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Ionic Defects in Halide Perovskite Solar Cells

Ionic Defects in Halide Perovskite Solar Cells

presented by Carsten Deibel at the MRS Spring Meeting 2022 on 9th May at 11:00 AM in Hawai'i Convention Center, Level 3, 319A

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Carsten

May 12, 2022
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  1. www.tu-chemnitz.de/physik/OPKM MRS Spring Meeting, Honolulu· 9. Mai 2022 · deibel@physik.tu-chemnitz.de

    Carsten Deibel Institut für Physik Technische Universität Chemnitz Ionic Defects in 
 Halide Perovskite Solar Cells Optik und Photonik kondensierter Materie                  
  2. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Contributors • Sandhya Tammireddy & Sebastian Reichert @

    TUC • Yana Vaynzof & Qingzhi An et al @ TU Dresden • Aron Walsh & Young-Won Woo @ Imperial & Yonsei U • Jan-F Pietschmann & Jens Flemming @ TUC
  3. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Capacitance in the time and frequency domain transparent

    anode p n W 𝜀 𝑅 𝑅 s 𝑅 p perovskite cathode HTL ETL ≈ i - 𝑍 = 𝑉 𝑎 𝑐 𝐼 𝑎 𝑐 = 1 1 𝑅 p + i 𝜔 𝐶 + 𝑅 s 𝐶 + ETL HTL E x additional capacitance Cion by ion accumulation Debye double layer + - 4
  4. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Impedance spectroscopy (IS) 1. Impedance spectroscopy – C(ω)


    - varying measurement frequency ω
 à defect/ion characterisation (et, N → EA , D, σ) 𝑍 = 𝑉 𝑎 𝑐 𝐼 𝑎 𝑐 = 1 1 𝑅 p + i 𝜔 𝐶 + 𝑅 s C log( ) ω Cgeo ΔC2 ΔC1 𝑒 t2 𝑒 t1 transparent anode 𝜀 𝑅 perovskite cathode HTL ETL - + + + inflexion point 
 → migration rate et 5
  5. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de IS: Example à two defects (β, γ) found

    (an additional one, δ, is seen in DLTS) find migration rate et by inflexion points → extrema of 1st derivative, β γ β γ 6 S. Reichert, J. Flemming, Q. An, Y. Vaynzof, J.-F. Pietschmann, C. Deibel Phys. Rev. Applied 13, 034018 (2020) MAPI-based solar cell
  6. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Deep-level transient spectroscopy (DLTS) 1. Impedance spectroscopy –

    C(ω)
 - varying measurement frequency ω
 à defect/ion characterisation (et, N → EA , D, σ) 𝑍 = 𝑉 𝑎 𝑐 𝐼 𝑎 𝑐 = 1 1 𝑅 p + i 𝜔 𝐶 + 𝑅 s transparent anode 𝜀 𝑅 perovskite cathode HTL ETL - + 7 2. Deep-level transient spectroscopy (DLTS) – C(t)
 - applying filling pulse (voltage or light)
 à defect/ion characterisation (et, N → EA , D, σ) (ideally also rel. polarity of defect: 
 - majority, + minority) t V ΔC C0 t C 𝑪 ( 𝒕 ) = 𝑪 𝟎 ± ∆ 𝑪 𝐞 𝐱 𝐩 (− 𝒆 𝐭 𝒕 ) sign: majorities: - minorities: + ∆ 𝐶 ∝ trap concentration 𝑒 t ∝ exp(− 𝑬 𝐭 𝑘 B 𝑇 ) 𝑪 ( 𝒕 ) = 𝑪 𝟎 ± ∆ 𝑪 𝐞 𝐱 𝐩 (− 𝒆 𝐭 𝒕 ) DLTS in this context: also known as Transient Ion Drift
  7. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de DLTS: Example capacitance transient à three defects (β,γ,δ)

    can be analyzed β γ δ Downloaded 01 Feb 2005 to 146.103.254.11. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp D. V. Lang, 
 J. Phys. Appl. 45, 3023 (1974) double boxcar method with rate window t2/t1 e t(T) = 1/τ max(T) for this rate window migration rates et(T) = 1/τmax(T) 8 MAPI-based solar cell
  8. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Do we observe ionic or electronic defects? 𝝉

    𝟐 𝝉 𝟏 DLTS: R-DLTS: → all observed defects are ionic energy band trap level - 𝝉 𝟏 𝝉 𝟐 capture emission semiconductor defect: emission time longer then emission time,
 τ1 ≫ τ2 - 𝝉 𝟏 𝝉 𝟐 - ionic defect: migration back = migration forth,
 τ1 ≈ τ2 9 M. Futscher, C. Deibel ACS Energy Lett 7, 140 (2022)
  9. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Arrhenius comparison with literature Note on potential ionic

    defect assignment β → γ → (still mysterious ;-) δ → (also: why only in DLTS?) 𝑉 + I 10 Yang et al., Science 356, 1376 (2017) Futscher et al., Mater. Horiz. 6, 1497 (2019) Rosenberg et al., J. Appl. Phys. 122, 145701 (2017) Samiee et al., Appl. Phys. Lett. 105, 153502 (2014) Xu et al., Nature Photonics 13, 418 (2019) S. Reichert, Q. An, Y. W. Woo, A. Walsh, Y. Vaynzof, C. Deibel Nature Commun. 11, 6098 (2020) Literature comparison
  10. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Most dominant defect β: what is it? 11

    S. Tammireddy, S. Reichert, Q. An, A. D. Taylor, R. Ji, F. Paulus, Y. Vaynzof, C. Deibel ACS Energy Lett. 7, 310 (2022) Comparison MAPI, TripleCat, CsPbI3 • migration rates in MAPI, Triple cation, CsPbI3 are in the same range. • present in all: Pb or I • Pb requires high activation energies for vacancy formation • β likely iodide related defect, V+ I
  11. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de DLTS transients are not mono-exponential experimental mono-exp fit

    12 → adapted evaluation method needed g(et ) is the inverse Laplace transform 
 of C(t): experimental decay: Laplace transform:
  12. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Distribution of migration rates S. Reichert, J. Flemming,

    Q. An, Y. Vaynzof, J.-F. Pietschmann, C. Deibel Phys. Rev. Applied 13, 034018 (2020) 13
  13. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Diffusion coefficients from migration rates with 14

  14. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Meyer–Neldel rule for ionic defects 15 with where

    Activation energy alone not sufficient to categorise ionic defects → Meyer–Neldel rule. Nature Commun. 11, 6098 (2020)
  15. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de More information on β from IS 16 𝑒

    𝑡 ∆ 𝐶 2 𝑛 = 𝑘 𝐵 𝑇 ∆ 𝐶 2 𝑒 2 𝜀 0 𝜀 𝑅 Mobile ion densities 𝑛 = 𝑁 ⋅exp( − ∆ 𝐻 𝑓 2 𝑘 𝐵 𝑇 ) formation enthalpy total ion density <latexit sha1_base64="j6hOCITyEwRPMKEH2EJbNpmQ+xM=">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</latexit> / DN = Dmobilen Ion conductivity 𝐷 = 𝐷 0 exp − ∆ 𝐻 𝑚 + ∆ 𝐻 𝑓 2 𝑘 𝐵 𝑇 Average diffusion coefficient 𝐷 = 𝑘 𝐵 𝑇 𝜀 0 𝜀 𝑅 𝑒 𝑡 𝑒 2 𝑁 migration enthalpy activation energy EA
  16. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de For instance, total ionic defect concentration 17 For

    both systems, β is likely • iodide vacancy at under-stoichiometry, confirming earlier result • could it be: iodide interstitial at over-stoichiometry? Triple cation MAPI β β
  17. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Conductivity from IS vs literature: β 18 ACS

    Energy Lett 7, 310 (2022) 10-10 10-9 10-8 10-7 Conductivity [S/cm] 4.5 4.0 3.5 3.0 1000/T [1/K] σmigration vs MAI:PbAc2 2.96 2.98 3.00 3.02 3.04 3.06 <latexit sha1_base64="Ji37tJgorCsEZUVSDBlcflig7Nc=">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</latexit> mig = et ✏0✏R ↓ 338 K β N. Leupold, F. Panzer et al.
 Eur. J. Inorg. Chem. 2882 (2021) 30 #m thick MAPbI 3 layer (see Figure S3 for details). PADM processed halide perovskite layers typically exhibit a relatively large surface roughness, which potentially accelerates the equilibration with the surrounding iodine atmosphere. This reduces the measurement time, which in turn is beneficial in terms of sample degradation and reproducibility. The tetragonal crystal structure of the MAPbI 3 powder is maintained in the PAD-film as evidenced from XRD (Figure S4). Furthermore, the absence of additional signals in the diffractogram of the PADM- processed sample compared to the powder XRD indicates that the MAPbI 3 layers are phase-pure. Besides that, the reflexes in the XRD pattern of the layer are slightly broader compared to the corresponding reflexes of the powder, suggesting a reduction of the crystallite size due to the PADM. The electrical conductivity of the MAPbI 3 samples was determined by impedance spectroscopy (IS) between 1 Hz and 10 MHz. The IS spectra were fitted with an equivalent circuit, consisting of two RC parallel elements and a Warburg element. The electrical conductivity, , was calculated by taking into account the dominating resistor, the geometry of the electrodes and the layer thickness (see Figures S2 and S5 for details). Since exposing halide perovskites to light and air can have a significant influence on their conductivity,[27] all measurements were conducted in darkness and in a dry and oxygen-free nitrogen atmosphere. defect species. As mentioned earlier, ionic defects in MAPbI 3 can in principle result from Schottky or Frenkel disorder.[12–14] However, at the moment no clear consensus regarding the dominant disorder type in MAPbI 3 has evolved yet.[4,13,14,16,29,30] Nevertheless, as Schottky disorder in MAPbI 3 was suggested to have a relatively low formation enthalpy of ~0.1 eV,[14] we consider Schottky disorder in the following defect chemical considerations (see SI for defect chemical modelling consider- ing Frenkel disorder). Figure 2. Electrical conductivity as a function of iodine partial pressure of powder aerosol deposited MAPbI 3 films calculated from impedance spectra. 2884 Eur. J. Inorg. Chem. 2021, 2882–2889 www.eurjic.org © 2021 The Authors. European Journal of Inorganic Chemistry published by Wiley-VCH GmbH VCH Dienstag, 20.07.2021 210889 [S. 2884/2889] 1 338 K see also: A. Senocrate, J. Maier et al.
 Angew. Chem. Int. Ed. 56, 7755 (2017) measured on lateral device geometry β is the most „conductive“ ionic defect we are aware of
  18. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Back to MAPI: Defect β vs solar cell

    performance 19 3.04 ratio → highest power conversion efficiency → maximum change in absolute entropy of formation → minimum formation enthalpy → minimum migration enthalpy → lowest density of total ionic defects (β) ACS Energy Lett 7, 310 (2022)
  19. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Take away – defect spectroscopy in halide perovskites

    is dominated by ionic rather than electronic defects – migration rates show wide distribution for each defect – different activation energies can still belong to the same ionic defect species → Meyer–Neldel rule – β is likely and dominates the ionic conductivity – MAPI stoichiometry with best solar cell performance coincided with minimum formation/migration enthalpy and lowest density of total ionic defects of β V+ I 20 - 𝝉 𝟏 𝝉 𝟐 -
  20. www.tu-chemnitz.de/physik/OPKM MRS Spring Meeting, Honolulu· 9. Mai 2022 · deibel@physik.tu-chemnitz.de

    Acknowledgements 21 Thanks for having me! Thanks to my group and our partners! Thank you @ MRS Spring!