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PHYSICAL REVIEW B 15 AUGUST 1998-IIVOLUME 58, NUMBER 8

Collective and single-particle excitations in the photoyield spectrum of Al

S. R. Barman*Fritz-Haber-Institut der Max Planck Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany

P. HaberleDepartmento de Fı´sica, Universidad Tecnica Federico Santa Maria, Valparaiso, Chile

K. HornFritz-Haber-Institut der Max Planck Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany

~Received 9 February 1998!

Using angle- and energy-resolved photoyield spectroscopy, we investigate the properties of the multipoleplasmon excitation. At higher energies, a systematic dependence of the photoyield on the photon angle ofincidence is observed and explained on the basis of classical Fresnel theory, indicating the possibility ofobtaining information about optical constants from such measurements. A feature above the multipole plasmonis assigned to the excitation of a bulk plasmon by the photon field.@S0163-1829~98!51132-0#

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Collective excitations are of fundamental importanceunderstanding the response of a metal to an incident elemagnetic field, and have attracted the attention of physicover many years.1 The collective excitations originate fromthe oscillatory modes of the surface electron density, whappear at the poles of the surface reponse function,causes an enhancement of the photoemission intensity. Texcitations occur below the bulk plasmon frequency (vp)where, due to the dynamic screening of the external field,microscopic surface electric field varies rapidly and deviaappreciably from the classical Fresnel fields.2 Above \vphowever, the surface becomes transparent to the incidendiation and the Fresnel equations are expected to be vEvidence for an increase in the total photoyield below\vpwas observed on thick alkali metal films in the early workMonin and Boutry.3 An enhancement of surface photoyiewas also observed in Mg,4 Al,5 In,6 Be,7 and Na layers onCu,8 though most of the early studies suffered from probleof surface roughness and the total yield measurement tnique. The advantage of angle- and energy-resolved ptoyield ~AERPY! over the total yield measurements is thatdoes not have contribution from the inelastically scattesecondary photoelectrons, which is difficult to analyze amay also depend on surface quality and sample preparahistory. The first reliable study of collective excitations, uing the AERPY technique, was performed by LevinsoPlummer, and Feibelman for Al~100!.9 They showed thatthere is a large increase in photoyield belowvp , with a peakat a relative frequency of 0.8vp .9,10 The experimental resulcould only be explained by calculating the photoemissmatrix element explicitly, taking into account the variationthe electric field at the surface, which is generally neglecDifferent theoretical studies1,2,11–15concerning the nature othe collective modes have been performed to explain theperimental data of Levinson, Plummer, and Feibelman. T0.8vp peak has been assigned to a multipole surface plasexcitation.

Although in recent years there has been improvementhe predictive capability of theory,1,16–19 a comprehensive

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experimental study of collective excitations on a metal sface using photons has been lacking. The advantage of uphotons rather than electron-energy-loss spectroscopy20,21

~EELS! is that the dominant monopole surface plasmmode is not excited by photons, and thus weaker surfmodes~for example, the multiple mode! can be observedMoreover, due to the finite detector aperture in EELS,qi50 multipole plasmon is mixed with the monopole plamon mode.22 In this paper, we report investigations of thphotoresponse in Al~111! using AERPY spectroscopy. Wexamine the different types of collective excitations~includ-ing multipole plasmon and threshold excitations! that are al-ready known to exist,1,17,19and present evidence for a colletive excitation above\vp at 16 eV. Furthermore, a singleparticle excitation related feature above\vp dispersessystematically as a function of photon incident angle, andexplained by Fresnel theory. The agreement between expment and calculation suggests the possibility of obtaininformation about optical constants of surfaces using stechniques.

The measurements were carried out on the 1-m SeNamioka and toroidal grating monochromator~TGM4!beamlines at the Berliner-Elektronone-SpeicherrinGesellschaft fu¨r Synchrotronstrahlung~BESSY! storage ringusing a commercial angle-resolving electron spectrom~ADES400 from VG, U.K.! at a base pressure of310211 mbar. Electropolished Al~111! crystals werecleaned by repeated sputtering and heating cycles; a s~131! low-energy electron diffraction pattern was observfrom the clean surface. The AERPY spectra were measuusing p-polarized light by recording the intensity at thFermi level (EF) in the energy- and angle-resolved mode,avoid contribution from the inelastically scattereelectrons.19 The data were collected in the normal emissigeometry as a function of the angle of incidence~a!, definedwith respect to the sample normal~see inset of Fig. 1!. Boththe sample and the analyzer were rotated by the same a

R4285 © 1998 The American Physical Society

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R4286 PRB 58S. R. BARMAN, P. HABERLE, AND K. HORN

in order to changea, so that the normal emission collectiogeometry is unchanged. The plane of incidence was theror symmetry plane of the crystal, either along t110 (G K) or 1 12 (G M ) directions. In order to improvethe quality of the data and to decrease the measuring tthe intensity atEF was measuared in the constant initial sta~CIS! mode at typical binding energies of 0.1 or 0.3 ePhotoemission spectra were also recorded to confirm thedata. The data were normalized as described in Ref. 19.

A representative AERPY spectrum for Al~111!, taken inthe CIS mode at 0.1 eV binding energy, is shown in Fig.The work function cutoff for the threshold of photoemissiis observed at 4.5 eV. The peak at 13 eV is related toexcitation of the multipole plasmon that enhances the phemission signal. The multipole plasmon decays by transring its energy to electron-hole pairs.23 A similar mechanismof plasmon decay has been suggested for Na clusterReinerset al..24 We have observed that there is an increasethe intensity of the entire photoemission energy distributcurve in the multipole plasmon region. This indicates thatelectron-hole transitions occur from the entire valence baThe multipole peak has a triangular shape~full width at halfmaximum 3 eV! with a sharp increase in intensity belo\vp ~at 15 eV for Al! and a relatively gradual decreasbeyond the maximum. The large width of the multipole plamon in Al is in agreement with the total photoabsorpticalculations.2,18 The present results and our recenpublished19 data on alkali metal layers, indicate that thwidth of the multipole plasmon increases with increaselectron density. This trend agrees with the published thretical results.2,14The multipole plasmon appears at a relatifrequency ofvm50.85vp with respect to the bulk plasmofrequency. It should be noted that the time-dependent lodensity approximation~TDLDA ! jellium calculation, whichtakes into account the exchange correlation potential,dicts this value to be 0.8\vp .14 The appearance of the mutipole at somewhat higher frequency compared to the calation indicates that the electron density is possibly lpolarizable on the Al~111! surface as compared to a jelliumsurface.1 It is interesting to note that the multipole plasmoappears at a similar relative frequency~around 0.8vp) for all

FIG. 1. Angle- and energy-resolved photoyield spectrumAl ~111! measured by the intensity atEF in normal emission geometry with a545°. vm andvp correspond to multipole and plasmofrequencies, respectively. The measurement geometry is showthe inset.

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metals so far studied irrespective of their electron density1,19

Although the different theoretical calculations agree on taspect, the physical reason for this behavior is not fuunderstood.1 In the work by Levinson, Plummer, and Feibeman on Al~100!,9 the multipole plasmon peak appeaaround 12.5 eV (0.83vp) and the overall shape of the peaksimilar to the Al~111! surface. However, taking advantagethe high quality of data it would be interesting to investigathe crystal face dependence of photoyield. A significantcrease of intensity is observed in the experimental spectbelow 7 eV, towards the work function cutoff. This is thevidence for the collective threshold excitation phenomenwhich has been predicted by TDLDA calculations.17

We now turn to the discussion of the photoyield in tregion above the multipole plasmon response. The spectin the frequency region abovevp shows two weak humpsaround 20.5~feature A! and 16~feature B! eV ~shown byarrows in Fig. 1!. The occurrence of these features is surpring, since according to LDA-based jellium calculations, ttotal photoabsorption abovevp is featureless.15 Data onAl ~100! by Levinson, Plummer, and Feibelman also exhibibroad feature around 20 eV.9 These features are not due tolarger photoemission matrix element for certain final statto which the states atEF can couple~as in the final stateresonances!, since they remain at the same energy positfor different initial states~between 0 to 1 eV binding energy!. Moreover, the shape of the final bands is such tthere are no direct transitions from the Fermi level in thphoton energy. In order to understand the origin of thefeatures, AERPY spectra~open circles! have been recordedas a function of angle of incidence~a! (20°<a<55°) fornormal emission collection geometry~Fig. 2!. It turns outthat the higher energy feature A shifts systematicallylower energies with decreasinga, while feature B does noshift. As indicated by arrows, ata555° feature A is around23 eV and moves to 20.3~19.2! eV at a545° ~40°!. Ata535° it appears around 18 eV and overlaps with featureAt a525° the two features completely overlap, resultingan enhanced and broadened peak, while ata520° this peakbecomes narrower. In contrast, the multipole plasmon ateV does not shift with angle, its origin being due to nonloceffects that cannot be explained by Fresnel theory. Tshoulder appearing at 10.6 eV in this set of AERPY specis due to the excitation of the monopole surface plasmonappears at\vp /A2 ~10.6 eV!. A relatively rough surface canprovide the momentum for the monopole surface plasmto be excited by the photons. The surface plasmon, whhas been seen in earlier photoyield studies,4–6,9 does not ap-pear in the data shown in Fig. 1 where a different cryswith a carefully electropolished surface was used. The wglitch at 24 eV~Fig. 2! is related to the Al 2p core-levelintensity, excited by the third-order light from the toroidgrating monochromator, moving throughEF .

In order to understand the changes in the AERPY speabove\vp , we have calculated the electric field within thsurface, using the classical Fresnel equations forp-polarizedlight.25 The experimentally determined refractive index~n!and the extinction coefficient~k! ~Refs. 26, and 27! for Al~shown in Fig. 3! were used as inputs to the calculation. Tgeometry of the experiment is such that the plane of in

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PRB 58 R4287COLLECTIVE AND SINGLE-PARTICLE EXCITATIONS . . .

dence is a mirror symmetry plane of the crystal; for normemission, the final state is symmetric. Thus, consideringsymmetry (L1) of the initial state atEF , photoelectronsfrom the Al~111! surface are excited only by the norm(EZ) component of thep-polarized light. Figure 2 shows thcalculatedEz

2 ~normal! andEy2 ~parallel! components of the

electric field as functions of photon energy for differenta.

FIG. 2. Angle- and energy-resolved photoyield spectraAl ~111! measured at normal emission collection geometry withp-polarized light as a function of the angle of incidence~a!. Thespectra are shifted with respect to each other, and the zero ofspectrum is indicated on the left vertical axis.Ez

2 ~solid line! andEy2

~dashed line! are the calculated perpendicular and parallel comnents of the Fresnel fields inside the surface, normalized toincident field. The calculated curves are shifted with respect toexperimental spectra for ease of comparison, and the zero is shon the right vertical axis. The arrows show the dispersion of feaA.

FIG. 3. Comparison of the energy position of feature A~filledcircle! with the peak position of calculatedEz

2 ~solid line! and theangle of incidence for the onset of total internal reflectionaT(hn)~dashed line!. Refractive index~n! and extinction coefficient~k! ofAl refer to the right vertical axis.

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Ez2 (hn) exhibits a broad peak fora555°, which becomes

narrower and shifts systematically to lower energies withcreasinga. The Ey

2 component exhibits a steplike featurethe same frequency whereEz

2 exhibits a peak, and has ncounterpart in the experimental spectra. In Fig. 3 we copare the position of feature A with that ofEz

2 and the agree-ment is found to be excellent. The intensity measured inAERPY spectrum is due to photoemission from states atEF ,which is governed by the photoemission matrix elemez^ f uA•p1p•Au i & z2, whereA is the vector potential,p is theelectron momentum, andu i & and u f & are the initial and finalstates, respectively. On increase of the electric field (EZ)within the surface, the matrix element and hence the ptoyield is enhanced. For this reason, the dispersion of feaA and the peak of the normal component of the Fresnel fiare in good agreement~Fig. 3!, signaling the success oFresnel theory to explain this single-particle excitationlated feature. A dip at 15 eV appears in all the spectracause at\vP ~'15 eV for Al! the surface becomes transpaent to the incident photons. The total photoabsorption\vp , according to the theoretical formulations,2 is zero.However, the experimental spectrum shows a finite intenat the dip which increases for decreasinga due to the dis-persion of feature A towards lower energy. Thus, the finintensity at the dip occurs in part due to photoemission frwithin the surface, and the disagreement with theory aribecause only surface photoabsorption is considered informulation.

The calculated angle of incidence for the onset of tointernal reflection,aT@5 sin21(n)#, is shown as a function ophoton energy in Fig. 3. For example, ata530, total internalreflection occurs for\v<17.6 eV. The extinction coefficien~k! is small compared to the refractive index~n! in the energyrange of interest~Fig. 3!. In such a situation, the maximumof EZ

2 as function ofa occurs aroundaT . The variation ofnandk with photon energy shifts this maximum as well asaTin a similar way. Thus, the variation of the maximumEz

2(\v) with a, exhibits a similar variation as that ofaT asa function of photon energy~Fig. 3!. So, the dispersion ofeature A is correlated toaT(\v). An important outcome ofthis observation is that, for surfaces with an unknown refrtive index, photoyield data could be used to obtain suchformation. The shape of theEz

2 peak is similar to that offeature A, which could also be used to extract the\v depen-dence of the optical constant; however, a possible variaof the photoemission matrix element needs to be consideMoreover, the presence of direct transitions, final state renances, or collective excitations would complicate the anasis.

Feature B, which appears at 1.07\vp ~16 eV!, does notdisperse with angle, unlike feature A. The behavior is simto features related to collective excitations~viz, the multipoleplasmon! that do not disperse.Ez

2 does not show any enhancement in that region~Fig. 2!, which means that featureB cannot be explained by classical Fresnel fields. The tphotoabsorption calculations by Feibelman using the LDbased random phase approximation technique2 indeed showa hump betweenvp and 1.2vp . This feature is observedonly when the microscopic variation of the field is taken inaccount, as in the case of the multipole plasmon,9 indicating

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R4288 PRB 58S. R. BARMAN, P. HABERLE, AND K. HORN

that the origin of feature B is related to a collective excition. We have found a similar feature for thick K layegrown on Al~111!.19,28 The spectra exhibits a dip at 3.8 e(\vp53.8 eV for K! with a feature appearing at 4 eVwhich is at a similar relative frequency of 1.05vp , as in Al.When an electromagnetic wave withv>vp is incident, lon-gitudinal electrostatic waves associated with oscillatcharge densities exist in a conducting medium along withtransverse electromagnetic field. Forp-polarized light, thelongitudinal and transverse waves can interfere atsurface.1 The excitation of bulk plasmons (v>vp) at thesurface or in thin films of a conducting medium have berelated to the longitudinal polarization wave.29 Thus, the

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peak ovserved at 16 eV finds a natural explanation in teof photon induced excitation of longitudinal bulk plasmowith q.0. To our knowledge, this is the first experimentobservation of such a coupling in a metal surface. Detacalculations might provide an explanation for the shapethis feature as a function of frequency.

We thank A. Liebsch and W. Ekardt for useful discusions, and Y. Cai and H. Haak for help during the measuments. This work has been supported by the European Cmunity Grant No. CI1*-CT93-0059 ~DG 12 HSMU!,Fondecyt Chile under Grant No. 1970122 and tBundesministerium fu¨r Bildung und Forschung under GranNo. 056220LA3.

,

*Present address: Inter University Consortium, University CampKhandwa Road, Indore, M.P., 452017, India.

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