Photocurrent Generation in Bulk vs Bilayer Devices: Quantum

Article pubs.acs.org/JPCC

Photocurrent Generation in Bulk vs Bilayer Devices: Quantum Treatment of Model Rubrene/7,7,8,8-Tetracyanoquinodimethane Heterojunctions for Organic Solar Cells Rui M. Pinto*,†,‡ †

INESC MN and IN, Rua Alves Redol No. 9, 1000-029 Lisboa, Portugal CQFM, Instituto Superior Técnico, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal

‡

S Supporting Information *

ABSTRACT: The primary kinetic processes leading to photocurrent generation in rubrene/ 7,7,8,8-tetracyanoquinodimethane (rubene/TCNQ) heterojunctions are investigated using a combination of quantum-chemical methods, Marcus nonadiabatic electron-transfer theory, and Onsager−Braun model for charge separation. Charge-transfer (CT), -recombination (CR), and -separation (CS) rates are obtained for heterodimers representative of two device models: single-crystal planar bilayer, in which crystal orientation is preserved and rubrene’s fused π-system is sterically hindered, and bulk-heterojunctions (BHJs), where donor and acceptor molecules approach cofacially with the π-system fully exposed. Results point to low geminate pair recombination due to higher donor−acceptor separation in crystalline bilayers, while maintaining ultrafast CT (∼109 s−1). Moreover, HOMO−LUMO coupling is an order of magnitude higher in cofacial orientation, leveraging CR in BHJs for which kCR ∼ 106 s−1 and kCT ∼ 109 s−1. This work provides a molecular perspective rationale for the high photoresponse reported for rubrene/TCNQ single-crystal bilayer interfaces.

1. INTRODUCTION Excitonic solar cells based on organic materials are viewed as the next low-cost alternative to amorphous silicon (a-Si) devices, with power efficiencies climbing at constant pace, currently above 10%.1,2 Organic compounds offer remarkable advantages over inorganics in photonic applications: solution processable, ease of preparation, and the ability of engineering at the molecular level their electronic structure, tuning essential parameters to device performance.3 Today’s most common organic photovoltaics are based on bulk-heterojunctions4−6 (BHJs), in which a blend of donor (D) and acceptor (A) materials is sandwiched between electrodes of different work functions. Such a blended network maximizes the interfacial area and reduces the distance an exciton must diffuse from its generation to its dissociation site, hence, increasing performance. DA materials can also be stacked together in planarbilayer HJs,7 enabling higher control over morphology and the ability of tuning independently each material deposition and treatment.8 An intermediate solution arises from mixed planarbilayer HJs,9 where a BHJ layer is deposited between donor and acceptor layers. Even if no convergent trend regarding nanomorphology exists,8,10,11 precise knowledge of interfacial domain structure is required to engineer and maximize photocurrent generation.12,13 Photocurrent generation in bulk, mixed, or bilayer excitonic cells begins with light irradiation of the DA heterojunction, leading to the formation of donor (acceptor) intramolecular excitons. Such excitons can relax nonradiatively back to the ground state (GS) or diffuse to the interface and evolve to a © 2014 American Chemical Society

charge-transfer (CT) state, giving rise to interfacial excitons with rate kCT. CT excitons can dissociate in a two-step process, first to weakly bound polaron pairs and then to free polarons. Alternatively, they can recombine with rate kCR, returning the DA system to its GS. These events (see Figure 1a) can be summarized as: kEX

DA + hν ⎯→ ⎯ D*A k CT

D*A ⎯→ ⎯ (D+A−) k CR

(D+A−) ⎯→ ⎯ DA k CS

(D+A−) ⎯→ ⎯ D+•A−•

After separation, free carriers must propagate through organic layers and ultimately be collected at electrodes. Thus, alongside CT and CR, diffusion (first) and transport (at the end) may also limit cell efficiency. Figures of merit for such processesexciton diffusion length, LD, and charge-carrier mobility, μare extremely dependent on the morphology of the DA system. It is expected that, in systems with long-range order and π−π stacking, mobility becomes higher and transport/collection is enhanced. In fact, very recently, organic single crystals (SC) laminated to form planar-bilayer HJs showed enhanced photoresponse (∼1 A W−1) in the visible.14 Received: September 25, 2013 Revised: December 15, 2013 Published: January 13, 2014 2287

dx.doi.org/10.1021/jp409583q | J. Phys. Chem. C 2014, 118, 2287−2297

The Journal of Physical Chemistry C

Article

ΔE = E Rub/TCNQ − (E Rub + E TCNQ )

(1)

while the distance between molecules along the z-axis is varied. ERub/TCNQ denotes the energy of the heterodimer, and ERub and ETCNQ correspond to the energy of the monomers. Molecules were approximated either cofacially or preserving the relative orientation found in their crystal structure, i.e., with stacked (a,b) facets, in order to mimic the most probable morphology found in BHJs or bilayer HJs, respectively. The interfacial dimer orientation mimicking single-crystal bilayer HJs follows exactly that of a real device, fabricated from single crystals of TCNQ and rubrene employing the lamination technique.14 On the other hand, choosing cofacial orientation for BHJ dimers relates to the fact that several small-weight organic molecules used in solar cells form cofacial aggregates in thin films. Examples include CuPc27 and porphyrins derivatives.28 Also in polymer:fullerene systems there is evidence for preferential cofacial arrangement: nanomorphology studies on PCDTBT:PCBM devices revealed that breaking preexisting π−π stacking worsens hole transport and decreases the opencircuit voltage (VOC).29 Given that a certain degree of structural freedom is inherent to the fabrication process of BHJs (spincoating, and solvent evaporation often via postannealing), it is probable that molecules bearing π-systems relax to the lowest energy conformation. In the case of rubrene/TCNQ this means cofacial alignment (as we will see further on). At each point, the intramolecular geometries were kept frozen (i.e., rigid-body approximation). Displacement and rotation were probed at fixed approximation distances (z = cte), corresponding to minima in the interaction energy curves. Interaction was calculated using the Hartree−Fock (HF) method and density functional theory (DFT), the latter employing Becke’s three-parameter and Lee−Yang−Parr functionals (B3LYP). The latter accounts only for 20% HF exchange, irrespectively of interaction range. Since it includes a range-dependent amount of HF exchange that results in improved modeling of CT states, the long-range corrected Coulomb attenuated method (CAM)−B3LYP functional30 was also used. To account for London dispersion interactions, Grimme’s correction31 (D3) was applied to all methods. For each method, the default parameters implemented in GAMESS32 were used. Basis-set superposition error was estimated using the counterpoise method and found negligible ( 1010 V/ m) does separation exceed recombination for cofacially oriented molecules in BHJs. The larger e−h distance leading to enhanced CS, computed for bilayer HJs, agrees with recent experiments on nonfullerene DA systems,58 where controlling steric interaction at an DA interface was taken as a general design principle toward increasing photocurrent. Among figures of merit used in organic solar cells characterization, the external quantum efficiency (EQE) gives an indication of the maximum achievable performance under ideal operation conditions (ohmic contacts, no losses due to

4. CONCLUSION Primary kinetic processes leading to photocurrent generation in rubrene/TCNQ heterojunctions were investigated using computational chemistry, Marcus nonadiabatic electron-transfer, and Onsager−Braun charge-separation theory. Two main heterodimer orientations were considered as interface models: one mimicking BHJs devices; another mimicking crystalline bilayer devices. In the BHJ model, donor and acceptor approximate cofacially and π−π interaction is maximized. In bilayer devices, the crystal structure is preserved. Results show that maximizing π−π overlap in BHJs leads to a stabler CT complex, but not to increased L/L coupling, essential to CT exciton generation. In fact, only geminate recombination is leveraged when considering cofacial orienta2294



Article

thanks H. Alves and E. M. S. Maçôas for helpful comments and guidance.

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Figure 10. Combined CT and CS efficiency (ηCTηCS) as a function of the electric field F, considering bulk (- -) and bilayer (−) HJs, for T = 300 K, ϵs = 3, and μ = μp + μn ∼ 20 cm2/(V s). The dotted line corresponds to 5 V applied to a 50 nm thick device.

tion, by an effective increase of H/L coupling. In crystalline bilayer model, CR is extremely slow and CT is a subnanosecond process. L/L coupling is practically unaffected by DA distance, but the increased equilibrium distance (z ∼ 11 Å) lowers the e−h binding energy, formed after splitting of the donor exciton. This lower e−h binding energy increases the efficiency for charge separation, reaching 100% even at low applied electric fields. In the BHJ model, CS is only efficient above 10 8 V/m, hindered by a high geminate pair recombination rate (kCR ∼ 107 s−1). Albeit computational chemistry gives only a simplistic view of the fundamental processes behind real device operation, it highlights which direction to follow in order to increase performance of organic solar cells. In that sense, this study shows some benefits of using single-crystal bilayer systems rather than BHJs: low geminate recombination due to higher DA separation, while maintaining ultrafast charge transfer.

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates of crystalline rubrene and TCNQ and heterojunction models (Tables S1−S4), energies in ground, ionic, and excited states (Table S5), Marcus input parameters (Tables S6 and S7), interaction energy scans with HF and B3LYP (Figure S1), B3LYP energy levels, 1D bulk effects, and additional electronic couplings (Figures S2−S4), and text describing energy coupling matrices. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +351-21-3100237. Fax: +351-21-3145843. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS R.M.P. acknowledges the Advanced Computing Laboratory at University of Coimbra for providing computing resources, and FCTFundaçaõ para a Ciência e Tecnologia for financial support with Grant No. SFRH/BPD/84820/2012. The author 2295



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Photovoltaic Charge Generation. J. Am. Chem. Soc. 2011, 133, 12106− 12114.

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Photocurrent Generation in Bulk vs Bilayer Devices: Quantum

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