Upgrade to Pro — share decks privately, control downloads, hide ads and more …

Life and Times of an Electron in a Perovskite Solar Cell

Aron Walsh
March 27, 2019

Life and Times of an Electron in a Perovskite Solar Cell

Invited presentation at Computational Molecular Science (2019)
https://warwick.ac.uk/fac/sci/chemistry/news/events/cms2019/

Aron Walsh

March 27, 2019
Tweet

More Decks by Aron Walsh

Other Decks in Research

Transcript

  1. Computational Molecular Science (2019)
    Life and Times of an Electron in a
    Perovskite Solar Cell
    Prof. Aron Walsh
    Imperial College London, UK
    Yonsei University, Korea
    Materials Design Group: https://wmd-group.github.io @lonepair

    View full-size slide

  2. Life of a Photoexcited Electron*
    *In a semiconductor host, where the terms electron and (charge) carrier are used

    View full-size slide

  3. “Total” Crystal Hamiltonian
    Crystals are not frozen in space and time. Should
    consider vibrational and electronic excitations
    Source: D. C. Wallace – Statistical Physics of Crystals and Liquids (2002)
    Crystal Potential
    static model
    Electronic
    Excitations
    Harmonic Phonons
    vibrations
    Anharmonic
    Interactions
    Electron-Phonon
    Coupling

    View full-size slide

  4. Exciting Perovskites
    A. (Rapid) Theory of Crystal Dynamics
    B. Vibrations of CH3
    NH3
    PbI3
    C. What Size is an Electron?
    D. Research Challenges

    View full-size slide

  5. Why Phonons?
    Collective vibrational excitations of crystals:
    N atoms vibrate as 3N phonon modes, ⍵(q)
    Essential for:
    • Free energy of crystals
    • Vibrational spectra
    • Thermal expansion
    • Phase transformations
    • Heat flow
    • Electrical conductivity
    Crystal
    momentum

    View full-size slide

  6. Theory of Crystal Dynamics
    Anharmonicity
    All higher-order terms
    Harmonic Phonons
    Ionic Forces
    = 0 at equilibrium
    Crystal potential expanded with ion displacements (r)
    Crystal Potential
    static model
    Born and Huang, Dynamical Theory of Crystal Lattices (1958)
    Collective vibrational excitations of crystals:
    N atoms vibrate as 3N phonon modes, ⍵(q)

    View full-size slide

  7. Harmonic Approximation (HA)
    U(Q)
    Q
    Real PES HA
    ! " =
    1
    2
    &"'
    ( " = −
    *! "
    *"
    = −&"
    • Analytic solutions
    • 3N normal modes
    w/ frequency ω
    i
    • ": normal mode
    coordinate
    Energy
    Force
    Schematic courtesy of Dr Jonathan Skelton (now University of Manchester)
    Weak
    anharmonicity

    View full-size slide

  8. “Jacob’s Ladder” of Crystal Dynamics
    Frequency shifts
    temperature & pressure
    Variety of anharmonic techniques available
    – alternative is (large-scale) molecular dynamics
    Mode lifetimes
    linewidths & conductivity
    Thermal expansion
    Grüneisen parameters
    Phonon frequencies
    thermodynamics & spectra
    Phonopy, Phon, and built
    into most DFT packages
    Phono3py
    ShengBTE
    AlmaBTE
    Alamode, D3q, SCALID
    TDEP, Phono4py… machine
    learning assisted
    Many other codes available

    View full-size slide

  9. Organic-Inorganic Phonon Challenges
    J. K. Bristow et al, PCCP 18, 29316 (2016)
    Complex structures with large vibrational range

    View full-size slide

  10. Issue Cause Solution
    Large unit
    cells
    100–1000s of atoms
    Large computers /
    interaction cutoff radii
    Missing H
    No information on H
    location from XRD
    Electron counting and
    chemical knowledge
    Defective
    structures
    Missing ligands or clusters
    (up to 25%)
    Explicit simulation of
    defect processes
    Symmetry
    breaking
    Average structure from X-
    ray diffraction (with no H)
    Check phonons for
    imaginary modes
    Unphysical
    dynamics
    Large phonon range (0–
    3500 cm-1) can result in
    slow MD equilibration
    Avoid initialisation
    from random
    displacements
    Organic-Inorganic Phonon Challenges

    View full-size slide

  11. Exciting Perovskites
    A. (Rapid) Theory of Crystal Dynamics
    B. Vibrations of CH3
    NH3
    PbI3
    C. What Size is an Electron?
    D. Research Challenges

    View full-size slide

  12. Hybrid Organic–Inorganic Perovskites
    Brief History
    (1958) – Photoconductivity in CsPbI3
    (Møller)
    (1978) – Synthesis of CH3
    NH3
    PbI3
    (Weber)
    (1994) – Metallic transition in CH3
    NH3
    SnI3
    (Mitzi)
    (2009) – Perovskite dye cell (Miyasaka)
    (2012) – Planar thin-film solar cell (Snaith)
    Inorganic
    CsPbI3
    Hybrid
    CH3
    NH3
    PbI3
    or MAPI

    View full-size slide

  13. Phonon Modes of CH3
    NH3
    PbI3
    High-frequency: confined CH3
    NH3
    + modes

    View full-size slide

  14. Phonon Modes of CH3
    NH3
    PbI3
    Low-frequency: PbI3
    - and coupled modes
    Unit: cm-1

    View full-size slide

  15. Harmonic Phonon Dispersion, ω(#)
    Gold-Parker et al, PNAS 115, 11905 (2018)
    Calculated acoustic modes of
    orthorhombic CH3
    NH3
    PbI3
    (Phonopy; PBEsol)
    Measured inelastic neutron
    scattering on single crystals
    (led by Mike Toney, SLAC)
    Excellent agreement for
    energies and dispersion
    Calculations can be compared to IR/Raman
    spectra (q~0) or X-ray/neutron scattering
    3 meV = 0.7 THz = 24 cm-1

    View full-size slide

  16. Anharmonic Phonon Lifetimes, ω(#, τ)
    Phonons are quasiparticles with individual
    lifetimes determined by their scattering rates
    Gold-Parker et al, PNAS 115, 11905 (2018)
    Lifetime and
    linewidth
    Theory (Phono3py; PBEsol) gives upper limit of lifetime as only
    3-phonon scattering is included (assumed to be dominant)
    Acoustic phonon linewidth: From Γ to X point

    View full-size slide

  17. Ultra-Low Thermal Conductivity
    Heat carrying modes in CH3
    NH3
    PbI3
    involve Pb-I
    octahedral network with very short lifetimes
    Gold-Parker et al, PNAS 115, 11905 (2018)
    Calculated lattice
    thermal conductivity
    (Phono3py; PBEsol)
    At T = 300 K
    GaAs: 48 W/m/K
    CH3
    NH3
    PbI3
    : 0.1 W/m/K
    Integrated
    thermal
    conductivity
    20 meV = 4.8 THz = 160 cm-1

    View full-size slide

  18. Low-Frequency Dielectric Response
    High-frequency
    from
    QSGW+SOC
    Low-frequency
    from harmonic
    phonons
    (DFT/PBEsol)
    Low-frequency optic
    phonon modes
    Sum over phonon modes λ
    with Born charges Z

    View full-size slide

  19. Exciting Perovskites
    A. (Rapid) Theory of Crystal Dynamics
    B. Vibrations of CH3
    NH3
    PbI3
    C. What Size is an Electron?
    D. Research Challenges

    View full-size slide

  20. Carrier Generation and Cooling
    Long-lived hot carriers upon photoexcitation
    Effective mass and heat diffusion models:
    Frost, Whalley, Walsh, ACS Energy Letters 2, 2647 (2017)

    View full-size slide

  21. Nature of Electron and Hole Carriers
    Charge carriers in crystals are quasiparticles
    defined by electron-lattice interaction: polarons
    Effective mass (Bohr) radius r ~ 10 nm

    View full-size slide

  22. Nature of Electron and Hole Carriers
    Charge carriers in crystals are quasiparticles
    defined by electron-lattice interaction: polarons
    Large polaron radius r ~ 2.5 nm

    View full-size slide

  23. 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 < 200 cm2V-1s-1
    APL Materials 2, 081506 (2014); ACS Energy Lett. 2, 2647 (2017)

    View full-size slide

  24. Transport of Electron and Hole Carriers
    Reality: non-parabolic band structure, anharmonic
    vibrations, multi-mode dielectric response
    Lucy D. Whalley et al, Phys. Rev. B 99, 085207 (2019)
    Electronic band structure
    Predicted carrier mobility
    Mobility limited by Fröhlich scattering
    https://github.com/jarvist/PolaronMobility.jl
    T = 300 K
    Parabolic m* regime

    View full-size slide

  25. Exciting Perovskites
    A. (Rapid) Theory of Crystal Dynamics
    B. Vibrations of CH3
    NH3
    PbI3
    C. Life of an Electron
    D. Research Challenges

    View full-size slide

  26. 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)

    View full-size slide

  27. Electron-Hole Recombination
    Conversion efficiencies of solar cells are limited by
    non-radiative trap-mediated recombination
    Band (large polaron) electron

    View full-size slide

  28. Electron-Hole Recombination
    Conversion efficiencies of solar cells are limited by
    non-radiative trap-mediated recombination
    Electron trapped at point defect

    View full-size slide

  29. Shockley & Read, Phys. Rev. 87, 835 (1952); Hall, Phys. Rev. 87, 387 (1952)
    Electron-Hole Recombination
    Conversion efficiencies of solar cells are limited by
    non-radiative trap-mediated recombination
    Beyond SRH: defects levels are not fixed, but vary with the charge state.
    Recombination is a multi-level phonon-emission process
    Valence
    band
    Conduction
    band
    Trap level
    Shockley-Read-
    Hall (SRH) process
    1st order kinetics
    k
    SRH
    ∝ [e]

    View full-size slide

  30. Structural relaxation (electron-phonon coupling)
    is a critical component of carrier capture
    Q = configuration coordinate [change in local structure with charge state]
    Huang & Rhys, Proc. RS 204, 406 (1950); Henry & Lang, Phys. Rev. 15, 989 (1977)
    Radiative (weak coupling)
    Defect luminescence
    Defect in charge
    states E1
    and E2
    Non-Radiative (strong coupling)
    Phonon emission
    Electron-Hole Recombination

    View full-size slide

  31. Requires: (a) defect concentrations, trap levels,
    configurational coordinates of each charge
    First-Principles Carrier Capture Rates
    [Point defect review] Ji-Sang Park et al, Nat. Rev. Mater. 3, 195 (2018)
    Chemical Potential Limits
    github.com/jbuckeridge/cplap
    Self-consistent Fermi Level
    github.com/jbuckeridge/sc-fermi
    Equilibrium
    defect populations

    View full-size slide

  32. First-Principles Carrier Capture Rates
    Group developers:
    Dr Sunghyun Kim
    Dr Samantha Hood
    Defectq=0 + eCB
    - Defectq=-1
    Requires: (b) vibrational wavefunctions and
    electron-phonon interaction strength
    github.com/WMD-group/CarrierCapture.jl
    Anharmonicity Included
    Solve Schrödinger equation for
    each potential energy surface
    Following harmonic approach of Alkauskas et al, Phys. Rev. B 90, 075202 (2014)
    Static coupling
    approximation

    View full-size slide

  33. Redox Processes in Metal Halides
    2X# + h& → X(
    #
    V centre
    X# + X)
    # + h& → X(
    #
    H centre
    Whalley, Crespo-Otero, and Walsh, ACS Energy Letters 2, 2713 (2017)
    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 (PV-CDT)

    View full-size slide

  34. Conclusion
    Electrons in semiconductors are under the
    influence of lattice vibrations. It is often
    necessary to go beyond the harmonic approx.
    especially for “soft” halide perovskites. Next step:
    ab initio prediction of solar cell efficiency limits
    Project Collaborators: Sunghyun Kim, Jonathan
    Skelton, Jarvist Frost, Lucy Whalley, Samantha Hood;
    Ji-Sang Park; Mark van Schilfgaarde (Kings); Sam
    Stranks (Cambridge); Mike Toney (SLAC)
    Slides: https://speakerdeck.com/aronwalsh

    View full-size slide