1 02/05/2023 [email protected] Tin & Titanium Vacancy-Ordered Halide Perovskites: Cs2 (Sn/Ti)X6 Seán R. Kavanagh*, Shanti M. Liga, Christopher N. Savory, Gerasimos Konstantatos, Aron Walsh & David O. Scanlon* 

2 02/05/2023 [email protected] Tin & Titanium Vacancy-Ordered Halide Perovskites: Cs2 (Sn/Ti)X6 Seán R. Kavanagh*, Shanti M. Liga, Christopher N. Savory, Gerasimos Konstantatos, Aron Walsh & David O. Scanlon* 

3 ‘Perovskite-Inspired’ Materials? 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) 

4 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) Alternative Crystal Structures but Chemically-Similar: -> Cations with filled (semi-)valence orbitals Sb2 Se3 & Sb2 S3 : X. Wang, Z. Li, S.R. Kavanagh et al. Phys. Chem. Chem. Phys. 2022 X. Wang, A.M. Ganose, S.R. Kavanagh et al. ACS Energy Lett. 2022 X. Wang, S.R. Kavanagh et al. Under Review at Phys Rev Lett Sn2 SbS2 I3 : S.R. Kavanagh et al. Materials Horizons 2021 A. Nicolson, S. R. Kavanagh et al. Under Review at J. Am. Chem. Soc. AgBiS2 & NaBiS2 : S. R. Kavanagh‡ & Y. Wang‡ et al. Nature Photonics 2022 S. R. Kavanagh‡ & Y. Huang‡ et al. Nature Communications 2022 Cu2 SiSe3 : A. Nicolson, S.R. Kavanagh et al. Under Review at ACS Energy Lett. Also BiOI, SbSeI, Cu2 GeSe3 … ‘Perovskite-Inspired’ Materials? Perovskite Structure: AI 2 BIBIIIX6 : Cs2 AgBiBr6 & Cs2 AgSbBr6 : A. H. Slavney et al. J. Am. Chem. Soc. 2016 S. R. Kavanagh‡ & Z. Li‡ et al. J. Mater. Chem. A, 2020 AI 2 BIVX6 : Cs2 TiX6 & Cs2 SnX6 : M. Chen et al. Joule, 2018 S. R. Kavanagh et al. J. Phys. Chem. Lett., 2022 S. R. Kavanagh‡ & S. M. Liga‡ et al. In Submission AI 3 BIII 2 X9 : Cs3 Bi2 Br9 : B.-B. Yu et al. J. Mater. Chem. A, 2019 C. J. Krajewska, S. R. Kavanagh et al. Chem. Sci., 2021 

6 • M4+: Sn4+, Te4+, Ge4+, Ti4+, Zr4+, Hf4+ • Isolated MX6 octahedra • Non-toxic • Fully-oxidised cations: Stability ⬆ • Solution synthesis (nanocrystals / thin films) • Best solar cell performance of η = 3.3% for Cs2 TiBr6 (best non-Sn lead-free perovskite efficiency)2 1. Y.-T. Huang, S. R. Kavanagh, D. O. Scanlon, A. Walsh and R. L. Z. Hoye, Nanotechnology, (2021), 32, 132004. 2. M. Chen, M.-G. Ju, A. D. Carl, Y. Zong, R. L. Grimm, J. Gu, X. C. Zeng, Y. Zhou and N. P. Padture, Joule, (2018), 2, 558–570. AI 2 MIVX6 ≋ A(00/MIV)X3 Perovskite-Inspired: Vacancy-Ordered (Double) Perovskites 

7 Cs2 MX6 – Crystal Structure AI 2 MIVX6 ≋ A(00/MIV)X3 

8 Cs2 MX6 – Crystal Structure AI 2 MIVX6 ≋ A(00/MIV)X3 

9 Cs2 MX6 – Crystal Structure Cs2 SnCl6 Cs2 SnBr6 Cs2 SnI6 Cs2 TiCl6 Cs2 TiBr6 Cs2 TiI6 Δa (Hybrid DFT) +2.8% +3.5% +2.7% +2.6% +2.9% +2.3% Δa (Hybrid DFT + vdW) -0.4% +0.1% -0.9% -0.6% -0.6% -1.5% aExp (Å) 10.36 10.77 11.64 10.24 10.68 11.50 ΔEg w/vdW (eV) -0.14 -0.23 -0.31 -0.04 -0.08 -0.15 Strong dispersion (vdW) interactions between ’molecular’ MX6 octahedra (also for related vacancy-ordered A4 MX6 ) Improved agreement with experiment ✅ Bandgap decrease ⬇ Hybrid DFT = HSE06+SOC a(Cl) < a(Br) < a(I) a(Sn) > a(Ti) 

10 Cs2 MX6 – Electronic Structure • Filled (d10/s2) ➡ empty (d0/s0) cation subshells • Non-bonding (rather than anti- bonding) VBM, with weaker dispersion & heavier hole masses. AIMIIX3 ➡ AI 2 MIVX6 Cs2 SnI6 • Disperse Sn s – X p interactions • Low me (CBM) for Cs2 SnX6 Symmetry-forbidden Symmetry-allowed 

11 Cs2 MX6 – Electronic Structure Cs2 SnI6 

12 Cs2 MX6 – Electronic Structure AIMIIX3 ➡ AI 2 MIVX6 • Filled (d10/s2) ➡ empty (d0/s0) cation subshells • Non-bonding (rather than anti- bonding) VBM, with weaker dispersion & heavier hole masses. • Weak Ti d – X p interactions • Flat Ti d CBM • Heavy me (CBM) for Cs2 TiX6 Cs2 TiI6 Symmetry-forbidden Symmetry-allowed 

13 Cs2 MX6 – Electronic Structure Cs2 TiI6 

14 Cs2 MX6 – Electronic Structure Cs2 SnCl6 Cs2 SnBr6 Cs2 SnI6 Cs2 TiCl6 Cs2 TiBr6 Cs2 TiI6 Eg, Optical (Hybrid DFT; eV) 4.5 2.9 1.2 4.0 3.0 1.9 Eg, Optical (Experiment; eV) 4.4-4.9 2.7-3.3 1.25-1.3 2.8-3.4 1.8-2.3 1.0-1.2 Hybrid DFT = HSE06+SOC+vdW • Agreement with experiment for Cs2 SnX6 • Severe overestimation of experimental bandgap by DFT for Cs2 TiX6 Eg (Cl) > Eg (Br) > Eg (I) Bandgap overestimation for Cs2 TiX6 witnessed across the literature: Chen, M. et al. Joule 2, 558–570 (2018). Ju, M.-G. et al. ACS Energy Lett. 3, 297–304 (2018). Kong, D. et al. J. Mater. Chem. C 8, 1591–1597 (2020). Euvrard, J., Wang, X., Li, T., Yan, Y. & Mitzi, D. B. J. Mater. Chem. A 8, 4049–4054 (2020). Mahmood, Q. et al. Materials Science in Semiconductor Processing 137, 106180 (2022). Li, W., Zhu, S., Zhao, Y. & Qiu, Y. Journal of Solid State Chemistry 284, 121213 (2020). Cucco, B. et al. Appl. Phys. Lett. 119, 181903 (2021). … 

15 Cs2 TiX6 – Electronic Structure (Reminder) Cs2 TiI6 

Cs2 TiX6 – Electronic Structure GW ➡ Worse bandgap overestimation (as found by Cucco at al.1) GW+BSE ➡ Excellent agreement! 1. Cucco, B. et al. Appl. Phys. Lett. 119, 181903 (2021). 

17 Cs2 TiX6 – Electronic Structure GW ➡ Worse bandgap overestimation (as found by Cucco at al.1) GW+BSE ➡ Excellent agreement! 1. Cucco, B. et al. Appl. Phys. Lett. 119, 181903 (2021). 

18 Cs2 MX6 – Electronic Structure 

Cs2 MX6 – Electronic Structure 

20 Cs2 MX6 – Electronic Structure Cs2 TiI6 Cs2 SnI6 Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975 

Cs2 MX6 – Ultra-Strong Excitons Ultra-strong exciton binding despite relatively low electronic bandgaps. -> Similar results obtained with vertex-corrected GŴ (courtesy of Dr. Chris Savory) -> Calculation parameters triple-checked Similar results reported: Cucco, Katan, Even, Kepenekian, Volonakis ACS Mater Lett 2023 Bhumla, Jain, Sheoran, Bhattacharya J Phys Chem Lett 2023 Zhang, Gao, Cruz, Sun, Zhang, Zhao arXiv:2211.05323 Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975 

Cs2 MX6 – Ultra-Strong Excitons 1. B. Cunningham, M. Gruening, D. Pashov and M. van Schilfgaarde, arXiv:2106.05759 [cond-mat], (2021). 2. S. Acharya, D. Pashov, A. N. Rudenko, M. Rösner, M. van Schilfgaarde and M. I. Katsnelson, npj Comput. Mater., (2021), 7, 208. Suspiciously large GW quasiparticle bandgaps, and thus exciton binding… Underscreening of electron interactions in GW1,2 could result from localized orbitals and large vacant space? -> Similar results obtained with vertex-corrected GŴ (courtesy of Dr. Chris Savory) -> Calculation parameters triple-checked Similar results reported: Cucco, Katan, Even, Kepenekian, Volonakis ACS Mater Lett 2023 Bhumla, Jain, Sheoran, Bhattacharya J Phys Chem Lett 2023 Zhang, Gao, Cruz, Sun, Zhang, Zhao arXiv:2211.05323 Kavanagh et al. J. Phys. Chem. Lett. 2022, 13, 10965–10975 

Cs2 SnX6 = Mostly stable under air, thermal, water & photo stresses. X = I (Cs2 SnI6 ) shows some very slow decomposition in air. X = Br, Cl ➡ Stable in (humid) air. 23 Cs2 MX6 – Stability Saporov et al. Chem Mater 2016 

Cs2 TiX6 : X = I: Unstable in air. X = Br: Stable under heat and light. Stability in air? • 1Chen et al. Joule 2018 ➡ Thin films, stable in humid air • 2Kong et al. J. Mater. Chem. C 2019 ➡ Powder, slight decomposition in humid air • 3Euvrard et al. J. Mater. Chem. A 2020 ➡ Powder, decomposition in humid air (~20h) • 4Grandhi et al. Nanomaterials 2021 ➡ Nanocrystal films, slow decomposition in air (~1 wk) X = Cl: Very slow decomposition in air (~1-2% over 2 weeks).2,4 24 Cs2 MX6 – Stability Cs2 TiBr6 Cs2 TiI6 

Intrinsic Thermodynamic Stability Cs2 SnI6 Cs2 SnBr6 Cs2 SnCl6 Cs2 TiI6 Cs2 TiBr6 Cs2 TiCl6 Hybrid DFT + vdW Decomposition Energy (eV) +56 meV +129 meV +174 meV +75 meV +120 meV +162 meV 25 • Positive decompositions energies ➡ Thermodynamically stable in each case, as witnessed experimentally (stable in inert atmospheres) • Van der Waal’s dispersion interactions found to be significant in stabilizing Cs2 MX6 : Cs2 SnI6 Cs2 TiI6 Hybrid DFT Decomposition Energy (eV) +14 meV +51 meV Hybrid DFT + vdW Decomposition Energy (eV) +56 meV +75 meV Increasing stability as X: I -> Br -> Cl 

External Decomposition in Oxygen/Water • O2 decomposition significantly more favourable for M = Ti as expected (strong stability of TiO2 ) • O2 decomposition less favoured as X -> I, Br, Cl. Note: Reaction kinetics ignored here. Reactants Products ΔH (eV) Cs2 SnI6 + O2 SnO2 + 2CsI + 4I(s) -2.43 Cs2 SnBr6 + O2 SnO2 + 2CsBr + 2Br2(l) -0.10 Cs2 SnCl6 + O2 SnO2 + 2CsCl + 2Cl2(g) +0.82 Reactants Products ΔH (eV) Cs2 TiI6 + O2 TiO2 + 2CsI3 + 4I(s) -4.90 Cs2 TiBr6 + O2 TiO2 + 2CsBr + 2Br2(l) -1.70 Cs2 TiCl6 + O2 TiO2 + 2CsCl + 2Cl2(g) -0.38 Aqueous Decomposition: Cs2 MX6 + H2 O ➡ MO2 + 2 CsX + 4HX(g) Gaseous product (4HX(g) ) means reaction energy ΔE is a function of pHX (i.e. environment-dependent) 

• Experimentally, Cs2 MX6 found to be hygroscopic and to exhibit accelerated decomposition under humid oxygen atmospheres. • Calculations find aqueous decomposition to be thermodynamically favoured under certain HX(g) partial pressure ranges. • Additionally, potential kinetic/catalytic effect from surface hydration. O2 /H2 O Decomposition 27 Humid Air Dessicated Air E.G: Cs2 (Ti0.4 Sn0.6 )Br6 

Cs2 MX6 Stability: Conclusions • Cs2 SnX6 far more stable than Cs2 TiX6 in ambient atmospheres. • However Cs2 TiX6 is interesting because: • Ultra-strong Frenkel excitons ➡ Playground to study associated physical phenomena • Initially, promising photovoltaic performance (diminished by identification of strong excitons however) • Non-linear optics: Only known third-harmonic generation (THG) active lead- free perovskite, thanks to centrosymmetric crystal structure.1 • Can we alloy Sn/Ti to tune stability and optical/electronic properties? 28 1Grandhi et al. Nanomaterials 2021 

Special Quasirandom Structures (SQS) with hybrid DFT including spin-orbit coupling 29 Cs2 (Snx Ti1-x )X6 

30 d(Ti – X) in Cs2 (Snx Ti1-x )X6 ≃ d(Ti – X) in Cs2 TiX6 d(Sn – X) in Cs2 (Snx Ti1-x )X6 ≃ d(Sn – X) in Cs2 SnX6 Cs2 (Snx Ti1-x )X6 Consistent behaviour across all X = I, Br, Cl HSE06+SOC+vdW 

31 Cs2 (Snx Ti1-x )X6 : Optical Properties Cs2 (Snx Ti1-x )I6 Cs2 (Snx Ti1-x )Br6 Quasiparticle spectrum with hybrid DFT + SOC ➡ negligible hybridization/mixing 

Experiment 32 Cs2 (Snx Ti1-x )X6 : Optical Properties Theory (Linear sum of endpoint excitonic spectra) 

Energy-lowering reconstructions prevalent in a wide & diverse range of materials/defects. 33 Importance of Defect Structure Searching! More details in Thursday morning’s talk: EL04.05.02: Symmetry-Breaking and Reconstruction at Point Defects in Perovskites April 13, 9-9.15 AM 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 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 • ICs 0, ICs -1, ICs -2 • TiCs 0, TiCs +1, TiCs +2, TiCs +3 • ITi 0, ITi -1 • TiI +2, TiI +5 • Csi +1 

VTi -4 – Fully-ionised Titanium Vacancy Unperturbed; Slightly contracted octahedron ShakeNBreak: Iodine trimer; ΔE = -0.8 eV 

VTi -1 Unperturbed; distorted contracted octahedron ShakeNBreak: double Iodine trimer; ΔE = -1.1 eV 

VTi -1 Unperturbed; distorted contracted octahedron ShakeNBreak: double Iodine trimer; ΔE = -1.1 eV 

VTi 0 – Neutral Titanium Vacancy Unperturbed; distorted contracted octahedron ShakeNBreak: effective ITi + VI complex -> ΔE = -1.6 eV 

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 

TiI +5 – Fully-ionised Titanium-on-Iodine Unperturbed; Ti-Ti bond, distorted octahedron ShakeNBreak: off-centred Ti to vacant octahedral site -> ΔE = -2 eV 

TiI +5 – Fully-ionised Titanium-on-Iodine Unperturbed; Ti-Ti bond, distorted octahedron ShakeNBreak: off-centred Ti to vacant octahedral site -> ΔE = -2 eV 

TiI +5 – Fully-ionised Titanium-on-Iodine Unperturbed; Ti-Ti bond, distorted octahedron ShakeNBreak: off-centred Ti to vacant octahedral site -> ΔE = -2 eV 

Energy-lowering reconstructions prevalent in a wide & diverse range of materials/defects. 42 Importance of Defect Structure Searching! More details in Thursday morning’s talk: EL04.05.02: Symmetry-Breaking and Reconstruction at Point Defects in Perovskites April 13, 9-9.15 AM 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 Cs2 TiI6 : Large energy lowering of ΔE: -0.4 – -2.5 eV for many native defects, due to: • Multinary composition • Reduced crystal symmetry • Space to distort / ‘open’ crystal structure • Presence of ionic & covalent bonding 

Conclusions Highly localised, isolated MX6 octahedra yield ‘molecular salt’ behaviour Ultra-strong Frenkel excitonic binding (Eb ~ 1 eV) in Cs2 MX6 (where M = d0 cation), resolving longstanding discrepancies between theory and experiment. Symmetry-breaking and reconstruction rampant for defects in Cs2 MX6 Other exciting applications for these unusual materials with strong exciton binding, extremely weak inter-octahedral interactions and facile mixing? Quantum defects?... 

Acknowledgements Shanti Liga & Prof G. Konstantatos Profs Aron Walsh & David O. Scanlon @Kavanagh_Sean_ [email protected] Kavanagh et al. ‘Frenkel Excitons in Vacancy- Ordered Titanium Halide Perovskites (Cs2 TiX6 )’ J. Phys. Chem. Lett. 2022, 13, 10965–10975 Liga‡ & Kavanagh‡ et al. In Submission 

45 Cs2 (Snx Ti1-x )X6 : Optical Properties Cs2 (Snx Ti1-x )I6 Cs2 (Snx Ti1-x )Br6 Quasiparticle spectrum with hybrid DFT + SOC ➡ negligible hybridization/mixing 

Experiment 46 Cs2 (Snx Ti1-x )X6 : Optical Properties Theory (Linear sum of endpoint excitonic spectra)