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Quantum Mechanochemical Coupling in Halide Perovskites

Aron Walsh
September 30, 2019

Quantum Mechanochemical Coupling in Halide Perovskites

Invited presentation at PSCO (2019), https://www.psco-conference.org.

Aron Walsh

September 30, 2019
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  1. Quantum Mechanochemical
    Coupling in Halide Perovskites
    Prof. Aron Walsh
    Imperial College London, UK
    Yonsei University, Korea
    Electric polarisation fields in CH3
    NH3
    PbI3
    (MAPI)

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  2. Chemistry of Halide Perovskites
    ABX3
    compounds with flexibility for atomic or
    molecular A, B, and X components
    Valence rules for 1:1:3 compounds
    X = 2- (Oxides; A + B = 6+)
    • A = 1+, B = 5+ (e.g. KTaO3
    )
    • A = 2+, B = 4+ (e.g. SrTiO3
    )
    • A = 3+, B = 3+ (e.g. GdFeO3
    )
    X = 1- (Halides; A + B = 3+)
    • A = 1+, B = 2+ (e.g. CsSnI3
    )
    Electrostatic analysis: J. M. Frost et al., Nano Letters 14, 2584 (2014)
    A = CH3
    NH3
    +

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  3. Chemistry of Halide Perovskites
    Double Perovskites (A2
    BB’X6
    )
    e.g. 2Sn(II) à Ag(I) + Bi(III)
    e.g. 2Pb(II) à In(I) + Bi(III)
    Indirect band gaps / Phase
    competition / Order-disorder
    Layered Perovskites (Ax
    By
    Xz
    )
    e.g. Sn(II) à Bi(III)
    • A3
    B2
    X9
    , A2
    BX4
    types
    • <100>, <110> and <111> sequences
    Potential issues with double perovskites: ACS Energy Lett. 1, 949 (2016)

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  4. Physics of Halide Perovskites
    Principles of Chemical Bonding and Band Gap Engineering
    in Hybrid Halide Perovskites, J. Phys. Chem. C. 119, 5755 (2015)
    Semiconductors with strong optical absorption,
    light carrier masses, efficient dielectric screening
    Photovoltaic device consequences
    • Weak exciton binding (EB
    < kB
    T in 1:1:3 compounds)
    • High carrier mobility (phonon scattering limited)
    • Semiconductor alloys (on A, B, and X sites)

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  5. Semiconductors with a Twist
    Current-voltage hysteresis
    Snaith et al, JPCL (2014); Unger et al, EES (2014)
    Rapid chemical conversion between halides
    Pellet et al, CoM (2015); Eperon et al, MH (2015)
    Photoinduced phase separation
    Hoke et al, CS (2015); Yoon et al, ACS-EL (2016)
    Electric-field induced phase separation
    Xiao et al, NatM (2015); Yuan et al, AEM (2016)
    Photo-stimulated ionic conductivity
    Yang et al, AChemie (2015); Kim et al, NatM (2018)

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  6. Semiconductors with a Twist
    Mixed ionic-electronic charge transport
    Ionic Conduction of the
    Perovskite-Type Halides
    Ionic Conductivity of
    CsPbCl3
    and CsPbBr3
    Large Photoeffect on Ion
    Conduction in Perovskites

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  7. Semiconductors with a Twist
    Nature Comm. 6, 8497 (2015); ACS Energy Lett. 3, 1983 (2018)
    Reservoir of charged point defects in
    thermodynamic equilibrium, e.g. V-
    MA
    , V2-
    Pb
    , V+
    I
    A. Walsh et al, Angew. Chemie 54, 1791 (2015)
    Figure 3. Iodide ion vacancy migration from DFT calculations (a) Calculated migration
    Vacancy Ea
    (eV)
    I- 0.6
    CH3
    NH3
    + 0.8
    Pb2+ 2.3
    D ~ 10-12 cm2s-1
    at T = 300 K
    [PBEsol/DFT in 768 atom supercell
    with nudged-elastic band]
    Bulk diffusion barrier

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  8. Semiconductors with a Twist
    Phonon mode assignments: PCCP 18, 27051 (2016)
    Vibrations, librations, and rotations of molecular
    components inside the crystals
    Rocking MA+
    mode at 2.5 THz
    Animation of
    calculated phonon
    eigenvector
    (PBEsol/Phonopy)

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  9. Semiconductors with a Twist
    Quasi-elastic neutron scattering [Piers Barnes]: N. Comm. (2015)
    2D IR spectroscopy [Artem Bakulin]: JPCL (2015)
    Inelastic X-ray scattering [Simon Billinge]: ACS Energy Lett. (2016)
    Inelastic neutron scattering [Mike Toney]: PNAS (2018)
    Vibrations, librations, and rotations of molecular
    components inside the crystals
    30HE, United Kingdom
    in
    ls.
    he
    nd
    ve
    py
    nic
    Librations Rotations
    Theory

    Experiment

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  10. Talk Motivation and Outline
    Does crystal strain influence the
    operation and performance of halide
    perovskite solar cells?
    A. Background
    B. Perfect crystal response
    C. Imperfect crystal response

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  11. Polarisation and Strain in Crystals
    Ferroelectricity – switchable crystal polarisation
    Ferroelasticity – switchable crystal strain
    Strain (ε) hysteresis
    Polarisation (P) hysteresis

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  12. Polarisation and Strain in Crystals
    Ferroelectricity – switchable crystal polarisation
    Ferroelasticity – switchable crystal strain
    Strain (ε) hysteresis
    Polarisation (P) hysteresis
    Can be coupled through the
    piezoelectric effect (where
    crystal symmetry allows)
    Material Ferroelectric Ferroelastic
    BaTiO3
    Yes Yes
    LiH3
    (SeO3
    )2
    Yes No
    YBa2
    Cu3
    O7-x
    No Yes
    Ferroelastic domains
    in YBa2
    Cu3
    O7-x
    Group theory can aid
    classification, but
    chemistry determines
    the magnitude
    Aizu, PRB 2, 754 (1970)

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  13. Ferroelectric Pb Halide Perovskites
    Paper titles from the literature on one material!

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  14. Ferroelectric Pb Halide Perovskites
    Paper titles from the literature on one material!
    Some analysis misled by
    polarisation signatures
    of interface charging, ion
    transport and/or crystal strain

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  15. Ferroelectric Pb Halide Perovskites
    Room T phase of CH3
    NH3
    PbI3
    is tetragonal with
    reports of polar and non-polar space groups
    M. T. Weller et al, Chem. Comm. 51, 4180 (2015)
    Non-polar: I4/mcm
    Powder neutron
    diffraction (ISIS,UK)
    Molecular orientational
    disorder above 160K
    a0a0c- Glazer tilting pattern

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  16. Ferroelectric Pb Halide Perovskites
    Room T phase of CH3
    NH3
    PbI3
    is tetragonal with
    reports of polar and non-polar space groups
    Garten et al, Science Advances 5, eaas9311 (2019)
    Single
    crystal
    XRD
    Averaged
    over space
    and time
    Local
    structure is
    hidden
    Polar
    Non-polar

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  17. Non-Ferroelectric Pb Halide Perovskites
    Local symmetry breaking (polar nanodomains)
    but paraelectric over longer ranges
    [Led by Simon Billinge] A. N. Beecher et al, ACS Energy Lett. 1, 880 (2016)
    Fits of pair-distribution
    function data to three
    space groups over two
    length scales
    CH3
    NH3
    PbI3
    at T = 350 K

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  18. Crystal strain patterns have a complex
    heterogeneity across multiple length scales
    “Supergrains”
    <110> quiver plot
    Nanofocus XRD at ESRF
    Micro-XRD at ALS
    Over 20 µm: 0.3% strain
    [Led by Sam Stranks] T. W. Jones et al, Energy and Environ. Sci. 12, 596 (2019)
    Strain in Pb Halide Perovskite Films

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  19. Origins of Strain in Halide Perovskites
    • Transformational – variation in crystal
    orientation, e.g. following the cubic-to-
    tetragonal phase transition (a=b≠c)
    • Compositional – variation in distribution of A,
    B, or X species, e.g. Br-rich regions in (Br,I)
    solid-solutions
    • Interfacial – mesoporous metal oxide
    substrate likely to influence strain gradients
    in thin halide perovskite films

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  20. [Image] Nat. Comm. 8, 14547 (2017); J. Phys. Chem. C 120, 5724 (2016)
    Twin domains in CH3
    NH3
    PbI3
    as a result of cubic-
    to-tetragonal phase transition around 57℃
    Cubic (70℃)
    Tetragonal (25℃ )
    1µm 1µm
    (110)
    domains
    (TEM, SAED)
    Reversible
    with T
    Δa/a~0.3%
    Domains form to minimise stress
    Transformational Strain

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  21. Transformational Strain
    “Twinning in ferroelectric and ferroelastic ceramics: stress relief”
    G. Arlt, J. Mater. Sci. 25, 2655 (1990)
    Same features observed in BaTiO3
    – domains vary
    with grain size and shape distribution; sensitive to
    electron beam intensity in halide perovskites
    BaTiO3
    CH3
    NH3
    PbI3

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  22. Ferroelastic Response of Domains
    CH3
    NH3
    PbI3
    Perovskites: Ferroelasticity Revealed
    E. Strelcov et al, Science Advances 3, e1602165 (2017)
    Response to applied stress (polarised light micrograph)
    Beyond stress, perovskite structure also responds to
    electric fields (electrostriction) and light (photostriction)
    – also reversible and reproducible?

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  23. Talk Motivation and Outline
    Does crystal strain influence the
    operation and performance of
    perovskite solar cells?
    A. Background
    B. Perfect crystal response
    C. Imperfect crystal response

    View full-size slide

  24. Unusually, Pb and Sn halides have positive
    bandgap deformation due to filled cation s2 band
    Band Gap Deformation in CH3
    NH3
    PbI3
    Deformation potential: J. M. Frost et al., Nano Letters 14, 2584 (2014)
    Pressure dependence: T. Wang et al, EES 10, 509 (2017)
    Deformation potential:
    • ⍺
    V
    = 2.5 eV
    • Dilation increases Eg
    • Compression decreases Eg
    • Behaviour also seen with T and P
    0.5% volume change: Eg
    ± 13 meV
    Ehrler group
    (AMOLF)
    HSE06+SOC

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  25. Band Gap Deformation in CH3
    NH3
    PbI3
    Unixial behaviour
    Same magnitude of Eg
    change
    with uniaxial strain in CH3
    NH3
    PbI3
    E&ES 12, 596 (2019)
    Unusually, Pb and Sn halides have positive
    bandgap deformation due to filled cation s2 band
    Youngkwang Jung

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  26. Talk Motivation and Outline
    Does crystal strain influence the
    operation and performance of
    perovskite solar cells?
    A. Background
    B. Perfect crystal response
    C. Imperfect crystal response

    View full-size slide

  27. Defects: Equilibrium Property of Crystals
    Point defects minimise the Gibbs free energy of a
    crystal – balance between enthalpic cost of bond
    breaking and entropic gain from disorder
    n = N exp
    −ΔGDefect
    k
    B
    T






    Defect
    concentration
    Defect energy
    Lattice sites
    Frenkel (1925); Jost (1933); Mott & Littleton (1938), etc.

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  28. Defect formation energies (concentrations and
    distributions) are functions that can be tuned
    F. A. Kröger “Chemistry of Imperfect Crystals” (1964)
    Atomic chemical potentials
    [growth & annealing conditions]
    Defects: Control Distributions
    Fermi level
    [function of n, p, T]
    Defect free energy
    of formation
    Crystal strain
    [internal or applied]

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  29. Vacancies in Strained CH3
    NH3
    PbI3
    Crystal strain has a large (linear) effect on
    vacancy formation and distribution
    Formation of VI
    + calculated as a
    function of uniaxial strain up to 0.5%
    (DFT/PBEsol in tetragonal supercell)
    T. W. Jones et al, Energy and Environ. Sci. 12, 596 (2019)
    compressive
    tensile

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  30. Vacancies in Strained CH3
    NH3
    PbI3
    Formation of VI
    + calculated as a
    function of uniaxial strain up to 0.5%
    (DFT/PBEsol in tetragonal supercell)
    T. W. Jones et al, Energy and Environ. Sci. 12, 596 (2019)
    T = 300 K equilibrium thermodynamics
    Crystal strain has a large (linear) effect on
    vacancy formation and distribution

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  31. Interstitials in Polycrystalline CsPbI3
    Grain boundaries can act as sinks for excess
    iodine due to strain relief (large crystal relaxation)
    J. S. Park et al, ACS Energy Letters 4, 1321 (2019)
    400 atom model of a Σ5 [130] tilt boundary in
    CsPbI3
    . Formation energy: 0.23 J/m-2
    Relative energy of
    excess iodine, Ii
    +
    Accumulation of charged iodine interstitials
    at the grain boundary (up to 1018 cm-3):
    linked to relaxation energy (I–I bond length)

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  32. Next Step: Carrier Capture Rates
    Group developers:
    Dr Sunghyun Kim
    Dr Samantha Hood
    Defectq=0 + eCB
    - Defectq=-1
    Non-radiative recombination: defect concentrations
    and capture cross-sections are now accessible
    github.com/WMD-group/CarrierCapture.jl
    Solve the Schrödinger equation
    for each potential energy surface
    Building on approach of Alkauskas et al, Phys. Rev. B 90, 075202 (2014)
    Static coupling
    approximation

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  33. Next Step: Carrier Capture Rates
    Non-radiative recombination: defect concentrations
    and capture cross-sections are now accessible

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  34. Next Step: Carrier Capture Rates
    First PV applications to the “well behaved”
    tetrahedral semiconductor Cu2
    ZnSnS4
    (CZTS)
    SRH limit S-Q limit
    JSC
    28.91
    mA/cm2
    28.91
    mA/cm2
    VOC
    0.84 V 1.23 V
    FF 86.4% 90.0%
    Efficiency 20.9% 32.1%
    Theoretical Cu2
    ZnSnS4
    solar cell
    efficiency (“best case scenario”)
    CdS
    CZTS
    d(1+/0)
    d(2+/1+)
    2
    1
    0
    1
    Energy (eV)
    200 100 0
    Position (nm)
    ϵ(2+/1+)
    E
    F
    ϵ(1+/0)
    Neutral
    trap
    Repulsive
    trap
    Giant
    trap
    V
    S
    -Cu
    Zn
    1+ V
    S
    2+
    Sn
    Zn
    1+
    Sn
    Zn
    2+
    Cu Sn
    1−
    1000/T (1/K)
    σn (cm2)
    0 2 4 6 8 10
    10−30
    10−27
    10−24
    10−21
    10−18
    10−15
    10−12
    (a ) (b)
    Giant traps (capture cross-section)
    Perovskites are coming soon (several technical challenges to overcome…)
    Work of Dr Sunghyun Kim, In Preparation (2019)
    [He is looking for a faculty position in 2020!]
    J. Mat. Chem. A 7,
    2686 (2019)

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  35. Conclusion
    Electron and defect distributions in halide
    perovskites are sensitive to many factors. Strain
    even in single compositions can be important; the
    influence in mixed-anion systems is likely larger.
    More theory and experiment is required!
    Collaborations: Youngkwang Jung, Lucy Whalley, Youngwon
    Woo, Jacob Wilson, Sunghyun Kim, Samantha Hood; Jarvist
    Frost (ICL); Ji-Sang Park (Kyungpook); Sam Stranks
    (Cambridge); Bruno Ehrler (AMOLF); Mike Toney (SLAC)
    Slides: https://speakerdeck.com/aronwalsh @lonepair

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