Charge transport in organic (polymer based) devices

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

Transcript

1. www.tu-chemnitz.de/physik/OPKM E-MRS Spring Meeting · 19th June 2018 · deibel@physik.tu-chemnitz.de Michael Heiber and Carsten Deibel Optik und Photonik kondensierter Materie Institut für Physik Technische Universität Chemnitz Charge transport in organic 
 (polymer based) devices
2. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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
3. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de • 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 1 down <latexit sha1_base64="zBSaFeIPPns8h00NhlyrlQ9dcO0=">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</latexit> <latexit 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C. Heiber et al, Phys Rev Lett 114,136602 (2015) M. C. Heiber et al, Phys Rev B 93, 205204 (2016)
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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
6. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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
7. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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
8. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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
9. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Field Dependence of Mobility W. D. Gill, J. Appl. Phys. 43, 5033 (1972) µ / exp ⇣ p F ⌘ <latexit sha1_base64="MzvhqaL1G3xMN7k2Lv6IUA9EM9U=">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</latexit> <latexit sha1_base64="MzvhqaL1G3xMN7k2Lv6IUA9EM9U=">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</latexit> <latexit sha1_base64="MzvhqaL1G3xMN7k2Lv6IUA9EM9U=">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</latexit> <latexit sha1_base64="MzvhqaL1G3xMN7k2Lv6IUA9EM9U=">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</latexit>
10. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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 <latexit sha1_base64="/cWbmPYNHi2FQD2gK2UUk5a6XEQ=">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</latexit> <latexit 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11. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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)
12. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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).
13. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Tortuosity of Charge Transport Pathways • Tortuosity (τ) used to quantify the quality of the transport pathways • Tortuosity (τ) 
 = Shortest transport path / film thickness
14. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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).
15. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Fundamental Questions How do morphological characteristics: 1. domain size 2. disorder 3. tortuosity affect the magnitude of the mobility and the electric- field dependence?
16. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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
17. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Creating Anisotropic Morphologies Cross-sectional images created using Igor Pro GIFs powered by ezgif.com Jxy = 0.1 <latexit sha1_base64="itCcLhYT7ZYXcL/wKZf6KByYh88=">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</latexit> <latexit 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18. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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)
19. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Tortuosity and Blend Ratio Tortuosity is increased when blend ratio decreases (from the perspective of the charge carrier in the „less material phase“)
20. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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
21. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Effect of Disorder on Mobility
22. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de Field Dependent Mobility in Neat Films in unitless parameters µ0 = a2⌫0e , F0 = ea <latexit sha1_base64="Do0HLlSuc4daL6soq4VdeTGaNtY=">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</latexit> <latexit sha1_base64="Do0HLlSuc4daL6soq4VdeTGaNtY=">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</latexit> <latexit sha1_base64="Do0HLlSuc4daL6soq4VdeTGaNtY=">AAADeHicjVJba9RAFD67UXvxttVHXwYXUUGWZBHal8LipfhSqNBtC01dZrKz6bC5dSZpqWH/jr/GVwX/ivjQb8akVIuXCZM5c853vvPl5IgiUab0/W+drnfj5q2l5ZXV23fu3rvfW3uwZ/JKR3Ic5UmuDwQ3MlGZHJeqTORBoSVPRSL3xfy1je+fSm1Unu2W54U8SnmcqZmKeAnXpDcK02ris00WzjSPav5hyMLMeuSiDo2KU754EZ5UfMq2rsCaSC35YtLr+wPfLXbdCBqjT83aydc6PQppSjlFVFFKkjIqYSfEyeA5pIB8KuA7oho+DUu5uKQFrSK3AkoCweGd4x3jdth4M9wtp3HZEaok2BqZjJ5gbzlGAbStKmEbnD+wPzpf/McKtWO2Cs9xCjCuOMZt+Es6BuJfmWmDbLX8T6ZAVosX7mumsGLolnjmsFs9NmZwP0O3LCsDZ5txFfO3DpY0ow3XOYVeFM5jexpdaniDiHaVbYTRW4eMwSHc/RQ1Mpxj1LN/tGVgrrtWO3endCxZw8jBp51uZfVgpoLfJ+i6sTccBP4geP+yP3rVTNcyPaLH9AwTtE4jekc70BHRJ/pMX+hr97vHvKfe85/QbqfJeUi/LG94AWnJuYo=</latexit> <latexit sha1_base64="Do0HLlSuc4daL6soq4VdeTGaNtY=">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</latexit>
23. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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 ! <latexit sha1_base64="R1tPR+SFktRMBTHbbZbhJwfk62w=">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</latexit> <latexit sha1_base64="R1tPR+SFktRMBTHbbZbhJwfk62w=">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</latexit> <latexit sha1_base64="R1tPR+SFktRMBTHbbZbhJwfk62w=">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</latexit> <latexit sha1_base64="R1tPR+SFktRMBTHbbZbhJwfk62w=">AAADg3icjVJdSxwxFL3raKv2w7U+9iV0KVgKy4wI7Ysg/VgKIljoquDIkozZMex8Ncna2mF/lL+m9K39Hz54EmekrfQjQyYnN+ece+dORJUpY8PwW2cumF+4c3dxafne/QcPV7qrj/ZNOdWJHCZlVupDwY3MVCGHVtlMHlZa8lxk8kBMXrvzgzOpjSqLD/a8ksc5Tws1Vgm3CI26O/FY86SO8+nMvUbhjG0xB+oQMJafKxZncmzXWSyk5Sw2H7Wtr0WDWT2AADSt0lP7bNTthf3QD3YbRA3oUTP2ytVOl2I6oZISmlJOkgqywBlxMniOKKKQKsSOqUZMAyl/LmlGy9BOwZJgcEQneKfYHTXRAnvnabw6QZYMU0PJ6CnmwDsKsF1WCWywXmJ+8bH0jxlq7+wqPMcq4LjkHXcRt3QKxr+UecNsa/kfpYCq5Qv/NSdAKeqWeCbAbT3uzGD/Cd1yrgyereJnzt86aGlML33nFHpR+YjraXJTwxucaJ/ZnTB665kpPITfnyFHgXWIfO6Ptg7Md9fVzv0qvUvROHL4aV+3cvXgTkW/36DbYH+jH4X96P1mb/tVc7sW6TE9oXXcoBe0Te9oD3UkdEFf6Tv9CBaC58FGsHlNnes0mjX6ZQRbV+Rrvc8=</latexit>
24. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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)
25. www.tu-chemnitz.de/physik/OPKM deibel@physik.tu-chemnitz.de 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!
26. www.tu-chemnitz.de/physik/OPKM E-MRS Spring Meeting · 19th June 2018 · deibel@physik.tu-chemnitz.de Acknowledgments … and thank you! Michael Heiber