Semiconductors with ultra-low thermal conductivity: What can we learn from modelling?

Presented at a Royal Society of Chemistry Solid-State Chemistry Group (SSCG) webinar.

Transcript

1. Dr Jonathan Skelton Department of Chemistry, University of Manchester (jonathan.skelton@manchester.ac.uk) Semiconductors with ultra-low thermal conductivity: What can we learn from modelling?
2. The global energy challenge RSC SSCG, 28th August 2020 | Slide 2 34 % 26 % 19 % 18 % 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 ( = 1) are considered industrially viable 1. Provisional UK greenhouse gas emissions national statistics (published June 2020) 2. EPSRC Thermoelectric Network Roadmap (2018) Dr Jonathan Skelton
3. Thermoelectric materials Dr Jonathan Skelton = 2 ele + lat - Seebeck coefficient - electrical conductivity lat - lattice thermal conductivity ele - electronic thermal conductivity G. Tan et al., Chem. Rev. 116 (19), 12123 (2016) RSC SSCG, 28th August 2020 | Slide 3
4. Lattice thermal conductivity Phonons are generated at the hot side of the material and transport energy to the cold side Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 4
5. Modelling thermal conductivity A. Togo et al., Phys. Rev. B 91, 094306 (2015) latt () = 1 0 ෍ () ⊗ () Dr Jonathan Skelton The simplest model for latt is the relaxation time approximation (RTA) - a closed solution to the phonon Boltzmann transport equations Modal heat capacity Mode group velocity λ Average over phonon modes λ Phonon MFP Mode lifetime λ = 1 2Γλ = RSC SSCG, 28th August 2020 | Slide 5
6. Modelling thermal conductivity Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 6
7. How good is the RTA model? Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 7 A. Togo et al., Phys. Rev. B 91, 094306 (2015)
8. The heat capacity Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 8 = B ℎ B 2 exp Τ ℎ B exp Τ ℎ B − 1 2
9. The group velocity Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 9 λ λ λ PbS PbSe PbTe J. M. Skelton et al., Phys. Rev. B 89, 205203 (2014)
10. The phonon lifetime Γ = ෍ ′′′ Φ−′′′ 2 × { ′ + ′′ + 1 − ′ − ′′ + ′ − ′′ + ′ − ′′ − − ′ + ′′ } Decay Collision Three-phonon interaction strength (includes conservation of momentum) Conservation of energy Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 10 A. Togo et al., Phys. Rev. B 91, 094306 (2015)
11. Anharmonic materials Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 11
12. Anharmonic Materials I: MAPbI3 Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 12 Inorganic perovskite: SrTiO3 Hybrid perovskite: MAPbI3
13. Anharmonic materials 1: MAPbI3 Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 13 A. Gold-Parker et al., PNAS 115 (47), 11905 (2018) GaAs MAPbI3
14. Anharmonic materials 1: MAPbI3 Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 14 A. Gold-Parker et al., PNAS 115 (47), 11905 (2018) GaAs MAPbI3 = 1 3 2 ෍ ′′′ Φ′′′ 2
15. Anharmonic materials 1: MAPbI3 A. Gold-Parker et al., PNAS 115 (47), 11905 (2018) Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 15
16. Anharmonic materials 1: MAPbI3 A. Gold-Parker et al., PNAS 115 (47), 11905 (2018) Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 16
17. Anharmonic materials 1: MAPbI3 Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 17 A. Gold-Parker et al., PNAS 115 (47), 11905 (2018)
18. Anharmonic materials 2: Bi2 Sn2 O7 Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 18 Rahim et al., Chem. Sci. 11, 7904 (2020) -Bi2 Sn2 O7 Pyrochlore (ത 3) - > 900 K -Bi2 Sn2 O7 Distorted () - < 390 K
19. Anharmonic materials 2: Bi2 Sn2 O7 Rahim et al., J. Mater. Chem. A 8, 16405 (2020) Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 19 GaAs Bi2 Sn2 O7
20. Anharmonic materials 2: Bi2 Sn2 O7 Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 20 Collision Decay Rahim et al., J. Mater. Chem. A 8, 16405 (2020) ෨ Γ = 18 ħ2 2 , = 18 ħ2 2 (1) , + 2 (2) ,
21. Summary Dr Jonathan Skelton The RTA models latt as a sum of contributions from individual phonon modes dependent on: (1) the heat capacity ; (2) the group velocity ; and (3) the linewidth/lifetime Γ / The vary slowly with frequency and are likely the least interesting target for controlling latt is related to the chemical bond strength and atomic mass - are reduced with heavy atoms and weak chemical bonding The linewidth/lifetime has two components: 1. The ph-ph interaction strength - 2. The shape of the phonon frequency spectrum - 2 , In the hybrid perovskite MAPbI3 , the motion of the A-site MA cation is very strongly coupled to the PbI3 cage and acts as a scattering centre In the ternary oxide Bi2 Sn2 O7 , structural distortions induced by the active Sn lone pair spread out the phonon spectrum and allow for a high density of energy-conserving scattering events RSC SSCG, 28th August 2020 | Slide 21
22. Acknowledgements Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 22
23. https://bit.ly/3lilEON These slides are available on Speaker Deck: