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Materials Modelling for Solar Cells: Perovskites and Beyond

Aron Walsh
August 17, 2018

Materials Modelling for Solar Cells: Perovskites and Beyond

Invited talk given at the CAMD Summer School (Denmark, 2018) covering solar cells from an atomistic modelling perspective

Aron Walsh

August 17, 2018
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  1. 2018 CAMD Summer School
    Materials Modelling for Solar Cells:
    Perovskites and Beyond
    Prof. Aron Walsh
    Imperial College London, UK
    Yonsei University, Korea
    Materials Design Group: https://wmd-group.github.io @lonepair

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  2. Solar Electricity & Fuel
    Electricity
    Solar Cells
    Chemical Energy
    Solar Fuels
    High efficiency (20–50%)
    Low efficiency (< 10%)
    Physics (electron–hole separation) is easier than
    chemistry (oxidation/reduction reactions)
    Fusion Reactor
    174,000 Terawatts
    reaches the Earth’s surface

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  3. Fundamentals of Solar Cells
    • Electromagnetism (light)
    • Quantum Electrodynamics (light/matter interaction)
    • Solid State Physics (electronic band theory)
    • Solid State Chemistry (optimising materials)
    • Soft Matter Physics (glasses and polymers)
    • Statistical Mechanics (defects and disorder)
    • Thermodynamics (device operation and limits)
    • Electrical Engineering (devices, systems, and grids)
    • Economics and Politics (realise solar electricity)
    Slide adapted from J. M. Frost: https://speakerdeck.com/jarvist

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  4. Many Photovoltaic Technologies
    Shockley and Queisser (1961); Polman et al, Science 352, 307 (2016)
    High performance
    “Established”
    Fundamental
    research
    Theoretical limit for
    single-junction cell
    (2018)

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  5. Challenge for Emerging Solar Cells
    GaAs efficiency is close to the theoretical limit,
    while Si is cheap. New materials must perform!
    Metal
    oxides
    Cu2
    O
    (6%)
    Bi2
    FeCrO6
    (8%)
    Co3
    O4
    (<1%)
    Metal
    sulphides
    SnS
    (5%)
    Cu2
    ZnSnS4
    (13%)
    FeS2
    (3%)
    Metal
    halides
    CsSnI3
    (10%)
    CH3
    NH3
    PbI3
    (23%)
    BiI3
    (1%)
    Examples of materials studied for thin-film photovoltaics
    (% sunlight to electricity conversion in photovoltaic devices)
    M. A. Green et al, Solar cell efficiency tables (version 52)

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  6. Talk Outline: Solar Energy
    A. Role of Materials Modelling
    B. Thin-Film Photovoltaics:
    • Kesterites (A2
    BCX4
    )
    • Perovskites (ABX3
    )
    C. Outlook for Materials Design

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  7. Thin-Film Solar Cells
    Cu(In,Ga)Se2
    CdTe
    From indirect (Si) to direct bandgap
    semiconductors for enhanced light absorption
    Light absorbing layer is a p-type semiconductor

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  8. From Materials to Devices
    Existing technologies benefited from decades of
    materials and device optimisation
    Complex chemical processes
    in CdTe solar cells:
    • Cu diffusion
    • CdCl2
    annealing
    • Cd(S,Te) formation
    • (Cd,Zn)S formation
    http://www.nrel.gov/pv/cadmium-telluride-solar-cells.html
    Cu
    S,Te mixing
    Cd,Zn mixing

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  9. Modelling Thin-Film Solar Cells
    Active Solar Absorber
    • Optical response
    • Electronic structure
    • Electron transport
    • Defect levels
    Front Electrical Contact
    • Band offsets
    • Interfacial states
    • Interfacial dipoles
    • Modification layers
    Back Electrical Contact
    • Band offsets
    • Ion diffusion
    • Interfacial reactions
    • Modification layers
    Device Modelling
    • Efficiency losses
    • J–V behaviour
    • Carrier collection
    • Layer optimisation

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  10. Open-Source Community Software
    http://www.solcore.solar; https://github.com/dalonsoa/solcore5

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  11. Reproducible Analysis in Publications
    https://github.com/WMD-group/hot-carrier-cooling
    Global movement of #openscience for
    transparency, reproducibility, and data-sharing

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  12. Talk Outline: Solar Energy
    A. Role of Materials Modelling
    B. Thin-Film Photovoltaics:
    • Kesterites (A2
    BCX4
    )
    • Perovskites (ABX3
    )
    C. Outlook for Materials Design

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  13. Brief History of Kesterite Solar Cells
    Cu2
    CdSnS4
    cell (1977); Cu2
    ZnSnS4
    cell (1988);
    12.6% Cu2
    ZnSn(S,Se)4
    record by IBM (2014)
    Wagner & Bridenbaugh (1977); Ito & Nakazawa (1988); Wang, Mitzi et al (2014)

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  14. Kesterite Quaternary Semiconductors
    2
    4
    2
    1a×1a×2a zincblende
    superlattice
    Charge-conserving substitutions to construct
    multi-component semiconductors
    “High-throughput” Density Functional Theory: Phys. Rev. B 79, 165211 (2009)
    2+ 2-
    1+ 3+
    4+
    2
    4
    2

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  15. • Mixed phases e.g. Cu2
    ZnSnS4
    à Cu2
    SnS3
    + ZnS
    • Cation disorder e.g. Cu-Zn, Cu-Sn, Zn-Sn mixing
    • Deep level defects i.e. fast non-radiative recombination
    • Interface reactions e.g. MoS2
    and SnS/SnS2
    formation
    Challenging for theory, simulation, and experiment!
    Issues Facing Kesterite Solar Cells
    Wallace, Mitzi and Walsh, ACS Energy Letters 2, 776 (2017)
    Champion solar cells suffer from large voltage
    deficit, e.g. for CZTS (Eg
    ~ 1.50 eV), VOC
    < 0.75 V

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  16. Defects in Photovoltaic Materials
    Point defects in solar cells: J. Park et al, Nature Rev. Mater. 3, 194 (2018)
    Good: population of charge carriers required for p-n
    junctions; Bad: voltage loss by e- h+ recombination
    Defect-mediated recombination
    often dominates under “1 sun”.
    Described by 1st order kinetics
    of the Shockley-Read-Hall (SRH)
    process (more on this later…)

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  17. Polytypes and Stacking Faults
    SiC and ZnS have a large
    number of known polytypes
    Image from: M. Grundmann, Physics of Semiconductors (2006)
    Labelled with Ramsdell notation
    ΔE between cubic (ABC) and hexagonal (AB)
    polytypes is small for tetrahedral semiconductors

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  18. Polytypes for Multernary Systems
    S. Chen et al, Physical Review B 82, 195203 (2010)
    “Cubic” ABC-derived “Hexagonal” AB-derived
    Binary
    AX
    Zincblende (!"
    #$%) Wurtzite (P6
    3
    mc)
    Ternary
    ABX2
    Chalcopyrite (I"
    #2d) BeSiN2
    (Pna2
    1
    )
    Quaternary
    A2
    BCX4
    Kesterite (I"
    #)
    Stannite (I"
    #2m)
    WZ-Kesterite (Pc)
    WZ-Stannite (Pmn2
    1
    )

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  19. Polytypes for Multernary Systems
    S. Chen et al, Physical Review B 82, 195203 (2010)
    “Cubic” ABC-derived “Hexagonal” AB-derived
    Binary
    AX
    ZnS ZnO
    Ternary
    ABX2
    CuFeS2
    BeSiN2
    Quaternary
    A2
    BCX4
    Cu2
    ZnXS4
    Ag2
    ZnXS4
    (X = Si, Ge, Sn)
    Cu2
    CdXS4
    Ag2
    CdXS4
    (X = Si, Ge, Sn)

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  20. Stacking Faults in Kesterites
    Kattan et al, Nanoscale 8, 14369 (2016); Appl. Mater. Today 1, 52 (2015)

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  21. Stacking Faults in Kesterites
    TEM image of CZTS. Inset
    atomic model is of CZTS
    oriented along [110]
    zone axis. From the
    group of Klaus Leifer at
    Uppsala University using
    samples from Edgardo
    Saucedo at IREC

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  22. Atomic Models of Extended Defects
    J. Park et al, Phys. Rev. Mat. 2, 041602 (2018)
    3D atomic models to
    describe stacking faults (a-c),
    a grain boundary (d), and
    anti-site boundary domains
    [Cu-Zn à Zn-Cu] (e-f)
    Jisang Park

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  23. DFT Calculation of Extended Defects
    Formation energy
    (eV/nm2)
    J. Park et al, Phys. Rev. Mat. 2, 041602 (2018)
    Formation energy
    from an Ising model
    Shifts in valence (VBO) &
    conduction (CBO) bands
    [weak electron barriers]
    Se
    HSE06; PAW / plane
    wave basis in VASP

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  24. Types of Point Defects in Kesterites
    Lattice imperfections formed in thermodynamic
    equilibrium and/or through materials processing
    Vacancies
    VCu
    , VZn
    , VSn
    , VS
    Interstitials
    Cui
    , Zni
    , Sni
    , Si
    Antisites
    CuZn
    , CuSn
    , ZnCu
    , etc.
    The copper vacancy and
    Cu-on-Zn antisite are the
    dominant acceptor defects
    responsible for native p-
    type behaviour of CZTS
    S. Chen et al, Adv. Mater. 25, 1522 (2013)

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  25. Point Defects: Theory and Experiment
    Calculable from DFT Observable
    Energy change
    ΔE/ΔH/ΔG
    • Heats of formation
    and concentrations
    • Diffusion barriers
    Defect ionisation level
    (Optical)
    Optical absorption;
    photoluminescence;
    photoconductivity
    Defect ionisation level
    (Thermal)
    Deep-level transient
    spectroscopy; thermally
    stimulated conductivity
    Defect vibrational modes
    ⍵(q,T)
    • IR / Raman spectra
    • Diffusion rates
    • Recombination rates

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  26. SRH: Shockley & Read, Phys. Rev. 87, 835 (1952); Hall, Phys. Rev. 87, 387 (1952)
    Non-Radiative Carrier Capture
    SRH analysis: mid-gap defects are most active
    Beyond: defects levels are not fixed, but vary with the charge state. Non-
    radiative recombination is a multi-level phonon-emission process

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  27. Structural relaxation (electron-phonon coupling)
    is a critical component of carrier capture
    Non-Radiative 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 recombination
    [Defect luminescence]
    Defect in charge
    states E1
    and E2
    Non-radiative recombination
    [Phonon emission]

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  28. Revisit: Deep Defects in Cu2
    ZnSnS4
    [HSE06/DFT supercells
    including finite-size
    effects: sxdefectalign]
    S. Kim et al, ACS Energy Lett. 3, 496 (2018)
    Defects involving Sn produce
    the deepest levels.
    The sulfur vacancy is low
    energy. It should act as a
    double donor [VS
    2+ + 2e-], but
    produces no levels in the band
    gap… inert?
    Sunghyun Kim
    Note: quasi-particle energies,
    not single-particle eigenvalues

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  29. VS
    Assisted Recombination
    S. Kim et al, ACS Energy Lett. 3, 496 (2018)
    Kim Recombination Model
    1. Population of VS
    + formed
    in thermal equilibrium
    2. Hole capture VS
    + to VS
    ++
    under illumination
    3. Electron capture to
    recover VS
    + (10−13 cm2)*
    IR Photon
    Assisted (~0.6 eV)
    Static approximation: Alkauskas et
    al, Phys. Rev. B 90, 075202 (2014)

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  30. VS
    Assisted Recombination
    S. Kim et al, ACS Energy Lett. 3, 496 (2018)
    Testable Model?
    1. Recombination rate
    should be enhanced by IR
    light (~2000 nm)
    2. Role of VS
    + could be
    confirmed by spin (EPR)
    VS
    + is associated with Sn(III) species.
    EPR signal for Sn(III) in ZnS matches a
    brief 2010 report for CZTS. C. Chory et
    al, DOI: 10.1002/pssc.200983217
    Sn lone pair
    associated with
    sulfur vacancy
    (excess electrons)
    IR Photon
    Assisted (~0.6 eV)

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  31. Beyond Dilute Defects in Kesterites
    Cross-section of typical cell [IBM]
    Cd/Zn mixing
    Cu/Zn mixing
    MoS2
    /SnS2
    formation

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  32. Talk Outline: Solar Energy
    A. Role of Materials Modelling
    B. Thin-Film Photovoltaics:
    • Kesterites (A2
    BCX4
    )
    • Perovskites (ABX3
    )
    C. Outlook for Materials Design

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  33. 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

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  34. Why Halide Perovskites?
    Essentials for Solar Cells
    • Strong optical absorption (Eg
    ~ 1.6 eV)
    • Light electron and hole masses (conductive)
    • Easy to synthesise (cheap and scalable)
    Advanced Features
    • Dielectric screening: carrier separation (weak
    excitons) and transport (low scattering rates)
    • Slow e-h recombination: low losses, large VOC
    o Relativistic effects – spin-orbit coupling
    o Polar nano-domains – dynamic fluctuations
    o Phonon scattering – limit non-radiative events

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  35. Perovskites: Model vs Reality
    Plastic crystal behaviour probed by Quasi-Elastic Neutron Scattering (P.
    Barnes, DOI: 10.1038/ncomms8124); 2D IR Spectroscopy (A. Bakulin,
    DOI: 10.1021/acs.jpclett.5b01555); Inelastic X-ray Scattering (S. Billinge,
    DOI: 10.1021/acsenergylett.6b00381) with simulations

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  36. Intersection of Hard and Soft Matter
    Jarvist Frost
    CH3
    NH3
    PbI3
    3D periodic boundary
    (80–640 atoms)
    25 fs per frame
    0.5 fs timestep
    based on PBEsol
    forces at T=300K
    “As soft as jelly”
    J. M. Frost, K. T. Butler, A. Walsh, APL Mater. 2, 081506 (2014)
    Combination of density functional theory, GW
    theory, lattice dynamics, molecular dynamics,
    classical Monte Carlo, continuum device models

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  37. Dielectric Response
    Standard Inorganic Dielectric
    Organic-Inorganic Dielectrics
    Microstructure
    Conductivity
    Contacts
    Lattice dynamics
    Optical response
    Stat. mechanics
    Sum of:

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  38. Dielectric Response
    High-frequency
    from
    QSGW+SOC
    Low-frequency
    from harmonic
    phonons
    (DFT/PBEsol)
    With Mark van
    Schilfgaarde

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  39. “Giant Dielectric Constant”
    JPCM 20, 191001 (2008)
    JPCL 5, 2390 (2014)
    J. M. Frost and A. Walsh, Acc. Chem. Res. 49, 528 (2016)

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  40. “Giant Dielectric Constant”
    JPCM 20, 191001 (2008)
    JPCL 5, 2390 (2014)
    J. M. Frost and A. Walsh, Acc. Chem. Res. 49, 528 (2016)

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  41. Bananas are Lossy Dielectrics
    J. F. Scott, J. Phys. Conden. Matter 20, 2 (2007)

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  42. Mixed Ion–Electron Conductors
    Current-voltage hysteresis
    [Snaith et al, JPCL (2014); Unger et al, EES (2014)]
    Rapid chemical conversion between halides
    [Pellet et al, CM (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
    [Xing et al, PCCP (2016); Kim et al, NatM (2018)]

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  43. Mixed Ion–Electron Conductors
    Nature Comm. 6, 8497 (2015); ACS Energy Lett. 3, 1983 (2018)
    Reservoir of charged point defects (site vacancies)
    in thermodynamic equilibrium: V-
    MA
    , V2-
    Pb
    , V+
    I
    A. Walsh et al, Angewandte 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]

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  44. Talk Outline: Solar Energy
    A. Role of Materials Modelling
    B. Thin-Film Photovoltaic Technologies:
    • Kesterites (A2
    BCX4
    )
    • Perovskites (ABX3
    )
    C. Outlook for Materials Design

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  45. Solar Absorber Shopping List
    • Low-cost and non-toxic elements
    • Direct optical bandgap (1–2 eV)
    • Easy to deposit and scale-up production
    • Semiconductor with low carrier concentrations
    • Tolerant to impurities and microstructure
    • Chemically stable at interfaces
    • Workfunction matched to electrical contacts

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  46. Solar Absorber Shopping List
    • Low-cost and non-toxic elements
    • Direct optical bandgap (1–2 eV)
    • Easy to deposit and scale-up production
    • Semiconductor with low carrier concentrations
    • Tolerant to impurities and microstructure
    • Chemically stable at interfaces
    • Workfunction matched to electrical contacts
    What can we reliably calculate
    from first-principles modelling?

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  47. Does it Absorb Sunlight?
    Simple descriptor: Eg
    . Advanced: optical absorption
    and detailed-balance for a thin-film
    SLME metric: Yu and Zunger, Phys. Rev. Lett. 108, 068701 (2012)
    Detailed balance: Blank et al, Phys. Rev. App. 8, 024032 (2017)
    Materials Chemistry
    Structure/Composition
    o Orbital character
    o Band widths
    o Band degeneracy
    o Selection rules

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  48. Is it Stable?
    Experiment (Scragg)
    Kesterite Unstable
    CZTS Stable
    Simple descriptor: ΔHf
    . Advanced: secondary
    phases under realistic growth conditions (ΔGf
    )
    Materials Chemistry
    Structure/Composition
    o Choice of elements
    o Stoichiometry
    o Synthetic routes
    o Metastability
    Kesterites: Jackson and Walsh, J. Mat. Chem A 2, 7829 (2014)
    Perovskites: Zhang et al, Chin. Phys. Lett. 3, 036104 (2018) [arXiv 2014]
    Cu2
    ZnSnS4
    à
    Cu2
    S + ZnS + SnS +S(g)

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  49. Does it Conduct (p–i–n)?
    CZTS Stable
    Simple descriptor: me
    * and ΔH(q,q’) for key
    defects. Advanced: self-consistent EF
    analysis
    Materials Chemistry
    Structure/Composition
    o Band energies
    o Growth conditions
    o (Co-)dopants
    o Solid-solutions
    Analysis of SnS: Y. Kumagai et al, Phys. Rev. Appl. 6, 014009 (2016)
    Defect review: J. Park et al, Nature Rev. Mater. 3, 194 (2018)
    Self-consistent
    defect cycle

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  50. Will Carriers Live or Die?
    Defect tolerance : Walsh and Zunger, Nature Mater. 16, 964 (2017)
    Defect review: J. Park et al, Nature Rev. Mater. 3, 194 (2018)
    Simple descriptor: ΔH(q,q’) point defect levels.
    Advanced: prediction of carrier capture rates
    Materials Chemistry
    Structure/Composition
    o Redox active ions
    o Lattice vibrations
    o Passivation
    o Post-processing

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  51. How to Extract Charge?
    CZTS Unstable
    CZTS Stable
    Simple descriptor: ɸ (workfunction). Advanced:
    structure matching and interfacial effects
    Materials Chemistry
    Structure/Composition
    o Atomic levels
    o Coordination
    o Reactivity
    o Interface layers
    QM/MM band energies: D. O. Scanlon et al, Nature Mater. 12, 798 (2013)
    ELS for perovskites: K. T. Butler et al, J. Mater. Chem. C 4, 1129 (2016)
    Electronic matching
    Lattice strain
    Site overlap
    for A
    find B with
    low Schottky barrier &
    small lattice mismatch &
    high atomic overlap

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  52. Evolution of Computational Materials
    CZTS Unstable
    CZTS Stable
    Quick-start machine learning guide: K. T. Butler et al, Nature 559, 547 (2018)
    Can we build a robust figure-of-merit and virtual
    screening procedure for thin-film solar cells?
    Potential for combining first-principles predictions with experiments
    and databases for data-driven materials discovery

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  53. Conclusions: Modelling for Solar Cells
    • Many simulation approaches required to describe
    range of processes (length and time scales)
    • First-principles techniques are having impact on
    emerging photovoltaic technologies
    • Further developments needed for quantitative
    predictions to enable true materials discovery
    Slides: https://speakerdeck.com/aronwalsh
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