Electron spectroscopy of alkali metal surfaces by deexcitation of metastable He atoms

187

Surface Science 180 (1987) 187-202 North-Holland, Amsterdam

ELECTRON SPECTROSCOPY OF ALKALI METAL SURFACES BY DEEXCITATION OF METASTABLE He ATOMS B. WORATSCHEK Institut

ftirPhysikalische

*, W. SESSELMAN, Chemie,

J. KijPPERS,

Universitiir Miinchen,

G. ERTL **

Fed. Rep. of Germany

and H. HABERLAND Fakultdt Received

ftirPhysik, Universitiit Freiburg Fed. Rep. of Germany 10 June 1986; accepted

for publication

6 October

1986

Auger deexcitation of metastable He atoms yields electron energy distributions arising from the outermost atomic layers which may be compared with corresponding UPS data. This technique exhibits a much higher sensitivity for the s-derived valence states of the alkali metals than UPS. The recorded spectra do, however, not directly reflect the surface density of valence states, but are strongly modified by matrix element effects. A simple model based on tunneling of the valence electrons of a free-electron gas metal through a rectangular potential barrier into the He core yields energy distributions which can be fitted very well with the experimental data, and in particular it reproduces the observed exponential decrease of the emission intensity towards higher binding energies. The mean distance (dAD) from which deexcitation predominantly occurs is the only adjustable parameter of this model, and the resulting values for (dAD) are in the range of 3-5 A from Li to Cs as expected. Singlet He* atoms are converted to about 95% into the triplet state from where deexcitation occurs. The rate constant for this spin-flip process is estimated to be of the order of 1014 s-t. Characteristic differences exist between the spectra of bulk alkali metals and of adsorbed monolayers.

1. Introduction Deexcitation of metastable noble gas atoms A* occurs at surfaces with low work function through Auger deexcitation (AD) or Penning ionisation, whereby a valence electron of the target T fills the hole of the ground state of A* and the electron in the excited level is ejected [l-4]: A* +T+A+T++e-(E,). * Present address: IBM Almaden Research Center, San Jose, CA 95120-6099, USA. ** Present adress: Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-1000 Berlin 33, Germany.

0039-6028/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

188

B. Woratschek

et al. / Electron spectroscopy of alkali

metal

surfaces

The kinetic energy of the emitted electron, ckin, is simply related energy with repect to the Fermi level, E,, through

to its binding

(1) where E& is the effective excitation energy of the metastable in front of the surface, and $I is the work function. The kinetic energy distribution of the emitted electrons is dependent on the density of valence states at the surface, but might be strongly modified by matrix element effects as is demonstrated in a recent quantum mechanical treatment [5]. Eq. (1) is rather similar to the energy balance in UPS: Ekin=hv-EEB-$.

Here the photon energy hv replaces the excitation energy E,“;,, and the spectral features arising from both techniques are expected to be displaced on the ekin-scale by the amount hv - E& from each other. Characteristic differences are to be expected, however, due to the different excitation cross sections, and due to the fact that metastable deexcitation spectroscopy (MDS) probes only the valence electronic structure of the outermost atomic layer while UPS has a finite information depth and will usually exhibit pronounced contributions from bulk states. 2. Experimental The experimental arrangement has been described in detail previously [6]. A beam of thermal (&kin = 60 meV) ‘S or 3S He* atoms is created by electron bombardment of a He nozzle beam. The energy distributions of the emitted electrons were determined by means of a hemispherical analyzer with a resolution of 0.15 eV. Alkali metal films with a thickness of at least 10 atomic layers were prepared by evaporation from SAES getter sources onto a clean Cu(ll0) surface held at 140 K. These films showed no ordered LEED patterns, indicating that they were polycrystalline. A low base pressure of 5 x 10-r’ Torr ascertained that the surfaces were atomically clean for long enough times. The most sensitive monitor for the state of surface cleanness was the MDS technique itself, which exhibited substantial changes of the spectral features after adsorption of spurious amounts of residual gases. 3. Results and discussion 3.1. General spectral features: MDS versus UPS Since surfaces

singlet He* atoms are very effectively converted at alkali metal into the triplet state prior to deexcitation [2,3], the MD spectra

B. Woratschek et al. / Electron spectroscopy of alkali metal surfaces

189

cs-sp, :

.2 hv-21.2eV

Cs-6s

I. . +b 'i.

‘. .:,:$.b. ‘zy,,l,’ . c: 1.:-::

A

:

7-t:

$2 '(x50)

I.I

20 Fig. 1. Energy distributions

16

of electrons

12 8 4 Ekin (eV 1

emitted by photons a clean Cs surface.

(hv = 21.2 eV) or 3S He* atoms

from

presented in this section are due to deexcitation of 3S He*. This species has an excitation energy Ez = 19.8 eV if it is far away from the surface. From the shift of characteristic spectral features on the ekin-scale with respect to UPS E,?; was determined to be 19.5 k 0.1 eV in front of the alkali metal surfaces. The UPS data shown for comparison were obtained with He1 photons with hv = 21.2 eV. Spectra recorded from a clean Cs surface with both techniques are displayed in fig. 1; they contain - among other features - peaks arising from direct ionisation of the 6s- and Sp-derived levels as marked. The intense peak in the MDS data at the highest kinetic energies arises from 6s-valence band, quite similar as reported previously for a monolayer of adsorbed Cs [3]. The cross section for excitation of these states by the He1 photons is, on the other hand, very low, and the corresponding features in the UPS data become therefore only visible after intense magnification. The. MD spectrum exhibits an additional peak (ho,,) at a kinetic energy 2.1 eV lower than the 6s-peak which is due to surface plasmon losses [7-91. The

corresponding feature in UPS is at 2.8 eV below the 6s-maximum (hw,,) and is ascribed to bulk plasmon losses [8]. This difference nicely demonstrates the surfaee sensitivity of MDS, while UPS probes mainQ bulk properties. The peak denoted by A appears at identical kinetic energies in both spectra and is due to an C$W-Auger transition, whereby a hole in the Cs Sp,,,-level is filled by a valence electron. The cZ,W tr~sition involving a 5p,,,-hole is strongly suppressed due to rapid p3,2 -+ p1,2 Caster-Kronig transitions [lo]. The short lifetime of the p1/2- hole manifests itself also in the larger widtb of the 5p,,, if compared with the 5p,i,-p eak ]g]. A weak bump below peak A in the Ma spectrum might again be due to plasmon losses; in the UPS data it would be masked by the Sp,,,-emission. Corresponding spectra for Rb are reproduced in fig. 2 and show features similar to those with Cs. The bulk and surface plasmon energies of 3.2 and 2.4 eV, resp~tiv~ly, are in a~~~~~t with iiterature data [8]. Peak A is caused by a N,VV-Auger transition. In the UP data it is accompanied by single and double pfasmon losses. Fig. 3 shows data for K. The M,,W-Auger peak A [ll] appears at even higher kinetic energy. fn the MD spectrum it is hardly ~sce~ible from the

191

B. Woratschek et al. / Electron spectroscopy of alkali metal surfaces

/ 2:

.:’

20 Fig. 3. Energy

distributions

16

of electrons

12

6

4 Ekinid' ‘I

emitted by photons surface.

or 3S He*

atoms

from a clean

K

background following the K-4s emission on the low kinetic energy side. This background is due to secondary electrons; its intensity increases continuously from Cs to Li parallel to the increasing density of valence electrons. 3.2. Electron emission from

the valence states

The major advantage of MDS over UPS with the present systems is obviously its high sensitivity for emission from the valence band. Corresponding spectra for the whole series of alkali metals are reproduced in fig. 4 on an E,-scale with the Fermi level as reference (E, = 0). All data are characterized by a pronounced peak below E, followed by a tail whose intensity increases from Cs to Li due to the effect of increased secondary electron emission mentioned above. The shapes of the valence band emission are at pronounced variance to the densities of states of free-electron metals, D(E) - a, which, according to theoretical calculations [12], represent the properties of the alkali metals rather well. This apparent discrepancy is illustrated in fig. 5 for the case of Cs: The steep rise of the emission at E, is followed by an exponential decay, which contrasts with the parabolic theoretical density of states with a band width of 1.6 eV [12]. Recent angle-resolved UPS measurements with Na revealed that the actual band width is narrower (2.5 eV) than predicted by theory (3.2 ev> but that the parabolic E(k) dispersion of a nearly free-electron gas is well fulfilled [13]. In

192

B. Woratschek

et al. / Electron spectroscop_v of ulkali metal surfaces

0

1

binding Fig. 4. ‘S He*-deexcitation

spectra

2

3

energy

[eVl

from the valence band range of the various

alkali metals

addition, at certain photon energies the UP spectrum showed a further very narrow peak directly below the Fermi level which was attributed to the existence of a charge-density wave (CDW) [13,14]. It is very unlikely that the features of the present spectra are associated with such CDW structures for various reasons: (i) CDW is a bulk effect while our technique probes only the outermost electronic structure of a solid. (ii) CDW peaks should be much narrower (i.e. limited by the instrumental resolution) than the observed peaks. (iii) Their orientation is restricted to a very narrow angle within the direction perpendicular to the densely packed (110) plane [14], which was confirmed by the ARUPS work [13]. The present experiments were performed with polycrystalline films and the spectral features could already be observed in the monolayer range, i.e. without the existence of periodicity normal to the surface. LEED investigations [15] and total-energy calculations [16] indicate no noticeable alteration of the surface structure of alkali metals which could give rise to a distortion of the electronic structure at the surface, and recent calculations revealed no evidence for the existence of surface resonances [17].

B. Worutschek et al. / Eleciron spectroscopy of alkali metal surfaces

193

binding energy IeV 1

(Y-z--

D(E)

‘S He’ 17

16 15 14 kinetic energy [eV]

Fig. 5. Experimental electron energy distribution from a Cs surface (dots) together with the density of states D(E) of the free,:electron metal. P(E) is the best fit to the experimental data through eqs. (3)-(5).

Therefore, it is concluded that the difference of the shape of the experimental electron energy distribution to that of a free-electron gas density of states is due to matrix-element effects, and it will be shown that the essential features can be fairly well understood by a simple model. According to fig. 6a the rate for Auger deexcitation from an occupied state f k) at the surface is determined to a first-order approximation by the square of the overlap of 1k) with the hole in the ground state of He*, 11s). ]ls) is essentially concentrated to a sphere with 0.3 A radius [18] around the He nucleus. Since the AD process occurs far outside the surface, only the exponentially decaying tail of 1k) will be of relevance, which within the Sommerfeld model is proportional to exp( - &R). (En is the binding energy of the valence electron with respect to EF.) It is quite obvious that the states close to the Fermi level contribute more to the overlap and therefore to the total deexcitation rate (summed over all 1k)), I”,,, than those with larger binding energies. Hence we expect that the exponential decrease of r,, with

194

B. Woratschek et al. / Electron spectroscopy of alkali metal surfaces

e

E

vat :-‘-’ EF ” P

2s

e

1s

t met01

He”

metal

He core

al

b)

J Fig. 6. (a) Mechanism

of deexcitation potential

of a He* atom in front of an alkali metal surface. underlying analysis of the data.

(b) Model

\lE, dominates the intensity distribution of the spectrum, more or less irrespective from the actual density of states. Since the [Is) He wave function is strongly localized compared with the free-electron-like metal states 1k), the radial dependence of [Is) is approximated in our model by a delta function at the He nucleus and at a distance d,, from the Sommerfeld edge. Our simple &ode1 consists in replacing the actual potential of the type shown in fig. 6a by a rectangular potential (fig. 6b), and by treating the 1k) + 11s) transition as a tunnel process across this potential barrier with thickness d,, and height +. V, is the valence band width which is taken from the literature [19], and C$is the work function which was determined experimentally from the total width of the He I photoelectron spectra. The latter two parameters are listed in table 1.

Table 1 Experimental work functions +, valence band widths (dAr,), and the sum of alkali + Li atomic radii dA_,i Element Li Na K Rb cs

2.4 + 0.1 2.450.1 2.3 k 0.1 2.0+0.1 2.0 + 0.1

Va [19], average

VB(eV)

(4mXh

4.74 3.24 2.12 1.85 1.59

3.1+ 0.4 4.0 f 0.4 4.4kO.3 4.6f0.4 5.liO.3

distances

3.0 3.3 3.8 3.9 4.1

of deexcitation

B. Woratschek et al. / Electron spectroscopy of alkali metal surfaces

The “intrinsic” energy distribution of electrons will within this model be given by distance d,,

&

G(E)-r,,(E)-

created

by deexcitation

at a

(3)

exp[-f@n(V,+9-E)d,,]D(E).

AD

The

195

energy

scale is now defined by the bottom of the valence band, i.e. is the binding energy with respect to E,, and D(E) is the occupied density of states. The electronic transition is governed by Coulomb interaction which is reflected by the term l/d,, [20]. According to this model the measured electron distributions should exhibit a steep onset at E, and an approximately exponential decrease towards lower kinetic energies. This is qualitatively in agreement with the experimental data and indicates that the model takes into account the dominating effect governing the spectra. The measurable “extrinsic” energy distribution P(E) is, however, broadened due to the following effects: (i) The electron spectrometer has a limited resolution of 0.15 eV. (ii) Deexcitation occurs over a limited range of distances over which also the available effective excitation energy E& varies, causing a corresponding broadening of the spectral features [6,21]. Both effects are combined into a Gaussian with parameter r

E = V, - E,, where E,

A(E)

-r-l

evl - Wr)‘]

with which G(E) energy distribution P(E)=Cf’deG(E-+4(e). -Eo d AD in G(E)

has to be convoluted

(4) in order

to reproduce

the “extrinsic”

(9

has now to be replaced by its average value (dAD). The rise of steep. the emission onset at E, would without these effects be infinitely (Apart from temperature effects due to Fermi-Dirac statistics which are, however, negligible.) The actual increase of intensity at E, determines the parameter r, independently of (dAD), and the resulting values were in the range 0.22-0.25 eV. The only unknown parameter in P(E) is (d,,), the average distance at which deexcitation occurs. This quantity can now be determined by calculating P(E) for various values of (d,,) until the best agreement with the corresponding experimental data is reached. The full line in fig. 5 represents the best fit which could be achieved in this way in the case of Cs. It should be emphasized that this fit is very little affected by the width of the valence band Va and by the work function +. The presented data therefore allow no determination of the actual bandwidth. On the other hand this result shows, however, that the exponential decrease of the emission intensity with increas-

196

B. Womtschek et al. / Electron spectroscopy of alkali metal surfaces

0

1

2

3

E, IeVl

Fig. 7. The experimental MDS data from the valence bands of the various alkali metals (dots) are fitted through eqs. (3)-(5) with a single parameter (CIAD) (full lines).

ing E, is primarily determined by (dAD), which quantity may therefore be derived on the basis of the applied model. In principle, the following effects might be of additional importance: (i) The deviation of the effective excitation energy of the metastable atom, E& from the free gas phase value which, however, is included in the kinetic energy of the onset of emission, respectively the parameter r. (ii) The actual potential is certainly not of the rectangular shape as plotted in fig. 6b and will be modified by image force effects. (iii) The application of a tunneling model instead of explicitly calculating the matrix elements is certainly a severe simplification. The only justification which we have for the applied model is the good fit of the experimental data (shown in fig. 7) with a single parameter, (dAD), which turns out to be of the expected order of magnitude. Resulting values for (dAD) are listed in table 1 and are in the range of 3-5 A. They increase in the same sequence as the bulk lattice constants, viz. Li + Cs. More specifically, a He* atom is chemically similar to a Li atom and

B. Woratscheket al. / Electronspectroscopyof alkalimetalsurfaces

197

therefore also the interaction of He* with an alkali metal surface is expected to bear some similarity with that of Li. The last column of table 1 lists the sum of the metallic radii of alkali + Li, dA_Li, as given by the nearest-neighbor but is distances in the bulk materials. d,_,i shows the same trend as (dm), systematically smaller. This conclusion should probably not be overstressed in view of the crude approximation applied for the analysis, but we find further support for it from the results of gas phase experiments: Here the maximum of the deexcitation probability is usually found at the minimum rmin of the interaction potential which would correspond to the equilibrium distance of the molecule AHe* [6], and a similar tendency (r&(He*) >, r,,(Li)) has been found [22]. We may conclude that Auger deexcitation at surfaces occurs also predominantly at a separation which is close to the equilibrium distance rather than near the classical turning poing. Ez - E& was found to be about 0.3 eV, which again indicates that deexcitation takes mainly place in the attractive part of the interaction potential. In any case the derived order of magnitude for (dAD) clearly shows that metastable noble gas atoms used for MDS probe essentially the long range part of the surface density of states. The measured energy distribution therefore does not reflect the local density of states in the surface (i.e. in the limit d,, + 0) but rather the electronic structure as it is “seen” by an atom or molecule approaching and chemically interacting with the surface. 3.3. He* singlet to triplet conversion Fig. 8 shows kinetic energy distributions from the valence band region of Cs which were recorded with both ‘S and 3S He* species. The main peak as well as the plasmon loss appear at exactly identical kinetic energies, although the excitation energies (E,* = 20.6 and 19.8 eV, respectively) differ by 0.8 eV, and one would therefore expect that the spectral features are displaced by the same amount with respect to each other on the kinetic energy scale (cf. eq. (1)). The ‘S He* spectrum exhibits indeed an additional small peak (p) whose emission starts at 0.8 eV higher kinetic energy than that of the main peak (a) and which has obviously to be attributed to deexcitation of ‘S He*. It is quite evident that about 95% (derived from the ratio of the respective integrated peak intensities) of the ‘S He* particles are converted into 3S He* from where deexcitation into the ground state occurs: ka3SHe*+T+He+T++e kb

‘S He* +T c

He+T++e.

(a) (b)

This efficient conversion process had already been detected previously with adsorbed layers of K [2] and Cs [3] and was observed in the present work also

198

B. Woratschek

et al. / Electron spectroscopy

18 Fig. 8. Kinetic

energy distributions

17 16

of a&di metal surfaces

15 14 EkJeV

of electrons emitted He* atoms.

from a clean Cs surface

either by ‘S or 3S

with all surfaces of (bulk) alkali metals. The mechanism for this conversion process as proposed in ref. [3] is depicted schematically in fig. 9. A singlet atom in front of the surface may undergo a different Auger transition in which a valence electron from the target fills the hole in the 2s-level (instead of the ls-level as is the case with deexcitation into the ground state), whereby the already present 2s-electron with opposite spin is shifted upwards in energy and tunnels into empty states of the solid. This spin-flip process is associated with the creation of an electron-hole pair at the surface and requires a sufficiently large density of empty states above E,.

Fig. 9. Mechanism

for He* ‘S + 3S conversion

in front of an alkali metal surface.

B. Woratschek et al. / Electron spectroscopy of alkali metal surfaces

199

The halfwidth of peak /3 in fig. 8 is considerably smaller than that of peak (Y.If we apply formally eq. (5) for its analysis, a value of about 50 A for (din) would result which is physically unrealistic. The competition between processes (a) and (b) will be governed by the overlap of target levels 1k) with the wave functions of the 2s and Is-hole states, respectively. Since the 2s-functions are spatially much more extended it becomes quite plausible why the singlet -+ triplet conversion dominates. In addition it is to be expected that direct deexcitation of ‘S He* will only take place with finite probability with those metal wave functions which are reaching far into the vacuum. These are just the states close to the Fermi level and it becomes thus plausible why peak /I is so narrow. If we consider the processes (a) and (b) as two parallel reactions, the fact that only about 5% of the emitted electrons arise from step (b) means that the ratio of the rate constants k,: k, is about 20. The rate constant for direct Auger deexcitation is of the order 1013 s- ’ [22], so that we estimate that the rate constant for singlet + triplet conversion is at least of the order 1014 s-l. One might expect that the probabilities for branching into the two channels is affected by the velocity of the incident particles [23]. No effect was however detected if the velocity was increased by a factor of two. 3.4. MDS data from monolayers of adsorbed alkali metals Characteristic differences occur between the spectra of bulk alkali metals and of those from monolayers adsorbed on Cu(ll0) as can be seen from fig. tiy’ A n intense peak arising from s-valence electron derived states is also present with the monolayers. (In a previous publication [4] it was demonstrated that adsorbed K atoms even in the limit of zero coverage are not completely ionized but exhibit a finite density of occupied 4s-states.) The width of these peaks is narrower from which on a smaller width of the valence bands may be concluded (although the MDS data do not yield the bandwidth as outlined in section 3.2). Simple physical arguments for such a reduction of band width due to a “quantum size” effect can be found in a paper by Burt and Heine [24]: These authors calculate a bandwidth of 1.1 eV for a free monolayer of Cs as compared with 1.6 eV for bulk material. It should be kept in mind, however, that in the present case the valence electrons will be involved in bond formation with the substrate. (ii) The binding energies of the Rb 4p- and Cs Sp-levels are somewhat larger with the bulk materials than with the monolayers. (iii) With the monolayers both the Auger peaks as well as the plasmon losses are practically missing. The Auger transitions require two valence electrons near the same core. If the valence electrons have lost their free-electron character due to localization in the chemisorption bond with the substrate

200

B. Woratschek t-1al. / Electron spectroscopy of alkdi metal surfaces

K ..K-4s

.‘K-4s

Rb-4pv2 : \ ;

/

’ Rb-5s

Rb

Rb-4py

“Rb-5s

’ ,;Rt

.‘,Cs-6s

j’i.’ If, .O

4

0

12 EB [eVl

Fig.

16

F=O

.:cs cs-5p i’ /d’ ri s’

: I\ 4

8

12 Es

16

[eVl

10. ‘S He* deexcitation spectra recorded from bulk samples (left-hand side) monolayers adsorbed on Cu(ll0) (right-hand side) of K, Rb and Cs.

or from

these transitions will be suppressed. A similar argument holds for the excitation of plasmons, which might, however, slightly show up as shoulders on the high E,-sides of the valence band emissions. Although adsorbed alkali monolayers are metallic in nature [25,26], the present results demonstrate that their electronic surface properties are still distinctly different from those of the bulk material.

4. Conclusions The electronic properties of clean surfaces of polycrystalline Li, Na, K, Rb, and Cs were investigated by means of metastable deexcitation spectroscopy (MDS). Due to the low work functions of these systems the recorded electron energy distributions arise from the Auger deexcitation mechanism and can be directly compared with corresponding UPS data. Apart from features arising from direct ionisation of valence and core states also plasmon losses and Auger transitions can be identified with both techniques. MD.9 has a much higher excitation cross section for the s-derived valence states than UPS.

B. Woratschek et al. / Electron spectroscopy

ofalkali metal

surfaces

201

The spectra from the valence bands do not exhibit the e-dependence as expected for free-electron metals, but rather the emission decays exponentially with increasing binding energy. This effect is mainly attributed to the varying overlap between the metal wave functions and the Is-hole of He* which governs the deexcitation probability. A simple model based on tunneling of the metal valence electrons through a rectangular potential well to the He* core yields satisfactory agreement with the measured spectra, if the distance over which deexcitation occurs is fitted to 3(Li)-5(Cs) A. This result confirms the picture that a He* atom is chemically similar to a Li atom and feels an attractive interaction upon approaching an alkali metal surface from where deexcitation occurs. The very effective conversion of ‘S He* into 3S.He* prior to deexcitation as observed previously with adsorbed alkali overalyers [2,3] takes equally place at the surface of bulk alkali metals. This effect is ascribed to a competition between two processes: (a) Transition of a target electron into the 2s-hole of ‘S He*, accompanied by back-tunneling of the other 2s-electron (with opposite spin) into an empty state of the metal. (b) Transition into the Is-hole of ‘S He* giving rise to direct electron emission. While the rate constant of the latter process is of the order 1013 s-l [22], that for the former is estimated to be about 1014 s-l - a result which becomes again plausible from overlap arguments. Monolayers of K, Rb and Cs adsorbed on Cu(ll0) show no longer Auger peaks (involving two valence electrons) nor plasmon losses in the MDS data, indicating differences in the electronic properties between adsorbed layers and bulk material.

Acknowledgement Partial support of this work by the Deutsche Forschungsgemeinschaft 128) and the Fritz-Haber-Institut is gratefully acknowledged.

(SFB

References [l] H. Conrad, G. Ertl, J. Kiippers, W. Sesselmann and H. Haberland, Surface Sci. 100 (1980) L461. [2] J. Lee, C. Hanrahan, J. Arias, F. Bozso, R.M. Martin and H. Metiu, Phys. Rev. Letters 54 (1985) 1440. [3] B. Woratschek, W. Sesselmann, J. Kiippers, G. Ertl and H. Haberland, Phys. Rev. Letters 55 (1985) 611. [4] B. Woratschek, W. Sesselmann, J. Kiippers, G. Ertl and H. Haberland, Phys. Rev. Letters 55 (1985) 1231. [5] F. von Trentini and G. Doyen, Surface Sci. 162 (1985) 971.

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B. Woraischek et al. / Electron spectroscopy of alkali metal surfcrces

[6] H. Conrad, G. Ertl, J. Kippers, W. Sesselmann and H. Haberland, Surface Sci. 121 (1982) 161. [7] G. Ebbinghaus, W. Braun, A. Simon and K. Berresheim, Phys. Rev. Letters 37 (1976) 1770. [8] G. Ebbinghaus and A. Simon, Chem. Phys. 43 (1980) 117. [9] G. Ebbinghaus, W. Braun and A. Simon, Z. Naturforsch. 31b (1976) 1219. [lo] R.G. Oswald and T.A. Callcott, Phys. Rev. B4 (1971) 4122; J.A. Smith and W. Pong, Phys. Rev. B12 (1975) 5931. [ll] L.G. Petersson and SE. Karlsson, Phys. Scripta 16 (1977) 425. [12] V.L. Moruzzi, J.F. Janak and A.R. Williams, Calculated Electronic Properties of Metals (Pergamon, New York, 1978). [13] E. Jansen and E.W. Plummer, Phys. Rev. Letters 55 (1985) 1912. [14] A.W. Overhauser, Phys. Rev. Letters 55 (1985) 1916. [15] S. Andersson, J.B. Pendry and P.M. Echenique, Surface Sci. 65 (1977) 539. [16] K.P. Bohnen, Surface Sci. 115 (1982) L96. [17] L.F. Mattheis, quoted in ref. [13] as personal communication. [18] S. Fraga, J. Karwowski and K.M.S. Saxena, Handbook of Atomic Data (Elsevier, Amsterdam, 1976). [19] N.W. Ashcroft and N.D. Mermin, Solid State Physics (Holt-Saunders, Tokyo, 1976). [20] SW. Wang and G. Ertl, Surface Sci. 93 (1980) L75. [21] W. Sesselmann, B. Woratschek, G. Ertl, J. Ktippers and H. Haberland, Surface Sci. 146 (1984) 17. [22] H. Haberland, Y.T. Lee and P.E. Siska, Advan. Chem. Phys. 45 (1981) 487. [23] H.D. Hagstrum, Phys. Rev. 96 (1954) 336. [24] M.G. Burt and V. Heine, J. Phys. Cl1 (1978) 961. 1251 B.E. Hayden, K.C. Prince, P.J. Davie, G. Paolucci and A.M. Bradshaw, Solid State Commun. 48 (1983) 325. [26] S.A. Lindgren and L. Walldtn, Phys. Rev. B22 (1980) 5967; Solid State Commun. 28 (1978) 283.