2 28/05/2024 skavanagh@seas.harvard.edu Vacancy-Ordered Halide Perovskites for High Entropy Semiconductors Seán R. Kavanagh, Shanti M. Liga, Gerasimos Konstantatos, David O. Scanlon & Aron Walsh

High Entropy Semiconductors? • Major growth in research on high entropy (metallic) alloys & ceramics/oxides in recent years. • However, discovery & design of high entropy semiconductors has been sparse. • Lower melting/decomposition temperatures • Typically more covalent bonding • A key challenge is the high synthesis temperatures (>1000 ℃) required to achieve mixing, as well as complex synthesis processes (e.g. hot rolling). 3

High Entropy Semiconductors? • Major growth in research on high entropy (metallic) alloys & ceramics/oxides in recent years. • However, discovery & design of high entropy semiconductors has been sparse. • Lower melting/decomposition temperatures • Typically more covalent bonding • A key challenge is the high synthesis temperatures (>1000 ℃) required to achieve mixing, as well as complex synthesis processes (e.g. hot rolling). 4

How can we reduce Tsynthesis ? ➡ Need to reduce mixing enthalpies Gmix = Hmix - TSmix Target Properties: • Soft / easily-distorted lattice, to accommodate ionic radii variations • Non-directional (i.e. ionic) bonding, yielding high structural uniformity, flexibility and ion solubility 5

6 1. A. E. Maughan, A. M. Ganose, D. O. Scanlon, J. R. Neilson, Chem. Mater. 2019, 31 (4), 1184–1195 2. Y.-T. Huang, S. R. Kavanagh, D. O. Scanlon, A. Walsh and R. L. Z. Hoye, Nanotechnology, (2021), 32, 132004. 3. 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. A2 MX6 ≋ A(0/M)X3 Vacancy-Ordered Double Perovskites

7 1. A. E. Maughan, A. M. Ganose, D. O. Scanlon, J. R. Neilson, Chem. Mater. 2019, 31 (4), 1184–1195 2. Y.-T. Huang, S. R. Kavanagh, D. O. Scanlon, A. Walsh and R. L. Z. Hoye, Nanotechnology, (2021), 32, 132004. 3. 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 Vacancy-Ordered Halide Double Perovskites • Photovoltaics • Photocatalysts • White-light emission / phosphors • Thermoelectrics • Photo detectors • Non-linear optics (THG active) • … • High entropy semiconductors?

8 A+: Spectator ion (Cs+, Rb+, K+, MA+…) M4+: Sn4+, Te4+, Ge4+, Ti4+, Zr4+, Hf4+, Pt4+, Pd4+, Re4+… X -: Halide ion (I -, Br -, Cl -, F -) • Isolated MX6 octahedra • Fully-oxidised cations ➡ ionic M-X bonds • Solution synthesis (nanocrystals, thin films and single crystals) 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 Vacancy-Ordered Halide Double Perovskites

9 AI 2 MIVX6 Vacancy-Ordered Halide Double Perovskites Key Properties: • Weak orbital hybridization between octahedra • Significant van der Waals attraction between octahedra (~10% volume contraction)1 Consequences: • Effective “zero-dimensional” / molecular salt behaviour • Ionic and vdW bonding, negligible covalent contributions • Ultra-strong excitonic effects, despite relatively low band gaps1,2 1. Kavanagh et al. J. Phys. Chem. Lett. 2022 2. Cucco et al. Mater. Lett. 2023

How can we reduce Tsynthesis ? ➡ Need to reduce mixing enthalpies Gmix = Hmix - TSmix Target Properties: • Soft / easily-distorted lattice, to accommodate ionic radii variations • Non-directional (i.e. ionic) bonding, yielding high structural uniformity and cation solubility 10

How can we reduce Tsynthesis ? ➡ Need to reduce mixing enthalpies Gmix = Hmix - TSmix Target Properties: • Soft / easily-distorted lattice, to accommodate ionic radii variations ✅ (inter-octahedral voids, significant vdW effects) • Non-directional (i.e. ionic) bonding, yielding high structural uniformity and cation solubility ✅ (negligible covalency) 11

Special Quasirandom Structures (SQS) with hybrid DFT including spin-orbit coupling. 12 A2 {M}X6 : Mixing Energetics “Quasirandom” radial distribution function g(r) g(r)supercell ≃ g(r)random

13 A2 {M}X6 : Mixing Energetics Liga‡ & Kavanagh‡ et al. J. Phys. Chem. C 2023

14 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 Consistent behaviour across all X = I, Br, Cl HSE06+SOC+vdW A2 {M}X6 : Mixing Energetics

15 A2 {M}X6 : Facile Mixing in Solution Liga‡ & Kavanagh‡ et al. J. Phys. Chem. C 2023

16 Room (20℃) & low (80℃) temperature synthesis of single crystals in solution

17 A2 {M}X6 : Optical Properties Negligible orbital hybridization ➡ Additive type behaviour: ⍺(A2 {M}X6 ) ≃ x1 *⍺(A2 M1X6 ) + x2 *⍺(A2 M2X6 ) + …

18 A2 {B}X6 : Stability? ➡ Again, additive type behaviour: ΔH(A2 {M}X6 ) ≃ x1 *ΔH(A2 M1X6 ) + x2 *ΔH(A2 M2X6 ) + … • A2MIVX6 thermodynamically stable in inert atmospheres • O2 decomposition to MIVO2 thermodynamically favoured (except X = Cl), but kinetically inhibited. • Hygroscopic; decomposition accelerated in aqueous environments. • Stability increases as X -> I, Br, Cl, F. • vdW interactions contribute significantly to stability. Liga‡ & Kavanagh‡ et al. J. Phys. Chem. C 2023

Takeaways Isolated MX6 octahedra yield: Dominant ionic & vdW bonding, with flexible crystal structure due to vacant space between octahedra. ➡ Ultra-low mixing enthalpies ➡ Low-temperature solution synthesis of mixed compositions Novel class of easily-synthesized, low-gap, excitonic high-entropy semiconductors! Liga‡ & Kavanagh‡ et al. J. Phys. Chem. C 2023 Folgueras et al. Nature 2023

Final Notes Modelling Considerations: • vdW interactions crucial! (Volume, electronic properties, stability…) • Strong excitonic behaviour (DFT unsuitable for electronic properties) 1. Padelkar et al. Phys. Rev. Appl. 2024 Halide mixing also relatively facile!1 High-entropy mixed-cation mixed-anion semiconductors?

Acknowledgements Shanti Liga & Prof G. Konstantatos Profs Aron Walsh & David O. Scanlon @Kavanagh_Sean_ skavanagh@seas.harvard.edu Kavanagh et al. ‘Frenkel Excitons in Vacancy- Ordered Titanium Halide Perovskites (Cs2TiX6)’ J. Phys. Chem. Lett. 2022, 13, 10965–10975 Liga‡ & Kavanagh‡ et al. ‘Mixed-Cation Vacancy- Ordered Perovskites (Cs2 Ti1–x Snx X6 )’ J. Phys. Chem. C. 2023, 43, 21399–21409 Paper Links:

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. 22 Cs2 MX6 – Stability Saporov et al. Chem Mater 2016

Cs 2 TiX 6 : 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 23 Cs2 MX6 – Stability Cs 2 TiBr 6 Cs 2 TiI 6

Intrinsic Thermodynamic Stability Cs 2 SnI 6 Cs 2 SnBr 6 Cs 2 SnCl 6 Cs 2 TiI 6 Cs 2 TiBr 6 Cs 2 TiCl 6 Hybrid DFT + vdW Decomposition Energy (eV) +56 meV +129 meV +174 meV +75 meV +120 meV +162 meV 24 • 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 Cs2MX6: Cs 2 SnI 6 Cs 2 TiI 6 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) Cs2SnI6 + O2 SnO2 + 2CsI + 4I(s) -2.43 Cs2SnBr6 + O2 SnO2 + 2CsBr + 2Br2(l) -0.10 Cs2SnCl6 + O2 SnO2 + 2CsCl + 2Cl2(g) +0.82 Reactants Products ΔH (eV) Cs2TiI6 + O2 TiO2 + 2CsI3 + 4I(s) -4.90 Cs2TiBr6 + O2 TiO2 + 2CsBr + 2Br2(l) -1.70 Cs2TiCl6 + 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, Cs2MX6 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. O 2 /H 2 O Decomposition 26 Humid Air Dessicated Air E.G: Cs2(Ti0.4Sn0.6)Br6

Cs2 MX6 Stability: Conclusions • Cs 2 SnX 6 far more stable than Cs 2 TiX 6 in ambient atmospheres. • However Cs 2 TiX 6 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? 27 1Grandhi et al. Nanomaterials 2021

Energy-lowering reconstructions prevalent in a wide & diverse range of materials/defects. 32 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

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

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

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

Ti Cs +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

Energy-lowering reconstructions prevalent in a wide & diverse range of materials/defects. 41 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