Surface plasmons, the collective oscillations of conduction electrons in metallic nanostructures, have emerged as an essential elementary excitation in condensed matter, giving rise to multiple practical applications. They can capture distant radiation and focus it within subwavelength regions, defying diffraction limits,1,2 resulting in potent near-fields and profound field amplifications.3 These attributes have propelled innovative applications of plasmonics, such as highly sensitive biosensing,4 photothermal therapy for cancer,5 photovoltaics,6,7 and photocatalysis. 8
Surface plasmons exhibit finite lifetimes, decaying either by photon emission (radiatively) or the creation of electron-hole pairs (nonradiatively). Over the past decade, the radiative decay pathway has been researched extensively, yielding the development of efficient nanoantennas that amplify and steer emissions from individual emitters.9,10 Recent research has focused on leveraging nonradiative decay for applications.11 Hot carriers can initiate chemical reactions in adjacent molecules, even those that demand high energy under conventional thermal conditions.12,13 Moreover, plasmon-induced hot carriers offer a potent means to transform light into electrical currents,14 fostering novel solar energy converters15 and circumventing the bandgap limitations of traditional photodetectors.16
While the direct excitation of hot carriers on metal surfaces using high-intensity laser pulses has been a longstanding practice in surface femtochemistry, exploiting surface plasmon decay to amplify hot carrier generation is a recent development. This significant advance stems from the remarkably boosted light harvesting ability of collective plasmon excitations, combined with the substantial enhancement of the plasmon-induced field when metals are nano-confined. Comprehending the underlying physical mechanisms driving plasmon-induced hot carrier generation is essential to leverage these benefits fully. Although theoretical frameworks elucidating this phenomenon exist,17-18[i]19[ii]20[iii]21[iv]22 a suitable experimental methodology to validate these models still needs to be developed.
X-ray absorption spectroscopy (XAS) provides a way to investigate the interplay between X-ray photons and matter, simultaneously unveiling unparalleled insights into a material’s electronic and chemical characteristics. When X-ray photons are directed toward a material, they can be absorbed by core electrons, resulting in these electrons shifting to higher energy states. The precise energy at which this absorption occurs depends on the specific element's electronic structure and its local environment. Hot carriers emerge from the interaction between external electric fields and valence electrons, creating electrons and holes with energies above and below the Fermi level (EF).
Transient XAS (aka time-resolved XAS (TR-XAS)) probes empty states around theFermi energy and, in the case of d10 metals with the L3-edge transition, provides direct information about the amount of carrier participation and their nonequilibrium energy distributions.23 At synchrotrons, such dynamical measurements are typically hampered by limited temporal resolution (~ 5 ps) and photon density,24 impeding real-time observations of the hot carrier generation process.8 However, this limitation has been surpassed by the advent of hard X-ray free electron lasers (XFELs),25 capable of delivering intense and ultrashort hard X-ray pulses (up to 30 keV at the European XFEL26 and 12 keV at SwissFEL (used in this study) 27) of less than 50 fs in duration.27,28 With this unique combination of high photon energies and ultrashort pulses, time-resolved XAS has become an exceptionally valuable experimental probe of dynamical processes. Typical time-resolved measurements are implemented in a pump-probe scheme, where an optical-frequency pump laser triggers electron dynamics, and the X-ray probe captures the evolving nonequilibrium electron distribution. Over the past few years, femtosecond TR-XAS studies have been used to probe photoinduced electronic and structural changes in photoexcited transition metal oxides29 and complexes.30 In this study, TR-XAS was used to observe the generation and relaxation of plasmon-induced hot carriers in gold nanoparticles directly.31,32
The widely accepted understanding of how localised surface plasmon resonance (LSPR) excitation leads to hot carrier formation and subsequent thermalisation, including the hypothesised timescales for each process, is summarised in Figure 1A.8,22 Briefly, the light electric field induces a coherent excitation of Au valence electrons. The excited electrons' coherence dephases due to Landau damping after the light excitation elapses. The process is expected to take 10-100 fs, resulting in a non-Fermi-Dirac distribution of hot carriers. The carriers undergo multiplication, eventually reaching a Fermi-Dirac distribution and thermal relaxation after ~1 ps. This description of hot carrier formation has been deduced from physical models that underpin our understanding. Still, it has never been validated experimentally due to the lack of element-specific techniques with sufficient temporal resolution. However, the attempts from Bigot et al.33 and Lehmann et al.34 with femtosecond optical pump-probe investigations with ionising probe pulses, which provided earlier evidence for hot electrons and their dynamics, should be mentioned. Nevertheless, no information could be extracted about the hot holes.
Figure 1B illustrates the TR-XAS approach for tracking the density of states (DOS) changes induced by LSPR excitation. More specifically, the study focuses on the X-ray absorption near edge structure (XANES) part of the XAS spectrum, which contains the electronic changes in the element, i.e., information on LSPR-induced hot carrier formation. The transient data was collected using the classic pump-probe methodology for optical spectroscopy. The technique involves "pumping" a sample with an initial laser pulse and then "probing" it with a delayed pulse to observe the changes induced by the pump pulse. In the present case, the probe is an fs X-ray pulse from the XFEL. To prevent the excitation of damaged Au NPs induced by intense XFEL pulses, a liquid jet was employed to circulate the Au NPs and the solution was refreshed every four hours.
Since nanoparticle measurements at XFELs are uncommon, it was essential to validate that the XANES spectra collected with this radiation represent the sample. Figure S1 shows the steady-state XANES spectra of Au foil and nanoparticles measured at the Au L3-edge transition (2p3/2à 5d) at the synchrotron (Solaris synchrotron, Poland). Au has a [Xe] 4f14 5d10 6s1 electronic structure, i.e., with a filled d-shell, which results in a slight absorption edge only visible due to some level of s-d shell hybridisation. For comparison purposes, the signal was plotted against Pt ([Xe] 4f14 5d9 6s1) (Fig. S2), revealing the method sensitivity to empty states within the metal 5d shell and, to some extent, the s-shell due to this hybridisation. In this study, Au NPs with an average particle size of 8 ± 2 nm were used, as confirmed by atomic force microscopy (AFM) and dynamic light scattering (DLS) (Figs. S3 and S4). The Au NPs have a LSPR centered at nominally 520 nm (2.38 eV) according to UV-vis spectroscopy (Fig. S5).
The steady-state XANES analysis established that the Au NPs exhibit an electronic structure resembling bulk gold, as reported elsewhere.22,35 This agreement is further corroborated by our theoretical calculations, showing the evolution of the DOS as function of particle size (Fig. S6). The unexcited XANES spectrum of the Au NPs, measured at XFEL (SwissFEL, Switzerland) and the synchrotron, displayed a consistent shape. This consistency supports the applied methodology's ability to capture the transient alterations in the electronic structure of gold before the sample gets damaged, i.e., probe-before destruction concept.36, 37 XFELs have only recently provided access to hard X-ray energies, allowing one for the first time to probe the Au L3-edge.
Ultrafast time-resolved XANES data were acquired with the XFEL source as a probe, following the excitation of 5 mM Au NPs at 532 nm (~ 2.33 eV), utilising a 15 nm full width at half maximum (FHWM) bandwidth, a pulse duration of approximately 75 fs, and a power density of 98 mJ/cm2 (equivalent to 4 µJ within a 60 x 60 µm2 spot). The choice of this precise plasmon excitation energy was to induce LSPR through intra-band s- to s-shell excitation while minimising interband excitation (d- to s-shell excitation). The centre of the Au d-shell is located at 2.5-2.58 eV (~ 496-480 nm) from the metal Fermi level (EF),38,39 meaning that the laser pulse with 2.33±0.13 eV (15 nm FHWM) photon energy can only excite the low energy tail of the d-shell at best. Figure 1C compares the XANES spectra of unexcited (unpumped spectrum) and excited (pumped spectrum) recorded at Dt =100 fs time delay after excitation at 532 nm. Optical excitation induced a spectral downshift in energy and decreased XANES whiteline intensity, corroborating that it induced changes in the gold electronic structure around its Fermi-level energy, and the TR-XAS can track the changes.
To better illustrate the results, the XANES difference spectrum (pumped-unpumped XANES spectra) is also shown in Figure 1C. The difference spectrum is dominated by the positive signal below and a negative signal above the Au EF. Transient L3-edge XANES readily capture changes in the density of unoccupied states, particularly those induced in the d-shell, either directly or through processes like hybridisation with the s-shell. Accordingly, a positive signal correlates with an increase in density of states (DOS); conversely, a negative signal (i.e., a bleached signal) indicates a decrease in empty states. Therefore, the positive signal below the Au EF is ascribed to the formation of a hot hole population induced by the plasmon optical excitation. In contrast, hot electrons give rise to the negative signal above the Au EF, consistent with empty states filling. The transient signal directly demonstrates the generation of hot carriers through LSPR decoherence via Landau damping (the non-radiative pathway dominant in small nanoparticles).21,24,40 Most notably, the hot hole and electron signals are neither symmetric nor have the same integrated magnitude. This is related to the XANES higher sensitivity to empty states formation and the L3-edge transition changes in the d-shell that is part of the valence, where the hot holes are formed.
To establish the time scales for plasmon damping (g) and the average lifetime of carriers (t), kinetic traces were extracted at the maximum of the hot hole intensity (11916 eV, 2.5 eV below Au EF (Figure 2B)) and the excited electron intensity (11922 eV, 3.0 eV above Au EF (Figure 2C)) populations, as depicted in (Figure 2A). The kinetic data from the time scans were fitted by a model published elsewhere,41 described in SI equations S1 and S2. In brief, the data collected at 11916 and 11922 eV were fitted with a convolution of temporal instrument response function (Gaussian) with a monoexponential decay (with a time constant ). The resulting fit is the solid green in Figure 2B. Due to the low signal-to-noise ratio for the hot electron data, the error bars are relatively large. However, qualitatively, it is possible to see that the signal has dynamics similar to the hot holes.
The γ time can be extracted from the transient signal onset time because it is the point at which the Au DOS starts to change, i.e., the fingerprint for hot carrier formation. In this particular case, it was estimated to be 24.6 ± 6 fs, corroborating that plasmon decoherence occurs between 10-100 fs.24 Following plasmon damping, the hot carriers undergo a carrier multiplication reaching a maximum at 105 ± 8 fs, estimated from rising edge analysis. The lifetimes of the hot carriers were determined from a single exponential decay to be 498 ± 35 fs with complete carrier thermalisation occurring within 1.5 ps. These time constants align with previous postulations24 but are here substantiated through direct measurement. The confirmed ultrafast hot carrier dynamics in plasmonic nanoparticles are the primary bottleneck in plasmonic applications.
To estimate the number of electrons engaged when exciting 5 mM Au NPs at 532 nm, utilising a 15 nm full width at half maximum (FHWM) bandwidth, a pulse duration of approximately 75 fs, and a power density of 98 mJ/cm2, the positive signal variance at 0 and 100 fs were integrated. This integrated signal was then juxtaposed with the signal difference between the Au and Pt L3-edges (Fig. S2). Note that the signal difference between Au and Pt relates to 1e- less in Pt valence states, i.e., the integrated positive signal of the difference between Pt and Au corresponds to the equivalent of having 1e- from each Au atom participating in the resonance. Employing this simple methodology, we estimated that each gold atom contributed with 0.19e- at the start of the resonance, which underwent multiplication until 105 fs, reaching a maximum of 0.46e- from each Au atom contributing to hot carrier formation at this excitation power.
Assuming an excitation volume of 60 x 60 x 100µm3 and considering the Au solution concentration (5 mM), one can expect 1.5 x 108 nanoparticles in the excited volume. An 8 nm Au NP has »12000 atoms, equating to about 1.8 x 1012 Au atoms in the excited volume. The photon density in the optical pulses is about 1013, from which 20% is absorbed according to UV-Vis, implying that the excited volume absorbs around 2x1012 photons. This suggests an excitation of about 1e- per atom of Au, from which 19% are converted into hot carriers at the onset, multiplying to about 46% within 100 fs. The observation suggests that hot carrier generation is a prime decay channel of Au LSPR and undoubtedly the most significant mechanism in nonradiative decay.
After verifying the generation of hot carriers, the next step is the investigation of the dynamics of their energy distribution - a significant yet elusive aspect in the realm of plasmonic hot carriers, particularly when it comes to holes. Our understanding is derived mainly from theoretical studies20,4243 and indirect techniques.22,33,34,44 For example, internal quantum efficiency measurements have inherent limitations as they solely quantify carriers injected into an acceptor layer, like a semiconductor, failing to provide insights into the dynamic behaviour of the carriers in the metal. While the hot electrons can only populate the empty states within the sp-shells, the holes can be in sp- and d-shells, confirmed by valence band – X-ray photoelectron spectroscopy (VB-XPS) shown in Figure 3A. It is evident when the VB-XPS is overlapped with the transient XANES spectrum (recorded at time zero) that the generated holes are indeed located throughout the entire valence, including the d-shell, despite the optical pulse energy allowing primarily sp-shell excitation.
Figure 3B shows the energy distribution and population of the carriers at different time delays after excitation. As expected, the plasmonic excitation depopulates and populates states below and above the Fermi energy. The ultrafast carrier-carrier interactions during dephasing and multiplication determine their energy and respective population. The hot carrier energy distribution goes beyond single photon energy for hot electrons and holes. Moreover, it is noticeable that both carrier populations and the width of their energy distributions increase until about 100 fs, decreasing asymptotically after that. A slight asymmetry exists between hot electron and hot hole populations, which cannot be fully explored here due to the probe's lower sensitivity to hot electrons.
The rapid depopulation of electrons in the d-shell is expected due to the broad energy overlap between the d and sp-band, which provides a high density of d-electrons that couples with the plasmonic resonance and dissipates its energy.43 However, this does not explain the observation of carriers having energies above the photon energy, even considering that the Au core-hole lifetime broadening is 5.41 eV at the L3-edge,45 which inevitably broadens the energy scale. Achieving precise energy distributions of carriers requires high-resolution measurements,46 which implies extended acquisition times rarely offered at XFEL facilities. Nonetheless, hot holes are distributed across the entire valence electronic structure, and their energy distribution increases up to 250 fs (Figure 3C) before relaxing. These two observations indicate the involvement of carrier multiplication mechanisms that can increase the carrier population and their energy distribution, an effect that has yet to be reported.43 Note that the low optical laser fluency and short pulse duration used in this experiment make it highly unlikely that multiphoton excitation of single electrons occurs.
Regarding carrier multiplication, there are two scattering mechanisms: impact excitation and Auger heating,47,48 The predominant mechanism in carrier multiplication is impact excitation, where an excited electron (hole) undergoes Coulomb scattering, losing energy and momentum and giving rise to an additional electron-hole pair. The distinctive feature of impact excitation is a rise in the number of carriers and a simultaneous reduction in their energy. Conversely, Auger heating characterises the non-radiative recombination of an electron with a hole, where the energy and momentum are transferred to an electron (hole) within the same shell. The hallmark of Auger heating is a decline in the number of carriers and an increase in their energy.
To enhance the visualisation and comprehension of the hot hole multiplication process, the shape of different spectra regarding charge width and charge energy was analysed (see Figure 3C). The details of the data analysis procedure are outlined in the SI. Commencing with the average hot carrier distribution energy, it remained constant until 100 fs before exhibiting a subsequent decrease. This implies the LSPR dephasing process extends to 100 fs, increasing the nonequilibrium hot carrier population through the impact excitation scattering mechanism. However, examining the hot carrier distribution width, reflecting the energy distribution of the hot holes unveils a relative surge in the energy distribution beyond the time when the hole population is at its maximum (approximately 100 fs), i.e., the energy distribution of hot holes increases up to 250 fs. This observation is noteworthy, especially considering this process competes with hole thermalisation, occurring within tens of femtoseconds in metals. The broadening induced by the core hole relaxation cannot account for the increase in distribution width, as it should have smeared the energy resolution from the outset, preventing the difference signal from accurately reflecting the valence state of gold. This suggests the involvement of a mechanism that generates carriers with higher energy than the dephasing process produces - specifically, the participation of Auger heating. This mechanism has yet to be considered in plasmon relaxation dynamics, altering the current understanding of hot carrier formation, multiplication, and relaxation in plasmonic materials.
In this work, we presented the results from an ultrafast X-ray absorption experiment conducted at the XFEL involving citrate-capped gold nanoparticles excited at their LSPR with minimum intraband excitation. This experiment enabled the real-time observation of the generation and subsequent relaxation of hot carriers. The plasmon damping was determined to be 25 fs, with a maximum hot carrier population of 0.46e- from each Au atom detected at 105 fs after excitation. The lifetimes of the hot carriers were estimated to be 498 fs, with complete carrier thermalisation occurring within 1.5 ps. Energy scans conducted at varying delay times revealed that the energies of these carriers conform to the density of states of the metal, with some carriers possessing energies that exceed the photon energy, consistent with an Auger heating scattering mechanism. The observation impacts hot carrier applications, particularly those that are based on the energy of the hot carriers, such as photocatalysis and photovoltaics. For instance, without the Auger process, chemical reactions with redox windows larger than photon energy could not be catalysed. Similarly, the open circuit voltage of photovoltaic devices could not exceed the voltage offered by a single photon. The novel insight into plasmon induced hot carrier generation and dynamics provided here is likely to significantly impact applications for years to come.
[i]. Kornbluth, M., Nitzan, A., Seideman, T. Light-Induced Electronic Non-Equilibrium in Plasmonic Particles. J. Chem. Phys. 138, 174707 (2013).
[ii]. Govorov, A. O., Zhang, H., Demir, H. V., Gun'ko, Y. K. Photogeneration of Hot Plasmonic Electrons with Metal Nanocrystals: Quantum Description and Potential Applications. Nano Today 9, 85–101 (2014).
[iii]. Manjavacas, A., Liu, J. G., Kulkarni, V., Nordlander, P. Plasmon-Induced Hot Carriers in Metallic Nanoparticles. ACS Nano 8, 7630–7638 (2014).
[iv]. Rossi, T. P., Erhart, P., Kuisma, M. Hot-Carrier Generation in Plasmonic Nanoparticles: The Importance of Atomic Structure. ACS Nano 14, 9963-9971 (2020).