Fingerprinting technique in low-energy electron diffraction

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Surface Science 314 (1994) 243-268

Fingerprinting

technique in low-energy electron diffraction

H. Over *7a,M. Gierer a, H. Bludau a, G. Ertl a, S.Y. Tong b aFrifz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin (Dahlem), Germany b Department of Physics and Laboratory of Surface Studies, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA (Received 1 February 1994; accepted for publication 4 April 1994)

Abstract The most important part in solving complex surface structures is a promising guess of the starting configuration if an automated structure refinement is employed. The “fingerprinting technique” is able to provide such information quasi-directly from experimental low-energy electron diffraction (LEED) data for a class of surface structures. The application of this method to LEED is based on the local scattering picture. Because of the short mean-free path of LEED electrons, the energy dependence of LEED intensities of fractional-order beams is mainly influenced by the local geometry of the adsorbate complex. By comparing experimental W curves (fractional-order beams) of an unknown structure with those whose structure has been successfully analyzed, it is frequently possible to obtain

information on the basic structural elements of the unknown surface system. For instance, similar N curves suggest similar structural elements. In this paper, the fingerprinting idea will be substantiated by several representative examples.

1. Introduction

LEED structure analysis is a very powerful tool to obtain information of the geometry of adsorbates on single crystal surfaces as demonstrated by several hundreds of successftilly solved structures [l]. However, due to strong multiple scattering involved in the diffraction process and to the phase problem inherent in every diffraction technique, each of these structure analyses becomes an independent and cumbersome task. A structural determination has to start from scratch with a trial surface model which is varied until satisfying agreement between experimental

* Corresponding author. 0039-6028/94/$07.00 0 1994 SSDI 0039-6028(94)00202-K

and calculated ZV data is accomplished: a socalled trial-and-error survey of parameter space [WI. In the last several years, much effort has been devoted towards adapting dynamical LEED theory to the requirement of directed structural searches, namely the application of efficient optimization schemes [41. As in X-ray crystallography, various models (serving as a starting configuration in the optimization scheme) must be tried and results verified with a series of separate automated searches. The main difference between LEED and X-ray diffraction (XRD) is that with the latter method a number of techniques exist that can produce a suitable guess of the structure “quasi’‘-directly from the experimental data, e.g. the Patterson

Elsevier Science B.V. All rights reserved

244

H. Ot:er et al. /Surface

analysis and Fourier synthesis [51. So far, no adequate method has been found for LEED, where a good initial guess of the structure is the essential prerequisite for a successful solution of a surface structure. The use of other techniques plays a beneficial role in suggesting certain structural elements of a good starting configuration, for example, high-resolution energy electron loss spectroscopy (HREELS) (giving the local symmetry of the adsorbate particle) and scanning tunneling microscopy @TM) (providing sometimes a direct image of the lateral arrangement of the adatoms). Also, chemical and physical argumznts such as bond lengths falling within about 0.2 A of the sum of covalent radii often restrict the variety of possible starting configurations considerably. In this paper, we will outline a method which allows the finding of a promising guess of a starting configuration (serving as an input of a conventional structural refinement) based on experimental II/ data applying the fingerprinting technique in LEED (Fig. 1) [6]. This technique has been used routinely in ultraviolet photoelectron spectroscopy (UPS) and HREELS - among other techniques - where the spectra of a surface species are compared with the spectra of the same species introduced into a known chemical compound or cluster. Vibrational excitations are used to identify the chemical nature of this species by comparison with internal vibration frequencies measured in compounds containing the proposed ligand. Similar features in UP spectra are interpreted as resulting from similar types of bonds formed by an atom or molecule under examination. The Blyholder model provides an illustrative example which describes the adsorption of CO on transition metals analogous to metal carbonyls. Using UPS fingerprinting proves that CO is bonded to the metal surface through the carbon end [71. Translating this idea to LEED, we have to compare experimental (fractional-order beams) II/ curves of an unknown surface structure Sl with those having already been solved by a structural analysis: S2. If these experimental II/ curves are similar, the major part of the structure of both surfaces should be the same, thus furnishing us with a promising starting configuration for an

Science 314 (1994) 243-268

multiple

scattering

experiment

,..3

(RD~R,J

b R-factor minimum?

I

I

Fig. I. A flow-chart of an automated structural refinement applying an optimization scheme. The starting configuration can often be supplied by a fingerprinting argument. Suppose the crystallographic data of the surface structure S2 are known and assume further that the W data of the unknown surface structure Sl are similar to those of S2. Then the structural parameters of S2 serve as a good candidate for the starting configuration for automated structural refinement of surface structure Sl.

automated search of the unknown structure Sl (cf. Fig. 1). Since several hundreds of surface structures have already been solved over the last 20 years [l], a large body of experimental LEED intensity data is available for such comparisons. In this paper we explore the potential offered by the fingerprinting technique applied to the LEED structural search. LEED intensities of fractional-order beams can be decomposed into two contributions: One is attributed to the local geometry of the adsorbate complex (adsorbate in combination with possible reconstructions of the substrate) and the other originates from the long-range order. The application of the fingerprinting technique in LEED is based on the fact that only the first one is dependent on the energy of the incoming electrons as demonstrated by Yang, Jona and Marcus [8] and later taken up by Heinz, Starke and Bothe [9] to compare II/ features in LEED and diffuse LEED.

H. Over et al. /Surface

A theoretical description of the “local scattering picture” in LEED has briefly been given by Saldin et al. [lo] in order to interpret diffuse LEED intensities. The long-range order, on the other hand, is necessary to produce well-defined LEED spots. The dependency of the IV curves mainly on the local geometry has some simple consequences. Consider for example an adsorbate overlayer which forms two different LEED structures on a substrate. If the multiple scattering within the adlayer is weak, which is frequently the case for normal electron incidence, the intensity of the fractional-order beams is dominated by multiple scattering between the adatom and the neighboring substrate atoms. Supposing the adsorption sites are the same in both structures, the N curves of common fractional-order beams are expected to be similar (and vice versa). This local scattering picture is also valid if long-range order is not perfectly developed. For instance, atoms at the perimeter of islands experience an environment within the overlayer different from that in the interior of the islands, but they have nearly the same scattering properties due to weak scattering between the adatoms. Consequently, the size of islands is assumed to have no influence on the IV curves. The fingerprinting technique is not confined to the application of automated structural refinements but also has impact on the interpretation of experimental data such as direct identification of metastable phases and adsorption sites without applying any full dynamical calculation. This last issue contradicts the intuitive notion that LEED ZV data contain almost no apparent information of the local adsorbate geometry. This article is designed to give impetus to various practical applications of the fingerprinting idea in LEED. We start the discussion with some theoretical remarks on the “local picture” of the scattering process which determines the energy dependence of LEED intensities of fractional beams (Section 2). We restrict our considerations to fractional-order beams since they are known to be more sensitive to the actual configuration of atoms associated with the superstructure unit mesh than integral-order beams which

Science 314 (1994)

243-268

245

behave often in an “unpredictable” way. Next we present representative examples where the fingerprinting technique provides information of the coverage- and temperature dependence of the local adsorbate geometry in simple surface structures (Section 3.1). This list of examples is not intended to be complete. The first example is devoted to the system O/Cu(OOl) which was investigated by Yang et al. [8]. This system is the first application of the fingerprinting technique in LEED. A particularly interesting example represents the K-Al(lll)-(fi x 6)R30° system [ll] for which the adsorption site depends on the temperature. This is manifested by very different N curves in the low- and high-temperature phases. The fingerprinting technique is not restricted to systems in which the LEED patterns have common beams as, e.g. in [p(2 X 1) and p(2 X 2)] or [cc2 x 2) and p(2 x 2)l systems. This is demonstrated with the system O/Ni(lll) which shows a p(2 X 2) [12] and a (fi X 6)R30” structure [13]. Mixing and comparing appropriate beams give direct evidence for the same adsorption site in both phases. An “other way round” example for the fingerprinting technique in LEED will be given with Cs/Ru(OOOl) [14] and K/Ru(OOOl) [15] where different adsorption sites are discriminated solely on the basis of experimental data. We continue the discussion with coadsorbate systems where structural findings of the respective pure phases provide crucial clues for solving these complex surface structures (Section 3.2). The applicability of the fingerprinting technique is not limited to the same adsorbate species. It is also possible to compare local geometries of different species as long as they have similar phase shifts. This is usually the case when the respective atomic numbers are not too different as will be exemplified with the systems CO and N, on Ru(OO01) (Section 3.3) [Xl. Another interesting example is presented by metal atom adsorption on Si(ll1) which creates a (6 X &)R30° overlayer (Section 3.4). As shown by Fan and Ignatiev [17], Li and Ag adsorbed on SXlll) produce very similar IV spectra. This effect has been ascribed very recently to the occurrence of similar building blocks in these structures consisting of Si trimers

H. Over et al. /Surface

246

in combination with multi-layer relaxations in the Si substrate [18]. As in the case of coadsorption systems, complex structures can be solved by separating them into smaller structural units. This issue will be demonstrated with the O/Rh(llO)(2 x 2)pg system [19] where each of the nonequivalent beam sets carries particular information on the atomic configuration (Section 3.5). The beam set belonging to the (2 X 1)pg unit mesh is associated with a zigzag chain of oxygen (as found by comparison with the O/Rh(llO)-(2 X 1)pg structure), while the (1 X 2) unit mesh is related to a missing row-type reconstruction of the substrate.

2. Local scattering

picture

For an ordered surface structure, say a (p x q)-overlayer structure (e.g., (a x fi)R30”, p(2 X 2), etc.), the intensity of a diffracted beam characterized by the two-dimensional reciprocal lattice vector g of the overlayer is given by I,( E) =

k fi( k,,

2

ko)eickuekg)‘~

j=l

with

E = ik,

. k, = ik,.

k,,

(1)

where k, and k, denote the wave vectors of the incident and diffracted electron field, E is the energy of the LEED electrons inside the surface, n is the number of atoms in the three-dimensional unit cell as determined by the two-dimensional superstructure unit cell (p x q) times the thickness of the surface slab (roughly the elastic penetration depth of electrons: about lo-20 A>, rj specifies the position of the atoms in the unit cell, and fj is the (renormalized) form factor of atom j. The relation between the renormalized scattering factor fi and the scattering amplitudes as usually described in the framework of multiple scattering is given in Appendix A. Formula (1) comprises two terms: The first term contains the positions and the scattering properties of the

Science 314 (1994) 243-268

atoms in the unit cell and is strongly affected by multiple scattering effects. The second term expresses the long-range order leading to well-defined diffraction spots on the LEED screen. This factor is to a first approximation energy-independent and proportional to MN’, where N = N, *N, is the number of unit cells which contribute coherently to the diffracted intensity (depends on the transfer width of the electron beam and the size of ordered domains) and M is the number of such “coherent” areas probed by the incoming electron beam which add up incoherently. In this way, the effects of long-range order and local geometry on the LEED intensity data are separated. The energy dependence of the diffraction intensity is confined to the first term and thus governed by the local geometry of the adsorbate complex including adsorbate-induced restructuring of the substrate. It is important to notice that the renormalized scattering factor fj summarizes the effect of all scattering paths which end up at atom j (cf. Eq. (Al)). If there is two-dimensional disorder, the corresponding LEED intensities scale like MN which is usually by several orders of magnitude smaller than contributions associated with ordered structures. Hence, conventional n/ spectra of LEED spots provide information only about the ordered parts of the surface. We will restrict the further discussion to IV curves of fractional-order beams which are known to essentially carry the information on the geometric arrangement of atoms associated with the superstructure. N data of integer-order LEED beams are not advantageous to use as they are dominated by scattering processes which involve bulk atoms only. In general, the expression for the LEED intensity (1) can be separated as I, =

( c

fj(kg,

k,)

e-iAkgrJ

’ jE(pXq) +

wtth

,t~xl)fi(kg. k,)

epiAkeq12

Ak, = k, -kc,,

where the first sum runs over all atoms which are associated with the “(p X q)” periodicity and the second sum is related to atoms which have the

H. Over et al. / Surfnce Science 314 (1994) 243-268

affected substrate atom: (pxq) atom adatom

0

(1x1) atom

Fig. 2. Schematic diagram indicating those substrate atoms whose (renormalized) atomic form factors are strongly affected by the presence of an adatom and are thus belonging to the overlayer net. The atomic scattering factor is defined by all scattering paths which end up at this atom under consideration. Strong forward scattering and the strong damping of traveling electrons help to assign such substrate atoms.

“(1 x 1)” periodicity. For fractional-order beams, this equation can be simplified in a way that the term summing over atoms belonging to the (1 X 1) unit mesh drops out:

Zg,frac= j,~xr)&(~g,fra,.

12.(3)

kJ e-iAkgrJ

Notice that the atoms in deeper layers, even if they belong to atoms imposing a geometrical (1 X 1) lattice, are partially included in the renormalized atomic form factor fi of overlayer atoms via multiple scattering: The atomic form factor fj is associated with all scattering paths which end up at atom j. In addition the “(1 X 1)” atoms which are neighbors of the adatoms or strongly affected by the predominant forward scattering of the adatoms have to be considered (p X q) overlayer atoms and hence to be included in the sum in Eq. (3) (see Fig. 2). The reason is that the atomic form factors of these (1 x 1) atoms are altered due to the presence of adsorbate atoms via multiple scattering, and this effect becomes the more important the closer the substrate atoms are located to the adatom. In other words, the three-dimensional (p x q) “cluster” should be chosen

247

large enough to include all significant multiple scattering paths. Assume at first the simple case of diffraction by a single overlayer where each unit cell contains one atom. All scattering paths which contribute to the intensity of the fractional-order beams must therefore go through these adsorbate atoms. These contributions are the larger the shorter the scattering paths are. This means that ZV curves of fractional-order beams are determined by the scattering properties of the adatom and its local environment, while contributions of atoms further away are strongly damped due to inelastic scattering. In this sense, IV curves and the local scattering picture are intimately correlated: The wave field scattered by the adatom “illuminates” the surrounding substrate atoms. This fact is also the basis of LEED holography where the adatom serves as a beam splitter [20,21]. Particularly, the dependency of IV curves on the adsorption site is caused by multiple scattering between the adsorbate and neighboring substrate atoms. On the other hand, the II’ curves of fractional order beams are independent on the coverage and the long-range order as long as scattering paths between adatoms can be neglected; this point will be discussed in Appendix B. Similar conclusions can also be drawn for an adsorbate layer which induces only small distortions of the substrate lattice. In this case, the induced superlattice of the substrate atoms represents a pseudo-(1 x 1) structure so that the single scattering contributions of the substrate (via interference) have only little effect on the N curves of fractional-order beams and the multiple scattering properties are nearly unaffected. If more than one over-layer is involved, e.g. with coadsorbate systems, a discussion within the local scattering picture is somewhat complicated by interference between scattering paths of different overlayers. If, however, one of these adatoms is a much stronger scatterer than the others (this resembles the heavy atom approximation in X-ray crystallography), the local approach can again be employed very efficiently. This will be demonstrated with the system Cs/O/Ru(OOOl) compared to the respective ordered structures of

248

H. Ouer et al. /Surface

Science 314 (1994) 243-268

Cs/Ru(OOOl). Cs is a much stronger scatterer than 0. Assuming the Cs lattice is not heavily distorted by coadsorption of oxygen, corresponding IV curves of fractional-order beams related to the Cs sublayer should be similar to N curves collected for the clean Cs/Ru(OOOl) phase. In the remainder of this section, we discuss reasons for LEED intensity modulations with energy. From Eq. (A2) or (1) it becomes immediately clear that, even for the kinematic approximation, the appearance of several overlayers brings about an intensity modulation of the diffracted beam (defined by g) as a function of the incident electron energy due to interference between scattered waves originating from different overlayers; the condition for constructive interference is determined by the momentum transfer perpendicu-

ing are much backscattering.

lar to the surface A k, I =/m and is thus energy-dependent. In addition, the atomic scattering factor is also energy-dependent (but with weaker influence) due to the energy dependence of the phase shifts 6,. Both effects cause n/ curves to be energy-dependent even in the kinematical limit. However, a great deal of the features observed in experimental LEED IV curves emanate from multiple scattering effects. Due to strong forward scattering several strong forward-traveling beams in addition to the incident beam are generated. Each of these can be backscattered by deeper lying overlayers and interfere with the amplitudes resulting from scattering at the first overlayer. Because the energies for constructive interference in each of these cases are different, many features in the IV curves are generated. Generally, the influence of intralayer scattering on n/ curves is much weaker than the contribution arising from interlayer scattering (note that quasi-dynamical LEED is based on this assumption [22]). A simple explanation for the weakness of multiple scattering within the adlayer is that at normal incidence such multiple scattering requires at least two large-angle (near 90”) scattering events between distant adatoms, while for interlayer scattering only one backscattering event is necessary; remember that the cross sections for 90” scatter-

3.1.1. Oxygen adsorption on Cu(OO1)

3. Examples

smaller

than

for

forward

or

and discussion

In this section, we will concentrate on several examples where LEED fingerprinting can readily be employed to gather structural information either to find a promising starting configuration required in an automated structural refinement or to discriminate between different surface structures exhibiting the same LEED pattern. The degree of agreement of experimental IV curves of fractional-order beams is quantified by using Pendry’s r-factor T,, [231, provided IV data are available in digital form. 3.1. Simple overlayer structures on metal surfaces In their pioneering paper of fingerprinting in LEED, Yang, Jona and Marcus [S] investigated the evolution of superstructure LEED IV curves of the system O/Cu(OOl). With increasing exposure to oxygen at 570 K, the LEED pattern changed gradually from the diffuse 42 x 2) to Th ey observed that the frac(2fi x fi)R45”. tional-order IV curves essentially remain unaltered even if the LEED pattern becomes quite diffuse (see Fig. 31, whereas those of integer-order beams change drastically. The authors concluded

(l/2,1 /2) (Expt.)

l

- ’ -’

l

?‘//,

--_----,-------_ l 04, 9 yJh . %h ---------------

72.0 x IO-5 2.0 x 10-5

l

Theory c(2x2), 0 in 4-fold hollow I

I

I

I

5’0

,

I

I

I

S’@

100 Energy

i eV

Fig. 3. The (l/2, l/2) LEED spectrum of the system O/Cu(OOl) essentially remains unchanged with the 0 coverage even if the LEED pattern becomes quite diffuse. A comparison with calculated IV data indicates that 0 atoms sit always in fourfold coordinated sites [S].

H. Over et al. /Surface Science 314 (1994) 243-268

from this stability of the fractional-order spectra that the oxygen atoms maintain the same environment irrespective of the coverage, and also that multiple scattering within the adlayer is negligible. In particular, the oxygen atoms reside in fourfold sites for the (simple) ~(2 x 21 structure as found by a LEED structure analysis [S]. Consequently, oxygen should also occupy the same site in the more complicated (26 X filR45’ structure which is in line with conclusions drawn from X-ray photoelectron spectroscopy (XPS) and Xray photoelectron diffraction (XPD) [24,25]. More recent studies on this system point, however, towards a more complex picture; see for example Refs. [26-301. While the c(2 x 2) structure seems to represent an adlayer arrangement with 0 occupying fourfold hollow sites, the (2fi x &)R45O structure is characterized by a missing-row-type reconstruction. Despite the different unit cells, the local adsorption geometry of oxygen in both phases turned out to be quite similar (and hence consistent with the observation of similar N curves of common fractional order LEED beams) except for the coordination number with respect to neighboring Cu atoms in the first Cu layer which changes from four to three when going from the c(2 x 2) to (2& X filR45’ 126,281. This view has been corroborated by recent LEED simulations in which, starting from the c(2 x 21-O structure, the introduction of a missing-row-type reconstruction (leading to a (2\/2 X \/2)R45’ structure) revealed stable N curves of common fractional order LEED beams

adsorbed oxygen shows the persistence of a (2 x 2) LEED pattern over a wide 0 coverage. The LEED intensities (at a fixed energy) of the oxygen-induced superstructure beams, however, exhibit in the course of oxygen deposition maxima at coverages of 0.25 and 0.5 indicating two different ordered structures 1311. Supplementary HREELS measurements [32] and investigations on a stepped Ru(0001) surface [33] for the high coverage phase have demonstrated that the Ru(OOl)-(2x2)-0

3.1.2. Oxygen adsorption on Ru(0001) The next example deals with oxygen adsorption on Ru(0001). For this system, dissociatively

Ru(OOl)-(2x1)-0

(a)

(4 O/Ru(0001)-p(2 x 2) O/Ru(0001)-p(2 x 1) -----I

I

I

I

I’

U80) ;!)A(1’2’1’2 ,,

WI. In the light of these new results, the data of Yang et al. [8] have been reinterpreted. Considering the relatively high adsorption temperature in this measurement (about 570 K) it could be possible that in both phases the main structural element consists of an oxygen atom surrounded by three next-neighbor Cu atoms, i.e. a local missing-row-type structure; recall that the c(2 X 2) LEED pattern was quite diffuse thus indicating strong disorder.

249

.’

0

\*.._r.

100 200 300 400 500 Energy (eV)

._A...

0

100 200 300 400 500 Energy (eV)

Fig. 4. Fractional-order IV curves (experiment) from ORu(0001) p(2x 1) and p(2x 2) are shown in panel (b). The close similarity of both data sets points towards the same adsorption site of oxygen and the unimportance of intralayer scattering within the oxygen overlayer even at a coverage of l/2. Corresponding overlayer models are depicted in panel (a).

250

H. Overetal./Surface

LEED pattern has to be attributed to a superposition of three rotational p(2 X 1) domains rather than a honeycomb structure. Thus, the two distinct maxima in LEED intensity can be ascribed to the development of a p(2 X 2) and a ~(2 X 1) structure. A direct inspection of corresponding IV curves (recall that in both cases the LEED pattern is identical), depicted in Fig. 4, immediately shows the adsorption sites to be the same. This has also been confirmed by two quantitative LEED analyses [34,351. In both cases, oxygen atoms occupy threefold hcp sites, and small differences in the oxygen-induced substrate distortion result only in small deviations in the IV curves. Applying an optimization scheme in LEED, one could use the knowledge of one of the adsorption geometries as a promising guess for the starting configuration of the other (discarding alternative O-adsorption geometries) and hence find these structural parameters easily by a single shot. 3.1.3. Potassium adsorption on Al(I11) The adsorption of potassium on Al(111) produces for low temperature (90 K) and for room temperature (300 K) an ordered (a x 6IR30 structure as observed in LEED [ll]. Although the LEED pattern at both temperatures is the same, from comparison of the experimental LEED intensity curves for the two structures, as shown in Fig. 5, it can be seen that the corresponding local ad-geometry must be significantly different. This discrepancy in the IV data is quantified by an overall r,-factor of 0.84. Furthermore, intensities measured at low temperatures (90 K) after adsorption at 90 K and warming to 300 K are identical to those measured after deposition at 300 K alone indicating the occurrence of an irreversible, order-preserving phase transition. This example demonstrates the ,importance of comparing IV curves instead of LEED patterns only, even if the adsorbate coverage remains unchanged. Routinely this check should therefore be performed. A detailed LEED analysis of K/Ah1111 confirmed the local adsorbate geometries for both phases to be indeed very different [ill: At low temperature the adatoms occupy on-top sites on a rumpled substrate while at room

Science 314 (1994) 243-268

F-K

d3xd3)R30°

rP=0.80

n

;

+

(l/3,113)

0.83 (213, 213) \ n,,....~..~r........""~"~,..,,

I

0

I

50

I

I

I

I

I

I

J

100 150 200 250 300 350 Energy I eV

Fig. 5. The adsorption of K on AMlll) for low temperatures (90 K) and for room temperature (300 K) produces, in either case, a (fi x 6) LEED pattern. However, the corresponding W curves (fractional-order beams) are significantly different, thus strongly suggesting that both overlayers are significantly different. The r-factors for single beams are indicated in the figure. The overall r-factor is 0.84. A quantitative LEED analysis confirmed this view: at 90 K potassium resides in an atop position while at 300 K potassium occupies substitutional sites [ill.

temperature a reconstruction of the substrate takes place in a way that the K atoms occupy surface substitutional sites. 3.1.4. Oxygen adsorption on Ni(ll1) Upon oxygen exposure, two distinct ordered structures on Ni(ll1) are observed with LEED, namely a p(2 x 2) and a (6 x &)R30” phase. As found by LEED structural analyses [12,13], in both overlayer structures the oxygen atoms sit in fee hollow sites. At a first glance, LEED fingerprinting should not be applicable because both phases do not possess any common fractionalorder LEED spots. Yet, the modulus of the parallel component of the momentum transfer is very similar and hence the perpendicular component of the momentum transfer for certain sets of beams, e.g., the (l/3, l/3) beam and the (l/2, 0)

H. Over et al. /Surface Science314 (1994) 243-268

251

between the p(2 X 2) and the (6 x fiIR30” structure on the fee (111) surface is the symmetry fee-site ::2. d of the first-order fractional LEED beams. While :: ii 1x5 : 3. I .* for the (6 x 6) structure all first fractionalorder beams are symmetrically equivalent, the f G 1 \. y .~...~......,,........t..:~.....~~~.~~.~!....., p(2 x 2) structure reveals only a threefold symmes i *f. i’i I try: the (l/2, 0) and (0, l/2) beams are non: ;;:i , .‘... CO,1/2) . ::i _i \* : i:: equivalent. Therefore, it is not very surprising : **_... --*..**_ 3 L p. .. .._ i’““’ u..: ii ._.. - .._,....... I *... : that none of these n/ curves fit very well to that of the (l/3, l/3) beam. However, if the average of (l/2, 0) and (0, l/2) beams is used, the ob~~~ ih 1 (0,1/2)+(1/2,0) tained agreement with the N curve associated with the (l/3, l/3) beam is remarkably good: rr = 0.21. Only theoretical data were used because the experimental data are restricted to a rather small energy range up to about 150 eV. Ni(lll)-(2x2)-0

I

50

I

100

I

150

/ Ni(lll)-(d3xd3)R30°-0

I

200

I

250

Energy / eV

I

300

I

350

400

Fig. 6. A comparison of calculated IV curves of the (l/3, l/3) beam with the (l/2, O), (0, l/2) and (l/2,0)+(0, l/2) beams from the O/Ni(lll)-(6 X fi) and O/Ni(lll)-2x2 structure, respectively. For both structures the same ad-geometry was used: 0 atoms reside in threefold fee-hollow sites. The N curves of the (l/3, l/3) beam and the (l/2,0)+(0, l/2) beam (averaging is required to maintain the same symmetry of the first fractional-order beams in both phases) are very similar (r-factor rp = 0.211, thus indicating that in both structures the 0 adsorption site should be the same.

beam, and therefore one expects that the N curves are similar if the adsorption site is the same and the azimuthal dependence of the diffracted LEED intensities is averaged out. Analogous simulations with the systems H,O/Pt(lll) and K/Ni(lOO) have shown that this averaging procedure gives reliable results [36,34]. Note that most of the features observed in Iv curves are determined by interference of electrons originating from different layers, and these conditions in turn are governed by the momentum transfer perpendicular to the surface (and hence dependent on the energy). This situation is illustrated with the Ni(lllM2 X 21-O and the Ni(lll)-(6 X fi>-0 phase in Fig. 6 for calculated II/ curves only. One major difference

3.1.5. Alkali-metal adsorption on Ru(0001) These adsorption systems serve as “the other way round” examples to the results presented so far. Upon deposition of alkali metals (Na, K, and Cs> on Ru(OOOl), p(2 x 2) and
Table 1 Structural results of alkali-metals adsorbed on RutOOOl) for different coverages obtained by LEED analyses Alkali-metal/Ru(OO01): LEED analyses Alkali

Structure

Site

Radii (A)

cs [141

2x2

on-top

(6 x fi)R30 2x2

hcp fee

1.90 2.17 1.94

(6 x fijR30” 2x2

hcp fee

(6

hcp

K

f151

Na 1391

x fiIR30”

1.98 1.58 1.58

252

H. Over et al. /Surface

With the systems Na and K/Ru(OOOl), a change of the adsorption geometry from fee sites in the p(2 x 2) to the hcp sites in the (fi x \j5)R300 phase has been derived [l&39]. A more pronounced effect was found with Cs/Ru(OOOl). There the position of the Cs atoms changes from atop sites to hcp sites when the coverage is increased from 0.25 to 0.33 [14]. A comparison of experimental IV curves of the first fractional-order beams verifies these findings, as can be seen from Fig. 7a; corresponding r-factors are 0.67 (Na), 0.52 (K), and 0.66 (Cs). The IV curves are markedly different, and hence the adsites should be substantially different. An averaging of half-order beams is not required in these cases because the LEED patterns already show sixfold symmetry due to the presence of two domains whose unit cells are rotated by 60”. If, however, in model calculations the same adsites are assumed in both phases, the corresponding IV curves for the first fractional-order beams are strikingly similar, as demonstrated in Fig. 7b, and underlined by the respective r-factors: rp drops to 0.17 (Na), 0.22 (K), and 0.19 (Cs). An (experimental) example where for both the (6 x 6) and the (2 x 2) phase the same adsorption site has been found is provided by the system sulfur

Science 314 (1994) 243-268

on Ru(0001). The unique local geometry of S at different coverages is manifested by the striking similarity of the experimental LEED IV curves of the (l/3, l/3) and the (l/2, 0) beam [401. In order to substantiate the local scattering picture and to estimate the number of substrate atoms to be considered in the sum of Eq. (5) (three-dimensional (& x 6) “cluster”), simulations were performed in which the scattering from deeper layers is successively switched on. In Fig. 8, these calculations are displayed for the first three layers in comparison with a full slab calculation, whereby the system K/Ru(OOOl) was chosen with K occupying the fee site in the (2 X 2) phase and with the hcp site in the (6 x \ir> phase. It becomes evident from inspection of these curves that the spectral features (position and intensity of peaks) are already well reproduced with a three-layer slab ((K + 2Ru) layer) for the hcp- and the fee-configuration. 3.2. The coadsorbate system Cs / 0 / Ru(0001) A particularly interesting example for using the fingerprinting concept in LEED is given by coadsorbate systems where each constituent is able to form an ordered overlayer and for which

Alkalis on Ru(0001): hcp-site

(2X~-structlre,j(l,i,o)~be~ --(*j3x~3)-~tm$+, (!/3,\/3&beam I I I , I , 240 280 200 1 120 160 Energy

/ eV

-

(2x2)-structure,(l/Z, O)-beam ,,.,.....,. (‘i3xd3)-structure, (l/3, l/3)-beam

1

100

8

I 200

8

I

t

300

, 400

8 !501

Energy / eV

Fig. 7. (a) Experimental IV curves of the first fractional-order beam of the (6 x 6) and the (2 X 2) phase for various alkali metals on Ru(0001). The pronounced differences for both phases in each alkali-metal system indicate different adsorption sites. Corresponding r-factors are included. (b) On the other hand, if the same adsite (e.g. hcp) is chosen in model calculations for both periodicities, corresponding IV curves are almost identical. Corresponding r-factors are indicated.

H. Over et al. /Surface

the structural parameters of the corresponding single-species structures have already been determined. This will be exemplified with Cs and 0 coadsorbed on Ru(0001). Dependent on the Cs coverage, exposure of oxygen to a Cs-precovered Ru(OOO1)surface leads to a large wealth of mixed phases with long-range order [41]. The general property of stabilizing alkali-metal adlayers by the addition of oxygen is reflected by the substantial increase of the desorption temperature of Cs in the presence of coadsorbed oxygen which suggests strong attractive interactions between both species [41]. In the following, we restrict our discussion to two selected Cs-precovered Ru(0001) surfaces for which LEED structure analyses have already been performed, namely the Cs-(2 X 2) and Cs-(6 x 6) structures. Oxygen exposure to these CsI

I

I

I

3

I

K-Ru(OOOl)-d3xd3

250 Energy (eV) Fig. 8. The evolution of N curves ((2/3, 2/3) beam) when successive scattering from deeper layers is switched on: (i) single adlayer, (ii) single adlayer+first Ru layer, (iii) single adlayer + first two Ru layers: (a) for the fee geometry and (b) for the hcp geometry.

Science 314 (1994) 243-268

253

o,,= 0.33

0.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

o,-

Fig. 9. Experimental phase diagrams of the mixed phases of Cs and 0 adsorbed on Ru(0001) starting from a pure Cs phase with coverage 0.33 and 0.23 which are related to (6 X 6) and p(2 X 2) structure, respectively, after Ref. [41].

Ru(0001) surfaces leads to the formation of several ordered Cs-0 surface structures, as illustrated by the qualitative phase diagrams in Fig. 9 among which two systems are only considered in detail. 3.2.1. Cs-0-R&0001)-(6x J3)R30° Starting with an ordered Cs/Ru(OOOl)-(6 X fi)R30° structure with Cs coverage 8,, = 0.33, already the addition of small amounts of oxygen leads to the development of a new incommensurate superstructure accompanied by a gradual vanishing of the (6 x fi)R30” LEED pattern [42]. This observation is consistent with a strong interaction of oxygen with the Cs layer. Oxygen exposure between 0.3 and 0.9 L followed by annealing above the onset of Cs desorption in the clean Cs/Ru(OOOl)-(6 X &)R30” system gives rise to the appearance of another (6 X 6)R30 structure with a better ordering than in the corresponding pure Cs/Ru(OOOl) system. The stoichiometry of Cs : 0 is 1: 1. Starting point of the analysis of the Cs-ORu(OOOl)-(6 X &)R30” phase was the solved structure of the Cs-Ru(OOOl)-(6 X &)R30 phase without coadsorbed 0 atoms 1141. There the Cs atoms occupy threefold coordina!ed hcp sites with a Cs-Ru layer spacing of 3.15 A. It has also been found for this phase that IV curves calculated for any other type of high-symmetry adsorption site differ considerably from the experimental data. With the (6 x 6)R30” coadsorption system, on the other hand, the ZV data recorded show close similarities to those of the

H. Over et al. /Surface

0.39

rF =

4%

rP =

(213, 2/3)

.,A

Ru-Cs-0 (43x43) ...I.“..*.. Ru-Cs (43x43) I

50

pure Cs-(16 X fi)R30” adlayer (see Fig. lOa). The overall r,-factor is 0.42. Together with the fact that Cs is a much stronger scatterer than 0, it becomes evident that the Cs atoms are still occupying hcp sites at almost the same distance from the first Ru layer. This situation resembles very much the heavy atom approximation used in X-ray crystallography [5]. For the location of the 0 atom, the following positions may now be envisioned: (1) on-top of a Cs atom, (2) twofold symmetric bridge position across two Cs atoms, and (3) in a threefold hollow site. With the former two configurations the positions of the oxygen nuclei would be above the plane formed by the Cs cores for the reason of a very limited space for oxygen atoms below the plane. Due to strong forward scattering, particularly at higher electron energies, oxygen located above the Cs layer should exert strong influence on the IV data, which, however, has not been observed. Therefore, we are left with variations of a model where oxygen atoms occupy threefold-coordinated sites in a nearly unaltered Cs-Ru(OOOl)-(6 X fi)R30” overlayer. A recent LEED structure analysis [42] confirmed these predictions in detail and revealed a “salt-like” Cs-O-(6 x 6)R30” structure in which the oxygen atoms reside in threefold hollow sites (with respect to the Cs layer) 1.5 A below the plane formed by the alkali-metal adlayer (cf. Fig. lob). The found increase of the hard-sphere radius of oxygen with respect to a pure 0 overlayer has been explained in terms of a net transfer of electronic charge from Cs (possibly mediated by the Ru substrate) to the oxygen. This effect, in turn, gives rise to the observed reduction of 0.1 A of the effective Cs radius if

+ts? lJ3’

0.51f

\ 0

Science 314 (1994) 243-268

I

I

I

I

I

100 150 200 250 300 3

Energy / eV

(W

Fig. 10. (a) Experimental

IV curves for the pure Cs-Ru(OOOl)in comparison with the coadsorbate phase Cs-O-Ru(OOOl)-6 X 6. The striking similarity indicates a dominating structural element which is present in both structures. Due to the fact that Cs is a much stronger scatterer than 0 (heavy atom approximation), this structure element should be the adsorption site of Cs. The single-beam r-factors are indicated. The overall r,-factor is 0.42. (b) Atomic coordinates for both phases as found by conventional LEED analyses. AX

fi

phase

H. Over et al. /Surface Science 314 (1994) 243-268

a)

0 ‘e’o

r, = 0.30

*

&y".28

W2,O)

w2, *,,

(1,1/2) w (312, 0)

~rP=Ct.13 rP = 0.21

(3/2,1/2) M -

m-n

Ru@OO1)-Cs-0 (2d3x2d3)R30° RuOC+I1Ks ~(2x2)

(Expt.1

300

100 Ener~

/

400

eV

Fig. 11. (a) The favored model for the Cs-O-Ru(OOOl)-(26 X2fi) phase. The right panel shows the schematic LEED pattern. Common LEED beams are indicated by large black circles. (b) Half-order LEED spectra of the pure CsRu(OOOl)-2x 2 phase compared with respective IV data collected for the Cs-O-Ru(ODO1)-(26 X26) phase. The close similarities in N curves of both phases strongly suggest the same Cs adsite. The single-beam r-factors are indicated. The overall r,-factor is 0.24.

compared X fi)R30”

with the system.

pure

Cs-Ru(OOOl)-(6

3.2.2. Cs-0-Ru(OOOl)-(2\/3 x 2fi)R30° structure Starting with a pure RuKlOOlM2 x 2)-Cs surface, after exposure to oxygen, a well-ordered (2& x 2filR30° structure is evolved containing three Cs and two 0 atoms in the unit cell. In the (26 X 26)R30° LEED pattern the (2 x 2) spots prevail, signaling that Cs atoms very likely form a

255

pseudo-(2 X 2) lattice; recall that Cs is a much stronger scatterer than 0. Typical 2fi spots, on the other hand, are then essentially a consequence of the oxygen position in combination with small distortions of the Cs overlayer. A comparison of the half-order IV curves of both the Cs-(2 x 21 and the coadsorbate phase (26 x 26jR30” shows striking similarities (see Fig. lib), thus indicating that the Cs atoms remain (nearly) in the same location, namely the on-top position. This similarity is also corroborated by an overall r-factor of 0.24. We are again faced with the heavy atom approximation which allows us to find the Cs position in a quite direct way starting from the information about the corresponding “clean” Cs(2 x 2) phase. For this special system the knowledge of the Cs adsorption site is of particular importance since at least three Cs and two 0 atoms have to be taken into account and also the first Ru layer as an additional overlayer (12 Ru atoms) has to be included. This makes LEED intensity calculations very computing-time consuming. Distortions in the first Ru layer have already played a significant role in the structure analysis of the pure Cs-(2 x 2) phase [141 to achieve a low r-factor and thus to render this structure analysis more reliable. Accordingly, one expects that distortions in the first Ru layer will play the same important role also for the analysis of the (26 x 2fi) phase. Automated structural refinements including the positions of the two oxygen atoms and distortions of the Cs overlayer as well as the first Ru layer are currently underway. The most promising model found so far favors a model which is schematically depicted in Fig. lla [43]. It is evident that the Cs position remains almost on-top as had been found for the Cs(2 X 2) structure. 3.3. Molecular adsorption on metal surfaces In this section, we report results on molecular adsorption of nitrogen on Ru(OO01) in comparison with CO adsorption on the same substrate surface. Roth molecules form an ordered (6 X filR30” overlayer structure. The (fi X filR30” structure of CO/Ru(OOOl) has al-

H. Overet al/Surface Science314 (1994)243-268

-

N2/Ru(OOOl)

-

CO/RtJ(0001)

"-_

C- and N-induced Ni(lll)-c(5fi x 9)rect structures produce LEED ZI/ curves which are very similar [46], thus underpinning this view. Therefore, alone from inspection by eye it is possible to infer that also the N, molecules reside in on-top positions with the molecular axis perpendicular to the surface plane. The N-Ru and N-N bond lengths should be comparable to those found with the CO/Ru(OOOl) system. Most recently, Bludau et al. confirmed this prediction by a LEED structural analysis [16].

rp = 0.21

(213, 213)

(413, 113)

3.4. Adsorption of metal atoms on the (111) surface of Si and Ge

50

100

150

200

250

300

Energy /eV Fig. 12. From the similarities of IV data for N, and adsorbed on Ru(OO01) in a (fi X 6) lattice it is evident CO and N, molecules reside in atop-positions with molecular axis perpendicular to the Ru(0001) surface The single-beam r-factors are indicated in the figure. overall r,-factor is 0.38.

CO that their [16]. The

ready been the subject of LEED structure analyses [44,45]. These studies clearly indicated that CO molecules are adsorbed through their carbon atoms over single Ru atoms (i.e., in “on-top” position) with the molecular axis being normal to the surface plane. The Ru atom coprdinated with CO is displaced outwards by 0.07 A. A comparison of II/ curves for N, and CO adsorbed on Ru(0001) is depicted in Fig. 12. Both sets of II/ curves reveal a remarkable similarity in a sense that the same sequence of peaks and valleys appears (the respective overall r-factor is rP = 0.38). Only small shifts of peaks at lower energies (I 100 eV> allow one to distinguish between these two systems. It is known that the particular form of phase shifts is more important in the low energy range than for energies greater than, say, 100 eV. Additionally, the atomic numbers of N, C and 0 differ only by &-1 so that similar phase shifts are expected; compare also Fig. 13 where polar plots of the scattering amplitudes of N, C and 0 at an energy of 100 eV are shown. A very recent LEED study has shown that

The atomic structure and bonding of metal atoms on semiconductor (Si, Ge) surfaces have been the focus of many studies over the past 30 years in order to gain general insight into the formation of metal-semiconductor interfaces as prompted by important applications. A number of reconstructions have been observed on these surfaces upon metal adsorption [47-501. For instance, the adsorption of both Ag and Li atoms on the (111) surface of Si as well as Ge under certain conditions induces a (6 x fi)R30” re-

Fig. 13. The atomic numbers of N, C and 0 differ only by k 1 so that corresponding phase shifts are similar as demonstrated by respective polar plots of the (single-atom) scattering amplitude at 100 eV.

H. Over et al. /Surface

Science 314 (1994) 243-268

257

order to satisfy two of the three dangling bonds per unit cell. The remaining dangling bond is terminated by bonding with Ag atoms so that an atomic arrangement is created where no dangling bonds are left, Another frequently observed surface structure is the (3 x 1) phase which is formed by adsorption of Ag and Mg on Si(ll1) as well as with alkalimetal adsorption on either Si(lll) or Ge(ll1). The geometric configuration of the (3 X 1) structure remains, however, still elusive and has not been determined in detail so far. Both kinds of surface structures, the (3 x 1) and the (6 x 6) phase, are quite interesting as far as the potential of fingerprinting ideas in LEED is concerned: For each of these phases for a given substrate, the IV curves turned out to be very similar irrespective of the deposited metal species. The actual comparison of the experimental IV curves can be found in the literature [17,23,49,64-671.

s Fig. 14. Schematic of the honeycomb-chained trimer model (HCT) which has been found to represent the (6 XV!?) Siflll) surface structure induced by various metal adsorbates: M = Ag, Li, and Mg. Staggered-shadowing circles represent Si trimers which form the basic structural elements of these surfaces. Large and hatched circles represent the metal atoms.

construction whose atomic geometries were believed to be readily determined due to the small size of the unit cell. Yet, the derivation of the ultimate geometric structure of the Ag/Si(lll)fi x fisurface, for example, took more than 20 years with application of almost every surface analysis technique. The breakthrough was reached for this system with X-ray diffraction experiments which firmly established a honeycomb-chained trimer model (HCT) [51,52]. This HCT model has subsequently been corroborated by alternative techniques [52-601 (except LEED) foremost among which are STM [59,61-631 and total energy calculations [601. In the HCT model (Fig. 14), the Ag atoms substitute the top Si layer at positions slightly displaced laterally from bulk sites. The Si atoms in the layer below then form trimers located over the fourth layer Si atoms in

3.4.1. Metal-induced Si(lll)-(6 X fi)R30” reconstruction Recently, LEED N data of the metastable clean Si(lll)-(6 x fi)R30° phase and the (6 x &)R30” phase induced by adsorption of different metals like Ag and Li have been shown to be remarkably similar to each other [17,65]. The weak influence of the metal atoms on the IV spectra led to the speculation that the metal atoms do not participate in the long-range ordering in these systems and thus provide no contributions to the LEED intensities; note that conventional LEED only probes the ordered part of a surface structure (cf. Section 2) and that Ag and Li are very different from one another in their scattering properties. However, such a conclusion is at odds with findings on the Ag-fi-Si structure obtained by many other techniques which clearly supported a model in which the Ag atoms form a flat layer in a honeycomb-chained trimer arrangement. In a very recent LEED structure analysis, this puzzle has been unraveled [18]. It has been shown that similarities in IV spectra of different metalcovered systems are due to the presence of common and predominant “scattering blocks” of

258

H. Ouer et al. /Surface

near-neighbor Si substrate atoms [68]. These scattering blocks with essentially the same short-range order in the different metal-induced surface structures produce similar features in the N data, particularly for the fractional-order beams. Furthermore, the weak influence of the metal atoms on the II/ data was rationalized in terms of a pseudo-(1 x 1) configuration where the metal atoms are located at “open sites” on the Si lattice. Thus, in the kinematic picture single scattering of metal atoms will not strongly contribute to the LEED intensity of fractional-order beams; the only way for metal atoms to contribute is through a higher-order scattering of nearby Si atoms. Because the IV spectra were measured at normal incidence, the strongest scattering path involving a metal atom is that between it and the Si atom directly underneath (dominant forward scattering). A weak influence of the metal atom therefore requires that this metal-Si vertical distance is large. It is immediately clear that this requirement is met with the coordination of the Ag atoms in the HCT model (see Fig. 20). In this model, the Ag atoms are located above the $th layer Si atoms with an Ag-Si distance of 6.7 A. Qualitatively, the measured Ii/ data of the Lia-Si surface show great similarities with those of the Ag-a-Si system so that the geometric parameters found with Ag-a-Si can serve as a promising starting configuration for an automated search by dynamical LEED for the Li- fiSi system. In doing so, the Li-a-Si surface was easily determined. The Si(lll)-(6 X fi)R30”-Au system, on the other hand, offers an interesting counter example. The experimental ZY data for this system are different from corresponding data of the Ag and Li systems which points towards different dominating “scattering blocks”. Indeed the main structural feature in the Au-a-Si is that Si trimers in the second layer are absent; instead, Au atoms in the top layer are trimerized which center over fourth-layer atoms [69-711. This model is called conjugate honeycomb-chained trimer (CHCT) model after Ding, Chan and Ho

WI. For the Ge(ll1) substrate, the same phenomenon has been observed. Fan and Ignatiev

Science 314 (1994) 243-268

[64] have pointed out that the LEED ZV spectra for the (6 x fi)R30” structure of Ag/Ge(lll), Li/Ge(lll) and a clean Ge(ll1) metastable reconstruction are also very alike. The comparison with corresponding Si(lll)-(6 x fi)R30” phases leads to the surmise that in these Ge(ll1) systems common scattering blocks are present which are formed by second layer Ge trimers in combination with distortions in deeper Ge layers. Also the weak influence of metal atoms on the II’ curves points toward a location of these atoms at “open sites”. Finally, in the clean (6 X fi)R30 phase of Ge(lll), no ordered metal atoms are involved. As a consequence, the common scattering blocks must consist solely of substrate atoms. Very recently, Huang et al. [72] have carried out II/ spectra analysis for Ag-Ge(l1 l)-(43 x &)R30” based on dynamical LEED calculation and have provided quantitative support for this description. Using the above reasoning, we expect that with Li- fi-Ge the same near-neighbor scattering block of Ge atoms exists and thus strongly favor a HCT model, although the precise atomic coordinates have not been determined because of a limited data base. 3.4.2.

(3

X

1)

reconstructions

on

Ge(ll1)

and

Si(lll)

At submonolayer coverages of metal atoms, a (3 X 1) reconstruction of the Si(ll1) as well as of the Ge(ll1) surface can be induced. These phases have been reported for Ag and Mg on Si(ll1) [49,64,66,67] and alkali-metal adsorption on either Si(ll1) or Ge(ll1) [50,64,66,67]. In several recent qualitative LEED studies, it has been pointed out that many of the (3 x 1) phases cited above exhibit very similar ZP’ curves [64,66,67]. This led to the conclusion that these phases have similar structures and that the different metal adsorbate atoms do not participate in the (3 x 1) long-range ordering. The (3 X 1) structure has been attributed to a reconstruction of the Si(ll1) and the Ge(ll1) surfaces that is stabilized by the presence of the metal species, but metal atoms do not form a (3 x 1) overlayer at all. Indeed, detailed STM studies [63,731 have shown that both the filled and empty-state STM images of the (3 X 1) re-

H. Over et al. /Surface Science 314 (1994) 243-268

construction of Si(ll1) induced by Li and Ag adsorption are likely to represent the same structure. However, the STM images showed no evidence of any structural disorder that might be associated with the metal atoms. Comparing the situation for the (3 x 1) structures with that of the (6 x 6) structures, it seems therefore plausible to propose a model where the dominating and common “scattering block” consists of substrate atoms and metal atoms again located at “open sites”. A LEED structure analysis has, however, so far not succeeded to determine the atomic positions of the Na-Si(lll)-(3 x 1) structure [74] (and via fingerprinting technique the other metal-induced (3 x 1) reconstructions). In particular, the missing top-layer model proposed by Wan et al. [73] was extensively examined. This model consists of parallel r-bonded chains of Si atoms (which could serve as dominating “scattering blocks”) where the dangling bonds in each chain are capped by Na atoms.

3.5. The O/Rh(llO)

0

0

. . 0

0

0

system

The O/Rh(llOl system has been shown to be very interesting from a structural point of view due to the presence of a rich variety of LEED structures depending on the 0 coverage and the sample temperature [75-791. In particular, adsorption of 0 at 120 K leads to a (2 x l)pg structure which is stable for temperatures up to about 450 K over a wide coverage range indicating island growth. If this phase is annealed at 700 K, several ordered phases are formed (depending on the initial oxygen coverage) among which the (2 X 2)pg and the c(2 X 8) structures will be inspected here more closely. As a peculiarity of this system, hydrogen or CO reduction of these two phases results in (1 X 2) and (1 X 4) structures which are metastable and revert to (1 X 1) at temperatures above 480 K 178,791. The (1 X 2) structure has been shown to be of the missing-row type 180,811 so that it is obvious that the c(2 x 8) and the (2 x 2)pg structure may contain a (1 x 4)

lh(110) -(2x1) PgdC

. .

259

I

.D.O

Rh(ll0) 4x2) “Missing Row”

I

0.0.

Starting configuration for automated refinement Rh(ll0) 42x2)~20

Fig. 15. The utility of fingerprinting ideas for solving the structure of the O-(2 X 2)pg arrangement on Rh(ll0) is illustrated here. The similarity in fractional-order Iv data of (1 X 2) and (2 X 2)pg structures (associated with the (0, l/2) beam set) points towards the same substrate reconstruction, namely the missing-row reconstruction, while the similarity of N data related to the (l/2, 0) beam set ((2 x 1)pg in comparison with (2 x 2)pg favors the oxygen position to be over the second Rh layer coordinated to two Rh atoms in the first Rh layer [19].

H. Over et al. /Surface

260

Science 314 (19941 243-268

and (1 x 2) missing-row-type reconstruction, respectively, as one of the major structural elements. STM studies have explicitly shown this type of reconstruction to be present and have further revealed that the (1 x n) (n = 2, 4) consists of missing rows, spaced by n substrate lattice vectors [82,83]. The adsorption of oxygen onto these reconstructed Rh(l10) surfaces is supposed to finally produce the phases ~(2 X 8) and (2 X 2)P!%

The atomic coordinates of the low-temperature Rh(llO)-(2 X l)pg-0 phase has been determined in a very recent LEED structure analysis. The adlayer model derived consists of oxygen zigzag chains where the 0 atoms are located in threefold-coordinated sites in touch with two Rh atoms in the first Rh layer on an otherwise undistorted Rh(ll0) surface [19] (see Fig. 15). Now let us turn to the (2 x 2)pg structure which consists of (1 X 2) missing rows as mentioned above. In order to get some information about the adsorption geometry of the 0 atoms,

i 1

\*\J, .

/’

rp=0.29//\

4

I/

/ ‘, ,r\ ” \ ’ L/

LEED has been taken as a fingerprinting technique: The IV curves of common fractional-order beams of the (2 X 1)pg and the (2 X 2)pg structure (see Fig. 21) have been compared (corresponding r-factor is 0.29). This comparison suggests that oxygen atoms reside in threefold-coordinated sites in both phases. Therefore, only three promising models are left (serving as starting configurations in an automated structure refinement) in which the oxygen atoms are located in threefold sites above the second Rh layer (twoand onefold coordinated with respect to the Rh atoms in the first layer) and alternatively above the third Rh layer. The best-fit model obtained by this LEED analysis [19,79] comprises a missing-row reconstruction with 0 atoms located in threefold sites above the second Rh layer; the oxygen atoms are coordinated to two Rh atoms in the first layer (cf. Fig. 15). A quite complex Rh-0 structure represents the c(2 x 8)-phase which is built up by a (1 X 4) missing-row reconstruction [83] together with an

(l/2,1) ’ ‘, (2x2) --L

(1/2,7/8)+(1/2,9/g)

Energy / eV

Fig. 16. N data belonging to the (l/2, 0) beam set from the (2 X l)pg, (2 X 2)pg and ~(2 X 8) structure are presented. The sum of IV curves (l/2, 7/S) and (l/2, 9/8) is the natural substitute for the (l/2, 1) data from (2 X 1)pg and (2 X 2)pg; note that in the c(2 x 8) phase no (l/2, 1) beam exists. Their close similarity points towards the same adsorption site of oxygen (small filled circles) [84,8S]. A tentative model for the c(2 x 8) structure, compatible with models found for the (2 X 1)pg and the (2 X 2)pg phase, is shown. The r-factors with respect to the (2 X 1)pg structure are included.

H. Over et al. /Surface

oxygen adlayer on this reconstructed surface. The question to be addressed concerns the oxygen adsorption sites. In Fig. 16, the N curves of the (l/2, 1) beams of the (2 X 1)pg and (2 X 2)pg phases are compared with the averaged IV spectra of the (l/2, 7/8) + (l/2, 9/8) beam in the c(2 X 8) configuration from which a remarkable similarity is evident [84] as quantified by rr = 0.20 [85]. As a consequence, the oxygen atoms are expected to sit in threefold-coordinated positions most likely coordinated to two Rh atoms in the first Rh layer as suggested by the 0 positions found in the (2 X 1)pg and (2 X 2)pg systems. An averaging of the (l/2, 7/8) and (l/2, 9/8) beam is required because no (l/2, 1) beam is present in the c(2 x 8) phase. The 0-p(2 X 1)pg zigzag chains (designated A and B in Fig. 16) are parallel-shifted along the [liO] direction by one substrate-lattice vector that makes up the c(2 X 8) phase. The 0 zigzag chains are furthermore chosen in a way that they are related to those already found with the (2 x 1)pg and (2 x 2)pg structures. The local 0 coverage of 3/4 is consistent with the reported coverages for the c(2 X 2n) structures [76-791: the 0 coverage is varied continuously from 0.5 to 1.0 by adjusting the number of missing rows according to the relation (n - 1)/n [82]. While this model is compatible with experimental observations, it is yet tentative, and further investigations are needed to solve the detailed atomic structure. Currently, a full dynamical LEED structure analysis of this system is underway [85].

Science 314 (I 994) 243-268

261

not desorption of CO or a phase transformation of the CO structure takes place. To that end, the ZV data of the electron-induced (2 X 2) structure can be compared with corresponding data of the clean (2 x 2)-O-Ru(0001) phase. The close similarity of both sets of N data points directly towards a (2 X 2) structure formed by oxygen, thus clearly indicating that the conversion from the fi x fi into the (2 X 2) phase is due to decomposition of CO molecules. 3.6.2. Cs-O-Ru(0001) system Upon oxygen exposure to a Cs-covered Ru(0001) surface with a Cs coverage smaller than 0.15 (exhibiting no LEED pattern), the evolution of a (2 x 2) LEED pattern has been observed 1411.A comparison of measured IV data (Fig. 17) with corresponding ZV data from the (2 X 2)-ORu(0001) phase reveals that the (2 X 2) phase is built up by oxygen rather than by an ordered Cs-0 mixed phase. This conclusion is corroborated also by IV curves of the pure Cs-(2 X 2) phase which are significantly different from those found here. The averaged r-factor between IV

3.6. LEED fingerprinting providing an experimental “technique” 3.6.1. CO dissociation on Ru(0001) During observation of the LEED pattern of a CO-(fi X 6) layer, the intensity of fractionalorder beams diminishes gradually as a function of time and a (2 X 2) pattern evolves. This effect is obviously the consequence of an electron-induced damaging of the CO-(& x fi> overlayer. This was also previously observed by Madey and Menzel [86] using vibrational spectroscopic methods. Alternatively, LEED may also be used for showing that in fact dissociation/ decomposition and

0

50

100 Energy /eV

150

200

Fig. 17. Oxygen exposure to a Cs-precovered Ru@OO1)surface (@c, = 0.15) produces a (2 X 2) LEED pattern. Corresponding fV data compared to IV curves from the (2X2)-O-Ru(0001) phase and the (2 x 2)Cs-R&001) phase demonstrate that the ordered part of the Cs-O-Ru(OOO1) surface is built up by oxygen rather than by a Cs-0 compound [41]. The averaged r-factor between IV data from the O-(2 X 2) and (2 X 2)-Cs-0 is 0.21, while that between the systems (2 x2)-Cs and (2X2)Cs-0 is 0.63.

H. Over et al. /Surface

(1,l)beam

40

80

120

Re(1010) - clean

160

200

240

280

320

360

Energy (eV) Fig. 18. N curves of the Re(lOi0) surface obtained by Davis and Zehner [SS] are compared with those collected by Lenz [87]. The marked difference of these data is due to different relaxation properties of Re(lOi0) which in turn are determined by the cleanliness of the sample. While (D-Z) data yield a contraction of the layer spacing, L data indicate an expansion as revealed by LEED calculations. data from the 042 x 2) and (2 x 2)-Cs-0 is 0.21, while that between the systems (2 x 2)-Cs and (2 X 2)-Cs-0 is 0.63.

3.6.3. Checking of the substrate quality LEED spectra of clean surfaces are quite sensitive to the sample quality. For the clean Re(lOi0) surface, e.g., it has been observed [87] that presumably small amounts of contaminations or disorder/ defects of the surface (which remove the contraction of the first layer spacing) result in IV curves which are markedly different from those having already been published [88] (see Fig. 18). A quantitative LEED analysis [89] on the basis of this new data-set indicates an expansion of the first Re layer spacing rather than a contraction as found for similar surfaces like Co(lOi0) [90,91] and Ti(lOi0) [92] and which is also at variance with a LEED analysis performed by Davis and Zehner on the same surface [SS]. 3.7. Epitaxial growth of metals on metal substrates In this section, our interest will concentrate on the important role that LEED plays in the study

Science 314 (1994) 243-268

of epitaxial growth of metal films on metal substrates, mostly focused on pseudomorphic growth; note that here alterations of ZV data of integerorder beams are considered. This application of LEED goes back to studies performed in Jona’s group [93]. Besides the qualitative inspection of the LEED pattern for characterizing the symmetry and the degree of order of the sample, measurements of LEED ZV curves collected for changing conditions of deposition often provide information on the particular growth mode, and less often on quantitative data of the atomic structures of ultra-thin films and metal-metal interfaces. If layer-by-layer (LBL) growth is observed (see Fig. 191, LEED analyses can be used for determining the atomic coordinates of the depositsubstrate combination. In the submonolayer regime the background of the LEED pattern increases slightly with the coverage and the IV data begin to change if compared with data of the pure substrate. When the first monolayer is completed, the background intensity gets again lower and the IV data are characteristic of an ordered overlayer structure which can be subject to a conventional LEED analysis. Illustrative examples are a pseudomorphic monolayer Cu grown on Pd(001) [94] and Fe on A~(0011 where Fe

d)

c)

b)

a)

(LBL)

WWl)

WW2)

Fig. 19. Development of an epitaxially grown metal film on a substrate surface according to layer-by-layer (LBL) mode and the island (Volmer-Weber) growth (VW). In each panel, the substrate is indicated schematically by a shadowed box. The amount of metal deposit increases from (a) to Cd). (VWl) and (VW2) represent two possible realizations of island growth that have been observed experimentally. LE = layer equivalent as defined by AES supposing uniformly distributed layers [1021.

H. Over et al. /Surface

atoms act as surfactants [95]. The completion of consecutive layers can be monitored and analyzed in the same way. The corresponding IV data change gradually with the number of layers until they finally become stable and exhibit N data related to the bulk material of the deposit, see for example the system Mg/Ru(OOOl) [96]. In the case of three-dimensional island growth (Volmer-Weber VW: VW1 and VW2 in Fig. 19), on the other hand, less quantitative information is available. Yet, differences between LBL and VW are evident by the evolution of LEED spectra with deposition. In the initial stage, small three-dimensional metal islands formed on the substrate enhance the background of the LEED pattern but do not change the IV curves (in contrast to LBL growth!) With continuing deposition (Fig. 19b) the background increases further, and in both cases, VW1 and VW2, the LEED spots become broader compared with the clean substrate because regions of clean surface are now smaller. While in case VW2, the N curves remain unchanged to those of the clean surface, in case VWl, the LEED spectra begin to get different due to contributions from both the bare patches of substrate and the flat tops of deposit islands. At an even later stage (Fig. 19~) in case VWl, N data are almost unaffected by the substrate, rather they are dominated by flat-top is-

40

80

120

160

200

240

Energy WI Fig. 20. Experimental LEED spectra of the (10) and (11) beam of the Fe(ll0) surface. The sum of these N curves is compared with the overall LEED intensity of the SLEEDspot-cluster = first-order beam (as a function of the energy) from a 6 LE-thick Fe film on Ru(OOO1)[99].

Science 314 (1994) 243-268

263

lands with different heights. In case VW2, the LEED pattern vanishes. Examples for both types of VW growth are Fe on Pd(001) (VW11 [97] and Fe on Ag(OO1) (VW21 [98]. A particularly interesting example as far as fingerprinting in LEED is concerned represents the Stranski-Krastanov growth mode of Fe on Ru(0001) [99]. The first monolayer of Fe is pseudomorphic with the hexagonal Ru(OO01) lattice with Fe occupying hcp sites. Thicker films give rise to a complex LEED pattern comprising clusters of five spots around the positions of the Ru(0001) 1 x 1 pattern. This LEED pattern has been explained by the superposition of rotationally equivalent domains of two equivalent Kurdjunov-Sachs orientations of bee Fe0101 on Ru(OOOl), thus indicating the growth of three-dimensional domains of bee Fe(ll0) onto the hexagonal net of pseudomorphic Fe on Ru(0001). This view was strongly supported by the striking similarity of N curves of the cluster of LEED spots in Fe/Ru(OOOl) with the averaged experimental IV curves of the (10) and (11) beams of clean bee Fe(ll0) [lo01 (cf. Fig. 20).

4. Concluding

remarks

Several examples were presented where the concept of fingerprinting has been successfully applied to facilitate structural analyses by proposing a promising guess of starting configuration and to gain information of the local ad-geometry quasi-directly. In the context of automated structural refinement, this method is particularly fruitful, if coadsorbate systems are considered as exemplified with the O-Cs-Ru(OO01) system. The application of fingerprinting is not restricted to structure analysis by LEED but also gives direct evidence of phase transformations even if the periodicity of these structures persists. As shown in Jona’s group, fingerprinting ideas are also suitable to quantify epitaxial growth of metals on metals and to discriminate between layer-by-layer mode and Volmer-Weber mode of growth. The “quality” of substrate surfaces can readily be checked by comparing IV data with data known from the literature and hence ensure unique con-

264

H. Over et al. /Surface

ditions in different laboratories. It is furthermore possible to monitor the decomposition of adsorbed molecules if the fragments are able to form their own superstructure. Structural insight through comparison of ZV curves of surface structures with known atomic geometry with those to be analyzed does therefore call for a data bank of experimental IV curves; or at least every publication of a structure analysis by LEED should contain all experimental IV curves used in the analysis so that inspection and comparison by eye can be done. The advantage of a data bank, however, would be that r-factors can readily be calculated.

Science 314 (1994) 243-268

+ik,,r,

Xe

ei(ktj-ks)r, Ii

=

j$lfi(k,, ko) ei(k[J-kx)rl

(AlI

given in the giant matrix notation [loll. X comprehensively comprises the effect of multiple scattering which is zero in the kinematic limit. Using the relation between Legendre polynomials Pr and spherical harmonics Y,,,, (the addition theorem [loll), the scattering amplitude in the kinematic limit can be expressed as A@) n

=c j=

Acknowledgements

The authors thank W. Moritz and H. Wohlgemuth for fruitful discussions as well as M. Richard for technical assistance. H.O. acknowledges a post-dot scholarship from the Deutsche Forschungsgemeinschaft and also appreciates the hospitality of the Laboratory for Surface Studies at the University of Wisconsin/ Milwaukee (UWM) during his extended stay. M.G. is grateful for financial support by the Laboratory for Surface Studies at UWM. Work at UWM was supported by ONR Grant No. N00014-90-J-1749 and NSF Grant No. DMR-9214054.

Appendix A. Renormalized the giant matrix notation

scattering

factor

in

To elucidate the relationship between the renormalized form factor fj of atom j and the ordinary description of the scattering amplitude A, within the framework of multiple scattering, let us consider the following formula A,(E)

I

Xe i(k,,-k&r,

Xe i(k,,-k,P, -A&E)

=

2 fj(kg

- k,,) ei(kc)-kg)rl.

(A21

j=l

Recall that k,kO = (k, - k,)’ - 2E. Formula (Al) resembles very much that used for intensity calculation in the kinematic theory; in kinematic theory, each electron incident on a surface is diffracted only once by the surface. The only difference is that in the kinematic theory the atomic form factor f, is determined solely by the atomic scattering matrix of atom j and hence the momentum transfer k, - k, (cf. Eq. (3)). If multiple scattering between atom j and its neighboring atoms comes into play, f, depends separately on k, and k,. Thus, f, is not only determined by the atomic scattering matrix of atom j but also by the scattering properties of its surrounding atoms.

Appendix B. Important local scattering picture

scattering

paths

in the

In this section, we will examine the conditions under which the local scattering picture is valid,

H. Over et al. /Surface

Science 314 (1994) 243-268

265

i.e., the LEED N curves of fractional-order beams are independent of the coverage in overlayer structures. Let us consider at first a single atom which is adsorbed on an otherwise unreconstructed substrate surface (with 1 X 1 periodicity). Exclusive scattering among substrate atoms contributes only to the intensity of (1 x 1) LEED beams. As a consequence, each scattering path participating in the LEED intensity of fractionalorder beams must encounter the adatom at least once. According to Eq. (Al), the scattering amplitude is given by A(&“, 7 k,)

= c e-ik~@Tvp( cL,u

k,,,,

ki,) ei“inpw W)

with T,,( k,“, ) kin > 16r2i = jm$m, A ( k,,,,,

Fig. 21. (a) Typical scattering paths participated in the diffraction of low-energy electrons at a single atom adsorbed on an undistorted surface. (b) Going from a single atom to a layer of adatoms having the same local geometry, the indicated scattering paths have to be excluded so as to maintain the local scattering

X (1 - X)[mu,lfm,~Lt~~)i-“Y~~_*~( k,),

(B2)

where pi is the coordinate of the adatom and p,, (CL# 1) represent the coordinates of the surrounding substrate atoms. The matrices Tv&kOuf, kin) summarize the effect of all scattering paths which start at atom p (incident wave field kin) and finally scatter off atom v in direction k,,,. This formula can further be rearranged in a way that all scattering paths are assigned to four specific types which are illustrated in Fig. 21a:

Finally, the term D contains all scattering paths which start and end up at substrate atoms and encounter at least once the adatom on their way. In the next level of detail we consider a layer of atoms adsorbed on an undistorted substrate surface. All adatoms are supposed to have the same local geometry with respect to the substrate atoms. Neglecting all scattering paths which contain scattering events at different adatoms, the scattering amplitude can be written as: A(ko,t

A(&“, A

f

kin)

= T,,, c

ce

kin)

=

B =

c

T,,

ei(kin-kour)llr,(

A

+ B + C + D),

(B4)

TV, e-%t(Pv-pl),

where r, are the positions of the adatoms. The LEED intensity can thus be separated into a form factor F and a lattice factor G, where only F is dependent on the energy of the incident electrons and equals the corresponding expression for the scattering of a single adatom:

eiL(p,,-pl),

-ikodPu-PI)(

f j=l

CL+1

D=

9

= ei(k~n-kout)Pl( A + B + C + o),

U#l c =

picture.

( i’( - l)m~~(kO”t)

Tvp

_

T;‘bstr)

eikdP,-P1)_

@#I V#l

(B3) In A, all scattering paths which start and end up at the adatom are included. B (C) contains all scattering that starts at the adatom (substrate atoms) and ends up at a substrate atom (adatom).

I= IF/‘.

ICI2

with

F=A+B+C+D

and

G = 2

ei(k~n-kwt$r,.

j=l W)

2hh

H. Oner et al. /Surface

It is important to notice that G is energy-independent due to the experimental fact that ki, k C,Utis kept constant. In this approximation up to a constant prefactor, the IV curves of fractional-order beams are independent of the coverage and of the long-range order of the adatoms. Of course, this implies that all scattering events which link at least two adatoms are to be excluded. There are two types of such “bad” scattering paths as illustrated in Fig. 21b. The first one is intralayer scattering within the adlayer which can usually be neglected. The second type of scattering paths are those which link more than one adatom via the substrate and limit seriously the validation of the local scattering picture if the ad-ad distance becomes too small and the adatoms are strong scatterers. For adsorbates being weak scatterers the influence of this kind of scattering is small even for a coverage of 8, = 0.5, as has been demonstrated with the Ru(OOOl)-0 system (Section 3.1.2).

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