Time-resolved HAXPES using a microfocused XFEL beam: From vacuum space-charge effects to intrinsic charge-carrier recombination dynamics

Time-resolved hard X-ray photoelectron spectroscopy (trHAXPES) using microfocused X-ray free-electron laser (XFEL, hν = 8 keV) pulses as a probe and infrared laser pulses (hν = 1.55 eV) as a pump is employed to determine intrinsic charge-carrier recombination dynamics in La:SrTiO3. By means of a combination of experiments and numerical N-body simulations, we first develop a simple approach to characterize and decrease XFEL-induced vacuum space-charge effects, which otherwise pose a serious limitation to spectroscopy experiments. We then show that, using an analytical mean-field model, vacuum space-charge effects can be counteracted by pump laser-induced photoholes at high excitation densities. This provides us a method to separate vacuum space-charge effects from the intrinsic charge-carrier recombination dynamics in the time domain. Our trHAXPES results thus open a route to studies of intrinsic charge-carrier dynamics on picosecond time scales with lateral spatial resolution on the micrometer scale.

Scientific RepoRts | 6:35087 | DOI: 10.1038/srep35087 more than one photoelectron is ejected into the vacuum by the absorption of a photon pulse, the Coulomb interaction among the electrons on their way to the detector becomes relevant, which can result in severe energy and momentum distortions of the detected photoelectron spectra. Although both pump and probe pulse-induced space-charge effects can be controlled experimentally and theoretically 6,13,16,18,19 , they are at present inevitable in trHAXPES experiments since the pulse intensities have to be sufficiently strong to overcome the low photoionization cross sections at the high photon energies used in combination with the low repetition rates of the photon sources currently available [4][5][6] . The use of a microfocused photon beam, resulting in a smaller focal spot size on the sample surface, can be expected to aggravate the space-charge problem further due to the higher density of emitted electrons per area and pulse 13 .
In this work, we show that, contrary to expectations, under suitable experimental geometry, trHAXPES using a microfocused XFEL beam can be used to probe intrinsic charge-carrier recombination dynamics in the electron-doped perovskite oxide La:SrTiO 3 in the high pump excitation density regime. After a discussion of the general limitations arising from the use of a microfocused XFEL beam, namely sample ablation and XFEL-induced vacuum space-charge effects, we present (tr)HAXPES data of the Ti 1 s emission of La:SrTiO 3 recorded as function of pulse energy, incidence angle, and time delay between a low-photon energy (1.55 eV) pump pulse and the XFEL pulse as a probe. We then perform two different types of calculations to analyze the data. First, by means of numerical N-body simulations, we quantify the impact of microfocusing on the space charge-induced spectral shift and broadening of the photoelectron kinetic energy distribution. The results show that for extremely low photon incidence angles (relative to the sample surface) space-charge distortions can be effectively reduced at an increasing detection count rate for a given photon flux, albeit at the expense of a reduction in spatial resolution in one dimension. Second, using an analytical mean-field model, we address the role of vacuum space-charge effects in the high pump excitation density regime. By comparison with the experimental results, we can deconvolve vacuum space-charge effects from intrinsic charge-carrier recombination dynamics on the picosecond to nanosecond time scale. The results reveal a complex three-staged dynamical behavior for positive time delays, i.e., when the probe pulse follows the pump pulse. The successful application of micro-trHAXPES beyond space-charge effects establishes a novel method to gain insight into spatially resolved ultrafast bulk electron dynamics, e.g., in complex materials, at buried interfaces, or in electronic devices under in operando conditions.

Results and Discussion
Fundamental limitations to XFEL-based micro-HAXPES. We start by discussing two general limitations of solid-state photoelectron spectroscopy arising from the use of a microfocused, ultrashort-pulsed photon source with high peak intensities: sample ablation 21 and (probe-induced) vacuum space-charge effects 4,6,16,17 .
When using the unattenuated microfocused SACLA XFEL photon beam, fluences, i.e., pulse energies per area, of approximately 175 Jcm −2 are reached, which are well above the ablation threshold of the samples used, e.g., 80 Jcm −2 in the case of silicon 21 , resulting in severe sample damage [ Fig. 1(a,b)]. The magnitude of the ablation threshold fluence, F abl , for the single crystal La:SrTiO 3 sample used in the present study can be estimated as 90 Jcm −2 < F abl < 175 Jcm −2 . This type of radiation damage typically does not arise in experiments with an unfocussed XFEL beam (spot diameter ~700 μm) 4-6 . However, in order to perform photoelectron spectroscopy experiments, the average pulse energy has to be reduced further than just below the sample ablation threshold. This is because of vacuum space-charge effects, which can result in severe distortions of the recorded energy distribution curves. Figure 2(a) shows the evolution of the measured Ti 1 s HAXPES spectra of La:SrTiO 3 as a function of the average XFEL pulse energy. These data were recorded at a photon incidence angle of about 1° relative to the sample surface. The applied mean fluences ranged from 0.06 Jcm −2 up to 90.83 Jcm −2 . The latter value corresponds to a beam attenuation of 52%. With Figure 1. XFEL-induced sample ablation and experimental geometry. Radiation damages on the surfaces of Si (a) and La-doped SrTiO 3 (b) when operating with a microfocused XFEL beam at a fluence, i.e., pulse energy per area, of 175 Jcm −2 . The direction of photon incidence is indicated by arrows. (c) The angle of photon incidence ϑ (relative to the sample surface) can be varied by sample rotation, resulting in a changed spot diameter d x on the sample surface at a constant spot diameter d y . The axis of the entrance lens of the photoelectron spectrometer (z direction) was perpendicular to the direction of the photon beam (x direction) in all cases.
Scientific RepoRts | 6:35087 | DOI: 10.1038/srep35087 increasing XFEL pulse energies, the spectral distributions become broadened and shifted towards higher kinetic energies, until at the highest applied pulse energies no spectral features can be recognized anymore.
For a quantification of the observed space-charge effects, we have fitted the experimental data using Voigt profiles after subtraction of a Shirley-type background [ Fig. 2(a)]. The extracted spectral shift and broadening are shown in Fig. 2(b,c). The space-charge broadenings were calculated as where Δ E m is the measured, broadened (Gaussian) FWHM of the respective energy distribution curve and Δ E i = 1.43 eV is the 'intrinsic' linewidth as determined by high-resolution HAXPES experiments at the same photon energy 4 convoluted with the instrumental energy resolution (~1.25 eV FWHM). The data reveal the behavior known from previous XFEL photoemission experiments 6 and predicted by numerical N-body simulations 6,15 : near-to-linear dependencies of the spectral shift and broadening as a function of the average fluence or, equivalently, the number of excited photoelectrons N. The fitted linear slopes are (1.98 ± 0.26) eV/(Jcm −2 ) and (17.48 ± 0.96) eV/(Jcm −2 ) for the spectral shift and broadening, respectively. Thus, to perform photoelectron spectroscopy experiments with a microfocused XFEL beam, or more precisely, to obtain spectral widths where the spectral broadening is smaller than the intrinsic linewidth, the available photon intensity has to be reduced by at least 3 orders of magnitude resulting in prolonged acquisition times of 40 to 60 minutes in comparison to measurements with a less attenuated beam (however, at a repetition rate of only 30 Hz).
Incidence angle-dependence of probe pulse-induced space-charge effects. HAXPES experiments generally suffer from notoriously low photoionization cross sections at the typically used photon energies (6-8 keV) and thus comparably low detection count rates even at high-repetition-rate synchrotron radiation sources. A common approach to drastically increase the photoemission signal for a given photon flux is to measure in a grazing incidence geometry, i.e., to decrease the photon incidence angle relative to the surface while collecting photoelectrons in normal emission 22 .
One underlying factor is the angle dependence of the photoionization cross section as sketched in Fig. 3(b). When linearly polarized light is used as an excitation source, the photoionization cross section of the examined material shows an angular distribution depending on the so-called asymmetry parameter β 22,23 . For HAXPES, almost all subshells have positive β values 23 . Thus, the number of detected photoelectrons reaches a maximum in the direction parallel to the polarization vector, i.e., when measuring in a grazing incidence and normal emission geometry. Another factor is the reduced light penetration depth at grazing incidence, which results in an increased number of excited electrons with an inelastic mean free path longer than their escape depth. By further reducing the photon incidence angle to a fraction of a degree, one could additionally reach surface sensitivity by exploiting the critical angle for total external reflection.
However, at first glance somewhat counterintuitively, the photoemission data, shown here for the example of the Au 4f core-level emission of gold (β = 0.7075 23 ) measured with soft X-ray photoelectron spectroscopy, not only exhibit a drastic increase in photoemission intensity, i.e., number of ejected photoelectrons, with decreasing incidence angle, but also a decrease in the measured space charge-induced spectral shift [ Fig. 3(a)].
In the following, we examine the impact of the relevant incidence angle-dependent experimental parameters on the space charge-induced spectral shift by means of numerical N-body simulations. The three most important parameters are: (i) the shape, i.e., eccentricity ε of the elliptical spot profile, (ii) the horizontal spot diameter d x and the related change in spot area, as well as (iii) the number of emitted photoelectrons N.  , where a is the minor and b the major axis of the ellipse, is increased beyond a value of ε > 0.99 [ Fig. 4(b)]. For a microfocused elliptical beam of 100 μm 2 spot size, for example, this eccentricity corresponds to spot dimensions of (4.25 y . Thus, space-charge effects can indeed be reduced at a given photon flux and spot size by choosing an elliptical instead of a circular spot profile. Intuitively, the effect can be understood as a transition of the photoelectron cloud from a compact two-dimensional disk of charge to an elongated quasi-one-dimensional chain of charge, which comes along with a decreased Coulomb potential. Given the above approach, we can now use it to optimize the conditions in our micro-HAXPES experiments. Figure 5(a,b) shows the calculated elongation of the horizontal spot diameter as a function of incidence angle, starting from a circular Gaussian-shaped spot profile, as well as the corresponding change in eccentricity for three different initial spot diameters. The space charge-induced spectral shift at a spot diameter of d y = 2.5 μm is reduced by > 20% (with respect to normal photon incidence) when an eccentricity of ε > 0.997 is reached, corresponding to a photon incidence angle of 4.5° relative to the surface plane. This is directly reflected in a drastic decrease of the simulated space-charge shift as a function of incidence angle by one order of magnitude (when keeping the number of photoelectrons constant) [ Fig. 5(c)]. Importantly, even when the non-linear increase in the number of ejected photoelectrons at low photon incidence angles [ Fig. 3(a)] is included, the expected increase in space charge-induced shift due to its near-to-linear dependence on the number of ejected photoelectrons is  To check this prediction, we have experimentally determined the angular dependence of the space-charge shift and broadening by analyzing the Ti 1 s emission of La:SrTiO 3 as a function of photon incidence angle in a range of 3.5° to 1° [ Fig. 5(e)]. For a quantification of the observed spectral distortions, we have fitted the experimental data with Voigt profiles after subtraction of a Shirley-type background. Best fits are included in Fig. 5(e). The (Gaussian) broadening was calculated as described above. The extracted spectral shifts and broadenings are presented in Fig. 5(f,g): With decreasing photon incidence angle the measured spectral broadening as well as the space charge-induced shift in kinetic energy decrease, in good qualitative agreement with the results of our numerical N-body simulations. Note that the numerical simulations underestimate the measured spectral broadening by a factor of about 2.5. We tentatively attribute this discrepancy to the deviations of the experimental angle and energy distributions from being isotropic and monoenergetic 6 , respectively. Any anisotropy in the photoelectron emission 9,10 as well as the inclusion of a secondary photoelectron background 15 or other photoemission lines 17 in the initial spectral distribution may give rise to enhanced spectral broadenings at a given number of excited photoelectrons.
Summing up, the above results establish a simple experimental approach to reduce both data acquisition time as well as space-charge effects in (micro-)trHAXPES experiments at ultrashort-pulsed XFEL facilities with respect to experiments conducted in a non-grazing photon incidence geometry. Importantly, we note that in comparison to our previous trHAXPES experiments on La:SrTiO 3 , in which an unfocused XFEL photon beam was used at a pump and probe photon incidence angle of ϑ ≈ 15° (relative to the sample surface) 6 , the reduced photon incidence angle of ϑ ≈ 1°-1.5° leads to an up to 15-fold reduction of the effective XFEL penetration depth, = × ϑ L L sin eff , where L(8 keV, ϑ = 90°) ≈ 5.5 nm 24 . By contrast, the pump laser penetration depth, which is assumed to be in the order of 52 nm as reported for the related material SrRuO 3 25 , does not change significantly upon reduction of the incidence angle 26 . Hence, whereas similar incident pump laser fluences and thus similar excitation densities were used in the two experiments, the present grazing-incidence measurements enable us to be more sensitive to surface effects due to the drastically decreased effective XFEL probing depth.  The relaxation dynamics of the extracted shift in kinetic energy as well as the spectral width show a distinctly different character for positive and negative delays [ Fig. 6(c,d)]. For negative delays both decay on a 100 picosecond time scale, whereas for positive delays three-staged dynamics can be observed. The measured spectral shift and broadening, first, decrease within a few tens of picoseconds toward a minimum at kinetic energies and spectral widths, respectively, lower than the mean values of the unpumped spectrum, before, second, recovering toward positive shift and broadening values and, finally, relaxing back into equilibrium on a nanosecond time scale.

Space-charge and charge-carrier recombination dynamics in trHAXPES.
To understand the origin of this dynamics, we first present the results of mean-field model calculations neglecting the possible presence of (quasi-)stationary photoholes at the surface (p = 0 photoholes per pump electron). Long-living photoholes near the surface may in principle arise from pump laser-induced multiphoton electron emission into vacuum, electron-hole separation following internal photoexcitation in a space-charge layer beneath the surface, or a combination of both. We note that distinguishing between these processes is principally difficult because they manifest similarly in the measured spectral photoelectron distributions 20,[27][28][29] . To identify the dominant mechanism, one could for example exploit the expected differences in the pump fluence dependence of the effects: While surface photovoltage effects typically saturate at high pump fluences 30   Figure 6(c) shows the time dependence of the Ti 1 s shift extracted from the experimental data in comparison to the calculated results. To reproduce the maximum positive kinetic energy shift as well as the negative delay dynamics, the number of pump electrons had to be set to 3.5 ⋅ 10 6 . The beam spot diameters as well as the mean pump-and probe-electron velocities, on the other hand, were taken from the experiment. The mean kinetic energy of the emitted pump electrons was determined from the measured energy distribution curve displayed in Fig. 6(a).
When neglecting any possible influence of pump laser-induced photohole effects at the surface (p = 0) and only accounting for pump laser-induced space-charge effects in vacuum, the model can not reproduce the observed three-staged dynamics for positive time delays [Fig. 6(c)]. However, when we take into account stationary photohole states (p > 0) as well as possible bi-exponential electron-hole recombination inside the strongly electron-doped SrTiO 3 sample (with time constants τ 1 and τ 2 ), the model can qualitatively describe the observed delay dependence of the spectral shift (see Sec. Methods). In fact, the calculations give a successively better agreement with the experimental data for an increasing number of photoholes at the surface [ Fig. 6(c)]. The best agreement can be found if p = 0.9 stationary photoholes per excited pump electron are assumed.
We note that in our simple 1D model the position of the minimum at kinetic energies lower than the mean value of the unpumped spectrum is mainly determined by the time constant τ 1 , which, however, at the same time defines the recovery rate toward positive kinetic energy shift values. The chosen value of the time constant τ 1 appears to be the best fit between both stages. The subsequent relaxation into equilibrium is mainly governed by the value of the time constant τ 2 . The charge-carrier recombination time constants of τ 1 = (150 ± 20) ps and τ 2 = (5 ± 0.5) ns chosen to reproduce the observed dynamics [ Fig. 6(e)] as well as the assumed charge population ratio + + N N to 1 2 of (9 ± 0.5) to 1 are in good agreement with the findings of time-resolved photoluminescence experiments in the high excitation density regime on undoped SrTiO 3 samples 33,34 . The microscopic origin of these recombination processes, however, remains an interesting subject for further investigations. We note that similar effects, i.e., negative shifts in kinetic energy due to the influence of photoholes in the high excitation density regime, have recently also been observed in time-resolved extreme ultraviolet photoelectron spectroscopy of solutions 35 .
In view of the simplicity of the model, the agreement between calculated and measured results is remarkable. Our simple mean-field model can be used to deconvolve pump laser-induced extrinsic space-charge dynamics and intrinsic charge-carrier recombination dynamics in high kinetic energy photoelectron spectroscopy. The combined experimental and theoretical approach thus establishes trHAXPES as a novel spectroscopic tool for determining electron recombination dynamics with bulk sensitivity.
In conclusion, we have realized a successful application of trHAXPES using a microfocused XFEL photon beam. To this end, we first determined the impact that focal spot sizes of a few micrometers have on the inevitable space charge-induced spectral distortions of the recorded photoemission spectra. By means of numerical simulations and experiments, we found lowering the photon incidence angle to be a viable approach to reduce XFEL-induced space-charge effects at an increased detection count rate, albeit at the expense of a loss of spatial resolution in one dimension. Importantly, by an application of micro-trHAXPES to electron-doped SrTiO 3 and the use of a simple analytical mean-field model, we could then deconvolve extrinsic vacuum space-charge effects from intrinsic charge-carrier recombination dynamics in the time domain. Our results reveal a bi-exponential decay of the pump excitation-induced photoholes on a picosecond to nanosecond time scale, in good agreement with the findings of time-resolved photoluminescence studies. Hence, these results establish trHAXPES with lateral spatial resolution on the micrometer scale as a novel technique to determine intrinsic spatiotemporal charge-carrier dynamics on ultrafast time scales.

Methods
Experimental techniques. (Tr)HAXPES experiments were performed at beamline 2 (experimental hutch 3 providing a microfocused beam) of the SACLA XFEL facility at SPring-8 36,37 using ultrashort (Δ t ≈ 10 fs), quasi-monochromatic (Δ E ≈ 1 eV) XFEL pulses with a photon energy of ~8 keV at a repetition rate of 30 Hz. The XFEL pulse timing jitter was at maximum ~250 fs. The average XFEL fluence was about 175 Jcm −2 , corresponding to ~4.1 × 10 9 photons per pulse, with 10% fluctuation over 30 shots. The pulse energy at the sample was adjusted by inserting Si and Al attenuators of varying thickness into the beam. Typical attenuation factors were in the range of up to 1000-2500. All photoemission spectra were recorded using a Scienta R4000-10 kV electron analyzer. For the (tr)HAXPES experiments the pass energy was set to 200 eV at an entrance slit width of 1.5 mm resulting in a nominal analyzer energy resolution of 0.75 eV and thus a total experimental energy resolution of about 1.25 eV. The typical data acquisition time for one spectrum was about 40-60 minutes.
For the time-resolved pump-probe photoemission studies, the XFEL probe pulses were complemented by synchronized optical pump pulses delivered by a Ti:Sapphire amplifier system with a photon energy of 1.55 eV, a pulse length of Δ t ≈ 40 fs, and incident fluences of up to 30 mJcm −2 . The effective probe and pump beam spot sizes on the sample (full width at half maximum) were about 2.5 × (40-145) μm 2 and 190 × (2300-5000) μm 2 , respectively, depending on the photon incidence angle, which was chosen in a range of 3.5° to 1° (relative to the sample surface). In this scheme, the horizontal pump spot diameter was limited by the sample size. Pump and probe beam hit the sample quasi-collinearly with an angle of 1° between the beams. In this experimental geometry, the relative delays between pump and probe pulses are maintained when measuring in a grazing photon incidence geometry. However, the optical path for the photon pulses increases along the major axis of the spot profiles and the photoelectron excitation process is thus spread in time (by < 2 ps along the footprint of the XFEL beam). The temporal overlap of the pulses was determined using an ultrafast photodiode with a rise time of 30 ps and the pump-probe time delay was adjusted by using an optical delayline. As single crystal samples, 5% La-doped SrTiO 3 as well as undoped Si were chosen. The equilibrium sample temperature during all experiments was set to 300 K. Complementary soft X-ray PES experiments were conducted on a polycrystalline gold sample at the undulator beamline BL17SU of SPring-8 using a photon energy of 600 eV at a total energy resolution of 200 meV. Soft X-ray PES and (tr)HAXPES experiments were carried out using the same experimental setup with the photoelectron emission direction being perpendicular to the direction of photon incidence.
Numerical N-body simulations. For the numerical simulation of the XFEL pulse-induced space-charge effects, we used a modified Barnes-Hut treecode algorithm for Coulomb force calculation and a leap-frog integration scheme to solve the equations of motion. The details of these numerical N-body simulations are described elsewhere 10,13 . The approach is to gradually evolve an N-electron distribution in front of the sample surface, assuming initial Gaussian spectral, temporal, and spatial profiles. The isotropically emitted photoelectrons interact on their way to the detector. The evolution of the photoelectron distribution is calculated until Coulomb forces become negligible, which typically occurs after a few nanoseconds. The space charge-induced distortions of the kinetic energy distribution, i.e., spectral shifts and broadenings, are quantified by fitting a Gaussian profile to the final spectral distribution of the photoelectrons reaching the detector. For these calculations, we neglected a possible presence of mirror charges below the sample surface. For all simulations, the initial kinetic energy of the initially isotropic photoelectron distribution was set to E i = 3025 eV at a Gaussian FWHM of 1.45 eV, correponding to the "intrinsic" linewidth of the Ti 1 s emission of La:SrTiO 3 at the used photon energy 4 . The Gaussian temporal profile was assumed to have a FWHM of 10 fs in all cases. Mean-field model. To reproduce the measured pump-probe delay dependence of the pump laser-induced spectral shift, we extended a simple mean-field model, which was successfully used to describe pump laser-induced space-charge effects in trHAXPES experiments 5,6 . The basic assumption of this model, sketched in Fig. 7, is to approximate the electron cloud excited by the pump pulse as a Gaussian charge distribution moving at the average pump-electron velocity v pump in the direction normal to the surface (z direction). The on-axis potential of such a charge distribution can be calculated numerically as 38,39 ∫ π ε σ σ σ where N − is the number of electrons, e the elementary charge, ε 0 the electric constant, σ x,y,z are the respective standard deviations of the Gaussian charge distribution, and z is the axial distance from its center. The radial expansion of the electron cloud is incorporated by assuming a two-dimensional expansion with the mean pump-electron velocity.
To account for long-living photoholes at the surface (z = 0) arising from multiphoton electron emission or separation of photoexcited electron-hole pairs in a surface space-charge layer, an additional positive charge distribution of N + = p ⋅ N − charge carriers, p ∈ [0, 1], is introduced, equaling the shape of the pump electron charge distribution directly after its birth. Electron-hole recombination mechanisms inside the sample, such as nonlinear Auger recombination, single-carrier trapping, or other microscopic carrier recombination processes, are included by phenomenologically assuming a bi-exponential decay of the number of positive charge carriers, = + + + + N t N t N t ( ) ( ) ( ) 1 2 , based on the results of time-resolved photoluminescence studies of SrTiO 3 in the high excitation density regime 33,34,40,41 .
The inital z seperation between the centers of gravity of the probe electron and the pump electron spatial distribution depends on the pump-probe delay t and is given by where m e is the electron mass and E is the probe-electron kinetic energy for t < 0 (probe pulse before pump pulse) or the average pump-electron kinetic energy for t ≥ 0, respectively. The final change in kinetic energy of the probe For both (a) negative and (b) positive delays t the N − -electron cloud emitted by the pump pulse is modeled by a Gaussian charge distribution with standard deviations σ x,y,z and the probe electron is allowed to move only in the direction of normal emission (z direction). Long-living photohole states at the surface (z = 0), N + (t), are modeled as the positive mirror image of the pump electron charge distribution directly after its birth. For negative delays t, these positive charges are considered to be completely screened by the pump electron disk, while for positive delays a bi-exponential decay of the number of photoholes is assumed. The final pump laserinduced shift in kinetic energy, Δ E kin , is calculated as the probe-electron potential energy eV directly after the birth of the pump electrons (a) or the probe electron (b).