Unraveling Atomic and Electronic Surface Structure and Dynamics from Angular Photoelectron Distributions

: Angle-resolved photoelectron spectroscopy (ARPES) is a powerful tool in solid state sciences. Beside the direct measurement of the energy-momentum dispersion relation, the angular distribution of the photoelectron current reveals the structural environment of the emitting atoms via photoelectron diffraction effects. Moreover, in the case of molecular layers, the angular distribution of emission from molecular orbitals can be directly related to their charge density distribution via so-called orbital tomography. In the present paper we summarize our efforts undertaken over the past 12 years to add the dimension of time to these two methods via pump-probe experiments with femtosecond resolution. We give a comprehensive introduction to standard ARPES and time-resolvedtwo-photon photoemission and then focus on our efforts towards time-resolved versions of photoelectron diffraction and orbital tomography. Both, optimization of experimental parameters and data acquisition procedures, as well as new numerical tools are needed in order to realize such challenging full stop missing after experiments. focuses on interfacial electron dynamics, in particular molecular layers on semi-conducting substrates, studied by time-resolved photoemission and orbital tomography.


Jürg
Osterwalder studied physics at ETH Zürich and graduated in the group of H.C. Siegmann in 1985. During a postdoctoral stay in the group of C. Fadley at the University of Hawaii, he became familiar with photoelectron diffraction, which he helped to establish as an important tool in surface science after joining the group of L. Schlapbach at the Université de Fribourg.
Since 1994 he is professor at the Physics Department at UZH. His research covers many topics in surface science ranging from metalsemiconductor interfaces over topological materials to heterogeneous catalysis.

Introduction: Photoemission from Surfaces
God made the bulk, the surface was invented by the Devil. This famous sentence is attributed to Wolfgang Pauli [1] who thereby expressed the embarrassment of having to deal with a discontinuity in an otherwise perfectly periodic lattice. The surface atoms have different environment due to missing chemical bonds at the outer surface. Therefore, the electronic charge distribution and the atomic positions adapt in order to minimize the surface free energy. The surface properties are the key for charge transfer at interfaces between solids or solids and their gaseous or liquid environment, and their understanding is thus crucial for any application in e.g. catalytic processes. Moreover, the surface properties can be tuned by deposition of thin solid films or molecular layers in order to enhance electron transfer rates and, thereby, catalytic activity, or else protect unstable material against corrosion in harsh environments, for instance. [2] For the investigation of the electronic and atomic structure of surface systems, a full wealth of methods are available, like scanning probe microscopies, electron diffraction or photoelectron spectroscopy. While most experiments are taking place in ultrahigh vacuum under well defined conditions in order to avoid contamination of the surfaces by residual gases, special techniques and setups allow measurements in ambient pressure [4] or even in liquid environments. [5] In the present paper we will give an overview of recent developments in photoelectron spectroscopy from ordered surface systems with special emphasis on experiments to observe electron and structural dynamics on femtosecond timescales in systems excited by light. After a short general introduction to angle-resolved photoemission, the results of one of our own time-resolved studies will be presented in order to highlight the power of fem-cess. The component perpendicular to the surface plane is not conserved due to the broken symmetry of the truncated crystal perpendicular to the surface plane. In the so-called free-electron final state approximation the photoelectron is described as a plane wave propagating inside the crystal in a constant potential V0, the inner potential. The value of V 0 is usually obtained by fitting and of the order of 10 eV. [6] At the surface the potential rises to the vacuum level, which reduces the kinetic energy of the photoelectron. This can be treated like an optical refraction using Snell's law. Finally, we can determine the electron momentum inside the solid and, together with the binding energy of the initial state, the full dispersion relation E( ) − E F : Here hν, ϕ, θ, and E kin denote the photon energy, the workfunction of the sample surface, the polar emission angle with respect to the surface normal, and the kinetic energy measured in vacuum, respectively. k║ and k ⊥ are the wavevector components inside the crystal and parallel and perpendicular to the sample surface, respectively, which are related to the crystal momentum vector by . In the case of two-dimensional (2D) systems like monolayers of organic molecules, there is no dispersion with component perpendicular to the surface, and the relevant component parallel to the surface can be calculated using momentum conservation according to Eqn. 1. Owing to the periodic crystal structure, the momentum, however, is only conserved modulo a reciprocal lattice vector, which means that we may expect contributions from higher Brillouin zones in our ARPES spectra. In practice these contributions have very weak intensities as demonstrated by Vo it and co-workers. [7] Therefore, we may assume that the free-electron-like final state in the surface has the same parallel component of the momentum as the free photoelectron in vacuum. The mean-free path of electrons in the final state is very small, ranging from a few Ångström at kinetic energies of about 50 eV to roughly 1 nm at 1 keV. The mean-free path follows for most materials the so-called universal curve which has a minimum around 50 eV and increases with the square root of the energy towards higher energy. [6] From this curve one might expect a large mean-free path when going from the minimum towards low energy [8] but even at typical laser photon energies of about 6 eV ARPES the probing depth is limited to about 1 nm according to experience. There is a second effect of the limited mean-free path Λ(E kin ), which should be kept in mind: the exponential decay of a free-electron-like wave translates into a broadened perpendicular component of the electron momentum of the order of . This means that in case of truly 3D material, the momentum resolution can be greatly enhanced increasing the energy, and thereby Λ(E kin ). Thus, for practical purposes, the experimental parameters will always be a compromise between the accessible range versus resolution in energy and momentum [8] , photoionization cross-sections [9] , and finally the stability of the sample, which often limits the time available for the measurements.
Besides the bare dispersion relation and many-body effects, the treatment of which is beyond the scope of this paper, the angular distribution of the photocurrent contains a lot of additional valuable information which can be exploited to obtain information about the equilibrium and transient atomic structure and electronic density distribution as we will see below.
(1) tosecond pump-probe photoemission measurements and the need for advanced theory tools to understand and interpret such data. In the subsequent section, two effects contributing to the angular distribution and the interpretation of the resulting patterns will be reviewed: (i) the scattering of the photoelectrons at neighboring atoms (photoelectron diffraction) and (ii) the anisotropic emission due to the initial state wavefunction (orbital tomography). We discuss the experimental realization and information. We wish to point out that this paper is not meant to provide a comprehensive review over these fields but to highlight the additional feasibility studies carried out by us in the framework of a Swiss National Center of Competence in Research in order to extend the scope of conventional spectroscopies into the femtosecond time domain. At the end of this paper and as an outlook, we will conclude by giving an overview over the current possibilities to carry out experiments at user facilities.

Angle-resolved Photoelectron Spectroscopy (ARPES)
Angle-resolved photoelectron spectroscopy (ARPES) is a widely used tool in solid state sciences to access the momentumresolved electronic structure of solids. A comprehensive overview can be found in many reviews and books, like e.g. the book of Hüfner. [6] Briefly, the method is based on the photoelectric effect: Absorption of a vacuum ultraviolet photon (VUV, 8-50 eV, with extended range up to ≈100 eV, termed EUV or XUV) or soft x-ray photon (above VUV up to 1 keV) leads to the emission of a photoelectron. By measuring the kinetic energy of the photoelectron and using energy conservation the binding energy of the electron in the solid can be calculated and referenced to some particular energy level like the Fermi . Depending on the range of photon energies used, one speaks of ultraviolet photoelectron spectroscopy (UPS) or x-ray photoelectron spectroscopy (XPS). In ARPES, the emission angle of the photoelectron from a singlecrystalline sample is measured in addition to its kinetic energy. From this we can calculate the momentum vector inside the crystal as follows: Due to the translational symmetry of the crystal surface parallel and the broken symmetry of the truncated crystal perpendicular to the surface plane, the parallel component of the momentum of the photoelectron is conserved in the emission pro-

Frontiers in ultraFast spectroscopy and dynamics
The dynamics and energy distributions of the electrons reaching the surface are very different in the two cases. The surface producing a (1 x 1) low-energy electron diffraction (LEED) pattern, suggesting a surface-truncated bulk-like structure, shows population of two conduction band states at the surface [ Fig. 2(A) and (B)]. The one at higher energy (CBS at 2.4 eV) decays on a time scale of a few tens of femtoseconds, while the one at lower energy represents the conduction band minimum (CBM at 1.5 eV) that decays over a longer time scale. Using such data sets we can extract the intensity of the states as function of delay as shown in The charge distribution, energy levels, and concomitant lattice deformations of such defects can be modeled using densityfunctional theory (DFT) in supercell slab geometries for different charge states of the vacancies. [12] Comparing time-resolved spectra of the defect states with the DFT results then allows us to identify the charge states and compute the capture coefficients. The charge distributions of the trapped states and the suggested trapping processes modeled in these calculations are visualized in Fig. 4. Since the oxygen defects in the (√3 x √3)R30°surface

Time-resolved ARPES
Our goal is not to give a full account of time-resolved photoemission here but simply to demonstrate, using the results of a recent project as an example, how the concept works and how it can be used as a platform for extending related methods to the time domain. As schematically shown in Fig. 1, photoelectrons can not only be generated by single photons of sufficient energy but also using a sequence of two photons in separate light pulses: the first pulse populates an intermediate state (pump pulse) and the second pulse then probes the transient population (probe pulse). The method is then called two photon photoemission (2PPE). By varying the time delay between pump and probe pulses the dynamics like e.g. population relaxation rates can be measured in real time and with femtosecond resolution (see e.g. Ref. 10 for a review). For such purposes, low photon energies between about 3 and 6 eV are often used, the sum of which must be sufficient to excite the electrons above the vacuum level. Such pulses can conveniently be produced using non-linear optical crystals and the output of a commercial femtosecond laser system, which usually provides near-infrared pulses of 800 to 1064 nm (1.55 to 1.17 eV).
As an example to highlight the power of time-resolved ARPES, data are shown in Fig. 2 which were taken from cuprous oxide Cu 2 O for two different surface treatments, the preparation of a bulk-terminated, stoichiometric 1x1-surface and a second preparation which produces a surface layer with a high density of oxygen vacancies. The latter vacancies mutually repel each other and form an ordered surface reconstruction with a √3 × √3 R30°periodicity. [11]  and references therein). Single-scattering codes like SSC (Single-Scattering Cluster calculations [28] ) proved to be sufficient for interpreting many of these diffraction patterns, while more advanced multiple scattering codes often provide better results and even reproduce subtle details. [29,30] The direct information provided by the forward scattering signals makes time-resolved XPD a particularly attractive tool for recording molecular movies of structural dynamics at surfaces. An x-ray probe pulse can produce a forward projected photoemission image of the molecular structure at variable time delays after the pump excitation pulse, complementary to ultrafast electron diffraction. [31] Using molecular mechanics to produce time dependent cluster coordinates for SSC calculations such a movie was simulated for CO molecules on a Pt(111) surface, which were resonantly excited by a THzpump pulse. [32,33] Since XPD experiments measure over a macroscopic surface area, the trajectories of hundreds of CO molecules were combined for ensemble averaging. As a result the thermal motion of the molecules at room temperature averages to a mean orientation which shows up as a diffraction maximum in the direction of the CO-bond axis. After the pump pulse the collective motion is reflected in the periodic and damped oscillation of the diffraction maximum in the timeresolved data.
Adsorbed molecular layers cannot be pumped too strongly in order to avoid desorption. In view of such time-resolved XPD experiments we therefore tested the sensitivity to only partial excitation of a small fraction of the molecules present on the surface mimicking real experimental conditions. We used azobenzene molecules which undergo a configurational change from trans to are situated mainly in the top surface layer, these experiments furthermore illustrate the high surface sensitivity of 2PPE at these photon energies.
We emphasize here that such investigations are beyond the possibilities of conventional ARPES studies because the relevant states are only transiently populated and thus invisible for onephoton-photoemission experiments.
As already mentioned in the preceding section, the use of low photon energies has certain advantages like high cross-sections and increased momentum resolution. In many cases, however, the important dynamics take place at higher momenta, like e.g. at the border of the Brillouin zone. The momentum range accessible to the experiment is essentially given by the photon energy (see Eqn. 1): To reach sufficiently large momenta to cover the full Brillouin zone the photon energy must by increased. As a rule of thumb, photon energies of the order of 20 eV are used in ARPES from fcc metals like Cu or Au to reach the high symmetry points at k ≈ 1.5 Å −1 . [6] Femtosecond pulses with VUV photon energies for ARPES can be produced in laboratory scale experiments using high-harmonic generation (HHG) [13] as will briefly be discussed in the final section of this paper.

Photoelectron Diffraction
The geometry of a typical angle-resolved photoemission experiment is sketched in Fig. 5. One way of recording the full emission pattern is to vary the sample orientation with respect to the electron detection direction and to record spectra or photoelectron intensities at each step. [14] It was realized early on that the intensity of core level photoelectrons exhibits maxima which are caused by elastic scattering of the photoelectrons at neighboring atoms of the emitter atom. [16] The direct wave and the scattered waves interfere and produce a pattern in the far field, similar to an holographic image of the emitter environment. [17] Moreover, at x-ray energies, the scattering probability has a sharp maximum for small-angle scattering (see Fig. 5), which then produces on top of the actual interference pattern a strong intensity maximum in the direction pointing from the emitter to a nearby scatterer. Thus, this forward focusing effect produces maxima in directions which correspond to the emitter-neighbor bond axes and, thereby, provides direct information about the local geometry around the emitter site. [18] The method is called x-ray photoelectron diffraction (XPD) and was successfully applied to many systems including noble metals, [19] adsorbed and self-assembled molecular layers, [20][21][22][23] ultrathin films [24] and the like (for more details see Refs. 25-27 The sample is rotated around two axes, and the polar angle and the sample azimuth are varied. A pattern is recorded by sequential rotation and data acquisition steps [14] . Bottom panel: elastic scattering probability as function of scattering angle for two kinetic energies, 25 eV (black dashed line) and 772 eV (red line). (Taken from ref. 15.) cis configuration when exposed to visible or ultraviolet light. We could show that the shift of the photostationary equilibrium with light exposure could be observed in XPD. [34] In comparison with multiple-scattering calculations, the number of molecules which underwent isomerization could be estimated to about 8%. These experiments thus demonstrated the sensitivity of XPD experiments in a situation where a relatively small fraction of adsorbed molecules is involved in structural changes, thus suggesting that time-resolved XPD experiments of this kind should be feasible.
An example for XPD from an adsorbed molecular layer is shown in Fig. 6: emission from the Sn 3d 5/2 core level which is well localized in the center of a phthalocyanine molecule results in the pattern in Fig. 6(f) which is displayed in stereographic projection with the radial coordinate being tan /2, where is the polar emission angle with respect to the surface normal. The pattern is clearly different from that of the substrate (Fig. 6(e)). We may impose the 3-fold symmetry of the substrate in order to improve the contrast as shown in Fig. 6(g). Moreover the direct comparison with the substrate pattern and the calculation allows us to determine the orientation of the molecules, which have their mirror axis rotated by 15°relative to the densely packed atomic rows of the Ag(111) surface ( Fig. 6(h)). This latter informaiton is not easily accessible by conventional electron diffraction methods.
Pulsed x-ray sources are scarce and currently limited to a few x-ray free-electron lasers and some exceptional high-harmonic generation (HHG) light sources. [35,36] In contrast HHG light sources in the VUV region have become readily available in many labs. [13,[37][38][39] Therefore, we have explored the amount of structural information that can be gained from photoelectron diffraction experiments in this excitation regime, that often provides only access to valence states and not to core levels. Due to the dispersion of itinerant valence states, the intensity must here be integrated over the full bandwidth as was first shown in ultraviolet photoelectron diffraction (UPD) experiments on Cu(111). [40] If several bands of different symmetry are crossing the signals must be disentangled before integration. Moreover, due to enhanced large-angle scattering at low kinetic energies (see Fig. 5), the strong forward focusing maxima are missing and interference effects appear more strongly. As a consequence the data are less straightforward to interpret and require more advanced simulations for quantitative analysis. [41] It was shown, however, that the method still provides information about the structural environment of the emitting state, in particular in the case of non-dispersing molecular states. [42] In Fig. 7 we show the valence band spectrum of SnPc/ Ag(111) taken with a helium discharge lamp and photons of 21.2 eV energy. Two prominent peaks are observed beside the onset of the partially occupied LUMO. [15] These two peaks are assigned to HOMO and HOMO-1. The latter is strongly localized at the central Sn atom and serves as emitter for the UPD measurement shown in Fig. 8(b). SSC calculations for this excitation energy were carried out using the adsorbate geometry obtained from the XPD measurements (Fig. 6). They agree reasonably well with the experimental data, considering further that the latter contain also contributions from the underlying Ag(111) substrate, as can be easily recognized when considering the measurement from the clean substrate at the same binding energy (Fig. 8(a)). Three sharp maxima show up close to normal emission in both, calculations and experiment. Their 3-fold symmetry and their absence in the calculation for the free molecule suggest that these maxima are caused by interference with electron waves back scattered at the 3-fold symmetric substrate surface. Indeed, the variation of the adsorption height of the molecule above the surface layer in the SSC calculations leads to a variation in polar angle of these three maxima. Thus, fitting the simulated positions in order to match the experimental pattern allows the height to be determined with sub-Ångström precision. [15]  and purely electronic information through the momentum-resolved density of states measured by the experiment. [43] At the X-point, the electronic structure has a large gap at the Fermi energy which means that any photoelectrons observed there are excited by indirect transitions involving phonons. In these processes they lose their memory on the initial excitation within the electronic band structure and therefore any dispersion related intensity modulation. Thus, without energy integration, their intensity modulation can be attributed to photoelectron diffraction effects.
Assuming a localized Bi 6p valence state we performed SSC calculations for the equilibrium and for the distorted crystal structure in order to identify spots in momentum space where the modulation of the diffraction intensity is expected to be strong. The results are displayed in Fig. 11 together with transients taken such a point (marked by the arrow in Fig. 11b). As we can see the intensity modulations at these points is identical to that found earlier at the X-point confirming our hypothesis that the transient represents the modulation of the lattice structure. Hence, within a single experiment we measure the electron dynamics and the structural dynamics, what gives us the unique possibility of determining the phase lag between the modulation of the atomic structure and the concomitant modulation of the electronic density of states. [43] Orbital To mography As explained in the preceding section, interference of the outgoing electron waves generates a pattern in the final state of the photoemission process. The full final state may thus be written as a coherent superposition of direct emission and scattered waves. As proof-of-principle experiment for time-resolved UPD, we have chosen Bi(111), because the excitation with an short infrared pump pulse leads to strong displacement of the electronic charge density and to the impulsive excitation of coherent A 1g phonons. [44] These phonons show up as strong modulations of the energy and intensity of valence states in time-resolved photoemission spectra. [45,46] We observe such oscillatory modulations in delay scans of valence band spectra taken with VUV photons as shown in Fig. 9. [43] Interestingly the phase of the modulation depends on the momentum we are looking at as can be seen in Fig.  10: the intensity modulation at the X-point is shifted by about half a period with respect to that at the Γ-point (normal emission). This highlights one of the main differences between core-level XPD and valence level UPD experiments: the latter contain structural For light elements such as carbon, however, the scattering crosssections are small and multiple scattering further reduces the experimental anisotropies in the VUV-range. Moreover, for delocalized initial states like π-states in organic molecules, interference effects due to backscattering from the substrate as observed in the case of the localized HOMO-1 in Sn-Pc [15] are averaged over the spatial extent of the initial state wavefunction and are thus greatly reduced. Nevertheless, a well-defined pattern with large variations in intensity is observed when looking at angular distributions from such delocalized molecular states. These patterns were shown to be the results of the angular dependence of the excitation matrix element: [47] According to Fermi's golden rule an for a given photon energy the photoemission rate into a direction is proportional to the matrix element squared of the optical excitation. Assuming that final state scattering is negligible we can approximate the final state wavefunction by a single plane wave at wavevector (for a detailed discussion of this assumption the reader is referred to Refs. 48,49). With being the vector potential of the incident light wave and, thus, defining the polarization vector, the square of the matrix element can be rewritten as: [47,50] where the last line refers to the Fourier transform of the initial state wavefunction. Put in other words, the angular intensity distribution represents the squared modulus of the Fourier transform of the emitter orbital. For constant photon energy and kinetic energy, the photoelectron momentum vector moves on a spherical plane with the radius being given by the photoelectron momentum inside the sample. Therefore, tuning the photon energy allows one to take spherical cuts at different radii and to obtain the full 3D Fourier transform of the initial-state wavefunction. For this reason, this method usually is referred to as orbital tomography. In pioneering experiments, Puschnig and collaborators recorded and calculated such ARPES data from delocalized occupied states in well-ordered molecular layers on metal substrates: [47,48,50] The projection of the ARPES data according to Eqn. 1 onto the two momentum components parallel to the surface was termed a photoelectron momentum map (PMM). The experimental PMMs are compared to simulated patterns obtained by density-functional calculations of the molecular states followed by a Fourier transform into momentum space. [47] The direct inverse Fourier transform of the PMM into real space is not possible because the experiment only provides the intensity while the phase is lost. In principle, the missing phase information can be obtained from the dichroism in measurements carried out with different circular light polarizations. [52] An alternative solution is provided by optics in the case that such data are not available: Indeed, Kliuiev et al. showed that the angular pattern recorded in an ARPES experiment is equivalent to the diffrac-(2) Fig. 12: Optical diffraction experiment mimicking plane-wave emission from a pentacene π-orbital. (a) Scattering target produced by lithography with the same shape than the orbital; (c) diffraction pattern of a laser beam taken behind the target. The ratio of wavelength to object size was the same for the optical experiment as for photoemission using 50 eV photons and (f) show the amplitude and phase distribution in the plane of the target, respectively, both reconstructed using a phaseretrieval algorithm. tion pattern produced by an electromagnetic plane wave which is diffracted off from an object of the same shape as the initial state orbital. [51] The authors then used phase-retrieval methods known from coherent diffraction in order to obtain phase information by an iterative algorithm.
An example for such a reconstruction of the pentacene LUMO including the phase of the wavefunction is given in Fig. 13. In principle, no additional input was needed because the size of the molecule can be initially guessed from the autocorrelation function and then iteratively computed using the so-called shrink-wrap algorithm. [51] This size parameter is used as boundary condition to accelerate convergence. It allows the wavefunction amplitude and phase outside the molecule to be set to zero at each iteration of the algorithm because the molecular states are assumed to be confined within single molecules. Depending on the number of different orientations of the molecules present on the surface as well as the knowledge of some properties of the molecules like point group symmetries, the reconstruction may be time-consuming but has the advantage of giving direct experimental access to the wavefunctions of the molecular states. [51,53] Moreover, when investigating molecular layers, the periodicity and the size of the surface unit cell usually are obtained from LEED, while the orientation of the molecules is often inferred from steric considerations. As a complementary method and similar to XPD, the analysis of the PMMs yields the orientation of the molecules adsorbed on the substrate, as will be demonstrated with data taken from the ambipolar charge-transfer complex tetrathiafulvalene-dipyrazine TTF-PYZ 2 assembled in dense-packed monolayers and bilayers on Ag(110). [54] The molecules form a well-ordered monolayer when deposited on Ag(110). The angular distribution exhibits two strong maxima along the crystalline [11 − 0]-direction of the Ag substrate as shown in Fig. 14. The higher the parallel momenta at which these peaks appear, the more localized in the center they are in real space. These maxima correspond to the HOMO, which is centered at the central TTF moiety and which has donor functionality within the complex. [56] The position of the maxima gives direct information about the orientation of the molecules. In this case the long axis of the molecules is aligned with [11 − 0] as shown in Fig. 14. Moreover, a comparison of the data with theoretical simulation allows us to determine the bending angle of the molecules, which undergo a slight structural change when absorbed on the surface. [54] A sub- sequent second layer grows differently with the molecules being tilted with respect to those of the first layer and including a mirror domain. The binding energy of the HOMO states cannot be distinguished in energy in the valence band spectra, but the position of the aforementioned maxima shift in angle with respect to the substrate lattice. Hence, the tilt angle for the second layer and the mirror domain can directly be read from the angular pattern. [54] Furthermore, the PMMs provide some sort of fingerprinting used to identify molecular states because the assignment of peaks in valence band spectra to states is often ambiguous due to missing information about the hierarchy of the states. This fingerprinting is even possible if multiple orientational domains are present on the surface, like in the case of the complex macrocycle pyrphyrin with and without Co metal center [57] , which is a catalyst molecule for water splitting. [58] Adsorbed on an Ag(110)-surface the molecules exhibit multiple orientational domains. [55] The valence spectrum of the cobalt containing variant taken with 35 eV photons shows five molecular states as shown in Fig. 15. The five PMMs which correspond to the valence band peaks are shown in the top raw (raw data) and second row (after background subtraction) of the panel on the right-hand-side of Fig. 15. The molecular states were computed using DFT and the corresponding PMMs were simulated from the charge densities. The results are shown in the two bottom rows. Since the prediction of exact binding energies and even the orbital order is often difficult to obtain from DFT, the comparison with the experimental PMM data allows us to unambiguously identify the peaks and binding energies of the five states observed with the computed charge densities and molecular states. [55] Ve ry recently, using a combination of advanced instrumentation comprising a high-repetition-rate HHG light source [38] and a new electron detection scheme [59] , Wallauer et al. succeeded in taking the first time-resolved PMMs of transiently populated LUMO states. The sample was a layer of 3,4,9,10-perylene-tetracarboxylicdianhydride (PTCDA) deposited on Cu(001), which was prepared with an ultrathin surface oxide layer for decoupling the molecules from the metal substrate. [60] The experimental setup is shown in Fig. 16. The molecules self-assemble in two orthogonal orientations on the surface. A pump pulse in resonance with the HOMO-LUMO transition populates the LUMO. Depending on the polarization of the pump light, either molecules in a particular orientation or else all molecules can be excited. The photoelectrons are then produced by the time delayed VUV probe pulse and detected as function of parallel momentum and energy. Some time-resolved PMMs of HOMO and LUMO are shown in Fig. 17 as function of pump-probe time delay. Using oblique light incidence, the HOMO-LUMO transitions can be excited for both orientations of the PTCDA molecules, as can be seen in the experimental PMMs as well as in the simulations on the right-hand-side. While the HOMO intensity appears to be constant as function of delay (initial state bleaching can usually be neglected under typical experimental conditions) the LUMO only appears after the pump pulse and then decays on the timescale of about 100 fs. [60] The success of this experiment shows that the measurement of excited state dynamics in real time and real space is possible using ARPES techniques. We may conjecture that in future experiments this method and the possibility of finger-printing or even reconstruction of charge densities from ARPES data will be of great help in understanding the dynamics of charge and energy transfer in solid interfaces.

Outlook: Experimental Facilities
We have seen that the angular photoelectron distribution contains a wealth of valuable information which help to determine the atomic structure and electronic charge density distributions in solid surfaces. Using pump-probe techniques, both methods can be extended to real time methods with femtosecond resolution. The results together with the bandstructure and excited state lifetimes obtained from time-resolved ARPES measurements provide a complete picture of the dynamics after excitation by a pump pulse.
Such experiments take advantage of major technological developments over the past years. The number of parameters which need to be scanned for getting such a complete data set is large: The kinetic energy, two angles for the parallel momentum components, and finally the time delay require the acquisition and  [11 − 0]. b) Valence band spectrum taken with 35 eV photons and using a so-called k-PEEM detector at the NanoESCA beamline of the Elettra synchrotron; the data were integrated over the momentum range of the detector. c) Comparison of experimental and simulated tomography data showing raw data in the top raw and processed data in the center row. The data processing included the subtraction of the background signal caused by sharp Ag bands and the correction for the 2 term according to Eqn. 2. Bottom rows: simulated patterns from the molecular states summed up for three different adsorption geometries, and below, molecular orbitals derived from the DFT results and eventually assigned to the peaks (i) through (v) found in the valence band spectrum. (Adapted from ref. 55.) analysis of at least 4-dimensional data sets. Parallel data acquisition schemes were developed resulting in so-called kPEEM momentum microscopes. They can be realized by using the Fourier image of a hemispherical photoemission microscope (PEEM) which is imaged by a second hemispherical analyzer onto a 2D detector. [61] The detector images then represent the PMM at the kinetic energy setpoint of the analyzers. A second variant uses time-of-flight technique converting electron flight time into kinetic energy. Here, the different emission angles are images by an electrostatic lens system onto the 2D delay-line detector imaged such that the image again represents the photoelectron distribution in momentum space. [62,63] The latter requires a pulsed light source owing to the flight time measurement but has the advantage of recording energy and the full parallel momentum vector at each single shot. One of the main drawbacks of such instruments is the large space-charge which appears at intermediate focii of the imaging system with pulsed light sources. The inelastically scattered low-energy secondary electrons do not contribute to the actual signal but contain most of the photoelectrons and produce image distortions and energy shifts. One possibility to overcome this problem is the introduction of a retarding lens at the entrance of the analyzer repelling the secondary electrons close to the vacuum energy cut-off, which was demonstrated recently. [64] On the other hand, pulsed light sources based on high-harmonic generation of VUV pulses by intense femtosecond infrared pulses in noble gas jets proved to be an excellent source for timeresolved ARPES experiments. [13,37] With the advent of high-repetition rate femtosecond laser amplifiers, ARPES experiments from solids at photon energies of 20 to 100 eV with repetition rates in the 100 kHz range were demonstrated by several groups. [38,39] On top of that, many efforts were made to extend the photon energy range of laboratory experiments up to the so-called water window between the carbon K absorption edge at about 290 eV and the oxygen K-edge at about 530 eV, because this range is particularly well suited for the study of organic molecules. [35,36] Such sources might be used for time-resolved photoelectron diffraction experiments at soft x-ray energies. Moreover, there are user facilities with dedicated ARPES endstations like the Artemis beamline at the Central Laser Facility in UK [65] , the TRex facility at Elettra Sinchrotrone (IT) [66] or Harmonium at LACUS at EPFL. [67] All are HHG sources with photon energies up to about 100 eV and repetition rates of several kilo-Hertz, which are prerequisite for minimizing spacecharge problems while providing high signal strength in ARPES experiments. With the advent of free-electron lasers, the range of available photon energies was extended into the soft to hard x-rays but the repetition rates are usually too low (about 100 Hz) for photoemission experiments from solids. A notable exception well suited for time-resolved ARPES is given at FLASH (DESY) with up to 4000 pulses per second, [68] a beamline equipped with a momentum microscope, [69] and a beamline with THz undulator radiation available as pump. [70] In the near future, the upgrade of the free electron laser LCLS-II of the Stanford National Ac- celerator Laboratory includes a tremendous increase in repetition rate to about 1 MHz, [71] and a dedicated ARPES endstation will be designed in view of time-resolved photoelectron diffraction experiments at LCLS-II. [72] Such experimental stations together with small spot sizes and flexible pump scheme extending into the THz-range for resonant pumping of low-energy modes on one side, and into the UV range for investigation of wide-band gap materials will open new possibilities for studying all kinds of solid materials with unprecedented resolution in space and time.