A quantitative comparison of time-of-flight momentum microscopes and hemispherical analyzers for time- and angle-resolved photoemission spectroscopy experiments
J. Maklar, S. Dong, S. Beaulieu, T. Pincelli, M. Dendzik, Y.W. Windsor, R.P. Xian, M. Wolf, R. Ernstorfer, L. Rettig
AA quantitative comparison of time-of-flight momentummicroscopes and hemispherical analyzers for time-resolvedARPES experiments
J. Maklar, S. Dong, S. Beaulieu, T. Pincelli, M. Dendzik ∗ , Y.W. Windsor, R.P. Xian † , M. Wolf,R. Ernstorfer, and L. Rettig Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
August 14, 2020
Time-of-flight-based momentum microscopy has a growing presence in photoemission studies, asit enables parallel energy- and momentum-resolved acquisition of the full photoelectron distribu-tion. Here, we report table-top extreme ultraviolet (XUV) time- and angle-resolved photoemissionspectroscopy (trARPES) featuring both a hemispherical analyzer and a momentum microscopewithin the same setup. We present a systematic comparison of the two detection schemes andquantify experimentally relevant parameters, including pump- and probe-induced space-chargeeffects, detection efficiency, photoelectron count rates, and depth of focus. We highlight theadvantages and limitations of both instruments based on exemplary trARPES measurements ofbulk WSe . Our analysis demonstrates the complementary nature of the two spectrometers fortime-resolved ARPES experiments. Their combination in a single experimental apparatus allowsus to address a broad range of scientific questions in trARPES. Angle-resolved photoemission spectroscopy(ARPES) is a key technique to investigate theelectronic structure of solids. By extractingthe kinetic energy and angular distribution ofemitted photoelectrons, one gains direct accessto the quasiparticle band structure . Combiningthis technique with a pump-probe approachallows studying the electron dynamics after op-tical excitation on a femtosecond timescale. Inrecent years, time-resolved ARPES (trARPES)has been successfully applied to many fields in Current address: ∗ Department of Applied Physics, KTH Royal Institute ofTechnology, SE-11419, Stockholm, Sweden † Department of Neurobiology, Northwestern University,Evanston, IL, 60208 USA materials science, such as control of quantummatter , photo-induced phase transitions and the investigation of electronic states andphases not accessible in equilibrium . Ad-vances in laser-based extreme ultraviolet (XUV)sources using high harmonic generation innoble gases now enable space-charge freephotoemission up to MHz repetition rates athigh time and energy resolution (10s of fs/meV)and at wavelength up to the far XUV .The most commonly used electron spectrom-eter in trARPES is the hemispherical analyzer(HA) . Here, the photoelectrons enter an elec-trostatic lens system followed by two hemispher-ical deflector electrodes acting as a dispersiveband-pass energy filter, as sketched in Fig. 1(a).Subsequently, the electrons are projected onto a2D multi-channel plate (MCP) detector, which1 a r X i v : . [ phy s i c s . i n s - d e t ] A ug llows parallel detection of kinetic energy andemission angle. However, this detection ap-proach is rather inefficient, as only a single two-dimensional (2D) cut in a narrow energy and mo-mentum window of the 3D photoelectron distri-bution can be simultaneously captured.The more recent detection scheme based on atime-of-flight (ToF) energy analyzer overcomesthis limitation: The momentum microscope(MM) is based on a cathode-lens electron mi-croscope . By applying a high positive volt-age to an electrostatic objective lens placed closeto the sample surface, all emitted photoelec-trons are steered into the lens system resultingin an acceptance of the complete 2 π solid an-gle. In analogy to optical microscopy, a recipro-cal image is generated in the back focal plane ofthe objective lens, corresponding to the surface-projected band structure. Next, the photoelec-trons pass through a field-free ToF drift tube.Finally, their 2D momentum distribution and ki-netic energy (encoded in the arrival time) aredetected at a single-electron level using an MCPstack combined with a position-sensitive delay-line detector (DLD). Ultimately, the ToF-MMenables parallel acquisition of the 3D photoelec-tron distribution I ( E kin , k x , k y ) across the fullaccessible in-plane momentum range (at low ki-netic energies limited by the parabola of the pho-toemission horizon) and within a large energyrange from the threshold energy to the hard X-ray regime , as illustrated in Fig. 1(b).In principle, trARPES is expected to benefitgreatly from the improved parallelization in dataacquisition of the ToF-MM for several reasons:(i) The excited-state signal is usually orders ofmagnitude lower than that of the occupied statesin equilibrium , which necessitates ef-ficient detection. (ii) Prediction of the relevantenergy-momentum regions of photoexcited statescan be difficult, and a time-resolved mappingof the entire first Brillouin zone (BZ) with aHA is typically not feasible. (iii) Various pho-toinduced electronic processes can occur simul-taneously, spread over a large energy-momentumrange, which are now accessible within a single measurement. However, while the MM theo-retically constitutes the ultimate photoelectrondetector, certain limitations, such as increasedspace-charge effects and constraints of theDLD detection rate, compromise the experimen-tal practicability in particular for pump-probeexperiments. Therefore, a detailed benchmarkof these two photoelectron detection schemes isof great interest.In this article, we present a table-top XUVtrARPES setup that combines a ToF-MM anda conventional HA and investigate their respec-tive operational capabilities. We quantify crit-ical parameters, such as depth of focus, experi-mental count rates, acquisition times, and space-charge effects. By two exemplary trARPES ex-periments – excited-state band structure map-ping at a fixed time delay and tracking of theexcited population dynamics – we demonstratethe advantages and limitations of both instru-ments and illustrate the benefits of combiningboth types of analyzers. After an overview ofour experimental setup in Sec. 2, we will intro-duce some important aspects specific to the MMin Sec. 3. Section 4 finally compares the two spec-trometers based on our experimental data, fol-lowed by a discussion in Sec. 5. The table-top XUV light source consists ofan optical parametric chirped pulse amplifier(OPCPA) generating fs light pulses at 1.55 eVand 500 kHz at an average power of 20 W (40 µ Jpulse energy) . A beamsplitter at the exit of theOPCPA extracts a portion of the pulse energyas a 1.55 eV or frequency-doubled 3.1 eV syn-chronized optical pump. The probe pulses arefrequency-doubled in a beta barium borate crys-tal and focused onto a high-pressure argon jetfor up-conversion to the XUV via high harmonicgeneration. By a combination of a multilayermirror and metallic (Sn) filters, only the 7th har-monic (21.7 eV) is transmitted to the analysis2 x (Å -1 )sample Momentum Microscope
3D detector I(E , k , k ) kin x y E kin k k x k y Hemispherical Analyzer
2D detector I(E , k ) kin ıı pumpprobe Δt - e cloudLaser-based XUV probe21.7 eV
500 kHz, 10 photons/s< 40 fsOptical pump1.55 / 3.10 eV, 500 kHz, 1 / 0.25 μ J< 40 fs reciprocal image plane with contrast aperturesGaussian image plane with field aperturesTOF drift tubek ıı VB k ıı E kin k x k y Photo-emission horizon E k i n CBVBCB maxmin(a) (b)(d) (e)(c) VBCB E - E ( e V ) VB M maxmin G KK ´ k x k y delay line detector Fig. 1: (a) Schematic layout of the setup. (b) Illustration and (c) experimental data of a 3D dataset ofWSe acquired with the MM. (d) Sketch and (e) data of a 2D energy-momentum cut acquired with the HA.The momentum direction within the hexagonal BZ of WSe is indicated in red. The excited-state signalabove the valence band maximum of the exemplary datasets (pump-probe delay t = 0 fs, absorbed fluence F abs = 150 µ J / cm ) is enhanced by a factor of (c) 100 and (e) 75. In all MM measurements, the extractorvoltage is V extr = 6 kV and the sample-extractor distance is 4 mm with the sample surface aligned perpendicularto the optical axis of the instrument. chamber . Then, the pump and probe beamsare focused onto the sample in a near-collineargeometry, and the emitted photoelectrons are de-tected with a HA (SPECS PHOIBOS 150 2D-CCD) or a ToF-MM (SPECS METIS 1000). TheMM is mounted on a linear translation stage con-nected to the analysis chamber by a vacuum bel-low and can be retracted to avoid collision withthe cryogenic 6-axis carving manipulator whenusing the HA.The detection unit of the MM features anMCP followed by a DLD. Each registered eventdirectly corresponds to a single photoelectron.Saving this data stream at a single-event levelpermits event-wise correction and calibration,and selective binning later during analysis .The operating principle of the DLD limits thecount rate to a single electron per pulse , re-sulting in maximum rates of ∼ × cts/s, cor-responding to the repetition rate of the laser sys-tem. For the case of the HA, the photoelectronsare first multiplied in an MCP and subsequently accelerated onto a phosphor screen, which is im-aged by a CCD camera. Thus, a single photo-electron generates several counts spread over ad-jacent pixels. To obtain an estimate of the actualphotoelectron count rate, we calibrated the CCDresponse in the regime of distinct single-electronevents. To quantify relevant experimental pa-rameters of both spectrometers (see Sec. 4), weintroduce the metrics emitted electrons per pulse ,i.e., the total photoelectron yield per pulse esti-mated from the sample photocurrent, and de-tected electrons per pulse , corresponding directlyto the count rate of the MM and to the rescaledCCD count rate of the HA, respectively.The material used for the benchmark studyis bulk tungsten diselenide (2H-WSe ). Thislayered semiconductor exhibits an indirectbandgap , a sharp electronic band structureand a distinct electronic response upon near-infrared optical excitation . Exemplary datasetsacquired with both detectors on WSe at tempo-ral pump-probe overlap are shown in Figs. 1(c,e).3he MM captures the entire photoemission hori-zon (momentum disk with radius k (cid:107) ,max ≈ .
15 ˚A − ), exceeding the first BZ of WSe , andthe full energy range from the pump-pulse-induced population in the conduction band (CB)to the secondary electron cutoff. In contrast,the HA covers an energy window of a few elec-tron volts (at a reasonable energy resolution) anda narrow momentum range resulting from thelimited acceptance angle of ± ° (Wide AngleMode). The momentum resolution orthogonalto the dispersing direction is determined by thewidth of the slit located at the entrance of thespherical deflector. All HA data were recordedwith a slit width of 0.5 mm, corresponding to amomentum integration of ≈ − , and a passenergy of 30 eV.Using the MM, the angle between the pumpand probe beams and the sample surface normalis fixed at 65 ° . For comparability between thedetectors, we align the sample in a similar ge-ometry in the HA measurements, which yieldsthe Σ-K momentum cut shown in Fig. 1(e). Allsamples are cleaved at room temperature in ultrahigh vacuum ( < × − mbar).Whereas the energy resolution of ourtrARPES setup is limited by the bandwidth ofthe XUV probe pulses to ∼
150 meV, the HAoffers an improved momentum resolution overthe MM. Based on band structure data, weestimate an effective momentum resolution ofthe MM and the HA of 0.08 ˚A − and 0.04 ˚A − ( ∼ ° ), respectively. The ultimate instrumentresolution is reported as < × − ˚A − ( < . ° ) for the HA and < × − ˚A − for theMM . However, achieving such optimalconditions with the MM requires very highextractor voltages and tedious optimization ofthe lens settings and corrector elements. Before starting our systematic comparison of thetwo spectrometers, we introduce further features T r an s m i ss i on ( % ) XUV spotsize (FWHM in μ m)
25 50 d FA ( μ m)3002001000 3000(a) (b) 80 125 200100x ( μ m) y ( μ m ) FA 1000FA 750FA 500FA 200 minmax Fig. 2: (a) PEEM image of the XUV beam foot-print at an incidence angle of 65 ° (spot profile ≈ × µ m FWHM) on a WSe sample at amagnification of 7.6. Projected field aperture sizesare illustrated in color (diameters in µ m). (b) Cal-culated transmission as a function of field aperturediameter for selected probe spot sizes, taking intoaccount the angle of incidence. Experimentally de-termined values, corresponding to the apertures in-dicated in panel (a), are marked by red diamonds. of the MM arising from the similarity to opti-cal microscopy. Firstly, both a reciprocal anda Gaussian real-space image plane form con-secutively in the electron-optical lens column,which can be selectively projected onto the DLD.Thus, by choice of lens settings, the instrumentcan be used either for band structure mappingor to investigate the real-space distribution ofphotoelectrons via photoemission electron mi-croscopy (PEEM) . Secondly, apertures canbe inserted in both image planes, which enablestrARPES at high spatial selectivity and time-and momentum-resolved PEEM.We first focus on the use of field apertures in-serted into the Gaussian image plane, which canbe used to study the electronic band structureof spatially inhomogeneous or small samples be-low the size of the probe spot down to the mi-crometer range, see Fig. 2(a). The electron trans-mission losses resulting from field apertures areshown in Fig. 2(b) for various probe spot sizes.The effective source size, defined by the fieldaperture or the spot size, also determines thedepth of focus (DoF), i.e., the energy windowwith sharp momentum resolution, resulting fromthe chromatic aberrations of the electron lenses.To investigate the DoF, we insert a grid in themomentum image plane, and analyze the sharp-4ess of the resulting grid lines as a function of ki-netic energy for various field apertures, shown inFig. 3. For the aperture diameter d FA = 200 µ m,we observe sharp grid lines superimposed on theband structure of WSe reaching from the va-lence band (VB) down to almost the entire sec-ondary electron tail. However, with increas-ing aperture size, the energy window of sharpmomentum imaging narrows. To quantify thistrend, we perform a 2D Fourier transform ofthe iso-energy contours, and analyze the magni-tude of the spatial frequency peaks correspond-ing to the grid periodicity as a function of en-ergy, shown in Fig. 3(c-d). Similar to the depthof field in optical imaging , we find that theDoF follows an inverse square dependence of theaperture diameter, see Fig. 3(e).To achieve a uniform performance in a typicalrange of interest of few eV, it is necessary to havea DoF of ∼
10 eV. For this, the effective sourcesize has to be reduced to ∼ µ m, which corre-sponds to a field aperture diameter of 200 µ m forthe chosen magnification settings. At the givenspot size of 80 × µ m , this reduces the photo-electron transmission to 6 % of the total yield, asshown in Fig. 2(b). However, to compensate fortransmission losses, the XUV flux and therebythe total number of emitted electrons cannot bearbitrarily increased. Here, space-charge effectshave to be considered, as discussed in the fol-lowing section. Thus, for high spatial selectivityand a large DoF without significant transmissionlosses, the size of the XUV spot is an importantparameter to consider. A fundamental limitation of photoemission withultrashort light pulses is space charge. TheCoulomb repulsion within a dense photoelectroncloud can modify the electrons’ angular and en-ergy distribution, and can significantly deterio- -2-1012 k y ( Å - ) -2 -1 0 1 2k x (Å -1 ) -15-10-50 E - E VB M ( e V ) -2 -1 0 1 2k x (Å -1 )-15-10-50 E - E VB M ( e V ) -2 -1 0 1 2k x (Å -1 )(a) (b)(c) FA200 FA500 I n t en s i t y ( no r m . ) -16-12-8-40 E-E VBM (eV)(d)
FWHM3.04 eV E = -6.8 eV d FA ( μ m) ∝ d FA -2 (e) 1086420 D o F ( e V ) -10010 y ( Å )
150 x (Å)
Fig. 3:
2D cut of a MM measurement along theK-Γ-K direction with a square grid in the momen-tum image plane for field apertures of diameters(a) 200 µ m and (b) 500 µ m. (c) Iso-energy con-tour at the focus energy (sharpest momentum im-age), see the white dashed line in panel (b), ford FA = 500 µ m. (d) Intensity of the Fourier trans-form peak corresponding to the grid spacing, see thered box in the inset, as a function of energy. TheFWHM of the peak is extracted from a Gaussian fit(black dashed curve). The inset shows the Fouriertransform of the iso-energy contour in c. (e) Depthof focus (FWHM) versus aperture diameter with aninverse quadratic fit. rate momentum and energy resolution. Spacecharge and its dependence on source parameters,such as pulse duration, flux, and spot size, havealready been studied extensively . Here, wecompare the space-charge effects for both detec-tion schemes using the energy shift and broad-ening of the energy dispersion curve (EDC) ofthe spin-orbit split VBs at the K point of WSe ,5ee Fig. 4. In the regime of few emitted photo-electrons per pulse, the band structure measure-ments of both detectors are in excellent agree-ment, see panels (a) and (c). When increasingthe XUV source flux (and thereby the densitywithin the photoelectron cloud), the MM spec-trum rapidly shifts towards higher energies andbecomes drastically broadened, while the HAspectrum is only weakly affected, see panels (b)and (d).For the MM, energy distortions arise above ∼
100 emitted electrons per pulse, roughly oneorder of magnitude before distortions appearin HA measurements, see Figs. 4(e-f) and thediscussion below. While the transmission andthereby the effective count rate decrease for asmaller field aperture size, we find that spacecharge is rather independent of the apertures.This demonstrates that its major contributionstems from the Coulomb interaction of photo-electrons on their trajectories prior to the Gaus-sian image plane, in agreement with simulationresults for the case of hard X-ray ARPES . Inother words, to employ the MM at a reason-able resolution, the source flux and the result-ing number of emitted photoelectrons per pulsehave to be chosen carefully. For instance, whenusing the aperture d FA = 200 µ m (allowing for alarge DoF), at ∼
350 emitted photoelectrons perpulse the spectrum is already critically broad-ened. However, due to transmission losses and animperfect detection efficiency, this correspondsonly to a final DLD photoelectron detection rateof ∼ . Incontrast, using a HA, space-charge effects arespatially uniform and arise only in proximity tothe sample surface, when fast and slow electronsare spatially confined to a dense photoelectrondisk.For illustration, we estimate the involved timeand length scales of the spread of the photo-electron cloud along its trajectory for both in-struments. In the HA, it takes ≈
90 ps to sep-arate electrons of highest kinetic energy (corre-sponding to the VB maximum, E kin ≈
17 eV)from the secondary electron tail (exemplary en-ergy E kin ≈ µ m, during which thefast electrons have traveled 220 µ m. In the MM(at an approximate average potential within theinitial lens elements of 2 kV), it takes ≈ .In summary, space-charge effects and DoFconstrain the XUV spot size and photon fluxin MM experiments. In the discussed configu-ration (spot size 80 × µ m ), a reduction of thespot size would allow to omit field apertures intypical band mapping experiments. Due to theincreased transmission for smaller spot sizes, theXUV flux could be lowered significantly, effec-tively reducing space-charge constraints, whichwould permit acquisition close to the DLD detec-tion limit of 1 count per pulse. While decreasingthe spot size below a certain limit again leadsto critical space-charge distortions, the MM re-quires photocurrents of only few photoelectronsper pulse. Thus, the lower limit of the XUV spotsize due to space-charge effects is expected to bein the range of a few micrometers .6 E - E VB M ( e V ) k x (Å -1 ) k x (Å -1 ) 1.21.00.8 k x (Å -1 )-10 E - E VB M ( e V ) x (Å -1 )(a) 280240200 B and w i d t h ( m e V ) MM: FA 200MM: FA 500MM: no FAHActs/pulse:0.5 0.5 0.5 0.05250200150100500 B and s h i ft ( m e V ) MM: FA 200MM: no FA(b)(c) (d) (e)(f) � �
EDC80 e /pulse 5500 e /pulse550 e /pulse30 e /pulse MM MMHA HA
HAMM: FA 500Emitted photoelectrons / pulse
Fig. 4: (a,b) False-color plots of MM cuts ( d FA = 200 µ m) and (c,d) HA measurements along the Σ-K directionat selected photoelectron emission rates. The EDCs at the K point are shown with a fit by two Gaussians (redcurve). (e) FWHM and (f) energy shift extracted from the fit to the upper band at the K point as a functionof emitted photoelectrons per pulse. The MM bandwidth values without an aperture deviate from the othercurves, as the spectra are already significantly blurred due to the low DoF. Linear fits (dashed lines) serve asguides to the eye. Selected photoelectron detection rates are indicated by vertical lines. The effective electrondetection rate of the HA is orders of magnitude below the MM, since a drastically smaller energy-momentumwindow is covered in a single measurement. Next, we discuss the total count rate of bothinstruments achievable under these space-chargerestrictions. From the total photoelectron yield,the detector count rate and effective electrontransmission, we estimate a detection efficiencyof 5 % of the MCP/DLD stack of the MM. Tak-ing into account the transmission losses at thefield aperture ( d FA =200 µ m), roughly 0.3 % ofthe total emitted photoelectrons are detected.For the HA, the effective transmission is on theorder of 0.03 %, as only a narrow 2D energy-momentum plane is detected in parallel. There-fore, the fraction of detected electrons (at anMCP efficiency of 10 %) is 0.003 %.Taking into account the space-charge limit ofapproximately 100 emitted photoelectrons perpulse, the MM count rate is restricted to ∼ ∼
350 times below the rate ofthe HA, resulting from the reduced XUV sourceflux ( ∼ × ), transmission losses at the aperture( ∼ × ) and a lower detection efficiency ( ∼ × ). Next, we discuss common trARPES scenar-ios to highlight the advantages of each instru-ment and the benefit of combining both detec-tors in a single setup. As a first use case we7how the (excited-state) band mapping of WSe upon excitation with near-infrared optical pulses( λ pump = 800 nm). Using the MM, we acquirethe quasiparticle dispersion across the full pho-toemission horizon in a single measurement ata fixed sample geometry. We gain access tothe band structure of the first projected BZ upto 1.55 eV above the VB, see the transient oc-cupation of the CB at the K and Σ points inFigs. 5(b,c). For a static 3D band mapping us-ing the MM, typically 10 − total eventsare required, at our count rate achievable in ∼ −
10 minutes (Fig. 5(a)). In order to accuratelyresolve the much weaker signal of excited states,typically ∼ events are detected within ∼ ∼
10 minutes. Mapping the full irre-ducible part of the BZ with the HA (by sam-ple rotation or by using a deflector arrangement)requires at a comparable momentum resolution ∼
60 sequential scans. This procedure is furthercomplicated by the fact that high emission an-gles are difficult to access and spectra have tobe merged and mapped from angle to momen-tum space. In addition, light polarization, flu-ence and photoemission matrix elements mightchange during such a mapping procedure using asample manipulator. Thus, to get an overview ofthe full (excited-state) dispersion relation, bandmapping with the MM is highly advantageous.Another typical use case of trARPES is theinvestigation of the transient carrier relaxationdynamics along certain pathways in momentumspace. In WSe , electrons are initially excitedinto the conduction band (CB) at the K val-ley, followed by a relaxation into the global CBminimum at the Σ point, discussed in detailelsewhere . As such relaxation dynamicsare often highly localized in momentum space,information on selective regions in momentumspace is sufficient to study the temporal evolu-tion. Measuring such dynamics with the MMresults in a 4D data set (3D + time) of the full -3-2-1012 210-1 1.20.8-101 -1 0 1(a) (b)(c) (d)-101 -1 0 1-101 k y ( Å - ) -1 0 1 E VBM ± 30 meV E = 1.6 ± 0.2 eVHA � � �� � ��� � � � E - E VB M ( e V ) MM MM � ' k II MMVB maximum CB populationk x (Å -1 )k x (Å -1 )k x (Å -1 ) Fig. 5:
MM iso-energy contours of (a) the VB max-imum and (b) the transiently excited CB popula-tion. (c) Extracted energy-momentum cuts alongthe high-symmetry directions. (d) Data acquiredwith the hemispherical analyzer, corresponding tothe energy-momentum window indicated by thewhite box in panel (c). The intensity of the CBsis enhanced by a factor of 75 in both datasets( t = 0 ±
50 fs, hν = 1 .
55 eV, F abs = 150 µ J/ cm ).For comparability, the momentum integration or-thogonal to the plotted direction of the MM cuts in(c) is matched to the HA measurements. energy-, momentum- and time-dependent bandstructure, which requires ∼ events and ac-quisition times of 20 hours and more. In con-trast, using the HA, only the relevant energy-momentum region is recorded, and we can utilizethe higher photon flux and larger transmissionwithin this window, yielding an acquisition timein the range of 1-2 hours for a time trace. Toillustrate these differences, Fig. 6(a) shows thetime traces of the conduction band populationat the K and Σ points for both spectrometers,measured for 1 hour (HA) and 20 hours (MM),respectively. Both data sets show similar statis-tics and scatter, as visible from the residualsof the exponential fits. In contrast, comparing8 .00.50.0 I n t en s i t y ( no r m . ) R e s i dua l s ( % ) � t (fs) 0 100 200 � t (fs)MM: Σ HA: Σ HA: � MM: � MM: Σ HA: Σ HA: � MM: � � fast = 32±4 fs � fast = 31±9 fs � fast = 32±4 fs � fast = 40±19 fs hour MM: 20 hours HA: 1 hour MM: 1 hour Fig. 6:
Time traces of the integrated excited-statesignal at the K and Σ valleys for acquisition timesof (a) 1 hour (HA) and 20 hours (MM), and (b)an equal acquisition time of 1 hour for both instru-ments. The excited-state signal of the MM data isextracted from an energy-momentum plane corre-sponding to the HA measurement. The time tracesare fitted with a single-exponential (Σ) and double-exponential (K) decay curve convolved with a Gaus-sian, respectively. The fit results are shown in solidcurves, along with the time constants (standard de-viation as uncertainty) of the fast decay componentof the transient population at K. While the residu-als in panel (a) show similar levels of noise for bothinstruments, the MM time traces in (b) feature sub-stantial scatter. the data for similar acquisition times (Fig. 6(b))shows much larger scatter in the MM traces dueto the lower number of acquired events. This isalso represented in the accuracy of the fit param-eters. Even if we sum the symmetry-equivalentlocations in the Brillouin zone that the MM datacover, the HA still permits much faster data ac-quisition of a limited energy-momentum region.This allows for a time-dependent systematic vari-ation of external parameters (e.g. temperature,pump fluence, etc.) – challenging with the MM.However, if the electron dynamics over an ex-tended momentum space region are of interest or comparing different momentum points not si-multaneously accessible within the angular rangeof the HA is required , the MM is clearly advan-tageous. A further critical aspect in trARPES are thespace-charge effects induced by electrons emit-ted by the pump pulses. Multi-photon photoe-mission and emission at surface inhomogeneitiescan generate a significant number of low-energyelectrons. Depending on the pump-probe timedelay, this can lead to complex interactions withthe probe-pulse-induced electron cloud .While this phenomenon plays a secondary rolewhen exciting WSe at hν = 1 .
55 eV, it be-comes increasingly important as the photon en-ergy of the pump pulses approaches the ma-terial’s work function, since the order of thenonlinearity needed for multiphoton ionizationdecreases. In the following, we systematicallystudy the pump-induced space-charge effects at hν = 3 . F abs = 20 µ J/cm ), the MM spectra exhibit asevere non-uniform broadening and shift mostpronounced at the Γ point, see Fig. 7. In thisfluence regime, the low-energy electrons releasedby the pump pulses greatly outnumber probe-pulse-induced photoelectrons, shown in panel(e). The pump-pulse-induced space-charge ef-fects strongly depend on delay and extendover several ps around the temporal pump-probeoverlap, see panel (d). Here, one has to care-fully distinguish the true temporal overlap fromthe space-charge maximum at positive delays.As sketched in Fig. 7(f), space-charge interactionis particularly critical at positive delays (pumppulse precedes the XUV probe), since the fastprobe photoelectron cloud traverses through thecloud of slow, pump-pulse-emitted electrons onits path to the detector. In the MM, the rela-tive difference between the velocities of the twoelectron species is minute due to the high ac-celeration field of the extractor, similar to theinteraction between the primary and secondaryelectrons within the probe-pulse electron cloud9 x (Å -1 )420-2 1.00.0 k x (Å -1 )(a) (b) (c) (d)3 μ J/cm � � μ J/cm (f) (g) 420-2-10 -5 0 5 10 � t (ps)20 μ J/cm EDC � E - E VB M ( e V ) x (Å -1 )20 μ J/cm MM: EDCsno pump F abs = 20 μ J/cm HA MM (h)(e) Abs. Fluence (µJ/cm )Abs. Fluence (µJ/cm )0 0interaction region t = 0 fs 1.00.60.40.2 B and w i d t h ( e V ) B and s h i ft ( e V ) Photoelectrons / pulsex10 T O F ( n s ) p u m p p r o b e Fig. 7: (a-c) False-color plots of 2D MM cuts along the momentum direction indicated by the red line in panel(a) for various pump fluences ( hν = 3 . t = 0 fs). (d) Total momentum-integrated EDC as a function oftime delay. (e) Total intensity versus ToF at equilibrium (black) and with optical pump at t = 0 fs (red). (f)Illustration of the interaction of the pump- and probe-pulse-emitted photoelectron clouds. For positive timedelays, the probe electron cloud (purple disk) pierces through the low-energy electrons emitted by the pump(blue disk). The critical interaction region (light blue) between the two electron species is indicated for bothinstruments. (g,h) Fit results (analogous to Fig. 4) of width and shift of the VB at the K point as a functionof absorbed fluence ( t ≈ FA = 200 µ m) and of emitted photoelectrons per pulse. The sharp onset of thespace-charge effects in the MM measurements demonstrates the high nonlinearity of the pump-pulse-inducedphotoemission. discussed in Sec. 4.1. As a result, the criticalinteraction region extends far into the lens col-umn. Moreover, also the low-energy electronsemitted by the pump pulses travel along the op-tical axis, which enhances the energy shift andbroadening at the Γ point. In contrast, in thefield-free region between the sample and the HA,the relative speeds of both electron clouds differstrongly, so the interaction region is limited to asmall volume close to the sample. This leads topump-pulse-induced space-charge effects alreadyat significantly lower excitation densities whenusing the MM as compared to a HA, as shownin Figs. 7(g-h).Ultimately, this significantly limits the exper-imental flexibility of the MM with regard toexcitation wavelengths approaching the samplework function, and strongly restricts the appli- cable excitation fluences. For our test case of hν = 3 . . Here,pump-induced space charge strongly shifts anddistorts the spectra near the Γ point, and atthe same time heavily blurs the dispersion at K,which makes it difficult to discern the excited-state signal at 10 − of the level of the VB. Incontrast, at comparable excitation densities, theHA delivers a sharp band dispersion, a well-resolved spin-orbit splitting of the VB, and aclear excited-state signal within reasonable in-tegration times, illustrated in Fig. 8. Also, theHA permits significantly increased excitation flu-ences creating a larger excited-state populationwithout considerable distortions and allows evenhigher excitation photon energies providing alarger window into the conduction band disper-10 x (Å -1 )420-2 E - E VB M ( e V ) � �� �� HA - 26 μ J/cm k x (Å -1 )10 -4 -3 -2 -1 I n t en s i t y ( no r m . ) VBM (eV)(c) EDCs at K point HA: 0.04 x 0.10 Å -2 MM: 0.04 x 0.10 Å -2 MM: 0.30 x 0.30 Å -2 MM - 20 μ J/cm Fig. 8:
Excited-state band mapping along theΓ − Σ − K direction ( t = 0 fs, hν = 3 . sion. Our case studies show that, despite the paral-lel detection of the full energy and momentumrange, the ToF-MM in its current state doesnot replace, but rather complement the HA. Thecombination of the two complementary detectionschemes in a single setup allows us to address abroad variety of scientific questions. To illustratethe complementary role of both instruments, letus consider the scenario of studying a novel ma-terial. For an initial characterization, the MM isbest suited, as it permits an efficient mapping ofthe full band structure and gives an overview ofall relevant carrier relaxation pathways within the entire projected BZ. After identifying cen-tral energy-momentum regions with the MM, theHA can be used to quickly analyze the dynamicswithin specific energy-momentum regions at highmomentum resolution, and to systematically ex-plore the experimental parameter space (e.g. flu-ence and temperature dependence) in a time-resolved fashion. Moreover, the HA can pro-vide access to experimental parameter ranges,e.g., excitation wavelengths, fluences and polar-izations, that are not feasible using the MM dueto space-charge restrictions or the experimentalgeometry (grazing-incidence illumination).A complementary advantage of the MM is thepossibility to measure samples that are suscepti-ble to XUV beam damage, as only a very limitedXUV flux is required due to the efficient photo-electron detection. In addition, we note here alsoa few additional experimental difficulties con-nected with the MM. Firstly, flat sample surfacesare needed to prevent field emission resultingfrom the high extractor voltage. Secondly, a flatand isotropic sample holder is required to pre-vent distortions of the extractor fields. Thirdly,acquisition with the MM requires processing andstorage of large data sets ( ∼
100 GB for a typicaldata set of 10 events), and involves complexdata binning and analysis procedures .Determination of the complete (time-resolved)electronic band structure dynamics with the MMbears an enormous potential. Most directly, it al-lows to track complex momentum- and energy-dependent scattering phenomena, shines lighton quasiparticle lifetimes , and permits bench-mark comparison to band structure theory . Asthe MM measurements are performed at a fixedsample geometry, it allows to investigate higher-order modulation effects of the photoemission in-tensity, such as orbital interference . In addi-tion to comprehensive band structure mapping,the MM bears further conceptually new mea-surement configurations. The use of aperturesin the real-space image plane permits spatial se-lectivity of band structure measurements downto the micrometer scale. Furthermore, the useof apertures in the reciprocal image plane allows11o extract the real-space photoelectron distribu-tion at high momentum-selectivity via PEEM.This novel technique allows to study spatial in-homogeneities that involve subtle momentum-variations, such as the formation of domainboundaries of symmetry-broken states, the im-pact of defects on ordering phenomena, andthe spatial distribution of intertwined complexphases after photoexcitation . We have demonstrated a dual-detector XUVtime-resolved ARPES setup, and benchmarkedthe characteristics of a time-of-flight electronmomentum microscope and a hemispherical an-alyzer, using metrics such as depth of focus,pump- and probe-pulse-induced space-charge ef-fects, and experimental acquisition times. Theunique combination of analyzers enables a fullview of the band structure dynamics across theentire photoemission horizon using the momen-tum microscope and a rapid data acquisitionacross a limited energy-momentum region athigh momentum resolution using the hemispher-ical analyzer. Furthermore, the possibility toachieve high spatial selectivity and the option ofmapping the (time-dependent) real space photo-electron distribution of confined spectral featuresvia momentum-resolved photoemission electronmicroscopy allow for entirely new perspectives.
See the supplementary material for a video of thetemporal evolution of the excited-state signal inWSe acquired with the MM (iso-energy contourat 1 . ± . We thank S. Kubala, M. Krenz, D. Bauer,R. Franke, J. Malter, M. Wietstruk (SPECS GmbH), A. Oelsner, M. Kallmayer, and M.Ellguth (SurfaceConcept GmbH, Mainz) fortechnical support. We also thank G. Sch¨onhense(University of Mainz) for enlightening discus-sions. This work was funded by the MaxPlanck Society, the European Research Coun-cil (ERC) under the European Union’s Horizon2020 research and innovation program (GrantNo. ERC-2015-CoG-682843), the German Re-search Foundation (DFG) within the EmmyNoether program (Grant No. RE 3977/1) andthrough the SFB/TRR 227 ”Ultrafast Spin Dy-namics” (projects A09 and B07). S.B. ac-knowledges financial support from the NSERC-Banting Postdoctoral Fellowships Program.
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