Boosting laboratory photoelectron spectroscopy by megahertz high-order harmonics

For an argon gas jet as generation medium, the HHG spectrum as back reflected from a Ag(001) crystal is shown in figure 2(a). Under these conditions, the photons are reflected at an angle of $22.5{}^\circ$ onto the chevron channelplate in the DLD of the ToF spectrometer. The absolute photon flux is estimated by using the reflectivity of silver at 32 eV (≈0.1 [43]) together with the detection efficiency of the channelplate (≈0.1 [44]). The maximum photon flux from argon is located at a photon energy around 32 eV with a value of $1.2\times {{10}^{5}}$ photons/s, which is less than one photon per laser pulse at this high repetition rate of 0.7 MHz. In total, the generated HHG spectrum covers the energy range from 20 to 40 eV with argon as the generation medium.

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The HHG photon flux can be greatly enhanced by using xenon as the generation medium. In figure 2(b), the HHG spectra from xenon driven at 0.7 and 1 MHz are displayed. Due to the high photon flux generated from xenon, these spectra have to be measured indirectly according to the number of photoelectrons entering the ToF spectrometer within an acceptance angle of $\pm 1.5{}^\circ$, corresponding to about 0.03% of the full $2\pi$ solid angle above the sample surface. A reflection measurement, as completed for argon, can only be performed for photon energy near 16 eV with moderate photon flux and is shown by the blue dashed curve. The photon flux at 16 eV from xenon is estimated to be 4.6 × 10⁷ photons/s or 66 photons/pulse at 0.7 MHz. At the maximum of the spectrum around 25 eV, the photon flux is estimated to be 8 × 10⁸ photons/s (1100 photons/pulse). Switching to 1 MHz leads to lower photon flux because of a lower pulse energy setting of the pumping laser. The maximum photon flux at 1 MHz is around 1.5 × 10⁸ (150 photons/pulse) at the photon energy of 22.7 eV. Note that the HHG intensity is more than three orders of magnitude higher than in our previous HHG study where a laser oscillator at 4 MHz was used [39]. Using xenon, the available photon energies are lower than using argon and range from 14 to 32 eV. Below 14 eV, the transmission of the toroidal grating, which is optimized for 40 eV, drops significantly [45].

According to the results in figure 2(b), we can estimate the total yield of photoelectrons. At the maximum of the spectrum for a photon energy of 25 eV at 0.7 MHz, we measured around 8 × 10⁴ electrons/s emitted into 0.03% of the $2\pi$ full hemisphere. This small solid angle of detection was set by turning off all the electron lenses of the ToF spectrometer and was intentionally used to avoid damage of the detector at high count rates. As a rough estimation, a simple scaling up to the full $2\pi$ hemisphere leads to a photoelectron yield of 2 × 10⁸ electrons/s emitted from the sample at 0.7 MHz, which corresponds to around 300 electrons/pulse. About 5 × 10⁷ electrons/s emitted from the sample is estimated from experiments at 1 MHz, and this emission intensity is marginally above the space-charge onset of one electron/pulse. The ratio of the estimated number of photoelectrons to the number of incident photons per second is about 0.25. This value is a factor of three higher than the known photoemission yield [46, 47] and can be ascribed to the emission angle and light polarization dependence that are neglected in the estimation. In figure 1(a) we show the conservative estimation of the total yield of photoelectrons at around 1 × 10⁷ electrons/s at 1 MHz, which is close to the optimal condition in the ToF working region.

To demonstrate the efficiency of our present setup, we present a fast photoemission measurement from Ag(001) at 1 MHz with a photon energy of 22.7 eV. The angle of incidence of light is $45{}^\circ$ and the light is p-polarized. In figure 3, we show the data from a single measurement with an acquisition time of 10 s and nominal kinetic and pass energy setting as 16 and 60 eV, respectively. Within this short time, we detected a total number of 3 × 10⁶ photoelectrons and this count rate is indicated in figure 1(b) for comparison with other photoemission experiments. The photoelectrons are analyzed according to their ToF and hit positions on the DLD in the spectrometer. This analysis yields the three-dimensional photoemission intensity as a function of energy $(E)$ and momentum components $({{k}_{x}},{{k}_{y}})$ parallel to the surface $I({{k}_{x}},{{k}_{y}},E)$. The two-dimensional slices of the photoemission intensity with energy versus momentum are shown in figures 3(a) and (c), $I({{k}_{x}},E)$ and $I({{k}_{y}},E)$, respectively. In figure 3(e), we depicted the line profiles I(E) at fixed k_x = ±0.35 Å⁻¹ from figure 3(a). Clear features of the d bands from 4 to 7 eV below the Fermi energy (E_F) with high intensity are observed and the weak intensity above 4 eV is attributed to the sp bands. The cutoff at 8 eV is due to the limit of the electron lens system in the ToF spectrometer at the chosen setting.

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Closer inspection of the dispersion of the photoemission features in figure 3(a) reveals a clear asymmetry between the positive and negative k_x sides. As indicated by the arrows in figures 3(a) and (e), on the negative side of k_x we observed three branches of d bands, whereas on the positive side, only two branches can be seen. This asymmetry in photoemission pattern can be further identified in the momentum distribution of photoelectrons $I({{k}_{x}},{{k}_{y}})$, as shown in figures 3(b) and (d) for different energies. The momentum distribution has a mirror symmetry with respect to the k_x axis but no mirror symmetry about the k_y axis. This observation can be explained by the experimental geometry as defined by the Ag(001) surface with fourfold symmetry and by the linearly polarized incident light within the optical plane on which the k_x axis is located. The linear polarization of light is 45$^{\circ }$ tilted from the surface normal and simultaneously has a component parallel to the k_x momentum direction, as well as another component perpendicular to the surface. These two electric field components can cause interference in the matrix element of photoemission and result in an asymmetric distribution of photoelectrons [49, 50]. As a consequence, breaking the original fourfold symmetry with the incident off-normal light leads to a twofold pattern, which has only mirror-symmetry about the k_x axis in our case. The appearance of the threefold pattern in figure 3(b) can be considered as a special case of a mirror-symmetric pattern with respect to the k_x axis at this specific binding energy.

To check whether space-charge effects have an influence on the present experiments, we follow the well-established method in the literature and compare the Fermi-edge in photoemission spectra measured with different count rates [34, 40]. In figure 3(f), we show the angle-integrated photoemission spectra near the Fermi energy (E_F) measured with $1.3\times {{10}^{5}}$ and $4.4\times {{10}^{4}}$ electrons/s and the fits with a step function convoluted by a Gaussian function. From the fit, the position of the Fermi edge in these two spectra can be evaluated and their difference is less than 10 meV. We therefore exclude significant space-charge effects much higher than 10 meV, which is in accordance with our expectation for the MHz high repetition rates, as discussed in figure 1. The full-width-at-half-maximum (FWHM) of the Gaussian functions in the fits is around 250 meV. By taking into account the thermal broadening of the Fermi–Dirac distribution that corresponds to a FWHM of around 100 meV at 300 K, we estimate the energy resolution in the present experiments as 230 meV. This value is larger than that in our previous measurements on the surface state of Cu(111) surfaces using a lower photon energy [39]. As included in the energy resolution, about 180 meV can be attributed to the bandwidth of the HHG light source at a photon energy of 22.7 eV, whereas the other 150 meV comes from the energy resolution of the ToF spectrometer for the present lens setting of a 12 eV energy window. This estimated bandwidth of the harmonics corresponds to a transform-limited pulse duration of about 9 fs from generation, which is subsequently stretched by the monochromator grating to about 2 ps.

The features of electronic bands observed in photoemission spectra in figure 3 can be qualitatively interpreted by the band structure of Ag(001), as shown in figure 4(a) [48]. With a photon energy close to 23 eV, the dominant photoemission signals come from the resonance between Ag d and unoccupied sp bands. Similar transitions from the d bands can also take place at higher photon energies of 30 and 39 eV as observed in figure 4(b). In addition, at a lower photon energy of 18 eV, a resonance between sp bands occurs and photoemission signals from the Ag sp bands with stronger dispersion along the momentum direction k_x is observed, as shown in the lowest panel of figure 4(b).

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In conventional laboratory photoemission experiments using a hemispherical energy analyzer in combination with a discharge lamp, the sequential azimuthal rotation of the sample is necessary for a three-dimensional $I({{k}_{x}},{{k}_{y}},E)$ data set. Based on the 180 min measurement by Reinert et al with an angular acceptance of $\pm 7{}^\circ$ and a high-energy resolution of 3.5 meV, we estimate an acquisition time of 10 min for a measurement with comparable momentum range and energy resolution to our results in figure 3 [51]. This longer acquisition time than our present HHG-based experiments can be attributed to an order of magnitude lower photoemission intensity from the surface states and the slow subsequent sample rotation in their experiments. Using the PEEM-based spectrometer to collect all emitted photoelectrons, a three-dimensional data set $I({{k}_{x}},{{k}_{y}},E)$ typically takes 0.5 to 1 h [4, 5]. A comparable measurement using our present setup requires a 30 times longer acquisition time than for the data in figure 3 and the total measurement time is about 5 min. Therefore, our setup is more efficient than these laboratory experiments using a laboratory discharge lamp either with a hemispherical energy analyzer or a PEEM-based spectrometer.

Despite the lower efficiency of these laboratory ARPES experiments using a discharge lamp, they may be advantageous due to the high-energy resolution coming from the narrow width of the ionization lines. On the other hand, the HHG-based ToF experiments provide a more simple control over the polarization of light as well as the possibilities for time-resolved pump-probe experiments.

In comparison to laboratory light sources such as discharge lamps or HHG, synchrotron radiation can provide significantly higher photon flux at a higher repetition rate, as indicated in figure 1. Therefore, synchrotron-based ARPES experiments can be generally more efficient than our laboratory HHG-based ARPES experiments. In order to compare the relative efficiency, in the following, we discuss the space-charge-limited ARPES experiments using synchrotron in the normal operation mode in combination with a hemispherical energy analyzer, as well as in the single-bunch mode with a ToF spectrometer.

For experiments with a hemispherical energy analyzer, we estimate the acquisition time of space-charge-limited synchrotron ARPES experiments using a count rate of 200 photoelectrons per pulse near the onset of space-charge effects ($\Delta E$ = 1.4 meV) at a 500 MHz repetition rate [34]. Assuming this count rate as the maximum intensity in experiments and an isotropic distribution of photoelectrons, there are 10¹¹electrons/s emitted from the sample and 3 × 10⁹ electrons/s within the ±15° emission angle enter the hemispherical energy analyzer. To acquire a two-dimensional momentum distribution with a range and a resolution comparable to our results in figure 3, experiments with the hemispherical energy analyzer need to include 240 steps within the 180° azimuthal sample rotation. Therefore, the effective count rate for measuring a three-dimensional data set $I({{k}_{x}},{{k}_{y}},E)$ is reduced by a factor of 1/240 and ends up at 1 × 10⁷ electrons/s. This count rate is about two orders of magnitude higher than that in our HHG-ToF experiments and proves that the synchrotron-based experiment with a hemispherical energy analyzer is more efficient. The higher efficiency of synchrotron ARPES experiments is directly related to their two orders of magnitude higher repetition rate than our HHG light source and this aspect was overlooked in an earlier comparison in [11].

In strong contrast to ARPES using the hemispherical energy analyzer, experiments with a ToF spectrometer require a reduced repetition rate of the synchrotron radiation [6, 17]. The single-bunch mode at several synchrotron facilities operates at a repetition rate in the range from 1.25 MHz at BESSY [16, 17] and NSLS [12], to 3 MHz at ALS [15] and 5 MHz at ESRF [14]. Despite the much more intense light from synchrotron than in our laboratory HHG setup, the detected photoelectron count rate would not be significantly higher beyond 10⁶ counts/s due to the limit of the imaging detectors. Therefore, we estimate a conservative maximum count rate of synchrotron-based ToF PES of around 10⁶ counts/s, which can be reached using our laboratory HHG-based experiments.