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The role of energetic and spatial 
 traps in organic solar cells

Carsten
May 23, 2017

The role of energetic and spatial 
 traps in organic solar cells

Invited Talk at E-MRS Spring Meeting in Strasbourg, France. Symposium L "New materials for organic electronics: from synthesis to processing, characterization and device physics"

Organic bulk heterojunction solar cells contain a complex morphology of two organic semiconductors. The energetic distribution of localised states depends strongly on both, the properties of the neat materials and the blend morphology. Therefore, energetics and morphology play a major tole for the physical processes involved in photocurrent generation, for instance the recombination of charge carriers. This nongeminate recombination occurs across the donor-acceptor interface through charge transfer states. In disordered materials with low charge carrier mobilities it is usually described by the so called reduced Langevin rate. The latter is often orders of magnitude smaller than predicted by the Langevin rate, which is proportional to the sum of electron and hole mobility. Based on kinetic Monte Carlo simulations, we find that for typical phase dimensions, the nongeminate recombination is governed rather by the geometric mean of mobilities [1,2]. Another property of nongeminate recombination in organic blend systems is that the recombination order is often, particularly at low temperatures, increased above the expected order of two as two particles are involved. We present transient absorption data of organic semiconductor blends and show how the order or recombination relates to both, the diode ideality factor [3] and the energetic disorder. We will discuss what is required to bring these different perspectives into one unified picture for recombination in organic solar cells.

[1] M. C. Heiber et al. Phys. Rev. Lett. 114, 136602, 2015
[2] M. C. Heiber et al. Phys. Rev. B 93, 205204, 2016
[3] K. Tvingstedt and C. Deibel. Adv. Ener. Mater. 6, 1502230, 2016

Carsten

May 23, 2017
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  1. www.tu-chemnitz.de/physik/OPKM E-MRS Spring Meeting · 23rd May 2017 · [email protected]

    Carsten Deibel Optik und Photonik kondensierter Materie Institut für Physik Technische Universität Chemnitz The role of energetic and spatial 
 traps in organic solar cells
  2. www.tu-chemnitz.de/physik/OPKM [email protected] Usual suspect for nongeminate recombination (1) finding of

    charge carriers → mobility μ (2) recombination event (faster than (1)) LUMO HOMO (1) (2) (1) }R(n) / (µe + µh)n2 Langevin recombination P. Langevin, Ann. Chim. Phys. 28, 433 (1903)
  3. www.tu-chemnitz.de/physik/OPKM [email protected] Recombination dynamics μe = 4⋅10-3 cm2/Vs μh =

    2⋅10-4 cm2/Vs kl ≈ 2⋅10-15 cm3/s SCLC mobilities from Mihailetchi et al, AFM 16, 699 (2006) P3HT:PCBM 2 4 6 8 1022 2 4 6 8 1023 2 4 6 8 Est. Carrier Concentration [m-3 ] 10-9 10-8 10-7 10-6 10-5 10-4 Time [s] Langevin
  4. www.tu-chemnitz.de/physik/OPKM [email protected] Recombination dynamics TA data: Gorenflot et al, JAP

    115, 144502 (2014) μe = 4⋅10-3 cm2/Vs μh = 2⋅10-4 cm2/Vs kl ≈ 2⋅10-15 cm3/s P3HT:PCBM 2 4 6 8 1022 2 4 6 8 1023 2 4 6 8 Est. Carrier Concentration [m-3 ] 10-9 10-8 10-7 10-6 10-5 10-4 Time [s] Langevin TA @ 300 K
  5. www.tu-chemnitz.de/physik/OPKM [email protected] Recombination dynamics ζkl = 5⋅10-17 cm3/s Reduction factor

    ζ ≈ 1/40 Recombination order 2.8 (not 2) μe = 4⋅10-3 cm2/Vs μh = 2⋅10-4 cm2/Vs kl ≈ 2⋅10-15 cm3/s P3HT:PCBM 2 4 6 8 1022 2 4 6 8 1023 2 4 6 8 Est. Carrier Concentration [m-3 ] 10-9 10-8 10-7 10-6 10-5 10-4 Time [s] Langevin reduced Langevin TA @ 300 K
  6. www.tu-chemnitz.de/physik/OPKM [email protected] Outline conclusions spatial effects role of morphology energetic

    effects disorder, traps reduction factor recombination order
  7. www.tu-chemnitz.de/physik/OPKM [email protected] Minimum mobility model What happens between these two

    extreme cases? Langevin recombination homogeneous system Minimum mobility model separate donor and acceptor phase kL / (µe + µh) R = kn2 kmin / min(µe, µh) Koster et al, APL 8, 052104 (2006)
  8. www.tu-chemnitz.de/physik/OPKM [email protected] Kinetic Monte Carlo Simulation of Hopping • hopping

    transport • energetic disorder, e.g. Gaussian density of states distribution • blend morphology • determine μe, μh, and R=k(μe, μh)⋅np separately but simultaneously Acceptor Donor + E-Field − c.f. Bässler, PSSB 175, 15 (1993)
  9. www.tu-chemnitz.de/physik/OPKM [email protected] Simulated Nongeminate Recombination Small domains: almost as homogeneous

    system, Langevin R = knp k = e ✏ (µe + µh) = kL
  10. www.tu-chemnitz.de/physik/OPKM [email protected] Simulated Nongeminate Recombination Large domains: min mobility, Koster

    et al, APL 88, 052104 ︎2006︎ R = knp k = e ✏ min (µe, µh)
  11. www.tu-chemnitz.de/physik/OPKM [email protected] Simulated Nongeminate Recombination Typical case: mix of both!

  12. www.tu-chemnitz.de/physik/OPKM [email protected] Simulated Nongeminate Recombination R = knp k =

    e ✏ f1(d)2Mg(d) (µe, µh) where Mg = ✓ µg e + µg h 2 ◆1/g power law mean (Hölder-Mittel) d (nm) f1 g Case small domains < 5nm ≈ 1 1 arithmetic mean typical case 10–35 0,5–1 0 geometric mean large domains > 50nm < 0,5 -1 harmonic mean k / ✓ 1 µe + 1 µh ◆ 1 k / ✓ µe + µh 2 ◆ k / (µeµh)1/2
  13. www.tu-chemnitz.de/physik/OPKM E-MRS Spring Meeting · 23rd May 2017 · [email protected]

    Reduced recombination by here for P3HT:PCBM Intermediate Conclusions: Morphology Koster et al. APL 86,
 123509 (2005) Burke et al. AFM 5, 1500123 (2015) redissociation (1-P) ≈ 0,1 phase separation ζphase ≈ 0,2 gradients ζgrad = f(V,T) not without electrodes! PRB 2, 1483 (2009) PRL 114, 136602 (2015), PRB 93, 205204 (2016)
  14. www.tu-chemnitz.de/physik/OPKM [email protected] Outline conclusions spatial effects role of morphology energetic

    effects disorder, traps
  15. www.tu-chemnitz.de/physik/OPKM [email protected] Trap density (Lower Limit) P3HT:PCBM: 6-8⋅1022 m-3
 P3HT:

    1⋅1022 m-3 Exp. Tail 
 with EU ~ 55meV 6 8 1020 2 4 6 8 1021 2 4 6 8 1022 trap density [m-3 ] 400 300 200 100 activation energy [meV] P3HT:PC61 BM PC61 BM P3HT exp. tail fit T3 T2 T1 Thermally Stimulated Currents: Tail States A. Foertig et al, PRB 86, 115302 (2012) / exp ✓ E EU ◆ 1021 2 3 4 5 6 7 8 9 1022 trap density [m-3 ] 0.30 0.25 0.20 0.15 0.10 0.05 0.00 Energy [eV] PTB7:PC70BM with DIO
  16. www.tu-chemnitz.de/physik/OPKM [email protected] Recombination rate where: λ+1 = EU/kT+1 Nongeminate Decay

    Dynamics 4 6 8 10-5 2 4 6 8 10-4 2 4 6 8 10-3 ΔOD 10-8 10-7 10-6 10-5 10-4 Time [s] T [K] 30 59 91 112 143 200 250 300 P3HT:PCBM 30K 300K J. Gorenflot et al, JAP 115, 144502 (2014) R = k · n +1 7 6 5 4 3 2 1 λ+1 300 250 200 150 100 50 T emperature [K] P3HT P3HT:PCBM
  17. www.tu-chemnitz.de/physik/OPKM [email protected] Different Solar Cells The optimized PTB7:PCBM version efficiency

    (PCE) a 280 nm thick MDMO–PPV performance. The results of the temp summarized in Figure 5. similar behavior, the differe individual shortcomings. Th shows, e.g., almost no limi ture. This is purely assigned ration current (J0 ) at 300 K o the exponential current reg shunt effects are already alm cool the device we see, as J0 the shunt limitation also c Hence, the shunt is actually in the other cells; it is just part of the current at room t At room temperature, th a noticeable difference betw curve until we reach rather rior conductivity of this part minimizes the voltage losses PPV based device. However www.MaterialsViews.com -1.0 -0.5 0.0 0.5 1.0 -150 -100 -50 0 50 100 150 J(A/m2) Voltage (V) P3HT:PCBM60 PTB7:PCBM70 MDMOPPV:PCBM60 PCDTBT:PCBM70 Device J SC (A/m2) V OC (V) FF PCE (%) P3HT:PCBM60 79.5 0.58 0.65 3.0 PTB7:PCBM70 126.4 0.72 0.71 6.5 MDMO-PPV:PCBM60 18.0 0.83 0.40 0.6 www.MaterialsViews.com -1.0 -0.5 0.0 0.5 1.0 -150 -100 -50 0 50 100 150 J(A/m2) Voltage (V) P3HT:PCBM60 PTB7:PCBM70 MDMOPPV:PCBM60 PCDTBT:PCBM70 Device J SC (A/m2) V OC (V) FF PCE (%) P3HT:PCBM60 79.5 0.58 0.65 3.0 PTB7:PCBM70 126.4 0.72 0.71 6.5 MDMO-PPV:PCBM60 18.0 0.83 0.40 0.6 PCDTBT:PCBM70 83.9 0.87 0.56 4.1 Figure 4. AM 1.5 1 Sun illuminated I–V curves and corresponding pho- tovoltaic figures of merit of the four selected OPV cells. K. Tvingstedt & CD, AEM 6 ,1502230 (2016)
  18. www.tu-chemnitz.de/physik/OPKM [email protected] the o equat yields PPV:P tial cu resist

    In the the JS straig down ages sub-e strong space the JS steepe is pro prono surfac face r will le www.advenergymat.de Determine ideality factor nid from Voc(jsc)… th eq yi P ti re In th st do ag su st sp th st is pr su fa w www.advenergymat.de FULL PAP equation for O yields a voltage PPV:PCBM dev tial current seem resistive losses In the exponen the JSC –VOC cu straight, wherea down more and ages the injec sub-exponential strongly influen space charge li the JSC –VOC rela steeper slopes a is probably due pronounced el surface recomb face recombina will lead to a pa selectivity of at electrodes, forc (pinning). We cannot explain back bending ( even higher il ilar observation made on very e The behavior h parasitic oppos Schottky diode gram, but with Figure 3. A) Absolute JSC (Suns) and B) VOC (Suns) at 300 K, allowing C) the comparison MDMO-PPV:PCBM
  19. www.tu-chemnitz.de/physik/OPKM [email protected] Determine ideality factor from Voc(jsc), not dark! P3HT:PCBM

    K. Tvingstedt & CD, AEM 6 ,1502230 (2016) j ( V ) = j0 ✓ exp ✓ qV n id kT ◆ 1 ◆ j ph j sc( V ) = j0 ✓ exp ✓ qV oc n id kT ◆ 1 ◆ Extract diode ideality factor:
  20. www.tu-chemnitz.de/physik/OPKM [email protected] Diode Ideality Factors: weak temperature dep. 1.5 1.4

    1.3 1.2 1.1 1.0 0.9 Ideality factor 280 240 200 160 Temperature [K] P3HT:PCBM60 PTB7:PCBM70 MDMO-PPV:PCBM60 PCDTBT:PCBM70
  21. www.tu-chemnitz.de/physik/OPKM [email protected] Diode Ideality Factors from Current-Voltage 1.8 1.6 1.4

    1.2 1.0 Ideality factor 300 250 200 150 Temperature [K] P3HT:PCBM Jsc(Voc) (tvingstedt2016) © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (7 of 13) 1502230 wileyonlinelibrary.com PPV based device. However, at lower temperatures, the devia- tion becomes more pronounced and also begins at substantially smaller current densities, also for this higher mobility material. The PTB7:PCBM70 cell (Figure 5B) shows a similar behavior as nergy Mater. 2016, 1502230 PCDTBT:PCBM70 83.9 0.87 0.56 4.1 e 4. AM 1.5 1 Sun illuminated I–V curves and corresponding pho- taic figures of merit of the four selected OPV cells. e 5. JSC –VOC versus dark I–V for A) P3HT:PCBM60, B) PTB7:PCBM70, C) MDMO–PPV:PCBM60, and D) PCDTBT:PCBM70 cells as a function of erature.
  22. www.tu-chemnitz.de/physik/OPKM [email protected] Diode Ideality Factors from Transient Absorption © 2016

    WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim (7 of 13) 1502230 wileyonlinelibrary.com PPV based device. However, at lower temperatures, the devia- tion becomes more pronounced and also begins at substantially smaller current densities, also for this higher mobility material. The PTB7:PCBM70 cell (Figure 5B) shows a similar behavior as nergy Mater. 2016, 1502230 PCDTBT:PCBM70 83.9 0.87 0.56 4.1 e 4. AM 1.5 1 Sun illuminated I–V curves and corresponding pho- taic figures of merit of the four selected OPV cells. e 5. JSC –VOC versus dark I–V for A) P3HT:PCBM60, B) PTB7:PCBM70, C) MDMO–PPV:PCBM60, and D) PCDTBT:PCBM70 cells as a function of erature. 7 6 5 4 3 2 1 Order of Decay 300 250 200 150 100 50 Temperature [K] P3HT P3HT:PCBM λ+1 1.8 1.6 1.4 1.2 1.0 Ideality factor 300 250 200 150 Temperature [K] P3HT:PCBM Jsc(Voc) (tvingstedt2016) TA (gorenflot2014) P3HT TA (gorenflot2014) nid = ✓ 1 2 + 1 2 ◆ 1 van Berkel et al, JAP 73, 5264 (1993)
 Deibel et al, APL 103, 043307 (2013)
  23. www.tu-chemnitz.de/physik/OPKM [email protected] Diode Ideality Factors: Zoom Out © 2016 WILEY-VCH

    Verlag GmbH & Co. KGaA, Weinheim (7 of 13) 1502230 wileyonlinelibrary.com PPV based device. However, at lower temperatures, the devia- tion becomes more pronounced and also begins at substantially smaller current densities, also for this higher mobility material. The PTB7:PCBM70 cell (Figure 5B) shows a similar behavior as nergy Mater. 2016, 1502230 PCDTBT:PCBM70 83.9 0.87 0.56 4.1 e 4. AM 1.5 1 Sun illuminated I–V curves and corresponding pho- taic figures of merit of the four selected OPV cells. e 5. JSC –VOC versus dark I–V for A) P3HT:PCBM60, B) PTB7:PCBM70, C) MDMO–PPV:PCBM60, and D) PCDTBT:PCBM70 cells as a function of erature. 7 6 5 4 3 2 1 Order of Decay 300 250 200 150 100 50 Temperature [K] P3HT P3HT:PCBM λ+1 nid = ✓ 1 2 + 1 2 ◆ 1 1.8 1.6 1.4 1.2 1.0 Ideality factor 300 250 200 150 100 50 Temperature [K] P3HT:PCBM Jsc(Voc) (tvingstedt2016) TA (gorenflot2014) P3HT TA (gorenflot2014) van Berkel et al, JAP 73, 5264 (1993)
 Deibel et al, APL 103, 043307 (2013)
  24. www.tu-chemnitz.de/physik/OPKM [email protected] Compared to Models for Exponential Tails van Berkel

    et al, JAP 73, 5264 (1993) corresponds to = EU kT with exp tails / exp ✓ E EU ◆ nid = ✓ 1 2 + kT 2EU ◆ 1 EU=55 meV (TSC) EU=30 meV • direct recombination: nid=1 • gaussian tails: nid≈1 • exp. tails roughly capture trend at lower temperature, but not constant ideality (>1!) at T ≥ 200 K 1.8 1.6 1.4 1.2 1.0 Ideality factor 300 250 200 150 100 50 Temperature [K] P3HT:PCBM Jsc(Voc) (tvingstedt2016) TA (gorenflot2014) Models vanberkel1993 hawks2014 EU =30 meV EU =55 meV
  25. www.tu-chemnitz.de/physik/OPKM [email protected] Some Conclusions reduced recombination: phase sep, gradients, redissociation

    high recombination order: • ideality factor: trap-assisted recombination, 
 not direct recombination • actual tail state distribution unclear • even exponential plus gaussian cannot explain ideality factor @ room temperature
  26. www.tu-chemnitz.de/physik/OPKM E-MRS Spring Meeting · 23rd May 2017 · [email protected]

    Acknowledgments … and thank you! Michael Heiber Kristofer Tvingstedt