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Plasmon Induced Electron-Hole Separation at the Ag/TiO(110) Interface Jie Ma, and Shiwu Gao ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.9b03555 • Publication Date (Web): 08 Aug 2019 Downloaded from pubs.acs.org on August 10, 2019

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Plasmon Induced Electron-Hole Separation at the Ag/TiO2(110) Interface Jie Ma∗,† and Shiwu Gao∗,‡ †Key Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics and Advanced Research Institute of Multidisciplinary Science, Beijing Institute of Technology, Beijing 100081, China. ‡Beijing Computational Science Research Center, Beijing, 100193, China. E-mail: [email protected]; [email protected]

ABSTRACT Plasmon induced electron-hole separation at metal-semiconductor interfaces is an essential step in photovoltaics, photochemistry, and optoelectronics. Despite its importance in fundamental understandings and technological applications, the mechanism and dynamics of the charge separation under plasmon excitations have not been well understood. Here, the plasmon induced charge separation between a Ag20 nanocluster and a TiO2 (110) surface is investigated using time-dependent density functional theory simulations. It is found that the charge separation dynamics consists of two processes: during the first 10 fs an initial charge separation resulting from the plasmon-electron coupling at the interface, and a subsequent charge redistribution governed by the sloshing motion of the charge-transfer plasmon. The interplay between the two processes determines the charge separation and leads to the inhomogeneous layer-dependent distribution of hot carriers. The hot electrons are more efficient than the hot holes in the charge injection, resulting in the charge separation. Over 40 % of the hot electron-hole pairs are separated spatially from the interface. Finally, the second 1

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TiO2 layer receives the most net charges from the Ag nanocluster rather than the interfacial layer. These results reveal the mechanism and dynamics of the charge separation driven by the surface plasmon excitation, and have broad implications in plasmonic applications. KEYWORDS: electron-hole separation, plasmonics, hot carriers, direct charge injection, time-dependent density functional theory

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Collective oscillations of conducting electrons in finite systems form localized surface plasmon resonances (LSPR). The LSPR excitation induces large surface fields around the hot spots, which is the basis for various sensing and surface spectroscopies. 1–4 Simultaneously, the LSPR decays and generates hot electrons and holes. These hot carriers have received paramount attentions recently due to their potential applications in photovoltaics, optoelectronic devices, and photocatalytic reactions. 5–13 While the transient dynamics of hot carriers is difficult to measure experimentally, the generation rates and energy distributions of hot carriers have been obtained theoretically on several prototype structures. 14–19 In particular, the formation of LSPR and its decay into electron-hole pairs have recently been revealed using Kohn-Sham orbital-based wave function decompositions 20,21 in real-time time-dependent density functional theory (rt-TDDFT) simulations. So far, the theoretical studies have been mostly limited to isolated nanoclusters and bare metal surfaces, where hot carriers eventually recombine or dissipate into thermal excitations without leaving the metal surfaces. Interfacial plasmon induced electron-hole separation in heterostructures, which is the driving force underlying many plasmonic processes, remains largely unexplored. Early picture of the plasmon induced charge transfer (PICT) at metal-semiconductor interfaces is conceived of as a three-step scenario: it starts with the plasmonic generation of hot electron-hole pairs in metals, followed by the transport of hot carriers to the interface and then the transfer across the Schottky barrier at the metal-semiconductor interface. 6 The time scale of the three-step process was estimated to be 100–1000 fs based on the nonadiabatic molecular dynamics 22 and the Fowler’s law for the ballistic transport. 23 On such a time scale, the carrier injection should compete with the dissipation within the metal structures, which limits the efficiency for the charge separation. 24,25 There could also exist a surface photoemission phenomenon, which directly excites electrons from the metal to the semiconductor, but such transitions are usually too weak compared with plasmon absorptions. 26,27 Recently, a direct mechanism of the PICT has been proposed, 28–33 where the charge separation occurs on a much shorter time scale of ∼20 fs 28,30,33 with a quantum efficiency larger

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than 25 %. 28,31–33 The direct PICT mechanism was attributed to the electronic coupling between the LSPR of the Au tips and the CdSe nanorods. 28 Theoretical simulations of the PICT process between a Ag147 and a Cd33 Se33 cluster 34 seemed to support the ultrafast time scale for the direct charge transfer, but yielded no significant charge separations. Unfortunately, the cluster model is known to poorly describe the semiconductor surface, because it inevitably introduces artificial surface states and as a result cannot correctly reproduce the semiconductor band gap. 35,36 Both the surface states and the band gap are essential for the interfacial plasmonic coupling and the charge separation at the interface. The mechanism and dynamics of the electron-hole separation and its dependence on the specific interface compositions 28 have yet to be explored. Here, we report on the real-time dynamics of the plasmon induced charge separation at a prototype metal-semiconductor interface, a Ag20 nanocluster adsorbed on a rutile TiO2 (110) substrate, using rt-TDDFT simulations. The TiO2 is widely used 30–32,37–41 for photocatalysis and solar cells. The tunable LSPR of metallic nanostructures 42,43 can bring down the optical absorption band well below the semiconductor band gap (more than 3 eV for the TiO2 ) and can thus enhance the photoabsorption in the solar spectrum. 44 The Ag20 has been synthesized experimentally, which has a characteristic plasmon resonance in the visible range. 45,46 Upon adsorption, the plasmon peak becomes redshifted and broadened, which is a signature for the substrate screening and the electronic coupling between the Ag20 and the TiO2 substrate (interfacial electronic coupling). 47,48 It is found that the charge separation involves two main processes: i) an initial charge separation within 10 fs resulting from the direct plasmon-electron coupling via the interfacial states, and ii) after 10 fs, a further charge redistribution governed by the sloshing motion of the charge-transfer plasmon (CTP). The charge separation finishes at about ∼40 fs, when the CTP becomes quenched. We also find that the hot electrons are more efficient than the hot holes in the charge injection, due to different interfacial couplings. The hot holes are less mobile, and are mostly localized on the Ag20 and the first layer of the semiconductor substrate. This essential difference results

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in the charge separation at the interface, and determines the layer-resolved distributions of hot carriers in the TiO2 slab. Overall, 40 % of the excited electron-hole pairs are spatially separated, and the second TiO2 layer gets the most net charges from the Ag20 nanocluster. Our simulations are in line with the recently proposed direct PICT mechanism, 28 and reveal the charge separation dynamics in time and space domains. In addition, the role of the CTP mode in the charge injection and separation at the metal-semiconductor interface is unambiguously identified. RESULTS AND DISCUSSION Charge separation in the Ag20 -TiO2 system. The Ag20 nanocluster has been studied experimentally and theoretically. 45,46 It adopts the tetrahedral structure in the gas phase with a diameter estimated to be around 1 nm, and has a LSPR that is characteristic for the Ag nanoclusters. 45,46 In order to correctly reproduce the electronic structure and the LSPR of Ag in our simulations, the energies of the Ag d bands have been shifted according to the experimental data 49 following our earlier recipe. 20 The rutile TiO2 (110) substrate is modelled by a four-layer slab. To reproduce the correct electronic structure of the TiO2 , a similar correction to the energies of the Ti d bands is made, so that both the band gap of the bulk TiO2 and the electron affinity of the TiO2 (110) slab are in good agreement with the experimental data (see the Methods and the Supporting Information). The optimized structure of the Ag20 -TiO2 ground state is shown in Fig. 1a. The geometry of the Ag20 has been slightly distorted upon adsorption. This distortion does not appreciably affect the electronic structure nor the LSPR frequency of the isolated Ag20 . The optical absorption spectrum of the Ag20 -TiO2 system is shown in Fig. 1b. For comparison, the absorption spectra of the isolated Ag20 and the bare TiO2 (110) slab are also plotted. Upon adsorption, the LSPR peak of the Ag20 is redshifted from 3.6 eV for the isolated nanocluster to 3.2 eV in the adsorbed phase with a broadening of about 1 eV. The redshift is due to the substrate screening, and the broadening is a characteristic for the

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strong coupling in the Ag20 -TiO2 system, which allows possible direct charge injections via the LSPR decay. 47,48 The optical absorption of the TiO2 slab is very weak in this energy range. To excite the LSPR of the Ag20 nanocluster, we apply a laser pulse resonant to the LSPR frequency as marked by the black arrow in Fig. 1b to perform the rt-TDDFT simulations (see the Methods). The net charge in the TiO2 slab is plotted as a function of time in Fig. 2 (the black solid line), which is calculated using Eq. 11. The negative value shows that the excited electronhole pairs from the Ag20 have been spatially separated, and the hot electrons are injected into the TiO2 slab leaving the hot holes back in the Ag20 . Two distinct regions can be observed: during the first 10 fs, the magnitude of the net charge (the absolute value) rapidly increases as the hot electrons rush into the TiO2 slab; after 10 fs, the net charge shows some small fluctuations. The energy stored in the LSPR mode of the system, calculated using Eq. 15, is also plotted in Fig. 2 (the pink line). The LSPR decays in 10 fs, in accordance with the time scale of the initial charge separation. The rapid charge separation during the first 10 fs is thus directly driven by the LSPR decay. The time scale of the initial charge separation agrees favorably with the experimental results of 20 fs in Au-CdSe 28 and < 10 fs in Ag-TiO2 . 30 Similar fast charge separations were also observed in the Au-TiO2 system experimentally. 33 The charge separation efficiency is defined as the ratio of the injected net charges to the total excited electron-hole pairs (see the Supporting Information). The number of excited electron-hole pairs is shown in Fig. S1. After 10 fs, it converges to ∼0.0021, and thus in total over 40 % of the electron-hole pairs have been separated spatially with the electrons injected into the TiO2 substrate. The obtained efficiency can support the previous experimental observations. 28,31–33 After 10 fs, the small fluctuations of the net charge suggest that a small portion of the injected charges are sloshing back and forth between the Ag20 and the TiO2 slab, resulting in an additional charge redistribution up to 30–35 fs. As discussed below, such a charge redistribution is governed by the CTP mode formed in the coupled system. To pin down the LSPR effect on the charge separation, we have also performed a control

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calculation for the non-interacting system with the same laser pulse, yet freezing out its charge density response as described in ref. 20. In the non-interacting simulation, the Hamiltonian evolution is decoupled from the charge density response, i.e., H = H[ρ(0), t], which corresponds to the λ = 0 (non-interacting) model in ref. 50. Such a decoupling removes any plasmon excitations in the system. The net charge in the TiO2 slab for the non-interacting model is plotted as the blue dashed line in Fig. 2. Notice that decoupling the Hamiltonian from the density response ρ(t) effectively removes the electronic screening. The optical absorption calculated by the non-interacting Hamiltonian for the bare TiO2 slab is approximately ten times stronger than that obtained using the interacting Hamiltonian. Therefore, the net charge injection into the TiO2 is much overestimated in the non-interacting model. The dashed line in Fig. 2 is renormalized by the absorption strength of the bare TiO2 at the laser frequency. The net charge injection for the non-interacting model is much weaker, and remains nearly constant after 8 fs without showing any sloshing motion of the CTP mode. The minor charge separation reflects the laser induced direct coupling between the Ag20 nanocluster and the TiO2 in the absence of the plasmon excitation. The control calculation demonstrates that the LSPR of the Ag20 greatly enhances the charge separation between the Ag20 and the TiO2 slab. Hot electrons versus hot holes. The origin of the charge separation can be analyzed by projecting the time-dependent wave functions onto the eigen states. Figure 3a shows the populations on all the eigen states at 20 fs. The negative/positive values indicate the hot electron/hole populations according to Eq. 17. At t = 20 fs, the LSPR has fully decayed. The generated hot carriers are not yet thermalized, and their energy distributions can reflect the transient electron-hole transitions involved in the LSPR decay. The energy distribution of all the electron-hole pairs is displayed in Fig. S2, showing a single peak at 3.2 eV. According to the resonant condition ∆ωi,j ≈ 3.2 eV, we can identify two groups of the electron-hole-pair excitations as the LSPR decay channels: the group I corresponds to the transitions from the states around −1 eV (hot holes on the Ag s bands) to the states around 2.2 eV as marked

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by the red rectangles in Fig. 3a, and the group II corresponds to the transitions from the states around −2.7 eV (hot holes on the Ag d bands) to the states around 0.5 eV as marked by the blue rectangles in Fig. 3a. Figure 3b displays the separate contributions to the net charge in the TiO2 from the two excitation groups. The net charge is dominated by the group I excitations and its origin can be traced back to the nature of the electron-hole pairs. Figure 3c shows the density of states of the Ag s+p and d states of the Ag20 -TiO2 system respectively, and the grey regions mark the conduction and valence band continuums of the TiO2 slab. Comparing Fig. 3a with 3c, it is clear that the hot electrons of the group I are located inside the conduction band continuum of the TiO2 , and are mainly derived from the Ag s and p states. Figure 3d shows the hot electron density, defined by Eq. 12, at t = 20 fs. It is mainly on the surface of the Ag20 and on the Ti atoms (with a small portion on the oxygen atoms). The hot electron density is rather delocalized and extends to all the four layers of the TiO2 slab due to the strong hybridizations between the Ag s, p states and the TiO2 conduction bands. This explains why the hot electrons of the group I can be efficiently injected into the TiO2 slab. On the other hand, the hot holes of the group I are located inside the band gap of the TiO2 slab. The direct charge injection occurs through the resonant tunnelling between the Ag20 and the TiO2 . The hot holes of the group I have negligible injections, because there are no resonant states in the TiO2 slab. As a result, the hot electrons of the group I excitations are the major source for the charge injection. For the group II excitations, the hot electrons are located partly inside the conduction bands and partly within the band gap of the TiO2 . Only the hot electrons in the conduction bands can be eventually injected into the TiO2 slab. On the other hand, the hot holes of the group II are located within the valence band continuum of the TiO2 . They can in principle be injected into the TiO2 slab. However, the hot holes of the group II are mainly derived from the Ag d states. As shown in Fig. 3e, the hot hole density is located exclusively on the Ag atoms of the nanocluster, and inside the TiO2 slab it has only minor distributions

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on the oxygen p states of the interface (top) layer. Compared with the hot electron density in Fig. 3d, the hot hole density is strongly localized around the Ag20 nanocluster. This is because the Ag d states are more localized than the s or p states, and thus have less hybridizations with the valence bands of the TiO2 slab. Therefore, the hot holes of the group II are less efficient in the charge injection than the hot electrons of the group I. This demonstrates that the LSPR relaxation at the interface is very different from that in isolated nanoclusters or bare surfaces. References 15 and 20 showed that in an isolated Ag surface or nanocluster, the main channel for the LSPR decay was through the generation of hot holes at the top of the Ag d bands. Here we see that those hot holes play a much less important role in the charge injection process. Since both the hot electrons and hot holes of the group II can be injected into the TiO2 slab, their contributions to the net charge injection tend to cancel each other. It explains why the group II electron-hole pairs contribute much less to the charge separation than the group I. The excitations on the Ag d states actually limit the charge separation efficiency. In addition, Fig. 3b indicates that from 10 to 20 fs, slightly more hot holes are injected into the TiO2 from the group II excitations (the blue line is positive), and after 20 fs the hot electron injection is slightly dominant in the group II (the blue line becomes negative). The nonequilibrium distribution between the hot electrons and hot holes leads to the charge separation in space. At the metal-semiconductor interface, the electronic coupling between the metal and the semiconductor surface states leads to the hybridized states, which offer important channels for the plasmon induced charge injection and separation. A correct description of the interfacial coupling using the slab model is crucial to properly describe the charge injection and separation in such systems. Layer-resolved distributions. Further insights into the mechanism and dynamics of the charge separation can be gained by analyzing the layer-resolved distribution of the net charges in the TiO2 slab, which is plotted in Fig. 4a. During the first 10 fs, the charges are injected into all the four TiO2 layers with a sequential time delay between the neighboring layers. The first layer gets the most net charges during this period, the second layer follows as the

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next most, and the fourth layer gets the least. This is easy to understand, because the first layer is the closest to the Ag20 and the fourth layer is the farthest. After 10 fs, the net charge distributions show fluctuations. From 15 fs, the second layer receives more net charges. In contrast, the magnitude of the net charge in the first layer drops significantly after 10 fs and ends up with a much smaller value than those in the second and third layers. This result seems to be counter intuitive, as one would expect that the interfacial layer should receive the most injected charges. The seeming confusion can be better understood when we separately plot the layerresolved populations of hot electrons and hot holes in the TiO2 slab as shown in Fig. 4b. Here the populations of hot electrons are negative and those of hot holes are positive according to the definitions of Eqs. 12 and 13. The net charge in Fig. 4a is the sum of the populations of hot electrons and hot holes. The hot electrons extend to all the four TiO2 layers, although the number of hot electrons (the absolute value) gradually decreases when the TiO2 layer is located further away from the interface. On the contrary, the hot holes only enter the first TiO2 layer due to the hybridization with the Ag d states, and do not enter the rest three layers due to the absence of electronic couplings. Therefore, the magnitude of the net charge in the first layer, which has the most hot electrons among the four layers, is reduced due to the partial neutralization of the hot holes. The second layer has fewer hot electrons than the first layer, but it receives nearly no hot holes. This applies to the third and fourth layer, and so forth. We can conclude that the second TiO2 layer receives the most net charges, while the first layer receives the largest number of hot electrons and hot holes. The second layer has stronger charge separation effect than the interfacial layer. The fourth layer always receives the fewest charges. In this sense, the charge injection and separation is mainly a surface process, and the few surface layers receive the most charges. We expect that this conclusion remains qualitatively the same in simulations with larger silver clusters and thicker TiO2 slabs. To analyze the fluctuations of the layer-resolved net charges after the initial charge sepa-

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ration, we plot in Fig. 4c the layer-resolved currents calculated by Eq. 19 at the four planes marked by the dashed lines in Fig. 1a. Positive values indicate net electron injections from the Ag20 to the TiO2 . All the currents have rapidly-oscillating components and slowlyvarying components. The rapidly-oscillating components are associated with the LSPR of the Ag20 . Since the first plane is close to the Ag20 , its current is strongly modulated by the LSPR compared with the other three currents. The direction (sign) of the current is mainly determined by the slowly-varying component, which corresponds to a charge sloshing motion between the Ag20 and the TiO2 . It can be assigned as the CTP mode across the interface. The CTP was mostly discussed in coupled metallic dimmers. 51–54 When two metallic nanoclusters are connected by a conductive channel, the CTP can emerge. A key feature of the CTP is the oscillating current across the dimmer. In essence, the CTP describes a low-frequency charge sloshing across the interface between any conducting structures. 55 In the Ag20 -TiO2 system, the charge injection makes the TiO2 an effective conductor and it is also a signature for the conductive channel between the Ag20 and the TiO2 . Thus, the CTP mode can emerge. The character of the CTP is confirmed by the oscillating current at the interface as shown in Fig. 4c. The Fourier transform of the oscillating current shows a peak at ∼0.15 eV. A detailed inspection of the optical absorption spectrum can confirm the CTP mode as marked by the red arrow in Fig. 1b. In Fig. S3, we show that the low-frequency peak in the optical absorption spectrum disappears when there is negligible charge transfer in the system, which confirms that the low-frequency peak is induced by the CTP mode. Figure 4b shows that the populations of hot holes are rather stable after 10 fs, while those of hot electrons are fluctuating. The CTP is therefore formed mainly by the hot electrons rather than hot holes. The charge density sloshing driven by the CTP mode is illustrated in Fig. 5 at four characteristic sequences. The first column (Fig. 5a and e) plots the total charge density difference between 10 fs and 0 fs. Figure 5a shows that all the four TiO2 layers receive electrons while Fig. 5e shows that the Ag20 nanocluster loses electrons during this period. It

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is in agreement with the layer-resolved currents shown in Fig. 4c. This is the initial phase of the charge separation directly driven by the LSPR excitation and its subsequent decay. Between 15 fs and 10 fs the total charge density difference (Fig. 5b and f) shows that all the four layers continue to receive electrons while the Ag20 loses some electrons. However, Figure 5f suggests that the first and second layers simultaneously lose electrons. The positive currents shown in Fig. 4c during this time period imply that the top two layers still receive electrons from the Ag20 , but simultaneously they lose electrons because a portion of the hot electrons injected during the initial phase move deeper into the third and fourth layers of the TiO2 substrate. This process is driven by the sloshing motion of the CTP. From 10 to 15 fs, the charge separation therefore continues. Around 15 fs, the currents at the four planes turn to negative in sequence as shown in Fig. 4c, which indicates the electrons are moving backwards from the TiO2 slab to the Ag20 . The total charge density difference between 24 fs and 15 fs is shown in Fig. 5c and g. The third and fourth layers lose electrons, and the Ag20 receives electrons. The top two layers receive electrons from the bottom two TiO2 layers and simultaneously give electrons back to the Ag20 . As a result, the injected electrons in the bottom TiO2 layers are moving back towards the Ag20 through the top two layers. From 15 to 24 fs, the injected electrons have a backflow and thus the charge separation is reduced. After 24 fs, the currents become positive again in sequence, and the electrons are sloshing into the TiO2 for the second time. The total charge density difference between 34 fs and 24 fs is shown in Fig. 5d and h, which look similar to Fig. 5a and e but differ in amplitude. The Ag20 loses electrons and the TiO2 receives electrons. The charge separation increases again. In Fig. 4c, the currents get damped at about 40 fs. The time scale compares favorably well with the lifetime broadening of the CTP mode extracted from the absorption spectrum of the coupled system. We can therefore conclude that the charge separation dynamics consists of two processes: a fast initial charge separation associated with the LSPR decay

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and a charge sloshing governed by the CTP mode. In a long-time (picoseconds or even nanoseconds) simulation without an applied voltage, the hot carriers will recombine and the system will return to the ground state; however, the electron-hole recombination cannot be observed within several tens of femtoseconds. The Ag20 has a characteristic plasmon resonance similar to those larger nanoclusters. 46 The plasmonic spectrum, which is a coherent superposition of electron-hole pair excitations, is correctly represented by the Ag20 . The density of states of the Ag-TiO2 interface, namely the single-particle spectrum, is also correctly represented by the Ag20 -TiO2 . The density of states for a larger system, the Ag55 -TiO2 , is shown in Fig. S4. It is similar to that of the Ag20 -TiO2 : the Fermi energy is close to the TiO2 conduction bands and there are Ag s and p states inside the TiO2 band gap. For the above reasons, the plasmonic coupling and decay channels would be similar in larger systems. Thus, our findings should be applicable to larger Ag nanoclusters. Most importantly, the mechanism and dynamics for the charge separation revealed in this work will remain unchanged for larger nanoclusters. Finally, we would like to point out that our study of the PICT differs from ref. 22. Reference 22 used the nonadiabatic molecular dynamics to study the charge transfer in the Au20 -TiO2 system, initiated by a single electron excitation, namely by lifting one electron from the valence band to the conduction band. In contrast, our work starts with the resonant plasmon excitation of the Ag20 with many electron-hole pairs excited coherently. The two works reveal two different mechanisms: ours study the direct charge injection induced by the LSPR decay and ref. 22 studied the transfer of a single electron. CONCLUSIONS In summary, we have studied the dynamics of the electron-hole separation at the Ag20 TiO2 interface under the LSPR excitation using rt-TDDFT simulations. The charge separation has two processes. The first process is an initial charge separation associated with the LSPR decay. It is due to the strong interfacial hybridization of the electronic states

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between the Ag nanocluster and the TiO2 substrate, which builds a direct channel for the ultrafast charge injection. The fast charge injection occurs on a time scale of 10 fs, the same as the LSPR decay. Due to the different interfacial couplings, the hot electrons are injected into all the four TiO2 layers whereas the hot holes are strongly localized around the Ag20 and the interfacial TiO2 layer, leading to the electron-hole separation at the interface. Over 40 % of the excited electron-hole pairs are separated spatially. Such a high charge separation efficiency can support the previous experimental observations 28,30–33 and is promising for plasmonic applications. In the second process, a further charge sloshing between the Ag nanocluster and the semiconductor substrate appears due to the CTP mode. The CTP mode modulates the charge separation and distribution in the semiconductor substrate. It shufflers the injected hot electrons into the second and third layers. As a result, the second layer gets the most net charge in the TiO2 slab after 15 fs. The fourth layer always gets the least charges, showing the charge injection and separation is a surface effect. The interplay between the LSPR and the CTP determines the charge separation and redistribution at the metal-semiconductor interface. Although the conclusions are obtained in a small system, we believe that the essential conclusions remain valid in large systems. Our findings contribute to the general understandings of the plasmon induced hot carrier dynamics and have general implications. METHODS Computational setup. The rt-TDDFT simulations are performed within the local density approximation (LDA). 56 The norm-conserving pseudopotentials are employed and the valence electrons are expanded using plane waves with an energy cutoff of 36 Ry. The plane-wave basis set should be more accurate than the local-orbital basis sets, although more computationally expensive. The system is modeled using a supercell with the periodic boundary condition, which is essential to correctly mimic the surface states and the band gap of the semiconductor substrate and thus the charge separation.

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The Ag20 is chosen as a minimal cluster, whose LSPR is characteristic for Ag nanoclusters. 45,46 Its most stable structure is the tetrahedral structure. Because the LDA cannot predict correct energies for the Ag d bands, we follow the same recipe in ref. 20 to make the Ag d bands in agreement with the experimental X-ray photoemission spectroscopy data. 49 For the rutile substrate, the TiO2 (110) is the most stable surface. The LDA cannot predict the correct TiO2 band gap nor the band edge energies of the (110) surface. To get the correct electronic structure, the energies of the Ti d states have been corrected following the recipe in ref. 20 (see the Supporting Information). The calculated band gap of the bulk TiO2 is 3.01 eV and the calculated electron affinity of the TiO2 (110) surface is 4.37 eV, both in agreement with the experimental data. 57,58 The band edge energies of the TiO2 (110) surface (the ionization energy and the electron affinity) converge at four TiO2 layers (see Table S1). Thus, the four-layer TiO2 model is used to mimic the (110) surface. The surface unit cell is expanded by 5 and 2 times along the x and y directions (a 5 × 2 supercell), to eliminate the interaction between the adsorbed Ag20 nanocluster and its periodic images. The lateral size of the supercell is around 15 × 13 ˚ A2 . The vacuum in the supercell is around 7 ˚ A. Each TiO2 layer has 40 O atoms and 20 Ti atoms. The supercell contains in total 260 atoms (160 O atoms, 80 Ti atoms, and 20 Ag atoms). The Brillouin zone integration is sampled with the Γ point only. The supercell size effects are discussed in the Supporting Information (Fig. S5), which do not alter our results. The ground state structure of the Ag20 -TiO2 system is obtained using the DFT based geometry optimization. The Ti atoms of the third layer are fixed at their bulk positions and all the other atoms are fully relaxed. In the rt-TDDFT simulations, we ignore the phonon effects and only focus on the electron-electron interaction. The electron-phonon interaction sets in on a time scale of picoseconds, 6,12,18,59 which is much longer than the time scale of the direct charge separation process, and is thus safely ignored. For the rt-TDDFT simulations, we employ the algorithm developed in ref. 60. The fast rt-TDDFT algorithm allows to use a large time step of 0.05 fs, and thus reduces the computational cost. It has been applied in

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previous studies of plasmon decays. 20 To excite the LSPR of the Ag20 -TiO2 system, an external electric field is introduced to mimic a laser pulse, √ E(t) = E0 sin(ωL t) exp[−(t − t0 )2 /2σ 2 ]/ 2πσ

(1)

The direction of the electric field E is perpendicular to the TiO2 surface. The σ, ωL , and |E0 | are the duration, central frequency, and amplitude of the electric field, respectively. In this study, we set ωL = ωp = 3.2 eV (resonant to the LSPR peak), σ = 6 fs, |E0 | = 10−3 Hartree·Bohr−1 , and t0 = 0. We have also tested t0 = 15 fs, and the result is shown in Fig. S6. Compared with the t0 = 0 case, the charge separation of the t0 = 15 fs case is delayed by ∼10 fs and all the other features are almost identical. This is because for the t0 = 15 fs case the laser is too weak in the first 10 fs and few electrons have been excited. Charge separation calculations. One may think of using the TDDFT charge density, which is given by ρ(r, t) =

∑

|ψi (r, t)|2

(2)

i

where ψi (r, t) is the TD wave function of the i-th electron, and the summation is over all the electrons in the system. Suppose we have a TD wave function ψi (t) that starts as an eigen state ψi (0) = ϕi . The TD wave function can be expanded by the eigen states. For simplicity, we suppose the expansion is nonzero only on the i-th and j-th eigen states (i.e., there only are excitations to the j-th eigen state). The expansion is given by

ψi (t) = Ci,i (t) exp(−iωi t)ϕi + Cj,i (t) exp(−iωj t)ϕj

(3)

where ωi and ωj are the eigen energy of the i-th and j-th eigen states, respectively. The Ci,i (t) and Cj,i (t) are the expansion coefficients. Because the laser pulse is weak, the off-diagonal 2 ). The coefficient Cj,i (t) is a small number, and the diagonal coefficient Ci,i (t) = 1 − O(Cj,i

16


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TDDFT charge density is ∗ ρ(r, t) = |ψi (r, t)|2 = |Ci,i (t)ϕi |2 + 2Re[Ci,i (t)Cj,i (t) exp(−i∆ωj,i t)ϕ∗i ϕj ] + |Cj,i (t)ϕj |2

(4)

∗ where ∆ωj,i = ωj − ωi . The 2Re[Ci,i (t)Cj,i (t) exp(−i∆ωj,i t)ϕ∗i ϕj ] is the cross term between ϕi

and ϕj . For a resonant excitation, ∆ωj,i = ωL and Cj,i (t) varies slowly (compared with ωL ). Thus, the cross term in Eq. 4 oscillates at the frequency ωL . The electron/hole excitation term |Cj,i (t)ϕj |2 cannot be observed because it is proportional to |Cj,i |2 whereas the leading term of the cross term is proportional to Cj,i (notice that Cj,i is a small number due to the weak laser pulse). As a result, the TDDFT charge density ρ(r, t) oscillates at the frequency ωL , and the charge separation cannot be observed. In Fig. S7, we plot the TDDFT charge in the TiO2 slab as a function of time, which is calculated as the integral of the TDDFT charge density in the volume below the black dashed line in Fig. 1a. Indeed we observe an oscillation at the ωL frequency, and the oscillation amplitude is one order of magnitude greater than the net charge shown in Fig. 2. In order to observe the charge separation, we need to obtain the |Cj,i (t)ϕj |2 terms (hot electron and hot hole excitations), instead of the cross terms between the occupied and unoccupied eigen states. To calculate the hot electron and hot hole excitations separately, we project the TD wave function onto the hole (occupied) subspace and electron (unoccupied) subspace, respectively. For the i-th TD wave function, we have (e)

ψi (t) =

∑

Cj,i (t) exp(−iωj t)ϕj

(5)

Cj ′ ,i (t) exp(−iωj ′ t)ϕj ′

(6)

j∈unocc (h)

ψi (t) =

∑

j ′ ∈occ

Here ϕj is the j-th eigen state of the Ag20 -TiO2 system, which fulfills H0 ϕj = ωj ϕj . H0 is the ground state Hamiltonian, and ωj is the corresponding eigen energy. The j and j ′ label (e)

the unoccupied and occupied eigen states of the ground state. For ψi (t) the summation is

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(h)

over all the unoccupied eigen states, and for ψi (t) it is over all the occupied eigen states. For the charge separation analysis, it is necessary to decompose the charge density into different partial spaces. Here we propose two methods to decompose the charge density. The (e)

(h)

first one: we project the projected wave functions ψi (t) and ψi (t) onto a set of local basis located on every atom: (e)

(e)

(7)

(h)

(h)

(8)

βk,l,i (t) = < bk,l |ψi (t) > βk,l,i (t) = < bk,l |ψi (t) >

where |bk,l > is the l-th local basis located on the k-th atom. Thus, the number of electrons on the k-th atom is given by

nk (t) =

∑

(e)

(h)

[|βk,l,i (t)|2 + |βk,l,i (t)|2 ]

(9)

l,i

In this way, the charge density can be decomposed to every atom. The number of electrons in the TiO2 is calculated as nTiO2 (t) =

∑

nk (t)

(10)

k∈TiO2

where the summation is over all the Ti and O atoms. The net charge in TiO2 is calculated by the subtraction of the ground state charge at t = 0,

∆n = −[nTiO2 (t) − nTiO2 (0)]

(11)

The minus sign in front of the bracket is due to the definition that negative values indicate more hot electrons injected from the Ag20 to the TiO2 and positive values indicate more hot holes injected from the Ag20 to the TiO2 . The sign of the net charge indicates whether it is a net electron injection or a net hole injection, and the absolute value indicates the number of net charges injected into the TiO2 . Larger absolute values of the net charges indicate

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ACS Nano

stronger charge separations. The second one: we define the hot electron density and the hot hole density using the projected wave functions: ∑ (e) ∑ (e) ρ(e) (r, t) = −[ |ψi (r, t)|2 − |ψi (r, 0)|2 ] i

(12)

i

∑ (h) ∑ (h) ρ (r, t) = −[ |ψi (r, t)|2 − |ψi (r, 0)|2 ] (h)

i

(13)

i

The minus signs in front of the brackets are again due to the definition that the calculated hot electron density is negative and the hot hole density is positive. The absolute values indicate the spatial distribution of hot carriers. The total charge density is the summation of the hot electron and hot hole densities. We use the black dashed line in Fig. 1a as the boundary to decompose the charge density in the supercell. The hot electron and hot hole populations in the TiO2 can be calculated as the integral of ρ(e) (r, t) and ρ(h) (r, t) in the volume below the boundary respectively, and the net charge is the summation of the two terms. In this way, we can also calculate the charge injection into each TiO2 layer of the slab using the boundaries marked as the colored dashed lines in Fig. 1a. We find that the above two methods give essentially the same result, as shown in Fig. S8. The minor discrepancy, by less than 6 %, does not alter our conclusions. Thus, we believe our charge separation calculations are solid and reflect the true physics. Other quantities. The optical absorption spectrum is obtained from the imaginary part of the polarizability α(ω), which is calculated from the time-dependent dipole moment of the system 61 D(ω) = α(ω)E(ω)

(14)

where D(ω) and E(ω) are the Fourier transforms of the dipole moment and the electric field, respectively.

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The energy stored in the LSPR mode is estimated using the method described in ref. 20 ∑

Eplasmon (t) =

|Cj,i (t)|2 ∆ωj,i

(15)

(j,i)∈plasmon

where “(j, i) ∈ plasmon” indicates the Cj,i (t) belongs to the off-resonant rapidly-oscillating transition. It is a qualitative estimate that reflects the correct trend for the plasmon decay. The number of electrons projected onto each eigen state is calculated by the expansion coefficients Cj,i (t) as described in ref. 20:

Oj (t) =

∑

|Cj,i (t)|2

(16)

i

The change of the number of electrons on each eigen state (compared with the unexcited system) is ∆Oj (t) = −[Oj (t) − Oj (0)]

(17)

which gives the population of hot carriers. The minus sign in front of the bracket is due to the definition that negative ∆Oj (t) indicates hot electrons and positive ∆Oj (t) indicates hot holes. The current at a plane can be calculated from the net charge. The continuity equation gives

I J · dS = −

dn dt

(18)

Considering the periodic boundary condition and the fact that J = 0 in vacuum, we have ∫ J · dS = −

Is = s

dnbs dt

(19)

Here s indicates the plane marked as the dashed line in Fig. 1a, and nbs is the net charge below the s plane. Positive values indicate net electron injections from the Ag20 side to the TiO2 side.

20


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ACS Nano

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: xxxxxxx The TiO2 calculations, the number of excited electron-hole pairs and the charge separation efficiency, the energy distribution of electron-hole pairs, the check for the low-frequency peak in the absorption spectrum, the density of states for a larger structure, the tests on the supercell size effects, the test on the t0 parameter of the laser pulse, the number of charges in the TiO2 slab calculated using the TDDFT charge density, and the net charge in the TiO2 slab calculated using the two charge decomposition methods. The authors declare no competing financial interest. ACKNOWLEDGEMENTS This work is supported by the National Key R&D Program of China (No. 2017YFA0303404, No. 2016YFB0700700) and by the National Natural Science Foundation of China through NSAF U-1530401 and also by Science Challenge Project No. TZ2018004. J. M. acknowledges the support from the National Natural Science Foundation of China under Grant No. 11704027. We acknowledge the allocated computer time at the supercomputer facility TH2-JK at the Beijing Computational Science Research Center (CSRC). REFERENCES 1. Nie, S.; Emory, S. R. Probing Single Molecules and Single Nanoparticles by SurfaceEnhanced Raman Scattering. Science 1997, 275, 1102–1106. 2. Kuhn, S.; Hakanson, U.; Rogobete, L.; Sandoghdar, V. Enhancement of Single-Molecule Fluorescence Using a Gold Nanoparticle as an Optical Nanoantenna. Phys. Rev. Lett. 2006, 97, 017402.

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3. Hafner, J. H.; Mayer, K. M. Localized Surface Plasmon Resonance Sensors. Chem. Rev. 2011, 111, 3828–3857. 4. Green, M. A.; Pillai, S. Harnessing Plasmonics for Solar Cells. Nat. Photonics 2012, 6, 130–132. 5. Moskovits, M. The Case for Plasmon-Derived Hot Carrier Devices. Nat. Nanotechnol. 2015, 10, 6–8. 6. Clavero, C. Plasmon-Induced Hot-Electron Generation at Nanoparticle/Metal-Oxide Interfaces for Photovoltaic and Photocatalytic Devices. Nat. Photonics 2014, 8, 95–103. 7. Knight, M. W.; Sobhani, H.; Nordlander, P.; Halas, H. J. Photodetection with Active Optical Antennas. Science 2011, 332, 702–704. 8. Mukherjee, S.; Libisch, F.; Large, N.; Neumann, O.; Brown, L. V.; Cheng, J.; Lassiter, J. B.; Carter, E. A.; Nordlander, P.; Halas, N. J. Hot Electrons Do the Impossible: Plasmon-Induced Dissociation of H2 on Au. Nano Lett. 2013, 13, 240–247. 9. Atwater, H. A.; Polman, A. Plasmonics for Improved Photovoltaic Devices. Nat. Mater. 2010, 9, 205–213. 10. Brongersma, M. L.; Halas, N. J.; Nordlander, P. Plasmon-Induced Hot Carrier Science and Technology. Nat. Nanotechnol. 2015, 10, 25–34. 11. Erwin, W. R.; Zarick, H. F.; Talbert, E. M.; Bardhan, R. Light Trapping in Mesoporous Solar Cells with Plasmonic Nanostructures. Energy Environ. Sci. 2016, 9, 1577–1601. 12. Zhang, Y.; He, S.; Guo, W.; Hu, Y.; Huang, J.; Mulcahy, J. R.; Wei, W. D. SurfacePlasmon-Driven Hot Electron Photochemistry. Chem. Rev. 2018, 118, 2927–2954. 13. Wei, Q.; Wu, S.; Sun, Y. Quantum-Sized Metal Catalysts for Hot-Electron-Driven Chemical Transformation. Adv. Mater. 2018, 30, 1802082. 22


Page 22 of 34

Page 23 of 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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14. Manjavacas, A.; Liu, J. G.; Kulkarni, V.; Nordlander, P. Plasmon-Induced Hot Carriers in Metallic Nanoparticles. ACS Nano 2014, 8, 7630–7638. 15. Sundararaman, R.; Narang, P.; Jermyn, A. S.; Goddard III, W. A.; Atwater, H. A. Theoretical Predictions for Hot-Carrier Generation from Surface Plasmon Decay. Nat. Commun. 2014, 5, 5788. 16. Brown, A. M.; Sundararaman, R.; Narang, P.; Goddard III, W. A.; Atwater, H. A. Nonradiative Plasmon Decay and Hot Carrier Dynamics: Effects of Phonons, Surfaces, and Geometry. ACS Nano 2016, 10, 957–966. 17. Bernardi, M.; Mustafa, J.; Neaton, J. B.; Louie, S. G. Theory and Computation of Hot Carriers Generated by Surface Plasmon Polaritons in Noble Metals. Nat. Commun. 2015, 6, 7044. 18. Liu, J. G.; Zhang, H.; Link, S.; Nordlander, P. Relaxation of Plasmon-Induced Hot Carriers. ACS Photonics 2018, 5, 2584–2595. 19. Saavedra, J. R. M.; Asenjo-Garcia, A.; Javier Garcia de Abajo, F. Hot-Electron Dynamics and Thermalization in Small Metallic Nanoparticles. ACS Photonics 2016, 3, 1637–1646. 20. Ma, J.; Wang, Z.; Wang, L.-W. Interplay between Plasmon and Single-Particle Excitations in a Metal Nanocluster. Nat. Commun. 2015, 6, 10107. 21. Rossi, T. P.; Kuisma, M.; Puska, M. J.; Nieminen, R. M.; Erhart, P. Kohn-Sham Decomposition in Real-Time Time-Dependent Density Functional Theory: An Efficient Tool for Analyzing Plasmonic Excitations. J. Chem. Theory Comput. 2017, 13, 4779–4790. 22. Long, R.; Prezhdo, O. V. Instantaneous Generation of Charge-Separated State on TiO2 Surface Sensitized with Plasmonic Nanoparticles. J. Am. Chem. Soc. 2014, 136, 4343– 4354. 23


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

23. Govorov, A. O.; Zhang, H.; Gunko, Y. K. Theory of Photoinjection of Hot Plasmonic Carriers from Metal Nanostructures into Semiconductors and Surface Molecules. J. Phys. Chem. C 2013, 117, 16616–16631. 24. White, T. P.; Catchpole, K. R. Plasmon-Enhanced Internal Photoemission for Photovoltaics: Theoretical Efficiency Limits. Appl. Phys. Lett. 2012, 101, 073905. 25. Blandre, E.; Jalas, D.; Petrov, A. Y.; Eich, M. Limit of Efficiency of Generation of Hot Electrons in Metals and Their Injection inside a Semiconductor Using a Semiclassical Approach. ACS Photonics 2018, 5, 3613–3620. 26. Mitchell, K. The Theory of the Surface Photoelectric Effect in Metals-II. Proc. R. Soc. A 1936, 153, 513–533. 27. Kolb, D. M.; Przasnyski, M.; Gerischer, H. Optical Interfacial Electron Transfer between Metal Adatoms and a Semiconductor Electrode. Z. Phys. Chem. 1974, 93, 1–14. 28. Wu, K.; Chen, J.; McBride, J. R.; Lian, T. Efficient Hot-Electron Transfer by a PlasmonInduced Interfacial Charge-Transfer Transition. Science 2015, 349, 632–635. 29. Boerigter, C.; Campana, R.; Morabito, M.; Linic, S. Evidence and Implications of Direct Charge Excitation as the Dominant Mechanism in Plasmon-Mediated Photocatalysis. Nat. Commun. 2016, 7, 10545. 30. Tan, S.; Argondizzo, A.; Ren, J.; Liu, L.; Zhao, J.; Petek, H. Plasmonic Coupling at a Metal/Semiconductor Interface. Nat. Photonics 2017, 11, 806–812. 31. Ratchford, D. C.; Dunkelberger, A. D.; Vurgaftman, I.; Owrutsky, J. C.; Pehrsson, P. E. Quantification of Efficient Plasmonic Hot-Electron Injection in Gold Nanoparticle-TiO2 Films. Nano Lett. 2017, 17, 6047–6055.

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Page 24 of 34

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32. Furube, A.; Du, L.; Hara, K.; Katoh, R.; Tachiya, M. Ultrafast Plasmon-Induced Electron Transfer from Gold Nanodots into TiO2 Nanoparticles. J. Am. Chem. Soc. 2007, 129, 14852–14853. 33. Du, L.; Furube, A.; Hara, K.; Katoh, R.; Tachiya, M. Ultrafast Plasmon Induced Electron Injection Mechanism in Gold-TiO2 Nanoparticle System. J. Photochem. Photobiol., C 2013, 15, 21–30. 34. Kumar, P. V.; Rossi, T. P.; Marti-Dafcik, D.; Reichmuth, D.; Kuisma, M.; Erhart, P.; Puska, M. J.; Norris, D. J. Plasmon-Induced Direct Hot-Carrier Transfer at MetalAcceptor Interfaces. ACS Nano 2019, 13, 3188–3195. 35. Gao, S.; Wang, D. An Embedding Scheme for Calculating Charge Transfer between Adsorbates and Metal Substrates. J. Phys.: Condens. Matter 1990, 2, 2187–2198. 36. Wang, T.; Vaxenburg, R.; Liu, W.; Rupich, S. M.; Lifshitz, E.; Efros, A. L.; Talapin, D. V.; Sibener, S. J. Size-Dependent Energy Levels of InSb Quantum Dots Measured by Scanning Tunneling Spectroscopy. ACS Nano 2015, 9, 725–732. 37. Zhao, G.; Kozuka, H.; Yoko, T. Sol-Gel Preparation and Photoelectrochemical Properties of TiO2 Films Containing Au and Ag Metal Particles. Thin Solid Films 1996, 277, 147– 154. 38. Saito, K.; Tanabe, I.; Tatsuma, T. Site-Selective Plasmonic Etching of Silver Nanocubes. J. Phys. Chem. Lett. 2016, 7, 4363–4368. 39. Collado, L.; Reynal, A.; Fresno, F.; Barawi, M.; Escudero, C.; Perez-Dieste, V.; Coronado, J. M.; Serrano, D. P.; Durrant, J. R.; de la Pena O’Shea, V. A. Unravelling the Effect of Charge Dynamics at the Plasmonic Metal/Semiconductor Interface for CO2 Photoreduction. Nat. Commun. 2018, 9, 4986.

25


ACS Nano 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

40. Fang, Y.; Jiao, Y.; Xiong, K.; Ogier, R.; Yang, Z.-J.; Gao, S.; Dahlin, A. B.; Kall, M. Plasmon Enhanced Internal Photoemission in Antenna-Spacer-Mirror Based Au/TiO2 Nanostructures. Nano Lett. 2015, 15, 4059–4065. 41. Tian, Y.; Tatsuma, T. Mechanisms and Applications of Plasmon-Induced Charge Separation at TiO2 Films Loaded with Gold Nanoparticles. J. Am. Chem. Soc. 2006, 127, 7632–7637. 42. K Kelly and, E. C.; Zhao, L.; Schatz, G. The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment. J. Phys. Chem. B 2003, 107, 668–677. 43. Manjavacas, A.; Garcia de Abajo, F. Tunable Plasmons in Atomically Thin Gold Nanodisks. Nat. Commun. 2014, 5, 3548. 44. Linic, S.; Christopher, P.; Ingram, D. B. Plasmonic-Metal Nanostructures for Efficient Conversion of Solar to Chemical Energy. Nat. Mater. 2011, 10, 911–921. 45. Fedrigo, S.; Harbich, W.; Buttet, J. Collective Dipole Oscillations in Small Silver Clusters Embedded in Rare-Gas Matrices. Phys. Rev. B 1993, 47, 10706–10715. 46. Aikens, C. M.; Li, S.; Schatz, G. C. From Discrete Electronic States to Plasmons: TDDFT Optical Absorption Properties of Agn (n = 10, 20, 35, 56, 84, 120) Tetrahedral Clusters. J. Phys. Chem. C 2008, 112, 11272–11279. 47. Hovel, H.; Fritz, S.; Hilger, A.; Kreibig, V. Width of Cluster Plasmon Resonances: Bulk Dielectric Functions and Chemical Interface Damping. Phys. Rev. B 1993, 48, 18178– 18188. 48. Hoggard, A.; Wang, L.-Y.; Ma, L.; Fang, Y.; You, G.; Olson, J.; Liu, Z.; Chang, W.S.; Ajayan, P. M.; Link, S. Using the Plasmon Linewidth To Calculate the Time and

26


Page 26 of 34

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ACS Nano

Efficiency of Electron Transfer between Gold Nanorods and Graphene. ACS Nano 2013, 7, 11209–11217. 49. Barrie, A.; Christensen, N. E. High-Resolution X-Ray Photoemission Spectra of Silver. Phys. Rev. B 1976, 14, 2442–2447. 50. Bernadotte, S.; Evers, F.; Jacob, C. R. Plasmons in Molecules. J. Phys. Chem. C 2013, 117, 1863–1878. 51. Wen, F.; Zhang, Y.; Gottheim, S.; King, N. S.; Zhang, Y.; Nordlander, P.; Halas, N. J. Charge Transfer Plasmons: Optical Frequency Conductances and Tunable Infrared Resonances. ACS Nano 2015, 9, 6428–6435. 52. Perez-Gonzalez, O.; Zabala, N.; Borisov, A. G.; Halas, N. J.; Nordlander, P.; Aizpurua, J. Optical Spectroscopy of Conductive Junctions in Plasmonic Cavities. Nano Lett. 2010, 10, 3090–3095. 53. Zuloaga, J.; Prodan, E.; Nordlander, P. Quantum Description of the Plasmon Resonances of a Nanoparticle Dimer. Nano Lett. 2009, 9, 887–891. 54. Koya, A. N.; Lin, J. Charge Transfer Plasmons: An Overview of the Recent Theoretical and Experimental Developments. Appl. Phys. Rev. 2017, 4, 021104. 55. Gao, S. Nonlinear Response of Metal Nanoparticles: Double Plasmon Excitation and Electron Transfer. J. Chem. Phys. 2015, 142, 234701. 56. Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133. 57. Nowotny, J. Oxide Semiconductors for Solar Energy Conversion: Titanium Dioxide; CRC Press: Bosa Roca, 2011.

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58. Butler, M. A.; Ginley, D. S. Prediction of Flatband Potentials at SemiconductorElectrolyte Interfaces from Atomic Electronegativities. J. Electrochem. Soc. 1978, 125, 228–232. 59. Jang, Y. J.; Chung, K.; Lee, J. S.; Choi, C. H.; Lim, J. W.; Kim, D. H. Plasmonic Hot Carriers Imaging: Promise and Outlook. ACS Photonics 2018, 5, 4711–4723. 60. Wang, Z.; shen Li, S.; Wang, L.-W. Efficient Real-Time Time-Dependent Density Functional Theory Method and Its Application to a Collision of an Ion with a 2D Material. Phys. Rev. Lett. 2015, 114, 063004. 61. Lopata, K.; Govind, N. Modeling Fast Electron Dynamics with Real-Time TimeDependent Density Functional Theory: Application to Small Molecules and Chromophores. J. Chem. Theory Comput. 2011, 7, 1344–1355.

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(a)

(b)

Optical absorption spectra

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3

Ag

2

Ag

20

TiO

0

4

-TiO

20

1

2

2

3

4

5

Energy (eV)

Figure 1: (a) The calculated most stable structure of the Ag20 -TiO2 system. The silver, red, and cyan balls represent Ag, O, and Ti atoms, respectively. The four TiO2 layers are marked by the numbers on the left side. (b) The optical absorption spectra of the Ag20 -TiO2 system, isolated Ag20 , and bare TiO2 slab, respectively. The black arrow marks the LSPR peak of the Ag20 -TiO2 system, and the red arrow marks the CTP.

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Net charge in TiO

2

(10

-4

e)

-12 25 -10 20

-8 with plasmon

15

without plasmon

-6

10

-4

5

-2

10

20

30

40

50

eV)

0

-4

0

0

Energy stored in the LSPR (10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Time (fs)

Figure 2: The black solid line is the net charge in the TiO2 as a function of time. The negative sign indicates that hot electrons are injected from the Ag20 to the TiO2 with corresponding hot holes remaining in the Ag20 (i.e., charge separation). The pink line is the energy stored in the LSPR mode of the system as a function of time. The LSPR decays within 10 fs, on the same time scale of the initial charge separation, which shows that the initial charge separation is directly induced by the LSPR decay. The blue dashed line is the net charge calculated using the non-interacting model, in which no plasmon mode exists. It has been renormalized according to the optical absorption strength of the bare TiO2 . Without the plasmon excitation, the charge separation is largely reduced.

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4

(a)

e)

-10

(b)

(10

Hot carrier populations (10

-4

-4

e)

t = 20 fs

2

Net charge in TiO

0

-8

2

I

II

-2

I -6

II

-4

-2

0 -4

-3

-2

-1

0

1

2

3

0

4

Energy (eV)

(d)

(c)

10

10

20

30

40

50

Time (fs)

(e)

8 Ag s+p Ag d

6

DOS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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4

2

0 -4

-3

-2

-1

0

1

2

3

4

Energy (eV)

Figure 3: (a) The populations on the eigen states at 20 fs. The incident photon energy is 3.2 eV. Positive values indicate hot holes and negative values indicate hot electrons. The absolute value gives the number of hot carriers on the eigen state. The x-axis is the eigen energy. The Fermi energy is set to zero. The hot electrons and holes can be categorized into two excitation groups as marked by the red (group I) and blue (group II) rectangles, according to the resonant condition. The dashed grey lines mark the positions of the conduction band minimum and the valence band maximum of the TiO2 . (b) The contributions from the two electron-hole-excitation groups to the net charge in the TiO2 . (c) The projected density of states of the Ag20 -TiO2 system. The Ag s and p states are shown by the red line, the Ag d states are shown by the blue line, and the conduction band and valence band continuums of the TiO2 slab are shown by the grey regions. (d, e) The hot electron density (yellow) and the hot hole density (green) at t = 20 fs calculated by Eqs. 12 and 13, respectively.

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e)

-5

Hot electron populations (10

-4

Net charge in TiO

2

(10

-4

e)

-4

(a)

-3

-2

-1

0

(b)

-8

-6

-4

-2

0

2.5 (c)

Hot hole populations (10

-4

2 3

1.5

4

-4

e/fs)

e)

1

2.0

Current (10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.0

0.5

0.0

-0.5 0

10

20

30

40

50

2

4

6

0

Time (fs)

10

20

30

40

50

Time (fs)

Figure 4: (a) The net charges in the TiO2 layers marked in Fig. 1a. Negative signs indicate net electron injections into the TiO2 layer. Larger absolute values indicate more net charges in the TiO2 layer. (b) The populations of hot electrons (top panel) and hot holes (bottom panel) in each TiO2 layer. According to our definitions (Eqs. 12 and 13), the calculated populations of hot electrons are negative and those of hot holes are positive. The absolute value gives the number of hot electrons/holes in the TiO2 layer. (c) The currents at the planes marked as the colored dashed lines in Fig. 1a, calculated by Eq. 19. Positive values indicate net electrons moving downwards. In this figure, the different colors correspond to the different layers/planes defined in Fig. 1a.

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(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 5: The total charge density difference between 10 and 0 fs (a, e), between 15 and 10 fs (b, f), between 24 and 15 fs (c, g), and between 34 and 24 fs (d, h). The yellow color (a-d) indicates electron accumulations and the green color (e-h) indicates electron depletions.

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Graphical TOC Entry

LSPR decay

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TiO2(110

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