Tailoring Hot-Carrier Distributions of Plasmonic Nanostructures through Surface Alloying

Alloyed metal nanoparticles are a promising platform for plasmonically enabled hot-carrier generation, which can be used to drive photochemical reactions. Although the non-plasmonic component in these systems has been investigated for its potential to enhance catalytic activity, its capacity to affect the photochemical process favorably has been underexplored by comparison. Here, we study the impact of surface alloy species and concentration on hot-carrier generation in Ag nanoparticles. By first-principles simulations, we photoexcite the localized surface plasmon, allow it to dephase, and calculate spatially and energetically resolved hot-carrier distributions. We show that the presence of non-noble species in the topmost surface layer drastically enhances hot-hole generation at the surface at the expense of hot-hole generation in the bulk, due to the additional d-type states that are introduced to the surface. The energy of the generated holes can be tuned by choice of the alloyant, with systematic trends across the d-band block. Already low surface alloy concentrations have a large impact, with a saturation of the enhancement effect typically close to 75% of a monolayer. Hot-electron generation at the surface is hindered slightly by alloying, but here a judicious choice of the alloy composition allows one to strike a balance between hot electrons and holes. Our work underscores the promise of utilizing multicomponent nanoparticles to achieve enhanced control over plasmonic catalysis and provides guidelines for how hot-carrier distributions can be tailored by designing the electronic structure of the surface through alloying.

Prototypical plasmonic metals such as Ag [8,27], Au [3,4,28] or Cu [6,7] are used due to their outstanding optical properties.However, recently there has been increased interest in multicomponent NPs, such as antenna-reactor [29][30][31], core-shell [32] or single-atom alloys [29,33].This interest is motivated by the fact that typical plasmonic metals (Ag, Au or Cu) have the right optical properties but are poor traditional catalysts.In fact, using NPs with a plasmonic core and a catalytic surface alloy, several groups [29,30,32] have achieved better photocatalytic rates than with single-component systems.Several mechanisms can lead to improved reaction rates, and as the processes take place on picosecond or femtosecond scale they can be hard to distinguish.Assuming that the reaction barrier is lowered by an occupation change in an orbital of the reactant [19], the charge transfer can take place either directly by the LSP dephasing into a charge transfer excitation [24,27,34,35], or indirectly by scattering of a HC from the reactive surface of the NP.In the latter case, HCs need to be generated at the surface (directly through the decay of the LSP or through electromagnetic field enhancement, often called plasmon induced resonant energy transfer [30,36,37]) or scattered from HCs generated throughout the NP [38].To add further complexity, all processes eventually lead to local heating, which by itself usually increases catalytic activity, and care needs to be taken to disentangle these effects experimentally [19,[39][40][41][42]. Theoretical and computational modeling can provide insights into these processes, allowing the rational design of efficient devices [12,17,20,24,35,39,[43][44][45][46][47][48][49][50][51].Strategies for optimizing HC generation rates and tailoring HC distributions are particularly valuable.
In this work, we study the influence of surface alloying on HC generation in plasmonic Ag NPs.We find that already a modest surface alloy concentration in core-shell or core-crown configurations can enhance the generation of hot holes, and that the d-band position of the alloy dictates the energy distribution of the holes.We emphasize that in our NPs, the shell is photocatalytically active, in contrast to earlier work that considered a photoactive core and a catalytic shell [32,52].We model plasmon decay and HC formation using methods developed in our group [18,[20][21][22] based on real-time time-dependent density functional theory (RT-TDDFT) [53].We drive our systems with an ultra-short laser pulse, simulate the electron dynamics until the plasmon has decayed, and then analyze the distribution of carriers over the ground state Kohn-Sham (KS) states.The dephasing process of the LSP into HCs has been studied in detail before in Ref. 20,35, which also provide a detailed description of the methodology.

II. RESULTS AND DISCUSSION
A. Tuning the HC distribution via surface composition: Getting the holes to the surface We study the influence of alloying on HC formation by considering a few geometrically identical NPs.We compare unalloyed Ag with core-crown Ag-Pt NPs where substitutions are made in the top surface (Fig. 1a; see for details).These NPs have a LSP resonance at 3.3 eV corresponding to excitation along their long axis (Fig. 1b).The maximum of the LSP decreases while the peak broadens with increasing surface alloy concentration, in agreement with experiment [32].
The surface hole distribution (Fig. 1c, where the "surface" is defined in Fig. 1a), following resonant LSP excitation (laser pulse ℏω pulse = 3.3 eV), depends sensitively on the alloy concentration: The unalloyed NP has relatively few holes in the surface, in the energy range between −ℏω pulse and 0 eV.Already a modest surface alloy concentration of 17 % greatly increases the hole distribution, in particular between −1.5 and −0.5 eV.While the total number of holes (i.e., the integral of the distribution) increases with surface alloy concentration, the peak of the distribution also shifts closer to the Fermi level, thus yielding "colder" holes.In contrast, the total number of surface electrons decreases as Pt is added to the surface (Fig. 1d) while the distribution shifts to higher energies, corresponding to "hotter" electrons.
The projected DOS (PDOS) in the surface layer (Fig. 1e) indicates which surface states are available.In the unalloyed NP, the PDOS consists of many occupied and unoccupied Ag sp-states above about −4 eV as well as d-states below approximately −4 eV.The latter states do not appear in the hole distribution, as they are further away from the Fermi level than the energy supplied by the resonant laser pulse (3.3 eV).As Pt is substituted into the surface, Pt d-states appear between −1.5 and −0.5 eV, while the number of Ag d-states (around −4 eV) decreases.The gradual shift of a Ag-like d-band to a Pt-like d-band with increasing concentration coincides with the increased amount of hole formation after resonant laser excitation.With increasing Pt concentration, additionally the sp-states shift to higher energies, which is reflected in the electrons becoming "hotter".We note that while for the 269-atom NP studied here, which is about 2 nm in size, the density of states is discrete, for larger NPs it would approach a continuum.

B. Why does it work: Localizing the holes at the surface
For alloyed NPs, the increase in hole carriers at the surface comes at the expense of holes in the bulk (Fig. 2a; also see Fig. 3).While the number of holes at the surface doubles (100 % increase) for a 17 % surface alloy coverage compared to the unalloyed NP, the number of holes in the bulk is reduced by 20 %.This also applies to "hot" holes, which we here define as hole states with an energy of more than 1 eV below the Fermi energy.The concentration of the latter is enhanced almost threefold (183 %) at the surface while their concentration in the bulk is reduced by 2 % compared to the pure Ag NP.In the fully alloyed surface, these numbers increase to 196 %/337 % for all/hot holes in the surface and a reduction of 50 %/24 % in the bulk.Alloying thus pulls holes from the bulk to the alloyed surface, while the total number of holes decreases somewhat due to the broader LSP resonance (Fig. 1b).
The total number of excited electrons is also decreased by alloying, but the decrease is more severe in the surface than in the bulk (Fig. 2a).Hence there is a trade-off when alloying between increasing the amount of holes or electrons in the surface, such that at, e.g., 17 % surface alloy concentration one can excite both many electrons and holes (Fig. 3).Similar trends are observed for the hole distribution when exciting the system using an offresonant pulse (Fig. 2b-c), while the electron distributions change less systematically.
Electrons and holes differ qualitatively in how they are affected by alloying because electrons always populate spstates, which are delocalized in character, and holes may populate the Pt d-type states, which are localized.In the unalloyed NP, holes, hot holes, and electrons are fairly evenly distributed over the NP (Fig. 2d).The electrons are only in slight excess at the edges of the NP, which is due to preferential localization of carriers to undercoordinated surface sites [20].In the NPs with surface alloy concentrations of 17 % and 100 %, a large fraction of holes and hot holes are localized at alloy sites, while the density of electrons remains relatively uniform (Fig. 2e-f).The localization of holes at the surface also becomes apparent by comparing the surface hole distribution (Fig. 2g) to the bulk hole distribution (Fig. 2i), where the former even shows a non-monotonic variation with composition.In contrast, electron distributions in the surface (Fig. 2h) and bulk (Fig. 2j) are similar to each other because they are delocalized over the entire NP.The electron distributions are relatively unaffected by alloying except for an overall shift of states and decrease in intensity.
The number of hole carriers at the surface increases with alloying until it reaches a maximum at 75 % alloy concentration (Fig. 3), with the steepest increase at low concentrations.To understand why the increase is not simply linear with the alloy concentration (even after compensating for the lowered absorption; see Fig. S1), as one might expect, the mechanism of carrier formation has to be considered.Carriers are formed in pairs after plasmon decay, with the energetic difference between electron and hole equal to ℏω pulse [35].(Note that we do not consider electron-electron or electron-phonon scattering processes in our calculations.)The pulse frequency and width thus determine which electron hole pairs can form.However, the probability of electron-hole pair formation depends additionally on the coupling strength of the pair to the LSP.The saturation of hole formation at high concentrations could thus be caused by screening of the d-type holes and their interaction with the LSP.
For completeness, we also consider alloying of more than one full surface layer on one side of the NP (corecrown alloy) as well as layers on both sides (core-shell alloying; Fig. S2 and Fig. S3).As expected, this increases the total amount of holes in the surface (counting all alloyed layers), but there are fewer holes per layer due to the further decreased absorption.
Finally, we note that we can also generate holes in the d-band of Ag by using pulses that are sufficiently energetic to excite transitions to unoccupied states, i.e., for ⪆ 3.8 eV).The resulting hole densities are, however, notably lower than for less energetic pulses and the holes form predominantly in the bulk (Fig. S4).Highly energetic holes in the bulk are usually not the intended outcome, so this is not so relevant for the Ag-core-Ptshell system.It could, however, be of interest in, e.g., core-shell structures with an Ag shell and a core lacking a d-band (e.g., Al).

III. TUNING THE HC DISTRIBUTION THROUGH CHEMISTRY: MOVING THE DISTRIBUTION IN ENERGY
It is now instructive to explore the effect of the character of the alloyant on the hot carrier distribution.To this end, we compare the HC distribution for seven different alloyants from the d-block of the periodic table, while keeping the pulse frequency fixed to the LSP peak and the surface alloy concentration at 17 % (Fig. 4a-b and Fig. 5).The PDOS in the surface layer (Fig. 4c) shows the d-states of the alloyant shifting closer to the Fermi level as the alloyant is found further to the left in the periodic table, i.e, as the number of electrons in the outermost d-shell of the alloyant decreases.
The hole distribution appears to be a mixture of the bare Ag NP hole distribution (holes between −1 and −0.5 eV, corresponding to sp-states) and holes in the dstates of the alloyant, which is to be expected, as the surface consists of both Ag and alloyant atoms.
The energetic distribution of electrons is almost independent on the alloyant, as the valence band structure is relatively similar for all considered alloys, and because the unoccupied states are delocalized over the entire NP.The variation of the hot carrier distribution with surface concentration is similar as in the case of Pt (Fig. S5).
The working principle of HC generation in these NPs is that a LSP is induced in the Ag core by absorbing light, and decays into excited electron-hole pairs.The electron-hole pairs consist of both intraband sp-sp transitions and interband d-sp transitions, where the former are entirely delocalized and the latter consist of localized holes and delocalized electrons.The alloyants provide occupied d-states at the surface, allowing holes to form.By controlling the alloyant concentration and species the hot-hole distribution can thus be tuned (Fig. 6).The group 10 transition metals Pt and Pd produce holes between −2 and 0 eV.Moving to the left of the d-block of the periodic table, the d-band shifts closer to the Fermi level, so that the group 9, 8, and 7 elements Rh, Ru and Re generate holes between −1 and 0 eV.

IV. CONCLUSIONS AND OUTLOOK
We have modeled core-crown NPs with plasmonic Ag cores and transition metal crowns.Our results show that core-crown alloying can be effective for enhancing HC distributions at the surface of nanostructures.In particular, we have shown that the type of alloyant influences the energy of the holes in the resulting surface hot-hole distribution (Fig. 6) but has a very minor impact on the surface hot-electron distribution.The alloyant surface concentration determines the intensity of the HC distributions, as the number of induced holes increase with concentration while the number of electrons decreases.
In general, alloying broadens the optical absorption peak, and thus typically reduces the amount of energy absorbed when exciting the system with a laser resonant with the LSP.In part because of the lower absorption, the amount of excited electrons decreases with alloyant concentration.One should, however, probably also consider the additional effect of the intraband transitions coupling more weakly to the LSP when alloying.The mechanism of such an effect is hard to pinpoint.Despite the lower total absorption, the amount of holes increases non-linearly with increasing surface alloy concentration, and saturates around 75 %.The saturation could be explained by the presence of many holes in d-states screening the coupling between the plasmon and the interband transitions.
Based on our results, we would suggest to design as thin shells as possible in core-shell setups.Alloying less than one full layer is actually preferable as this approach enables the biggest gains in hot-hole enhancement without suffering a big loss in hot-electron generation.Even if for larger NPs the optical spectrum is not as significantly affected, there is the presumed effect of screening of the interband transitions.
In our work, the HC distributions reach a steady state after a few tens of femtoseconds, because our model does not include decay channels such as reemission, Auger scattering (would require a non-adiabatic exchange correlation (XC)-kernel) or electron-phonon scattering.For the HCs to do any useful work, such as catalyzing a chemical reaction, they would need to transfer across the interface to another system, possibly undergoing scattering processes in the NP; a process that may take several picoseconds [54].From an application point of view, the observable of interest would be the rate of HC transfer to the system of interest (or the catalytic rate) that is in competition with the various decay channels.Modeling these processes is beyond the scope of our work.Despite studies showing that relaxation times are somewhat dependent on alloyant [23,55], we can expect that a higher steady state HC distribution (that is barring the decay channels) predicted in our work, corresponds to a higher catalytic rate.
The HC distributions depend weakly on the pulse frequency, in the sense that the intensity, but not the shape, changes.We thus expect our analysis using a narrow Gaussian laser pulse in resonance with the LSP, to be also applicable for absorption of solar light.

A. Structures
All NPs that we consider are identical in geometry: cuboids consisting of 7-by-11 atomic layers (1.2-by-2 nm) of a fcc lattice.The lattice constant is 4.09 Å and we have not relaxed the structures, in order to study the effect of chemistry and not local geometry effects.We consider core-crown NPs alloys, where the top surface atoms (Fig. 1a) have been swapped to the alloy species, and core-shell NPs, where both top and bottom surfaces have been swapped.Additionally, we consider severallayer swaps and partial layer swaps (Fig. S7).

B. Computational details
The open-source GPAW [56,57] code package was used for all calculations.KS density functional theory ground state calculations were performed within the projector augmented wave [58] formalism using linear combination of atomic orbitals (LCAO) basis sets [59]; the pvalence [60] basis set, which is optimized to represent bound unoccupied states, was used for the metal species.The PBE [61,62] functional with a Hubbard +U correction [63] in the form by Dudarev et al. [64] was used, with U values 3.5 eV for Ag, 2.5 eV for Au, and 4.5 eV for Cu.A simulation cell of 25.6 Å × 25.6 Å × 38.4 Å was used to represent wave functions, XC, and Coulomb potentials, with a grid spacing of 0.2 Å for wave functions and 0.1 Å for potentials.The Coulomb potential was represented in numerical form on the grid, with an additional analytic moment correction [65] centered at the NP.Fermi-Dirac occupation number smearing with width 0.05 eV was used.The self-consistent loop was stopped when the integral of the difference between two subsequent densities was less than 1 × 10 −12 .Pulay [66]-mixing was used to accelerate the ground state convergence.
The LCAO-RT-TDDFT implementation [60] in GPAW was used for the RT-TDDFT calculations.A δ-kick strength of K z = 10 −5 in atomic units was used.The time propagation was done in steps of 10 as for a total length of 30 fs using the adiabatic PBE+U kernel.We computed carrier generation for an external electric field corresponding to an ultra-short Gaussian laser pulse of frequency ω, strength E 0 = 51 µV Å −1 , peak time t 0 = 10 fs, and duration τ 0 = 3.0 fs.Following the methods of Refs.20, 35, the computation of hot carrier generation was carried out by convoluting the first order density response of the δ-kick-calculation with the laser pulse, and the hot-carrier distributions were projected according to the atomic layer Voronoi weights.
We computed the total density of states as and the PDOS for the atomic layers as where ε k and ϕ (0) k (r) are the KS eigenvalues and wave functions.For visualization, the δ-functions in energy were replaced by a Gaussian (2πσ 2 ) −1/2 exp(−ε 2 /2σ 2 ) with width σ = 0.05 eV.

DATA AVAILABILITY
The data generated in this study are openly available via Zenodo at https://doi.org/10.5281/zenodo.10047664.

FIG. 1 .
FIG. 1. Distribution of hot carriers at the surface of Ag-Pt NPs as a function of composition.(a) NP geometry studied here, with the top surface marked, which is alloyed and where the carrier distributions are evaluated.(b) Absorption spectra of Ag-Pt NPs with different Pt surface concentrations.(c) Hole and (d) electron distributions at the top surface after resonant laser excitation as a function of surface composition.(e) Projected DOS (PDOS) of the top surface.The dotted lines in (c-e) correspond to the spectra shown in (b).

FIG. 2 .
FIG. 2. Hot carrier distribution in Ag-Pt NPs as a function of pulse energy and location.(a-c) Number of induced carriers in the surface and bulk, respectively after resonant (3.3 eV) and off-resonant (2.9/3.7 eV) laser excitation, for the unalloyed, optimally alloyed (17 %), and fully alloyed NP.The portion of carriers with an energy of more than 1 eV relative to the Fermi level are shown by solid bars (referred to as "hot carriers" in the text).The fraction of carriers with an energy below this threshold is indicated by hatched bars.(d-f) Visualization of hole, hot hole, and electron densities after resonant laser excitation for unalloyed, optimally alloyed (17 %), and fully alloyed NPs.The densities have been integrated over the z-direction.(g) Hole and (h) electron distributions in the surface and (i-j) in the bulk, as a function of surface alloy concentration.

7 FIG. 3 .
FIG. 3. Number of HCs at the surface of the corecrown Ag-Pt NP for different surface alloy compositions by energetic range after excitation with a laser at the LSP peak (3.3 eV).

FIG. 4 .
FIG. 4. Variation of hot carrier distribution with alloyant.(a) Hole and (b) electron distributions for Ag-alloy NPs with a surface composition of 17 % after excitation with a laser at LSP peak (3.3 eV).(c) PDOS in the top surface layer.

7 FIG. 5 .
FIG. 5. Number of hot carriers in the top surface for Agalloy NPs with a surface composition of 17 % after excitation with a laser at the LSP peak (3.3 eV).