Letter pubs.acs.org/NanoLett
Time-Domain Ab Initio Analysis of Excitation Dynamics in a Quantum Dot/Polymer Hybrid: Atomistic Description Rationalizes Experiment Run Long†,‡ and Oleg V. Prezhdo*,§ †
College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, 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 cells are an attractive alternative to the traditional cells. The original, simple models postulate that one-dimensional polymers have continuous energy levels, while zero-dimensional QDs exhibit atom-like electronic structure. A realistic, atomistic viewpoint provides an alternative description. Electronic states in polymers are molecule-like: finite in size and discrete in energy. QDs are composed of many atoms and have high, bulk-like densities of states. We employ ab initio timedomain simulation to model the experimentally observed ultrafast photoinduced dynamics in a QD/polymer hybrid and show that an atomistic description is essential for understanding the time-resolved experimental data. Both electron and hole transfers across the interface exhibit subpicosecond time scales. The interfacial processes are fast due to strong electronic donor−acceptor, as evidenced by the densities of the photoexcited states which are delocalized between the donor and the acceptor. The nonadiabatic charge−phonon coupling is also strong, especially in the polymer, resulting in rapid energy losses. The electron transfer from the polymer is notably faster than the hole transfer from the QD, due to a significantly higher density of acceptor states. The stronger molecule-like electronic and charge-phonon coupling in the polymer rationalizes why the electron−hole recombination inside the polymer is several orders of magnitude faster than in the QD. As a result, experiments exhibit multiple transfer times for the long-lived hole inside the QD, ranging from subpicoseconds to nanoseconds. In contrast, transfer of the short-lived electron inside the polymer does not occur beyond the first picosecond. The energy lost by the hole on its transit into the polymer is accommodated by polymer’s high-frequency vibrations. The energy lost by the electron injected into the QD is accommodated primarily by much lower-frequency collective and QD modes. The electron dynamics is exponential, whereas evolution of the injected hole through the low density manifold of states of the polymer is highly nonexponential. The time scale of the electron−hole recombination at the interface is intermediate between those in pristine polymer and QD and is closer to that in the polymer. The detailed atomistic insights into the photoinduced charge and energy dynamics at the polymer/QD interface provide valuable guidelines for optimization of solar light 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
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colloidal QD exhibit better morphological stability and higher electron mobilities. In addition, QDs improve light harvesting due to large absorption cross sections, which are easily tunable over the entire solar spectrum. The electron−phonon relaxation dynamics in QDs has attracted intense attention.4−14 Hot-carrier generation and carrier multiplication provide opportunities to improve conversion efficiencies of QD solar cells by reducing the loss of high-energy carriers.15,16 Novel synthetic methods enable control over size, shape,
ybrid photovoltaic cells based on polymers and inorganic nanocrystals possess significant potential for low-cost, scalable solar power conversion. Polymers harvest solar light and donate electrons in organic solar cells.1 Polymer solar cells offer the advantages of solution processing and straightforward chemical synthesis.2 At the same time, Coulomb interactions between charge carriers are significant in organic matter due to low dielectric constants, giving rise to strongly bound electron− hole pairs rather than to free charge carriers.3 Combined with the highly inhomogeneous energy landscape of electronic states, this drawback leads to losses of energy and charge carriers that significantly reduce the power conversion efficiency of polymer-based solar cells. Compared to fullerenes, used as electron acceptors in traditional organic solar cells, © XXXX American Chemical Society
Received: December 2, 2014 Revised: June 2, 2015
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Nano Letters composition, and structure of nanocrystal samples,17 broadening the spectrum of photocatalytic and photovoltaic applications. The combined advantages of organic polymer and inorganic QD materials open new ways to enhance further the solar cell performance.18 Many scientists have focused on the charge dynamics in polymer/fullerene systems forming the basis for organic solar cells.19−21 Understanding of these materials is limited due to unknown morphology and ordering. On the one hand, experiments reveal that ultrafast charge transport through delocalized band-like states in fullerene aggregates leads to efficient photovoltaice devices.22 Theoretical work indicates that only carriers that are thermally activated into the fullerene band states contribute to charge transport.23 On the other hand, poor contact between fullerenes can result in low density of interacting electronic states, leading to low light-conversion efficiencies. Replacing fullerene electron acceptors with a nanostructured inorganic semiconductor provides an alternative design, opening up a new class of hybrid organic/inorganic system.1,24−28 Hybrid systems are interesting due to both the relative ease of controlling the microstructure and the potential for efficient charge separation at low driving forces. The offsets between the donor and acceptor lowest unoccupied molecule orbitals (LUMO) for electron transfer and highest occupied molecular orbitals (HOMO) for hole transfer can be small because inorganic matter has high dielectric permittivity, lowering the electron−hole Coulomb binding energy and facilitating charge separation. In comparison, the low dielectric constant of organic matter results in strong Coulomb attraction between charges in polymer/fullerene hybrids, allowing time for losses due to nonradiative relaxation and charge recombination.29−32 Rather than an infinite semiconductor, a conjugated polymer is well represented by a collection of conjugated segments (oligomers) with different length and structural disorder.33 Relatively few studies have focused on charge generation in polymers with inorganic absorbing acceptors.24,25,27,34 Photoexcitation of the polymer can lead to electron transfer, whereas photoexcitation of the QD can result in hole transfer in such systems. The kinetics of the hole have not been widely studied, through it has been shown that hole transfer can play an important role in hybrid solar cells28 as well as in semiconductor sensitized solar cells.35 Often, the electron and hole transfer dynamics show different time scales. For example, in the CdSe QD and poly[2-methoxy-5-(3′,7′dimethyloctyloxy)-1,4-phenylenevinylene] (MDMO-PPV) hybrid system, electron transfer from the polymer to the QD occurs on a subpicosecond time scale, whereas hole tranfser shows a broad range of times from subpiconsecond to several nanoseconds.28 Similar electron and hole transfer dynamics have been reported for the CdS QD and P3HT hybrid system.24 The experiments motivate the current time-domain ab initio study. Traditionally, one employs Marcus theory36−39 in order to characterize the dependence of the electron transfer rate dependence of donor−acceptor coupling and energy gap, the latter known as the driving force. Developed initially for intraand intermolecular electron transfer, Marcus theory assumes a large rearrangement of nuclear configuration, which brings the electronic donor and acceptor energies in resonance. The energy of the nuclear rearrangement is called the reorganization energy. The electron transfer rate in the traditional Marcus theory reaches a maximum when the reorganization energy matches the donor−acceptor gap, ovbiating the need for the
nuclear rearrangement. If the energy gap becomes too large, the nuclear rearrangement requires thermal activation again, and the rate decreases, leading to the so-called Marcus inverted region.37 Our recent time-domain ab initio simulation40 has rationalized the absence of the Marcus inverted region in electron transfer from a CdSe QD to a molecule.41 Rather than requiring a nuclear rearrangement, energy conservation is achieved by an Auger-type hole excitation in the QD electron donor. The complexities and ultrafast time scales of charge transfer dynamics in nanoscale materials and the competion of charge transfer with other processes, including nonradiative relaxation and Auger-type energy exchange, strongly motivate time-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 than polymers in the QD/polymer interaction region, QDs have a much higher projected density of states (PDOS). The conjugated polymer acts more as a molecule than an infinite semiconductor. The charge transfer to the QD is faster than to the polymer due to a higher density of acceptor states. Both transfers occur on a subpicosecond time-scale as a result of strong donor−acceptor coupling, in excellent agreement with the experimental work.1,24 The hole injected into the polymer loses its energy by coupling to high-frequency molecular vibrations. In comparison, the electron couples to a broader range of motions, including low-frequency QD modes and collective polymer vibrations. The dynamics of electron injection into the QD is exponential, as expected with a high density of acceptor states. The dynamics of hole injection into the polymer and the subsequent hole nonradiative relaxation are highly nonexponential due to low density of local polymer states. The electron−hole recombination at the interface is slower than the electron−hole recombination in the polymer and faster than that in the QD, also in agreement with the experiment. The recombination rates affect directly the range of the observed charge separation time scales: Long excited state lifetime of the QD leads to a broad range of hole injection times. The efficient electron and hole transfers guarantee that both polymer and QD can be used as sunlight absorbers. The long excitation lifetime inside the inorganic medium suggests that efficient photovoltaic devices can have a high QD concentration. The study focuses on a poly(3-hexythiophene) (P3HT)/ CdSe QD interface. Such composites are promising candidates for hybrid solar cells1,24,25,34 because excitons generated in the polymer produce long-lived charge carriers due to the efficient separation of the electron−hole pairs across the P3HT/QD interface.1 Recently, Haque and coauthors reported ultrafast extraction of electrons from photoexcited P3HT into CdS QD occurring within 1 ps. The holes transferred from photoexcited CdS QDs into P3HT over a range of time scales from 1 ps up to 2 ns.24 Several factors determine efficiencies and time scales of charge transfer. Generally, large driving force, strong donor− acceptor coupling, and strong nonadiabatic coupling facilitate efficient charge separation. Following charge separation, the interfacial electron−hole recombination exhibits a variety of time scales, from picosecond to microsecond depending on solar simulator light intensity.1 The measured electron−hole recombination is much slower in QD than pristine P3HT, 6300 ps vs 90 ps, respectively.24 Despite the relatively fast electron− hole recombination inside P3HT, the fast electron transfer from P3HT to the QDs ensures that both materials can be used B
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The simulation cell contains a P3HT oligomer composed of six thiophene units and a CdS QD involving 33 S and 33 Cd atoms (Figure 2). The cell length is 23.7 Å along the polymer
in a symmetric manner: Sunlight absorption by both P3HT and QDs leads to the photovoltaic effect. Symmetric electron and hole dynamics is important for photovoltaic applications. Similar time scales for charge injection starting from two complementary materials eliminates additional channels for energy losses. For instance, imbalance in the electron and hole transfer can lead to accumulation of excitons in one of the subsystems. The exciton can undergo Auger-type relaxation in the presence of charges injected from the other material via formation of trions.42 Further, a large number of nondissociated excitons can decrease charge conductivity by providing energy for charge scattering with higher frequency phonons. Figure 1 demonstrates the energy levels involved in the photoinduced charge separation and recombination dynamics
Figure 2. Side views of the simulation cell along the periodic direction (top panel) and perpendicular to the periodic direction (bottom panel). Shown are the geometries of the P3HT/Cd33S33 system optimized at 0 K (left panel) and during molecular dynamics at 300 K (right panel). The light gray, brown, yellow, and pink spheres denote H, C, S, and Cd atoms, respectively.
Figure 1. Diagram of the energy levels involved in the photoinduced charge separation and recombination dynamics. Absorption of a photon hv by either P3HT or the CdS QD leads to charge separation ① due to electron or hole transfer, respectively. Competing with the separation, 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.
backbone.52 The P3HT side-chains are included fully. An 8 Å of vacuum surrounding the system everywhere in the direction perpendicular to the polymer chain eliminates spurious interactions between the periodic images. The type II band alignment of the P3HT/Cd33S33 interface, Figure 3, agrees with the experiments.1,24,34 The electron−hole recombination is simulated 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
at the type II P3HT/QD photovoltaic heterojunction. P3HT excitation leads to electron transfer, whereas QD excitation results in hole transfer, ①. Competing with the separation, the weakly bound electron and hole can undergo electron−hole recombination inside either material, ②. Following the separation, the charges can recombine at the interface, ③. The charge transfer, energy relaxation, interfacial electron−hole recombination, and electron−hole recombination inside polymer and QD occur in parallel and compete with each other. The nonadiabatic molecular dynamics simulation of the charge transfer, energy relaxation, and charge recombination dynamics are performed using the mixed quantum-classical fewest-switches surface hopping technique43 implemented within the time-dependent Kohn−Sham theory.44,45 The lighter electrons are treated quantum mechanically, whereas the nuclei, which are much heavier and slower, are treated classically. The approach provides a detailed ab initio picture of the coupled electron-vibrational dynamics on the atomic scale and in the time domain. The method was applied to study photoinduced processes in a variety of materials, including carbon nanotubes,46 fullerenes,13 graphanes,47 semiconducting,48,49 and metallic nanocrystals.50,51 The method was also used to investigate charge and energy transfer at interfaces of polymers with carbon nanotubes 52 and of TiO2 with molecules,53 quantum dots,54 and graphene.55 After an initial excitation, the simulated system is allowed to evolve in the electronic state manifold coupled to phonons. Nonadiabatic couplings, computed on the fly, cause electronic transitions. A detailed description of the method is presented in our previous publications56,57 and in the Supporting Information.
Figure 3. (a) Projected densities of states (PDOS) of the interacting P3HT and QD subsystems. Although QD is quasi-0-dimensional and P3HT is quasi-1-dimensional, the QD has higher DOS in the interaction region than P3HT, the opposite to the initial expectation. The inset shows the energy offsets between the donor and acceptor states for the electron and hole transfer. Energy loss during the transfer decreases device efficiency. (b) Charge densities of the donor and acceptor orbitals for the electron and hole transfer. The electron donor state is delocalized significantly between P3HT and QD. Similarity, the hole donor state is also shared by QD and P3HT. The acceptor states are localized in both cases. The vertical arrows between (a) and (b) relate the donor and acceptor orbital densities to the energies. C
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Both the electron transfer driving force of 0.87 eV and the hole transfer driving force of 1.41 eV are larger than exciton binding energy of P3HT and QD, respectively. Thus, one can anticipate barrier-less photoinduced electron and hole transfer and a range of scenarios. Different QDs will exhibit varying band offsets relative to P3HT and other polymers, affecting the driving force for the charge separation. The charge separation efficiency depends on a number of other factors in addition to the driving force, including the donor−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 quasizero dimensional materials, whereas polymers are infinitely periodic in one dimension. Simple models predict discrete energy levels in QDs and continuous bands in polymers. However, the atomistic calculations give a different picture. Generally, QDs exhibit discrete levels only close to the band gap.60,61 Indeed, Figure 3a shows that the CdS QD LUMO is separated from the LUMO + 1 by about 0.5 eV. At higher energies relevant for the photoinduced charge separation, the QD spectrum is continuous. Note that the Auger-assisted electron transfer, observed in the QD/molecule hybrids,40,41 is not required in the present case because, unlike molecules, polymers have continuous (though low) DOS. Cd33S33 used in the current simulation is a “magic” size cluster. It is closely related to Cd33Se33, which was observed experimentally,62 and whose properties have been studied extensively by Galli and co-workers63 and our group.60,64 The cluster has the stoichiometry and structure needed to eliminate defect states and to “heal” the surface. One may expect that surface passivation by an inorganic shell or organic ligands should change significantly the electronic structure of Cd33Se33. Our previous calculations show that surface reconstruction is highly efficient in Cd33Se33, which maintains the wurtzite topology of bulk CdSe. The calculated DOS of bare Cd33Se33 agrees well with the DOS of core/shell Cd33Se33/Zn78S78. Differences are observed only at high energies due to contributions of ZnS, which has larger band gap.60 Aliphatic surface ligands would increase the donor−acceptor separation and decrease the donor−acceptor electronic coupling. The created energy barrier would slow down both electron and hole transfer. The additional energy barrier can be eliminated by coordinating the conjugate organic subsystem directly with the inorganic QD.40,41,65−67 At high energies, significant hybridization between electronic states of QD and ligands facilitate intraband relaxation.64 The strength of the donor−acceptor coupling is directly reflected in the amount of mixing between the donor and acceptor orbitals. The mixing occurs due to interaction of the πelectron subsystem of P3HT and s, p, and d electrons of the undercoordinated S and Cd atoms of the QD. In general, the stronger the interaction, the more significant the mixing. The key electron and hole orbitals that participate in the charge transfer processes are shown in Figure 3b. The vertical arrows pointing from 3b to 3a show the energies of these states. The donor state for the electron transfer, the first picture in the left panel of Figure 3b, is delocalized significantly between P3HT and the QD, indicating strong donor−acceptor coupling. Similarity, the donor state for the hole transfer, the second picture in the right panel of Figure 3b, is also shared by P3HT and QD, suggesting that the donor−acceptor coupling is strong in this case as well. The donor states for the electron and hole transfers are mixed between P3HT and the QD because both
competition of the transfer processes with energy relaxation and charge recombination. The P3HT/QD geometry and separation characterize the strength of the interfacial interaction. Figure 2 shows the two projections of the simulated system, along and perpendicular to the P3HT backbone. The left panels show the system relaxed at 0 K, whereas the right panels give a snapshot from MD simulation at 300 K. Comparing the zero- and finite-temperature geometries, we observe that P3HT side-chains interact more strongly with the QD at room temperature. The interaction is primarily van der Waals. It is facilitated by thermal disorder and increased entropy, which destroy the perfect P3HT geometry and allow the side-chains to approach the QD. At the same time, the average separation between the QD and the P3HT backbone increases from 2.98 to3.47 Å in the higher temperature. P3HT is flat at 0 K, indicating that the π-electron system remains intact and the P3HT-QD interaction is purely van der Waals. As temperature increases, the QD structure changes little because the QD atoms are coordinated multiple times. Much more pronounced changes occur within the polymer, Figure 2. The P3HT side-chains fluctuate strongly, embracing the QD. The P3HT backbone undergoes undulating motions. The outof-plane displacements of the carbon and sulfur atoms have a strong effect on the electron, hole, and energy relaxation dynamics because the motions perturb the π-electron conjugation and change the energies of the P3HT electronic states. The low-frequency out-of-plane P3HT motions and CdS acoustic modes affect electronic energy levels. High-frequency carbon−carbon stretching modes do not significantly alter the electronic energies. They contribute to the nonadiabatic coupling because they are fast and create large nuclear velocities, dR/dt, that enter the nonadiabatic coupling matrix element, −iℏ⟨ φ̃ k|▽R|φ̃ m⟩•dR/dt. Figure 3a shows the projected density of states (PDOS) of P3HT and the QD in the P3HT/QD composite at 0 K. The PDOS clearly demonstrates formation of a type-II photovoltaic heterojunction between P3HT and the QD, as illustrated explicitly with the band edge offset in the inset. The lowest energy excited state formed at the heterojunction is a charge transfer state with the electron localized on the QD LUMO and the hole localized on the P3HT HOMO. Photoexciation of P3HT results in electron transfer to the QD, whereas photoexcitation of the QD induces hole transfer to P3HT. The energies lost to vibrational motions during the electron and hole transfer events are 0.87 and 1.41 eV, respectively. These values are canonical thermal averages. They indicate that 1.5 times more energy is lost after the QD excitation than after the P3HT excitation. However, it should be noted that the QD band gap can be tuned by changes in size and shape, and therefore, the orbital offset and energy loss can be reduced. Combined with the fact that QDs can harvest a broad range of the solar spectrum and generate multiple excitons, the QD photoexcitation can give rise to more efficient solar cells than the P3HT photoexcitation. To achieve charge separation, the electron and hole must overcome the Coulomb attraction, characterized by the exciton binding energy. The exciton binding energy of P3HT is 0.3 eV,58 which is smaller than the electron and hole transfer driving force of 0.87 and 1.41 eV (inset of Figure 3a). The exciton binding energies of CdS QDs range from 0.1 to 0.4 eV,59 depending on the QD size and dielectric constant of the surrounding medium that screens the Coulomb interactions. A nonpolar medium such as P3HT has a small screening effect. D
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between P3HT and the QD, whereas the final state is localized on the QD (Figure 3b), and therefore the CdS slow modes dominate. The high frequency modes of P3HT contribute more strongly to the hole dynamics (Figure 4). This is because the hole acceptor state is localized on P3HT, whereas the hole donor state is delocalized between the QD and P3HT. Generally, high frequency modes are more efficient in promoting charge transfer. Participation of high frequency modes in the hole transfer offsets the low density of acceptor states, further helping to balance the rates of the electron and hole injection. The dynamics of the charge separation and energy relaxation processes are characterized in Figure 5. Figure 6 presents the charge recombination dynamics. Parts a and b of Figure 5 show charge transfer, whereas parts c and d give energy relaxation. The times reported in the figure are obtained by exponential fitting for electrons, f(t) = f(t0) + Aexp(−t/τ1), and Gaussian fitting for holes, f(t) = f(t0) + Bexp(−0.5(−t/τ2)2). The qualitative difference in the electron and hole dynamics are remarkable, especially for the energy relaxation (Figure 5c,d). The transfer of the electron is exponential (Figure 5a) because the density of final states is high (Figure 3a). The hole transfer is Gaussian (Figure 5c) because the final state density is insufficient to transition from the dynamics to the kinetics regime. The phenomenon is particularly pronounced for the energy relaxation (Figure 5d), which proceeds along the low DOS manifold (Figure 3a). The electron transfer process is faster than the hole transfer because of the higher density of acceptor states in the QD. The average absolute values of the nonadiabatic coupling for the electron and hole relaxation are similar, 6.93 and 4.73 meV, respectively. The somewhat larger value contributes to the faster dynamics of the electrons. The calculated electron transfer time is faster than the experimental value, whereas the hole transfer time agrees well with the measurement.24 Most likely, the electron transfer from P3HT is faster in the calculation than in the experiment because the experimental data accounts for electron diffusion from distant P3HT chains toward the QD. In comparison, the initial step of the hole transfer 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. The situation is favorable for the charge separation because slow energy losses assist in overcoming the electron−hole binding energy at the interface and because it allows band-like charge transport at long distances.71,72 Solar cell performance is affected by charge separation, relaxation, and recombination. Figure 6 characterizes the recombination processes. Both electron−hole recombination in pristine species and at the interface of the hybrid system affect the charge carries lifetime, and in turn, solar cell current and performance. The exponential fits, f(t) = exp(−t/τ) + B, of the time-resolved populations describing the electron−hole recombination in P3HT and the QD produce 18 and 7580 ps, in good agreement with the experimental data.24 The lifetime of the excited electron−hole pair is significantly longer inside the QD than P3HT, as should be expected: The QD is rigid and has only low frequency phonons available to accept the electronic energy. Organic polymers have a wider range of phonons, including high frequency vibrations that provide a better match to the electronic energy quanta. Due to sample
subsystems have states at the donor energies. The acceptor states for the electron and hole transfers are strongly localized (middle pictures in Figure 3b) because these orbitals are isolated 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 electron transfer from P3HT to the QD is small, but the density of QD acceptor states is large. The leveling of the two factors leads to similar electron and hole injection times, several hundred femtoseconds, in agreement with the experiment.24 The donor−acceptor coupling is similar for both processes, and therefore, the observed relationship between the acceptor state densities is essential for the balanced charge separation dynamics. The observed relationship is opposite to what one may expect a priori. In addition to the details of the electronic structure of the hybrid system (Figure 3), knowledge of electron−phonon interactions is necessary for understanding of the photoinduced charge separation and energy relaxation. For instance, introduction of a molecular bridge in the C60-QD system accelerated electron transfer, even though the bridge was insulating and created a tunneling barrier.68,69 The phenomenon was explained by efficient electron−phonon energy transfer facilitated by the high-frequency modes of the bridge.70 Generally, vibrational motions alter electronic energies of the donor 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
Figure 4. Fourier transforms of the energy gaps between the donor and acceptor states for the electron (top) and hole (bottom) transfer. The electron couples to both high-frequency C−C stretches and lowfrequency modes, including P3HT torsions and Cd−S vibrations. The hole couples almost exclusively to the high-frequency modes. This is because the hole acceptor state is localized on P3HT composed of light atoms, whereas the electron acceptor state is on CdS composed of heavy atoms, Figure 3. The involvement of a broader range of vibrations provides additional channels for the electron transfer.
and hole transfer. The top panel depicts the FT of the gap between the P3HT and QD LUMOs, whereas the bottom panel shows the FT of the gap between the P3HT and QD HOMOs. The charge densities of the HOMO and LUMO orbitals are shown in Figure 3b. The electron transfer is promoted by the low-frequency Cd−S phonons and the torsional modes of the polymer < 300 cm−1. The highfrequency C−C stretching motions of P3HT contribute only slightly. The photoexcited state is delocalized significantly E
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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 fitted by 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 by coupling to phonons. The hole transfer from QD to P3HT occurs by slower nonadiabatic transitions. The hole-phonon energy exchange exhibits unusual behavior due to the low density of P3HT states, Figure 3a.
responsible for the faster component of the experimentally observed time-scales.73,74 Our polymer model is appropriate for studying the local polymer/QD interactions. Following the photoinduced charge separation, the electron and hole residing in the QD LUMO and the P3HT HOMO recombine within 33 ps. This time falls within the experimental range.1 The differences in the QD and P3HT light absorption properties, the photoinduced electron and hole transfer dynamics, and various charge recombination processes can be utilized for optimization of light harvesting, voltage, and current in solar cells. The current study shows that light harvesting by both QDs and polymers leads to efficient charge separation due to fast electron and hole transfer compared to exciton recombination. The electron−hole pair can survive tens of picoseconds at the interface, at which point it should be separated farther. Electron−hole pairs live much longer in QDs than polymers. Therefore, light harvesting by QDs is more favorable for the solar cell performance. By varying the QD size, one can harvest light over a broader range solar spectrum and generate multiple electron−hole pairs. Further insights into solar cell performance require studies of morphology and charge diffusion. In summary, we investigated the photoinduced electron and hole transfer dynamics, energy relaxation, and electron−hole recombination in a P3HT/QD hybrid. The behavior of P3HT and the QD in the interaction region requires an explicit atomistic description. The QD has high bulk-like density of states, whereas P3HT behaves similarly to a molecule and has a low state density. Electron injection into the QD is fast and exponential due to high acceptor state density. The hole dynamics involving P3HT is slower and notably nonexponential. The hole couples to high frequency modes of P3HT,
Figure 6. Charge recombination dynamics. The green, red, and black lines give electron−hole recombination at the P3HT/QD interface, inside P3HT, and inside CdS QD, respectively. The population decay starts as Gaussian and then proceeds exponentially. The interfacial recombination occurs faster than that in the QD and slower than that in the polymer, in agreement with the experiment.
differences, experiments report a broad range of excitons lifetimes in conjugated polymers.73,74 Because we employ a relatively short piece of the polymer that is in direct contact with the QD, we overlocalize polymer states. This increases the electron−phonon coupling and leads to faster energy losses. Considering pure polymer, the model can be viewed as a representation of localized trap-like states, which are likely F
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Nano Letters
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whereas the electron interacts with low frequency modes of the QD and the polymer. The charge separation is an order of magnitude faster than the energy losses, whereas the charge recombination processes are 1−3 orders of magnitude slower. The calculated time scales agree well with the experiments. The electron−hole recombination is much faster in P3HT than the QD, rationalizing why experiments exhibit multiple time scales of hole transfer from the QD to P3HT, whereas the electron transfer from P3HT to the QD does not occur beyond the first picosecond. The reported simulations provide a detailed description of the charge and energy transfer dynamics in the hybrid nanoscale material, leading to conclusions important for design of photovoltaic and photocatalytic devices.
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ASSOCIATED CONTENT
* Supporting Information S
A description of the simulation methodology is available. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/nl5046268.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS R.L. is grateful to the Science Foundation Ireland SIRG Program (grant no. 11/SIRG/E2172), UCD Seed Funding SF1003. O.V.P. acknowledges grant CHE-1300118 from the U.S. National Science Foundation.
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DOI: 10.1021/nl5046268 Nano Lett. XXXX, XXX, XXX−XXX
