Asymmetry in the Electron and Hole Transfer at a Polymer−CarbonNanotube HeterojunctionRun Long† and Oleg V. Prezhdo*,‡

†School of Physics, Complex & Adaptive Systems Laboratory, University College Dublin, Belfield, Dublin 4, Ireland‡Department of Chemistry, University of Rochester, Rochester, New York 14627, United States

*S Supporting Information

ABSTRACT: To achieve a high photon-to-charge conversion efficiency, theelectron−hole pair generated by photon absorption in organic photovoltaicsystems must overcome the Coulomb attraction, which often results involtage loss. Bearing this in mind, we performed ab initio time-domainsimulations of the charge separation and energy relaxation across an interfaceformed by poly(3-hexylthiophene) (P3HT) and a single-walled carbonnanotube (CNT). The dynamics of the positive and negative charges showedstrong asymmetry. Photoexcitation of the polymer leads to a 100 fs electrontransfer, in agreement with the experiment, followed by a loss of 0.6 eV ofenergy within 0.5 ps. Photoexcitation of the CNT leads to hole transfer,which requires nearly 2 ps, but loses only 0.3 eV of energy. The strongdisparity arises due to the differences in the localization of the photoexcited donor states, the number densities of the acceptorstates, and the phonon modes involved. Used as a chromophore, P3HT produces faster charge separation but leads to largerenergy losses and cannot harvest light in the red region of the solar spectrum. In contrast, CNT absorbs a broader range ofphotons and reduces energy losses but gives a less efficient charge separation. The complementary properties of the twochromophores can be utilized to improve the performance of solar cells by optimizing simultaneously light harvesting, chargeseparation, and energy relaxation, which affect the photovoltaic yield, current, and voltage.

KEYWORDS: Organic photovoltaics, poly(3-hexylthiophene), single-walled carbon nanotube, nonadiabatic molecular dynamics,time-domain density functional theory, charge separation, nonradiative relaxation

Organic photovoltaic cells, and bulk-heterojunction (BHJ)cells in particular, have been demonstrated as low-cost

alternatives to silicon-based solar cells, offering a promisinglong-term solution for clean, renewable energy.1−5 The lowdielectric constant of organic conjugated materials results insignificant Coulomb interactions between charge carriers andgives rise to a strongly bound electron−hole pair, called anexciton, rather than to free charge carriers.6 Upon excitondissociation by photoinduced charge transfer,7 the electron onthe acceptor (A) species and the hole on the donor (D) speciesare still interacting. If the bound electron−hole pairs cannotseparate, recombination will eventually occur, leading to solarcell efficiency losses. The challenge exists in separating thephotogenerated electron−hole pairs between electron-donatingand electron-accepting materials. When the exciton is localizedon the D material, the charge separation involves electrontransfer between the lowest unoccupied molecular orbitals(LUMOs) of D and A. The driving force is the energy offset ofLUMOs between D and A materials. Alternatively, if theexciton is localized on the A, the charge separation proceeds byhole transfer between the highest occupied molecular orbitals(HOMOs) of the A and D. It is driven by the energy offset ofHOMOs between the A and D materials. For BHJ solar cellsboth scenarios are possible, and a deeper understanding of thecharge generation, separation, and energy relaxation dynamics

is necessary for providing guidelines for the design of the nextgeneration of high-performance materials for organic photo-voltaics.Composites of poly(3-hexylthiophene) (P3HT) and single-

walled carbon nanotubes (CNTs) are promising candidates forBHJ solar cells,1−4 because excitons generated in the polymerproduce long-lived charge carriers due to the efficientseparation of the electron−hole pairs across the P3HT/CNTinterface.8 Utilization of P3HT/CNT hybrids as chargeextraction and active photoabsorption layers has produced a7.6% power conversion efficiency in an organic solar cellcomposed of a low band gap polymer donor and PC70BMacceptor.9 The high charge-carrier mobility of semiconductingCNTs and the possibility of solution processing provideadditional advantages for high-performance, low-cost applica-tions. CNTs have been identified as promising candidates forhigh mobility charge extraction paths10−12 and excitonicantennas.13,14 Conjugated polymers with extensive π-conju-gated structures interact strongly with CNTs.8,15−18 P3HT inparticular is one of the most common hole exaction materials inBHJ solar cells.19 It has been the subject of multiple

Received: March 1, 2014Revised: May 1, 2014Published: May 19, 2014

Letter

pubs.acs.org/NanoLett

© 2014 American Chemical Society 3335 dx.doi.org/10.1021/nl500792a | Nano Lett. 2014, 14, 3335−3341

This is an open access article published under an ACS AuthorChoice License, which permitscopying and redistribution of the article or any adaptations for non-commercial purposes.

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experimental and theoretical investigations.15−17,20 P3HTpossesses a high-carrier mobility21 and is commonly used infundamental studies as a benchmark polymer, because itselectronic structure and optical properties are well-known.Often, the charge injection yield in P3HT/CNT composites issmall because of the alternative pathway, involving fast energytransfer from P3HT to CNTs, and leading to an undesired lossof the photogenerated electrons and a relatively low efficiencyof P3HT/CNT solar cells to date.22,23

Recently, Nicholas and coauthors reported ultrafast extrac-tion of hot electrons from photoexcited P3HT into single-walled semiconducting CNT occurring on a 430 fs time scale.15

The injection of the photogenerated electrons is ultrafast,causing the electron and hole in the P3HT to part rapidly andreducing charge recombination. CNTs can be used aschromophores as well, with a clear advantage of reaching intothe read and near-infrared24 parts of the solar spectrum. CNTphotoexcitation leaves the electron inside CNT and causes holetransfer into P3HT. Figure 1 demonstrates the charge

separation dynamics following photon absorption of eitherP3HT or CNT, which form a type-II photovoltaic hetero-junction. Excitation of P3HT followed by electron transfer orexcitation of CNT followed by hole transfer lead to exactly thesame charge separated state. However, the dynamics of theseand competing processes can be very different in the twoscenarios. Solar cell properties and performance dependstrongly on these dynamics. The combination of the twolight absorbers and the ensuing excitation dynamics can beexploited to optimize light-harvesting, current, voltage, andefficiency of photovoltaic devices. In order to achieve this goal,one needs to obtain a detailed understanding of thephotoinduced processes, which can be produced by atomisticmodeling.The current Letter reports time-domain ab initio simulations

of the photoinduced dynamics in a P3HT/CNT system andconsiders implications of the obtained results to developingorganic solar cells. The first part of the simulations, focusing onelectron transfer from P3HT to CNT, relates directly to therecent experimental work by Nicholas and co-workers.15 Thesecond part, dealing with hole transfer from CNT and P3HT,makes experimentally testable predictions. Taken together, thetwo simulations provide a comprehensive description of theexcited state dynamics at the P3HT/CNT interface and lead tovaluable suggestions for photovoltaic device optimization. Thestudy establishes the electron and hole transfer mechanismsand time scales and characterizes the electronic states andphonon modes that facilitate the charge transfer and energydissipation. The obtained electron transfer time agrees with theavailable experimental observation.15 The driving force for both

electron and hole transfer is generally larger than the excitonbinding energies in P3HT and CNT, respectively. The electrontransfer is an order of magnitude faster than the hole transfer,because of a stronger donor−acceptor coupling, higher densityof acceptor states, and a broader range of participating phononmodes. The electron moves from P3HT to CNT primarily bythe adiabatic mechanism and then relaxes nonradiatively insideCNT. In contrast, hole transfer occurs simultaneously withenergy relaxation by the nonadiabatic mechanism. The transferof both electrons and holes is promoted primarily by the high-frequency C−C stretching modes of the two materials.Additionally, electron couples to lower frequency radialbreathing modes (RBM) of CNT and P3HT torsional motions.CNT is capable of harvesting a broader range of sunlight andreduces energy losses to heat. At the same time, it leads to lessefficient charge separation. In comparison, P3HT gives fastcharge separation but is limited to higher frequency sunlightand leads to more energy losses. The differences in the P3HTand CNT light harvesting, and subsequent dynamics, suggest atool for tuning solar cell properties. A broader range of solarphotons can be harvested, and losses of energy and voltage canbe reduced by increasing the CNT concentration and usingCNTs of different diameters and chiralities. On the other hand,high P3HT concentrations improve charge separation and givehigher currents.The simulations employ the quantum-classical fewest-

switches surface hopping technique25 implemented within thetime-dependent Kohn−Sham theory.26,27 In this approach, thelighter electrons are treated quantum mechanically, while theheavier nuclei are classical. The method has been appliedsuccessfully to study electron transfer and relaxation dynamicsat interfaces of TiO2 with molecular chromophores,28 quantumdots (QDs),29 and graphene,30 in carbon nanotubes,31

fullerenes,32 graphane,33 semiconducting quantum dots,34,35

and metallic36,37 nanocrystals. The approach provides a detailedab initio picture of the coupled electron-vibrational dynamicson the atomic scale and in the time domain. After an initialexcitation, the simulated system is allowed to evolve in theelectronic state manifold coupled to phonons. Nonadiabaticcouplings, computed on the fly, induce electronic transitions. Adetailed description of the method is presented in our previousstudies.26,31,35

The simulation cell includes a unit cell of the (10,2) CNTand a P3HT oligomer composed of six thiophene units (Figure2). The P3HT side-chains are included fully. At least 8 Å ofvacuum surround the system everywhere in the directionperpendicular to the CNT axis, to eliminate spuriousinteractions between the periodic images. Note that the systemcomponents are apolar and carry no dipole moment, makingthe periodic calculation easier to converge with the vacuumsize. The simulation cell measures 23.7 Å in the axialdirection.20 This setup provides a good representation of theexperiment,15 which focuses on the (6,5) CNT. In particular,the band alignment of the (10,2)/P3HT system, Figure 3, is thesame as in the (6,5)/P3HT composite. We chose the (10,2)CNT, because its unit cell contains 1.5 times fewer atoms thanthat of the (6,5) CNT. Further, the (10,2) CNT closelymatches the periodicity of the P3HT polymer, allowing us touse a smaller oligomer.The geometry optimization, electronic structure, and

adiabatic molecular dynamics (MD) simulations are performedwith the Vienna ab initio simulation package (VASP).38,39

Nonlocal exchange−correlation interactions are treated with

Figure 1. Diagram of the energy levels involved in the chargeseparation dynamics across the P3HT/CNT interface. (a) Excitationof P3HT results in electron transfer from P3HT to CNT. (b)Excitation of CNT induces hole transfer from CNT to P3HT.

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the Perdew−Burke−Ernzerhof (PBE) functional.40 The inter-action of the ionic cores with the valence electrons wasdescribed by the projector-augmented wave (PAW) ap-proach.41,42 The van der Waals long-range force is includedto stabilize the system for geometry relaxation and MDsimulation.43 After the geometry optimization at 0 K, thesystem is heated from 0 to 300 K during 4.0 ps, using uniformvelocity rescaling. Finally, trajectories for the nonadiabaticelectron-vibrational dynamics are generated in the micro-

canonical ensemble. The nuclear time step for the equilibrationand production runs is set to 1.0 fs. The electronic time step forthe nonadiabatic dynamics is 1.0 as. It is assumed thatphotoexcitation of either P3HT or the CNT creates a hole andan electron in the corresponding HOMO and LUMO. Thelowest energy bright excitation of P3HT is well-represented bythe HOMO−LUMO transition. On the other hand, the lowestenergy exciton in CNTs is typically dark. At the same time, thesplitting between the bright and dark excitons is small, andtherefore, the excitation energy is close to the HOMO−LUMOgap. Once the bright exciton is excited, it relaxes rapidly to theHOMO−LUMO exciton, losing nonradiatively only a smallamount of energy.The interaction between P3HT and CNT determines the

rates of electron and hole transfer and the competition of thetransfer processes with energy relaxation. In turn, the P3HT/CNT geometry and separation influence the strength of theinterfacial interaction. Figure 2 shows the optimized geometry(top panel) and a snapshot (bottom panel) from MDsimulation at ambient temperature. Comparing the zero- andfinite-temperature geometries, we observe that P3HT remainsbound to CNT at room temperature because van der Waalsinteraction stabilizes the two components, even though theaverage separation increases from 3.23 to 3.91 Å. P3HT is flatat 0 K, indicating that the π-electron system remains intact, andthe P3HT−CNT interaction is purely van der Waals. Astemperature increases, the CNT structure deforms slightly dueto RBM motions. P3HT changes structure to a much greaterextent, Figure 2 (bottom panel). The P3HT side-chainsfluctuate significantly, embracing the CNT, and the P3HTbackbone undergoes large-scale undulating motions. The out-of-plane displacements of the carbon and sulfur atoms have astrong effect on the electron, hole, and energy relaxationdynamics. The motions perturb the π-electron conjugation,changing the energies of the P3HT states. The low-frequencyout-of-plane P3HT motions and CNT RBMs affect electronicenergy levels, creating electron−phonon nonadiabatic coupling.High-frequency carbon−carbon stretching modes do notsignificantly alter the electronic energies but contribute stronglyto the nonadiabatic coupling, since they are fast and create largenuclear velocities, dR/dt, that enter the nonadiabatic couplingmatrix element −iℏ⟨φk|∇R|φm⟩·(dR/dt).Figure 3a shows the projected density of states (PDOS) of

P3HT and CNT in the P3HT/CNT composite underinvestigation at 0 K. The PDOS clearly demonstrates theformation of a type-II photovoltaic heterojunction, as illustratedexplicitly by the inset. The lowest energy excited state formedat the heterojunction is a charge transfer state with the electronlocalized on the CNT LUMO and the hole located on theP3HT HOMO. Photoexcitation of P3HT leads to electrontransfer onto CNT, while photoexcitation of CNT results inhole transfer to P3HT. The energies lost to vibrational motionsduring the electron and hole transfer events are 0.61 eV and0.36 eV, respectively. These numbers represent canonicalaverages and indicate that nearly twice more energy is lost afterP3HT excitation than after CNT excitation. Figure S1 showsthe evolution of the HOMOs and LUMOs of CNT and P3HTalong a representative part of the MD trajectory. Note that theP3HT LUMO fluctuates much more significantly than theP3HT HOMO, because the P3HT LUMO mixes with theCNT states (Figure 3b). The band-edge offsets between theCNT and the polymer represent the type-II heterojunction,which is preserved during thermal fluctuations at room

Figure 2. Top and side views of the simulation cell showing thegeometry of the system comprising the P3HT polymer and the (10,2)CNT, optimized at 0 K (top) and during molecular dynamics at 300 K(bottom). The light gray, brown, and yellow spheres denote H, C, andS atoms, respectively.

Figure 3. (a) Projected density of states (PDOS) of the P3HT/CNTsystem at 0 K. CNT has a much larger DOS than P3HT. The insetshows the energy offsets between the donor and acceptor orbitals forthe electron and hole transfer. Energy loss during transfer decreasesdevice efficiency. (b) Charge densities of the donor and acceptororbitals for the hole and electron transfer, left and right panels,respectively. The electron donor state is delocalized significantlybetween P3HT and CNT, while the hole donor state is localized onCNT. The acceptor states are localized in both cases. The verticalarrows between parts (a) and (b) relate the donor and acceptor orbitalimages to the energies. Notice in part (a) that the P3HT LUMO is inenergy resonance with a high density of CNT states, while the CNTHOMO is isoenergetic with a low density of P3HT states. Thisexplains why photoexcitation of P3HT promotes the electron to astate that is already delocalized onto CNT and why the electrontransfer is faster than the hole transfer (Figure 5).

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temperature. Combined with the fact that CNT has a smallerband gap, and therefore, can harvest the red part of the sunlightspectrum, the result indicates that CNT photoexcitation canlead to more efficient solar cells than P3HT photoexcitation.The corresponding efficiency estimates are provided in theSupporting Information.To achieve charge separation, the electron and hole must

overcome the Coulomb attraction, characterized by the excitonbinding energy. The exciton binding energy of P3HT is 0.3eV,44 which is smaller than the electron and hole transferdriving forces of 0.61 and 0.36 eV (Figure 3a). The excitonbinding energies of semiconducting CNTs range from 0.2 to0.5 eV, depending on CNT size, chirality, and dielectricconstant of the surrounding medium that screens the Coulombinteractions.45−47 A polar medium, such as water, can reducethe binding energy by a factor of 2.48 A nonpolar medium suchas P3HT has a smaller screening effect. The electron transferdriving force of 0.61 eV is larger than exciton binding energy inany CNT, while the hole transfer driving force of 0.36 eV iswithin the CNT exciton binding energy range. Thus, one cananticipate barrier-less photoinduced electron transfer and arange of scenarios, both with and without a Coulombinteraction barrier, for the hole transfer. CNTs may be bothsemiconducting and metallic, depending on chirality. Non-radiative energy losses to heat are very rapid in a metal, and it isharmful for achieving efficient charge separation and thephotovoltaic effect. Metallic CNTs should be excluded toincrease photovoltaic performance of a heterojunction. Theband gap of semiconducting CNTs depends on both diameterand chirality. Different CNTs will exhibit varying band offsetsrelative to P3HT and other polymers, affecting the driving forcefor the charge separation.In addition to the driving force, the charge separation

efficiency depends on a number of other factors, includingdonor−acceptor coupling and the density of acceptor states.Figure 3a shows that PDOS is higher for CNT than P3HT.Note that in a realistic system P3HT is likely to wrap aroundCNTs rather than being parallel. A more detailed research onthe effect of wrapping of conjugated polymers on their opticalproperties and relative alignments of the polymer and nanotubeoptical bands has been presented by Kilina and co-workers.49 Itwas shown that the main optical band of the polymer is blue-shifted when the polymer wraps around the tube. The bandalso becomes broader. Therefore, polymer wrapping candecrease of the valence and conduction band-edge offsetsbetween the polymer and the nanotube. Wrapped around theCNT, P3HT will have a higher relative PDOS (Figure 3a). Still,per unit cell of the combined system, the number of carbonatoms carrying π-electrons will be larger for CNT than P3HT.Therefore, the density of acceptor states is greater for theelectron transfer from P3HT to CNT than for the hole transferfrom CNT to P3HT.The key electron and hole orbitals that take part in the

relaxation processes are shown in Figure 3b. The energies ofthese states are indicated by the vertical arrows extending fromFigure 3b to 3a. The delocalization of the orbitals betweenP3HT and CNT characterizes the strength of the donor−acceptor coupling. In general, the stronger is the interaction,the more significant is the delocalization. The mixing occursdue to interaction of the π-electron subsystems of P3HT andCNT. The donor state for the electron transfer, top-left panelof Figure 3b, is delocalized significantly between P3HT andCNT, indicating strong donor−acceptor coupling. In contrast,

the donor state for the hole transfer, top-right panel of Figure3b, is localized strongly on CNT, suggesting that the coupling isweaker in this case.The analysis of the electronic structure of the P3HT/CNT

heterojunction indicates that all three factorslarger drivingforce, higher density of acceptor states, and stronger donor−acceptor couplingbenefit electron rather than hole transfer.More efficient charge separation resulting from photoexcitationof P3HT favor increased solar cell currents. At the same time,the large driving force results in significant energy losses,reducing solar cell voltage.A complete description of the electron−phonon dynamics,

leading to the photoinduced charge separation and energyrelaxation, relies on knowledge of both the electronic structureof the hybrid system (Figure 3) and electron−phononinteractions. Vibrational motions promote charge transfer andare responsible for solar energy losses to heat. Figure 4 presents

Fourier transforms (FTs) of the phonon-induced fluctuationsof the energy offsets between the donor and the acceptor statesfor the electron and hole transfer. In particular, the top panelshows the FT of gap between the P3HT and CNT LUMOs,while the bottom panel presents the FT of the gap between theP3HT and CNT HOMOs. The charge densities of the HOMOand LUMO orbitals are shown in Figure 3b, and the evolutionof these energy levels arising from thermal fluctuations of atomsis depicted in Figure S1. The frequency and amplitude of thedata characterize the phonon modes involved in the transferand the strength of the electron−phonon coupling, respectively.The electron transfer is facilitated by a broader range of phononmodes than hole transfer. The difference arises from the lowfrequency motions, <300 cm−1, associated with the torsionalmodes of the polymer and CNT RBM. The slow motions affectlocalization of the photoexcited state for electron transfer,shared between P3HT and CNT, Figure 3b (top-left panel). Incontrast, both donor and acceptor states for hole transfer arestrongly localized on CNT and P3HT, respectively, Figure 3b(right panels). As a result, the slow-frequency modes have littleeffect on hole transfer. The high-frequency C−C stretchingmotions of the polymer and CNT, with frequencies in the

Figure 4. Fourier transforms of the energy offsets between the donorand acceptor states for the electron (top) and hole (bottom) transfer.The electron couples to both high-frequency C−C stretches and low-frequency modes, including CNT RBM and P3HT torsional modes.The hole couples exclusively to the high-frequency modes. Theinvolvement of a broader range of vibrations provides additionalchannels for the electron transfer.

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1400−1600 cm−1 range, drive both transfer processes (Figure5). The stronger involvement of the low frequency modes inelectron rather than hole transfer contrasts with the electron−phonon relaxation in an isolated CNT.50 Here, the statedelocalization argument does not apply. Holes couple to lowerfrequency phonons, because hole orbitals have fewer nodesthan electron orbitals, better matching the nodal structure oflow-frequency vibrations.The computed average absolute values of the nonadiabatic

coupling for electrons and holes are 12.4 and 1.54 meV,respectively. The broader range of phonon modes and thestronger electron−phonon coupling contribute to the fasterelectron dynamics compared to the holes (Figure 5). This istrue of both charge transfer and nonradiative relaxation. Parts aand b of Figure 5 describe charge transfer, while parts c and dcharacterize energy relaxation. The time constants reported inthe figure are obtained by fitting the data to an exponential, f(t)= f(t0) + A exp(−t/τ1), for electrons, and to an Gaussian, f(t) =f(t0) + B exp(−0.5(−t/τ2)2), for holes. Exponential dynamics isindicative of a large number of final states, while Gaussianbehavior is associated with few final states. The number of finalstates for electron transfer is determined by the DOS of theCNT conduction band, while the number of final states for holetransfer is given by the DOS of the P3HT valence band. Theformer is significantly higher than the latter (Figure 3a),rationalizing the exponential and Gaussian dynamics. Generally,quantum dynamics starts in a Gaussian/quadratic manner,associated, for example, with the quantum Zeno effect,51 andthen develops into an exponential process, whose rate can bedescribed, for instance, by Fermi’s golden rule.The electron transfer occurs more than an order of

magnitude faster than the hole transfer for several reasons

(Figure 5a,b). The density of CNT states accepting the electronis significantly higher than the density of P3HT states acceptingthe hole (Figure 3a). This is because CNTs have a significantlylarger π-electron system than conjugated polymers. Thedonor−acceptor interaction is also stronger for the electrontransfer, as indicated by the notable delocalization of thephotoexcited donor state onto the acceptor (Figure 3b).Finally, the nonadiabatic electron−phonon coupling issignificantly stronger for the electrons than for holes, 12.4 vs1.54 meV, in part because of a wider range of phonon modesinvolved (Figure 4). The charge-phonon energy relaxation isalso faster for the electrons than holes (Figure 5c,d), due to astronger charge−phonon coupling and a higher density of CNTstates. The transfer of electron precedes electron−phononrelaxation, while the times of hole transfer from CNT to P3HTand hole relaxation inside P3HT are similar. The calculatedelectron transfer time is faster than the experimental value of430 fs.15 Most likely, this is because the simulation uses a P3HTmonolayer, while a few layers of P3HT are included in theexperiment, requiring electron diffusion from outer to innerlayers.To achieve computational efficiency, the simulation is based

on a minimalistic P3HT model, including a single polymerchain stretched along the CNT axis. In realistic systems, thepolymer wraps around the CNT, and possibly, several polymerchains surrounds the CNT. Specific details of an experimentalsystem can influence quantitative, but not qualitative,conclusions of the present work. Thus, a higher P3HT/CNTratio will decrease the difference in the P3HT and CNT DOS(Figure 3a) reducing the imbalance in the electron and holetransfer times from over 2 orders of magnitude to, perhaps, 1order of magnitude. The relative locations of the energy levels

Figure 5. Electron and hole transfer dynamics. Top panels (a and b) show decay of the population of the electron and hole donor states. Bottompanels (c and d) show evolution of the electron and hole energies. The energy relaxation is slower than the population decay. The data in (a and c)are well-fitted by an exponential, indicating that the electron dynamics includes many states. The hole dynamics (b and d) exhibits Gaussian decay,indicative of a limited number of states involved. This agrees with the difference in the P3HT and CNT DOS (Figure 3). The photoexcited electronis rapidly transferred from P3HT to CNT and then relaxes by coupling to phonons. The hole transfer from CNT to P3HT occurs by slownonadiabatic transitions, which simultaneously result in energy relaxation.

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should depend little on the species concentration, andtherefore, the conclusion regarding a significantly higher energyloss following electron compared to hole transfer will remainunchanged. Larger diameter CNTs will absorb light deeper intothe near-infrared region.The difference in the CNT and P3HT absorption spectra

and the strong imbalance between the photoinduced electronand hole transfer events can be utilized for optimization of lightharvesting, voltage, and current in solar cells. The experimentaldesigns use small amounts of CNTs in P3HT, e.g., 1%.15 Thisachieves rapid charge separation and high currents, at theexpense of lower voltages due to significant electron−phononenergy losses. Light from the red and near-infrared regions ofsolar spectrum is harvested only slightly. By increasing theCNT concentration, once can harvest light over a broaderrange of solar spectrum, while reducing energy losses to heat. Inaddition, electron mobility should increase due to betterconductivity of CNTs compared to P3HT. However, if theCNT concentration becomes high, the charge separationefficiency will be reduced, and the hole mobility can becomeproblematic due to the small concentration and low relativeconductivity of P3HT. The effect of the CNT/P3HTconcentration ratio on solar cell performance will depend onmixing and morphology52 in the CNT/P3HT hybrid material.An optimal concentration ratio can be chosen depending on aspecific goal.In summary, by applying our unique methodologies

combining time-domain density functional theory and non-adiabatic molecular dynamics, we investigated the photo-induced electron and hole dynamics in a CNT/P3HTcomposite material, in real-time and at the ab initio atomisticlevel of detail. The electron transfer dynamics following P3HTexcitation agrees well with the experimental data. Byconsidering the complementary, hole transfer process resultingfrom CNT excitation, we established that the electron and holedynamics are highly asymmetric. The electron transfer is anorder of magnitude faster than the hole transfer, due to a higherdensity of acceptor states, and stronger donor−acceptor andelectron-vibrational interactions. The electron-vibrational relax-ation is promoted primarily by the high-frequency C−Cstretching modes, with the hole relaxation additionallyinvolving low-frequency CNT and P3HT motions. Thesignificant differences in the light-harvesting properties ofP3HT and CNT, and in the subsequent charge separation andrelaxation dynamics, suggest that the properties of CNT/P3HTsolar cells can be tuned continuously, as desired. By increasingthe CNT concentration and using several different CNTssimultaneously, one can harvest a broader range of solarspectrum and reduce energy and voltage losses. By increasingthe P3HT concentration, one achieves better charge separationand higher currents. The reported simulations provide acomprehensive description of the charge and energy transferdynamics in the hybrid nanoscale material and suggest noveldesign principles for photovoltaic and photocatalytic devices.

■ ASSOCIATED CONTENT*S Supporting InformationEvolution of the highest occupied and lowest unoccupiedmolecular orbitals of the CNT and P3HT during the moleculardynamics simulation. Estimation of the power conversionefficiencies arising from photoexcitation of either CNT orP3HT. This material is available free of charge via the Internetat http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: oleg.prezhdo@rochester.edu.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSR.L. is grateful to the SIRG Program 11/SIRG/E2172 of theScience Foundation Ireland and University College DublinSeed Funding SF 1003. O.V.P. acknowledges grant CHE-1300118 from the US National Science Foundation.

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