Dynamical evolution of the Schottky barrier as a determinant contribution to electron-hole pair stabilization and photocatalysis of plasmon-induced hot carriers

The harnessing of plasmon-induced hot carriers promises to open new avenues for the development of clean energies and chemical catalysis. The extraction of carriers before thermalization and recombination is of primordial importance to obtain appealing conversion yields. Here, hot carrier injection in the paradigmatic Au-TiO$_{2}$ system is studied by means of electronic and electron-ion dynamics. Our results show that pure electronic features (without considering many-body interactions or dissipation to the environment) contribute to the electron-hole separation stability. These results reveal the existence of a dynamic contribution to the interfacial potential barrier (Schottky barrier) that arises at the charge injection pace, impeding electronic back transfer. Furthermore, we show that this charge separation stabilization provides the time needed for the charge to leak to capping molecules placed over the TiO$_{2}$ surface triggering a coherent bond oscillation that will lead to a photocatalytic dissociation. We expect that our results will add new perspectives to the interpretation of the already detected long-lived hot carrier lifetimes, their catalytical effect, and concomitantly to their technological applications.


Introduction
Plasmonic nanoparticles (NP) have striking light-harvesting capabilities that stem from the collective oscillation of conduction band electrons in resonance with light electric field, process known as localized surface plasmon resonance (LSPR). 1 Harnessing this optical feature has triggered a wide stream of research in areas related to light conversion as photocatalysis, and the development of photovoltaic systems. 2,3 For small NPs Landau damping, the decoherence of electrons involved in the plasmon excitation, is the fastest dissipative mech-anism of the energy absorbed by the LSPR photoexcitation, leading to the formation of electron-hole pairs excited beyond the thermal energy, usually named as hot carriers. [4][5][6] For many years, it was a common understanding that the electron-electron scattering would hindrance the harnessing of hot carriers generated during the LSPR excitation. Nevertheless, in the last decade experimental evidence showed that hot carriers injection to the medium, capping molecules 7 or semiconductors, 8 take place by an ultrafast mechanism (lifetime of ∼50 fs) that competes with thermalization. This fascinating discovery has pervaded the nanoscience community and placed the plasmon-induced hot carrier generation and exploitation as a research mainstream.
Chemical catalysis driven by plasmon-induced hot carriers has been proven in several chemical reactions involving oxidation or reduction of small molecules, 9,10 degradation of organic molecules, 11 and even in high energy cost reactions like water splitting [12][13][14] and H 2 dissociation. 15 On the other hand, ultrafast injection to semiconductors has also been thoroughly studied experimentally. [16][17][18] Furthermore, the lifetime of the injected carriers in semiconductors is under vigorous research because it sets the time bounds for their exploitation. Remarkably, this has been estimated in the order of hundreds of picoseconds 19,20 to nanoseconds, 21 challenging our interpretation of the problem and raising questions regarding the chemical catalysis mechanisms. 22 On the side of theoretical research, much effort has been invested to disentangle the hot-carrier generation process and their energy distribution in several plasmonic materials by means of many-body, 23 Nevertheless, much less has been done in the field of ab-initio simulations of the charge injection dynamics and the subsequent catalytic effect of hot carriers. Some recent benchmarks along this line are worth highlighting. Hot carrier injection from a metallic cluster to semiconductors have been studied by nonadiabatic molecular dynamics, 38,39 and recently a detailed description of the charge localization in a Ag-TiO 2 hybrid system has been performed by means of real-time time-dependent DFT (RT-TD-DFT). 40 Besides, nonadiabatic molecular dynamics has been employed to study the dissociation of H 2 on gold NPs dimers, 41 N 2 dissociation by hot carriers produced in silver wires 42 and water splitting over gold NP. 43 In this context, by means of real-time time-dependent tight-binding DFT (RT-TD-DFTB) electronic and electron-ion dynamics, we studied the hot carrier injection in the paradigmatic Au-TiO 2 system. To simulate nanosized structures, a new DFTB parameterization is presented that successfully describes the electronic properties of the hybrid NP. Regarding the charge injection, our simulations show that pure electronic features (without considering many-body interactions or dissipation to the environment) are enough to justify the electron-hole separation stability. Typically, the prolongation of the hot-carrier lifetimes in metal-semiconductor hybrid systems is attributed to the Schottky barrier (SB), i.e. the potential asymmetry rendered by the charge accumulation at the interface that occurs due to the Fermi level equalization, and the cooling of the electronic subsystem that together with the SB locks the electronic backscattering. Our results show intrinsic electron-hole separation stability without cooling interactions and even in the presence of laser pumping. This unveiled the existence of a dynamic contribution to the Schottky potential barrier (DSB) that arises at the charge injection pace, locking the electronic back transfer. It's important to state that this mechanism differs from the dynamical detuning of acceptor-donor states described in reference 44. This dynamic contribution to the electron-hole stabilization has been overlooked and can be a missing piece in the complex puzzle that renders the hot carrier lifetime in nanosized structures. Furthermore, the electron-hole stabilization provided by the DSB is important to describe the photocatalytic effect of the plasmon-induced hot carriers. Here we show that charge leaks to capping molecules placed over the TiO 2 surface triggering a coherent oscillation of the nuclei that will lead to a photocatalytic dissociation.
We expect that our results will add new perspectives to the interpretation of the already detected long-lived hot carrier lifetimes, their catalytical effect, and concomitantly to their technological applications. This effect arises from the electronic coupling between both NPs and increases as the energy increases due to the coupling of the electronic structure of both systems.

Results and discussion
To obtain information on the charge injection dynamics from the metal to the semiconductor, the [Au-TiO 2 -CO] cluster was irradiated with a continuum laser and a 50 fs laser pulse in resonance with the LSPR frequency. The charge separation is described by splitting the structure into two moieties, the metallic NP and the TiO 2 plus the CO molecules. It is important to stress that this direct transfer mechanism, mediated by the redistribution of the absorbed energy, is very similar to the type-II charge transfer mechanism in dyesensitized semiconductors, where is well established that the charge current follows a linear trend with the laser power. 48 Note that the main difference between both mechanisms is that in the dye-sensitized systems laser excites a charge transfer band, whereas, in the hot carrier transfer, the energy is absorbed by the plasmonic excitation and the direct transfer is an outcome of the energy deactivation. Observations (I) and (II) may be easily understood when considering electron-electron, electron-phonon scattering, and energy dissipation to the environment. Nevertheless, none of these are taken into account in results presented in figures 2 and S1. Hence, the dynamical outcome of our simulations unveils the existence of purely electronic ingredients that stabilize the photoinduced electron-hole pair formed between Au and TiO 2 NPs.
The first ingredient is the development of a dynamical contribution to the Schottky barrier (DSB) that arises as a consequence of hot carrier injection, locking the back transfer process even in the case of continuum irradiation. The electrostatic contribution to the DSB is presented in figure 3a as a volume rendering of ∆V = V t − V t=0 i.e. the developed electrostatic potential with respect to the ground state; note that this is different from the effective potential an electron would probe. ∆V is obtained from the dynamical atomic charges, the reference potential being zero at infinity as the system is an isolated cluster.
For clarity, we present a slice of the 3d rendering centered at the interparticle axes. In To add more information regarding the origin of the DSB component, we employed a dimer of the same Au NP and a 852-atom TiO 2 NP, this allows differentiating the bulk and out-layer atoms. The dimer is shined by a laser pulse that produces the charge transfer and we focus on the atomic charge evolution. We compute the difference of the atomic charge at the ground state and at the end of the dynamics (∆q). Figure S3 presents an x−z projection of ∆q 50 fs after the laser pulse ends. It can be clearly seen that the injected charge and the remaining holes lock at the interface in good agreement with reference 40. This information points to the origin of DSB as follows. The SB arises because of the Fermi level equalization between both materials. In that process, a ground state charge transfer occurs, and most of that charge pins to the interface giving rise to the SB. Now, if the plasmon-induced charge transfer also pins at the interface, it is expected that the resulting barrier should be modified, giving rise to DSB.
One SB feature is the current rectification provided by the barrier asymmetry. In figure   3c we show the charge rectification that arises when an electric field, polarized in the positive or negative x direction (E + and E − , respectively), is applied for 25 fs to the system after the Furthermore, as we are going to discuss in the following paragraphs, the locking of the back transfer provided by the potential barrier can help to understand the catalytic activity of the injected hot carriers when electron and ions dynamics are coupled.
The second ingredient is an entropic contribution to the charge separation stabilization.
As the charge is injected from the Au NP to the TiO 2 the total electronic entropy increases (see figure S5). Therefore, without additional driving forces, the electron transfer is irre-  It is interesting to note that due to the perturbation, part of the charge received by the TiO 2 is driven to the CO molecules. Remarkably, after the perturbation ends the charge leaking to the CO molecules remains linear until 250 fs, the longest time affordable for this kind of simulation and system size. As the charge reaches the CO molecules, the C-O bond is weakened and the bond distance increases as can be seen with a gray line. The bond distance is informed as a percent of change of the ground state distance. As the bond is weakened the interatomic oscillation increases rapidly keeping also a nearly linear growth pace as the running average (red line) highlights. The elongation of the molecular bond can be rationalized if we look at the molecular orbitals involved in the dynamics. Panel (b) presents a representative molecular orbital of those being populated during the charge injection. As can be appreciated, this possesses an antibonding nature in the C-O coordinate (see nodal plane highlighted with reds dashed lines) which denotes that the injected charge will lead to a photocatalytic dissociation. Figure S7 show that the general trends described for the CO molecules are also obtained for H 2 molecules, which point to the fact that the conclusions obtained regarding the DSB and its implication in the electron-hole stabilization and photocatalytic effect of the hot carriers are not a particularity of the model system.
It is important to stress that the results here discussed were obtained with zero initial velocities in all nuclear degrees of freedom (zero phononic temperature). Although this can be an unfavorable condition to observe a photocatalytic process as complex as the one here Furthermore, the electron-hole stabilization provided by the DSB is important to describe the photocatalytic effect of the plasmon-induced hot carriers. Here we show that charge leaks to capping molecules placed over the TiO 2 surface triggering a coherent oscillation of the nuclei that will lead to a photocatalytic dissociation. We expect that our results will add new perspectives to the interpretation of the already detected long-lived hot carrier lifetimes, their catalytical effect, and concomitantly to their technological applications.

Methods
Density Functional Theory. Density functional calculations were performed using the periodic open source Quantum Espresso software. 50 The PBE generalized gradient approxima-tion functional 51 for the exchange-correlation term was adopted using the high-throughput GBRV pseudopotentials, 52 with standard kinetic energy cutoffs of 40/200 Ry for the wavefunction/charge density, respectively. 10Å of vacuum space between nanostructures was used in each dimension to avoid spurious interaction between replicated cells. The reciprocal space was described within the Gamma approximation. Unless indicated, structures were fully relaxed using a force convergence of 0.01 eV/Å. The resulting parameterization was tested by comparing the binding energy and the Au-Ti bond distance obtained by DFT simulations. For this purpose, and considering the computational cost of a DFT geometry optimization, a model structure was generated using half of a 147 atom icosahedral Au NP and the TiO 2 NP (see figure S8). Furthermore, for the structural optimization, the Au atoms at the cut plane were held fixed. The binding energy difference between the Au and TiO 2 NP computed for the structure optimized at the DFT and the DFTB levels was ∼6% while the Au-Ti bond distance difference for the atoms at the interface was ∼1% Nanoparticle structure. The metallic NP was modeled by an icosahedron of 309 Au atoms. The TiO 2 NP was generated using a Wulff construction 57 from the anatase bulk geometry. In this approach we restricted the nanoparticle morphology to that exhibiting the most stable surface (101). 58 As a result, a stoichiometric bipyramid composed of eight (101) facets was built (see figure S9a). The smallest nanoparticle constructed in this manner consists of 105 atoms. The structure presents a danging-bond oxygen atom and low-coordinated Ti atoms at each apex. In order to avoid these sources of structure instability, the former NP was truncated in the apexes, as it has been done in previous studies. 59,60 Finally, six hydrogen atoms and two CO molecules were added to passivate the remaining dangling bonds of oxygen atoms and the low-coordinated Ti atoms, respectively (see figure S9b). In order to evaluate the structure stability of this nanoparticle, a molecular dynamic simulations based on a reactive force field 61 was performed using LAMMPS. 62 By means of a Nose-Hoover thermostat in the NVT ensamble, the oxide was first heated from 20 K to 300 K in 20 ps, and then kept at that temperature for the remaining 80 ps of the simulation. No reconstructions were observed. Moreover, the average coordination number (number of first neighbors) for Ti and O remain constant during the entire simulation. Finally, no significant changes were observed in the potential energy. It is then safe to conclude that the oxide nanoparticle is stable. Details are given in the supplementary material (see figure 10). At last, the whole system was reoptimized at the DFTB level. In the final structure, the CO-TiO 2 binding energy is on the order of 0.4 eV. As expected, this binding energy is smaller than those reported for perfect TiO 2 surfaces. 63 Electron and electron-ion dynamics For the quantum dynamic simulations of this nanosized system the electronic structure was treated at the self-consistent tight-binding  Table of Contents. This should be laid out "print ready" so that the sizing of the text is correct. Inside the tocentry environment, the font used is Helvetica 8 pt, as required by Journal of the American Chemical Society. The surrounding frame is 9 cm by 3.5 cm, which is the maximum permitted for Journal of the American Chemical Society graphical table of content entries. The box will not resize if the content is too big: instead it will overflow the edge of the box. This box and the associated title will always be printed on a separate page at the end of the document.