Abstract
Timeresolved hard Xray photoelectron spectroscopy (trHAXPES) using microfocused Xray freeelectron 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 chargecarrier recombination dynamics in La:SrTiO_{3}. By means of a combination of experiments and numerical Nbody simulations, we first develop a simple approach to characterize and decrease XFELinduced vacuum spacecharge effects, which otherwise pose a serious limitation to spectroscopy experiments. We then show that, using an analytical meanfield model, vacuum spacecharge effects can be counteracted by pump laserinduced photoholes at high excitation densities. This provides us a method to separate vacuum spacecharge effects from the intrinsic chargecarrier recombination dynamics in the time domain. Our trHAXPES results thus open a route to studies of intrinsic chargecarrier dynamics on picosecond time scales with lateral spatial resolution on the micrometer scale.
Introduction
Xraybased solidstate photoelectron spectroscopy is a powerful tool for the investigation of electronic properties in condensed matter systems, combining element and atomicsite specificity with sensitivity to the chemical environment^{1,2}. When photon energies in the hard Xray regime are used, the technique becomes more bulksensitive and is referred to as hard Xray photoelectron spectroscopy (HAXPES)^{3}.
The recent development of new Xray facilities such as Xray free electrons lasers (XFELs) provides unprecedented capabilities in terms of the Xray pulse duration available at high photon energies (down to a few tens of femtoseconds). Ultrashort hard Xray pulses, in particular, make it possible to determine transient bulk electronic structure dynamics by means of timeresolved HAXPES (trHAXPES) experiments through a pumpprobe scheme^{4,5,6}. By simultaneously exploiting the possibility of focusing the photon beam down to a spot size of a few tens of micrometers or even less, spatial resolution can be added to the timedomain information, thereby opening a novel path to timeresolved studies of, e.g., vertical heterostructures, inhomogeneously doped materials, or micrometersized samples.
A fundamental limitation to all variants of timeresolved photoelectron spectroscopy are vacuum spacecharge effects arising from the use of both ultrashort pump and probe pulses with high peak intensities^{5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}. Whenever 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 pulseinduced spacecharge 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 spacecharge 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 chargecarrier recombination dynamics in the electrondoped 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 XFELinduced vacuum spacecharge 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 lowphoton 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 Nbody simulations, we quantify the impact of microfocusing on the space chargeinduced 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) spacecharge 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 meanfield model, we address the role of vacuum spacecharge effects in the high pump excitation density regime. By comparison with the experimental results, we can deconvolve vacuum spacecharge effects from intrinsic chargecarrier recombination dynamics on the picosecond to nanosecond time scale. The results reveal a complex threestaged dynamical behavior for positive time delays, i.e., when the probe pulse follows the pump pulse. The successful application of microtrHAXPES beyond spacecharge 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 XFELbased microHAXPES
We start by discussing two general limitations of solidstate photoelectron spectroscopy arising from the use of a microfocused, ultrashortpulsed photon source with high peak intensities: sample ablation^{21} and (probeinduced) vacuum spacecharge 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)^{4,5,6}.
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 spacecharge 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 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 spacecharge effects, we have fitted the experimental data using Voigt profiles after subtraction of a Shirleytype background [Fig. 2(a)]. The extracted spectral shift and broadening are shown in Fig. 2(b,c). The spacecharge broadenings were calculated as , where ΔE_{m} is the measured, broadened (Gaussian) FWHM of the respective energy distribution curve and ΔE_{i} = 1.43 eV is the ‘intrinsic’ linewidth as determined by highresolution 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 Nbody simulations^{6,15}: neartolinear 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 angledependence of probe pulseinduced spacecharge 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 highrepetitionrate 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 socalled 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 corelevel emission of gold (β = 0.7075^{23}) measured with soft Xray 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 chargeinduced spectral shift [Fig. 3(a)].
In the following, we examine the impact of the relevant incidence angledependent experimental parameters on the space chargeinduced spectral shift by means of numerical Nbody 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.
Figure 4(a) shows the simulated spacecharge shift for a constant number of photoelectrons as a function of the horizontal and vertical spot diameter (for E_{kin} = 3025 eV and Δt = 10 fs). Unsurprisingly, the spectral shift decreases when increasing the spot area by elongating one or both of the spot diameters d_{x,y}, i.e., when decreasing the number of photoelectrons per area. More crucially, however, the spectral shift also decreases at a constant number of photoelectrons per area when the spot eccentricity , 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 × 30) μm^{2}, i.e., . Thus, spacecharge 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 twodimensional disk of charge to an elongated quasionedimensional 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 microHAXPES experiments. Figure 5(a,b) shows the calculated elongation of the horizontal spot diameter as a function of incidence angle, starting from a circular Gaussianshaped spot profile, as well as the corresponding change in eccentricity for three different initial spot diameters. The space chargeinduced 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 spacecharge 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 nonlinear increase in the number of ejected photoelectrons at low photon incidence angles [Fig. 3(a)] is included, the expected increase in space chargeinduced shift due to its neartolinear dependence on the number of ejected photoelectrons is compensated by the increase in spot area and eccentricity. Thus, overall, using a grazing incidence geometry should result in a decrease of spacecharge effects at an increasing number of emitted photoelectrons [Fig. 5(d)].
To check this prediction, we have experimentally determined the angular dependence of the spacecharge 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 Shirleytype 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 chargeinduced shift in kinetic energy decrease, in good qualitative agreement with the results of our numerical Nbody 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 spacecharge effects in (micro)trHAXPES experiments at ultrashortpulsed XFEL facilities with respect to experiments conducted in a nongrazing photon incidence geometry.
Spacecharge and chargecarrier recombination dynamics in trHAXPES
Finally, we exploit the novel approach and investigate the 1.55eVpump laserinduced dynamics of the Ti 1 s emission of Ladoped SrTiO_{3} as probed by the 8 keV XFEL radiation. The pump laser was set to a fluence of 30 mJcm^{−2} and the XFEL probe fluence on the sample was 0.17 Jcm^{−2}.
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 15fold reduction of the effective XFEL penetration depth, , 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 grazingincidence measurements enable us to be more sensitive to surface effects due to the drastically decreased effective XFEL probing depth.
Figure 6(b) shows the experimental spectra for various pumpprobe delays together with the best fits using Voigt profiles on a Shirleytype background. The zero of the energy axis is defined by the position of the Ti 1 s emission at a blocked pump beam. The maximum positive kinetic energy shift and broadening are observed at time zero, when pump and probe pulses overlap in time^{5,6,16,17,20}.
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 threestaged 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.
To understand the origin of this dynamics, we first present the results of meanfield model calculations neglecting the possible presence of (quasi)stationary photoholes at the surface (p = 0 photoholes per pump electron). Longliving photoholes near the surface may in principle arise from pump laserinduced multiphoton electron emission into vacuum, electronhole separation following internal photoexcitation in a spacecharge 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}, the number of photoholes left behind from multiphoton photoemission and the corresponding attractive Coulomb potential should increase nonlinearly as a function of pump fluence^{6,31}. Moreover, by choosing a holedoped sample, possible transient photovoltages should change sign under the same measurement conditions^{32}. Such investigations are, however, beyond the scope of the present work.
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 probeelectron 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 laserinduced photohole effects at the surface (p = 0) and only accounting for pump laserinduced spacecharge effects in vacuum, the model can not reproduce the observed threestaged dynamics for positive time delays [Fig. 6(c)]. However, when we take into account stationary photohole states (p > 0) as well as possible biexponential electronhole recombination inside the strongly electrondoped 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 chargecarrier 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 of (9 ± 0.5) to 1 are in good agreement with the findings of timeresolved 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 timeresolved 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 meanfield model can be used to deconvolve pump laserinduced extrinsic spacecharge dynamics and intrinsic chargecarrier 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 chargeinduced 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 XFELinduced spacecharge 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 microtrHAXPES to electrondoped SrTiO_{3} and the use of a simple analytical meanfield model, we could then deconvolve extrinsic vacuum spacecharge effects from intrinsic chargecarrier recombination dynamics in the time domain. Our results reveal a biexponential decay of the pump excitationinduced photoholes on a picosecond to nanosecond time scale, in good agreement with the findings of timeresolved photoluminescence studies. Hence, these results establish trHAXPES with lateral spatial resolution on the micrometer scale as a novel technique to determine intrinsic spatiotemporal chargecarrier 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 SPring8^{36,37} using ultrashort (Δt ≈ 10 fs), quasimonochromatic (ΔE ≈ 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 R400010 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 timeresolved pumpprobe 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 Δt ≈ 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 quasicollinearly 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 pumpprobe time delay was adjusted by using an optical delayline. As single crystal samples, 5% Ladoped SrTiO_{3} as well as undoped Si were chosen. The equilibrium sample temperature during all experiments was set to 300 K.
Complementary soft Xray PES experiments were conducted on a polycrystalline gold sample at the undulator beamline BL17SU of SPring8 using a photon energy of 600 eV at a total energy resolution of 200 meV. Soft Xray 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 Nbody simulations
For the numerical simulation of the XFEL pulseinduced spacecharge effects, we used a modified BarnesHut treecode algorithm for Coulomb force calculation and a leapfrog integration scheme to solve the equations of motion. The details of these numerical Nbody simulations are described elsewhere^{10,13}. The approach is to gradually evolve an Nelectron 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 chargeinduced 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.
Meanfield model
To reproduce the measured pumpprobe delay dependence of the pump laserinduced spectral shift, we extended a simple meanfield model, which was successfully used to describe pump laserinduced spacecharge 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 pumpelectron velocity v_{pump} in the direction normal to the surface (z direction). The onaxis potential of such a charge distribution can be calculated numerically as^{38,39}
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 twodimensional expansion with the mean pumpelectron velocity.
To account for longliving photoholes at the surface (z = 0) arising from multiphoton electron emission or separation of photoexcited electronhole pairs in a surface spacecharge 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. Electronhole recombination mechanisms inside the sample, such as nonlinear Auger recombination, singlecarrier trapping, or other microscopic carrier recombination processes, are included by phenomenologically assuming a biexponential decay of the number of positive charge carriers, , based on the results of timeresolved 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 pumpprobe delay t and is given by
where m_{e} is the electron mass and E is the probeelectron kinetic energy for t < 0 (probe pulse before pump pulse) or the average pumpelectron kinetic energy for t ≥ 0, respectively. The final change in kinetic energy of the probe electron, ΔE_{kin}(t), equals the inital total potential energy of the probe electron, e(V^{−}[z(t)] − V^{+}[z(t)]), where V^{−}[z(t)] is the potential of the pump electron distribution and V^{+}[z(t)] the potential of the photohole distribution. For simplicity, the photohole distribution is assumed to be completely screened by the pumpelectron disk for negative delays, i.e., V^{+}(t ≤ 0) = 0.
Additional Information
How to cite this article: Oloff, L.P. et al. Timeresolved HAXPES using a microfocused XFEL beam: From vacuum spacecharge effects to intrinsic chargecarrier recombination dynamics. Sci. Rep. 6, 35087; doi: 10.1038/srep35087 (2016).
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Acknowledgements
The experiments at BL2 of SACLA were carried out with the approval of JASRI (proposal nos. 2015A8016 and 2015B8003). The synchrotron radiation experiment was performed at BL17SU of SPring8 with the approval of RIKEN (proposal no. 20120001). The authors thank the operation and engineering staff of SACLA for their support during the experiments. We are grateful to the members of the engineering team of the RIKEN SPring8 Center for their technical assistance. This work was supported by the German Federal Ministry of Education and Research (BMBF) through project no. 05K12FK1. A.C. thanks JSPS for a GrantinAid for Scientific Research (Challenging Exploratory Research Project No. 15K13526). G.R. contributed under the NOXSS PRIN (2012Z3N9R9) project of MIUR, Italy.
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M.O. proposed the research and organized the experiments at SACLA. L.P.O., A.C., M.M., K.T., H.O., K.H., A.Q., R.M., R.S., M.N., A.K., K.M., Y.T., G.R., K.R. and M.O. performed the experiments at SACLA. M.O. carried out the experiments at BL17SU of SPring8. L.P.O. analyzed the data and performed all calculations. T.T., M.Y. and T.I. were responsible for SACLA operation. The manuscript was written by L.P.O. with input from A.C., M.O. and K.R. All authors discussed the results and commented on the manuscript.
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Oloff, LP., Chainani, A., Matsunami, M. et al. Timeresolved HAXPES using a microfocused XFEL beam: From vacuum spacecharge effects to intrinsic chargecarrier recombination dynamics. Sci Rep 6, 35087 (2016). https://doi.org/10.1038/srep35087
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DOI: https://doi.org/10.1038/srep35087
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