Ultrafast dynamics of occupied quantum well states in Pb/Si(111)

We investigate the ultrafast electron dynamics of occupied quantum well states (QWSs) in Pb/Si(111) with time-resolved photoemission spectroscopy. We find an ultrafast increase in binding energy of the QWSs driven by the optical excitation, while the electronic system is in a non-equilibrium state. We explain this transient energetic stabilization in the photoexcited state by an ultrafast modification of the Fermi level pinning, triggered by charge transfer across the Pb/Si interface. In addition, we observe the excitation of a coherent surface phonon mode at a frequency of ∼2 THz, which modulates the QWS binding energy.


Introduction
The structure and energetics of interfaces between semiconductors and metals are of importance from both a fundamental and a technological point of view. In semiconducting devices such as integrated circuits, solar cells or light-emitting diodes, interfaces to metal electrodes play a crucial role in device functionality. Thus, semiconductor surfaces and semiconductor-metal junctions have been intensively studied in a variety of systems [1]. In particular on silicon surfaces, the most commonly used semiconductor for device fabrication, a variety of interface structures and reconstructions with various metal adsorbates have been investigated [1][2][3][4][5][6]. Already for sub-monolayer (ML) coverages of metal atoms, the occupation of metal-derived surface states within the semiconductor band gap leads to a charge transfer between substrate and adsorbate atoms. This results in a space charge region near the semiconductor interface and the buildup of a Schottky energy barrier [1], which determines the energy band alignment at the interface. However, the ultrafast dynamics describing the response of the energy alignment at the interface to an optical excitation has received only a very little attention so far. First experiments focused on the dynamics of surface photo voltage (SPV) on a slow picosecond to nanosecond timescale [7][8][9], whereas the femtosecond dynamics directly after excitation remained unexplored.
Time-resolved photoemission (trPES) techniques have been quite successful in investigating the dynamics of excited electrons directly in the time domain. While time-resolved two-photon photoemission is sensitive to unoccupied electronic states and has been used to intensively study the dynamics of hot electron distributions and of surface and image potential states [10][11][12][13][14][15][16], time-and angle-resolved direct photoemission analyzes the occupied electronic bands under optical excitation. It has been quite successful in investigating electron dynamics in both simple metals [17,18] and layered correlated electron materials [19][20][21][22][23], where excitations specific to the ordered nature of the material as well as coherently excited phonons have been observed. However, to investigate the electronic dynamics within the bulk of normal metals, one has to overcome several challenges. Firstly, electronic bands with a strong dispersion perpendicular to the surface, like in many bulk metals, usually show only broad energetic features that limit a comprehensive analysis, due to the finite k ⊥ resolution in photoemission spectroscopy caused by the finite photoelectron escape depth. Secondly, electronic transport effects can drastically influence the observed dynamics and can be hard to disentangle from other effects [12,24,25]. The use of ultrathin metal films is one approach to overcome these difficulties. The ultrathin metal film breaks the periodicity along the surface normal and the 3 resulting electron confinement gives rise to sharp quantum well states (QWSs) at discrete energies in the occupied and unoccupied parts of the quantized band structure [26][27][28][29]. Owing to their quasi-two-dimensional (2D) character, QWSs show no k ⊥ dispersion [28] and their confinement to the ultrathin film effectively inhibits electron transport [29] for electron states with energies within the substrate band gap.
The QWS system of ultrathin epitaxial films of Pb on Si(111) presents a nearly ideal realization of such a quasi-2D model system, which has been intensively studied in the past [29][30][31][32][33][34][35][36][37][38][39]. Owing to the efficient confinement of the electronic wave functions to the metal film by the band gap of the semiconducting substrate, the system exhibits a series of welldefined and sharp QWSs [29,[35][36][37]. First investigations of the electron dynamics focused on the electron lifetime in unoccupied QWSs [29,40]. Here, we investigate the ultrafast dynamics of occupied QWSs and states at the Pb/Si interface after photoexcitation. We make use of the selection of Pb coverage and the respective QWS binding energies, as the latter are very sensitive to the energy alignment and the interface structure [6,38,39]. Thus, they can serve as a probe for the ultrafast processes at the metal-semiconductor interface. In addition, the laser-based photoemission with low kinetic energies is characterized by an enhanced bulk sensitivity [41], which allows the detection of interface states (ISs) at the buried Pb/Si interface.
We show that the ultrafast modification of the charge balance at the Pb/Si interface after optical excitation leads to an ultrafast change of the Fermi level pinning position and to a transient energy shift of the Si band gap. As a result, the QWS confinement condition is modified and leads to an energetic stabilization of the QWS system. In addition, we observe the excitation of a coherent surface phonon mode which modulates the QWS binding energy.

Experimental methods
The experimental setup and procedures have been described in detail elsewhere [35,40]. The investigated samples of thin epitaxial Pb films were grown in situ on Si(111) surfaces under ultrahigh vacuum (UHV) conditions (base pressure <1 × 10 −10 mbar). The surface of the silicon wafers was cleaned by repeated flashing to 1470 K, followed by a slow cooling ramp of −1 K min −1 to 970 K to form the Si(111)-7 × 7 surface reconstruction. The cleanliness of the surface was checked by low-energy electron diffraction. Epitaxial Pb layers were grown on the Si(111)- [35] by evaporation of Pb from a home-built Knudsen cell [35,36]. The evaporation rate of ∼0.5 ML min −1 was monitored by a quartz micro balance. Samples were grown in a wedge shape, facilitating measurements of various film thicknesses on a single sample preparation. A shallow thickness gradient of <0.5 ML mm −1 was used to ensure homogeneity of the electronic structure within the measured area [29]. To suppress surface diffusion of Pb atoms and island formation [37], the samples were kept at T = 80 K during the experiments.
trPES measurements were carried out using an amplified Ti : sapphire laser system (Coherent RegA 9050) operating at 300 kHz repetition rate. Its fundamental infrared (IR) output at hν 1 = 1.5 eV is used to optically excite the sample. Alternatively, the output of a tunable optical parametric amplifier (Coherent OPA) in the near-IR or visible range can be used for pumping. The ultraviolet (UV) probe pulses at hν 2 = 6.0 eV are generated by frequency quadrupling the RegA output by two consecutive β-bariumborate crystals and subsequent recompression by prism pairs. The IR pump pulses have a pulse duration of 55 fs, whereas the UV probe pulse are slightly longer with 80 fs due to nonlinear effects in the quadrupling process. The cross-correlation (XC) of pump and probe pulses results in an overall time resolution of 100 fs. These time-correlated pairs of femtosecond pump and probe laser pulses, hν 1 and hν 2 , respectively, are focused into the UHV chamber and spatially overlapped on the sample surface. Typical absorbed pump fluences are of the order of F = 50-1000 µJ cm −2 and below the damage threshold of Pb/Si(111) as no irreversible spectral changes were encountered. The binding energy of the photoemitted electrons is determined from their kinetic energy E kin analyzed in a time-of-flight spectrometer: E − E F = E kin + − hν. Here, denotes the work function and hν the photon energy of the probing laser pulse. The overall energy resolution of typically 50 meV is determined by the spectrometer resolution and the spectral width of the probe pulses. All measurements were carried out in normal emission geometry at the -point with an angular resolution determined by the spectrometer acceptance angle of ±3.5 • .
The metal-semiconductor interface between the Si substrate and the Pb film leads to a charge transfer between substrate and metal film, as the Fermi level E F is pinned by localized charges at the interface, the so-called metal-induced gap states (MIGS) [1]. This results in a space charge region of typically several 100 nm thickness within the Si substrate and leads to band bending near the surface depending on the doping level as sketched in figure 1(b) for a p-doped substrate. Photo-generated electron-hole pairs are separated in the space charge region and lead to a reduction in the band bending, see figure 1(c). This results in a potential difference between interface and bulk, known as surface photo voltage (SPV) [1].
The SPV manifests in a photoemission experiment as a rigid shift of the spectra, as the energy reference of the spectrometer is determined by the bulk Fermi level. Figure 1(a) shows photoemission spectra of 5 ML Pb/Si(111) with and without excitation by the pump pulse arriving after the probe pulse, i.e. at negative pump-probe delays. The details of the spectra will be discussed below. On a p-Si substrate, the spectrum is-in comparison to a reference spectrum taken without optical excitation (black/solid line)-rigidly shifted to higher kinetic energy (blue/large dashed line), including the secondary cutoff at low kinetic energies, which is determined by the sample work function. In contrast, on an n-Si substrate, the spectrum is shifted toward lower kinetic energy. This is well understood from the opposite orientation of the space charge field for n-and p-doped semiconductors, leading to a reversed charge separation. Additionally, the shift on an n-Si substrate is considerably larger. The amount of the SPV has been determined for various fluences for both n-and p-Si, as shown in figure 1(d). We note that (i) the SPV saturates for fluences F > 50 µJ cm −2 and (ii) is considerably weaker on p-Si. Thus, the usage of p-Si substrates and excitation fluences F > 50 µJ cm −2 , as used for all time-resolved measurements, minimizes the effect of the SPV and ensures flat-band conditions as shown in figure 1(c). Since the dynamics of the SPV happens on a nanosecond timescale [7], it can be considered as constant within the time interval of a few picoseconds after excitation investigated here 6 . An SPV induced by the probe beam is negligible as was checked by the variation of the probe fluence.

Results and discussion
In the following, we will discuss the modifications of the occupied electron states that occur on an ultrafast timescale and are driven by the photoexcitation. Here, we will discuss two main features: First, we will use moderate excitation densities and focus on a transient increase in binding energy that builds up on an ultrafast timescale within the time resolution of the experiment. In the second part, we analyze a periodic modulation of the QWS binding energy that is superimposed on the continuous shift and is attributed to the excitation of a coherent surface phonon mode.

Transient binding energy shift
Let us now turn to the spectral features and their modification with optical excitation. Figure 2(a) shows spectra of a 5 ML Pb film on Si(111) with a moderate excitation fluence of F = 60 µJ cm −2 before (filled black symbols) and 100 fs after excitation (open red symbols). Besides the high-energy cutoff at the Fermi energy and the sharp low-energy cutoff (secondary trPES Intensity max. (c) trPES spectra as in (a), but for 3 ML Pb/Si. Note the pronounced asymmetry of the hoQWS line shape near the silicon VBE, which is reduced upon excitation.
edge) at E − E F = −1.9 eV, determined by the sample work function of = 4.1 eV, we find three main features in the spectrum. The most prominent peak at E − E F = −0.26 eV is the hoQWS, which resides well above the silicon VBE at E − E F ∼ −0.4 eV. Its sharpness and high intensity evidence the strong confinement to the Pb surface layer, in agreement with earlier photoemission work [29,37,40]. In contrast, the broad QWR at E − E F = −0.94 eV lies within the Si valence band and is degenerate with bulk Si valence band states. The third feature at E − E F = −1.39 eV is assigned to an IS at the Pb/Si interface, as it appears at all coverages at roughly the same energy and does not show the characteristic energy dispersion of the QWSs in Pb/Si(111) [30,40]. Moreover, this state is also present on the bare Si(111)- surface and is less pronounced for higher Pb coverages, as photoemitted electrons from the interface have to traverse a thicker Pb film before emission into the vacuum. Upon photoexcitation, all states exhibit an energy shift E to higher binding energies, as recognized from the solid and dashed lines in figure 2(a), which mark the peak position before and after the laser excitation, respectively. This shift is rather small for the hoQWS, whereas it is considerably larger for the QWR and the IS. Quantum well states near the Si VBE, such as the hoQWS of a 3 ML film shown in figure 2(c), are characterized by a pronounced asymmetry of the line shape, indicating the transition from QWSs to QWRs, as the confinement weakens in the vicinity of the VBE. Upon excitation, however, in addition to the peak shift, this asymmetry is considerably reduced. As will be discussed in the following, this change in the line shape indicates a transient enhancement of the electronic confinement conditions of the QWSs.
At this point, we note that the shift in binding energy is qualitatively different from the energy shift induced by the SPV effect. The SPV leads to a shift of the whole spectrum, including the Fermi and the secondary edge (see figure 1) and does not change the peak position relative to the Fermi level. This is in contrast to the shift in binding energy after photoexcitation, which affects only the peak positions relative to the secondary edge and E F . This is apparent from the secondary edge and the Fermi cutoff in figure 2(a), which do not shift. Furthermore, the effect of the SPV is constant in the time window discussed here, and its direction depends on the doping level of the substrate. In contrast, the peak shift in figure 2 occurs in the same direction both on p-and n-doped Si samples (not shown).
The dynamics of the peak shift is analyzed in a false color representation of the trPES intensity as a function of the pump-probe delay, shown in figure 2(b). The peak position of the hoQWS, indicated by the blue markers, shows that the peak shift occurs on a very short timescale of ∼100 fs after excitation, followed by a slower relaxation toward the initial peak position. For a more quantitative analysis, the relative peak shift E is determined by fitting the trPES spectra with a series of Lorentzian lines and an exponential background function, multiplied with a Fermi-Dirac distribution and convoluted with an instrument function. The fits and the contributing peak functions are shown as thin black lines and shaded areas, respectively, in figures 2(a) and (c). For the hoQWS of 3 ML Pb/Si (figure 2(c)) a Doniach-Šunjić line shape [42] has been used in order to account for the pronounced peak asymmetry. The fit yields a Doniach-Šunjić asymmetry parameter α of 0.51 (1), which decreases significantly to 0.35(1) after photoexcitation, see figure 2(c).
The resulting peak shifts are shown in figure 3(a) for the three states in figure 2(a) as a function of pump-probe delay. For comparison, figure 3(b) shows the pump-probe pulse XC, determining the temporal resolution of the experiment and the temporal overlap of pump and probe pulses (time zero, t 0 ). To determine the maximal peak shift E max and the timescale of its recovery τ , exponential decay functions, E(t) = − E max exp(−t/τ ) + B, convoluted with the pump-probe envelope, are fitted to the data. Here, B accounts for a transient equilibrium after relaxation of the initial dynamics. For the hoQWS, we find a small maximal peak shift of E hoQWS max = 17(2) meV. In contrast, the QWR and the IS show a much stronger peak shift of E QWR max = 66(6) meV and E IS max = 52(4) meV, respectively. The relaxation times of all three states are found to be about 500 fs (τ hoQWS = 460(90) fs, τ QWR = 610(150) fs and τ IS = 600(90) fs).
The comparison of the peak shift transients with the pulse XC reveals that the initial buildup of the peak shift occurs within the time resolution of our experiment. We consider this ultrafast timescale as evidence for the electronic origin of the responsible processes, as electron-hole pairs are initially excited by the laser pulse. The energy transfer to the lattice occurs at later times and thus effects related with lattice dynamics are typically limited to slower timescales in metals. Electron thermalization and electron-lattice equilibration has been intensively studied in metallic systems [18,43] and can be described phenomenologically in the context of the 2TM [18,[44][45][46][47]. This model treats the electronic and phononic subsystems as two coupled heat baths with electronic temperature T el and lattice (phononic) temperature T ph , respectively. Although this model bears several limitations and simplifications, e.g. the assumption of a constant density of states or a thermalized electron system, model calculations of the 2TM can be used to estimate the electron-lattice equilibration time in Pb/Si, as shown in the inset of figure 3(a). In the calculation, electronic diffusion and transport processes have been neglected to account for the confinement to the ultrathin metal film and the experimental excitation conditions have been used. The calculated electronic temperature T el shows a steep rise at t 0 and a relaxation within 1 ps, comparable to the relaxation of the peak shift. In contrast, the lattice temperature T ph increases only slightly after several 100 fs, further supporting the electronic origin of the peak shift.
In order to compare the peak shifts found on different coverages of Pb/Si(111), the maximal peak shift E max of interface and quantum well states is plotted in figure 4 for various film thicknesses as a function of the respective equilibrium peak position. We find a pronounced dependence of E max from the peak position relative to the Si VBE: below the VBE, for QWRs and the ISs, we find a comparably strong shift of ∼60 meV, which does not depend within our accuracy on the energetic position. Above the VBE, however, for QWSs which are well confined In order to determine the amount of band gap shift, we recall that the ISs at higher binding energies are located at the Pb/Si interface and are derived from Si states. Thus, these states are fixed to the energy reference of the Si substrate, i.e. the position of the Si band edges. Hence, we can use the peak shift of the ISs as a marker for the transient band gap shift, which, in turn, leads to a change of the confinement and a shift of the QWS binding energy.
To test this hypothesis, we have performed a simulation in the framework of the phase accumulation model [28,37,48]. The energy position of a QWS is determined by the confined wave function along the metal film's normal direction. In this model, electrons propagating between the Pb/Si interface and the Pb surface are reflected at each interface, exhibiting a phase shift i and s , respectively. According to the Bohr-Sommerfeld quantization rule, the total phase accumulated during a round trip, , has to equal a multiple of 2π for a stationary state: = 2kd + i + s = n · 2π. (1) Here, k is the electron wave number, d the film thickness and n an integer number. This condition determines the allowed electron wave vectors and hence the energetic positions of the QWSs.
The phase factors i and s are energy dependent and two approximations are commonly used for these expressions. The surface potential is usually described by the image potential, leading to a phase shift of [28] where E V is the vacuum energy level. For modeling of the phase shift i at the Si/Pb interface, an empirical formula for the phase shift of π across a band gap in a two-band model is used [37,48,49]: with the valence band maximum E VBM and the size of the band gap E G . 0 denotes a phase offset used as a fit parameter to adjust the model to the data. Despite the simplicity of the model, we achieve reasonable agreement with the energy positions of the QWSs within the band gap [29] and reproduce the characteristic 2 ML periodicity of the dispersion of QWS binding energies with thickness [30]. The effect of a photo-induced band gap shift on the QWS energies was determined by shifting the band edge in the model by E VBM = −60 meV, the value that we determined from the ISs in the experiment. The resulting shift in QWS binding energy is plotted as red crosses in figure 4. We find close agreement with the experimentally determined peak shifts, which increase strongly toward the Si VBE, as indicated by the dashed line. Within the model, this is understood by the increasing slope of the arccos function near the band edge in equation (3), which results in a stronger response to the shift in the band gap at these energies. Now we discuss possible origins of the transient band gap shift at the interface. Since this shift occurs in the same direction on n-and p-doped silicon samples, we can exclude a direct influence of the space charge layer, as this is inversed in n-doped silicon and would lead to a reversed effect. Furthermore, the effect is also present for excitation wavelengths below the Si bulk band gap (not shown), where no excitation within the silicon substrate is possible by a onephoton absorption process. Thus, the shift of the band gap must be due to changes happening at the interface or within the Pb overlayer. Since the pinning position of the Fermi level at the interface is directly determined by the charge transfer at the interface and the population of MIGS, a modification of this charge balance upon excitation is the most likely origin of the observed effect.
Still, the direction of the peak shift toward higher binding energy is intriguing. A usual expectation would be that additional energy delivered by the optical excitation leads to a destabilization of the system, i.e. a softening of the electronic bonds and a decrease of binding energies. Here, however, we find an energetic stabilization upon photoexcitation, contrary to this expectation. From the experimentally observed increase in binding energy, we conclude that the strong perturbation by the optical excitation leads to a transient depopulation of MIGS and an electron transfer from the film to the bulk, as sketched in figure 5. This results in a stronger band bending on p-Si, as more bulk acceptors become negatively charged, and a downshift of the band gap relative to the Fermi level on an ultrafast timescale. In n-Si, the charge transfer leads to a reduction of the band bending, as additional bulk donors are neutralized. The IS located at the Pb/Si interface is shifted along with the band gap. In turn, the shifted band gap results in a change in the confinement condition for the QWSs in the metal film, which leads to a shift of their binding energies. Simultaneously, states near the band edge, which are only weakly confined before excitation and show asymmetric peak shapes, become more symmetric after excitation due to the enhanced confinement by the shifted band edge.

Coherent phonon excitation
In addition to the incoherent peak shift induced by the transient modification of the confinement condition, we find a coherent response of the system to the optical excitation if we increase the excitation by a factor of 20. Figure 6 slow shift of the binding energy after the recovery of the initial peak shift at t > 1 ps in figure 6, which was not observed at lower excitation densities (figure 3) and persists up to 3 ps. The transient binding energy of hoQWS as determined by fitting the peak position is depicted in figure 6(b) together with a polynomial background function. On top of the pronounced shift of the peak position which was discussed in the previous section, we see a weak periodic modulation of the peak position with a period of ∼500 fs. To analyze the oscillating contribution to the peak shift, the incoherent background determined by the polynomial fit is subtracted, yielding the coherent oscillatory part of the peak shift, E osc , which is shown in the lower panel of figure 6(b). Remarkably, the high dynamic range in trPES intensity of >10 5 : 1 combined with the systematic analysis of fitting the peak position enables the observation of very small relative energy variations of only ∼1 meV, which is significantly below the experimental energy resolution of 50 meV. A fit of a sine function to the data, shown as a thin red line, yields a frequency of ν = 1.97(6) THz and an initial oscillation phase of φ = 0.4(2) π, as indicated by the dashed extrapolation of the fit to zero pump-probe delay. A fast Fourier transform of E osc exhibits a sharp peak at a frequency of 2.0(1) THz that corroborates the results of the sine fit.
This brings up the question of the origin of the binding energy oscillation. The frequency of the oscillations of a few THz is in the range of acoustic or low-energy optical phonon modes of typical metals. Indeed, the optical excitation of coherent lattice vibrations by fs laser pulses is a rather common phenomenon and has been intensively studied in various materials [50][51][52][53]. One prerequisite for this process is the existence of phonon modes with finite energy at the Brillouin zone (BZ) center (q = 0), typically optical phonon modes, because the optical excitation does not provide a finite momentum. However, the face-centered cubic unit cell of Pb supports only acoustic phonon branches with vanishing energy at the BZ center. The phonon spectrum of Pb shows a pronounced peak around 2 THz [54,55] and the highest-energy modes around 2.1 THz are found in the longitudinal phonon branch near the BZ boundary along the -L direction [56], which is perpendicular to the film direction. To provide the momentum necessary for optical excitation of such modes, the broken symmetry perpendicular to the film has to be considered, giving rise to new phonon modes at the BZ center. More recent calculations of lattice dynamics in freestanding Pb slabs by Yndurain et al [57] predicted longitudinal surface phonon modes at the BZ center with frequencies around 2 THz that show an oscillatory behavior of the phonon frequency with varying slab thickness and describe oscillations of the topmost atomic layers perpendicular to the surface [57]. The existence of such surface phonon modes with frequencies around 2.1 THz at q = 0 has been experimentally confirmed by He atom scattering on thin Pb films grown on Cu(111) [58]. Thus, we consider the coherent excitation of a surface phonon mode as the origin of the periodic binding energy modulations.
Still, typical materials exhibiting coherent phonon excitations are semiconductors, semimetals or rare earth metals such as Tb and Gd [59]. In simple s-p metals such as Pb, coherent phonon excitation has not been observed so far. A reason for this could be the efficient screening of excited carriers, resulting in a low excitation probability. Furthermore, the usually considered excitation of coherent phonons by inelastic stimulated Raman scattering requires a resonant interband transition at the pump photon energy [51], which was not directly observed here.
At surfaces, an ultrafast charge separation has been discussed as the driving force for the excitation of coherent surface vibrations [60]. Such a charge separation could be mediated in the Pb/Si quantum well system as discussed in the following. The ultrafast excitation of a comparably large fraction of the valence electrons leads to a spatial redistribution of the electrons at the surface. This is a result of the vacuum potential, which presents a lower vacuum barrier for excited electrons at higher energies. Hence, their wave functions have a smaller damping outside the metal surface, leading to a larger electron density outside the film, the so-called electron spill-out. This leads to an electron dipole at the surface, which was already observed earlier in the modulation of the work function of Pb/Si(111) with Pb coverage due to the changing electron density near the Fermi level [35]. This ultrafast modification of the surface dipole induces a driving force on the surface atoms perpendicular to the surface, leading to the excitation of a coherent surface phonon mode.
This brings up the question of how the surface phonon mode modifies the binding energies of QWSs within the metal film. This can be understood from the strong sensitivity of the QWS binding energies to the width of the quantum well, i.e. the film thickness. If we consider the modification of the film thickness due to an oscillating topmost atomic layer, we can estimate the oscillation amplitude in real space from the phase accumulation model. From the amplitude of the coherent binding energy modulation of ∼1 meV we found in the experiment, we estimate for the 5 ML film that already a modification of ∼2‰ of the interlayer distance, i.e. <10 −2 Å, leads to the observed binding energy oscillation. This demonstrates that the high sensitivity of QWS binding energies to the film thickness provides a sensitive tool to study very small lattice dynamics in a well-defined low-dimensional system.

Conclusion and outlook
In summary, we have investigated the ultrafast electron dynamics in the quantum well system Pb/Si(111) after intense optical excitation using trPES spectroscopy. We find a transient shift of the binding energies of interface and quantum well states to higher binding energies, i.e. an energetic stabilization, which occurs within the time resolution of our experiment. This peak shift is found to be independent of substrate doping and excitation wavelength relative to the band gap, demonstrating an effect located at the interface between Si substrate and metal film. By analyzing the peak shift for various film thicknesses and QWSs at different positions relative to the substrate band gap, we identify a transient ultrafast shift of the band gap relative to the metal Fermi level as the origin of the peak shift, mediated by a photo-induced charge depletion of MIGS. This scenario is corroborated by a simulation within a phase accumulation model.
Thereby our experiments demonstrate an ultrafast modification of the Fermi level pinning position and hence the Schottky barrier height, which is a technologically important property for metal-semiconductor interfaces. Ultimately, this might lead the way toward electro-optical switching devices, at the interface of optical and electronic circuitry. Furthermore, the transient modification of the confinement condition of QWSs and the resulting influence on the QWS line shape and position demonstrate in a descriptive manner the influence of the quantum confinement on QWS wave functions in a prototypical quantum system. Therefore, it would be instructive to investigate QWSs on different substrates, e.g. QWSs in Pb/Cu(111) [16,61] or Pb/SiC [62] or with different interface structures [36,39] in future experiments.
Using a much stronger excitation fluence of F>1 mJ cm −2 , we observe in addition to this continuous shift a periodic modulation of the binding energy with a frequency of ν = 1.97(6) THz. We attribute this oscillation to a coherently excited phonon mode at the surface of the Pb film, to our knowledge the first observation of a coherent phonon in a simple s-p band metal. We suggest the coherent excitation of such surface vibrations through the ultrafast redistribution of carriers at the surface. The oscillation of the surface phonon's frequency with the film thickness predicted by Yndurain et al [57] encourages further systematic thickness-dependent investigations.