Theory-led discovery of high-performance thermoelectric materials for waste-heat recovery

Presented to the University of Warwick Theoretical Physics department on 21st June 2024.

Transcript

1. Dr Jonathan Skelton and Dr Joseph Flitcroft Department of Chemistry, University of Manchester (jonathan.skelton@manchester.ac.uk) Theory-led discovery of high-performance thermoelectric materials for waste-heat recovery
2. The global energy challenge 31 % 23 % 20 % 19 % 3 % 1000 MW nuclear power plant: o 650 MW waste heat o 3 % ≈ 20 MW ≈ 50,000 homes 300-500 W from exhaust gases: o 2 % lower fuel consumption o 2.4 Mt reduction in CO2 Thermoelectric generators allow waste heat to be recovered as electricity TEGs with ~3 % energy recovery (𝑍𝑇 = 1) are considered industrially viable 1. Provisional UK greenhouse gas emissions national statistics (published March 2022) 2. EPSRC Thermoelectric Network Roadmap (2018) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 2
3. Thermoelectric materials 𝑍𝑇 = 𝑆2𝜎 𝜅el + 𝜅latt 𝑇 𝑆 - Seebeck coefficient 𝜎 - electrical conductivity 𝜅ele - electronic thermal conductivity 𝜅lat - lattice thermal conductivity Tan et al., Chem. Rev. 116 (19), 12123 (2016) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 3
4. An ab initio modelling workflow Crystal structure Convergence testing Geometry optimisation Phonon calculation 𝜅latt Electronic structure 𝑆, 𝜎, 𝜅el 𝑍𝑇 = 𝑆2σ 𝜅el + 𝜅latt 𝑇 Scattering rates: DP, 𝜀∞ , 𝑍∗, 𝐶𝑖𝑗 Part 2 Part 1 Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 4
5. Modelling thermal conductivity Togo et al., Phys. Rev. B 91, 094306 (2015) The simplest model for 𝜅latt is the single-mode relaxation time approximation (SM-RTA) - a closed solution to the phonon Boltzmann transport equations 𝜿latt (𝑇) = 1 𝑁𝑉 ෍ 𝜆 𝐶𝜆 (𝑇)𝒗𝜆 ⊗ 𝒗𝜆 𝜏𝜆 (𝑇) 𝐶𝜆 - phonon heat capacities 𝒗𝜆 - phonon group velocities 𝜏𝜆 - phonon lifetimes (inverse linewidths Γ𝜆 ) 𝑁 - number of 𝒒 in summation 𝑉 - unit cell volume Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 5
6. Modelling thermal conductivity Tang and Skelton, J. Phys.: Condens. Matter 33, 164002 (2021) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 6
7. Modelling thermal conductivity Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 7
8. The IV-VI chalcogenides Zhao et al., Nature 508, 373 (2014) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 8
9. A comparative study GeSe GeTe SnSe SnTe 𝑃𝑛𝑚𝑎     𝐶𝑚𝑐𝑚  𝑅3𝑚    𝐹𝑚ത 3𝑚   𝑃𝑛𝑚𝑎 𝐶𝑚𝑐𝑚 𝑅3𝑚 𝐹𝑚ത 3𝑚 Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 9
10. A comparative study 𝜅𝐥𝐚𝐭𝐭 (𝑇 = 300 K) [W m-1 K-1] SnSe (𝐶𝑚𝑐𝑚) 0.96 SnTe (𝑃𝑛𝑚𝑎) 1.09 GeTe (𝑃𝑛𝑚𝑎) 1.32 SnSe (𝑃𝑛𝑚𝑎) 1.36 GeTe (𝐹𝑚ത 3𝑚) 1.57 GeSe (𝐹𝑚ത 3𝑚) 1.67 GeSe (𝑃𝑛𝑚𝑎) 2.36 SnTe (𝑅3𝑚) 4.18 GeTe (𝑅3𝑚) 4.36 SnTe (𝐹𝑚ത 3𝑚) 5.01 Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 10
11. Group velocities vs. lifetimes 𝜿latt ≈ 𝜏CRTA × 1 𝑁𝑉 ෍ 𝜆 𝜿𝜆 𝜏𝜆 = 1 𝑁𝑉 ෍ 𝜆 𝐶𝜆 𝒗𝜆 ⊗ 𝒗𝜆 × 𝜏CRTA Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 11
12. Group velocities vs. lifetimes 𝜿latt ≈ 𝜏CRTA × 1 𝑁𝑉 ෍ 𝜆 𝜿𝜆 𝜏𝜆 = 1 𝑁𝑉 ෍ 𝜆 𝐶𝜆 𝒗𝜆 ⊗ 𝒗𝜆 × 𝜏CRTA Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 12
13. Group velocities vs. lifetimes 𝜅𝐥𝐚𝐭𝐭 [W m-1 K-1] Τ 𝜅𝐥𝐚𝐭𝐭 𝝉𝐂𝐑𝐓𝐀 [W m-1 K-1 ps-1] 𝝉𝐂𝐑𝐓𝐀 [ps] SnTe (𝑃𝑛𝑚𝑎) 1.09 0.27 3.98 GeTe (𝑃𝑛𝑚𝑎) 1.32 0.34 3.91 SnSe (𝑃𝑛𝑚𝑎) 1.36 0.35 3.89 GeSe (𝑃𝑛𝑚𝑎) 2.36 0.39 6.03 SnTe (𝑅3𝑚) 4.18 0.69 6.07 GeTe (𝑅3𝑚) 4.36 0.87 5.01 SnTe (𝐹𝑚ത 3𝑚) 5.01 1.07 4.67 SnSe (𝐶𝑚𝑐𝑚) 0.96 1.09 0.88 GeTe (𝐹𝑚ത 3𝑚) 1.67 2.99 0.56 GeSe (𝐹𝑚ത 3𝑚) 1.57 3.29 0.48 Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 13
14. Group velocities vs. lifetimes Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 14
15. Group velocities vs. lifetimes 𝜅𝐥𝐚𝐭𝐭 [W m-1 K-1] Τ 𝜅𝐥𝐚𝐭𝐭 𝝉𝐂𝐑𝐓𝐀 [W m-1 K-1 ps-1] 𝝉𝐂𝐑𝐓𝐀 [ps] GeSe (𝐹𝑚ത 3𝑚) 1.57 3.29 0.48 GeTe (𝐹𝑚ത 3𝑚) 1.67 2.99 0.56 SnSe (𝐶𝑚𝑐𝑚) 0.96 1.09 0.88 SnSe (𝑃𝑛𝑚𝑎) 1.36 0.35 3.89 SnTe (𝑃𝑛𝑚𝑎) 1.32 0.34 3.91 SnTe (𝑅3𝑚) 1.09 0.27 3.98 SnTe (𝐹𝑚ത 3𝑚) 5.01 1.07 4.67 GeTe (𝑅3𝑚) 4.36 0.87 5.01 GeSe (𝑃𝑛𝑚𝑎) 2.36 0.39 6.03 SnTe (𝑅3𝑚) 4.18 0.69 6.07 Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 15
16. Anharmonicity vs. “selection rules” Γ𝜆 = 36𝜋 ℏ2 ෍ 𝜆′𝜆′′ Φ−𝜆𝜆′𝜆′′ 2 × { 𝑛𝜆′ + 𝑛𝜆′′ + 1 𝛿 𝜔 − 𝜔𝜆′ − 𝜔𝜆′′ + 𝑛𝜆′ − 𝑛𝜆′′ 𝛿 𝜔 + 𝜔𝜆′ − 𝜔𝜆′′ − 𝛿 𝜔 − 𝜔𝜆′ + 𝜔𝜆′′ } Decay Collision Three-phonon interaction strength (includes conservation of momentum) Conservation of energy Togo et al., Phys. Rev. B 91, 094306 (2015) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 16
17. Anharmonicity vs. “selection rules” 𝜏λ = 1 2𝜋Γ𝜆 Γ𝜆 ≈ 36𝜋 ℏ2 𝑁2 (𝒒𝜆 , 𝜔𝜆 ) × 𝑃𝜆 and Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 17
18. Anharmonicity vs. “selection rules” 𝑃𝑛𝑚𝑎 Other phases Other phases 𝑃𝑛𝑚𝑎 𝜏λ = 1 2𝜋Γ𝜆 Γ𝜆 ≈ 36𝜋 ℏ2 𝑁2 (𝒒𝜆 , 𝜔𝜆 ) × 𝑃𝜆 and Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 18
19. Anharmonicity vs. “selection rules” 𝝉𝐂𝐑𝐓𝐀 [ps] ෩ 𝑷 × 𝟑𝒏𝒂 𝟐 [eV2] Τ ෩ 𝑵𝟐 𝟑𝒏𝒂 𝟐 [THz-1] SnTe (𝑃𝑛𝑚𝑎) 3.98 9.07 × 10-9 1.70 × 10-2 SnSe (𝑃𝑛𝑚𝑎) 3.89 1.20 × 10-8 1.31 × 10-2 GeTe (𝑃𝑛𝑚𝑎) 3.91 1.35 × 10-8 1.15 × 10-2 GeSe (𝑃𝑛𝑚𝑎) 6.03 1.36 × 10-8 7.44 × 10-3 SnTe (𝑅3𝑚) 6.07 5.20 × 10-8 1.93 × 10-3 GeTe (𝑅3𝑚) 5.01 8.97 × 10-8 1.36 × 10-3 SnTe (𝐹𝑚ത 3𝑚) 4.67 1.09 × 10-7 1.20 × 10-3 SnSe (𝐶𝑚𝑐𝑚) 0.88 1.46 × 10-7 4.74 × 10-3 GeTe (𝐹𝑚ത 3𝑚) 0.56 1.31 × 10-6 8.35 × 10-4 GeSe (𝐹𝑚ത 3𝑚) 0.48 2.24 × 10-6 5.69 × 10-4 Calculate an averaged number of scattering pathways from 𝜏CRTA and ෨ 𝑃: ෩ 𝑁2 = ℏ2 72𝜋2 ෨ 𝑃𝜏CRTA Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 19
20. Trends in structure type 𝑃𝑛𝑚𝑎 𝐶𝑚𝑐𝑚 𝑅3𝑚 𝐹𝑚ത 3𝑚 Lower 𝒗λ : smaller Τ 𝜅latt 𝜏CRTA Stronger anharmonicity: larger ෨ 𝑃 → shorter 𝜏CRTA More allowed scattering pathways: larger ෩ 𝑁2 → shorter 𝜏CRTA Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 20
21. Interpretation: group velocities Guillemot et al., J. Mater. Chem. A 12, 2932 (2024) Walsh et al., Chem. Soc. Rev. 40, 4455 (2011) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 21
22. Trends in structure type 𝐶𝑚𝑐𝑚 SnSe: ? Low symmetry  Large(-ish) cell (𝑛𝑎 = 4)  Sn constrained to a locally-symmetric environment 𝜋-cubic SnSe: ? High symmetry  (Very) large cell (𝑛𝑎 = 64)  Sn local geometry similar to 𝑃𝑛𝑚𝑎 phase Abutbul et al., CrystEngComm 18, 1918 (2016) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 22
23. 𝝅-cubic SnSe Zhang et al., in prep. Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 23
24. An ab initio modelling workflow Crystal structure Convergence testing Geometry optimisation Phonon calculation 𝜅latt Electronic structure 𝑆, 𝜎, 𝜅el 𝑍𝑇 = 𝑆2σ 𝜅el + 𝜅latt 𝑇 Scattering rates: DP, 𝜀∞ , 𝑍∗, 𝐶𝑖𝑗 Part 1 Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 24 Part 2
25. Modelling electrical properties Ganose et al., Nature Comm. 12, 2222 (2021) We first define the spectral conductivity tensor: Σ𝛼𝛽 𝜖, 𝑇 = 1 8𝜋3 ෍ 𝑗 න 𝑣𝒌𝑗,𝛼 𝑣𝒌𝑗,𝛽 𝜏𝒌𝑗 𝑇 𝛿 𝜖 − 𝜖𝒌𝑗 𝑑𝒌 This is used to calculate the 𝑛th-order moments of the generalised transport coefficients: ℒ𝛼𝛽 𝑛 𝜖F , 𝑇 = න Σ𝛼𝛽 𝜖, 𝑇 𝜖 − 𝜖F 𝑛 − 𝜕𝑓 𝜖, 𝜖F , 𝑇 𝜕𝜖 𝜕𝜖 𝑓 𝜖, 𝜖F , 𝑇 = 1 exp Τ 𝜖 − 𝜖F 𝑘B 𝑇 + 1 Where: o The 𝒗𝒌𝑗 are obtained from a high-quality band structure o The 𝜏𝒌𝑗 can be: treated as a constant 𝜏el ; approximated by model equations for different scattering processes; or calculated from the electron-phonon coupling o The 𝜖F (= 𝜇) is set by the DoS and a specified extrinsic carrier concentration 𝑛 Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 25
26. Modelling electrical properties The 𝓛𝑛(𝜖F , 𝑇) are determined from a band structure, a model for the 𝜏𝑗𝒌 , and a specified 𝑛/𝑇: ℒ𝛼𝛽 𝑛 𝜖F , 𝑇 = න Σ𝛼𝛽 𝜖, 𝑇 𝜖 − 𝜖F 𝑛 − 𝜕𝑓 𝜖, 𝜖F , 𝑇 𝜕𝜖 𝜕𝜖 The electrical transport coefficients can be determined from the 𝓛𝑛(𝜖F , 𝑇) as: 𝜎𝛼𝛽 (𝜖F , 𝑇) = ℒ𝛼𝛽 0 (𝜖F , 𝑇) 𝑆𝛼𝛽 (𝜖F , 𝑇) = 1 𝑒𝑇 ℒ𝛼𝛽 1 (𝜖F , 𝑇) ℒ 𝛼𝛽 0 (𝜖F , 𝑇) 𝜅el,𝛼𝛽 (𝜖F , 𝑇) = 1 𝑒2𝑇 ℒ𝛼𝛽 1 (𝜖F , 𝑇) 2 ℒ 𝛼𝛽 0 (𝜖F , 𝑇) − ℒ𝛼𝛽 2 (𝜖F , 𝑇) Note that when using the CRTA (i.e. 𝜏𝒌𝑗 → 𝜏el ): o The 𝑺 are the ratio of two 𝓛𝑛 and the 𝜏el cancel o The 𝝈 and 𝜿el are obtained with respect to 𝜏el (𝜏el ~ 10-14 s) Ganose et al., Nature Comm. 12, 2222 (2021) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 26
27. Modelling electrical properties Flitcroft et al., Solids 3 (1), 155 (2022) Fixed 𝑇 = 800 K Fixed 𝑛ℎ = 1019 cm-3 Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 27
28. Oxychalcogenides: Bi2 ChO2 𝒂 [Å] 𝒃 [Å] 𝒄 [Å] 𝑽 [Å3] Bi2 SO2 3.81 3.81 11.90 173 Expt 3.87 3.84 11.92 177 Bi2 SeO2 3.87 3.87 12.12 182 Expt 3.88 3.88 12.21 184 Bi2 TeO2 3.96 3.96 12.68 199 Expt 3.98 3.98 12.70 201 Koyama et al., Acta Cryst. B 40, 105 (1984) Zhan et al., J. Am. Ceram. Soc. 98, 2465 (2015) Luu and Vaqueiro, J. Solid State Chem. 226, 219 (2015) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 28
29. Lattice thermal conductivity 𝑇 [K] 𝜅(Calc.) [Wm-1K-1] 𝜅(Expt.) [Wm-1K-1] Bi2 SO2 300 2.62 2.9 Bi2 SeO2 800 0.97 0.71 Bi2 TeO2 300 0.95 0.91 Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Zhang et al., J. Mater. Chem. C 7, 14986 (2019) Pan et al., Nano Energy 69, 104394 (2020) Luu and Vaqueiro, J. Solid State Chen. 226, 219 (2015) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 29
30. Electronic structure Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Pacquette et al., J. Photochem. Photobiol. A 277, 27 (2014) Tan et al., J. Am. Ceram. Soc. 101, 326 (2018) Luu and Vaqueiro, J. Solid State Chem. 226, 219 (2015) Bi2 SO2 : 𝐸g (Calc.) = 1.46 eV 𝐸g (Expt) = 1.5 eV Bi2 SeO2 : 𝐸g (Calc.) = 1.1 eV 𝐸g (Expt) = 1.77 eV Bi2 TeO2 : 𝐸g (Calc.) = 0.33 eV 𝐸g (Expt) = 0.23 eV Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 30
31. Electrical transport Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 31
32. Comparison to experiments Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 32
33. Comparison to experiments Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 33
34. Comparison to experiments Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) 𝑇 = 300 K 𝑇 = 800 K Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 34
35. Predicted 𝒁𝑻 Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 35
36. Predicted 𝒁𝑻 𝒁𝑻 𝒏 [cm-3] 𝑻 [K] 𝝈 [S cm-1] 𝑺 [µV K-1] 𝑺𝟐𝝈 [mW m-1 K-2] 𝜿𝐞𝐥 [W m-1 K-1] 𝜿𝐥𝐚𝐭𝐭 [W m-1 K-1] 𝜿𝐭𝐨𝐭 [W m-1 K-1] Bi2 SO2 (n) 0.33 2.5×1019 900 120 -186 0.41 0.23 0.9 1.13 Bi2 SO2 (p) 0.72 4×1019 900 24.7 545 0.73 2.63×10-2 0.92 2.53 8×1020 900 495 287 4.08 0.55 1.45 Bi2 SeO2 (n) 0.45 2.5×1019 900 193 -180 0.62 0.39 0.87 1.25 Bi2 SeO2 (p) 1.12 5×1019 900 44.4 512 1.16 6.56 ×10-2 0.93 2.62 5×1020 900 436 318 4.41 0.65 1.51 Bi2 TeO2 (n) 1.05 5×1019 900 554 -184 1.87 1.28 0.33 1.61 Bi2 TeO2 (p) 1.36 5×1019 540 340 250 2.13 0.31 0.54 0.85 1.51 1020 640 538 213 2.45 0.58 0.46 1.04 𝑍𝑇max = 0.38 reported for n-type (Bi1.9 Ta0.1 )SeO2 @ 𝑛 = 2.1×1019 + 𝑇 = 773 K 𝑍𝑇max = 0.13 reported for n-type Bi2 TeO2 @ 𝑛 = 1.1×1019 cm-3 + 𝑇 = 573 K Tan et al., Adv. Energy Mater. 9, 1900354 (2019) Luu and Vaqueiro, J. Solid State Chem. 226, 219 (2015) Flitcroft et al., J. Phys.: Energy 6, 025011 (2024) Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 36
37. Electrical properties of 𝝅-SnSe Zhang et al., in prep. Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 37
38. 𝒁𝑻 of 𝝅-SnSe Zhang et al., in prep. 𝒁𝑻 𝒏 [cm-3] 𝑻 [K] 𝝈 [S cm-1] 𝑺 [µV K-1] 𝑺𝟐𝝈 [mW m-1 K-2] 𝜿𝐞𝐥 [W m-1 K-1] 𝜿𝐥𝐚𝐭𝐭 [W m-1 K-1] 𝜿𝐭𝐨𝐭 [W m-1 K-1] Pnma (p) 2.07 3.16 ×1019 740 399 272 2.96 0.42 0.64 1.06 𝜋-cubic (n) 2.83 1020 740 183 -355 2.31 0.25 0.36 0.61 Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 38
39. Summary High-performance thermoelectrics require a balance of a 𝑆 and 𝜎 and low 𝜅 = 𝜅latt + 𝜅el The 𝜅latt can be modelled using the single-mode relaxation-time approximation: o Provides microscopic insight at the level of individual phonon modes o Analysis procedure to determine how differences in 𝑣𝜆 , 𝜏𝜆 , ෨ 𝑃 and ෩ 𝑁2 underpin differences in 𝜅latt between materials o 𝜅latt of flagship IV-VI chalcogenide TEs is a balance of inhomogeneous chemical bonding and anharmonicity introduced by tetrel lone pair activity The 𝑆, 𝜎 and 𝜅el calculated from electronic-structure calculations and approximate models for the 𝜏el : o Reproduce experiments reasonably well, taking into account sample variation o Can be used to explore p- and n-type doping over a wide range of carrier concentrations and “untangle” the interdependence of the 𝑆, 𝜎, 𝜅el and 𝑛 Microscopic insight from the models, and useful predictive accuracy, allow this approach to be used to identify and characterise novel TEs Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 39
40. Acknowledgements ... plus other students, mentors and collaborators too numerous to mention Dr J. M. Skelton and Dr J. M. Flitcroft University of Warwick, 21st June 2024 | Slide 40
41. These slides are available on Speaker Deck: https://bit.ly/3xvfaaj