Electroreflectance of Copper, Silver, and Gold Single Crystal Electrodes

Zeitschrift für Physikalische Chemie Neue Folge, Bd. 112, S. 69-83 (1978)© by Akademische Verlagsgesellschaft, Wiesbaden 1978

Electroreflectance of Copper, Silver,and Gold Single Crystal Electrodes

ByR. Kötz and D. M. Kolb

Fritz-Haber-lnstitut der Max-Planck-GesellschaftFaradayweg 4-6, D-1000 Berlin 33

Dedicated to Professor Heinz Gerischer on his 60th birthday

(Received December 11, 1978)

Electroreflectance j Cu / Ag / Au / SurfaceThe electroreflectance (ER) of Cu, Ag and Au single crystal electrodes has been studied in

aqueous solutions within the photon energy range from 1.8 to 5.2 eV for a variety of parameters.ER spectra of well-prepared low index surfaces were taken as a function of angle of incidence,crystallographic orientation and electrode potential in order to unravel the various effects whichcontribute to the metallic ER. Many of the observed experimental features in the ER spectra canbe qualitatively explained by three different contributions which together determine the total EReffect: (i) the free electron gas and its change in density at the surface with potential; (ii) theinfluence of the electric field on the bound electrons which reflects the band structure and thesymmetry of the metal surface; and (iii) corrugation effects which impose the surfacemicrostructure onto the free electron behaviour. First attempts on the quantitative evaluation ofthe surface dielectric constants are presented using Kramers-Kronig-Analysis. Finally, thesurface plasmon excitation on stepped surfaces is briefly discussed for Ag.

Es wurde der Elektroreflexions(ER)-effekt an Cu, Ag und Au-Einkristallelektroden inwäßriger Lösung für Photonenenergien zwischen 1,8 und 5,2 eV untersucht. Um die verschieden-artigen Mechanismen zu trennen, die diesen Effekt bewirken, wurden ER-Spektren an niedrig-indizierten Flächen als Funktion des Einfallswinkels des Lichts, der kristallographischenOrientierung und des Elektrodenpotentials aufgenommen. Die gemessenen Spektren lassen sichqualitativ durch eine Überlagerung dreier sehr unterschiedlicher Beiträge zur ER erklären: (1)freie Elektronen und ihre Dichteänderung an der Oberfläche durch das Potential ; (2) der Einflußdes elektrischen Feldes auf die gebundenen Elektronen, der die Bandstruktur und die Symmetrieder Oberfläche widerspiegelt; (3) die Mikrostruktur der Oberfläche, die die Eigenschaften derLadungsträger an der Oberfläche beeinflußt. Mittels Kramers-Kronig-Analyse wurde ein ersterVersuch unternommen, die optischen Eigenschaften der Oberfläche direkt zu bestimmen.Außerdem wurde die Oberflächenplasmaanregung an gestuften Einkristallflächen von Aguntersucht.

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70 R. Kotz and D. M. Kolb

1. Introduction

When an electric field is applied to the surface of a solid the reflectance atthe solid-ambient interface becomes a function of the field strength. Thischange in reflectance with field strength, the electroreflectance (ER), has beenstudied in great detail at semiconductor surfaces, where this effect allows one

to probe the band structure of the bulk [1,2]. The applied field, whichpenetrates several thousand Angstroms deep into a moderately dopedsemiconductor, destroys the translatorial invariance of the Hamiltonian andallows slightly non-direct electron transitions to be excited, the local bandstructure being completely retained because of the weakness of the field. At a

metal surface, however, any static electric field is screened within the firstatomic layer because of the high concentration ofmobile charge carriers. Yet,an ER effect has been observed for a variety of metals [3 —10]. These studiesusually have been performed at the metal-electrolyte interface, where bysimple double layer charging extremely high electric field strengths and largesurface charges can be conveniently induced. The extremely low penetrationdepth of the static electric field into the metal makes the ER a very promisingtechnique to probe the optical and electronic properties of the metal surface.However, in contrast to the ER of semiconductors, the ER on metal surfacesis still a rather poorly understood phenomenon, which needs furtherexperimental and theoretical study.

Early experiments were performed with polycrystalline surfaces. Theresults, mainly those for Ag and Au [5,11,12], were interpreted on the basis ofthe "free electron"-model developed by Hansen [3,4] and refined byMclntyre [12]. In this model it was assumed that the change in free electronconcentration at the surface due to the potential change is mainly responsiblefor the observed effect. However, a number of experimental observationscould not be explained by this model (which is well described in recent reviewarticles by Mclntyre [11, 12]) and therefore led to the conclusion that boundelectrons, which reflect the metal's band structure, are also involved in thefield induced changes [6, 7,13]. Measurements on well-defined single crystalsurfaces substantiated this aspect [14,15].

In the present study we describe a number of experimental resultsobtained from low index single crystal surfaces of Cu, Ag and Au, which giveevidence that the surface band structure of the metal and its change withpotential is viewed in the ER spectra. Besides contributions to the ER fromfree and bound electrons, as already discussed in the past, it has beensuggested recently [16] that a third effect may become dominant in certaincases : the surface micro-structure, which gives rise to the difference in ERsignals on stepped, high index surfaces and close packed, low index surfaces.Moreover, this effect may serve for another explanation for the polarizationanisotropy observed on the (110) single crystal surfaces [14,17]. Alltogether


Electre-réflectance of Copper, Silver, and Gold Single Crystal Electrodes 71

it seems that a quantitative understanding of the metallic ER could make thistechnique a powerful tool for in situ surface studies of metal electrodes.

2. ExperimentalThe ER spectra were determined by two slightly different techniques both of which are

already described in the literature. In the first case a rapid scan spectrometer (RSS B, HarrickInc., Ossining, N.Y.) was employed to measure the reflectance spectra of the electrode at twodifferent potentials [15,18]. The data were processed by a signal averager and the normalizedreflectance change, R/R, calculated. In the second case, the conventional modulation techniquewas used, where the reflectance change was detected by a lock-in amplifier [19]. Although the firstmethod is very convenient and allows fast and easy data handling, the sensitivity is still somewhatlower than in the second case. Therefore, the second technique was additionally employed inthose cases, where the ER signal was comparatively small.

In both experimental set-ups the electrochemical cell, a quartz cell with a semicircular quartzwindow of optical quality, was mounted on a

—

2 goniometer table with the samplephotomultiplier directly attached to the 2<p-arm. Hence the angle of incidence could beconveniently changed over a wide range (15° < < 85°).

Electrode surfaces were prepared in various ways to compare the surface quality. Films ofCull 11), Ag(lll), and Au(1ll), evaporated on cleaved mica at elevated temperatures, wereroutinely prepared and mostly used in our experiments. These films, about 1500Â thick, wereshown to have excellent quality single crystal surfaces of ( 111 ) orientation and were in most casesatomically flat [20], Since no surface preparation is involved this type of electrode is mostconvenient to use. In the case of Ag, melt grown single crystals were also prepared by standardmetallographic methods to yield the three low index faces (100), (110), and (111). These massivesilver electrodes were chemically polished before electrochemical experiments [21]. Finally a

copper single crystal cylinder with its symmetry axis parallel to [110] was also prepared for the usefor ER studies on the low index surfaces available by appropriate rotation of the cylinder. ThisCu cylinder was electrochemically polished before use in electrochemical studies [16].

The potential of the working electrode was controlled by standard electrochemicalequipment. All potentials are measured and quoted in this work with respect to the saturatedcalomel electrode (SCE). Aqueous solutions ofHC104, NaC104, H2S04 and Na2S04 were madeof triply distilled water and p.a. grade chemicals. The electrolyte was deaerated with purifiednitrogen.

3. Results

In the following, the ER spectra of carefully prepared single crystalsurfaces of Cu, Ag and Au are shown as a function of various parameters.These surfaces are flat and well-defined, even in an atomical sense. Since thedielectric function of an isotropie crystal becomes an at least uniaxial tensorat the surface, because of the perturbation normal to the surface, the angledependence of the ER effect seems to be a promising method to look for suchan anisotropy.

3.1. Angle dependenceThe E R spectra for Ag( 111 ) [15], Cu( 111) and Au( 111 ) on mica are shown

in Fig. 1 for various angles of incidence, ,, and s- and p-polarized light. In all


72 R. Kötz and D. M. Kolb

© ® ©

/eV--

Fig. 1. Electroreflectance spectra of Ag(lll), Cu(lll) and Au(l 11) electrodes in 0.5 M NaC104as a function of the angle of incidence, ,. (-) p-polarization. (-) s-polarization. (a)Ag(lll); potential step between -0.5 and 0.0 V. (b) Cu(lll); -0.8 and -0.3 V. (c) Au(lll);

-0.5 and 0.0 V

three cases the spectral shape for s-polarized light is independent of , and themagnitude changes according to a cosine law as predicted by the linearapproximation equations [e.g. see Eq. (24a) in ref. 22]. However, for p-polarized light the spectra change in shape strongly with t in a way, whichcannot be reproduced by the simple "free-electron" model. Several featuresare worthwhile noting, (i) The spectra ofAg(l 11) for p-polarization and non-normal incidence are no longer one-sided, as predicted by the free-electronmodel, but show a clear sign change in the energy region around 4.5 eV, wheretransitions at the X point of the Brillouin zone occur in Ag. In addition, a


Electroreflectance of Copper, Silver, and Gold Single Crystal Electrodes 73

pronounced dip in—

(AR/R)p is found at 3.8 eV, the volume plasmonexcitation energy for Ag. (ii) The relative growth of a peak in

—

(AR/R)p at3.5eV for Au(lll) and at 2.2eV for Cu(lll) with increasing ! is striking.These prominent peaks may in both cases be tentatively assigned totransitions at the L-point, namely (L3 -» EF) for Cu and (EF-> L% ) for Au.However, we find for Au, where the ER can be investigated on either side ofthe potential of zero charge (pzc), that the angle dependence is markedlyinfluenced by the bias potential. The pronounced peak at 3.5 eV for x > 45°is only seen at potentials negative of the pzc, while it is absent in thecorresponding spectra positive of the pzc. In the latter case the spectra aresimilar to those obtained for polycrystalline Au at high angles of incidence[8]. (iii) When we compare the magnitudes of AR/R for Cu(lll) on mica(Fig. lb) and for a massive Cu(lll) single crystal, we find the signal in thelatter case smaller by almost one order of magnitude. Previous studies in thislaboratory revealed that the ER effect for Cu is smallest for perfect (111)surfaces and considerably larger for high index faces, that is, stepped surfaces[16]. By comparison ofour data in Fig. 1 b and those previously obtained on aCu cylinder we have to assume that Cu(l 11 ) on mica has a less perfect surfacethan we generally assumed. One possible explanation would be that a

roughening of the Cu(lll) surface in the electrolyte takes place byreconstruction, especially when we are very close to the potential for Cudissolution [23]. Cu is the only metal where we are forced to work close to theCu/Cu2+ potential in order to apply potential steps as wide as possible.

3.2. Potential dependenceSince the screening power of the free electrons is changed slightly by the

electrode potential, the potential dependence of the ER effect should also beindicative of a bound electron contribution to the ER. A potentialdependence for Au [6] and Ag [24] has been found previously and interpretedalong these lines. We have studied the potential dependence of the ER effectfor Ag( 111 ), Au( 111 ) and Cu( 111) and the result is shown in Fig. 2 for Ag andAu. The spectral shape as well as the magnitude of the ER effect show acharacteristic dependence on the electrode potential U0, very pronounced forAg(lll) and Au(lll), but only minor for Cu(lll). The experimental resultsshow, that usually the signal decreases when the surface is charged negatively.This has been tentatively explained by a decreasing influence of the electrodepotential on the electron concentration at the surface [25]. A detailed study ofthe surface plasmon excitation by ATR has revealed that driving theelectrode potential negative of the pzc obviously does not change the electrondensity at the surface significantly [26]. At increasingly positive i/0-valueswith respect to the pzc, which can only be applied to Ag and Au, the shieldingaction of the free electrons is reduced more and more, revealing the boundelectron contribution. As is seen in Fig. 2 a for Ag(l 11) the structure around



Fig. 2. Electro-reflectance spectra of Ag(111) (a) and Au(111) (è) for various bias potentials U0.p-polarization.<p, = 45°. 0.5 M NaC104, except for Au(111) at +0.6 and +0.8 V (1 M HC104)

4.5 eV (275 nm), which we attributed to bound electrons (see sec. 3.1.), isindeed strongly potential dependent. Furthermore, we realize that thepronounced dip at 3.8 eV attributable to volume plasmon excitation vanishesat the most anodic U0. The spectral changes in AR/R for Au(l 11) at positiveU0 (Fig. 2 b) are very similar to those reported already by Mclntyre forpolycrystalline surfaces [6]. It may be worthwhile noting, that the shoulder in

—

(AR/R) around 2.0eV (620nm) at positive U0, which was observed forpolycrystalline Au [6,11], is also found for Au(lll). This shoulder was

frequently assigned to surface plasmon excitation at the positively chargedAu surface [6,11], where theoretically the necessary requirement e'Au surface =

£h2q may be fulfilled. However, since in our case surface plasmon excitationis not possible due to the flatness of the sample surface, this explanation canbe discarded.


Electro-reflectance of Copper, Silver, and Gold Single Crystal Electrodes

i

3

1

1

SÍ

75

3.0 3.5 4.0 /eV-

Fig. 3. Electroreflectance spectra ofAg(l 11) and Ag(100) in 0.5 M NaClCv 1 = 45°. -0.5 and0.0V. (a) Ag(lll), s-polarization, (b) Ag(100), s-polarization, (c) Ag(100), p-polarization

3.3. Dependence on crystallographic orientation

Any influence of the bound electrons on the ER effect would be seen mostclearly by comparing the ER spectra for various crystallographic faces of oneand the same metal. This was first demonstrated by Fúrtak and Lynch [14] forAg(100) and Ag(l 10) in a small region around the L point transitions at 3.8—

4.0 eV, but not discussed in any detail. In Fig. 3a and b we show the ERspectra of Ag(lll) and Ag(100) single crystal surfaces for s-polarized light,<p! =45° and otherwise same conditions. Several distinct differences are

discernable. The most striking difference is found in the high energy regionaround 4.5eV, where the structure in

—

(AR/R) for the (111) face, which we

assign to a transition at the Appoint, is completely absent for the (100) face.Obviously in the latter case those transitions at the Appoint, which are

sampled by the s-polarized light are not modulated by the static electric field.It is interesting to notice, however, that the s-like shape does appear on the(100) face when p-polarized light at non-normal incidence is used (seeFig. 3 c). We will discuss this observation later.

A remarkable polarization anisotropy of the normal-incidence ER effectfor the (110) surface has been observed for Ag [14] and Au [17] when theelectric field vector e of the light was rotated. For both metals the anisotropyis mostly determined by differences in magnitude and not so much in spectralshapes. This is quite different in the case of Cu. We have studied Cu(l 10) on aCu single crystal cylinder and spectra were recorded by employing themodulation technique. The results, normal-incidence ER spectra for [lTO]and [001] directions, are shown in Fig. 4. With the exception of a small energy



gl_ _ _ _ _ _ _I1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

/eV- Fig. 4. Normal-incidence electroreflectance spectra of Cu(110) in 1 H2S04 for the electric fieldvector of the light being parallel (-) and perpendicular (-) to the [110] direction. U0 =

—

0.3 V. AU = 100mV (peak-to-peak)./= 180 Hz. The electrode is a Cu single crystal cylinder

region around 3.5—

4.0 eV, we find the ER-effect always larger for e _L [110]than for ?|| [ITO], similar to the observations on Ag and Au [14,17]. ForCu(llO) the anisotropy is largest at energies (2.1 —2.6 and ~4.5eV), whereinterband transitions near the L-point (L3 -» EF and EF-> Lt) are assumed.The most marked difference in the two spectra, however, is the pronouncedstructure around 4.1eV for e± [110], which seems absent for e\\ [lTO].Besides, the peak maxima in

—

(AR/R) at 2.2eV occur at distinctly differentphoton energies.

3.4. Surface plasmon excitation on stepped Ag surfacesIn ER studies on polycrystalline Ag, surface plasmon (SP) excitation via

surface roughness is a commonly observed feature. It causes a derivative-likestructure in the ER spectra centered around 3.5 eV [15], where the necessaryrequirement, e'Ag = — 0, is fulfilled. This structure is completely missingwhen perfectly flat single crystal surfaces are used (see e.g. Fig. 1 a). Since thenatural roughness of a polycrystalline surface supplies a whole spectrum of/c-values, which are required for momentum conservation during opticalplasmon excitation, the SP excitation occurs over an extended k- and energy-region in the respective plasmon dispersion curve. In the search for a well-defined momentum source we prepared a stepped surface, assuming that theterrace width supplies the desired k in one direction. In Fig. 5 we show thenormal-incidence ER spectra of a Ag surface, which is tilted 3° against the(110) plane, with the steps along the [001 ] direction. The spectraare recorded for - ] and ?|| [110], which coincides with e being parallel and perpendicular tothe steps. The difference is striking. Forell [lTO] the structure around 3.5eV(350 nm) is extremely sharp and pronounced, while for the other directionsurface plasmon excitation is only weak, as indicated in —(AR/R) (dashed


Electro-reflectance of Copper, Silver, and Gold Single Crystal Electrodes 77

6

k

2

Ci:

^ 0CD

-2

-4600 500 400 300 200

-— /nmFig. 5. Normal-incidence electroreflectance spectra and static reflectance spectra of a stepped

Ag(l 10) surface. 0.5 M NaC104. -0.5 and 0.0 V. The steps lead in [lio] direction

line in Fig. 5). This is also seen in the static reflectance spectra for the twopolarisation directions at normal incidence (see insert in Fig. 5). In the firstcase a very sharp dip is observed due to strong SP excitation which is largelyabsent for the other direction. Since the steps should have a profound effectonly on SP excitation, we believe that outside the energy region for SPexcitation the two spectra reflect the anisotropy in the ER of the Ag(llO)surface.

4. Discussion4.1. The free electron contribution to the ER

The first successful approach to the understanding of the ER effect ofmetals was the free-electron model [11,12]. In this model it is assumed, thatthe concentration of free electrons on the surface is changed by the electrodepotential while the bound electrons do not respond to the applied electricfield because of perfect screening. Hence, separating the complex dielectricconstant of a phase j, ,- = ej

—

'/, into contributions from free and boundelectrons

êj = Hí + Hb (1)one can derive a potential dependent difference between the dielectricconstants of bulk metal and metal surface [11,12],

Surface ~ 4ulk = (4ulk,/-

1) ' (AN/N) (2)which is responsible for the observed reflectance change. In Eq. (2) / denotes the field induced, normalized change in the free electron con-

Ag (110) 3° [fìO]



1.5 2.0 2.5 3.0 3.5 4.0 45 5.0 5.5 6.0 /eV-

Fig. 6. Electroreflectance spectra of Cu(l 11) for 1 =45° and s- and p-polarized light. (-)Experimental curves for A U = 500 mV. (-) Calculated according to the free-electron model.AN/N = +0.2. (OOOO) Adding to the free-electron model a 0.1 eV shift of the onset of the

interband transition to higher energies

centration at the surface. Model calculations for metals like Cu, Ag and Aureveal that AN influences only the real part of the surface dielectric function,and not the imaginary part which is almost completely determined by thebound electron contribution, at least in the energy range discussed here. Forpolycrystalline Au and Ag, this model can reproduce the gross features of themeasured ER spectra [12]. However, these features arise mainly from the Í/R-effect always present for those metals whose reflectivity shows a rapidlyvarying energy dependence. Many details in the spectra could not beexplained by this simple model, indicating a substantial contribution fromother sources so far neglected in this approach. For example with Cu, thestrong peak in

—

(AR/R) at 2.2 eV is not at all reproduced by the free electronmodel (see Fig. 6, dashed line) [11]. The spectral shape, however, is obtainedfor Cu(l 11) in detail when we in addition assume the onset of the interbandtransition [L3 -> L2, (EF)] to be shifted by about 0.1 eV for a 500 mV potentialstep (dotted line in Fig. 6).

Although model calculations yield intitial information on the validity ofany theoretical assumption, a direct evaluation of the surface dielectricconstant remains most desirable. As a first approach we chose the Kramers-Kronig-Analysis (K.K.A) of the AR/R data to calculate surface dielectricconstants with the aid of the 3-layer model [27]. This method allows us toexclusively use reflectance data from s-polarised light for the evaluation thusavoiding possible difficulties with the use of p-polarization. It has beenshown, that in the latter case neglect of the full non-local dielectric response ata jellium surface, as inherently done in classical optics, may give rise to errors

[28]. ER spectra of Cu(lll), Ag(lll) and Au(lll) for s-polarized light were

KK-analysed for various potential steps, the details being described el-sewhere [29]. Typical results for Cu(lll) and Ag(lll) on mica are shown inFig. 7. The tail fit was chosen in such a way that £súrface is (i) always positive


Electro-reflectance of Copper, Silver, and Gold Single Crystal Electrodes 79

b1.0 2.0 3.0 4.0 5.0 6.0 1.0 2.0 3.0 4.0 5.0 6.0

fttu/eV--Fig. 7. Surface dielectric constants (-) for Cu(l 11) and Ag(l 11) as evaluated by Kramers-Kronig-Analysis of electroreflectance data for s-polarization and 1 = 45°. Thickness of thetransition region d=2k. (a) Cu(lll) negatively charged by dt/ = 500mV. (b) Ag(lll)positively charged by U = 500 mV. The solid lines represent the bulk dielectric constants

and (ii) as close as possible to e{¡u[k. We noticed that the tail fitting proceduredid not affect the spectral shape of the result, but did change the absolutevalues. The results shown in Fig. 7 are as follows, efface deviates in generalfrom fizuik as predicted by the free-electron model, although the absolutedifference is still larger than in the model calculation. Secondly, s¡'urf¡íce doesshow a marked deviation from e(,'ulk in contradiction to the free-electronmodel. For E's^T(ace (tito) a shift in the onset of the interband transitions isclearly discernable.

4.2. The bound electron contribution to the ER

The role of bound electrons in ER has first been considered by Hansen etal. [7] and substantiated by experiments of various groups [6,13—15]. Thismeans that the screening power of the free electrons is not sufficient to

completely shield the static electric field for the d electrons. The observedpotential dependence (see e.g. Fig. 2) is one of several convincing evidences.Hence, we can assume that the applied electric field F represents a strongperturbation near the surface for the more localized wave functionschanging their energies by an amount <f;| Vp\f¡> = ( \ \ f;>. Since theperturbation potential Vp is likely to be, in contrast to semiconductor ER,nearly of the same order as the atomic potentials, the perturbation shouldseverely affect the electron energies at the surface. Assuming the bandstructure parallel to the surface being retained, but only shifted in energy,transitions from and to the Fermi level should be modulated most strongly in


so R. Kötz and D. M. Kolb

energy, while those at critical points are believed to be affected much less. TheKKA (Fig. 7) as well as model calculations (e.g. Fig. 6) indicate substantialenergy shifts for (d -> EF) transitions, of the order of 0.1 eV for potential stepsof only a few hundred mV.

Besides energy shifts due to the strong static electric field F, the symmetryproperties of the surface dielectric tensor can also be extracted from ERspectra using single crystal surfaces. Although the incident, linearly polarizedlight samples individual branches of the star of k¡ differently for an interbandtransition at an off-center point ofthe Brillouin zone (k¡ 0), the summationover all equivalent branches leads to the known isotropie result for a cubiccrystal. In a semiconductor this degeneracy of the star of k¡ is lifted by an

applied electric field F, because the individual branches of the star are

affected differently [30]. For a cubic metal, however, we deal now with twodifferent sources for an anisotropy in ER. Firstly it is the surface itself,sampled in metallic ER, which gives rise to an atjeast uniaxial tensor for theoptical response, secondly it is the electric field F, which in addition may liftthe degeneracy of the star of k¡. Our experimental results suggest that an

interband transition near a critical point is strongly modulated by F only,when the field has a component in the principal direction of the critical point.This direction is given by that reciprocal lattice vector G, which supports theoptical excitation. The reason for this assumption to hold could either be themodulation of the matrix element or the joint-density-of-states. However,with the condition

F- G; 0 (3)and the polarization selection rule for optical excitation of an interbandtransition [31]

eG^O, (4)e being the electric field vector of the photon, many of the observed spectralfeatures in the ER of Cu, Ag and Au can be explained. This is demonstratedfor two examples. Firstly, we discuss the difference between 4.0 and 5.5 eV inthe spectra of Ag(lll) and Ag(100) for s-polarization (see Fig. 3). Thederivative-like structure in this region, which is only seen for Ag(lll), isassigned to the modulation of a transition at the X point. For the (100)surface, the 6 directions for this transition are either parallel (4) or

perpendicular (2) to the surface, so that either F-G, or e- G, is always zero.

Modulation is possible for Ag(lll) where these directions are at an angle of~55° to the surface, or for Ag(100) with p-polarization anàcp1 0, where a

component of e parallel to F is generated. In the latter case two of the sixtransitions near X(F

—

^directions) should now be modulated. This is indeedobserved (see Fig. 3c). Secondly, the angle dependence for Cu(lll) andAu(lll) (Fig. 1) can be understood along these lines. The interbandtransitions near the L-point (at 3.5 eV for Au and at 2.2 eV for Cu) are moststrongly affected in this model for F\\ G„ that is for G, perpendicular to the


Electroreñectance of Copper, Silver, and Gold Single Crystal Electrodes 81

surface. However, such transitions are excited optically only with p-polarization and favorably at high angles of incidence, as seen in themeasured spectra.

An interesting normal-incidence polarization anisotropy for AR/R hasbeen found at the (110) face of Ag [14], Au [17] and Cu (Fig. 4), when theplane of polarization is rotated with respect to the crystallographic orien-tation. Fúrtak and Lynch have offered an explanation based on a modulationofslightly indirect transitions [24,32]. Since their model predicts this effect tobe observable only for Ag and not for Au and Cu, the above mentionedfinding seems to invalidate this explanation. However, assuming Eq. (3) tohold as a necessary condition for the observation of bound electroncontributions, we can also explain the anisotropy effect for (110) surfaces, asis demonstrated for the 2.2eV transition in Cu at the L-point. For e|| [110]and normal incidence the light samples only 4 of the 8

—

L directions andin addition these 4 directions are all perpendicular to F. Therefore modu-lation is not possible. For è _L [110], however, we find at least 4 branches of thestar of G¡, for which Eqs. (3) and (4) are both fulfilled. Hence, in the latter case

an additional contribution from interband modulation is expected, yielding a

larger A R/R for ë A. [110] than for e 11 [110], which is indeed observed. For thevery same reason the unexpected change in the anisotropy to less than unity(Fig. 4) between 3.5 —4.0 eV for Cu(110) can be understood in this modelwhen we assume that in this energy region the contribution from transitionsat the X-point (X5 -* Xx, at 4.0 eV) is dominant.

4.3. The influence of the surface microstructureon the ER effect

It has been shown recently, that the ER for high index, open surfacesis much larger than for low index, densely packed surfaces [16].This has been tentatively explained by differences in the electron densitydistribution parallel to the surface. The electron concentration at a metalsurface decreases continuously from the bulk value to zero in a thin transitionlayer. On a highly corrugated surface the spreading of the electronsperpendicular to the surface should reproduce the wavy structure of thepositive background parallel to the surface. However, the smoothing effect[33] tends to reduce any structure in the density profile parallel to the surfaceby accumulating negative charge in the valleys. A charging of the metalelectrode by an applied electric field will affect the electron densitydistribution not only perpendicular but also parallel to the surface.

Ifone assumes this argument to hold on a very atomic scale, an alternativeexplanation of the polarization anisotropy for (110) faces seems feasible. Weconsider the (110) face to be an atomic grid. Then it would be reasonable toassume that the optical surface conductivity is different for the twodirections, [lTO] and [001], in the first case slightly higher than in the second.



In a simple picture we can rationalize, that in [110] azimuth the tail in electrondensity at the surface is pushed outward with negatively going electrodepotential without changing the density contours. In [001] direction, however,where the density contours are wavy, an increase in the charge concentra-tion at the surface with potential smoothes out this structure and, inversely, adecrease in concentration emphasizes the positive background structure.From this simple argument one can understand that the conductivity change,which determines AR/R, is larger in [001] than in [HO] direction.

The importance of the surface microstructure for the ER effect, e.g. thepresence of atomic steps in the surface, is especially clearly seen in surfaceplasmon excitation (Fig. 5). A regularly stepped surface obviously supplies awell-defined momentum value for plasmon excitation and hence allows tomeasure in that region of the plasmon dispersion curve which is notaccessable by ATR techniques. In our case the terrace width should be about60 Â, assuming steps of atomic height. This would correspond to a lvalue of0.1 Â"1 ! However, we cannot rule out at the moment, that higher steps andcorrespondingly larger terrace widths are also of crucial importance. Furtherexperiments are planned to explore the role of stepped surfaces in metallicER.

In summarizing, we have tried to unravel the various contributions to theER of metals. Measurements on single crystal surfaces reveal interestinginformation from electronic states at the very near surface region, but stillmore experiments are necessary until we can extract quantitative informationabout the metal's surface band structure. Furthermore, stepped surfacesseem to be a promising subject to be studied, which may help us to understandthe role of the surface structure in metallic ER.

References

1. M. Cardona, Modulation Spectroscopy. Academic Press, New York 1969.2. D. E. Aspnes and N. Bottka, in: Semiconductors and Semimetals, ed. by R. K. Willardson

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Electroreflectance of Copper, Silver, and Gold Single Crystal Electrodes