ShakeNBreak: Identifying Ground-State Defect Structures (SMTG Group Meeting Sept 2022)

Presentation for the Scanlon (SMTG) group meeting, September 2022.

Code docs here: https://shakenbreak.readthedocs.io/en/latest/
Preprint here: https://arxiv.org/abs/2207.09862

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

For other research articles and updates, check out my website at:
https://seankavanagh.com/

Transcript

1. 1 17/09/2022 Shaking and Breaking Seán Kavanagh SMTG Group Meeting 15/09/22
2. 2 17/09/2022 Shaking and Breaking Seán Kavanagh SMTG Group Meeting 15/09/22
3. Outline • Introduction • Example cases • Outlook • Ongoing development: Pymatgen breaking changes & extra user-friendly 3
4. Defect Calculation Workflow 4 Host primitive cell Goyal et al, Comp Mater Sci 2017
5. Defect Calculation Workflow 5 Host primitive cell Goyal et al, Comp Mater Sci 2017
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
12. Defect Calculation Workflow 12 ➡ Energy ➡ Concentration ➡ Transition Level ➡ Deep/Shallow ➡ Doping ➡ Carrier capture ➡ Diffusion ➡ …
13. Defect Calculation Workflow 13
14. Potentially the Wrong Defect! Mosquera-Lois & Kavanagh, Matter 2021 Mosquera-Lois, Kavanagh, Walsh, Scanlon, arXiv 2022 Standard defect supercell relaxation
15. 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
16. How Prevalent is This? Very Standard defect supercell relaxation Qualitatively alters transition levels, deep/shallow & carrier recombination for VCd in CdTe Kavanagh, Walsh, Scanlon ACS Energy Lett 2021
17. Defect Calculation Workflow 17
18. How Important is This? Very Incorrect: ➡ Energy ➡ Concentration ➡ Transition Level ➡ Deep/Shallow ➡ Doping ➡ Carrier capture ➡ Diffusion ➡ … Incorrect Structure ➡ Incorrect Formation Energy ➡ Standard Relaxation (Metastable) ShakeNBreak (Ground-state) ΔE ~ 2 eV NV(Sb) (Ground-state) / NV(Sb) (Metastable) = 1021 Example: VSb in Sb2 Se3 /Sb2 S3
19. How Important is This? Very Incorrect: ➡ Energy ➡ Concentration ➡ Transition Level ➡ Deep/Shallow ➡ Doping ➡ Carrier capture ➡ Diffusion ➡ … Incorrect Structure ➡ Incorrect Formation Energy ➡ VCd -1 VCd 0 VCd -1 h+ e- ShakeNBreak (Ground-state) Standard Relaxation (Metastable) h+ capture e– capture h+ capture e– capture
20. How Important/Prevalent is This? Very Incorrect: ➡ Energy ➡ Concentration ➡ Transition Level ➡ Deep/Shallow ➡ Doping ➡ Carrier capture ➡ Diffusion ➡ … Incorrect Structure ➡ Incorrect Formation Energy ➡ 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, arXiv 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
21. Structure Searching Strategies 1. Electron attractor method 2. Random sampling 3. Evolutionary Algorithm • Replace defect atom with more/less electronegative species to trap charge • Relax • Replace original atom • Relax Pham & Deskins, J Chem Theory Comp 2021
22. Structure Searching Strategies 1. Electron attractor method 2. Random sampling 3. Evolutionary Algorithm • Replace defect atom with more/less electronegative species to trap charge • Relax • Replace original atom • Relax • Works well for polaronic defects • Only works for polaronic defects • Requires manual effort • Requires intuition / prior knowledge of the polaron site • Biases toward one specific defect structure (polaron), which may not be the ground-state (as observed for e.g. VCd , VSb, VIn …) Pham & Deskins, J Chem Theory Comp 2021
23. Structure Searching Strategies 1. Electron attractor method 2. Random sampling 3. Evolutionary Algorithm • Generate wide range of trial structures by randomly placing atoms around defect site • (With minimum distance constraints) • Relax 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
24. Structure Searching Strategies 1. Electron attractor method 2. Random sampling 3. Evolutionary Algorithm • Generate wide range of trial structures by randomly placing atoms around defect site • With some minimum distance constraints 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 • Will find the ground state if you test enough structures, for each defect • Requires manual effort • Inefficient; requires many calculations so typically only possible with lower levels of theory (which often give incorrect defect structures) Ø Infeasible for typical full defect studies
25. Structure Searching Strategies 1. Electron attractor method 2. Random sampling 3. Evolutionary Algorithm Similar idea: • Generate trial structures from displacements around defect site • Calculate forces and energies • Mutate (-> new structures from evolutionary algorithm) • Repeat until convergence Arrigoni & Madsen npj Comp Mater 2021 Different hyperparameter choices ➡
26. Structure Searching Strategies 1. Electron attractor method 2. Random sampling 3. Evolutionary Algorithm Similar idea: • Generate trial structures from displacements around defect site • Calculate forces and energies • Mutate (-> new structures from evolutionary algorithm) • Repeat until convergence Arrigoni & Madsen npj Comp Mater 2021 • Powerful method for identifying defect ground-state and metastable structures • Can be enhanced with ML models • Requires manual effort (hyperparameter tuning for each defect species) • Inefficient; requires many calculations so typically only possible with lower levels of theory (which often give incorrect defect structures) Ø Infeasible for typical full defect studies
27. ShakeNBreak Idea: Leverage the localised “molecule-in-a-solid” behaviour of point defects: • Chemically-guided neighbour bond distortions: No. distorted bonds = ΔNo. 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
28. ShakeNBreak 11 relaxations with 𝚪-only sampling
29. ShakeNBreak 11 relaxations with 𝚪-only sampling
30. 11 relaxations with 𝚪-only sampling ShakeNBreak
31. 11 relaxations with 𝚪-only sampling ShakeNBreak
32. Distortion Factor 11 relaxations with 𝚪-only sampling (Spin-Unpolarised for simplicity) ShakeNBreak
33. 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 Efficient (<10% computational cost of full defect study) Automated & user-friendly (Python API & CLI; only one or two lines of code), trivially parallel… Distortion Factor ShakeNBreak
34. Other Example Cases So Far • Kat -> Defects in Y2 Ti2 O5 S2 , >0.2 eV energy lowering in >15% of cases • Adair -> VSi in Cu2 SiSe3 and others • Jiayi -> Defects in LMNO • Xinwei (Walsh group) -> Many energy-lowering distortions and metastable configurations in Sb2 Se3 and Sb2 S3 • Zhenzhu (Walsh group) -> Defects in BaZrS3 • Se -> Lower energy Sei • BiOI -> Loweer energy BiI • Disordered NaBiS2 -> Lower energy VNa 34
35. Looking Forward • Materials with hard bonds can require adjusting of rattle magnitude. Simple to adjust, but can we identify this beforehand? 35 • With low-symmetry systems, we often have many metastable configurations. SnB will give a good best guess of the groundstate structure (certainly better than an unperturbed relaxation), especially with the catch-all re-run step, but could we be more exhaustive?
36. • With low-symmetry systems, we often have many metastable configurations. SnB will give a good best guess of the groundstate structure (certainly better than an unperturbed relaxation), especially with the catch-all re-run step, but could we be more exhaustive? (Machine-Learned) Force-field approach? From standard SnB workflow: • ~10 relaxations with ~100 ionic steps per defect (hybrid DFT, Γ-point) • VASP MD MLFF uses ~100 reference structures (with energies & forces)… • But doesn’t featurise charge state; doesn’t know if it’s looking at VSe 0, VSe -1, VSe +1… ➡ Could test every possible distortion, identify groundstate & all metastable configurations with (near-)total confidence
37. Ongoing Development: Pymatgen 37
38. Ongoing Development: Identify a defect from a defect supercell? 38
39. 39 Ongoing Development: Identify a defect from a defect supercell? Harder than it initially seems… Need to: 1. Determine what type of defect is present, based on stoichiometry 2. Determine where exactly the defect is
42. Conclusions 42 • Obtaining the correct defect structure is important! • Energy-lowering reconstructions prevalent in a wide & diverse range of materials/defects. • Particularly common for materials: • With mixed ionic-covalent bonding; soft, polarisable, anharmonic bonds; low crystal symmetry and/or multinary composition ➡ Dimer formation & rebonding • Ionic systems where: • Defects/dopants introduce large distortions or yield Jahn- Teller/crystal-field effects • Polarons form ShakeNBreak = our method to combat this and aid the accuracy of defect calculations
43. Acknowledgements
44. Acknowledgements
46. 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
48. Unperturbed 48
49. Unperturbed 49
50. ShakeNBreak 50
51. ShakeNBreak 51
52. ShakeNBreak 52
53. ShakeNBreak 53
54. Unperturbed 54
55. Unperturbed 55
56. ShakeNBreak 56
57. ShakeNBreak 57
58. ShakeNBreak 58
59. ShakeNBreak 59
60. ShakeNBreak 60 Groundstate baby!