Surface reflectance spectroscopy: Its application to the study of very thin films

Thin Solid Films, I25 (1985) 129-142 ELECTRONICS

129

AND OPTICS

SURFACE REFLECTANCE SPECTROSCOPY: THE STUDY OF VERY THIN FILMS* Y. BORENSZTEIN

ITS APPLICATION

TO

AND F. ABELI%

Laboratoire d’optique des Solides. UnitP associke au CNRS 781, UniversitC Pierre et Marie Curie, 4 place Jussieu. 75230 Paris C&iex 05 (France) (Received

August

12,1984;

accepted

August

24, 1984)

We describe in this paper the technique of surface reflectance spectroscopy. Several models, which successively take into account the non-local, anisotropy and local field effects, are proposed as descriptions of the change in reflectance owing to the presence of adsorbates on the surface. The following examples of applications are presented: gas atoms or molecules adsorbed on metal surfaces in vacuum systems and very thin metal films deposited onto metallic surfaces either in electrolytes or in ultrahigh vacuum.

1. INTRODUCTION

Interest in the electronic structure of solid surfaces has increased in the past few years and much effort has been devoted to its investigation. The most important direction of research seems to be the study of chemisorption on atomically clean surfaces in ultrahigh vacuum using techniques such as UV photoemission, field emission and ion neutralization spectroscopies which provide information about the density of filled electron states near the surface. These techniques are essentially sensitive to the surface because of the short escape length of electrons in solids. In a few cases complementary information, i.e. the density of the empty states above the Fermi level and the dielectric response of the surface, is derived from the spectra of one-electron excitations obtained in electron energy loss spectroscopy experiments. For a long time the primary and most common technique for the investigation of the bulk electronic structure of solids has been optical spectroscopy. It provides information about the joint density of states which relates the initial states to the final states involved in the electronic transitions. Because of the great penetration depth of light in solids (100-500 A), optical experiments are not very sensitive to surface properties and were not used for their study until the 1970s. The development of modulation spectroscopies (e.g. electroreflectance and thermoreflectance spectroscopies)’ and very precise reflectance techniques, which have been used for example *Paper presented 13-17,1984.

0040-6090/85/$3.30

at the Sixth International

Conference

on Thin Films, Stockholm,

0 Elsevier Sequoia/Printed

Sweden,

August

in The Netherlands

130

Y. BORENSZTEIN,

F. ABEL&S

in studies of alloys2,3, was the starting point for reflectivity techniques which were sufficiently sensitive to be applied to the study of surface optical effects. The principle of differential reflectance spectroscopy, or surface reflectance spectroscopy (SRS), is to compare the reflectance R of a sample with the reflectance R’ of the same sample after its surface has been perturbed (by a thin film, chemisorption, roughness etc.). The relative reflectance change AR/R = (R’- R)/R, which is related to the change in the electronic structure of the surface, is measured. One interesting advantage of this technique compared with other surface techniques is that AR/R does not have to be measured in ultrahigh vacuum. Therefore investigations of surfaces in electrolytes or in gas atmospheres, even at high pressure, are possible. However, the last possibility has not yet been made use of. The aim of this paper is to give a brief overview of the application of SRS to thin films. We first present expressions for AR/R deduced from a linear approximation and discuss problems connected with anisotropy, non-local effects and local field effects. Several experimental set-ups have been described in the literature, and we present some information about them in Section 3. A few examples of the application of SRS, first for the study of gas adsorption on metal surfaces in ultrahigh vacuum and then for the study of metal adsorption and metal thin film growth on metal surfaces, either in an electrolyte or in ultrahigh vacuum, are described in Sections 4 and 5. 2.

THEORY

2.1. Linear approximation theory for an isotropic film We consider first the classical stratified-layer model with plane-parallel boundaries, as illustrated in Fig. 1. In the macroscopic continuum model each phase is assumed to have homogeneous and isotropic optical properties, which are unperturbed by interfacial interactions and are described by the bulk complex dielectric function: E(O) = E’(O)+ is”(o)

(1)

This model is quite good for s-polarized light (i.e. when the electric field is parallel to the surface) when the film is not too thin and the boundaries between the media are sharp. In contrast, for metallic media, particularly near their plasma frequency, the local approximation is not valid for p-polarized light (electric field in the plane of incidence) and a spatial dispersion treatment is needed. This model corresponds to the weak interaction limit and is more appropriate to physical adsorption systems than to those with chemisorbed monolayers. For very thin layers, anisotropy and local field effects must also be considered. By making simple linear approximations which are valid for d 4 A, where d is the thickness of the surface film and il is the wavelength of the light, McIntyre and Aspnes 4*5have derived the following expressions for the differential reflectance from the Fresnel relations:

SURFACE

REFLECTANCE

SPECTROSCOPY

131

OF VERY THIN FILMS

AR hdn, cos 8, s2-e3 l--~~(l/s~+l/~~)sin~8, -= Im (3) 1 1 -(t& + 1) sin20, ( E3 --Et R P for s- and p-polarized light respectively. Ed, .s2 and ~~ are the complex dielectric functions of the three media, n, is the refractive index of the ambient medium (sl = n,‘), 8, is the angle of incidence and Im indicates the imaginary part of the expression. The linear approximation is valid (+ 20%) for d/A < 0.03 for s polarization and for d/A < 0.01 for p polarization. It can be seen from eqns. (2) and (3) that the sensitivity of film detection is linearly proportional to the film thickness d, i.e. to the amount of material deposited on the substrate surface, and is inversely proportional to the wavelength for constant or slowly varying values of the dielectric constants. The sensitivity is generally greater for p-polarized light at oblique incidence. We can see from eqn. (2) that (AR/R), varies as cos0, and decreases with increasing 8,; the variation for p polarization is more complicated but can be approximated by a l/cos 8, variation for 0r < 45”; I(AR/R),I increases until 8, z 60” and decreases rapidly for greater angles of incidence (Fig. 2). The denominator of eqn. (3) is zero for

(>

l-

l+: (

sin20, =0 >

i.e. for El Sin2dl = -

EIQ

EI

+E3

This is the condition for surface plasmon excitation when ~~ is less than zero and is the Brewster angle of the substrate when ~~ is greater than zero. The optical behaviour of a thin isotropic surface film is characterized by the three parameters Ed’, Ed” and d. For a single angle of incidence only the two quantities (AR/R), and (AR/R), can be measured, and the value of d must be determined independently. The real and imaginary parts of the dielectric constant of the

0

El

q n,*

? m-1 a (u

, . 62 = E* * I E,

0

--2

q s

\

E.3=&j+i

E;

0

20

P \

40 60 6, f degrees)

80

Fig. 1. The classical stratified-layer model with plane-parallel boundaries. The angle of incidence of the light is 0,. E, and E, are the electric field vectors for s- and p-polarized light respectively. s,, s2 and sg are the local (frequency-dependent) dielectric functions of the three media. Fig. 2. The normalized change AR/R in the reflectivity of s- and p-polarized light caused by 1 monolayer (ML) of an absorbing film on a metal substrate: ---, l/cos 0r variation. The dielectric constants are a, = 1.333, sr’ = 6.75, .s2” = 9, Ed’ = - 12 and sg” = 16. The angle of incidence is 45” and d/i = 10e3. (From ref. 4.)

132

Y. BORENSZTEIN,

F. ABELl%

overlayer can be calculated6 from the values of (AR/R), and (AR/R),. In studies of adsorption on highly reflecting metallic substrates (e.g. silver or aluminium) (AR/R), is very small compared with (AR/R),, because the component of the standing-wave electric field parallel to the surface is close to zero at the surface. Under these conditions the dielectric constant of the thin film either cannot be determined or can be determined with poor accuracy only. However, this determination is easier for moderately reflecting substrates. If measurements of (AR/R),, are made at several angles of incidence the three parameters can be evaluated in principle from eqn. (3), although this does not seem feasible in practice. 2.2. Non-local efects In the previous model it is assumed that a sample can be represented as a semiinfinite bulk dielectric with a sharp surface and a local dielectric constant E(O).Many theoretical’-” and experimental investigations i2-i4 of non-local effects have been performed in the last few years and their influence on the optical properties of metallic samples is now quite well understood. Feibelman’ 5 neglected the local field effects and compared the above results with those of a more general model for a microscopic medium. He concluded that in the case of s polarization, for which the electromagnetic field varies slowly in the surface region, the McIntyre-Aspnes (MA) model gives a good approximation to the microscopic theory. However, in the p-polarized case the non-local relation between the current and the electric field cannot be approximated by the usual local relation because the electric field component normal to the surface is non-zero and varies rapidly in the surface region. Therefore the treatment leads to an integral expression for (AR/R),,. Unfortunately this expression is not immediately useful as it involves an integration over the undetermined electric field inside the reflecting system. We shall give expressions including both non-local and anisotropic effects in Section 2.3. 2.3. Anisotropy The assumption of isotropy used in the MA model is not justified for very thin films such as (sub)monolayers which are expected to exhibit an appreciable amount of anisotropy in their optical properties. Dignam and Moskovits’6,‘7 have derived quantitative expressions within the linear approximation for a uniaxial film on an isotropic substrate: (4) 8adn, cos 8l Im (E~-c~)(E~-cl sin2Bl)+a32 sin28,(cl/e,(cl -s3)(cl sin2Bl --~~cos~t?~) /?

1)

(5)

where E, and E,are the components of the thin film dielectric constant tensor normal and parallel to the surface. As an interesting consequence it has been pointed out that a thin transparent but anisotropic film on a metallic substrate yields AR/R values which, when calculated for an isotropic film, appear to indicate absorbing properties l7 . Therefore film anisotropy should be considered for quantitative analysis.

SURFACE REFLECTANCE

SPECTROSCOPY OF VERY THIN FILMS

Bagchi et al.‘* derived expressions for the change in reflectivity anisotropic film including non-local effects: 87~1,cos 8, Im 1

of an

(6)

8rrcn,cos e1 Im (sj -el sin28,)&i, + (El

2

133

-E3)(El

Sin28,

~~~~~

-

sin28, &I,

Eg COS28,)

(7)

where S/1, and &l, are quantities with dimensions of length defined by &i,(o) =

+ m dz{
(8)

s +cO

&l,(o)

=

dz((E,-l(a)(Z))-(E,-l(Z))}

-a,

The quantities labelled with the superscript (a) refer to the case when adsorbed impurities are present on the surface, while the corresponding quantities without the superscript refer to the clean metal. The mean values (E,) and (E,- ‘) are given by +a, dz’ E&l; z, z’) = (10) s -co +mdz’E,-l(W;z,z’) (11) s -52 where E~(o;z,z’) and E’,(o;z, z’) are the components of the dielectric tensor parallel and normal to the surface respectively; the tensor is assumed to be invariant along the surface. These equations enable us, in principle, to determine the real and imaginary parts of &l, and &I, by performing measurements at three different angles of incidence for p polarization and one angle of incidence for s polarization. Comparison of eqns. (6) and (7) with eqns. (4) and (5) shows that they are identical when (E,-l(Z))

=

&I, = d(&,-&J

(12)

6/t, =

(13)

and d(E,-l-&l-l)

This means (and this is the most interesting aspect of eqns. (6) and (7)) that, because of the twin properties of the non-locality and the surface-induced anisotropy of the dielectric response function on a semi-infinite medium, in general 1 This implies that, for reflectance purposes, the surface response can be approximated by an effective local but anisotropic response function. Thus a uniform anisotropic dielectric layer should be assumed in the simplest model for analysis of p-polarized differential reflectance spectra.

134

Y. BORENSZTEIN.

F. ABEL&S

2.4. Localfield efects

All the models described previously treat the thin layer phase as continuous, even for (sub)monolayers. It is necessary to relate the effective dielectric tensor of such films to the optical properties of the adsorbed species, i.e. to their polarization tensor, but no general microscopic theory is yet available although several attempts to derive such a theory have been made15Y’6919-21.Bagchi et a1.22 took local field effects into account by treating the interaction between the dipoles and the imaging dipoles within the quasi-static approximation and obtained expressions for E,and E, as functions of the polarizability tensor of an ordered two-dimensional square array of adsorbed atoms: 1 (14) st = l +4nY? 1 +(y/2)(5,-(5,) 1 (15) s, -1 = l-47ty2 d 1-r(&-51) where a, is the lattice parameter and d is the equivalent thickness of the adsorbate layer such that the volume per adatom is aI’d, y is the frequency-dependent polarizability normalized to the volume, &, is the dipolar sum due to the interaction of all the other dipoles with a given dipole and 5, is the dipolar sum due to the interaction of the imaging dipoles with the given dipole. Here Eiis taken to beunity. Figure 3 shows the reflectance (AR/R@, per unit coverage for p-polarized light incident on argon-covered aluminium at two values of the coverage (9 = 0.25 and 9 = 1). The polarizability of an argon atom is taken as the sum of Lorentz oscillators. The prominent peaks arise from structures in Im(.s,- 1). The most interesting feature of these results is that they do not simply scale with coverage. Rather, we notice a shift in the differential reflectance peaks as the coverage is changed. These features arise from the fact that in this theory the adsorbed atoms are not regarded as independent scatterers but their interaction is explicitly included in the calculation. These local field effects have been experimentally confirmed23 but the quantitative agreement with the calculations of Bagchi et a1.22 was very poor.

0.6 ,a z 0.4 2 a 2 TO. 0 -10

11

12 13 flwcev)

14

Fig. 3. Calculated differential reflectance per unit coverage of p-polarized light for argon-covered aluminium at two coverages: -, full monolayer; ---, quarter monolayer. All discrete transitions on the adatom were assumed to have the same energy width of 0.5 eV. (From ref. 22.)

3.

AN OPTICAL

SET-UP FOR SURFACE

REFLECTANCE

SPECTROSCOPY

Several types of optical set-up have been used to measure the change in reflectivity. A two-beam reflectometer is normally used24-26, but other techniques

SURFACE

REFLECTANCE

SPECTROSCOPY

OF VERY THIN FILMS

135

such as the differential reflectometer2’, the rotating light pipe reflectometer28 or the rapid scan spectrometer2g are available. Figure 4 shows an example of a differential reflectometer2’. A monochromatic beam is focused on a mirror (M) vibrating at 800 Hz which sends the beam up and down on the reflecting sample. The beam is alternately reflected on two areas of the sample for which the reflectivity difference is to be measured before being focused on a photomultiplier (PM). A feedback on the high voltage of the PM maintains a constant mean value of the delivered current as is usual in modulation spectroscopy. Lock-in amplifier detection at the frequency of the vibrating mirror combined with the feedback on the PM high voltage supply gives a signal proportional to AR/R. To obtain absolute values of AR/R the system must be calibrated, and this is performed by including a spectrophotometer in the apparatus which enables absolute values of the reflectivity to be measured. The sensitivity limit of this technique is about 10e4 in ARfR, which can be improved by storage of the measured data in a minicomputer.

Fig. 4. Principle of the differential spectrophotometer. The vibrating mirror M directs the optical beam alternately onto the two halves of the sample for which the slight difference in reflectance is to be measured. The synchronous detection (SD) and the feedback on the high voltage (HV) of the photomultiplier (PM) are also indicated.

4.

GAS CHEMISORPTION

ON METAL SURFACES

SRS has been used in several investigations of the chemisorption of gas atoms The samples are generally on metal surfaces in ultrahigh vacuum 21*23*26*28*30~3s. single crystals which are mechanically polished and then electropolished to achieve a smooth specular surface. The metal surface is cleaned during the experiments using various techniques such as oxidation treatment, Ar + sputtering and flashing to high temperature. For example, Anderson et aL31 studied the adsorption of O,, CO and Hz on Mo(100) and W(100). They demonstrated the existence of various bonding sites, intrinsic surface states and adsorbate-induced orbitals associated with the chemisorption bond. The measurements were made at a-fixed wavelength and increasing gas

136

Y. BOBENSZTEIN.

F. ABEL&

exposure. Figure 5 shows the reflectance change versus coverage induced by H, adsorption on W( 100). If adatom-adatom interaction is excluded, simple reasoning shows that the measured reflectance change AR/R per additional atom should be constant within the exposure range where adsorption into a single binding state occurs. H, adsorption on W(100) is dissociative and involves two binding states. Initially adatoms adsorb in the pZ state, which leads to the constant slope S, observed in region I of the curve obtained with photon energy ho = 1.40 eV. The constant slope SIIIin region III has a similar meaning (adsorption in the p1 state) but a different value (S,,,#S,) because adatoms adsorbed in the p1 and & states cause different changes in the surface electronic structure. Field emission studies have shown that the p2 state is depleted as the p1 state fills. Therefore adatoms adsorbed in region II not only contribute to the pi slope S,,, but make an additional contribution by causing adatoms in pZ states to undergo transitions to p1 states. As s, ZZ2S,,,, these transitions give a positive contribution to S,, which is sufficiently great to make the net S,, greater than zero. The curves for high hv values can also be explained in terms of these two effects. The observation of the intermediate spectra show that the situation is more complicated and that it involves a continuous change in bonding configuration and in adatom-adatom interaction effects. From the curves shown in Fig. 5, Anderson et al. 31 plotted the spectral dependence of the optical response for various coverages (Fig. 6). The continuous curves are the result of a calculation using the MA equation for normal incidence (eqn. (2)). Since the reflectivity change due to adsorption could be described in terms of an effective dielectric function, they assumed it to be the sum of a few lorentzian oscillators and adjusted the parameters to the experimental data. Both positive and negative values of the oscillator strengths were allowed in order to describe the production of new transitions associated with chemisorption and the quenching of intrinsic surface state transitions by adsorption respectively. The structure below 1.5 eV is therefore interpreted as being due to such a quenching of electronic transitions, while

-1.51 0

0.5 coverage

Fig. 5. Coverage dependence energies (from ref. 31).

1.0

of the reflectance

change

Fig. 6. Spectral dependence of the relative reflectance 9 = 0.19 (curve A) and 9 = 1.00 (curve B) (saturated curves. (From ref. 31.)

0

1

for H, adsorption

2 hw

3 (ev)

4

on W(100) at various

change for H, adsorption surface): 0, experimental

photon

on W(100) at coverages data; -, theoretical

SURFACE REFLECTANCE

SPECTROSCOPY

OF VERY THIN FILMS

137

structures above 1.5 eV are identified as new optical transitions lying at 2.2 eV for the 0.19 monolayer coverage and 2.5 eV and 5 eV for the monolayer coverage associated with adsorption in the initial pZ state and the PI state respectively. Blanchet et ~1.~~ studied H, adsorption on W(110). Their results provided interesting information on the geometry of the adsorbate sites. When polarized light was used the change in the direction of the electric field (parallel to the [ 1101 or [OOl] directions) induced new optical transitions or modified the strength of the existing transitions. By calculating the transition matrix elements for each model of the adsorbate geometry and comparing these with the experimental data they were able to identify the bridge sites as the most probable locations of the hydrogen atoms. Other valuable information can be gained from these studies as, for instance, in the work of Cunningham et ~1.~~ who demonstrated the influence of the interaction between adsorbates and of charge transfer induced by the optical excitations by the observation of coverage-dependent features in the experimental reflectivity spectra for rare gases adsorbed on single metal surfaces. This type of experiment is likely to be improved substantially in the near future, particularly by using fast automatic techniques such as optical multichannel analysers consisting of a detector with several hundred single channels coupled to a memory and a dataprocessing unit; such techniques would enable adsorption kinetics to be studied in real time and thus would provide more information on gas atom-metal systems. 5.

STUDIES OF METALLIC ADLAYERS ON METAL SURFACES

5.1, Electrochemistry studies Underpotential metal deposition offers the possibility of forming metal (sub)monolayers on foreign metallic substrates under equilibrium conditions and of varying their coverage by altering the potential. Differential reflectance spectroscopy has a wider applicability than modulation spectroscopy (limited to reversible changes in the surface states) and has been used to study the optical and electronic changes induced by the adsorption process or by film formation in an electrolyte environment36*37. As an example, we present here some results obtained by Kolb and K6tz3* who measured the changes in reflectivity of silver films electrodeposited onto Cu( 111) electrodes and confirmed the existence of silver bulk plasmons excited by p-polarized light as predicted by non-local theories. Figure 7 shows the AR/R spectra for a silver film 12 A thick. Whereas the calculation based on classical optics reveals a pronounced dip in the spectrum at 3.82 eV (the so-called plasma resonance absorption), the non-local approach does not, in agreement with the experimental results. The dip is observed for thicker films but is broadened and shifted to higher energies. This shift is in good agreement with the non-local treatment, which takes into account a supplementary longitudinal polarization wave, and with previous work by Lopez-Rios et al. 3g for silver films deposited onto aluminium substrates in ultrahigh vacuum, as indicated in Fig. 8. 5.2. Ultrahigh vacuum studies Few SRS investigations of the optical properties of very thin metal films on metallic surfaces have been performed in ultrahigh vacuum40-42. When the

Y. BORENSZTEIN,

0

1

10 film

20 thickness

F. ABEL&

fnm) .

,

Fig. 7. Differential reflectance spectra for Cu( 111) covered with a silver film 5 ML thick obtained with p-polarized light (0, = 45”): 0, experimental data; -, non-local model calculation; ---, local model calculation. (From ref. 38.) Fig. 8. Shift in the plasma resonance absorption energy for silver overlayers on Cu(ll1) as a function of the film thickness (0, = 45”): 0, experimental data from ref. 38; ---, calculation without spatial dispersion; -, calculation with spatial dispersion; x , experimental data from ref. 39.

interaction between the adatoms and the substrate is strong the bond strength may exceed that of the pure adsorbate material, and therefore the adsorbed metal atoms form a submonolayer and then successive monolayers on the metal surface, i.e. the film growth is continuous. This is the case for silver grown on Cu(lll) or for palladium on Ag( 111) 41s42. In other cases some clustering may occur. This is observed for copper growth on an Ag( 111) surface at room temperature. Figure 9

3

2

1 2.06

c

ev

0.4ML

0.2 ML

LL 0 \ [L -1

0

-2

-3

-4

2

fim

3 (@V)

4

Fig. 9. Differential reflectance spectra at normal incidence for copper (expressed in average MLs) deposited onto a silver film 600 A thick: --, MA equation for the film 1.2 ML thick. (From ref. 41.)

layers of various thicknesses spectrum calculated using the

SURFACE REFLECTANCE

SPECTROSCOPY

OF VERY THIN FILMS

139

shows the changes in reflectivity for various copper coverages on silver at normal incidence41. The silver substrate is prepared in situ by evaporation onto a smooth glass substrate, and therefore consists of crystallites with an area of a few tenths of a square micron with preferred [l 1 l] orientation almost perpendicular to the surface. The large feature with negative and positive peaks around 3.8 eV is related to the almost zero reflectivity of the silver substrate at this energy and is not the interesting point. Rather, our attention is focused on the negative feature between 1.4 and 3.6 eV which can be attributed to the absorption due to the copper atoms. The low energy onset of this optical absorption is 2.06 f 0.03 eV, which is precisely the energy of the threshold of interband absorption in bulk copper corresponding to electronic transitions from the top of the d band to the Fermi level. If the copper atoms collect at the surface to form large clusters, the copper film can be described by the bulk dielectric function; the AR/R signal can be expressed using the MA formula and is proportional to the mean (mass) thickness d,. This behaviour is indeed observed, and all the spectra ARfRd, normalized to the thickness are superimposed. The theoretical curve given in Fig. 9 for the film 1.2 ML thick, which was calculated using eqn. (2) with the bulk dielectric constant for copper, is in good agreement with the experimental data for hw < 3.5 eV. This suggests that the bulk copper d band is already formed in the copper clusters which constitute the film. The very sharp peak observed at 3.65 eV which is not reproduced by the theory is not well explained, but it is probably related to surface plasmon-like electromagnetic phenomena at the silver surface induced by the presence of the copper clusters. In contrast, palladium growth on an Ag( 111) polycrystalline surface follows a continuous Frank-Van der Merwe mode. The bulk properties are obtained for about 10 ML or more. Figure 10 shows the experimental (AR/R), spectra of a palladium film 16 ML thick deposited onto silver for s polarization at an angle of incidence of 60”. This film is too thick for the linear approximation to be valid. The MA ‘formulae are no longer appropriate and it is necessary to use an exact formulation (Fresnel equations) to calculate the change in reflectivity. The agreement of the exact calculation with the experimental data is very good. The spectra obtained with p-polarized radiation are not shown here but they are still sufficiently well reproduced by the theoretical calculations. At submonolayer coverage, the results are quite different. Figure 11 shows preliminary results for the change in reflectivity with p-polarized light at ambient temperature42. The calculation performed using the bulk dielectric constant (broken curve) does not reproduce the experimental data well. Although spectra in both s and p polarization were measured, it was not possible to obtain the effective dielectric constant of the adlayer because the reflectivity of the substrate was too high (see Section 2.1). The trough around 2.5 eV in the slope of the (AR/R), curve is interpreted as being due to an optical absorption related to the existence of a virtual bound d level (VBL). It is well known that for dilute Ag-Pd alloys the 4d electrons of palladium atoms are in resonance with the s-p conduction electrons of silver, leading to a VBL situated at about 2.O-2 . 1 eV43-45. A photoemission study of palladium overlayers on silver monocrystals was made by Smith et al. 46 They fitted their data using two lorentzians to represent the hybridized spin-orbit-split Pd 4d,,, and Pd 4d,,, levels; the centre of gravity of the surface resonance was found at 1.7 eV for palladium on Ag(100) and

140

Y. BORENSZTEIN, F. ABEL&S

0

-5

LL u‘ a -1. c-4 0

Y) s

-1c

Q 0 -15

-1.5

-2c

I

1.5

I

2

I

2.5 flu (eV)

I

:

3

Fig. 10. Differential reflectance spectrum of a palladium film 16 ML thick on a silver substrate for s-polarized light at 0r = 60”: loa, experimental data; ---, theoretical result obtained using the MA equation; -, exact calculation. Fig. 11. Differential reflectance spectrum of a palladium film 0.15 ML thick for p-polarized light at 8, = 60”: 0, experimental data; ---, theoretical result obtained using the MA equation and the bulk palladium dielectric constant;-, theoretical result using the MA equation and the VBL model fitted to the experimental data.

at 2.1 eV below the Fermi level for palladium on Ag( 111) after annealing at 500 “C to produce the bulk substitutional alloy. The continuous curve in Fig. 11 is the result of a calculation following the model of Caroli” and KjGllerstriim20 for the VBL in alloys. We considered, in a rather rough way, that the palladium overlayer 0.15 ML thick and the surface monolayer of silver formed a monolayer of an alloy containing 0.15 at.% Pd; the parameters involved in the expression for the dielectric function of this monolayer were then adjusted to the experimental data. The position of the VBL and its halfwidth were found to be 2.07 eV and 0.36 eV respectively, which are very close to the results obtained for the bulk alloy4’. We interpret this in the following way. Palladium atoms on polycrystalline Ag( 111) can migrate into silver to form a real alloy, whereas this occurs on single-crystal Ag(ll1) only after annealing. However, when palladium atoms are deposited onto a polycrystalline silver substrate cooled with liquid nitrogen no absorption band is visible: palladium atoms collect to form platelets whose d band is broadened and shifted to low energy with respect to the VBL. A band calculation would be used in this case to describe the palladium platelets. 6.

SUMMARIZING

REMARKS

SRS is a promising tool for the study of surfaces and adsorbed atoms. The information obtained for the electronic structure of these systems is complementary to that obtained with other techniques such as photoemission spectroscopy. Its sensitivity offers the possibility of investigating very thin adsorbed films (much

SURFACE REFLECTANCE

SPECTROSCOPY OF VERY THIN FILMS

141

thinner than 1 ML), but the theoretical interpretation of the data is not easy and it is necessary to take into account the non-local, anisotropy and local field effects in modelling the experimental results. Finally, it should be noted that SRS is a convenient technique for studying any phenomenon occurring at a surface and leading to a change in the reflectivity; for instance, it has been applied successfully to the study of roughness at a metal surface*‘. ACKNOWLEDGEMENT

This work was sponsored in part by the Direction des Recherches, Etudes et Techniques under Contract 821492. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

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