Experimental results from spectroscopic ellipsometry on the (7 × 7)Si(111) surface reconstruction: dielectric function determination

ELSEVIER

Surface Science 341(1995)

202-212

Experimental results from spectroscopic ellipsometry on the (7 X 7)SiO 11) surface reconstruction: dielectric function determination Z. Hammadi *, M. Gauch, P. Miiller, G. Quentel Centre de Recherches sur les M&anismes

de la Croissance Cristalline ‘, Campus de Luminy, case 913, F-13288 Marseille Cedex 9. France

Received 16 November 1994; accepted for publication 11 May 1995

Abstract The dielectric function of the (7 X 7) Si(l11) surface has been directly determined in UHV conditions by ellipso~etric measurements on a Si( 111) clean surface. The dielectric function obtained from ellipsometric spectra near the pseudo-Brewster angle (PB) has been calculated by means of a three-phase model (bulk, (7 X 7) transition layer and vacuum) in which optical properties of bulk Si are deduced from literature data and the thickness of the (7 X 7) transition layer is taken from the DAS model. Our calculation allows us to confirm the metallic character of the (7 X 7) transition layer and to point out

the previously found surface-state transitions at 2.6 and 3.4 eV and perhaps at 1.6 eV. Furthermore,a surface-statetransition has also been confirmed at 3 eV. Ellipsometric results depend on the crystallographic direction. This optical anisotropy is ascribed to some roughness anisotropy induced by steps. Keywords:

Ellipsometry; Low index single crystal surfaces; Silicon; Surface electronic phenomena

1. Introduction

(1 X 1) surface phases 121. The present work deals

The clean Si( 111) surface is characterized by a (7 X 7) superstructure below the transition temperature T, (- 830°C). This very stable reconstruction is generally easy to obtain: its atomic structure within the unit cell is thought to be described by the now classical DAS model [ 11 (dimer-adatom-stackingfault). The enhanced surface sensitivity of spectroscopic ellipsometry at the pseudo-Brewster angle has already allowed us to distinguish the (7 X 7) and

??

Corresponding author. E-mail: [email protected].

I Laboratoire associt aux universids II et 111. 0039-6028/95/$09.50 0 1995 Elsevier Science SsD/ 0039-6028(95)00592-7

B.V. All rights reserved

with the determination of the dielectric function, Ed,x ,) of the (7 X 7) phase at room temperature from the experimental ellipsometric results in the two crystallographic directions <[I101 and [211]) as determined by reflection high-energy electron diffraction (RHEED). Let us stress on the fact that optical properties of the Sic1 11) surface have already been gathered from ultraviolet photoemission spectra (UPS [3]), energy loss spectroscopy (ELS [3,4]) and reflectometry [5,6]. In such experiments, the surface-state transitions were derived from the electronic staate density difference between the clean Sic11 1) surface and the adsorbate-covered Si surface. In this paper, the di-

Z. Hammadi

et ~1. / Surjke

electric function of the (7 X 7) superstructure (noted as E~,~,)) is directly ded uced, without means of an adsorbate. In our three-phase mode1 [7], we used the well-known Aspnes data [8] for the bulk Si dielectric function and the DAS mode1 [l] to obtain the (7 X 7) superstructure thickness. The (7 X 7) superstructure evolution with the substrate temperature has also been studied using RHEED and ellipsometry; it will be published in a following paper.

2. Experimental Experiments were performed in a UHV chamber ( < IO- lo Torr). The silicon wafer (commercial CZ Si(l1 I), misorientation along the zone [liO] < 0.5, p-doped, p = 2 fi . cm-’ *OS), first degreased (with alcohol, trichloroethane and acetone), is cleaned in situ by flashing at 1150°C; it is then annealed at 700°C during 20 min in a vacuum of the order of IO-” Torr. The silicon is heated by Joule effect (dc current) and its temperature is pyrometrically controlled. After such a procedure, a clean (7 X 7) reconstructed silicon surface is reproducibly observed by RHEED (see Fig. I>. The RHEED apparatys uses a 20 kV energy electron-beam (A = 0.08 A) which strikes the surface at a glancing angle of approximately 1”. The experimental in situ arrangement allows us to switch from the RHEED analysis position to the ellipsometric configuration by a simple rotation of the crystal holder along its z-axis. Ellipsometry is now a currently used optical technique [9,10] which measures changes in the state of polarization ( p = tan 9 eiA) of an incident monochromatic light after reflection on a surface sample. The polarization state of the reflected light at Brewster incidence depends strongly on the surface properties [2,11,12]; we briefly state the physical principle involved before describing the ellipsometer. 2.1. Ellipsometry

at the pseudo-Brewster

angle

It is known that for a perfect dielectric material, irradiated by an elliptic polarized light at the Brewster angle, the reflected light is s-polarized (linearly polarized normal to the plane of incidence). This can be explained by considering electrons, in a dielectric,

Science

34 I ( 199.5) 202-212

203

as Hertzian oscillators which radiate no light in the direction of their oscillations; then, the only effective light component is the one perpendicular to the direction of the dipole oscillations. At the Brewster incidence tan * vanishes and cos d changes abruptly from - 1 to + I. But for a near dielectric material tan q is different from zero and the transition of cos A is not abrupt; one defines a pseudoBrewster angle when tan q is minimum. Because the transition of cos A is not abrupt a principal angle can be defined when cos A = 0 which is considered to be the pseudo-Brewster angle in the Si( I I I ) case. As a result, spectroscopic ellipsometry at the pseudo-Brewster (PB) angle is a very sensitive tool to study surface properties at an atomic scale such as the (7 X 7)Si( 111) reconstruction. 2.2. Ellipsometer Our automated ellipsometer (386 computer controlled) is built on the rotating analyser principle with the following sequence: Source, monochomator, shutter polarizer, sample, rotating analyser, PMT detector (Type 9798B S20/B). The beam of a quartz lamp is coupled to the enter slit of the computer-controlled monochromator (H. 10 Jobin-Ivon). The energizing monochromatic light goes through a lens which makes the exit slit image on the sample [ 131. The position of the polarizer, enclosed in a rotating mount driven by a computer controlled stepping motor, can be adjusted with a 0.001” resolution, in order to perform the calibration procedure. The optical inactivity, in our spectral range, of the calcite polarizer and analyser (glan Laser) avoids first order corrections. In the same way, UHV chambers windows (75 mm diameter, Crown BK7) are of interferometric quality and are mechanically mounted between helicoflex joint to prevent strain-induced birefringence; their slight deviation between the window axis and beam direction avoids multiple reflexion. In order to improve the measurement accuracy, the input signal of the 12 bits A/D converter is kept at a maximum constant voltage (9 V) through the feedback control of the PMT cathode voltage and automatic gain control of the amplifier stage. The accurate value of the incident angle is calculated from the Brewster transition energy with 0.1” accuracy for each experiment. In our experiments the

Z Hammudi

204

Fig. 1. RHEED Sic1

11)surface

beam is parallel

patterns of the reconstructed

(7 X 7) Sic1

where we have reported the directions to [Tl I] direction.

et uI./Surfuce

1I)

[ilO]

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341 (1995)

202-212

surface at room temperature

and [?I I]. (a) The electron

with a top view (b) of the reconstructed

beam is parallel to [TlO] direction.

(7 x 7)

(b) The electron

Z Hummadi et al./Surjbce

incident light is nearly p-polarized and strikes the surface at an angle of approximately 76” (see ellipsometer configuration in Fig. 2). Optimized precision of the measurement is also achieved by a variable polarizer position all along the spectrum such as tan P = tan F [ 141. The ellipsometric parameters tan 9 and cos A are recorded versus the photon energy E in the 1.6-3.5 eV energy range. The calibration is performed following the Aspnes’ procedure [ 151 to reach the two correction factors (attenuation, q, of the signal processing chain and phase shift, 8, of the rotating analyser and processing chain). The residual random and periodic noise correction can be made automatically at each wavelength (shutter on). The single zone measurement is averaged on 120 analyser mechanical rotations and during the two optical periods by mechani-

Z-+xis

Z-axis

L-V

&11 Fig. 2. Ellipsometer

configuration. The plane perpendicular to the

surface passing through the [i IO] or [zl I] direction is taken ns the incident plane in ellipsometry. parallel

sample.

to the [ilO]

The

light beam is respectively

and to the [!?I11 direction

of the Si(lll)

Science 341 (1995) 202-212

205

cal turn. The resolution has been checked on well known Au and Cd systems (6A = 0.01” and 6q < 0.005”). Notice that all our experimental results have been reproduced on thirty experiments with different samples.

3. Results and discussion 3.1. Experiments

results

At the PB angle, (cos A = O), the cos A(E) spectrum of a perfect dielectric sample exhibits a vertical while for semiconductors like Si, a transition, pseudo-vertical transition is observed. Nevertheless, we find slight differences in our experimental cos A spectra (Fig. 3) compared to the cos A spectrum calculated from Aspnes [8]. These slight differences Scos A and Stan 9 with Aspnes values are significant; for example, nearly 3 eV, they give A and q changes from Aspnes values roughly of 0.2-3” for A and 4-8” for ‘IE that have to be compared to our experimental accuracy 6A = 0.01” and 6YJ < 0.005” (see previous paragraph). Aspnes experimental values can be used, in first approximation, as the pure bulk-Si dielectric function since (1) they are obtained from ellipsometric measurements far from the Brewster incidence where the reflected light should depend strongly on surface properties, (2) Aspnes’ samples were prepared by a wet-chemical process and thus present an abrupt interface. Indeed, it is well known that this procedure leads to a vanishing transition layer between bulk and ambient. Then it is now admitted that Aspnes values represent the dielectric function of an ideal Si( 111) sample surface without any reconstruction (bulk plane (111)). In fact, real surfaces are known to be reconstructed and often rough because, flash and annealing in ultra-high vacuum lead to a thicker overlayer due to surface reconstruction and roughness induced by the heating. The contribution of this surface transition layer is important and cannot be neglected when ellipsometry measurements are performed on a reconstructed and rough surface near the pseudoBrewster angle. Then if Aspnes results are considered to be able to describe the pure bulk-Si function, the slight deviations to Aspnes data are due to the

206

Z. H~tmmudi el nl. /Sur@ce

Science 331 (1995) 202-212

-0.8

-1.2 2

1.5

2.5

3

3.5

E(eV) Fig. 3. Cos

A

spectra versus the energy at room temperature. (a) (-

direction of the incident beam. (c) (X

X

) Sic11 I) bulk. (b) (0

0 0)

(7 X 7) Sic1 I I) along the nlO]

X ) (7 X 7) Si(l I I) along the [!?I II direction of the incident beam.

01.38

0.3

5”

s 0

*

(C)

C

--(a) -C 2.5 E(eV) Fig. 4. Tan P

1 Sic1 11) bulk. (b) (0 0 0) (7 X 7) SKI X ) (7 X 7) Si(l II) along the [?I I] direction of the incident beam.

spectra versus the energy at room temperature. (a) (-

direction of the incident beam. (c) (X

X

I I)

along the [TlO]

2. Hummudi ef ~d./Surjtice

transition layer. It is the case for our experimental spectra (Fig. 3 and 4) which exhibit slight but reproducible and significant deviations from Aspnes spectra. For a slightly misoriented Si(ll1) surface, a (7 X 7) superstructure exists at a temperature T < 830°C on terraces between steps. It is obvious that the ellipsometric response results from the superstructure and step-roughness contributions. Atomic force microscopy has been used to estimate the surface-step roughness (experiments are made ex situ); the height and equidistance of the steps, shown on the profile and AFM pictures, give a misoriented angle of the Si(1 I 1) surface of 0.5” which is in agreement with the sample specifications of the manufacturer. The effective mean square roughness depends on the crystallographic direction. As the steps are parallel to the [i 101 crystallographic direction, the effective mean square roughness is out of resolution in the [ilO] direction while it increases to a maximum value in the [I 121 direction (approximately 40 A). For ellipsometry, the sample holder does not allow the [l 121 direction analysis. So we record the ellipsometric spectra of clean Si(ll1) along the two different incident beam directions (see Fig. 2) [ilO] and [21 I I (at 30” from [i lo] as shown respectively by the RHEED patterns (a) and (b) of the figure). The mean square roughness is allowed to be less in this direction than in the [ 1121. Fig. 3 and 4 represent the cos A and tan P spectra versus energy in the 1.6-3.4 eV range with the incident beam respectively parallel to [ilO] in spectra 3b, 4b (direction which corresponds to a minimal roughness) and to the [?l l] direction in spectra 3c, 4c (direction which corresponds to a higher but not maximal roughness). The Aspnes data [8] cos A and tan !P of an ideal bulk plane Si(l11) are also reported in spectra 3a and 4a. The inset of Fig. 4 gives the difference between tan !P experimental results and Apsnes data for both directions. Such a procedure puts in evidence some oscillations. Similarly, the slope (dcos A/d,!?),, lr,2 differs from experimental results and Aspnes data. The difference is minor for experiments carried out in the direction of lower roughness which puts in evidence an optical anisotropy. It is the same for tan ?P (see inset Fig. 4).

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Science 341 (19951 202-212

3.2. Determination

of the dielectric ,function

Because the (7 X 7) reconstruction is known to be isotropic in the DAS model (C,, group in Schoenflies notation [l]), the differences in tan ?P and cos A according to the crystallographic directions have to be referred to a step-roughness effect. Then, a good choice of the incident beam direction allows to discriminate the step-roughness effect from the (7 X 7) superstructure effect. To determine the dielectric function of the (7 X 7) superstructure. we choose to work in the direction of minimal roughness [i IO] to avoid any roughness effect. A more complete study of the effect of the roughness upon ellipsometric data as a function of the direction of analysis and the thermal treatment will be published later [ 161. In all case, they confirm our interpretation. Usually experimental results can be fitted by a three-phase model [7]. Although results are better described by microscopic models based on the local induced polarization [ 17,181 and the surface local field [19], the three-phase model [7] leads to an effective dielectric function that, as a first approximation, gives the principal characteristics of the dielectric function. So we used a three-phase model [7] which consists (as shown in Fig. 5) of: an infinite Si( I 11) substrate (with the optical constants [8] of bulk Si( 11 l>l X 1; see spectra 6a and 7a), a Si( I I I) 7 X 7 transition layer (with unknown dielectric t‘unction E~,~~)) an d vacuum. We estimate the transition

Vacuum v.

6 .3A I%

JSi(ll1) I &=&I

+

‘/

ix2

/

/Fig. 5. Ellipsometry (7 X 7) Si(

I 1I)

three-phase

model [7] of the reconstructed

surface. This model consists of an infinite Si(

substrate (dielectric function: E), a Si(l

I I)

(dielectric function: q, x ,)) and vacuum.

I I I)

(7 X 7) transition layer

208

2 Hammadi et al./Surface

layer thickness from the DAS model [l] (a three-level model [7]) to be about 6.3 A (2/3 of the interplanar distance d(, I ,) of the cubic crystal). It is interesting to point out that a strong variation of this thickness (up to 20%) does not lead to a significant difference in the dielectric function result [20]. From these considerations, cos A and tan ?J’ values for this three-phase model [7] are calculated versus the energy by a computer program. A fitting procedure is then used to determine the transition layer optical index of refraction, fiC7x7J: 97.7)

=97x7)

+

ik,,.,,.

effective parameters are 97 x 7) and k,7 x 7) lated to minimize the difference between the lated and experimental results of cos A, tan ?. these parameters, we determine the dielectric tion of the (7 X 7) transition layer:

The

&(7X7)

=

81(7X7)

+

calcucalcuFrom func-

‘&2(7X7).

The resulting effective &I(7x7j and ~~~~~~~spectra are respectively reported in Fig. 6 and 7 for the two directions of incidence and compared to the E,

Science 341(1995)

202-212

and Ed values of Sic1 11) bulk deduced from Aspnes data. Because the absolute value of the dielectric function is very sensitive to the incident angle accuracy, the spectra were normalized to the bulk transition at 3.4 eV. In Fig. 7, we plot czC7X7j~=f(E), where T is the (EJE~(~~~)) ratio measured at 3.4 eV. The same procedure is applied to E,(~x 7j. Disregarding first the differences between the incident directions [llO] and [211], the main features are (i> and (ii>: (i) The efC7x7j and E2(7x7j spectra exhibit a large peak around 3.4 eV with a higher value of E, than of E,C7x 7J under 3 eV. (ii> The 82(7x7j is quite different from the F~ with two peaks at 3 and 2.6 + 0.1 eV whereas the Ed curve asymptotically reaches zero under 3.1 eV. An additional broad peak could be seen around 1.6 eV, in an energy range where there are some experimental limitations due to the lamp and the detector. (iii> The g&7x 7J values depend much more on the direction of incidence <[I 101 or [?l 11) than the real Part

&I(7

X7)’

E(eW Fig. 6. Real part of the refractive index versus the energy. (a) (0 ??0 0 0 ?? ) E, of the Sic11k) bulk. (b) (M) E,(,~,) of the E~(,x ,) of the (7 X 7) transition layer along the [?I I] (7 X 7) transition layer along the hlO] direction of the incident beam. (c) c-1 direction of the incident beam.

209

Z Hammndiet al./Surface Science 341 (1995) 202-212

3

2s

4

3s

WW Fig. 7. Imaginarypart of the refractiveindex versus the energy. (a) (0 0 0 ??0 0) q of the Si(ll1) bulk. (b) (888) E~(,x ,) of the (7 x 7) transition layer along the filO] direction of the incident beam. (c) (M) q(, x7j of the (7 X 7) transition layer along the [211I direction of the incident beam.

3.3. Interpretation

part E* is linked to the joint density of states so that the peaks in E%,x ,) result from surface state transitions at 1.6, 2.6, 3 and 3.4 eV. In Table 1, our results are compared to the experimental results (ellipsometric studies [20,21] and reflectometry works [5,6]) and to recent theoretical imaginary

The intrinsic optical (7 X 7) surface properties are best described by the previous derived effective dielectric function q, x ,) in the direction of minimum surface roughness (curve (b) of Fig. 6 and 7). The

Table 1 Energy of the surface-statetransitions mentioned in the litemture comparedto our experimental results 1

-

Calculationsfor p polarization Noguez et al. (1994)

accuracy in :-~-2 weak t + +alculations or measures

1

1.8

2.2

2.6

3

3.4

3.8

210

2. Hummadi et al./Su@ce

calculations [22]. In its pioneer work, Meyer studied the optical Si response upon oxygen adsorption and found quite broad and poorly defined optical transitions. With the same kind of experiments (oxygen adsorption on silicon), Alameh et al. [6] used a surface differential reflectometry probe and described the surface optical response using Bagchi’s theory [23]. They found some surface optical absorption at 1.8, 2.4 and 3.9 eV though on their Fig. 2, an additional shoulder could be seen around 3 eV. If the photoemission results [24-271 are used, we can deduce the following interpretations as illustrated by the schematic energy level diagram of Fig. 8, where the left part represents the electronic state density of the bulk and (7 X 7) surface: (i) The 3.4 eV transition can be due to the S, (attributed to adatom and atoms of the second layer backbonds) to U, state transition (due to adatoms or backbonds). (ii) The 3 eV transition, not mentioned in previous experimental works, can be due to the state transition from S, (attributed to restatom dangling bonds) to the maximum of the bulk conduction band.

Science 341 (1995) 202-212

(iii) The 2.6 eV transition can be ascribed to two transitions: the first one takes place from a S, state to an empty state U, (due to an adatom p, orbital); the second one between a S, state to a U, state. It is presently impossible to distinguish between the contributions of each one. (iv) The last one transition at 1.6 eV can be associated to the transition from the initial surface state S, (adatom dangling bond states) to the empty surface state U,. It is important to point out that Noguez [22], using a semi-empirical tight-binding approach, calculated the electronic structure of the (7 X 7) layer transition. Calculations were carried out using a (7 X 7)Si(l I I> model built of a (2 X 2)Si(l II) adatom-restatom model and a (3 X 3)Si(lll) adatom-dimer stacking fault model. In our energy range, two experimental peaks at 2.6 and 3 eV coincide with the theoretical calculations. Noguez showed that the peak localization does not depend very much upon the light polarization state. However this dependence could explain some discrepancies in the experimental results given in the literature. These discrepancies

..

(7x’l)Si(lll)

EW) >

Fig. 8. Schematic energy level diagram which gives the electronic-state

density of the bulk Si and the (7 X 7) Si(l

surface-state transitions involved are reported in this diagram (see Photoemission results, Refs. [24-271).

I I)

surface; the

Z Hammadi et al./Surfnce

between experimental results and theoretical predictions could be due either to our fit by a three-phase model (which is only a very simple model) or to the fact that the main structural unit of the (7 X 7) cell is weakly different from the structural model used by Noguez [22]. In the [zll] direction of the incidence measurements, we point out the step-roughness contribution to the (7 X 7) surface dielectric function. In fact, it is seen on Fig. 7 that the roughness only smoothens the surface-state signature at 2.6 and 3 eV in cZc7x7). Adding a roughness to the Si bulk contribution using Bruggeman’s theory [28], we have been able to fit the cos A spectrum recorded in the [?ll] direction with the [ilO] cos A spectrum and could by this way attenuate the E *(, X,) peaks. Let us recall that in our experiment the incident light is nearly p-polarized so that for a perfect dielectric material, irradiated under Brewster incidence, there is no reflected light. Steps act as a set of rows of Hertzian oscillators. These oscillations radiate no light in the direction of their oscillations (roughly perpendicular to the surface because of the p-polarization and of the incident angle (N 76” see Fig. 2). Furthermore, in the direction of the row and in a first approximation, the contributions of the oscillators cancel by interferences so that the main part of the radiation due to a step is in a direction perpendicular to the steps, that means in the [li?] direction. Then it is easy to understand from a qualitative point of view, the origin of the roughness effect on the ellipsometric signal recorded in the direction of greatest roughness. We checked that the roughness itself cannot explain the peaks in E~(~X,).

211

Science 341 (1995) 202-212

induced by the [ilO] parallel steps that smoothens the surface ellipsometric response. As the imaginary part of the dielectric function E of a material is proportional to its electrical conductivity, the (7 X 7) reconstructed surface of Sic1 11) exhibits a metallic behaviour in the energy range under study. UPS data show a metallic edge at the Fermi level (see Fig. 8) that is consistent with ELS data and the results therein.

Acknowledgement The authors thank D. Pailharey (Groupe de Physique des Etats Condenses, FacultC des Sciences de Luminy - Marseille) for AIM measurements and valuable discussions.

References [I]

K. Takayanagi, hashi, J. Vat.

[2] P. Miiller,

Y. Tanishiro,

M.

Takahashi

Sci. Technol. A 3 (1985)

and S. Taka-

1502.

M. Gauch and G. Quentel, Surf. Sci. 313 (1994)

335. [3] J.E. Rowe, H. lbach and H. Froitzheim,

Surf. Sci. 48 (197s)

44. [4] J.M. Layet, J.Y. Hoarau, H. Liith and J. Derrien, Phys. Rev. B 30 (1984)

7355.

[S] P.E. Wierenga, A. Van Silthout and M.J. Spamaay, Surf. Sci. 87 (1979) 43. [6] R. Alameh and Y. Borensztein,

Surf. Sci. 251/252

(1991)

396. [7] D. Drude, Ann. Phys. JETP 3 (1891)

126.

[8] D.E. Aspnes and A.A. Studna, Phys. Rev. B 27 (1983) [9] See for example: Ellipsometry,

Proc.

1st Int. Conf.

Paris, January

I l-14

985.

on Spectroscopic

(1993).

Eds. A.C.

Boc-

cara, C. Pickering and J. Rivory: Thin Solid Films 233/234

4. Conclusion

(19931, and references therein. [IO] M. Gauch and G. Quentel, Thin Solid Films 233 (1993)

Our experimental results and an interpretation model allow us to determine surface-state transitions at 1.6, 2.6, 3 and 3.4 eV which are in agreement with literature data. As previously supposed, the (7 X 7) reconstruction can be seen as a transition layer (thickness d = 6.3 A; effective dielectric function E~,~ 7j) between the bulk Si and the vacuum. Thus, we think that the effective E(,~,) calculated from the experimental results obtained in the [i 101 direction is representative of the electronic properties of this transition layer. The observed optical anisotropy is

[I I] L. Rayleigh, Philos. Mag. 33 (1892)

I.

[ 121

IS (1931)

C. Bouhet, Ann. Phys., 106me S&e

5.

[13] D.E. Aspnes and A.A. Studna. Appl. Opt. 14 (1975) [14] D.E. Aspnes, J. Opt. Sot. Am. 64 (1974) [15] D.E. Aspnes and A.A.

53.

220.

639.

Studna, J. Opt. Sot. Am. 64 (1974)

812. [16] Z. Hammadi,

P. Miiller,

M. Gauch and G. Quentel,

to be

published. [17] D.V.

Sivukhin. Sov. Phys. JETP 3 (1956)

269.

[18] C.S. Strachan, Proc. Cambridge Philos. Sot. 29 (1933)

116.

[ 191 C.M.J. Wijers, R. Del Sole and F. Manghi. Phys. Rev. B 44 (1991)

1825.

[20] F. Meyer, Phys. Rev. B 9 (1974)

3622.

212

2 Humnmdi

1211 F. Meyer, [22]

(I 994) [23]

(I 979)

J.E. Rowe, 44.

A.I.

Shkrebtii

37.

R.G. Barrera

and A.K.

Science 341 (1995) [2S] G.V.

and R. Del Sole, Surf.

Sci. 318

342.

A. Bagchi, 20

[24]

Surf. Sci. 56 (1976)

C. Noguez,

et ul./Surjtice

Rajagopal,

Phys. Rev. B

Hanson

[26]

S. Bouzidi,

[27]

F.J. Himpsel ( 1984) 8

Surf. Sci. 48 (1975)

and R.I.G.

Uhrberg,

Surf. Sci. Rep. 9 (1988)

197.

4824. H. lbach and H. Froitzheim,

202-212

[28]

D.A.G.

Thesis,

University

and Th.

Fauster,

of Aix-Marseille J. Vat.

IS.

Bruggeman,

Ann.

Phys. 29 (1935)

II, 1993.

Sci. Technol. 636.

A 2