Time-Domain Ab Initio Analysis of Excitation Dynamics in a QuantumDot/Polymer Hybrid: Atomistic Description Rationalizes ExperimentRun Long†,‡ and Oleg V. Prezhdo*,§

†College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing NormalUniversity, Beijing 100875, P. R. China‡School of Physics and Complex & Adaptive Systems Lab, University College, Dublin, Ireland§Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States

*S Supporting Information

ABSTRACT: Hybrid organic/inorganic polymer/quantum dot (QD) solar cellsare an attractive alternative to the traditional cells. The original, simple modelspostulate that one-dimensional polymers have continuous energy levels, whilezero-dimensional QDs exhibit atom-like electronic structure. A realistic, atomisticviewpoint provides an alternative description. Electronic states in polymers aremolecule-like: finite in size and discrete in energy. QDs are composed of manyatoms and have high, bulk-like densities of states. We employ ab initio time-domain simulation to model the experimentally observed ultrafast photoinduceddynamics in a QD/polymer hybrid and show that an atomistic description isessential for understanding the time-resolved experimental data. Both electron andhole transfers across the interface exhibit subpicosecond time scales. The interfacialprocesses are fast due to strong electronic donor−acceptor, as evidenced by thedensities of the photoexcited states which are delocalized between the donor andthe acceptor. The nonadiabatic charge−phonon coupling is also strong, especiallyin the polymer, resulting in rapid energy losses. The electron transfer from the polymer is notably faster than the hole transferfrom the QD, due to a significantly higher density of acceptor states. The stronger molecule-like electronic and charge-phononcoupling in the polymer rationalizes why the electron−hole recombination inside the polymer is several orders of magnitudefaster than in the QD. As a result, experiments exhibit multiple transfer times for the long-lived hole inside the QD, ranging fromsubpicoseconds to nanoseconds. In contrast, transfer of the short-lived electron inside the polymer does not occur beyond thefirst picosecond. The energy lost by the hole on its transit into the polymer is accommodated by polymer’s high-frequencyvibrations. The energy lost by the electron injected into the QD is accommodated primarily by much lower-frequency collectiveand QD modes. The electron dynamics is exponential, whereas evolution of the injected hole through the low density manifoldof states of the polymer is highly nonexponential. The time scale of the electron−hole recombination at the interface isintermediate between those in pristine polymer and QD and is closer to that in the polymer. The detailed atomistic insights intothe photoinduced charge and energy dynamics at the polymer/QD interface provide valuable guidelines for optimization of solarlight harvesting and photovoltaic efficiency in modern nanoscale materials.

KEYWORDS: inorganic−organic photovoltaics, poly(3-hexylthiophene), CdS quantum dot, nonadiabatic molecular dynamics,time-dependent density functional theory, charge separation and relaxation

Hybrid photovoltaic cells based on polymers and inorganicnanocrystals possess significant potential for low-cost,

scalable solar power conversion. Polymers harvest solar lightand donate electrons in organic solar cells.1 Polymer solar cellsoffer the advantages of solution processing and straightforwardchemical synthesis.2 At the same time, Coulomb interactionsbetween charge carriers are significant in organic matter due tolow dielectric constants, giving rise to strongly bound electron−hole pairs rather than to free charge carriers.3 Combined withthe highly inhomogeneous energy landscape of electronicstates, this drawback leads to losses of energy and chargecarriers that significantly reduce the power conversionefficiency of polymer-based solar cells. Compared to fullerenes,used as electron acceptors in traditional organic solar cells,

colloidal QD exhibit better morphological stability and higherelectron mobilities. In addition, QDs improve light harvestingdue to large absorption cross sections, which are easily tunableover the entire solar spectrum. The electron−phononrelaxation dynamics in QDs has attracted intenseattention.4−14 Hot-carrier generation and carrier multiplicationprovide opportunities to improve conversion efficiencies of QDsolar cells by reducing the loss of high-energy carriers.15,16

Novel synthetic methods enable control over size, shape,

Received: December 2, 2014Revised: June 2, 2015Published: June 10, 2015

Letter

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© 2015 American Chemical Society 4274 DOI: 10.1021/nl5046268Nano Lett. 2015, 15, 4274−4281

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composition, and structure of nanocrystal samples,17 broad-ening the spectrum of photocatalytic and photovoltaicapplications. The combined advantages of organic polymerand inorganic QD materials open new ways to enhance furtherthe solar cell performance.18

Many scientists have focused on the charge dynamics inpolymer/fullerene systems forming the basis for organic solarcells.19−21 Understanding of these materials is limited due tounknown morphology and ordering. On the one hand,experiments reveal that ultrafast charge transport throughdelocalized band-like states in fullerene aggregates leads toefficient photovoltaice devices.22 Theoretical work indicatesthat only carriers that are thermally activated into the fullereneband states contribute to charge transport.23 On the otherhand, poor contact between fullerenes can result in low densityof interacting electronic states, leading to low light-conversionefficiencies. Replacing fullerene electron acceptors with ananostructured inorganic semiconductor provides an alternativedesign, opening up a new class of hybrid organic/inorganicsystem.1,24−28 Hybrid systems are interesting due to both therelative ease of controlling the microstructure and the potentialfor efficient charge separation at low driving forces. The offsetsbetween the donor and acceptor lowest unoccupied moleculeorbitals (LUMO) for electron transfer and highest occupiedmolecular orbitals (HOMO) for hole transfer can be smallbecause inorganic matter has high dielectric permittivity,lowering the electron−hole Coulomb binding energy andfacilitating charge separation. In comparison, the low dielectricconstant of organic matter results in strong Coulomb attractionbetween charges in polymer/fullerene hybrids, allowing timefor losses due to nonradiative relaxation and chargerecombination.29−32 Rather than an infinite semiconductor, aconjugated polymer is well represented by a collection ofconjugated segments (oligomers) with different length andstructural disorder.33 Relatively few studies have focused oncharge generation in polymers with inorganic absorbingacceptors.24,25,27,34 Photoexcitation of the polymer can lead toelectron transfer, whereas photoexcitation of the QD can resultin hole transfer in such systems. The kinetics of the hole havenot been widely studied, through it has been shown that holetransfer can play an important role in hybrid solar cells28 as wellas in semiconductor sensitized solar cells.35 Often, the electronand hole transfer dynamics show different time scales. Forexample, in the CdSe QD and poly[2-methoxy-5-(3′,7′-dimethyloctyloxy)-1,4-phenylenevinylene] (MDMO-PPV) hy-brid system, electron transfer from the polymer to the QDoccurs on a subpicosecond time scale, whereas hole tranfsershows a broad range of times from subpiconsecond to severalnanoseconds.28 Similar electron and hole transfer dynamicshave been reported for the CdS QD and P3HT hybridsystem.24 The experiments motivate the current time-domainab initio study.Traditionally, one employs Marcus theory36−39 in order to

characterize the dependence of the electron transfer ratedependence of donor−acceptor coupling and energy gap, thelatter known as the driving force. Developed initially for intra-and intermolecular electron transfer, Marcus theory assumes alarge rearrangement of nuclear configuration, which brings theelectronic donor and acceptor energies in resonance. Theenergy of the nuclear rearrangement is called the reorganizationenergy. The electron transfer rate in the traditional Marcustheory reaches a maximum when the reorganization energymatches the donor−acceptor gap, ovbiating the need for the

nuclear rearrangement. If the energy gap becomes too large, thenuclear rearrangement requires thermal activation again, andthe rate decreases, leading to the so-called Marcus invertedregion.37 Our recent time-domain ab initio simulation40 hasrationalized the absence of the Marcus inverted region inelectron transfer from a CdSe QD to a molecule.41 Rather thanrequiring a nuclear rearrangement, energy conservation isachieved by an Auger-type hole excitation in the QD electrondonor. The complexities and ultrafast time scales of chargetransfer dynamics in nanoscale materials and the competion ofcharge transfer with other processes, including nonradiativerelaxation and Auger-type energy exchange, strongly motivatetime-domain ab initio simulation.The current Letter shows that an atomistic description is key

to understanding of the photoinduced dynamics at a polymer/QD interface. Because QDs contain many more atoms thanpolymers in the QD/polymer interaction region, QDs have amuch higher projected density of states (PDOS). Theconjugated polymer acts more as a molecule than an infinitesemiconductor. The charge transfer to the QD is faster than tothe polymer due to a higher density of acceptor states. Bothtransfers occur on a subpicosecond time-scale as a result ofstrong donor−acceptor coupling, in excellent agreement withthe experimental work.1,24 The hole injected into the polymerloses its energy by coupling to high-frequency molecularvibrations. In comparison, the electron couples to a broaderrange of motions, including low-frequency QD modes andcollective polymer vibrations. The dynamics of electroninjection into the QD is exponential, as expected with a highdensity of acceptor states. The dynamics of hole injection intothe polymer and the subsequent hole nonradiative relaxationare highly nonexponential due to low density of local polymerstates. The electron−hole recombination at the interface isslower than the electron−hole recombination in the polymerand faster than that in the QD, also in agreement with theexperiment. The recombination rates affect directly the range ofthe observed charge separation time scales: Long excited statelifetime of the QD leads to a broad range of hole injectiontimes. The efficient electron and hole transfers guarantee thatboth polymer and QD can be used as sunlight absorbers. Thelong excitation lifetime inside the inorganic medium suggeststhat efficient photovoltaic devices can have a high QDconcentration.The study focuses on a poly(3-hexythiophene) (P3HT)/

CdSe QD interface. Such composites are promising candidatesfor hybrid solar cells1,24,25,34 because excitons generated in thepolymer produce long-lived charge carriers due to the efficientseparation of the electron−hole pairs across the P3HT/QDinterface.1 Recently, Haque and coauthors reported ultrafastextraction of electrons from photoexcited P3HT into CdS QDoccurring within 1 ps. The holes transferred from photoexcitedCdS QDs into P3HT over a range of time scales from 1 ps upto 2 ns.24 Several factors determine efficiencies and time scalesof charge transfer. Generally, large driving force, strong donor−acceptor coupling, and strong nonadiabatic coupling facilitateefficient charge separation. Following charge separation, theinterfacial electron−hole recombination exhibits a variety oftime scales, from picosecond to microsecond depending onsolar simulator light intensity.1 The measured electron−holerecombination is much slower in QD than pristine P3HT, 6300ps vs 90 ps, respectively.24 Despite the relatively fast electron−hole recombination inside P3HT, the fast electron transferfrom P3HT to the QDs ensures that both materials can be used

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in a symmetric manner: Sunlight absorption by both P3HT andQDs leads to the photovoltaic effect. Symmetric electron andhole dynamics is important for photovoltaic applications.Similar time scales for charge injection starting from twocomplementary materials eliminates additional channels forenergy losses. For instance, imbalance in the electron and holetransfer can lead to accumulation of excitons in one of thesubsystems. The exciton can undergo Auger-type relaxation inthe presence of charges injected from the other material viaformation of trions.42 Further, a large number of nondissociatedexcitons can decrease charge conductivity by providing energyfor charge scattering with higher frequency phonons.Figure 1 demonstrates the energy levels involved in the

photoinduced charge separation and recombination dynamics

at the type II P3HT/QD photovoltaic heterojunction. P3HTexcitation leads to electron transfer, whereas QD excitationresults in hole transfer, ①. Competing with the separation, theweakly bound electron and hole can undergo electron−holerecombination inside either material, ②. Following theseparation, the charges can recombine at the interface, ③.The charge transfer, energy relaxation, interfacial electron−holerecombination, and electron−hole recombination insidepolymer and QD occur in parallel and compete with eachother.The nonadiabatic molecular dynamics simulation of the

charge transfer, energy relaxation, and charge recombinationdynamics are performed using the mixed quantum-classicalfewest-switches surface hopping technique43 implementedwithin the time-dependent Kohn−Sham theory.44,45 Thelighter electrons are treated quantum mechanically, whereasthe nuclei, which are much heavier and slower, are treatedclassically. The approach provides a detailed ab initio picture ofthe coupled electron-vibrational dynamics on the atomic scaleand in the time domain. The method was applied to studyphotoinduced processes in a variety of materials, includingcarbon nanotubes,46 fullerenes,13 graphanes,47 semiconduct-ing,48,49 and metallic nanocrystals.50,51 The method was alsoused to investigate charge and energy transfer at interfaces ofpolymers with carbon nanotubes52 and of TiO2 withmolecules,53 quantum dots,54 and graphene.55 After an initialexcitation, the simulated system is allowed to evolve in theelectronic state manifold coupled to phonons. Nonadiabaticcouplings, computed on the fly, cause electronic transitions. Adetailed description of the method is presented in our previouspublications56,57 and in the Supporting Information.

The simulation cell contains a P3HT oligomer composed ofsix thiophene units and a CdS QD involving 33 S and 33 Cdatoms (Figure 2). The cell length is 23.7 Å along the polymer

backbone.52 The P3HT side-chains are included fully. An 8 Å ofvacuum surrounding the system everywhere in the directionperpendicular to the polymer chain eliminates spuriousinteractions between the periodic images. The type II bandalignment of the P3HT/Cd33S33 interface, Figure 3, agrees withthe experiments.1,24,34 The electron−hole recombination issimulated separately with the same isolated P3HT and the QD.The interaction between P3HT and the QD determines the

rates of the electron and hole transfer, as well as the

Figure 1. Diagram of the energy levels involved in the photoinducedcharge separation and recombination dynamics. Absorption of aphoton hv by either P3HT or the CdS QD leads to charge separation① due to electron or hole transfer, respectively. Competing with theseparation, the weakly bound electron and hole can undergo electron−hole recombination ② inside either material. Following the separation,the charges can recombine at the interface ③.

Figure 2. Side views of the simulation cell along the periodic direction(top panel) and perpendicular to the periodic direction (bottompanel). Shown are the geometries of the P3HT/Cd33S33 systemoptimized at 0 K (left panel) and during molecular dynamics at 300 K(right panel). The light gray, brown, yellow, and pink spheres denoteH, C, S, and Cd atoms, respectively.

Figure 3. (a) Projected densities of states (PDOS) of the interactingP3HT and QD subsystems. Although QD is quasi-0-dimensional andP3HT is quasi-1-dimensional, the QD has higher DOS in theinteraction region than P3HT, the opposite to the initial expectation.The inset shows the energy offsets between the donor and acceptorstates for the electron and hole transfer. Energy loss during the transferdecreases device efficiency. (b) Charge densities of the donor andacceptor orbitals for the electron and hole transfer. The electron donorstate is delocalized significantly between P3HT and QD. Similarity, thehole donor state is also shared by QD and P3HT. The acceptor statesare localized in both cases. The vertical arrows between (a) and (b)relate the donor and acceptor orbital densities to the energies.

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competition of the transfer processes with energy relaxationand charge recombination. The P3HT/QD geometry andseparation characterize the strength of the interfacial inter-action. Figure 2 shows the two projections of the simulatedsystem, along and perpendicular to the P3HT backbone. Theleft panels show the system relaxed at 0 K, whereas the rightpanels give a snapshot from MD simulation at 300 K.Comparing the zero- and finite-temperature geometries, weobserve that P3HT side-chains interact more strongly with theQD at room temperature. The interaction is primarily van derWaals. It is facilitated by thermal disorder and increasedentropy, which destroy the perfect P3HT geometry and allowthe side-chains to approach the QD. At the same time, theaverage separation between the QD and the P3HT backboneincreases from 2.98 to3.47 Å in the higher temperature. P3HTis flat at 0 K, indicating that the π-electron system remainsintact and the P3HT-QD interaction is purely van der Waals.As temperature increases, the QD structure changes littlebecause the QD atoms are coordinated multiple times. Muchmore pronounced changes occur within the polymer, Figure 2.The P3HT side-chains fluctuate strongly, embracing the QD.The P3HT backbone undergoes undulating motions. The out-of-plane displacements of the carbon and sulfur atoms have astrong effect on the electron, hole, and energy relaxationdynamics because the motions perturb the π-electronconjugation and change the energies of the P3HT electronicstates. The low-frequency out-of-plane P3HT motions and CdSacoustic modes affect electronic energy levels. High-frequencycarbon−carbon stretching modes do not significantly alter theelectronic energies. They contribute to the nonadiabaticcoupling because they are fast and create large nuclearvelocities, dR/dt, that enter the nonadiabatic coupling matrixelement, −iℏ⟨ φk|▽R|φm⟩•dR/dt.Figure 3a shows the projected density of states (PDOS) of

P3HT and the QD in the P3HT/QD composite at 0 K. ThePDOS clearly demonstrates formation of a type-II photovoltaicheterojunction between P3HT and the QD, as illustratedexplicitly with the band edge offset in the inset. The lowestenergy excited state formed at the heterojunction is a chargetransfer state with the electron localized on the QD LUMO andthe hole localized on the P3HT HOMO. Photoexciation ofP3HT results in electron transfer to the QD, whereasphotoexcitation of the QD induces hole transfer to P3HT.The energies lost to vibrational motions during the electronand hole transfer events are 0.87 and 1.41 eV, respectively.These values are canonical thermal averages. They indicate that1.5 times more energy is lost after the QD excitation than afterthe P3HT excitation. However, it should be noted that the QDband gap can be tuned by changes in size and shape, andtherefore, the orbital offset and energy loss can be reduced.Combined with the fact that QDs can harvest a broad range ofthe solar spectrum and generate multiple excitons, the QDphotoexcitation can give rise to more efficient solar cells thanthe P3HT photoexcitation.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,58 which is smaller than the electron and hole transferdriving force of 0.87 and 1.41 eV (inset of Figure 3a). Theexciton binding energies of CdS QDs range from 0.1 to 0.4eV,59 depending on the QD size and dielectric constant of thesurrounding medium that screens the Coulomb interactions. Anonpolar medium such as P3HT has a small screening effect.

Both the electron transfer driving force of 0.87 eV and the holetransfer driving force of 1.41 eV are larger than exciton bindingenergy of P3HT and QD, respectively. Thus, one can anticipatebarrier-less photoinduced electron and hole transfer and arange of scenarios. Different QDs will exhibit varying bandoffsets relative to P3HT and other polymers, affecting thedriving force for the charge separation.The charge separation efficiency depends on a number of

other factors in addition to the driving force, including thedonor−acceptor coupling and the density of acceptor states.Figure 3a shows that PDOS of the QD is higher than of P3HT.In a traditional description, QDs are viewed as quasizerodimensional materials, whereas polymers are infinitely periodicin one dimension. Simple models predict discrete energy levelsin QDs and continuous bands in polymers. However, theatomistic calculations give a different picture. Generally, QDsexhibit discrete levels only close to the band gap.60,61 Indeed,Figure 3a shows that the CdS QD LUMO is separated from theLUMO + 1 by about 0.5 eV. At higher energies relevant for thephotoinduced charge separation, the QD spectrum iscontinuous. Note that the Auger-assisted electron transfer,observed in the QD/molecule hybrids,40,41 is not required inthe present case because, unlike molecules, polymers havecontinuous (though low) DOS.Cd33S33 used in the current simulation is a “magic” size

cluster. It is closely related to Cd33Se33, which was observedexperimentally,62 and whose properties have been studiedextensively by Galli and co-workers63 and our group.60,64 Thecluster has the stoichiometry and structure needed to eliminatedefect states and to “heal” the surface. One may expect thatsurface passivation by an inorganic shell or organic ligandsshould change significantly the electronic structure of Cd33Se33.Our previous calculations show that surface reconstruction ishighly efficient in Cd33Se33, which maintains the wurtzitetopology of bulk CdSe. The calculated DOS of bare Cd33Se33agrees well with the DOS of core/shell Cd33Se33/Zn78S78.Differences are observed only at high energies due tocontributions of ZnS, which has larger band gap.60 Aliphaticsurface ligands would increase the donor−acceptor separationand decrease the donor−acceptor electronic coupling. Thecreated energy barrier would slow down both electron and holetransfer. The additional energy barrier can be eliminated bycoordinating the conjugate organic subsystem directly with theinorganic QD.40,41,65−67 At high energies, significant hybrid-ization between electronic states of QD and ligands facilitateintraband relaxation.64

The strength of the donor−acceptor coupling is directlyreflected in the amount of mixing between the donor andacceptor orbitals. The mixing occurs due to interaction of the π-electron subsystem of P3HT and s, p, and d electrons of theundercoordinated S and Cd atoms of the QD. In general, thestronger the interaction, the more significant the mixing. Thekey electron and hole orbitals that participate in the chargetransfer processes are shown in Figure 3b. The vertical arrowspointing from 3b to 3a show the energies of these states. Thedonor state for the electron transfer, the first picture in the leftpanel of Figure 3b, is delocalized significantly between P3HTand the QD, indicating strong donor−acceptor coupling.Similarity, the donor state for the hole transfer, the secondpicture in the right panel of Figure 3b, is also shared by P3HTand QD, suggesting that the donor−acceptor coupling is strongin this case as well. The donor states for the electron and holetransfers are mixed between P3HT and the QD because both

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subsystems have states at the donor energies. The acceptorstates for the electron and hole transfers are strongly localized(middle pictures in Figure 3b) because these orbitals areisolated energetically from the orbitals of the donor subsystems.The driving force for the hole transfer from the QD to P3HT

is large, but the density of P3HT acceptor states is small(Figure 3a). In comparison, the driving force for the electrontransfer from P3HT to the QD is small, but the density of QDacceptor states is large. The leveling of the two factors leads tosimilar electron and hole injection times, several hundredfemtoseconds, in agreement with the experiment.24 Thedonor−acceptor coupling is similar for both processes, andtherefore, the observed relationship between the acceptor statedensities is essential for the balanced charge separationdynamics. The observed relationship is opposite to what onemay expect a priori.In addition to the details of the electronic structure of the

hybrid system (Figure 3), knowledge of electron−phononinteractions is necessary for understanding of the photoinducedcharge separation and energy relaxation. For instance,introduction of a molecular bridge in the C60-QD systemaccelerated electron transfer, even though the bridge wasinsulating and created a tunneling barrier.68,69 The phenomen-on was explained by efficient electron−phonon energy transferfacilitated by the high-frequency modes of the bridge.70

Generally, vibrational motions alter electronic energies of thedonor and acceptor species, create nonadiabatic couplings,promote charge transfer, and cause energy losses to heat.Figure 4 shows Fourier transforms (FTs) of the energy

offsets between the donor and acceptor states for the electron

and hole transfer. The top panel depicts the FT of the gapbetween the P3HT and QD LUMOs, whereas the bottompanel shows the FT of the gap between the P3HT and QDHOMOs. The charge densities of the HOMO and LUMOorbitals are shown in Figure 3b. The electron transfer ispromoted by the low-frequency Cd−S phonons and thetorsional modes of the polymer < 300 cm−1. The high-frequency C−C stretching motions of P3HT contribute onlyslightly. The photoexcited state is delocalized significantly

between P3HT and the QD, whereas the final state is localizedon the QD (Figure 3b), and therefore the CdS slow modesdominate. The high frequency modes of P3HT contributemore strongly to the hole dynamics (Figure 4). This is becausethe hole acceptor state is localized on P3HT, whereas the holedonor state is delocalized between the QD and P3HT.Generally, high frequency modes are more efficient inpromoting charge transfer. Participation of high frequencymodes in the hole transfer offsets the low density of acceptorstates, further helping to balance the rates of the electron andhole injection.The dynamics of the charge separation and energy relaxation

processes are characterized in Figure 5. Figure 6 presents thecharge recombination dynamics. Parts a and b of Figure 5 showcharge transfer, whereas parts c and d give energy relaxation.The times reported in the figure are obtained by exponentialfitting for electrons, f(t) = f(t0) + Aexp(−t/τ1), and Gaussianfitting for holes, f(t) = f(t0) + Bexp(−0.5(−t/τ2)2). Thequalitative difference in the electron and hole dynamics areremarkable, especially for the energy relaxation (Figure 5c,d).The transfer of the electron is exponential (Figure 5a) becausethe density of final states is high (Figure 3a). The hole transferis Gaussian (Figure 5c) because the final state density isinsufficient to transition from the dynamics to the kineticsregime. The phenomenon is particularly pronounced for theenergy relaxation (Figure 5d), which proceeds along the lowDOS manifold (Figure 3a).The electron transfer process is faster than the hole transfer

because of the higher density of acceptor states in the QD. Theaverage absolute values of the nonadiabatic coupling for theelectron and hole relaxation are similar, 6.93 and 4.73 meV,respectively. The somewhat larger value contributes to thefaster dynamics of the electrons. The calculated electrontransfer time is faster than the experimental value, whereas thehole transfer time agrees well with the measurement.24 Mostlikely, the electron transfer from P3HT is faster in thecalculation than in the experiment because the experimentaldata accounts for electron diffusion from distant P3HT chainstoward the QD. In comparison, the initial step of the holetransfer from the QD involves P3HT chains next to the QD,and it is faithfully represented by the simulation.The charge-phonon energy relaxation is consistently slower

than the charge separation (Figure 5): The injected charges are“hot” and maintain excess energy for several picoseconds. Thesituation is favorable for the charge separation because slowenergy losses assist in overcoming the electron−hole bindingenergy at the interface and because it allows band-like chargetransport at long distances.71,72

Solar cell performance is affected by charge separation,relaxation, and recombination. Figure 6 characterizes therecombination processes. Both electron−hole recombinationin pristine species and at the interface of the hybrid systemaffect the charge carries lifetime, and in turn, solar cell currentand performance. The exponential fits, f(t) = exp(−t/τ) + B, ofthe time-resolved populations describing the electron−holerecombination in P3HT and the QD produce 18 and 7580 ps,in good agreement with the experimental data.24 The lifetime ofthe excited electron−hole pair is significantly longer inside theQD than P3HT, as should be expected: The QD is rigid andhas only low frequency phonons available to accept theelectronic energy. Organic polymers have a wider range ofphonons, including high frequency vibrations that provide abetter match to the electronic energy quanta. Due to sample

Figure 4. Fourier transforms of the energy gaps 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 P3HT torsions and Cd−S vibrations. Thehole couples almost exclusively to the high-frequency modes. This isbecause the hole acceptor state is localized on P3HT composed oflight atoms, whereas the electron acceptor state is on CdS composedof heavy atoms, Figure 3. The involvement of a broader range ofvibrations provides additional channels for the electron transfer.

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differences, experiments report a broad range of excitonslifetimes in conjugated polymers.73,74 Because we employ arelatively short piece of the polymer that is in direct contactwith the QD, we overlocalize polymer states. This increases theelectron−phonon coupling and leads to faster energy losses.Considering pure polymer, the model can be viewed as arepresentation of localized trap-like states, which are likely

responsible for the faster component of the experimentallyobserved time-scales.73,74 Our polymer model is appropriate forstudying the local polymer/QD interactions. Following thephotoinduced charge separation, the electron and hole residingin the QD LUMO and the P3HT HOMO recombine within 33ps. This time falls within the experimental range.1

The differences in the QD and P3HT light absorptionproperties, the photoinduced electron and hole transferdynamics, and various charge recombination processes can beutilized for optimization of light harvesting, voltage, and currentin solar cells. The current study shows that light harvesting byboth QDs and polymers leads to efficient charge separation dueto fast electron and hole transfer compared to excitonrecombination. The electron−hole pair can survive tens ofpicoseconds at the interface, at which point it should beseparated farther. Electron−hole pairs live much longer in QDsthan polymers. Therefore, light harvesting by QDs is morefavorable for the solar cell performance. By varying the QD size,one can harvest light over a broader range solar spectrum andgenerate multiple electron−hole pairs. Further insights intosolar cell performance require studies of morphology andcharge diffusion.In summary, we investigated the photoinduced electron and

hole transfer dynamics, energy relaxation, and electron−holerecombination in a P3HT/QD hybrid. The behavior of P3HTand the QD in the interaction region requires an explicitatomistic description. The QD has high bulk-like density ofstates, whereas P3HT behaves similarly to a molecule and has alow state density. Electron injection into the QD is fast andexponential due to high acceptor state density. The holedynamics involving P3HT is slower and notably nonexponen-tial. The hole couples to high frequency modes of P3HT,

Figure 5. Charge separation dynamics. Top panels (a, b) show decay of the population of the electron and hole donor states. Bottom panels (c, 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 fittedby an exponential. The hole state population (b) exhibits Gaussian decay. The energy relaxation for hole (d) cannot be fitted by a single exponential,a single Gaussian function, or a combination thereof. The photoexcited electron is rapidly transferred from P3HT to QD and then relaxes bycoupling to phonons. The hole transfer from QD to P3HT occurs by slower nonadiabatic transitions. The hole-phonon energy exchange exhibitsunusual behavior due to the low density of P3HT states, Figure 3a.

Figure 6. Charge recombination dynamics. The green, red, and blacklines give electron−hole recombination at the P3HT/QD interface,inside P3HT, and inside CdS QD, respectively. The population decaystarts as Gaussian and then proceeds exponentially. The interfacialrecombination occurs faster than that in the QD and slower than thatin the polymer, in agreement with the experiment.

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whereas the electron interacts with low frequency modes of theQD and the polymer. The charge separation is an order ofmagnitude faster than the energy losses, whereas the chargerecombination processes are 1−3 orders of magnitude slower.The calculated time scales agree well with the experiments. Theelectron−hole recombination is much faster in P3HT than theQD, rationalizing why experiments exhibit multiple time scalesof hole transfer from the QD to P3HT, whereas the electrontransfer from P3HT to the QD does not occur beyond the firstpicosecond. The reported simulations provide a detaileddescription of the charge and energy transfer dynamics in thehybrid nanoscale material, leading to conclusions important fordesign of photovoltaic and photocatalytic devices.

■ ASSOCIATED CONTENT*S Supporting InformationA description of the simulation methodology is available. TheSupporting Information is available free of charge on the ACSPublications website at DOI: 10.1021/nl5046268.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: prezhdo@usc.edu.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSR.L. is grateful to the Science Foundation Ireland SIRGProgram (grant no. 11/SIRG/E2172), UCD Seed FundingSF1003. O.V.P. acknowledges grant CHE-1300118 from theU.S. National Science Foundation.

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