Charge Transport Phenomena in OPVs

1. Charge Transport Phenomena in OPVs Papers by the Paul W. M. Blom Group University of Groningen, The Netherlands

2. Outline • Background Review • PRL 2004: Photocurrent Generation in BHJ • PRL 2005: Space-Charge Limited Photocurrent • Fundamental Question: Internal E-Field? • Adv. Func. Mater. Charge Transport in P3HT:PCBM BHJ(Jaewook’s paper – Using the model)

3. Concept Review of OPV Ops • Photons absorbed by polymer (primarily), creating excitons • Excitons to D/A interface within 10-20nm = μexciton * lifetimeexciton • Ultrafast (45fs) charge transfer occurs → “bound polaron pair” or “charge transfer state” • Metastable state lasting micro to milliseconds • Something causes this to either separate into e + h or (gemenately) recombine producing photoluminescence. • Thermalization or Brownian motion\E-field thought to be the cause of sep. • Charges travel via speeds determined by μe,h [m2/Vs] • Caused by internal E-Field (drift), population imbalance (diffusion) • Charges are either collected at electrodes or get stuck at another interface (go back to #4, but now called non-gemenate). Barker, Ramsdale, & Greenham, PRB (2003).

4. Photocurrent Generation in Polymer-Fullerene Bulk Heterojunctions V. D. Mihailetchi, L. J. A. Koster, J. C. Hummelen, and P.W.M. Blom, PRL (2004)

5. Conditions/Definitions • Materials: PPV polymer & PCBM BHJ (1:4) wt% • Light used: “white halogen lamp” 800W/m2 in N2 atmosphere • PhotocurrentJph=JL - JDCurrent generated by the light • Compensation voltage V0Voltage where Jph=0 • Internal Field: E=(V0-V)/L • V = applied voltage • L = thickness of the active layer • Most graphs x-axes are V0-V: Start at V0 and go NEGATIVE. • Generation Rate: G(T,E) Rate at which charge carriers are created (disassociated & make it to the electrodes) • Result for this system: G(V=0) only 60%

6. Analytical Theory • Bracketed term adds effects of carrier diffusion • Fixes low-field behavior • Calculated by Sokel & Hughes, JAP (1982) • μ-independent (assumes no recombination) • G is a function of Temp & Field • Gmaxmeasured via large reverse bias • P is prob. of charge sep. at interface Jph=eGL → Using Const. G = Bad

7. P(T,E) calc. from Onsager-Braun theory • Onsager: oppositely charged ions undergoing Brownian motion in electrolyte w/Coulomb & E-field don’t recombination • Braun: finite lifetime of charge transfer state • kD rate of disassociation, kF rate of recombination, kRrate of recapture • a initial sep. of bound pair, b=e3E/8πεk2T2, EB e-h binding energy • kR=e‹μ›/‹ε›(‹› = spatially averaged mobility and dielectric constant) • Goliber & Perlstein, J. Chem Phys (1984) • Adds distribution function for a • F(x) distribution of e-h distances • NF normalization Jph=eGL → Using Const. G = Bad Jph=eG(T,E)·L only

8. Results using full model Activation Energies Dotted line is result at room temp Assumes “blocking contacts” no band bending at interface No space-charge effects No recombination?!? Solid lines are numerical model Steady-state charge distribution for Ohmic contacts using Poisson’s & continuity equation, including diffusion and recombination at interface Jph(E) • Arrhenius plot: J(1/T) • Claim activation energies contain “combined effects of the distribution of binding energies, the temperature dependence of both charge carrier mobility and decay rate kF-1 as well as the effect of applied field” 0.01V ~0.9V P(V=0)~60%

9. Space-Charge Limited Photocurrent V. D. Mihailetchi, J. Wildeman, and P.W. M. Blom PRL (2005)

10. Confirms SCL Theory in an OPV • Drift lengths: • If one is less than thickness L, recomb. occurs • & if one is << than other, SPACE CHARGE!! • Space Charge Region: • L1 = wh • All Jphfrom this region • V1 ≈ V if imbalance large • Space Charge LimitMott-Gurney (circ. 1940) • J V2/L3 • if imbalance too large (>> 100x) Concepts: After Separation

11. 3 Limits of Charge Transport • Drift length imbalance • Space charge • Total thickness L1 → L • Saturation at high V • Solve L-eqs. for V(G): Diff G-dep. Major Assumption: G  ILP (Incident Light Power) Refs show true for “non-SCL” devices 1) Jph ILP1 Vsat ILP0 2) Jph ILP3/4 Vsat  ILP1/2 εr=2.6; μ=1.2x10-7 cm2/V s =0.5ms; G=1.56x1027 m-3s-1

12. Preliminary Results • BEH1MBM3-PPV:PCBM (1:4) • Use Reg. Rand. To reduce mobility (increase difference) • Diff. increases at lower temp. • Get ½ power dep. on V in mid-region • Low-V is diffusion limited • High-V is saturation RT

13. Important Results Critical Evidence of SCL • ½ Power regime: JILP1/4 • Sat. Regime: JILP • No discussion of why • VsatILP1/2 • Used lowest temp. due to largest ½ power regime • Fit highest ILP for G & modeled the rest • Vsat from intersection of linear fits

14. Questions to answer • What do activation energies mean in organics? • My experience is in inorganics w/doping: Ea gives energy in the band gap of the conductive state • What’s the J-dep. in the saturation regime from? • Is G always proportional to ILP?

15. The Internal E-Field • Blom and Greenham have different definitions?! • What is the definition? • No drift current? • No photo current? • No current at all? • Why do we only show effectsof external E-fields in diagram? Diffusion from dissociated excitons Barker, Ramsdale, & Greenham, PRB (2003).

16. Charge Transport & Photocurrent Generation in P3HT:PCBM BHJ Solar Cells V. D. Mihailetchi, HangxingXie, Bert de Boer, L. Jan Anton Koster, and Paul W. M. Blom Adv. Func. Mater. (2006) Uses full model for P3HT:PCBM (Numerical, but has all components discussed above – just uses Poisson’s equation to achieve steady state).

17. Parameters of Experiment • P3HT:PCBM BHJ (1:1) Annealing study to understand mechanism for 10-fold improvement in PCE • All annealing for 4min • Max PCE=3.5% annealing >110C • Measures μe,h(Tannealing) – discussed by Jaewook last time • μh improves 3 orders of mag., μe improves by 1 • Absorption of 1.5AM spectrum increases 60% • DSC shows feature at ~125°C & claims this is Tg • Don’t believe it! • Uses above theory to show that improvement mostly caused by increase in μh, eliminating space charge • Probably due to higher degree of P3HT crystallinity when annealed above 110C

18. Preliminary Data • BHJ initially lower mobility than pure P3HT films • High MW films crystallize w/out annealing, so annealing does nothing to mobility • Annealing improves both carriers • Holes back up to pure P3HT values • Electrons improved even further, but gap btwn the two is closed. • As cast & poorly annealed shows J(V1/2) (space charge) • Annealed at 120C shows no space charge • low-V J(V) diffusion-limited • high-V saturation regime

19. Evidence of SCL • High illumination expands SCL region to the short circuit point, reducing FF & PCE • Lower illumination reduces space charge buildup • Further evidence for SCL at 0.1V via J(ILP3/4) • At 3.0V (saturation regime) back to simple μ-limited current where J(ILP1) • Devices annealed >110C not μ-limited nor SCL: J(V1,ILP1)

20. ←Field and Temp. FittingNumerical Simulations↓ • Uses eqn. on slide 6 w/G(E,T)to fit Charge Transfer separation and lifetime • a=1.8nm and kF-1=50 μs, both larger than PPV • Uses Poisson eqn. to numerically calc JL-V w/just μp and Gmaxmeasured values for each annealing temp. • Disassociation prob.=90% above 110C • I think: P=90% for lower tempsif anneal longer