Ultrafast electron dynamics studied with time-resolved two-photon photoemission: intra- and interband scattering in C6F6/Cu(1 1 1)

The advances in femtosecond laser techniques facilitate the investigation of ultrafast electron dynamics at surfaces directly in the time-domain. We employ time-resolved two-photon-photoemission (2PPE) spectroscopy to study the electron dynamics of the unoccupied electronic states in hexafluorobenzene (C6F6) on Cu(1 1 1) serving as a model system for charge transfer across organic–metal interfaces. Our coverage-dependent study reveals a lifetime of the lowest unoccupied molecular resonance of 7 fs for a single monolayer (ML) which increases to 37 fs above 3 ML coverage. We find that the population build-up of the excited state is delayed by a characteristic time of about 10 fs with respect to the exciting laser pulse. By angle-resolved 2PPE spectroscopy, the mechanism of the delayed population rise is identified as intraband relaxation in the adsorbate band structure. The actual electron-transfer to the metal substrate occurs through interband scattering between the molecular resonance and substrate states on comparable timescales. Therefore the present study demonstrates that relaxation of hot electrons at molecule–metal interfaces include—even in the presence of strong electronic molecule–substrate interaction—also decay channels within the adlayer.


Introduction
Direct and inverse photoelectron spectroscopies facilitate comprehensive information on the static electronic structure of condensed matter. In addition, femtosecond time-resolved investigations in combination with first principle calculations of electronic excitations led recently to a profound understanding of electronic relaxation processes at metal surfaces [1]- [3]. These studies have focused mainly on low-index noble metal surfaces like Cu(1 0 0) or Cu(1 1 1) which exhibit pronounced surface and image potential states (IPS). Such twodimensional electronic band structures constitute well-defined model systems to study the ultrafast dynamics of elementary scattering processes and have been investigated extensively over the last decade. The field has certainly benefited from the high surface sensitivity of photoelectron studies as well as from complementary techniques like scanning tunnelling spectroscopy [1,4] and high-resolution valence band photoemission spectroscopy [1,5]. However, most of the recently achieved insight into the dynamics of image potential states is based on time-resolved photoemission, employing femtosecond Ti:sapphire laser sources.
Two-photon photoemission (2PPE) spectroscopy is a second-order process. Electrons are excited by a short laser pulse from below the Fermi level E F to bound intermediate states below the vacuum level E vac . Subsequently, these hot electrons are probed by excitation into the continuum of final states as illustrated in figure 1 (top panel). Early investigations by Fauster and Steinmann [6,7] employed tunable dye lasers where the pump and probe steps were mediated by the identical laser pulse with nanosecond pulse duration and later, in bichromatic 2PPE, by a fundamental pulse hν and its second harmonic 2hν, respectively. The first femtosecond time-resolved 2PPE studies have been performed on IPS of Ag(1 0 0) and Ag(1 1 1) by Schoenlein et al using a combination of a colliding-pulse mode-locked ring dye laser and a copper-vapour laser amplifier operating at 8 kHz resulting in 55 fs pulse duration [8]. The advent of high-repetition (∼80 MHz) modelocked Ti : Sapphire oscillators delivering ultrashort laser pulses of 50 fs enabled Aeschlimann and co-workers to investigate the relaxation time of photoexcited bulk electrons on Cu(1 0 0) [9]. The electronic lifetime was found to decrease rapidly with increasing electronic excess energy in qualitative agreement with Fermi liquid theory. Fann et al examined the dynamics of electron thermalization after excitation with intense femtosecond-laser pulses in Au films by employing time-resolved direct photoemission and analysis of the transient non-equilibrium electron distributions [10].
In recent years, scattering processes involved in the relaxation of quasi-particle excitations have been studied in great detail for bare low-index metal surfaces. Hot electrons generated by absorption of a femtosecond-laser pulse relax through various elastic and inelastic scattering processes via electron-electron, electron-phonon or electron-defect interactions. The damping 3 Institute of Physics ⌽ DEUTSCHE PHYSIKALISCHE GESELLSCHAFT rate or the inverse lifetime = τ −1 of IPS is proportional to f |Im(W )| i [1], whereby the lifetime is determined by the wave function overlap of initial states i (representing the IPS) with final states f (i.e. bulk states) and the screened electron-electron interaction W. Optical Bloch equations have been employed to describe the temporal evolution of the electron populations and coherences. Simple rate equations are justified in the limit of non-resonant excitation schemes due to inelastic scattering events. However, resonant optical excitation followed by relaxation through elastic scattering leading to dephasing requires an analysis by Bloch equations [2]. Electron momentum resolved studies identified intraband decay within one dispersing IPS band which competes with interband decay from the IPS into bulk states. Additional scattering centres introduced by adatoms allowed a detailed investigation of defect-induced quasi-elastic scattering. These processes have already become important at minute coverages [1,3,11]. At stepped copper surfaces, even asymmetric scattering rates have been observed for up-and downstairs electron momentum whereby the upstairs direction is favoured [3].
Upon adsorption of the highly polarizable rare gases, the IPS retain their character localized along the surface normal and delocalized parallel to the surface. As shown for the adsorption of Xe, a dielectric layer basically acts as a spacer layer and decouples the modified IPS from metal substrate states. Consequently, lifetimes generally increase [12] as accounted for by the dielectric continuum model (DCM) at least qualitatively [13]. The DCM, however, neglects the atomic (or molecular) structure of the adsorbate. It has been shown for Ar/Cu(1 0 0) that the heavier (i.e. more polarizable) rare gases present limiting cases where the DCM applies, but for a general description the atomic or molecular polarization is required to describe the experimentally determined lifetimes [14].
In general, the dynamics of electronic excitations at molecule-metal interfaces play an important role in various physical and chemical phenomena [15]. Electron transport across nanoscale junctions, interfacial electron transfer in electrochemistry, hot-electron mediated surface photochemistry, electron injection in dye-sensitized solar cells and charge injection in organic light-emitting diodes are all based on charge-transfer processes across interfaces. Molecules or atoms adsorbed on single crystal metal surfaces under ultrahigh vacuum (UHV) conditions constitute well-suited model systems to investigate the mechanism of electron transfer from metallic substrate states to unoccupied adsorbate resonances and, subsequently, back to the metal. In these systems, the electronic metal-molecule coupling is usually strong, and electron transfer occurs on femtosecond timescales. So far investigations have been focused on metal substrates with large sp-band gaps around the¯ -point like Cu(1 1 1) or Ag(1 1 1) which can hinder effective charge transfer between adsorbate states and the metal. Lifetimes of 10-55 fs depending on temperature (adsorbate geometry) have been obtained for Cs/Cu(1 1 1) where the antibonding sp-state of the alkali atom is excited [16]. This long lifetime made it possible to study the laser-induced adsorbate motion by a binding-energy shift with time and non-exponential decay dynamics [17]. On the other hand, for the 2π * resonance in CO/Cu(1 1 1), only an upper lifetime limit of 5 fs has been reported [18]. Thus, electronic lifetimes (also referred in this context as charge transfer times) are determined by the wave function overlap and the screened Coulomb interaction as demonstrated for the dynamics of IPS. In case of adsorbate resonances on metal surfaces, the interaction is furthermore strongly dependent on the symmetry of the excited state, as has been shown by Gauyacq [19]. Hotzel et al combined the concept of decoupling IPS from the metal by Xe adsorption and intraband decay dynamics [20]. They investigated N 2 molecules adsorbed on Xe/Cu(1 1 1) and identified the observed intraband scattering originating from electron-phonon interaction within the nitrogen adlayer on picosecond timescales.
A favourable example of a molecular resonance with an experimentally well accessible lifetime is C 6 F 6 /Cu(1 1 1). Hexafluorobenzene is an organic molecule with a molecular structure similar to C 6 H 6 ; however, the large electronegativity of fluorine decreases the electron density in the carbon backbone and leads to an electron affinity of 0.64 eV for free C 6 F 6 compared to −1.14 eV for gas phase benzene [21]. A first spectroscopic investigation of the C 6 F 6 /Cu(1 1 1) system byVondrak and Zhu using single-colour 2PPE resulted in the observation of an unoccupied molecular resonance (named peak A) derived from the lowest unoccupied molecular resonance (LUMO) at about 3 eV above E F [22]. Our subsequent investigation [23] agrees with this study and reports for coverages above 4 ML, a second broad resonance (named peak B) several 100 meV above the LUMO. Also the lifetimes τ A , τ B of both resonances have been studied and were found to increase with coverage from τ A (1 ML) = 7(3) fs to τ B (5 ML) = 32(8) fs. Although the timeresolution of this experiment was limited by the laser pulse duration of 65 fs, a delayed rise of the time-dependent electron population had to be included in the data analysis. The rise time agreed within experimental error bars with τ B which suggested an indirect population of state A by relaxation (interband scattering) from the higher lying state B.
In this paper, we report new results on ultrafast electron transfer dynamics in C 6 F 6 /Cu(1 1 1) obtained with an improved time resolution of 30 fs. We identified the delayed rise to originate from an intraband decay process within the molecular resonance A, which is delocalized parallel to the interface. Thereby, we show that ultrafast relaxation dynamics at molecule-metal interfaces consist not only of charge transfer processes between the substrate and adsorbate, but also relaxation processes within the molecular adsorbate band structure that cannot be neglected.

Experimental setup and data analysis
To access the ultrafast electron transfer dynamics and scattering processes, time-and angleresolved two-photon photoemission (2PPE) is employed. The experimental setup combines an ultrahigh vacuum (UHV) chamber (base pressure <10 −10 mbar) for sample preparation and photoelectron spectroscopy with a tunable femtosecond laser system. The Cu(1 1 1) crystal was prepared with repetitive cycles of argon ion sputtering at kinetic ion energies of 700 eV and successive annealing at 670 K for 5 min. The surface quality was inspected with low-energy electron diffraction (LEED) and the preparation was continued until sharp, low background LEED images from the Cu(1 1 1) surface were obtained. Within the resolution limits of Auger electron spectroscopy no O or C contamination was observed. Also, the work function, energetic positions, linewidths and lifetimes of the Cu(1 1 1) surface (SS) and IP state were monitored by 2PPE to confirm the surface quality. According to earlier investigations, this is a very sensitive surface characterization method because, e.g., terrace steps lead to increased scattering rates [3]. C 6 F 6 was adsorbed on Cu(1 1 1) at substrate temperatures of 140-160 K depending on the desired coverage. The substrate temperatures were chosen appropriately to prevent the adsorption of subsequent layers, as has been reported earlier [23]. Thermal desorption spectroscopy (TDS) was routinely used to determine the adsorbate coverage ( ) from the integrated desorption yield, recorded at the mass of the most prominent C 6 F 6 -fragment (CF + , 31 amu). C 6 F 6 coverages were investigated between 0.5 and 6 ML, where 1 ML coverage is defined by saturation of the monolayer desorption feature between 165 and 205 K in TDS [24]. All 2PPE measurements were performed at a substrate temperature of 100 K.

5
Institute of Physics ⌽ DEUTSCHE PHYSIKALISCHE GESELLSCHAFT For the 2PPE experiments, a regenerative amplifier (Coherent RegA 9050) operating at 200 kHz repetition rate is employed, which generates pulses with a duration (FWHM) 2 [25] of 55 fs at a centre wavelength of 800 nm (1.55 eV). The RegA output beam pumps two optical parametric amplifiers (OPAs), operating in the near-infrared (1100-1300 nm and 1.13-0.95 eV) and visible (470-730 nm and 2.64-1.70 eV) spectral regimes. Subsequent doubling and quadrupling of the OPA output allows to generate photon energies in the visible (2.25-1.91 eV) and near ultraviolet (UV) (4.51-3.82 eV) range. The extensive tunability allows us to carefully tune the laser photon energies to specific resonances of the molecule-metal interface and to follow their dynamics. The dispersion introduced by the optical path to both the visible and the UV pulses is pre-compensated with the use of prism pair compressors, thus resulting in nearly Fourier-transform-limited pulses with durations as short as 28 fs (FWHM) [25] at the position of the sample. The UV pulses are temporally delayed with respect to the visible pulses and are then focused onto the sample surface with polarizations parallel to the plane of incidence (p-polarization). The beam spots exhibit a Gaussian profile with a diameter of 100-150 µm, resulting in typical fluences of 100 µJ cm −2 for the visible and of 20 µJ cm −2 for the UV light. The size and overlap of the two laser beams are inspected with a CCD camera placed outside the UHV chamber at a position which exactly corresponds to the sample position.
To elucidate time-resolved 2PPE spectroscopy and the data analysis, we present in figure 1 2PPE data for the clean Cu (1 1 1) where hν probe is the probing photon energy and the sample work function. 3 In addition, angle-resolved studies access the component of the electron momentum parallel to the surface:hk = sin α √ 2m e E kin , where m e is the free-electron mass and α is the emission angle with respect to the surface normal.
In figure 1, a false colour representation of the photo-emission intensity represents the electron distribution as a function of both time delay (horizontal axis) and energy (vertical axis). To visualize low intensities, white contour lines (1, 5 and 10% of the maximum intensity) are appended to the colour-coded figure. Depending on the sequence of the laser pulses (or formally, the sign of the delay), the dynamics are probed either near E F or at higher intermediate  Institute of Physics ⌽ DEUTSCHE PHYSIKALISCHE GESELLSCHAFT alone have been subtracted from all spectra presented here. This background is typically in the order of 10% of the total signal. The two-dimensional data sets as shown in figure 1 can be analysed in two different ways: either by extraction of time-dependent 2PPE spectra as given exemplarily by the spectrum at t = 0 in the right panel of figure 1 or by the time-dependent photoelectron yield integrated over energy intervals centred on the state of interest (typically 100 meV full width). The latter procedure provides the temporal evolution of the electron population, referred to as cross correlation traces as shown in the bottom panel of figure 1. Returning to figure 1, we briefly discuss the main features of the time-resolved 2PPE spectra. Its cross correlation exhibits a delayed ( t = 18 fs) peak maximum with respect to the corresponding trace of the SS, which reflects the finite lifetime of the excited electron population [27,28] as well as the non-instantaneous population build-up at k = 0 [28,29]. The peak maximum shift of 18 fs at 100 K is in very good agreement with previous studies [28].  (1 1 1) surface exhibits a band gap at k = 0 in the projected surface band structure [28]. This excitation process occurs quasi-instantaneously and therefore the temporal envelope of the SS reflects the cross correlation of pump and probe pulses at the sample position and thus defines the time zero of the experiment [28].

Results and discussion
To introduce the results on C 6 F 6 adsorbed on Cu(1 1 1), we present in figure 2 the coveragedependent 2PPE spectra at zero delay for coverages up to = 6 ML. Adsorption of 1 ML C 6 F 6 on Cu(1 1 1) leads to a significant reduction in the intensity of the SS and the n = 1 IPS of the bare Cu(1 1 1) surface, however both peaks can still be clearly discerned. A pronounced adsorbate-induced feature marked 'A' appears at E − E F = 3.13(1) eV for = 1 ML. This feature originates from the LUMO of C 6 F 6, but is also influenced by the image potential in front of the Cu(1 1 1) surface, as discussed previously [22,23]. State A shifts to lower energies with increasing coverage and remains basically at constant energy E − E F = 2.82(2) eV for > 3 ML [23]. which broadens considerably at = 6 ML, but is located at a very similar energy. The shift of the low-energy cutoff in the 2PPE spectra reflects the lowering of the work function from 4.95(1) eV for the clean Cu(1 1 1) surface to 4.63(1) eV for 1 ML coverage which does not change significantly upon further adsorption of C 6 F 6 .
As pointed out previously [23], the unoccupied adsorbate-induced states A and B are localized along the surface normal but delocalized parallel to the surface. The dispersion and thus the delocalization of state A parallel to the surface increases with coverage resulting in an electron effective mass m eff ≈ m e for 5 ML, whereas state B remains more localized with m eff 2m e . Therefore, these states will be treated as quasi-free electron bands in the following.
To investigate the charge transfer dynamics in C 6 F 6 /Cu (1 1 1), femtosecond time-resolved 2PPE was employed. In figure 3 a false-colour representation of the energy-and time-resolved photoelectron yield detected in normal emission is presented exemplarily for 3 ML coverage. Both states A and B decay towards positive time delays, which confirms the above assignment of a population with the UV (hν 1 = 4.26 eV) and probing with the visible (hν 2 = 2.13 eV) pulses. State B is obviously only slightly higher in energy (∼300 meV) compared to A but decays significantly faster than A (about four times, see figure 5). This observation differs fundamentally from electron dynamics of IPS at metal surfaces where the lifetime increases due to the decrease in the wave function penetration into the bulk with the quantum number (n) [1,7]. The shorter  [19]. From the difference in the dynamics of states A and B, we therefore conclude that both resonances cannot be regarded as IPS but are derived from molecular states of C 6 F 6 . This conclusion is consistent with previous Xe-overlayer experiments [23] which show that states A and B must be predominantly localized within adsorbate layers and cannot be considered as IPS.
To analyse the decay quantitatively, we acquire cross correlation traces of state A for various coverages. This is shown in figure 4 on a linear and logarithmic scale in the left and right panel, respectively. The analysis of the cross correlation signals within a rate equation model yields the corresponding decay times [23]. Note that information on time zero and the laser pulse duration cannot be obtained through the SS on C 6 F 6 covered surfaces, but is retrieved from the clean Cu(1 1 1) surface after thermal desorption of the adlayer. In addition, this pulse characterization has been cross-checked by comparison with the cross correlation signal from short-lived states at energies E − E F = 4.1 eV. There, the lifetimes of 1-3 fs are considerably shorter [30,31] than the pulse duration confirming the time zero derived on clean Cu (1 1 1).
Inspecting the transient population of peak A, we identify in figure 4(a) a peak maximum at t = 28 fs due to the population build-up within the pulse duration and the subsequent population   1 1 1) shows a delayed ( t = 28 fs) peak maximum and a subsequent decay. The dotted line is an attempt to fit its temporal evolution with a single exponential decay mechanism which describes neither the position of the peak maximum nor the slope of the decay. The fit shown with a full line additionally includes a delayed rise mechanism and reproduces the data satisfactorily. (b) Semi-logarithmic presentation of cross correlations of state A obtained for various coverages. The positive delay of the peak maxima increases while the decay rate decreases with coverage. Both changes reflect the increase in the lifetime of the excited state electron population. The rise and decay times are extracted from fits (--) of a delayed rise mechanism. The non-vanishing intensity for negative delays is attributed to hot electrons pumped by the visible and probed by the UV laser pulses [26,30,31]. In the fits, this is taken into account by a second single exponential decay for t < 0.
decay. Furthermore, the temporal evolution exhibits a tail towards positive delays due to the finite lifetime of the electron population. To evaluate the decay rate of state A (associated with the electron transfer rate back to the substrate), a rate equation model is considered which assumes an instantaneous filling of the electron population at t = 0 fs and its subsequent exponential decay. To fit this model to the data, the time-dependent electron population is convoluted with the cross correlation of the laser pulses for sech 2 temporal envelopes. The shape of the laser pulse envelope is confirmed independently by the cross correlation trace of the SS of the bare Cu(1 1 1) surface. The result of the fit is given by the dotted line in figure 4(a). However, it reproduces neither the peak maximum nor the slope of the decay correctly. We find that the peak maximum in the cross correlations of state A appears always later than predicted by fits of a single exponential decay. This observation suggests a delayed rise of the excited electron population as already discussed by Gahl et al [23]. Due to the improved time resolution of the present investigation, we are now able to unambiguously identify the population mechanism. The population dynamics including a delayed rise mechanism is given by Therein N(t) denotes the electron population of state A that is probed in the final step of the 2PPE process.Ñ(t) is the transient electron population initially excited to an energetically higher lying state which is not probed in normal emission (at k = 0). 4 A possible mechanism would comprise electrons in state A at k = 0 which may relax via intraband scattering towards k = 0 or an interband scattering mechanism of electrons decaying from state B into A. The first term in (1) leads to a non-instantaneous build up of N(t) with a maximum at t > 0. This results in a further delay of the maximum in the transient population and a subsequently faster decay. The free parameters of rise and decay times are given by the lifetimes τ R and τ AD , respectively. The resulting fits are shown with solid lines in figure 4 and obviously reproduce all experimental data in an excellent manner, even over three orders of magnitude of the photoelectron intensity.
Taking into account the coverage-dependent investigations, we find that all transient populations of state A require a fit based on a delayed rise mechanism as well as a coverage dependence of both time constants. The peak maximum in the cross correlation traces shifts 12 Institute of Physics ⌽ DEUTSCHE PHYSIKALISCHE GESELLSCHAFT to later delays with increasing coverage, from 11 fs for 1 ML C 6 F 6 /Cu(1 1 1) to 28 fs for 3 ML. The quantitative analysis performed by fitting equation (1) to the time-resolved data results in the characteristic times τ AR and τ AD that are summarized in figure 5 as a function of coverage.
We have also obtained cross correlation curves for state B. We find that in contrast to A, a single exponential decay is sufficient to reproduce the temporal evolution of the population in state B (not shown). The resulting lifetimes τ B are included in figure 5. The decay times for state A increase from 7 fs for = 1 ML to 37 fs for 3 ML. Up to 6 ML, the decay time τ AD of state A remains constant within the experimental accuracy (±3 fs), while τ AR on the other hand exhibits a smaller, but constant increase from 7 fs for 1 ML to 13 fs for 6 ML. A similar trend is observed for the decay time τ B of state B which increases from 9 fs for 3 ML to 12 fs for the highest coverage.
The necessity to implement a delayed rise asks for a mechanism to populate state A. We start the discussion by assuming that the finite timescale τ AR for the population build-up could be attributed to electrons initially excited to higher lying energies which decay towards the bottom of the band of state A where they are finally probed at k = 0. As identified previously [20,29], this can be caused by two very fast relaxation channels of the surface resonance. Firstly, intraband relaxation along k of electrons, which are initially excited at k = 0 and decay within the band of state A to the bottom (arrow (2) in figure 6(b)), may lead to a delayed rise. Secondly, interband scattering of electrons from the higher lying state B or from bulk states into state A (arrow (3) in figure 6(b)) provides another possible mechanism. The fact that the rise time of the peak A corresponds to the decay time of state B could be an indication for the interband scattering mechanism as was proposed earlier [23]. However, as we explain in the following, angle-dependent investigations provide evidence that not the interband decay leads to the delayed rise, but intraband scattering along k within state A.
To identify the origin of the delayed rise, 2PPE spectroscopy has been carried out using the tunability of the visible OPA. Thereby, the occupied SS of Cu(1 1 1) acts as the initial state. By tuning the photon energies from below the transition between the SS and state A to energies above the transition to state B, an increase in the intensity of state A is expected if interband scattering B → A was operative. However, apart from an increase in the intensity of state B, we observe a constant intensity of state A when we cross the resonantly enhanced transition from the SS to state B (not shown). Thus we exclude an interband scattering mechanism B → A as the origin of the delayed rise. Note also that for 2 ML state B is not observed in 2PPE and is therefore unlikely to act as an additional higher lying state in interband scattering. The observed coincidence of the electron decay time of state B and build-up time in state A is thus considered to be accidental.
To test the intraband scattering mechanism, angle-dependent and time-resolved 2PPE measurements have been carried out. With this method we are able to probe the dynamics of electrons which are excited from well-defined, non-zero values of k into state A ( figure 6(b)). If the intraband scattering indeed contributes to the population evolution of state A, we expect the population build-up to be faster with increasing k values. To realize this experiment, probe pulses are generated with the infrared OPA with an energy of hν 2 = 2.15 eV and combined with the frequency-doubled RegA output at 3.09 eV as a pump so that the probe photon energies can be set independently of the pump. The photon energy hν 1 = 3.09 eV has been chosen for two reasons. Firstly, this photon energy is insufficient to populate state B. Secondly, state A can be populated only at non-zero k -values as indicated by the solid arrow in figure 6(   The cross correlation traces of state A for 3 ML C 6 F 6 /Cu(1 1 1) obtained in this manner for k between zero and 0.13 Å −1 are shown in figure 6(a). The trace at k = 0 exhibits a delayed peak maximum at t = 16 fs which shifts to t = 5 fs for k = 0.06 Å −1 . At k = 0.13 Å −1 , the peak maximum is located at zero time delay indicating an almost vanishing lifetime of the excited state. Therefore, at this point in k-space (i.e. close to excitation at k ≈ 0.18 Å −1 ), no delayed contribution to the population is observed because we essentially probe only the decay of the population. Thus we identify the intraband decay as the dominant mechanism of the delayed rise of the population of state A. Although a quantitative analysis of the cross correlation traces in terms of rise and decay times is inhibited by the significantly longer pulse duration, we are still able to qualitatively identify the influence of intraband decay as demonstrated in figure 6(a). 5 The delayed population build up at k = 0 requires a filling by electrons which are initially excited to higher lying electronic states and subsequently decay towards the centre of the surface Brillouin zone on a finite timescale (see figure 6(b)). From the angle-dependent experiments, it is clearly evident that this filling mechanism is provided by the intraband relaxation of electrons excited into the delocalized band of state A, which then relax towards the band bottom along k . The timescale of the intraband scattering determined by τ AD ≈ 10 fs is much below any lowenergy vibrational mode of C 6 F 6 [32], which suggests that the intraband scattering is linked to electron-electron interactions either within the adlayer itself or with the Cu substrate. In the latter case, the underlying mechanism should be the same as for the interband decay into the bulk and a similar coverage dependence of both characteristic times τ AR and τ AD would be expected, which is not observed (see figure 5). To resolve this issue, additional high-resolution angular-and time-resolved 2PPE experiments must be conducted to quantitatively determine the intraband scattering rate in C 6 F 6 /Cu(1 1 1) as a function of k and adsorbate coverage.

Conclusions and outlook
Summarizing, we have investigated the ultrafast electron dynamics at the C 6 F 6 /Cu(1 1 1) interface by femtosecond time and angle-resolved two-photon photoelectron spectroscopy. In accordance with earlier investigations, we find two molecular resonances at 2.82 and 3.24 eV above the Fermi level for a coverage >3 ML. At lower coverage, only the resonance A closer to E F is observed at higher energies (E − E F = 3.13 eV at 1 ML). The decay dynamics of the states A and B were analysed by rate equation models. We find that three time constants are required to describe the population dynamics, a decay time for A and B (τ AD and τ B ) and a rise time τ AR accounting for the delayed population build-up in state A. τ AD increases in a low coverage range up to 3 ML to a maximum value of 37 fs and remains constant for higher coverage. The origin of the delayed population built up in state A has been identified by angle-resolved studies to originate from intraband scattering within the band of state A. Our results highlight the potential of time-and momentum-resolved studies in revealing decay mechanisms at molecular-metal interfaces, which will play a key role in future molecular electronic devices.
The adsorbate-substrate system C 6 F 6 /Cu(1 1 1) represents a promising test case for ultrafast electron transfer dynamics suggesting a comparison with other experimental methods like resonant Auger-Raman spectroscopy ('core-hole-clock' method) [33]. This would provide a critical test of different experimental approaches and allow further insights into the underlying principles of charge transfer dynamics.