & Global Optimization for Defects 2. Case Studies: I. Charge-Carrier Recombination II. Self-trapped excitons, oxygen trimerization… 3. Machine-Learned Potentials for Defects? 4
4. CdTe: Motivation Most commercially-successful thin-film PV solar cell technology But PV efficiency has stagnated at 22.1% (out of a potential ~32%), limited by defects • Limited p-type doping concentrations • Defect-mediated electron-hole recombination 0 0.25 0.5 0.75 1 1.25 1.5 1.75 Open Circuit Voltage Unavoidable (Absorption, heat, radiation) Non-radiative recombination Current devices
5. 7 Defect-Induced CdTe: Defects Typical growth conditions (early versions) DFT: HSE(34.5% exchange), with spin-orbit coupling Supercell Dimensions: 13 Å Te-Rich Chemical Environment
6. 8 CdTe: Defects (early versions) Typical growth conditions DFT: HSE(34.5% exchange), with spin-orbit coupling VCd 0 VCd -2 VCd -1
7. Defect Recombination Huang, Kavanagh et al. Nanotechnology 2021
8. Defect Recombination e.g. ultra-pure silicon, GaAs, metal halide perovskites Huang, Kavanagh et al. Nanotechnology 2021
9. Defect Recombination Also crucial for photo-catalysts, LEDs, single-photon emitters (qubits)… Huang, Kavanagh et al. Nanotechnology 2021
10. Modelling Electron-Hole Recombination Kavanagh et al. ACS Energy Lett 2021 VCd -1 VCd 0 e– h+
11. VCd -1 VCd 0 VCd *0 Kavanagh et al. ACS Energy Lett 2021 Modelling Electron-Hole Recombination or e– h+
12. Kavanagh et al. ACS Energy Lett 2021 Modelling Electron-Hole Recombination or VCd -1 VCd 0 VCd *0 e– h+
13. VCd is a crucial defect to avoid in CdTe! Explains importance of Cl treatment (partially passivates VCd) Suggests Cd-rich growth conditions are optimal -> Matching current record devices1 1. Li et al. Nature Energy 2021 ACS Energy Lett 2021 Modelling Electron-Hole Recombination or VCd -1 VCd 0 VCd *0 e– h+
14. Standard defect supercell relaxation Exploring the Energy Landscape Mosquera-Lois & Kavanagh*, Matter 2021
15. Defect supercell Bulk supercell = ΔH d Defect Calculation Workflow !! = #exp −Δ) *" + (+ corrections) Squires & Kavanagh et al. In Preparation; Mosquera-Lois, Kavanagh et al. Chem Soc Rev 2023
16. Defect supercell Bulk supercell = ΔH d Defect Calculation Workflow (+ corrections) Structure determines: • Formation energies ØConcentrations ØDoping ØThermodynamics… • Localisation (deep vs shallow) • Recombination activity • Migration • Catalytic activity • ... Chadi & Chang Phys Rev B 1989 Lany & Zunger Phys Rev Lett 2004 Du & Zhang Phys Rev B 2005 Morris, Pickard, Needs Phys Rev B 2008 Varley et al J. Phys.: Condens. Matter 2011 Kehoe, Scanlon, Watson, Chem Mater 2011 Krajewska, Kavanagh et al. Chem Sci 2021 Osterbacka, Wiktor J Phys Chem C 2022 Kononov et al. J. Phys.: Condens. Matter 2023 …
17. Does it matter? Further Examples: • Gallium vacancies, migration and compensation in Ga2O3 1 • Catalytic activity (divalent metal dopants in CeO2)2 • Persistent Photoconductivity in Si, GaAs DX centres3,4 • Hydrogen Complexes in Silicon5 • Defect absorption / bandgap lowering (Sn-doped Cs3Bi2Br9)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. Du & Zhang Phys Rev B 2005 4. Chadi & Chang Phys Rev B 1989 5. Morris, Pickard, Needs Phys Rev B 2008 6. Krajewska, Kavanagh et al. Chem Sci 2021 7. Osterbacka, Ambrosio, Wiktor J Phys Chem C 2022 8. Lany & Zunger Phys Rev Lett 2004 Structure ➡ Energy ➡ Properties (recombination, catalytic activity, diffusion, conductivity…)
18. Why isn’t this an issue for bulk structure optimization? Good initial guesses from experimental databases, starting us close enough to the global minimum (usually) For unknown crystal structure prediction, this is a huge avenue of research, using particle swarm (CALYPSO), random sampling (AIRSS), genetic algorithms (USPEX)… But defects are unknown structures! No database of known defect structures. Ø Efficient structure-searching techniques required Pickard, Phys Rev B 2022
19. 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 (±50% range) ➡ Distortion mesh of trial structures • ‘Rattle’: Add small random displacements to break symmetry and aid location of global minimum • -> Relax Mosquera-Lois & Kavanagh* et al. npj Comp Mater 2023 Mosquera-Lois & Kavanagh* et al. J. Open Source Software 2022 Pham & Deskins JCTC 2020
20. 11 relaxations with !-only sampling ShakeNBreak
21. 11 relaxations with !-only sampling ShakeNBreak
22. 11 relaxations with !-only sampling ShakeNBreak
23. 11 relaxations with !-only sampling (Spin-Unpolarised for simplicity) : ShakeNBreak
24. Successfully reproduces all previously-reported cases (Benchmarks: Si, CdTe, GaAs, CeO2 , ZnO…) Energy-lowering reconstructions identified in a diverse range of materials & defects – found for defects in every material studied (Sb2 (S/Se)3 , In2 O3 , TiO2 , Se, SrTiO3 …) Can locate low-energy metastable structures ➡ Important for diffusion (transition states) and carrier recombination Efficient (<10% computational cost of full defect study) Automated user-friendly (Python API or CLI), trivially parallel… ShakeNBreak Mosquera-Lois & Kavanagh* et al. npj Comp Mater 2023 Mosquera-Lois & Kavanagh* et al. J. Open Source Software 2022
25. ShakeNBreak: Key Examples Battery degradation processes in Ni-rich cathodes [Murdock et al. Adv Mater 2024, Squires et al. ACS Energy Lett 2024, Cen et al. JMCA 2023…] Oxygen vacancy reconstructions in SrTiO3, key to photocatalyst performance [Ogawa, Kavanagh et al. In Submission] Un-stable polarons in CuSbSe2 [Lohan et al. Nature Comms 2025] Charge compensation in transparent conducting oxides [Li, Kavanagh et al. Chem Mater 2024, Cai et al. APL 2025…] Extreme charge compensation, defect metastability & impact on electron-hole recombination in antimony chalcogenide solar cells (Sb2(S/Se)3) [Wang, Kavanagh et al. PCCP 2022, ACS Energy Lett 2022, Phys Rev B 2023, Joule 2024, ACS Energy Lett 2024…] Quantum defects in CaO [Yuan & Hautier APL 2024] …
26. Structural Reconstructions at Defects … …
27. Outline 1. Metastability & Global Optimization for Defects 2. Case Studies: I. Charge-Carrier Recombination II. Self-trapped excitons, oxygen trimerization… 3. Machine-Learned Potentials for Defects? 41
28. Modelling Electron-Hole Recombination VCd -1 VCd 0 e– h+ Also crucial for photo-catalysts, LEDs, single-photon emitters (qubits)…
29. Modelling Electron-Hole Recombination or VCd -1 VCd 0 VCd *0 e– h+
30. Tei in CdTe: Also noted in: • GaN; Alkauskas et al. Phys Rev B 2016 (Spin metastabilities) • Sb2Se3; Wang, Kavanagh et al. Joule 2024 • CuInGaSe2; Dou et al. Phys Rev Appl 2023 • SrTiO3; Ogawa, Kavanagh et al. In Preparation Kavanagh* et al. Faraday Discussions 2022 Kavanagh* et al. ChemRxiv 2025 VSe in t-Se: Carrier Recombination and Metastability
31. ShakeNBreak: Key Examples Beyond defects; self-trapped excitons in low-dimensional vacancy-ordered perovskites (Cs4SnBr6 & Cs4PbBr6) -> Thermally-sensitive emission lifetimes permit ultra-sensitive remote thermal imaging1,2 1. Yakunin et al. Nature Materials 2019 2. Kang & Biswas J Phys Chem Lett 2018 3. Jung, Kavanagh et al. In Preparation ShakeNBreak identifies self-trapped exciton groundstate, explaining ultra-sensitive emission lifetimes3
32. Anion Dimerization / Trimerization Strong Compensation & 4-electron Negative- U Defects in Antimony Chalcogenides Oxygen Trimerization & Split Vacancies in Sb2O5 (Candidate TCO): Standard Relaxation (Metastable) Ground-state VSb -4 VSb 0 VSb VSe Also VCd in CdTe / CdSe, VZn in ZnS / ZnTe, VBi in Bi2S3, VTi in Li4TiS4, VIn in InAgS2…1 1. Mosquera-Lois et al. npj Comput Mater 2024
33. Outline 1. Metastability & Global Optimization for Defects 2. Case Studies: I. Charge-Carrier Recombination II. Self-trapped excitons, oxygen trimerization… 3. Machine-Learned Potentials for Defects? 49
34. Defect Calculations Are Expensive Requirements for sufficient accuracy: • Large simulation supercells • High levels of theory (hybrid DFT or above) • Many calculations (many defect/disorder configurations) • Requirement for structure-searching / global optimization • Inclusion of metastable states in predicting relevant properties (recombination, migration, quantum efficiency…) • … → Expensive, slow and limited 50
35. doped: Calculating Defects in Solids Kavanagh* et al. J Open Source Softw 2024 ! doped.readthedocs.io
36. Machine-Learned Interatomic Potentials • Bespoke models trained on smaller, targeted datasets; • Accurate, cheap to build, but restricted generality • “Universal”/”Foundation” models, trained on large, general datasets • Less accurate and expensive to build, but generalizable across chemical space DFT calculations ML Interatomic Potentials / Density Functionals Reproduction of quantum mechanical energies & forces
37. ShakeNBreak x M3GNet 53 Chen, Ping Ong. Nature Comput Sci 2022 Mosquera-Lois, Kavanagh, Ganose, Walsh. npj Comput Mater 2024 M3GNet re-trained on SnB relaxations in metal chalcogenides successfully predicts reconstructions for unseen defects in unseen compositions for 90% of cases. Energy differences quantitatively unreliable but qualitatively identifies distinct defect structures (~35% prevalence rate of energy-lowering reconstructions (ΔE < -0.1 eV) missed by standard relaxations)
38. Case Study: Split Vacancies 55 VX → Xi + 2 VX (‘Split-vacancy’) Varley et al J. Phys.: Condens. Matter 2011 Kononov et al. J. Phys.: Condens. Matter 2023 Li, Kavanagh et al. Chem Mater 2024 Kavanagh* arXiv (JPhys Energy Emerging Leaders) 2025 VGa in Ga2O3
39. Case Study: Split Vacancies 56 VX → Xi + 2 VX (‘Split-vacancy’) Varley et al J. Phys.: Condens. Matter 2011 Kononov et al. J. Phys.: Condens. Matter 2023 Li, Kavanagh et al. Chem Mater 2024 Kavanagh* arXiv (JPhys Energy Emerging Leaders) 2025 Displacement vs Distance to Defect
40. Case Study: Split Vacancies = Lower energy split vacancy VGa in Ga2O3; ΔE ~ 1 eV Electrostatic energy model: (i.e. Ewald summation)
41. Case Study: Split Vacancies 60 Kavanagh* arXiv (JPhys Energy Emerging Leaders) 2025 1 Fowler et al. J Appl Phys 2024 (c.f. ~10 previously- known cases)1 Kumagai et al. Phys Rev Mater 2021
42. “Exhaustive” = All ML-predicted split vacancies with energies within 0.35 eV of simple vacancy are candidates >2 orders of magnitude reduction of DFT calculations (“discovery acceleration factor”; DAF) Split Vacancies: Electrostatics & MLIPs Kavanagh* arXiv (JPhys Energy Emerging Leaders) 2025 MLIPs (Prevalence ~ 10%)
43. “Exhaustive” = All ML-predicted split vacancies with energies within 0.35 eV of simple vacancy are candidates >2 orders of magnitude reduction of DFT calculations (“discovery acceleration factor”; DAF) Split Vacancies: Electrostatics & MLIPs Kavanagh* arXiv (JPhys Energy Emerging Leaders) 2025 MLIPs (Prevalence ~ 10%) Wednesday, 260B Session MAR-L50
44. Split Vacancies: Electrostatics & MLIPs 63 Kavanagh* arXiv (JPhys Energy Emerging Leaders) 2025 (c.f. ~10 previously- known cases)1 1 Fowler et al. J Appl Phys 2024 Test Set: All known inorganic crystalline solids (ICSD), and predicted metastable materials on the Materials Project database.
45. Split Vacancies: Electrostatics & MLIPs 64 Kavanagh* arXiv (JPhys Energy Emerging Leaders) 2025 (c.f. ~10 previously- known cases)1 1 Fowler et al. J Appl Phys 2024
46. Split Vacancies: Conclusions • Far more common than known (~10 previously-known, now >10,000). • ~10% prevalence rate for cation vacancies in oxides/nitrides • Particularly common in ionic compounds with strong electrostatic driving forces. • Playing a crucial role in ion migration and doping. • Demonstration of the utility of foundation machine-learning potentials – with important caveats… Prevalence
47. Some Key Takeaways 1. Metastability & Global Optimization Defect energy surfaces can be complicated! ShakeNBreak = Accurate & efficient for defect structure-searching 2. Charge-Carrier Recombination Accurate modelling of defect-carrier interactions possible, but… Defect metastability is key! Often catalyzes recombination 3. Machine-Learned Interatomic Potentials (MLIPs) for Defects MLIPs can be powerful for defects – but important caveats! 66
48. Acknowledgements Profs David Scanlon & Aron Walsh doped.readthedocs.io shakenbreak.readthedocs.io @Kavanagh_Sean_ skavanagh@seas.harvard.edu Prof. Boris Kozinsky PhD (UCL & Imperial): Fellowship (Harvard): Thank you for listening!