Anisotropic Resistance of the Clean and Oxygen-Covered Cu(110

Jun 5, 2012 - A qualitative explanation of the anisotropic baseline shift can be given within existing theory, but for a quantitative description anis...
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Anisotropic Resistance of the Clean and Oxygen-Covered Cu(110) Surface in the Infrared Jan Pischel, Olaf Skibbe, and Annemarie Pucci* Kirchhoff Institute for Physics, Im Neuenheimer Feld 227, D-69120 Heidelberg, Germany S Supporting Information *

ABSTRACT: With mid-infrared spectroscopy at room temperature, we investigated the adsorption of oxygen on the clean, single-crystalline Cu(110) surface resulting in the well-known (2 × 1)O−Cu(110) added-row reconstruction. We observed an anisotropic change of broadband reflectance which corresponds to an anisotropic surface resistance change. The resistance change is more pronounced by a factor of 7 for the plane of light incidence parallel to the [11̅0] direction. However, even perpendicular to this direction, a small but significant change is observed. A qualitative explanation of the anisotropic baseline shift can be given within existing theory, but for a quantitative description anisotropic electronic scattering of the bulk is crucial. Our results may be relevant for the optical behavior of nanocrystallites.

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INTRODUCTION The theory of surface scattering (or more generally boundary layer scattering1) of metallic conduction electrons has been established in the first half of the 20th century by Fuchs2 and Sondheimer.3 It is only in the 1990s of the past century that Persson and co-workers refined this theory by taking into account the electronic nature of adsorbate−substrate interaction assuming a Newns−Anderson model for bonding.4−6 A great success of this model was the ascription of an infrared (IR) reflectance change to an adsorbate-induced change in dc conductivity by additional scattering at randomly distributed adsorbates and the explanation of the appearance of dipoleforbidden frustrated translations and rotations in IR spectroscopy.7,8 The property of adsorbates to affect the conductance of metallic substrates has further gathered attention by a report of the group around Bohn that mercaptans, which are known to form self-assembled monolayers on gold surfaces,9 can be detected down to a ten thousandth of a monolayer on thin gold films by exploiting this effect.10 This opened the door to the instrumentation of the effect for chemical sensing applications. To enhance sensitivity, the ratio of surface atoms to bulk atoms has to be maximized which finally leads to the use of nanowire sensors11−17 with lateral dimensions down to the atomic scale, where ballistic electron transport sets in and conduction is quantized.18 For wires with conductance at the lowest quantum step, Bogozi et al. reported a decrease of conductance as large as 50% upon dopamine adsorption.11 Further sensitization of mesoscopic nanowires is achieved by the use of porous nanowires, which again enlarges the surface to volume ratio.13 A very recent review about conductance-based chemical sensing in metallic nanowires was published by Duan et al.1 © 2012 American Chemical Society

For some of the applied sensors, the observed resistance changes are believed to have their origin in adsorbate-induced restructuring of the monatomic wires15 or in the presence of semiconducting chemically responsive interparticle boundaries.17 In the case of monatomic chains, it is no longer correct to talk about conventional adsorption since simulations have shown that in this case “adsorbates” may become part of the nanowire and may even enlarge its conductance19opposite to what is predicted by the traditional theory for macroscopic systems. Despite these constrictions, there is evidence by a number of studies1,11−14 that nanowires can be used to very sensitively detect molecules (also in solution) by the adsorbateinduced decrease in conduction. The high sensitivity of the substrate conductance to adsorption has been exploited in a recent experiment carried out by Rouhana et al. who measured the resistance variation of a gold thin film upon adsorption of short-chain mercaptans and disulfides via a four-point probe.20 They used the obtained data to reveal details on the adsorption kinetics and the underlying mechanism. The use of nanowire sensors for the investigation of adsorption kinetics has also been proposed and demonstrated by Lin et al.14 Considering the potential of adsorbate-induced surface resistance in sensing applications, it is evident that for a quantitative analysis reproducible fabrication of the detectors is an essential step. However, a better understanding of the underlying processes is de rigueur as well. One open question in that sense concerns the above-mentioned relation between an adsorbate-induced increase in surface resistance and changes in Received: April 2, 2012 Revised: June 4, 2012 Published: June 5, 2012 14014

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dielectric function ε of the substrate, w can also be expressed by the parameters introduced by Langreth28 as w = ζ′εζ. With the wave vector of incident radiation q (qx > 0, qz > 0, qy = 0), that of transmitted radiation q′, vacuum at z < 0, and the substrate at z > 0, the used parameters were defined as ζ = qz/qx = cot θ and ζ′ = q′z/qx = [ε(ζ2 − 1) + 1]1/2. Langreth extended Feibelman’s d-parameter formalism29 by again applying macroscopic boundary conditions and found an expression for the reflection coefficient of an adsorbate-covered surface that is related to the frequency-dependent surface polarizabilities parallel and perpendicular to the surface. Substituting the surface polarizability in another approximation by terms depending on Feibelman’s surface response function d, Persson4 came up with a similar expression, namely

IR broadband reflectance: McCullen et al. have shown that in contrast to the predictions of a simple model of free electrons with random point scatterers the ratio between these two effects depends not only on the substrate but also on the adsorbate and that an assumed change of the substrate electron density cannot account for it.21 The relevance of this relation lies among others in the ease of a contactless in situ measurement of the reflection change. In terms of a better understanding, Otto et al. made the interesting discovery that on the anisotropic Cu(110) surface the adsorbates carbon monoxide and ethene increase surface scattering in one but not in the other orientation.22 Consequently, with the proper alignment of a crystalline sensor the sensing efficiency can be significantly increased. Here, we report on our experiments on the same surface with oxygen as adsorbate. We will show that adsorption of oxygen contributes to surface scattering in both orientations and apply a theoretical description of adsorbate-induced change in broadband reflectance to our experimental results. Our results complete data from reflection-anisotropy spectroscopy in the visible range, where the observed anisotropy for the clean and oxygen-covered Cu(110) arises from the anisotropy of electronic transitions between the surface states at the Y̅point of the surface Brillouin zone.23−25 In contrast, in the midinfrared only intraband excitations are relevant for this system, and an anisotropy in reflectance corresponds to an anisotropy in electronic relaxation. The full information on surface contributions to electronic damping is extremely important for controlling plasmonic behavior of metal nanoparticles (e.g., ref 26). For the wet-chemical tailoring of single-crystalline nanoparticles, anisotropic electronic damping caused by adsorption of oxygen could be an important issue since nanowires often are prepared under considerable oxygen partial pressure and electronic damping hinders the propagation of surface plasmons for instance in metallic nanowires. Also, for clean metal particles, anisotropy in electronic scattering is important since it modifies the line width of a plasmonic resonance and in that way the quality factor and the sensor efficiency. The article is organized as follows: First, a short review of the theory of reflected IR light is given, and the applied substrate is introduced, followed by a description of our experimental setup and procedure. After that, the measurements are presented and analyzed. We conclude the article by giving a brief summary of its content.

ΔR RFresnel

=−

⎤ 4ω sin 2 θ ⎡ 1 Im d ⎥ ⎢⎣Im d⊥ + 2 ⎦ c cos θ sin θ

(2)

As Persson pointed out, the contribution of adsorbates to Im d⊥ can be neglected as compared to those to Im d∥. To evaluate the definition integral of d∥ (note that the induced currents J are proportional to the conductivity σ for a given electric field E at the surface) ⎛ d:=⎜ ⎝

∫

dz

−1 ∂σ ⎞ ⎛ ⎟ ⎜ ∂z ⎠ ⎝

∂σ ⎞

∫ dzz ∂z ⎟⎠

(3)

an expression for the conductivity is required which is according to Persson given by the approximation σ (z) = σbΘ(z) + Δσ Θ(z)Θ(lb − z)

(4)

where σb and lb are the values of the conductivity and the electron mean free path deep inside the bulk, respectively, and Θ(z) is the Heaviside step function. The underlying idea is to treat the adsorbate-covered surface as a layer of thickness lb of modified conductivity σb + Δσ on a substrate with the pure bulk properties. This is certainly perspicuous because only within a layer of thickness equal to or less than the bulk mean free path of the electrons surface scattering can be assumed to play an important role. This idea and inserting σ(ω) ∝ ω·(ε(ω) − ε∞) into eq 3 yield the following expression for the differential reflectance ΔR RFresnel

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=

8ωπlb ⎡ Δε(ω) ⎤ Im⎢ ⎥ cos θ ⎣ εb(ω) − ε∞ ⎦

(5)

The differential reflectance is a frequency-dependent function of the angle of incidence θ, the bulk mean free path of the electrons lb, the bulk dielectric function εb(ω), the dielectric background ε∞, and the adsorbate-induced change Δε(ω) of the dielectric function in the vicinity of the surface. The bulk mean free path depends on the bulk scattering rate ωτ,b (in units of cm−1) and the Fermi velocity vF via lb = vF/c ωτ,b, where c = 3 × 1010 cm s−1 is the speed of light in vacuum and c ωτ,b gives the number of scattering events per second. We used expression 5 (under the assumption that ε∞ ≡ 1) to simulate and to evaluate our spectroscopic results on the Cu(110) surface. The variation of the Fermi velocity is less than one percent for the directions considered in this article30 and can be assumed to be constant: vF = 1.13 × 106 m s−1 (ref 31 and refs therein). As is the case for any (unreconstructed) fcc(110) surface, the unit cell of this surface is rectangular which leads to the existence of close-packed ridges in the [11̅0] direction which

REVIEW OF THE THEORY The question of amplitude and polarization of reflected (IR) light at surfaces (or strictly spoken at interfaces) is an old one, and its fundamentals are discussed in many textbooks.27 Starting at a macroscopic point of view with Maxwell’s equations and imposing the corresponding matching conditions for the involved fields, one arrives at the Fresnel formulas. For the case of IR reflection spectroscopic measurements which means the use of p-polarized radiation, the reflection coefficient is given by 1−w rFresnel = (1) 1+w where the quantity w is given by cos θt/n cos θi; n is the refractive index of the substrate; and θi and θt are the angles of incoming and transmitted (refracted) radiation, the latter being determined by Snell’s law. Making use of ε = n2 with the 14015

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S/N 566), see Figure 2(a), and by comparing IR vibrational spectra of the system CO/Cu(110) to literature data.34−36 Following the experiments of Otto et al.,22 two different sample configurations were examined: In a first step the Cu(110) crystal was oriented in a way that the rows in the [11̅0] direction were parallel to the plane of incidence. This will be referred to as “parallel geometry” in the following. Then the sample was turned by 90° resulting in the [11̅0] rows being perpendicular to the plane of incidence which will be referred to as “perpendicular geometry”. Gaseous oxygen from Messer Griesheim of nominal purity 99.998% (checked by a quadrupole mass spectrometer) was dosed on the sample held at room temperature using a leak valve. The temperature was 294 K for perpendicular and 296 K for parallel geometry with fluctuations less than 0.2 K and a possible systematic error of up to 1 K. The oxygen partial pressure during exposure was held in the 10−9 mbar range. During that procedure, in situ measurements of the broadband reflectance were performed. This means that each spectrum shown here is the average over a certain range of oxygen exposure. The exposure given in the graphs is the one reached at the end of the corresponding spectrum. The time needed to acquire a single spectrum was roughly one minute corresponding to an exposure range covered of about 0.1 Lc. The exposure is given in corrected Langmuirs Lc (1 Lc = 1.33 × 10−6 mbar s·f) where a correction factor of f = 0.87 for the ionization probability of oxygen37 has been taken into account. For exposure, a systematic error of up to a factor of 2 is possible. However, relative statistic errors in exposure are much smaller. During the whole exposure range investigated in our experiment, the surface reconstruction is of the (2 × 1)O−Cu(110) added-row type (Figure 1), and incorporation of oxygen by the copper crystal does not take place.38 After each experiment, the oxygen-covered sample was heated to 200 °C, and the LEED pattern of the annealed (2 × 1)O−Cu(110) reconstruction39 has been observed at sample temperatures around 100 °C (see Figure 2(b)).

are separated by troughs oriented in the same direction (see Figure 1). The resulting anisotropy and openness are key

Figure 1. First layer of the highly anisotropic Cu(110) surface consists of rows in the [110̅ ] direction (left). For the (2 × 1)O−Cu(110) added-row reconstructed surface (right), the positions of oxygen atoms and copper adatoms within the added rows in the [001] direction as determined by Coulman et al.32 are indicated.

properties responsible for interesting phenomena like the oxygen-induced (2 × 1)O−Cu(110) added-row reconstruction32 (see Figure 1) or the anisotropic reflectance change discussed in this paper.

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EXPERIMENTAL SECTION The experiments were carried out in a UHV chamber described elsewhere33 using the commercial Fourier transform IR spectrometer IFS 66 v/S by Bruker Optics, Germany, together with a liquid nitrogen cooled MCT detector. The base pressure was 2 × 10−10 mbar or less. The spectra were taken with ppolarized light at grazing incidence (angle of incidence θ = 85°). Stability measurements actually showed a small frequency-dependent baseline drift above 3000 cm−1 which was very slowly oscillating in time. Compared to adsorbateinduced reflectance changes, these effects are negligibly weak. The copper crystal (MaTeck) was circular with a diameter of 10 mm and a thickness of 2 mm. The nominal alignment of the surface was (110) ± 0.1°. After insertion into UHV, the crystal was prepared by repeated cycles of Ar ion sputtering (ca. 0.6 A cm−2, 5−10 min) and subsequent annealing to approximately 530 °C (45 min). Surface purity and orientation were checked both by low-energy electron diffraction (Omicron SpectaLEED

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RESULTS Figure 3 shows the change in broadband reflectance observed during exposure of oxygen for both geometries investigated. Qualitatively the same behavior is observed for the two cases: the IR reflectance decreases over nearly the whole spectral range under investigation. The effect is most distinct in the

Figure 2. LEED patterns of the bare (a) and the oxygen-induced (2 × 1)-reconstructed (b) surface for perpendicular geometry (plane of incidence in horizontal direction). The kinetic energies were 150 eV (a) and 125 eV (b), respectively. 14016

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The spectral absence of any vibrational feature in the mid-IR spectra is not surprising as oxygen adsorbs atomically on Cu(110) at room temperature40 and the adsorbate−substrate stretching vibration at roughly 400 cm−1 (ref 41) is energetically below the range of the MCT detector. Figure 4 (bottom) shows the development of the recorded spectra with oxygen exposure in the wavenumber region of

Figure 4. Bottom: Change in reflectance induced by adsorption of oxygen for parallel (red squares) and perpendicular (blue triangles) geometry (see text for details) in dependence of oxygen exposure at the point of lowest relative reflectance, i.e., 2000 and 1400 cm−1, respectively. Ten spectra before dosing oxygen and 12 spectra after dosing (with negligible oxygen partial pressure) demonstrate the experimental stability. Top: Dependence of the fitting parameter ωads (the adsorbate induced surface scattering rate, see below) on oxygen exposure. For errors, see text.

Figure 3. Relative reflectance showing the broadband change induced by adsorption of oxygen for parallel (a) and perpendicular (b) geometry (see text for details). Note the different ordinate and abscissa ranges. Solid lines are the measured data; the dashed lines are fits (compare section “Discussion”). Exposures are given in corrected Langmuirs Lc.

region around 1000−2000 cm−1. For the case of perpendicular geometry, an unambiguous reflectance decrease is observed only below 4000 cm−1. We were able to reproduce this response to oxygen adsorption such that any parasitic effect (e.g., sample misalignment) can be excluded. A misalignment could also be excluded from the LEED pattern observed for the same, well-defined azimuthal position of the sample on the sample holder. Clearly, the broadband change due to oxygen adsorption is present in the case of perpendicular geometry where it almost vanishes for the adsorbates carbon monoxide and ethene. For parallel geometry, the change in broadband reflectance is much more pronounced which is in accordance with the findings of Otto et al.22 if it is taken into account that oxygen adsorbs on top of the ridges in the [110̅ ] direction. The effect for perpendicular geometry is reduced by a factor of 7 with respect to the parallel arrangement. Looking at the details of the change, it turned out that the spectral shape shows a significant difference in the position of the broad reflectance minimum. As we will show later with spectral simulations (see section “Discussion”), the observed difference in spectral shape can be attributed to two different bulk scattering rates for the respective geometries. A further proof for the physical reality of our findings is the fact that the absence of a baseline shift in perpendicular geometry according to Otto et al. could be reproduced with CO gas as adsorbate.

highest absorbance, i.e., around 2000 and 1400 cm−1 for parallel and perpendicular geometry, respectively. The data points in Figure 4 were determined by integration over an interval of width 200 cm−1 centered around the point of interest. As expected from theory, the change in reflectance is proportional to exposure at the beginning. This behavior starts to saturate already for exposures lower than 1 Lc, which is, at least partially, due to the decreasing area of the unreconstructed surface which remains available for oxygen adsorption.

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DISCUSSION Interpretation. We begin this section with a qualitative analysis of our observation. As shown before, oxygen-induced changes in surface resistance are anisotropic on the intrinsically anisotropic Cu(110) surface, and the main contribution to surface resistance is observed in parallel to the close-packed ridges. This is consistent with the work of Otto et al.22 who did not observe any change in surface resistance perpendicular to the rows. They explained their results by having a closer look at the induced currents at the surface: These may flow in the first layer if and only if there is a component of the electric field at the surface which is parallel to the atomic rows in the [11̅0] direction (compare Figure 1 and schemes in the Supporting Information). This situation is equivalent to observation in 14017

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Figure 5. Scheme of the surface cross section showing the scattering rates used in our model for the different regions of the bare (a) and the oxygencovered (b) surface. For the bulk, we consider a deviation ω0 to textbook data ωτ,b. The corresponding dielectric functions are εFresnel(ω) for the bulk region, εbare(ω) for the surface region in (a), and εads(ω) for the surface region in (b).

⎛ ΔR ads ⎞ R ads =⎜ + 1⎟ R bare ⎝ RFresnel ⎠

parallel geometry. For perpendicular geometry, electrons contributing to currents in the first layer would have to jump from ridge to ridge which is unlikely. This is why induced currents are restricted to second and deeper layers in that case. From such a qualitative picture, it is obvious that for adsorbates that sit on top of the ridges only the experiments carried out in the parallel geometry will be influenced by additional scattering of electrons at adsorbates. However, if any adsorbate sits in a 4-fold hollow site or if adsorption induces a reconstruction of the surface as is the case for oxygen on Cu(110), enhanced electron scattering may be expected also for currents flowing in the second and deeper layers (compare schemes in the Supporting Information). The oxygen atoms actually are sitting on top of the ridges as is deduced from STM measurements32 so that they directly contribute only to a change in surface resistance parallel to the ridges. However, they catch copper atoms diffusing on the flat terraces and integrate them into the reconstructed surface, thereby decorating places between the rows and thus in direct contact to the second layer. This should lead to an isotropically enhanced surface resistance and thereby to a contribution detectable also in perpendicular geometry. Mathematically, the change in the surface conductivity tensor can be expressed by ⎛1 0⎞ ⎛1 0⎞ ⎟ + Δσadatoms⎜ ⎟ Δσ = Δσoxygen⎜ ⎝0 0⎠ ⎝0 1⎠

⎛ ΔR bare ⎞ + 1⎟ ⎜ ⎝ RFresnel ⎠

(7)

We note that this model includes three different dielectric functions, namely, that of pure bulk copper, that of the bare surface, and that of the oxygen-covered surface (see Figure 5). We distinguished between scattering at the bare surface and additional scattering induced by the adsorption of oxygen. All of the dielectric functions are assumed to be Drude-type with a plasma frequency of ωP = 66 000 cm−1, see ref 31, and supposed to differ solely in the scattering rate, which is given by ωτ,b(ω) + ω0 for the Fresnel dielectric function εFresnel(ω), where ωτ,b(ω) = 192 cm−1 + 0.087ω is the copper bulk scattering rate derived from literature data42 (for details, see the Supporting Information) and ω0 accounts for possible deviations from it. A variation of the plasma frequency (which could be caused by an oxygen-induced change in electron density) had also been considered, but it did not improve significantly the fitting of our data. This is in accordance to the fact that the reflectance change is not sensitive to plasma frequency changes5in contrast to transmittance measurements of thin films, where broadband changes also arise from plasma-frequency changes due to charge transfer.31,43 A more sophisticated modified Drude model which yields a better description of the dielectric function from ref 42 (see the Supporting Information) does not improve the fits either and therefore is not considered here. Making use of Matthiessen’s rule, we added an additional surface scattering rate ωS, that we took to be independent of the wavenumber, for the description of the bare surface such that the overall scattering rate for εbare is given by ωτ,b(ω) + ω0 + ωS (Figure 5(a)). In a similar way, we finally defined the scattering rate of the adsorbate-covered surface as ωτ,b(ω) + ω0 + ωS + ωads where a further rate ωads accounts for changes in scattering induced by the adsorbate (Figure 5(b)). This includes potential changes in ωS which experimentally cannot be distinguished from changes in ωads. Inserting the, respectively, deduced Drude-type dielectric functions εFresnel(ω), εbare(ω), and εads(ω) into eq 5, and using eq 7, it should now be possible to fit the recorded spectra via the free parameters ωS and ωads. However, the different positions of the reflectance minimum can only be reproduced in the fit if different values for ω0 for the concerned geometries are used; i.e., if the bulk scattering rate is assumed to be anisotropic (see Figure 6). A reasonable spectral fit with the free parameters ωS (constrained to positive values) and ωads

(6)

in an appropriate coordinate system. This hypothesis that contact to the second layer might lift the anisotropy of induced surface resistance seems to be corroborated by experiments where we have investigated the IR reflectance baseline shift upon evaporation of copper atoms on the same Cu(110) substrate. Adatoms always sit between the parallel rows of the bare surface, and as expected, the decrease of reflectance (depending on adatom concentration) is, within the experimental errors, the same for both orientations. Simulation of the Spectra. To come to a more quantitative analysis of our data and to extract additional information from it, we started within the framework of existing theory, vide supra. The measured reflectances are not reflectances relative to the “true” bulk Fresnel reflectance RFresnel but measured relative to a spectrum which itself is modified by surface scattering at the pure surface. Therefore, we start by expressing the measured quantity Rads/Rbare, where Rads is the reflectance of the oxygen-covered surface and Rbare that of the bare surface, respectively, in terms of the known differential reflectances relative to the Fresnel reflectance (eq 5) 14018

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direction or the minimal group velocity (sound velocity) vg of the acoustic phonons which is provided by the transverse modes and which is smaller in the [11̅0] direction as well.45 The following semiquantitative argument shows that this is consistent with our findings (and that of Hanekamp et al.): The phonons which are most effective in decelerating the electrons constituting the induced currents (see first part of this section) are those which propagate parallel to these currents. Within the framework of the Debye approximation, the number of excited acoustic phonons of a branch i at a given temperature T is a monotonically decreasing function of its Debye frequency ωD,i (this is discussed to a further extent in the Supporting Information) which is, for conservation of the number of modes of that branch, proportional to the ratio of group velocity and corresponding real space periodicity vg,i/ai. Even though the periodicity is smaller in the [11̅0] direction, this ratio remains smaller in that direction such that more phonons are excited in the [110̅ ] direction than in the [001] direction. Now, the electron phonon scattering rate 1/τe−ph at room temperature can be assumed to be proportional to the number of excited phonons. This means that electron phonon scattering is dominated by the acoustical phonon branch with the highest number of excited phonons which coincides for the given reasons with the one with the lowest vg,i/ai ratio. The smaller this ratio (and the associated Debye frequency), the higher 1/ τe−ph will be for a given temperature, and the scattering rate in the [11̅0] direction is expected to be higher than in the [001] direction, consistently with what is observed experimentally. To summarize this section, for a reasonable spectral description, the bulk dielectric function of copper has to involve different scattering rates for the two directions [11̅0] and [100] involved in this study. It should be pointed out that although the IR reflection change is surface sensitive details of the adsorbate-induced baseline shift are depending crucially on the bulk properties of the metal substrate. This is an interesting aspect revealed by our analysis. In other words, the decoration of a metal surface by adsorbates leads to a “demasking” of detailed bulk properties that are otherwise hidden. Fitting Results. Using the insights described above, we were finally able to nicely simulate the spectra (see Figure 3). For this purpose, we used a Drude type dielectric function with ωP = 66 000 cm−1 and ωτ,b(ω) = 192 cm−1 + 0.087ω, modified by adding ω0 = 275 cm−1 ([110̅ ] direction) or ω0 = 57 cm−1 ([001] direction), respectively. The model was fitted to the spectral region with the highest IR intensity, namely, from 700 to 3000 cm−1, containing the region of strongest reflectance decrease. In this region, experimental stability is revealed by the constant reflectance before and after oxygen exposure (Figure 4). To reduce computation time and since we describe broadband changes, the number of data points per 100 cm−1 was thinned out to roughly 4 by averaging (compared to about 13 in the original spectra). It turned out that for parallel geometry ωS = 73 cm−1 (ωS = 122 cm−1 for perpendicular geometry) enables a good spectral description for all oxygen coverages under investigation. We obtained the dependence of the adsorbate scattering rate ωads on oxygen exposure. The development of this parameter is shown in Figure 4 (top). For the adsorbate-induced scattering rate qualitatively the same dependence on oxygen exposure is observed as for the baseline shift plotted in Figure 4 (bottom) which reflects the fact that the adsorbate-induced surface scattering is responsible for the reflectance change. Actually, besides the fact that the exact analytic dependence of the differential reflectance on the

Figure 6. Fit of the reflectance spectrum from Figure 3(a) for parallel geometry at an oxygen exposure of 5.0 Lc. The spectral shape is only reproduced with a positive ωS if ω0 = 275 cm−1 is added to the textbook bulk scattering rate ωτ,b(ω).

using Cu bulk textbook data with ω0 = 0 is impossible for parallel reflection geometry (red dotted curve in Figure 6), while for the spectra recorded in perpendicular geometry ω0 = 0 gives a fair agreement with the experiment. Adjusting the textbook bulk scattering rate by adding a direction-dependent ω0 allows perfect spectral fits for both geometries. A directiondependent change in the bulk mean free path lb (eq 5) follows. With optimum ω0 and ωS, the relative reflectance spectral shape is reproduced (see the Supporting Information); the strength of the overall reflectance decrease can be adjusted with the value of ωads that to a very good approximation acts as a wavenumber-independent scaling factor, as described already by Persson.8 The parameter ω0 turned out to be around 275 cm−1 for each spectrum referring to parallel geometry (this, of course, is related to the fact that the spectral shape of the absorbance does not vary from spectrum to spectrum), so that it could be taken as constant for the various oxygen coverages as expected based on its physical meaning. For the series of spectra taken in perpendicular geometry, a relatively small additional scattering rate ω0 = 57 cm−1 has been taken into account. A fitting of these spectra with the scattering rate deduced for the parallel geometry was clearly not possible. Different dielectric functions for the Fresnel reflectance of the different geometries correspond to an anisotropic conductivity in single-crystalline copper. It is interesting to compare this result to VIS/NIR ellipsometric measurements of the Cu(110) surface performed at room temperature by Hanekamp et al.44 They modeled their experimental results assuming one single Drude-type dielectric function with anisotropic scattering rate and observed an enhanced scattering rate in the [110̅ ] direction in accordance with our findings. The difference between the best-fit scattering rates for the two directions at room temperature was 197 cm−1 which compares well to our case of 169 cm−1 (combined bulk and surface anisotropies). For much higher temperatures they found increased rates for both directions but still with the higher value for scattering in the [11̅0] direction. This temperature-dependent behavior indicates the important role of phonon scattering. Textbook data on Cu phonon dispersion show important differences for the two directions, like in the maximum longitudinal (acoustic) phonon frequency which is smaller in the [11̅0] direction than in the [001] 14019

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Persson and F. Neubrech for helpful discussions. J. Pischel is a member of the Graduate Academy of the Heidelberg University via the graduate college “Connecting Molecular π-Systems into Advanced Functional Materials” and of the Heidelberg Graduate School of Fundamental Physics.

adsorbate scattering rate is quite complicated, it turned out that ΔR/R ∝ ωads/cos θ (see also ref 8). This relation was used for an estimate of the relative systematic error introduced by the uncertainty in the angle of incidence: Δωads/ωads = tan θΔθ. With θ = 85° and Δθ = π/180, the relative systematic error turns out to be around 20%. For different (yet still reasonable) bulk dielectric functions, changes in ωads in the order of 10% are observed. If all other quantities are assumed to be exact, the uncertainty of ωads resulting from the fitting procedure is negligible. Thus, the total (systematic) error of ωads is 22%.

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SUMMARY AND CONCLUSIONS We have investigated oxygen adsorption on the singlecrystalline Cu(110) surface by studying IR spectral reflectance changes. Our data analysis yields an anisotropic change in surface resistance. The main part of the change is induced in the [11̅0] direction, but unlike for carbon monoxide and ethene, a small change is observed in the perpendicular direction, too. This is, however, not in contradiction to the model notion introduced by Otto et al.22 if it is considered that adsorption of oxygen leads to a reconstruction of the surface involving copper atoms of the second layer. We were able to simulate the measured spectra by making use of the existing framework of theory. The simulated spectra were in excellent agreement with the experiment. A prerequisite for this accordance was the correct choice of the bulk dielectric function taking into account anisotropy. The effectively used scattering rates in the respective directions were taken as ωτ ,[1 1̅ 0](ω) = 467 cm−1 + 0.087ω

(8)

and ωτ ,[001](ω) = 249 cm−1 + 0.087ω

(9)

The additional electron scattering rate induced by saturation coverage of oxygen was found to be of the order of 13 cm−1 for parallel and 1 cm−1 for perpendicular geometry. This emphasizes the high sensitivity of the employed method to processes influencing the properties of electrons at metal surfaces.

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ASSOCIATED CONTENT

S Supporting Information *

Schemes visualizing the situation for different reflection and adsorption geometries; a detailed description of the modeling of the bulk dielectric function of copper on the basis of experimental data from ref 42; details on the dependence of the fitting function on the fit parameters; and remark on the dependence of the number of excited acoustic phonons on the Debye frequency. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

(1) Duan, B. K.; Zhang, J.; Bohn, P. W. Anal. Chem. 2012, 84, 2−8. (2) Fuchs, K. Math. Proc. Cambridge Philos. Soc. 1938, 34, 100−108. (3) Sondheimer, E. Adv. Phys. 1952, 1, 1−42. (4) Persson, B. N. J. Phys. Rev. B 1991, 44, 3277−3296. (5) Persson, B. N. J. Surf. Sci. 1992, 269−270, 103−112. (6) Persson, B. N. J. J. Chem. Phys. 1993, 98, 1659. (7) Persson, B. N. J.; Volokitin, A. I. Chem. Phys. Lett. 1991, 185, 292−297. (8) Persson, B. N. J.; Volokitin, A. I. Surf. Sci. 1994, 310, 314−336. (9) Schreiber, F. Prog. Surf. Sci. 2000, 65, 151−257. (10) Zhang, Y.; Terrill, R. H.; Bohn, P. W. J. Am. Chem. Soc. 1998, 120, 9969−9970. (11) Bogozi, A.; Lam, O.; He, H.; Li, C.; Tao, N. J.; Nagahara, L. A.; Amlani, I.; Tsui, R. J. Am. Chem. Soc. 2001, 123, 4585−4590. (12) Xu, B.; He, H.; Boussaad, S.; Tao, N. J. Electrochim. Acta 2003, 48, 3085−3091. (13) Liu, Z.; Searson, P. C. J. Phys. Chem. B 2006, 110, 4318−4322. (14) Lin, H.; Chen, H.; Lin, H. Anal. Chem. 2008, 80, 1937−1941. (15) Favier, F.; Walter, E. C.; Zach, M. P.; Benter, T.; Penner, R. M. Science 2001, 293, 2227−2231. (16) Murray, B. J.; Walter, E. C.; Penner, R. M. Nano Lett. 2004, 4, 665−670. (17) Murray, B. J.; Newberg, J. T.; Walter, E. C.; Li, Q.; Hemminger, J. C.; Penner, R. M. Anal. Chem. 2005, 77, 5205−5214. (18) Landauer, R. IBM J. Res. Dev. 1957, 1, 223−231. (19) Häkkinen, H.; Barnett, R. N.; Landman, U. J. Phys. Chem. B 1999, 103, 8814−8816. (20) Rouhana, L. L.; Moussallem, M. D.; Schlenoff, J. B. J. Am. Chem. Soc. 2011, 133, 16080−16091. (21) McCullen, E.; Hsu, C.; Tobin, R. Surf. Sci. 2001, 481, 198−204. (22) Otto, A.; Lilie, P.; Dumas, P.; Hirschmugl, C.; Pilling, M.; Williams, G. P. New J. Phys. 2007, 9, 288. (23) Weightman, P.; Martin, D. S.; Cole, R. J.; Farrell, T. Rep. Prog. Phys. 2005, 68, 1251−1341. (24) Sun, L. D.; Hohage, M.; Zeppenfeld, P. Phys. Rev. B 2004, 69, 045407. (25) Stahrenberg, K.; Herrmann, T.; Esser, N.; Richter, W. Phys. Rev. B 2000, 61, 3043−3047. (26) Kusar, P.; Gruber, C.; Hohenau, A.; Krenn, J. R. Nano Lett. 2012, 12, 661−665. (27) Jackson, J. D. Classical Electrodynamics, 3rd ed.; Wiley: New York, 1998. (28) Langreth, D. C. Phys. Rev. B 1989, 39, 10020−10027. (29) Feibelman, P. J. Prog. Surf. Sci. 1982, 12, 287−407. (30) Lee, M. J. G. Phys. Rev. B 1970, 2, 250−263. (31) Fahsold, G.; Sinther, M.; Priebe, A.; Diez, S.; Pucci, A. Phys. Rev. B 2002, 65, 235408. (32) Coulman, D. J.; Wintterlin, J.; Behm, R. J.; Ertl, G. Phys. Rev. Lett. 1990, 64, 1761−1764. (33) Krauth, O.; Fahsold, G.; Pucci, A. J. Chem. Phys. 1999, 110, 3113−3117. (34) Horn, K.; Hussain, M.; Pritchard, J. Surf. Sci. 1977, 63, 244−253. (35) Hollins, P.; K. J. Davies, J. P. Surf. Sci. 1984, 75, 75−83. (36) Woodruff, D. P.; Hayden, B. E.; Prince, K.; Bradshaw, A. M. Surf. Sci. 1982, 123, 397−412. (37) Nakao, F. Vacuum 1975, 25, 431−435. (38) Habraken, F.; Bootsma, G.; Hofmann, P.; Hachicha, S.; Bradshaw, A. Surf. Sci. 1979, 88, 285−298. (39) Ertl, G. Surf. Sci. 1967, 6, 208−232. (40) Mundenar, J.; Baddorf, A.; Plummer, E.; Sneddon, L.; Didio, R.; Zehner, D. Surf. Sci. 1987, 188, 15−31.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 6221549863. Fax: +49 6221-549869. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge experimental support by S. Wetzel and R. Lovrinc̆ić and express their thanks to B. N. J. 14020

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(41) Skibbe, O.; Berge, K.; Meister, G.; Goldmann, A. Phys. Rev. B 2002, 66, 235418. (42) Ordal, M. A.; Bell, R. J.; Alexander, R. W., Jr; Long, L. L.; Querry, M. R. Appl. Opt. 1985, 24, 4493−4499. (43) Fahsold, G.; Sinther, M.; Priebe, A.; Diez, S.; Pucci, A. Phys. Rev. B 2004, 70, 115406. (44) Hanekamp, L.; Lisowski, W.; Bootsma, G. Surf. Sci. 1982, 118, 1−18. (45) Svensson, E. C.; Brockhouse, B. N.; Rowe, J. M. Phys. Rev. 1967, 155, 619−632.

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