Multispectral time-resolved energy–momentum microscopy using high-harmonic extreme ultraviolet radiation

Angle-resolved photoemission spectroscopy (ARPES) is the standard method to determine how electrons behave at surfaces of solid materials.^1–4 Monochromatic photons having ultraviolet (UV) energies or higher eject electrons from a material’s surface, and the photocurrent is measured as a function of electron kinetic energy, emission direction, and photon energy. Direction is encoded in two emission angles or, equivalently, in the two components of the surface-parallel momentum (k_x, k_y). Since the four measurement parameters can be straightforwardly related to the energy relative to the Fermi level (E − E_F) and three-dimensional (3D) momentum (k_x, k_y, k_z) of the electrons inside the material before photoexcitation,⁵ the measured intensity distributions readily provide multidimensional images of the electronic structure in portions of the four-dimensional (4D) energy–momentum space.⁶ Band structures and Fermi surfaces, and also momentum-dependent band renormalization and lifetime effects, can thus be accessed directly.^7–10 Another intriguing application is orbital tomography, which can provide reconstructed real-space tomograms of molecular orbitals on solid surfaces.^11,12 Depending on whether emission angles or surface-parallel momentum components are imaged onto the detector,^13–15 the technique is referred to as ARPES or momentum microscopy, respectively.

In this energy–momentum imaging, the photon energy is an important parameter in at least three different ways. First, the photon energy determines the maximum detectable electron kinetic energy, 3D momentum, and, thus, the volume of the probed portion in energy-momentum space.¹⁶ Second, scanning the photon energy allows us to retrieve the surface-perpendicular momentum component k_z and, hence, to perform full 4D energy–momentum imaging.^6,10,17,18 Third, tunability in the photon energy can also be useful to enhance the contrast of specific features in ARPES data by exploiting excitation resonances, escape-depth variation, or matrix-element effects.^19,20

In principle, the same relevance of the probing photon energy and its tunability also applies to time-resolved ARPES (trARPES) or time-resolved momentum microscopy,^21–23 in which time, or more precisely the time delay (t_D) between femtosecond-scale pump and probe pulses, is added as a fifth measurement parameter. Over the past fifteen years, trARPES has evolved into a powerful ARPES modality providing direct dynamical information on electronic structure at the fundamental time scales of electronic and atomic motion, particularly on photoinduced transient changes of electronic states and their population.^24–33 trARPES is now routinely performed using tabletop laser sources based on fourth and higher harmonic generation (HHG) in solids^34,35 and gases,^23,36–50 respectively, as well as using free-electron lasers (FELs) based on the self-amplification of spontaneous emission (SASE) of free electrons in undulators.²¹ The corresponding probe photon energies in trARPES range from the far UV to soft x-rays where a sweet spot currently is the intermediate extreme ultraviolet (XUV) regime.

In the XUV, HHG-based trARPES can optionally provide high time, energy, momentum, and spin resolution in conjunction with kHz to MHz repetition rates and a sufficiently wide detection window of the surface-parallel momentum (k_x, k_y) to fully cover typical Brillouin-zone (BZ) dimensions.^23,36–54 Moreover, HHG sources combined with monochromators enable multispectral measurements as they can deliver a usable, discretely tunable photon energy range of about 8–40 eV.^{36,37,41,44,45,47} However, this multispectral capability has so far rarely been exploited in trARPES experiments, and recently, several setups for HHG-based trARPES have even been optimized for operation at one specific photon energy only.^23,38,42,48 Here, contrary to this trend, we present the combination of a tunable, monochromatized, kHz-repetition-rate HHG source with a wide-momentum-acceptance time-of-flight (ToF) momentum microscope for efficient 4D energy–momentum mapping of ultrafast electronic structure dynamics. The overall system performance is demonstrated on bare and graphene-covered Ir(111).

Our multispectral-HHG trARPES setup, as schematically illustrated in Fig. 1, measures a 5D photoemission data hypercube I(E, k_x, k_y;k_z, t_D). The laser system gives the tuning of k_z and t_D, via adjustability of the probe photon energy and pump–probe delay, respectively, and the ToF momentum microscope provides the basic parallel 3D measurement of I(E, k_x, k_y).

The schematic layout of the laser system is shown in Fig. 1(a).⁵⁵ A Ti:sapphire laser amplifier (Wyvern 1000, KMLabs), operated at an output power of ≈12 W and a repetition rate of 6 kHz, delivers laser pulses at a center wavelength of ≈790 nm, pulse duration of ≈50 fs (FWHM, full width at half maximum), and pulse energy of ≈2 mJ. A quarter of the amplifier output is coupled into the pump branch, propagated through a delay stage, and focused onto the sample in the ultrahigh vacuum (UHV) photoemission chamber. The spot size of the pump beam on the sample is typically about (100 × 400) μm². The available pump-pulse energy of 500 μJ can be used for frequency conversion or attenuated to the mid-nJ to low-μJ level for 790 nm excitation of the sample below the space-charge limit.^56,57

The remaining 75% (≈50 fs, ≈1.5 mJ/pulse) of the amplifier output are coupled into the probe branch and focused with a lens (focal length f = 500 mm) into an Ar-filled waveguide capillary (XUUS, KMLabs), where higher harmonics in the XUV are generated. During operation, the Ar pressure inside the capillary is ≈60 mbar, while the pressure outside stays below $≈5×10−3$ mbar. A ZrO₂-coated toroidal mirror (f = 307 mm) is used to focus the multispectral XUV light onto the entrance slit of the monochromator and to separate out much of the fundamental radiation. ZrO₂ specifically provides XUV reflectivity comparable to Au for photon energies around 40 eV and reduced reflectivity at 1.5 eV.^58–60 The remaining 790 nm light is blocked using few-100 nm thick Al filters. Differential pumping is used to maintain a 5-orders-of-magnitude pressure difference between the HHG source and the monochromator chamber. A rotatable Au-coated toroidal grating (f = 163 mm) with 550 lines/mm (TGM300, Horiba Jobin Yvon SAS) images the entrance slit onto the exit slit with the selected higher harmonic light. For the 25^th harmonic, the footprint on the monochromator grating is estimated to be (1 × 1.7) mm², translating into a nominal temporal probe pulse broadening of 57 fs. A second toroidal mirror (f = 520 mm) focuses the selected and monochromatized XUV light onto the sample at an angle of 22° with respect to the surface. This mirror is rotatable and can alternatively direct the beam to a gas-phase experiment with combined ion- and electron-ToF spectroscopy.^61,62 Behind the refocusing mirror, the pump and probe beams propagate almost collinearly to the sample. At the sample, the XUV beam has a spot size of (70 × 800) μm² and a flux of 3 × 10⁸ photons/s in the brightest harmonics, which are usually the 23^rd and 25^th (see central panel of Fig. 4). The practically usable part of the harmonic spectrum contains all eight odd harmonics from the 15^th to the 29^th corresponding to a photon energy range of 23.6–45.5 eV. According to ray-tracing simulations, the temporal probe pulse broadening due to the monochromator lies in the range of 50–100 fs for all harmonics, independent of the slit size. The spectral resolution of the monochromator and the beamline is in the range of 100–240 meV under measurement conditions with slit sizes of 150 μm. In particular, for the higher harmonics, the monochromator selects only a given harmonic rather than clipping the harmonic’s spectral bandwidth. The overall high stability of the HHG source enables pump–probe experiments over several days, with the temporal overlap (time zero) remaining within the experimental time resolution. Average drifts in HHG intensity stay within 30% over a week of continuous operation (with the possibility to retune and restore reduced intensity).

The ToF momentum microscope employed in our laboratory-based setup is the same instrument used for FEL-based photoemission spectroscopy at the PG2 beamline of FLASH (DESY, Hamburg).²¹ The high photoelectron detection efficiency of the instrument, which compensates for the moderate repetition rate of the photon pulses, results from a combination of three separate capabilities: (i) direct 2D momentum imaging with a field of view of ±2.4 Å⁻¹ in both surface-parallel momentum directions, (ii) simultaneous ToF energy recording in an energy window of 7 eV, and (iii) multi-hit detection of up to three electrons per pulse. The underlying principle of slit-less 3D photoelectron energy–momentum detection is implemented as follows:¹⁵ The photocurrent emitted from the surface is imaged into an achromatic surface-parallel momentum image at the back-focal plane of the cathode objective lens; this hyperspectral image is subsequently magnified and high-pass-filtered by two lens systems, before it is spectrally dispersed in a field-free drift tube and finally captured on a delay-line detector (DLD). The eight-segment DLD (DLD6060-8s, Surface Concept) used in the current setup consists of two stacked four-quadrant DLDs rotated by 45° with respect to each other. This novel detector provides improved multi-hit detection capability compared to a single one- or four-quadrant DLD, as well as improved resolution of hits occurring near segment boundaries. The length of the drift tube (800 mm) and temporal resolution of the detector (≈150 ps) translate into a nominal energy resolution of $<$40 meV for typical electron drift energies of 10–30 eV. The nominal momentum resolution is $<$0.01 Å⁻¹, as given by the momentum field of view, active detector area (60 mm diameter), and the spatial resolution of the detector (≈80 μm).

The 3D energy–momentum measurement system, based on single-event detection, fills in the photoemission data cube I(E, k_x, k_y) over energy and momentum intervals with a characteristic width of 7 eV and 4.8 Å⁻¹, respectively, at a repetition rate of 6 kHz. When delay-time scanning is added, the resulting size of a typical 4D data hypercube is ≈100 GB. An efficient data acquisition and data processing workflow is implemented using an open-source software package developed for high-throughput multidimensional photoemission spectroscopy experiments.⁶³ Figure 1(b) shows a 3D representation of an exemplary dataset taken from graphene/Ir(111). Four different 2D cuts through this dataset are shown in Fig. 2, including the Fermi surface map I(E_F, k_x, k_y) [Fig. 2(a)] and selected band maps I(E, k₀, k_y) [Fig. 2(b)] and I(E, k_x, k₀) [Figs. 2(c) and 2(d)] for different constant values of k₀ corresponding to lines passing through high-symmetry points of the graphene BZ, as indicated in Fig. 2(a). In these maps, the strongest signal stems from the π-band of graphene, with its linear dispersion toward E_F and point-like Fermi surface at the K and K′ points. The Ir 5d bands appear as much weaker features. Their interaction with the π-band, however, leads to distinct kinks in the π-band dispersion.⁶⁴ The presented data vividly illustrate the efficiency and completeness of the ToF momentum microscopy approach for photoelectron detection.

We have characterized the performance of the experimental system by measuring the near-E_F electronic structure and the above-E_F carrier dynamics of graphene-covered and pristine Ir(111), respectively. Standard Ir(111) cleaning procedures and graphene growth recipes were applied.⁶⁵ Surface quality was checked by low-energy electron diffraction. All photoemission measurements were done at room temperature.

We estimated the effective experimental energy and momentum resolutions from the Fermi-level crossing of the graphene π-band in the graphene/Ir(111) sample. Figure 3(a) shows a room-temperature E–k photoemission intensity map, which was measured in the vicinity of the K point with a photon energy of 33.4 eV (21^st harmonic) using probe-only photoemission. Also shown are the momentum distribution curve (MDC) extracted at E_F (top panel) and an energy distribution curve (EDC) obtained by the MDC method⁶⁶ (right panel), representing the energy distribution of fitted MDC peak areas.

The EDC was fitted with a room-temperature Fermi–Dirac distribution function convoluted with a Gaussian resolution function [Fig. 3(a), right panel]. The resulting Gaussian FWHM, corresponding to the total energy resolution, is (96 ± 4) meV. This value includes a contribution of the photon source and monochromator of about 90 meV. The contribution of the electron spectrometer including space-charge broadening is estimated to be 30 meV. Over the entire usable spectral range of ≈24–46 eV, the effective energy resolution varied between 80 and 135 meV, where the photon energy dependence of the grating resolution at fixed slit widths makes the dominant contribution. Note that these values are better than those given above for photon resolution because the field aperture of the momentum microscope typically acts as a virtual exit slit, selecting an effective field of view on the sample of ≈70 μm.

The Gaussian FWHM determined from the momentum distribution curve at E_F is (0.096 ± 0.003) Å⁻¹ [Fig. 3(a), top panel]. After subtracting the intrinsic π-band momentum width of 0.031 Å⁻¹,^67,68 the remaining effective momentum resolution is (0.091 ± 0.003) Å⁻¹. We attribute the deterioration with respect to the nominal momentum resolution to less than optimal sample quality, electronic noise, and timing jitter in the position measurement on the detector. With varying probe photon energy, no noticeable changes of the momentum resolution were detected.

To estimate the temporal cross correlation between pump and probe pulses, we performed pump–probe photoemission measurements on pristine Ir(111) using pump and probe photon energies of 1.57 and 36.1 eV (23^rd harmonic), respectively, and an incident pump fluence of 2.42 mJ/cm². Figure 3(b) shows a momentum-integrated E–t_D intensity map depicting the transient generation and relaxation of hot electrons above E_F. A corresponding intensity transient (black data points), obtained by integrating over energies larger than E_F, is overlaid. This signal was fitted with a step function multiplied by an exponential decay and convoluted with a Gaussian function. The resulting Gaussian FWHM is (95 ± 5) fs, giving an estimate of the temporal system response function. Based on this value and with a modeled pump-pulse duration of (67 ± 5) fs FWHM at the sample position (obtained by using an autocorrelation measurement in combination with a modeling of the additional optics), we estimate the duration of the probe pulse to (67 ± 5) fs FWHM, assuming uncorrelated Gaussian-shaped pulses.

The key novel characteristic of our experimental setup is the combination of highly efficient 3D photoemission intensity I(E, k_x, k_y) imaging with a discrete tunability of the probe photon energy, thus making the energy–momentum mapping in trARPES k_z-dependent and 4D. Figure 4 illustrates this experimental advance.

The central panel of Fig. 4 displays two typical XUV spectra as a function of the monochromator energy. The spectrum indicated by the black line gives the calculated photon flux at the sample position. This signal was measured by a calibrated XUV-sensitive Si photodiode behind the exit slit of the monochromator and corrected for beamline transmission, including Al-filter attenuation to prevent photocurrent saturation. The second spectrum (red line) represents the electron count rate at the detector, as measured from an electrically biased graphene/Ir(111) sample by the ToF momentum microscope under otherwise typical measurement settings. The practically usable photon energy tuning range is 23.6–45.5 eV, at a spacing of $≈3.1$ eV, corresponding to the odd harmonic orders 15–29. The cutoff at ≈48 eV is typical for Ar gas as a generating medium.⁶⁹ 

The panels surrounding the XUV spectra in Fig. 4 show Fermi surface maps taken from graphene/Ir(111) with all eight harmonics. These 2D intensity maps are extracted from the full 3D data cubes that were originally measured. The data acquisition times varied from 2 to 12 h. The multispectral Fermi surface maps reflect a superposition of the point-like 2D Fermi surface of graphene (centered at the corners of the indicated hexagonal graphene BZ) and the complex multi-sheet 3D Fermi surface of Ir(111). There is no photon energy-dependent change in the shape of the graphene Fermi points, whereas the variation in the shape of the Ir 5d intensity pattern, i.e., k_z dispersion, is pronounced. Another observation is that the relative contribution of the Ir 5d signal to the total photoemission intensity at E_F is continuously suppressed upon increasing the photon energy from 23.6 to 45.5 eV. We attribute this effect to a decrease in the electron escape depth upon approaching the minimum of the universal curve of the inelastic mean free path around a kinetic energy of ≈50 eV:⁷⁰ With increasing surface sensitivity, less photoemission signal is obtained from Ir(111), which is covered by a graphene monolayer.

Under the assumption of free-electron-like final states within the direct-transition model of ARPES, constant-energy maps, such as the ones displayed in Fig. 4, map onto a spherical surface in 3D momentum space. The kinematic equation relating the surface-perpendicular momentum component to the other measurement parameters is⁵ 

where hν is the photon energy and m* and $V0*$ are the effective electron mass and inner potential (referenced to E_F) of the nearly free-electron final-state parabola, respectively. The empirical parameters for Ir(111) are m* = 1.07m_e and $V0*=10$ eV.⁷¹ Using Eq. (1) and exploiting point symmetry about the center of the BZ (Γ point), a tomogram of the 3D Fermi surface can be reconstructed from the stack of Fermi surface maps shown in Fig. 4.

Figure 5 displays the reconstructed portion of the 3D Fermi surface for graphene/Ir(111). Three sets of isosurfaces can be identified: the non-k_z-dispersive graphene Fermi rods centered at the corners of the hexagonal graphene BZ as well as an inner hexagon-shaped Fermi surface sheet and an outer star-shaped Fermi surface sheet derived from Ir 5d bulk states. The reconstructed Ir 5d Fermi surface sheets are in good agreement with a 3D Fermi surface tomogram obtained from pristine Ir(111) by soft x-ray momentum microscopy.⁷¹ The available photon energy range translates into a finite k_z probing interval of Δk_z = 0.9 Å⁻¹, smaller than the characteristic k_z dimension (⁠$ΓL̄=1.42$ Å⁻¹) of the fcc BZ of Ir(111). Thus, our tomographic data cover ≈39% of the BZ volume. For crystalline materials with smaller k_z dimensions, particularly layered 3D electron materials,^9,10,17,35 larger portions of the bulk BZ or entire bulk BZs can be scanned. Similarly, for layers of 3D molecules,⁷² 3D orbital momentum tomograms can be recorded.

In conclusion, by combining a 790-nm-driven kHz-repetition-rate HHG source with a toroidal-grating monochromator and a high-detection-efficiency ToF momentum microscope, we have realized an experimental setup for probe photon energy-dependent time-resolved XUV-ARPES with good data collection efficiency and sub-100 fs time resolution. The photon energy tuning range is ≈24–46 eV, sufficient to map band structures and Fermi surfaces as well as molecular orbital densities over an k_z interval of ≈1 Å⁻¹. The system thus specifically enables k_z-selective probing of ultrafast electronic structure dynamics in 3D materials as well as ultrafast 3D orbital tomography of molecular layers.^33,73 Moreover, the setup complements time-resolved momentum microscopy in the XUV to soft x-ray regime at the FEL FLASH, for which the same ToF momentum microscope is used.²¹ The two complementary probe photon sources particularly enable a unique merging of trARPES with time-resolved x-ray photoelectron spectroscopy^74–76 and diffraction⁷⁷ for combined investigations of ultrafast electronic, chemical, and geometric structure dynamics.

This work is dedicated to the late Wilfried Wurth. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project ID 491245950, and via the Collaborative Research Center (CRC) 925, Project ID 170620586 (Project B2). We thank Holger Meyer and Sven Gieschen for support with the instrumentation. We also thank former members of Wolfgang Eberhardt’s group, particularly Daniel Ramm, for help with the design and initial installation of the HHG source.

The authors have no conflicts to disclose.

M. Heber and N. Wind contributed equally to this paper.

Michael Heber: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Nils Wind: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Dmytro Kutnyakhov: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Federico Pressacco: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Tiberiu Arion: Conceptualization (supporting); Methodology (supporting); Writing – review & editing (supporting). Friedrich Roth: Conceptualization (supporting); Methodology (supporting); Writing – review & editing (supporting). Wolfgang Eberhardt: Conceptualization (supporting); Funding acquisition (supporting); Methodology (supporting); Resources (supporting); Writing – review & editing (supporting). Kai Rossnagel: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.