Influence of elastic scattering on the measurement of core-level binding energy dispersion in x-ray photoemission spectroscopy
E. F. Schwier, C. Monney, N. Mariotti, Z. Vydrovà, M. García-Fernández, C. Didiot, M. G. Garnier, P. Aebi
IInfluence of elastic scattering on the measurement of core-level binding energydispersion in x-ray photoemission spectroscopy
E. F. Schwier , C. Monney , N. Mariotti , Z. Vydrovà , M. García-Fernández , C. Didiot , M. G. Garnier , P. Aebi Département de Physique and Fribourg Center for Nanomaterials,Université de Fribourg, CH-1700 Fribourg, Switzerland and Research Department Synchrotron Radiation and Nanotechnology,Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland (Dated: October 29, 2018)In the light of recent measurements of the C 1s core level dispersion in graphene [Nat. Phys. , 345 (2010)], we explore the interplay between the elastic scattering of photoelectrons and thesurface core level shifts with regard to the determination of core level binding energies in Au(111)and Cu Au(100). We find that an artificial shift is created in the binding energies of the Au 4f corelevels, that exhibits a dependence on the emission angle, as well as on the spectral intensity of thecore level emission itself. Using a simple model, we are able to reproduce the angular dependenceof the shift and relate it to the anisotropy in the electron emission from the bulk layers. Our resultsdemonstrate that interpretation of variation of the binding energy of core-levels should be conductedwith great care and must take into account the possible influence of artificial shifts induced by elasticscattering.
I. INTRODUCTION
The general assumption of non dispersing core levelsis only valid for fully localized states, but due to thecontinuous nature of the electronic wave function, theorbitals of core levels can exhibit weak hybridization evenfor binding energies of up to a few hundred eV. This hasbeen demonstrated for gaseous molecules like C H andN and in recent measurements on graphene by Lizzit etal. who were able to determine the bandwidth of the C1s core level to be 60 meV. The corresponding theoreticalprediction from ab initio calculations support the claim,that these orbitals are not completely degenerated.To resolve the dispersion of core levels and the sizeof the Brillouin zone in solids with x-ray photoelectronspectroscopy (XPS), high angular and energy resolutionsare necessary. In addition to that, there exist two mecha-nisms that introduce a broadening into the measurement.These are the quasi elastic scattering of the photoelectronwith the atoms of the crystal as well as the influence ofphonons on the photoemission process . A third factorwhich has not been considered until now and that canintroduce a systematic error to the measurement of thedispersion in core-level binding energies is introduced inthis paper with the demonstration of an angular depen-dent artificial shift, created by the existence of unresolvedenergetically shifted surface core levels.The surface core level shift ( ∆ E SCLS ) describes theenergy shift between the core levels attributed to the bulkand the surface of a crystal . It arises from a combina-tion of initial and final state effects. The non continu-ous charge distribution and the reduced number of neigh-bouring atoms at the surface of the crystal can changethe coulomb potential in the topmost layers with respectto its bulk value. This leads to a shift in the core levelbinding energies of the surface atoms. In addition to this,interactions between the photoelectron and a partiallyscreened photohole, that is created during the photoe- mission process, will also influence the surface core levelshift. Measurements on noble metal films , 5d metals graphite and rare-earth crystals have shown that thedisplacement between bulk and surface core levels can bepositive as well as negative and possesses an amplitudeof up to several hundred meV. . . . . . . surfacebulk a) b) (100)(101)[110][111] [001] Figure 1: a) Contribution to the scattering amplitude fromthe surface atoms (light grey) and the bulk atoms (dark grey).Closed packed directions in the bulk change the scattering am-plitude for different emission angles. The contribution fromthe surface layer remains almost constant up to grazing emis-sion. b) A typical 2 π angular scan in stereographic projectionwith intensity anisotropy due to scattering of photoelectrons.The high symmetry directions are visible as forward focusingpeaks (points), while high symmetry planes in the bulk man-ifest themselves as Kikuchi bands (lines). Normal emissionis plotted at the center while the black circle corresponds toemission at grazing angles. Maximum and minimum intensitycorresponds to white and black, respectively. It is important to note that at kinetic energies above500 eV the strong anisotropy in the individual electron-atom scattering leads to a focusing of electron flux alongdirections pointing from the emitting atom to the scat-terer (Fig. 1 a) . This effect is also known as x-rayphotoelectron diffraction (XPD). In 2 π angular XPD pat-terns (Fig. 1 b) high symmetry directions as well as low a r X i v : . [ c ond - m a t . o t h e r] O c t index lattice planes can be identified through forward fo-cusing peaks and Kikuchi lines. Both structures are usedto provide local information about the atomic structurenear the surface .In this work we focus on the influence of the elasticscattering of photoelectrons on the binding energy of corelevels. We demonstrate a correlation between the bind-ing energy and the emission intensity of the core leveland propose a mechanism that explains the angular de-pendence of core level binding energies. II. EXPERIMENT
All measurements were performed with an upgradedSCIENTA SES 200 analyzer, allowing for multiple angleparallel detection, using a non-monochromatized MgK α ( hν = 1253 . eV ) x-ray anode as excitation source. Acomputer controlled 5-axis manipulator allows rotationsof the sample along the polar and azimuthal directionswith a precision of 0.1° and 0.2°, respectively. The angu-lar acceptance of the entrance hole was 2.4°. The energysteps of the spectra were set to 19 meV for the 2 π an-gular scans and to 50 meV for the other measurements.All spectra were taken at room temperature with par-allel detection in angle and energy. During the mea-surement, the pressure in the chamber did not exceed2 × − mbar. The crystals were prepared with multi-ple sputter and annealing cycles. The sputtering accel-eration voltage was set to 1.5 kV and the incident angleof the argon ions was chosen to be 65° off normal whilethe sample was rotated.To determine the influence of the elastic scatteringof photoelectrons on the binding energy of core levels,we have chosen the Au 4f doublet of the Au(111) andCu Au(100) surfaces, as they exhibit a relatively largesurface core-level shift (Au(111): ∆ E SCLS = 0 . ± . eV and in the case of Cu Au(100): ∆ E SCLS =0 . ± . eV from the works of DiCenzo et al. and ∆ E SCLS = 0 . ± . eV ). Also, the surfacepreparation and properties of the Au(111) herringbonereconstruction as well as the Cu Au(100)-c(2x2) sur-face reconstruction are well documented.The annealing temperature of the Au crystal was setto 600 °C in order to obtain the herringbone surface re-construction. The Cu Au was heated up to 450 °C andcooled down within several hours across the transitiontemperature (T C = 390 °C) to obtain the c(2x2) recon-struction. The pressure never exceeded 8 × − mbar.After each preparation cycle, the surface order and clean-liness were tested with LEED and XPS measurements,respectively. III. RESULTS
Two spectra (Fig. 2) of the Au 4f doublet on Au(111)were taken at the same polar angle, but at two different i n t en i t y ( a r b . un i t s )
85 84 83 82 81binding energy (eV)
90 88 86 84 82 80
Au(111) - Au 4f
Figure 2: Two spectra of the Au 4f / core level of Au(111),taken at 68° off normal at azimuthal angles corresponding tothe [001] symmetry direction (dark grey) and 12° off symme-try (light grey). A shift of 40 meV (arrows) is visible. Bothspectra are normalized to the maximum intensity of the Au4f / peak. Inset: The whole Au 4f doublet with Shirleybackground. The grey area below the peak corresponds tothe interval used for the general fitting procedures. (see text) azimuthal angles. While one was measured in a direc-tion that coincides with a low index crystal direction, theother spectrum was measured 12° away from that sym-metry point. The energy broadening of the Au 4f peak al-lows to approximate its shape with a Gaussian profile in-cluding a constant background. Fitting the two Au 4f / peaks with this profile gives a shift of ∆ E B = 40 ± meV between the binding energy of the two spectra. Consider-ing the relatively high electron energies and the broaden-ing inherent to the XPS experiment here, it is clear, thatthe shift cannot by attributed to a dispersion induced byweakly hybridized Au 4f core levels.To determine the angular dependence of the shift in thespectra of Au(111), a 2 π solid angle emission scan of theAu 4f doublet was measured. The intensity of the elec-tron emission was recorded as a function of the core levelbinding energy E B , the polar angle Θ and the azimuthalangle Φ , generating a complete set of energy spectra asa function of the emission angles. In addition to that apolar angle was chosen, were a high resolution azimuthalscan was performed. The resulting spectra I ( E B , Θ , Φ) were fitted in energy with a Gaussian profile, includinga constant background. To test the stability of the fit,an increased fitting interval as well as a fixed width forthe Gaussian profile were implemented into the fit with-out changing the quality of the results. In addition, thesame behavior was found for the Au 4f / peak or uponusing a Voigt profile with a nonzero Lorenzian componentor a Shirley type background.To increase the contrast of the anisotropy in the peakheight h ( Θ , Φ ) and the binding energy shift ∆ E B ( Θ , Φ )of the Au 4f / peak a smooth background was subtractedfrom each dataset. The resulting diffraction pattern areplotted in a stereographic plot (Fig. 3 a). Comparison of Au(111)
0° 20° 40° 60° 80°20°40°60°80° binding energyheight minmax a) b) ! E B ( m e V ) ! (°) he i gh t ( a r b . un i t ) Figure 3: a) Stereographic projection of the angular depen-dence of the height (left half) and binding energy (righthalf) of the Gaussian profile used to fit the Au 4f / peak ofAu(111). The position of the azimuthal cut is marked in blueb) Plot of the height h (black) and binding energy E B (red)of the Au 4f / peak from Au(111) as a function of azimuthalangle, taken at Θ = 68 °. Grey arrows mark correspondingfine structures. The error bars from the fitting parametersare in the top left of the azimuthal plots. the height and binding energy shows that the main fea-tures in the scattering anisotropy, i.e., the forward focus-ing peaks as well as the Kikuchi lines, are clearly visiblein both height and binding energy. Even fine structuresof the anisotropy are replicated in the binding energy asit can be seen in the data from the high resolution az-imuthal scan (Fig. 3 b, arrows). As all of these featurescorrespond to electron diffraction induced by the bulk or-dering of low index closed packed crystal directions andplanes a bulk mediated effect can be proposed.The binding energy of the Au 4f / exhibits a decreaseof several 100 meV in the untreated data while changingthe polar angle from normal to grazing emission. Thisshift is proportional to / cos Θ and can be interpretedas an increased ratio between the emission from surfaceand bulk core levels caused by the finite electron meanfree path. Even though this variation is only dependenton the polar angle, it suggests that the surface core levelshift plays a role in the original observed shift shownin Fig. 2. To support this hypothesis, the Cu Au(100)alloy was chosen for further measurement, as it exhibits alarger surface core level shift and should therefore exhibita larger amplitude in ∆ E B during the azimuthal scans.The same 2 π angular scan and a corresponding highresolution azimuthal scan were performed for the Cu Aucompound. The correlation between the peak height h ( Θ , Φ ) and the binding energy E B ( Θ , Φ ) of the Au 4f / peak (Fig. 4 a and b) is similar to the results found forAu(111). A comparison between the maximum ampli-tude of the shift ∆ E B for Au(111) ( ∆ E B ≈ meV , Fig.3 b) and Cu Au(100) ( ∆ E B ≈ meV , Fig. 4 b) sup-ports the proposed influence of the size of the surface corelevel shift on the amplitude of the angular dependence inthe binding energy shift. Cu Au(100)
0° 20° 40° 60° 80°20°40°60°80° binding energyheight minmax a) b) ! E B ( m e V ) azimuthal angle " (°) h e i g h t ( a r b . un i t ) Figure 4: a) As Fig. 3 a) for Cu Au(100). b) As Fig. 3 b)for Cu Au(100) with
Θ = 58 °. IV. MODEL
This dependence of the binding energy on the emis-sion angle can be understood if the different scatteringamplitudes between photoelectrons from the surface andbulk components are considered. We propose a simplemodel (Fig. 5 a), that by considering the Au 4f / peakas a sum of a surface and a bulk component, can de-scribe the measured azimuthal dependence of ∆ E B . Themodel peak consists of two Gaussian peaks with identicalwidth ( σ = 1 . eV ), corresponding to our experimentalbroadening. We assume that the measured anisotropy inthe azimuthal scan (Fig. 4 b) is caused entirely by theangular dependence of the scattering of the bulk com-ponent. The mean surface to bulk ratio ( S/B = 0 . )for an emission angle of Θ = 58 ° on Cu Au, was cal-culated from the results of DiCenzo et al. . To ac-count for the uncertainty of the binding energy separationbetween the surface and the bulk component, two setsof fits were performed using values for ∆ E SCLS corre-sponding to the upper ( ∆ E SCLS = 0 . eV ) and lower( ∆ E SCLS = 0 . eV ) limit of the literature values forthe surface core level shift of Cu Au. The variation inthe fit between the two values is visualized through aconfidence band in the plot.The resulting composite peak was fitted with a Gaus-sian profile, in the same manner as the measured dataand the binding energy shift was plotted as a function ofthe azimuthal angle. In Fig. 5 b (top) the dependence ofthe calculated binding energy (grey band) is compared tothe experimental results (red). The model predicts a shift ∆ E B , which is larger than the experimental results. Thiscan be corrected by relaxing the oversimplified assump-tion of a Gaussian profile with a constant peak width.Note also that, using a Voigt Profile instead of a Gaus-sian does not change the overestimation of the bindingenergy shift.A good agreement between the model and the experi-ment can be achieved if the width of the Gaussian peakcorresponding to the bulk emission is allowed to vary a) b) ! E B ( m e V ) " (°) ! E B ( m e V ) Cu Au(100) =const =var he i gh t ( a r b . un i t ) -85 -84 -83binding energy (eV) bulk surface Figure 5: a) Peak composition considered for the model. Thebulk peak (dark grey) changes its height (dotted line) as afunction of azimuthal angle, while the surface contribution(light grey) stays constant. The composite peak (black) ex-hibits an apparent shift (dotted line). b) Comparison of themeasured binding energy shift ∆ E B (red) with the confidencebands (see text) from a model peak composition assuming aconstant (grey, top) and variable (grey, bottom) bulk peakwidth. (Fig. 5 b, bottom). A possible mechanism that wouldlead to a variation of the peak width is the increase of theinformation depth through electron diffraction. Along di-rections were forward focusing takes place, the electronscontributing to a core level spectra will on average beemitted from a greater depth and travel a longer paththrough the solid, thus increasing the inelastic losses ofthe photo electrons. Another possible source for a peakbroadening is the change in cross section for scatteringevents with the atoms in the closed packed directions,leading to an increase in quasi elastic losses.In a first order approximation, the broadening is as-sumed to scale linearly with the intensity variation of thebulk peak. This can be reasoned by comparing the infor-mation depth with the emitted intensity, which both scalewith the mean free path. The gain in the intensity thatis created through the forward focusing, will increase themean depth from where electrons are emitted and there-fore increase the possibility of occurrences of processesthat involve energy loss. This approximation is still ap-plicable, if the defocusing of photoelectrons through mul-tiple scattering events in forward focusing directions is taken into account, as it effectively introduces a scal-ing factor to the intensity emitted in forward focusingdirections.If a linear dependence of the bulk peak width on thebulk anisotropy is implemented into the model ( σ (Φ) = σ h (Φ) /h , with σ and h being the average peak widthand height, respectively) and the resulting compositepeak is again fitted in the same way as described above,the calculated confidence band for the binding energyshift (Fig. 5 b (bottom)) coincides with the results from the experiment.The amplitude of the shift ∆ E B is comparable to thepredicted and measured bandwidths, created through thehybridisation of partially hybridized states . In experi-ments that probe the dispersion of such states, it is pos-sible that an artificial shift as described above, induces asystematic error.In the absence of an unresolved surface core level, ashift will nonetheless be present if at least two energet-ically separated lattice sites for the same element existand if the coordination of those sites inside the latticeleads to distinct electron scattering patterns. In thatcase, the anisotropic electron emission and the correla-tion between the intensity of the core level emission andits binding energy, would be even more complicated.Even in the case of measurements on systems as simpleas monolayers, the emission from two differently coordi-nated sites within the layer (i.e., C 1s in graphene withpartial H adsorption ) should lead to a shift throughmultiple scattering within the layer and with the sub-strate atoms. However, as the extend of the scattering ofsuch processes is usually weak compared to bulk medi-ated scattering, the amplitude of such shifts is expectedto be weaker as well. V. CONCLUSION
We have demonstrated that the emission angle depen-dent shifts in the binding energy of the Au 4f / corelevel, that were observed on Au(111) and Cu Au(100)surfaces, can be explained by a simple mechanism basedon a peak composition that includes an energetically un-resolved surface core level. Our model uses the surfacecore level shift, the intensity ratio between the surfaceand bulk emission, the overall peak broadening and thediffraction of photoelectrons emitted from bulk latticesites. It is able to explain the shift in binding energy be-tween measurements at different emission angles and itscorrelation to the emission intensity.The measured shifts are qualitatively described by amodel that assumes a constant width for the bulk contri-bution. However, if a dependence of the peak width tothe anisotropy of the emission is introduced, the exper-imental results and the calculated values match withinthe error range.
Acknowledgments
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