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

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.

Jonathan Skelton

August 28, 2020
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  1. Dr Jonathan Skelton
    Department of Chemistry, University of Manchester
    ([email protected])
    Semiconductors with ultra-low thermal conductivity:
    What can we learn from modelling?

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  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

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  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

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  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

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  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

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  6. Modelling thermal conductivity
    Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 6

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  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)

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  8. The heat capacity
    Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 8

    = B

    B

    2
    exp Τ

    B

    exp Τ

    B
    − 1 2

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  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)

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  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)

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  11. Anharmonic materials
    Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 11

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  12. Anharmonic Materials I: MAPbI3
    Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 12
    Inorganic perovskite: SrTiO3
    Hybrid perovskite: MAPbI3

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  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

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  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

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  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

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  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

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  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)

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  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

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  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

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  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)

    Γ
    =
    18
    ħ2

    2

    ,
    =
    18
    ħ2


    2
    (1)
    ,
    +
    2
    (2)
    ,

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  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

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  22. Acknowledgements
    Dr Jonathan Skelton RSC SSCG, 28th August 2020 | Slide 22

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  23. https://bit.ly/3lilEON
    These slides are available on Speaker Deck:

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