AUGER CVV SPECTRA OF CHEMISORBATES : DYNAMICAL SCREENING AND GEOMETRY EFFECTS

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AUGER CVV SPECTRA OF CHEMISORBATES : DYNAMICAL SCREENING AND GEOMETRY

EFFECTS

M. Cini, A. d’Andrea

To cite this version:

M. Cini, A. d’Andrea. AUGER CVV SPECTRA OF CHEMISORBATES : DYNAMICAL SCREEN- ING AND GEOMETRY EFFECTS. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-785-C9-788.

�10.1051/jphyscol:19879138�. �jpa-00227248�

AUGER CVV SPECTRA OF CHEMISORBATES : DYNAMICAL SCREENING AND GEOMETRY EFFECTS

M. CINI and A. D'ANDREA

Istituto di Metodologie Avanzate Inorganiche, CNR, Area della Ricerca di Roma, CP 10, I-00016 Monterotondo, Italy

Resume-Nw avons 4tendu l a t h b r i e des formes spqtrales Arger CW des atomes

&mi-adsor& pcur y inclure explkicltement les degres de liberte'des plasmons de surf9ce. Puisque leur f* w, est finle, l a polarisation du sobstrat et Is&ran de la repulsion t r w - t w presentent une diviation ar rapport a' la description 6lectrostaticp uaelle. La solution exacte du m&le perrnet d ' Q t d w les c o p x t i o n s d y n a r n i p pour diffedntes gdometries de c(lem1sorptlon. Nous presentom ici des r6sultats pour des atomes chihi-adsorbeb en position de sommet, pont et centre.

Abstract-We have extaxied the theory of Auger CW 1lneh.jpes of &emisorbates in order to inclode explicitly the surface plasmon degrees of freedom. Since their frequency ^y is finite, the &strate polarization and the screening of the b l e h o l e repulsion deviate from the usual electrostatic description. The exact solution of

t h

model allows to study the dynarnical corrections for dfferent chemisorption geometries. Here we present results for atoms chemisorbed in the atop, bridge and centre positions.

Gynarnical W . - A n Au er CW transition taking place on a chemisorbed atom

produces a sudden ptw!atlrn of the electrostatic patentlei h t exclks the substrate surface plasmons; In turns the dynamlcal potential of the excitations affects the prop ation of the final-state valence holes and hence tha Auger trurn. We d e s c k the final state of the Auger t r d t h by the follow~ng t%%ltolan [il H = Htb

+

^Uo~o+llo-

+

w&tb

+

g [n,,, tn, 1 [b+bt )

.

⁽¹⁾

Here, Htb stands for an ~ n d e p d e n t p a r t i c l e , tight birdkg model of cknisorption,

where EO and cS are the adatom and substrate atom energy levels, V is the adatom-

@strate hopping integral, Vs is the hopping Integral between &trate atoms, and

2

^is restricted to nearest neighbaP-s. The second term in (1) represents the hole- hole repulsion, with Uo glven by the gasphase (1.e. unscreened) Coulomb integral between two holeti at the chemisorbate site 0. Screening effects are doe to the surface plasrnons, of frequency ^y and annlhilatlon -tor 6. The third term in (1) represents the free plasmon field, w M e the last term models the holeplasmon interaction of strength g; in our model surface plasmom polarize around holes at site 0, but are insensitive to delocalized hole states. Assumlng the core-hole lifetime is long enough, the Auger spectrum can be described in the two-steps model a d is

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879138

C9-786 JOURNAL DE PHYSIQUE

proportional to the density of final states. The latter is given by the imaginary part of the Green's function

Dlw) = (O,O,cJ [u - H t i 0 ) - I 10,0,c>

.

¹³

The expectation value is taken with respect to the state 10,0,c>, where both final state holes are at site 0, and the lasmons; are in a coherent state due to the effect of the primary core hole. f can b Aown [i] that if the limit %=>a, g=>m

a

proached

m

szx3 a way that X = '1% remains finite, the above model reduces to

%

usual hson-free d e e i p t i o n of kuger CW line shapes 12.31. In other terms,

*r

H => Htb[co) t U ~ o + no- 14)

N

with the relaxed level

a

=

a

- AE antj the statical1 screened repulsion U = UO - 2AE. The latter theory has been quite swcessful 14, but has the obv~ous weahie56 of describing larization effects only In the static limit. Like the static h r

,

the present one allows a exact solmim, whkh i s achieved by a recently devefoped method [5,6]. In Ref. [i], we have studied the d narnical corrections for the case of an adatom chemisorbed in the 'at@' position,

&

^is, sitting on tcp of a &strate atom belo ing to the [lo01 face of a si l e cublc srkstrate. The scbstrate is represen3 by a finite duster including% third d g h b o u r s of the adatom.

'RE j summation of Eq. 12) then contains a single term. The results show the most dramatic deviations; from the static llmit when the plasmm frequency wo is comparable to the r~lperturbed virtual level width W. In such circumstances one can draw no definite distinction between maln line an3 satellite s t w t u r e s , and m w quasiatomic states ^can tjroaden &stantially if they can mix with the band continuum b plasmon emission. A quaIitatively similar behavim is redicted in the spectra o r solids 171 dus m bulk plasmm e x c i t a t i a On the other

b,

if

w

>>W, the maln line shape is accurately given by the static theory; however i t loses art of the Intensity, Uhich is f din the p k s m m satellites, that do not r rod- t i e shape of the mala peak. Whn

o.

is several urnes W but not ex&ngly"Parge, interesting deviations from the static theory ma axour depending on the parameters. In Fi . I , we have chosen for illustration c0 =

Yev,

V =lev, Vg = O.SeV, 0. =10 eV, g=fev and Uo = 12eV. These eters, however arbitrary, could reasonably represent an e l e n m s g a t l v e atom

ms

^boded to a substrate atom more s t m g l y than a h s t r a t e atoms am themselves. In the static theory [Fig. ial the screened U is 2.2 eV ad W = 2ev% the sobstrate berd width is 6eV, a d the CW 11

turns out to be distorted bandlike. The intensity of this spectrum was reduced *a factor q[-AE\& to simulate the effwt of intrinsb l o s s . I n the dynamical t;$ory (Fig. 161, the main line shape IS slgnfficantl narrower; the f ~ r s t plasmon satellite (mt &own) 1s f a r away on the right hrd s1& of the flgue, bein crnlered d 0 eV. Note that the static theo p d ! c t s tba energy levels (& PosLtlm) much better than the intensities, whi.uhGX depend an tbe overlaps and are sensittve to the boson dressiq of the wavefonctlons.

Effects af Geometry.-Aloog with the 'at position, we mnsider chemisorptlon in the 'bridge' and 'center' geometries. In the%r1dgeq case, the adatom is symmetrically bonded to two neighbowkg surface atoms; in the 'centre' position i t lies above the

centre of a square wlth 1 bonds to the atoms a t the corners. T h s e geometries were m s i d e r e d by C y r o t ~ c k m a m and mxorkers long ago [a] to study the in ^the local article density of s t a b p in the tight-binding model of Eq.

tbe pmblem%%vlasl rmh more complex d there are more parameters in the theory. In rincfple. d d e r e n t geometries w u l d entail different values of V; shxlld

8

also vary L. to hi? varying di~tances from the surface plane, since AE is refated to t f ~ image potential. In the present paper, however, we wish to make abstraction from these o b v ~ w s eter adjustments in order to uderstand qualitatively the l n t r i ~ l c effects of e g e o m e t r y a d tapology. h f o r e we have kept the same set

parameters are g t w in% text..

Figure 2-The same as Ffg. i, but for a chemlsorbate

m

the bridge geometry.

Figure 3-The same as Fig. i, but for a ckmiwrbate in the centre geometry

of parameters In all cases, except the lng integral V which was varied in order to keep the semrd moment d p mstant?%part from eometry, the three situatims that we consider are mnparable in all naseects, inclufirg t b overall strenght of tb chemiso tion bond. In Figures 2 and 3 we report the results of the staticaI and dynamics calculations for the bridge a d centre geometries. The stalic intensities are reduced by expl-A€/&.

C9-788 JOURNAL DE PHYSIQUE

As in Fig. 1, level shifts are seen to be sll t, and the leftmost levels, that corres nd to the final g r a d states, are shl

8

ed to higher bindiog energies.

1rstea8Ptf-e peaks m ths right fwd side are shifted to the ite dtrectlon.

Howver, the main

ctPn

es am produced by intensity dstr%ions. In the bridge and centre geometries, k e distortions dw to d namical effects are even more evident than in the atop pition, and tend to &m r k region near the centre of the main line, making it narrower and more symmetric. A common trend emerges and the overall effect 16 to make the three d lcaI llneshapes more similar to each other than their static counterparts. x e v e n for the p m t set of parameters, when the statlc theory axlld be antlclpated to be a reasonable

~proxlmatlon. signlflca dynamlcal corrections east. As in tha case of 'atop' mlsorptlon, more dramatic effects are found wfien c ~ , 1s reduced relative to the hopplng integrals. A more complete report of thresults is In preparation.

REFERENCES

1-M.Cini and A.DSAndrea, I1 ~ u o v o Cimento 6D,25 (1985) 2-M.Cini,Solid State Cornmu?. 20,605 11976) and 24,601 (1977) 3-M.Cini,Phys.Rev.B17,2788 11 978)

4-P. Weightman,Reports on P ress in Physics 45,753 11 982) 5M.Cini. b s . Rev. 817,243 (1978)

6-M.Clni and A.D'Andrea, Review in J Ph s.C, In press 7-M.Cin1 and A.D'Andrea, F%ys.Re%9.6540 8984).

8-F.Cymt-Lackmm,M,C.klonqueres and J.P.Caqad,J.Phys.C7,925 (1974)