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Unsolved Mysteries of Halide Perovskites

Aron Walsh
November 26, 2018

Unsolved Mysteries of Halide Perovskites

Invited presentation at the Fall Meeting of the Materials Research Society (#f18mrs) in "ET05: Fundamental Aspects Of Halide Perovskite (Opto)electronics And Beyond"

Aron Walsh

November 26, 2018
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  1. Materials Research Society (Fall Meeting 2018)
    UnsolvedMysteries of
    Halide Perovskites
    Prof. Aron Walsh
    Imperial College London, UK
    Yonsei University, Korea
    Materials Design Group: https://wmd-group.github.io @lonepair
    From @KamatlabND

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  2. Halide Perovskites – What we Know
    Introduction to underlying physics in 2014 MRS talk:
    https://speakerdeck.com/aronwalsh
    ABX3
    compounds with strong optical absorption,
    light carrier masses, efficient dielectric screening
    Device consequences
    • Weak exciton binding (EB
    T in 3D perovskites)
    • High carrier mobilities (limited by optic scattering)
    • Semiconductor alloys (A, B, X lattice sites)

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  3. 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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  4. 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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  5. 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 ~ 10-12cm2s-1
    at T = 300 K
    [PBEsol/DFT in 768 atom supercell
    with nudged-elastic band]
    Bulk diffusion barrier

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  6. Mysteries of Perovskites
    A. Charge Carrier Localisation
    B. Spontaneous Lattice Strain
    C. Defects and Doping

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  7. Nature of Electron and Hole Carriers
    Charge carriers in crystals are quasi-particles
    defined by electron-lattice interaction: polarons
    Effective mass (Bohr) radius

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  8. Nature of Electron and Hole Carriers
    Charge carriers in crystals are quasi-particles
    defined by electron-lattice interaction: polarons
    Polaron radius

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  9. Nature of Electron and Hole Carriers
    Fröhlich electron-lattice interaction
    ! =
    1
    2
    1
    %&

    1
    %(
    )
    ℏ+
    2,+

    -
    .
    GaAs = 0.1
    CdTe = 0.3
    CH3
    NH3
    PbI3
    = 2.4
    SrTiO3
    = 3.8
    Intermediate coupling regime: Large polaron
    Variational solution for
    Feynman polaron model
    rP = 4 unit cells
    mP
    * = 0.2 me
    (+30%)
    µP < 100 cm2V-1s-1
    Jarvist
    Frost
    APL Materials 2, 081506 (2014); ACS Energy Lett. 2, 2647 (2017)

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  10. Real-Space Hot Polaron Cooling
    Excess excitation energy contained in polaron,
    with slow exchange to the bulk crystal
    Frost, Whalley, Walsh, ACS Energy Letters 2, 2647 (2017)
    Low Density
    n < 1018 cm-3
    High Density
    n > 1018 cm-3
    (Laser source)
    Notebooks: https://github.com/WMD-
    group/hot-carrier-cooling

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  11. Ultra-Low Thermal Conductivity
    Phonon-phonon interactions 103 stronger
    (shorter lifetimes) in CH3
    NH3
    PbI3
    than GaAs
    Whalley et al, PRB 94, 220301(R) (2016); Gold-Parker et al, PNAS, Online (2018)
    Calculated lattice
    thermal conductivity
    (Phono3py; PBEsol)
    T = 300K
    GaAs (!)
    38 (calculated)
    45 (measured)
    MAPI (!)
    0.05 (calculated)
    ~0.5 (measured)

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  12. Open Question: Rashba Polarons
    Does symmetry breaking (non-centrosymmetry)
    alter the physics of polarons in perovskites?
    CH3
    NH3
    PbI3
    CsPbI3
    QSGW+SOC
    calculations on
    ab initio MD
    trajectory
    QUESTAAL
    Code
    With Mark van
    Schilfgaarde
    McKechnie et al, Phys. Rev. B 98, 085108 (2018)
    Rashba-Dresselhaus splitting of valence & conduction bands (300 K)
    ↑ ↓

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  13. Open Question: Rashba Polarons
    Sensitive to material form and quality? Carrier
    concentrations? Length and time scale of measurements?
    Does symmetry breaking (non-centrosymmetry)
    alter the physics of polarons in perovskites?

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  14. Mysteries of Perovskites
    A. Charge Carrier Localisation
    B. Spontaneous Lattice Strain
    C. Defects and Doping

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  15. “Ferroelectric” Pb Halide Perovskites
    Paper titles from the literature on one material!

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  16. “Ferroelectric” Pb Halide Perovskites
    Paper titles from the literature on one material!
    Many reports misled by
    polarisation signatures
    of interface charging, ion
    transport and/or lattice strain

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  17. Ferroelastic Domain Formation
    [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

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  18. Ferroelastic Domain Formation
    “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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  19. Scales of Disorder in Perovskites
    Lattice strain patterns have a complex
    heterogeneity across multiple length scales
    “Supergrain”
    <110> quiver plot
    Nanofocus XRD at ESRF
    Micro-XRD at ALS
    Over 20 µm: 0.3% strain
    [Led by Sam Stranks] T. Jones et al, arXiv 1803.01192 (2018)

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  20. Open Question: (Photo)Electrostriction
    New perspective on ferroic effects: J. N. Wilson et al, arXiv 1811.01832 (2018)
    No convincing explanation or model for what
    drives lattice expansion up to Δa/a = 1%
    Reversible changes with timescales of ms to hours,
    suggests defect formation and redistribution

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  21. Mysteries of Perovskites
    A. Charge Carrier Localisation
    B. Spontaneous Lattice Strain
    C. Defects and Doping

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  22. Point Defects in Photovoltaic Materials
    Good
    Bad
    Population of Charge Carriers
    Shallow donors and acceptors
    Limit Charge Carrier Mobility
    Ionised and neutral impurity scattering
    Non-radiative e-h Recombination
    Deep level defects
    Coupled ion & electron transport,
    defect aggregates, and redox reactions
    Ugly
    Defect Tolerance: A. Walsh and A. Zunger, Nature Materials 16, 965 (2017)

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  23. Many Defects but Few Carriers
    Lead halide perovskites are intrinsic – low carrier
    concentrations, resistant to extrinsic p or n doping
    Carrier Conc. Technique Reference
    109 cm-3
    Hall effect on pressed
    pellets of CH3
    NH3
    PbI3
    Stoumpos et al, Inorg
    Chem 52, 9019 (2013)
    109 cm-3
    Impedance
    measurements on
    photovoltaic devices
    Pockett et al, J Phys
    Chem C 119, 3456
    (2015)
    1014 cm-3
    Hall effect on thin films
    of CH3
    NH3
    PbI3
    Bu et al, J Mat Chem A 2,
    18508 (2014)
    1014 cm-3 = 1 carrier every 10 million unit cells (high purity CdTe)

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  24. Iodine Vacancy: High Concentration
    Low formation energy of VI
    + implies a high
    equilibrium donor concentration
    n = N exp
    −ΔGDefect
    k
    B
    T






    Defect
    concentration
    0.2 eV
    (VI
    + for EF
    = midgap)
    Lattice sites in MAPI
    If this was the sole defect: n = 1019 cm-3
    Calculations by groups of Y. Yan (2014), M.-H. Du (2014), D.O. Scanlon (2015)…

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  25. Electronic (Carrier) Compensation
    If the only defect present is VI
    + then a high
    electron concentration would be expected
    Concentration of
    ionised donors
    Concentration of
    conduction electrons
    Charge neutrality expression

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  26. Charge compensation by ionic defects determine
    the doping limits of most semiconductors
    Ionic (Defect) Compensation
    Defect self-compensation: G. Mandel, Phys. Rev. 134, A1073 (1963)
    Decades of literature: Kröger, Walukiewicz, Wei, Zunger; van de Walle, Catlow
    Recent review: Walsh and Zunger, Nature Materials 16, 965 (2017)
    Electronic
    regime
    Ionic
    regime
    Overall charge
    neutrality
    Donors Holes Acceptors Electrons

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  27. Self-Regulation of Charge
    A. Walsh et al, Angewandte Chemie 54, 1791 (2015)
    A high population of charged defects with overall
    charge neutrality – few excess electrons or holes
    Schottky disorder
    Frenkel disorder
    Two limits
    Both forms of
    stoichiometric
    disorder –
    common in oxide
    perovskites

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  28. High concentration of charged defects from
    equilibrium thermodynamics ≥ 1018 cm-3
    Perovskites: Soup of Charged Defects
    +
    +
    +
    +
    -
    -
    -
    -
    -
    ++ ++
    - -
    -
    Quantitative predictions difficult as beyond dilute defect limit
    and description of solution processing / precipitation reactions

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  29. Open Question: Deep Defects
    Non-radiative recombination rates are low, but
    still represent loss of 100–200 mV from ideal
    Ji-sang Park et al, Nature Reviews Materials 3, 195 (2018)
    Technique Trap Levels (eV)
    DLTS
    (Yang, Science 2017)
    0.46, 0.78, 0.82 below
    conduction band
    TSC
    (Baumann, JPCL 2015)
    0.5 from a band edge
    DLTS
    (Heo, EES 2017)
    0.62, 0.75 below
    conduction band
    Sensitive to growth but ≲ 1015 cm-3 traps

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  30. Open Question: Deep Defects
    2X# + h& → X(
    #
    V centre
    X# + X)
    # + h& → X(
    #
    H centre
    Whalley, Crespo-Otero, and Walsh, ACS Energy Letters 2, 2713 (2017)
    Halide redox: Hole trapping in V and H centres
    studied in metal halides since the 1950s
    Predicted excited-states
    TDDFT (PBE0 with SOC)
    in DALTON2016
    On-going work: Carrier
    trapping rates by Lucy
    Whalley (ICL)

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  31. Group Talks at #f18mrs
    Lone Pair Engineering for Polar Semiconductors
    Me again! Today 11:15 - EP01.01.09
    Effect of Stacking Disorder in Cu2
    ZnSn(S,Se)4
    Jisang Park, Wed 08:45 - ET11.09.02
    Charge Separation in Organic Solar Cells
    Samantha Hood, Wed 14:15 - EP05.10.03
    Extended Defects in Earth Abundant Inorganic Materials
    Jisang Park, Wed 14:15 - ET12.06.03
    Origin of Green-Light Emission in Cs4
    PbBr6
    Youngkwang Jung, Friday 8:30 AM - ET05.13.03

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  32. Conclusion and Outlook
    We learned a lot about halide perovskites since
    2012. Challenges remain for understanding
    structural & electronic properties, e.g. will there
    ever be a perovskite p-n homojunction?
    Project Collaborators: Lucy Whalley, Jarvist Frost,
    Jonathan Skelton, Jacob Wilson, Youngkwang Jung;
    Mark van Schilfgaarde (Kings); Keith Butler (ISIS);
    Sam Stranks (Cambridge); Chol-Jun Yu (Kim Il Sung)
    Piers Barnes (ICL); Mike Toney (SLAC)
    Slides: https://speakerdeck.com/aronwalsh

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