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Charge transport in organic 
 (polymer based) devices

Carsten
June 19, 2018

Charge transport in organic 
 (polymer based) devices

Field dependence of charge carrier mobility in organic blend devices, investigated by kinetic Monte Carlo simulations

Carsten

June 19, 2018
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  1. www.tu-chemnitz.de/physik/OPKM
    E-MRS Spring Meeting · 19th June 2018 · [email protected]
    Michael Heiber and Carsten Deibel
    Optik und Photonik kondensierter Materie
    Institut für Physik
    Technische Universität Chemnitz
    Charge transport in organic 

    (polymer based) devices

    View full-size slide

  2. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Charge Transport in View of OPV
    • Charges created at donor-
    acceptor interface in the film
    • Slow extraction ∝ low mobility
    leads to greater recombination
    losses
    • How does the nanoscale
    morphology affect the charge
    carrier mobility?
    → Kinetic Monte Carlo simulation
    Fullerene
    Aluminium Cathode
    Transparent Anode
    Polymer

    View full-size slide

  3. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    • hopping transport
    • energetic disorder, e.g. Gaussian
    • Miller Abrahams jump rate






    • Coulomb interaction considered
    • blend morphology
    Kinetic Monte Carlo Simulation of Hopping
    Acceptor
    Donor
    +
    E-Field

    c.f. Bässler, PSSB 175, 15 (1993). Critical perspective: Baranovskii, 1700676 (2018)
    ⌫ = ⌫0 exp ( rij)
    (
    exp

    Eij
    kT

    up
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    rij
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  4. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Simulated Nongeminate Recombination
    R
    AAADN3icjVI9T9xAEH1nQgKXEA4o01ickFKd7DTQoCC+RBMJEAdIBEVeszir89mW7QMBQqKnTX4Mv4DfkCpdlJaegreDHSWghKy1ntmZN2+ex6uy2BSl531rOEPPhp+/GBltvnw19nq8NTG5XaSDPNTdMI3TfFcFhY5NorulKWO9m+U66KtY76jeks3vHOm8MGmyVZ5ker8fRIk5NGFQMrSx+anV9jqeLPex41dO+/11c/4CwHo60WjhIw6QIsQAfWgkKOnHCFDw2YMPDxlj+zhjLKdnJK9xjiZrB0RpIgJGe3xHPO1V0YRny1lIdcguMXfOShcz3KvCqIi2XTX9gvaW+1Ri0V87nAmzVXhCq8g4KowfGC/xmYinKvsVstbyP5WKVTVeydcc0IuoW/Pp0a/12FzB8zGnZVldctYVv2P+NcESh5iTyRnOIpOInWn4S8MyM7l0thkXK4KMyKHkfMQeCW2X/ewfrRlcma7VHojVwpJUjAH5ctFtrB7eKf/hDXrsbL/r+F7H3/DaC4u4XyN4g2m85Q2axQLWsE4dIftc4gu+OlfOd+eH8/Me6jSqmin8sZybO2iGpjc=
    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
    p
    µeµh
    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
    AAADSnicjVLLThRBFD3ToAI+GGAHm46EhNWk240uia+4McHEARKGTLqaoqlMv6iqQXHCX7h2qx/jD/gRbtwRWXCq6CYqUalKVd2699xzT98uUefK2Cj61gmmpm/dvjMzO3f33v0H892FxS1TjXUq+2mVV3pHJEbmqpR9q2wud2otk0LkcluMnrn49rHURlXlW3tSy70iyUp1oNLE0jXsLg7MkbaTQTEeytDth6fD7mrUi/wIrxtxY6xurC1/X/oYTzarhU4XA+yjQooxCkiUsLRzJDCcu4gRoaZvDxP6NC3l4xKnmGPumChJRELviHvG227jLXl3nMZnp6ySc2lmhljjeukZBdGuqqRteJ5zffC+7K8VJp7ZKTzhKcg46xlf029xSMT/MosG2Wq5SaZgVosX/mv2aWXULTlHtFs9LmZ4f8duOdaQnG3Gr5h/ddDiAE985xR7UXuP62l6peE5I9pXdpEQLzwyI4fw92PWKHn2Wc/90ZYh9N112hN/Ss9SNowJ+bTXrZwevqn4zxd03dh61IujXvyGj+spLscMVvAQ63xBj7GBV9ikjhTv8Qmf8SX4GvwIzoKfl9Cg0+Qs4bcxNX0B8WWt+A==
    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
    M. C. Heiber et al, Phys Rev Lett 114,136602 (2015)

    M. C. Heiber et al, Phys Rev B 93, 205204 (2016)

    View full-size slide

  5. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Simulated Nongeminate Recombination
    R
    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
    p
    µeµh
    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
    M. C. Heiber et al, Phys Rev Lett 114,136602 (2015)

    M. C. Heiber et al, Phys Rev B 93, 205204 (2016)
    R ∝ μe
    μh
    Typical case

    View full-size slide

  6. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Charge Transport in View of OPV
    • Charges created at donor-
    acceptor interface in the film
    • Slow extraction leads to greater
    recombination losses
    • How does the nanoscale
    morphology affect the charge
    extraction time?
    → Kinetic Monte Carlo simulation
    Fullerene
    Aluminium Cathode
    Transparent Anode
    Polymer

    View full-size slide

  7. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Experimental Determination of Mobilities
    • example: time-of-flight photocurrent
    J. Lorrmann et al. J. Appl. Phys. 115, 183702 (2014)
    thickness L
    voltage V
    field F = V / L
    Aluminium Cathode
    Transparent Anode
    photo-
    current

    View full-size slide

  8. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Experimental Determination of Mobilities
    • example: time-of-flight photocurrent
    • geometric method (μgeo) overestimates the 

    mobility = expectation value μm of the mobility distribution
    • deviation more prominent at low electric fields and low temp
    J. Lorrmann et al. J. Appl. Phys. 115, 183702 (2014)
    ln f
    ð Þ
    Scheme
    J. Appl. Phys. 115, 183702 (2014)
    183702-6 Lorrmann et al.
    FIG. 2. Upper part: Mobility distributions p
    l
    (l) for three different tempera-
    tures T ¼ 130, 190, 300 K (from left to right) at a fixed electric field of.
    F ¼ 1:2 Â 108 V
    m
    . The vertical straight lines illustrate the four different defi-
    nitions of mobility ltr,m
    (dashed-double-dotted), lm
    (dashed), lgeo
    (solid),
    183702-6 Lorrmann et al.
    300 K
    190 K
    130 K

    View full-size slide

  9. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Field Dependence of Mobility
    W. D. Gill, J. Appl. Phys. 43, 5033 (1972)
    µ / exp
    ⇣ p
    F

    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
    AAADZnicjVLbbtQwEJ3dcGkLlC0I8cCLxQqpvKySCgkeKygVL5WKxLaVmqqy09nU2tywvYWy6l/0a3iFn+AP+AgeemwSBFRcHDkez5w5czIZ1RTaujj+0utHV65eu76wuHTj5q3l24OVOzu2npmMx1ld1GZPScuFrnjstCt4rzEsS1Xwrpq+8PHdEzZW19Ubd9rwQSnzSk90Jh1ch4NRWs5E2pi6cbVI+X0j0oInblWkip0UqX1r3HzzTKRG58fu8eFgGI/isMRlI2mNIbVru17pDSilI6opoxmVxFSRg12QJItnnxKKqYHvgObwGVg6xJnOaAm5M6AYCAnvFO8ct/3WW+HuOW3IzlClwDbIFPQIezMwKqB9VYZtcX7D/hB8+R8rzAOzV3iKU4FxMTBuwe/oGIh/ZZYtstPyP5kKWR1eha85gpVDN+OZwu70+JjF/R265VkFOLuMnzF/66CjCT0LndPoRRM8vqfZDw0biJhQ2UcEvQzIHBwq3E9Qo8I5Rj3/RzsGEbrrtctwcmCpWkYJPhN0a68HM5X8PkGXjZ21URKPktdPhuvP2+laoAf0kFYxQU9pnV7RNnRkdE4f6RN97n+NlqN70f3v0H6vzblLv6xIXAC5hrLo
    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

    View full-size slide

  10. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    1. 

    2. 



    3.
    Simple Kinetic Monte Carlo
    10
    -9
    2
    3
    mean mobility [cm
    2
    /Vs]
    16 x10
    3
    14
    12
    10
    8
    6
    4
    2
    0
    E
    1/2
    [(V/m)
    1/2
    ]
    L=2µm
    σ=50meV
    T=300K
    T=250K
    µ =
    vmax
    F
    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
    µ and D!
    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
    µ / exp
    ⇣ p
    F

    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
    1. 2. 3.

    View full-size slide

  11. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Field Dependence of Mobility in BHJ Blends
    • Electric field dependence predicted to change in a blend
    • Negative field dependence is often not observed
    experimentally
    • What role does morphology play?
    also c.f. simulations by 

    Koster, Phys. Rev. B. 81, 205318 (2010) and 

    Frost et al, Nano Letters 6, 1674- (2006).
    conjugated polymers, which show highly dispersive current
    transients, that mobility is not a well-defined material param-
    eter as for materials with a well-defined carrier transit time.
    However, following the practice of the field we use the above
    approach to facilitate comparison of electron and hole tran-
    sients in this paper and comparison of these transients with
    other reports. For the P3HT film, a hole mobility of 6.3
    −5 2
    10-7 10-6 10-5 10-4
    10-5
    10-4
    Current (A)
    Time (s)
    P3HT
    P3HT:F8TBT
    0 1 2 3 4 5 6
    2
    3
    4
    5
    6
    7
    8
    5
    Electric Field (x10 V/cm)
    TOF Mobility (x10 cm2 /Vs)
    -5
    FIG. 1. ͑Color online͒ Hole TOF transients of P3HT and a P3HT:F8TBT
    blend. The inset displays the electric field dependence of hole mobility in
    the blend.
    0 5.0x10-3
    1.0x10-2
    1.5x10-2
    2.0x10-2
    0
    1x10-6
    2x10-6
    3x10-6
    4x10-6
    5x10-6
    Current (A)
    Time (s)
    10-5 10-4 10-3 10-2
    10-8
    10-7
    10-6
    No background
    With ~ 2 mA/cm2 backgro
    10-5 10-4 10-3
    10-7
    10-6
    Current (A)
    m
    (a)
    (b)
    203310-2 C. R. McNeill and N. C. Greenham Appl. Phys. Lett. 93, 203310 ͑
    McNeill and Greenham,

    APL 93, 203310 (2008):
    μ(F) ↑ in neat polymer, 

    μ(F) ↓ in blend (see inset)

    View full-size slide

  12. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Detailed Measurements of the BHJ Morphology
    • TEM used to create cross
    sectional images
    • Slices are used to construct a
    3D image
    • Obtaining good contrast
    between phases is extremely
    difficult J. D. Roehling, K. J. Batenburg, F. B. Swain, A. J. Moulé, and I. Arslan,
    Adv. Funct. Mater. 23, 2115 (2013).

    View full-size slide

  13. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Tortuosity of Charge Transport Pathways
    • Tortuosity (τ) used to
    quantify the quality of
    the transport pathways
    • Tortuosity (τ) 

    = Shortest transport
    path / film thickness

    View full-size slide

  14. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Analysis of Charge Transport Pathways
    • Graph-Based Analysis
    of TEM tomography
    Tortuosity of paths in P3HT and fullerene to resp. electrodes
    O. Wodo, J. D. Roehling, A. J. Moulé, and B. Ganapathysubramanian, Energy Environ. Sci. 6, 3060 (2013).

    View full-size slide

  15. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Fundamental Questions
    How do morphological characteristics:
    1. domain size
    2. disorder
    3. tortuosity
    affect the magnitude of the mobility and the electric-
    field dependence?

    View full-size slide

  16. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Bulk Heterojunction Morphology Simulator
    Phase Separation
    Smoothing
    • Ising model for creating controlled 

    BHJ morphologies
    • Characterisation of domain size, 

    interfacial area to volume ratio, 

    tortuosity, and more
    https://github.com/MikeHeiber/Ising_OPV

    View full-size slide

  17. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Creating Anisotropic Morphologies
    Cross-sectional images created using Igor Pro

    GIFs powered by ezgif.com
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    z
    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  18. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Anisotropic Domain Growth
    • Anisotropic interaction energy causes anisotropic
    domain growth
    • Anisotropic domains have higher average tortuosity
    M. C. Heiber et al. Phys Rev Applied 8, 054043 (2017)

    View full-size slide

  19. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Tortuosity and Blend Ratio
    Tortuosity is increased when blend ratio decreases
    (from the perspective of the charge carrier in the
    „less material phase“)

    View full-size slide

  20. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Effect of Tortuosity on Mobility
    Negative field dependence is not inherent to blends!
    If disorder stays constant one can determine
    tortuosity differences between two morphologies

    View full-size slide

  21. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Effect of Disorder on Mobility

    View full-size slide

  22. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Field Dependent Mobility in Neat Films
    in unitless parameters µ0 =
    a2⌫0e
    , F0 =
    ea
    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
    AAADeHicjVJba9RAFD67UXvxttVHXwYXUUGWZBHal8LipfhSqNBtC01dZrKz6bC5dSZpqWH/jr/GVwX/ivjQb8akVIuXCZM5c853vvPl5IgiUab0/W+drnfj5q2l5ZXV23fu3rvfW3uwZ/JKR3Ic5UmuDwQ3MlGZHJeqTORBoSVPRSL3xfy1je+fSm1Unu2W54U8SnmcqZmKeAnXpDcK02ris00WzjSPav5hyMLMeuSiDo2KU754EZ5UfMq2rsCaSC35YtLr+wPfLXbdCBqjT83aydc6PQppSjlFVFFKkjIqYSfEyeA5pIB8KuA7oho+DUu5uKQFrSK3AkoCweGd4x3jdth4M9wtp3HZEaok2BqZjJ5gbzlGAbStKmEbnD+wPzpf/McKtWO2Cs9xCjCuOMZt+Es6BuJfmWmDbLX8T6ZAVosX7mumsGLolnjmsFs9NmZwP0O3LCsDZ5txFfO3DpY0ow3XOYVeFM5jexpdaniDiHaVbYTRW4eMwSHc/RQ1Mpxj1LN/tGVgrrtWO3endCxZw8jBp51uZfVgpoLfJ+i6sTccBP4geP+yP3rVTNcyPaLH9AwTtE4jekc70BHRJ/pMX+hr97vHvKfe85/QbqfJeUi/LG94AWnJuYo=

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  23. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Effect of Tortuosity on Normalised Mobility
    Low Tortuosity Medium Tortuosity High Tortuosity
    M. C. Heiber et al. Phys Rev Applied 8, 054043 (2017)
    Fit electric-field dependence to normalised Poole-Frenkel eqn
    µ
    µ0
    = µ00 exp
    r
    F
    F0
    !
    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  24. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Normalised Poole-Frenkel Coefficient
    • PF coefficient β depends on disorder, temperature, and
    tortuosity; but not on domain size (sim not shown)
    • Could be used to estimate relative tortuosity changes
    in different films
    M. C. Heiber et al.

    Phys Rev Applied 8, 054043 (2017)

    View full-size slide

  25. www.tu-chemnitz.de/physik/OPKM
    [email protected]
    Some Conclusions
    How does the nanoscale morphology affect the
    charge carrier mobility?
    • tortuosity 

    = actual transport path / ideal transport path
    • anisotropic domains: higher average tortuosity
    • tortuosity increases for decreasing blend ratio
    • combination of high disorder & high tortuosity 

    → negative field dependence of mobility
    Same principle for neat materials with polymer
    chains or aggregates having (pretty) different
    „intramolecular“ and „intermolecular“ mobilities!

    View full-size slide

  26. www.tu-chemnitz.de/physik/OPKM
    E-MRS Spring Meeting · 19th June 2018 · [email protected]
    Acknowledgments
    … and thank you!
    Michael Heiber

    View full-size slide