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Infrared reflection-absorption spectroscopy of dipole forbidden adsorbate vibrations
Journal of Ekctron Spectroscopy and Related Phenomena, W65 (1993) 23-38 0368-2046!93/$06.00 @ 1993 - Elaevier Science Publishera B.V. AlI rights reserved
23
INFRARED REFLECTION-ABSORPTION SPECTROSCOPY OF DIPOLE FORBIDDEN ADSORBATE VIBRATIONS
B.N.J. PERSSON AND AI. VOLOKITIN Insti tuf ftir FestkGrperforschung, Forschungszen trum Jiihch, Postfach 1913, D-52425 Jiilich, Germany
ABSTRACT We explain the origin of recent observations of so-called dipole-forbidden adsorbate vibrations in infrared-reflection-absorption spectroscopy (IRAS) of atoms and molecules adsorbed on metal surfaces. The excitation of these modes is indirectly mediated by the metal electrons and closely related to the concept of surface cesistivity. The theory is in very good agreement with the IRAS measurements of Hirschmugl et al. [Phys. Rev. Lett, 65 (1990) 4801 for CO on Cu(100) and in qualitative agreement with the measurements of Lin et al. [Phys. Rev. B, in press ] for CO on Ni(100).
1. Introduction Vibrations in adsorbates can be studied using infrared-reflection-absorption spectroscopy (IRKS), electron-energy-loss spectroscopy (EELS), or inelastic helium scattering ,(IHS). V-b I rational spectroscopy has traditionally been employed for identifying the types of bonds in molecules. Since the vibrational frequencies are affected by the nature of the adsorption bond, information about the binding sites and orientation of molecules on surfaces can often be deduced from IRAS or EELS. For example, the frequency of the C-O stretch vibration for CO adsorbed on metallic surfaces decreases with increasing coordination, and from the frequency shift alone it is often possible to deduce the binding sites on the surface. Of particularly interest are the low-frequency parallel vibrations, the so-called frustrated translations. The frequency of these modes reflects the lateral curvature, at the binding sites, of the adsorbate-substrate potential energy surface. This information is of utmost importance for the understanding of many static and dynamic properties of adsorbed layers, e.g. surface diffusion, the nature of adsorbate structures
and phase transitions in adsorbed layers. To give an example, it has been shown [l] that domain wall superstructures, which often occur at high coverage in sdsorbate systems, are usually stable only because the adsorbates along the domain walls can move away from the substrate symmetry sites in order to lower the total energy. The lineshape of adsorbate vibrations conta,ins information ambout energy transfer processes which is of fundamental importance for many surface processes such as vibrational relaxation in adsorbed molecules, chemical reaction at surfaces, surface diffusion, sticking, desorption, fluid-solid heat transfer, the Kapitza resistance, boundary lubrication, atom transfer in STM, local chemical modification with the STM and so on. Because of its high resolution (- 0.01 cm-l) IRAS is the most suitable method for studies of vibrational line shapes. In the context of IRAS from metal surfaces, it has generally been believed that only vibrational modes with a non-zero dynamical dipole moment normal to the surface can be detected. This conclusion was based on the strong screening of the parallel electric field at the surface. But recently parallel frustrated translations [H on W(100) an d on Mo( loo)] and frustrated rotations [CO on Cu( loo)] have been observed with IRAS. IHS is particularly suitable for studying the low-frequency frustrated translations, and it has been ampplied to CO on Ni( loo), Pt(lll), and Cu(100). [2,3] Until recently, the resolution of EELS was not high enough to resolve parallel frustrated translations for most adsorbates, e.g. CO. However, recently EEL spectrometers with a. resolution of better than 1 meV ha,vvebeen developed, and in an EELS study by Kisters et al. [4] all the adsorbate vibrational modes for CO on Ir(lOO) h ave been detected in off-specular EELS. In this paper we discuss in detail the IR-line shape of parallel adsorbate vibrations (frustrated translations and rotations). These modes are usually dipole-forbidden with respect to a normal electric field but have nevertheless been detected in IRAS; these measurements open up new applications for studying adsorbate vibrations. We demonstrate that the vibrational line shape of parallel a,dsorbate vibrations is closely connected to the problem of surface conductivity.
2. IR-spectroscopy
of dipole forbidden modes
When a beam of infrared radiation is incident on a metal surface covered by molecules, “dips” usually occur in the reflection spectra at those energies which correspond to vibrational excitations of the adsorbed molecules. The change in reflectivity due to the
25
adsorbed molecules is defined by A - AR =- &-R RO where R and R. are the intensity lecules, respectively.
RO
(1)
of the reflected beam with and without adsorbed mo-
Since the wavelength of the incident photons is much larger than the size of the molecules, the is usually assumed that the interaction between the radiation field and an adsorbed molecule is of the dipole fdrm Hint = -r; - E
(2)
where fi is the dipole moment operator of the molecule and E is the electric field evaluated at the site of the molecule. A beam of photons incident at the angle 6’to the surface normal can be decomposed into s- and p-polarized components. [5] Since the phase change of the s-component upon reflection from a metal surface is near K for any 0, the resultant of the incident and reflected electric fields becomes practically zero at the surface. Consequently, the dipole interaction between a s-polarized wave and the adsorbates is extremely weak. On the other hand, the normal electric field component at the surface associated with a p-polarized wa,ve is nearly twice as la.rge as that of the incoming wave, while the parallel electric field component is several orders of magnitude smaller than the normal component. Hence the intemction energy due to direct coupling between a p-polarized wave and the adsorbate dipoles will be strong only for modes with a non-zero dynamic dipole moment normal to the surface. The difference in magnitude between the normal and the parallel electric field components results in an (approximate) surface selection rule: only those uihtional modes that have a dynamic dipole rnonaent normal to the mrface are excitated in IRAS. It was therefore a surprise when formally dipole forbidden (with respect to a normal electric field) frustrated translations [II on W(lOO)] [6] and rotations [CO on Cu(loO)] [7] w h ere observed for adsorbates on metallic surfaces. In fact, these modes a,re observed as strongly as the dipole active modes even though the parallel electric field component at the surface is reduced by a factor Bll/El N LQ/L+,N 1O’2 compared with the normal electric field component and the corresponding In-intensity is reduced by the factor IJ?$/E~/~ N 10m4. The consideration above does not take into account the fact that due to the large polarizability of a metal, even a small parallel electric field component in the surface region can induce a noticeable current density in the metal. Interaction of the adsorbate vibrations with this current density can produce a noticeable change in the reflectivity. We will discuss this mechanism of indirect interaction below and we will show that the change in reflectivity due to dipole-forbidden modes can be of the same order of magnitude as that
26
associated with dipole-allowed modes. From studies of the former modes, one can obtain information about the mecha4nisms of electron surface scattering and surface conductivity. In fig. 1 we show the sharp Fano resonance for the frustrated rotation of CO adsorbed on Cu(100). [‘I] Note the peculiar anti-absorption structure a.ssociated with this mode, where, at resonance, the reflectivity is higher than awa,y from resonance. This result should be contrasted with those for modes with finite dynamical dinole moments normal to the surface, for which reflection “dips” usually occur. I
I
220
I
I
260 w(cm-l)
Fig. 1. IR-spectra of the frustrated is the result of theory, see text.
I
I
300
rotation for CO on Cu( 100). The thick dashed line
To explain the origin of the structure in Fig. 1, consider a metal surface with a low concentration of randomly distributed adsorbates. [a, 91 An incident IR light beam will induce a current in the metal. Let J]I be the component of the current parallel to the metal surface, jvst inside the metal. We can write J nevll, where VII is the parallel II = component of the electron “drift” velocity, just inside the metal. Adsorbales
on surfaces can perform
vibrations
parallel to the surface. These “fru-
27
strated translations” are usually dipole forbidden. Nevertheless, they can be excited in IR spectroscopy because they couple to the electronic current density Jll induced in the metal by the external driving field. To see this, note that the relative motion between an adsorbate and the collective motion of the electrons in the metal introduces a friction force f = --Mq(ti-vtr(l) acting on the adsorbate, where u denotes the parallel vibrational coordinate of the adsorbate and 11is the friction coefficient. This is similar to the force which acts on a body in streaming water, which, of course, depends only on the relative velocity between the body and the water. The equation of motion for u becomes Mii +
Mw$l+ Mq(li - v,,) =
0
where wu is the resonance frequency of the frustrated transla,tion. it follows that w2 - w; YI - ir = ,2 _ w; + iwrl TI The time-averaged P =
adsorbate
induced power absorption
(3)
, If VII N exp(-iwt)
is therefore
N(f e (VII- 5)) = NMq(v(;)h(w) = lVM7j(J~)h(w)/n2e2
where
h(w) =
wp up +w2q2
(w2(d -
then
(4
,
(5) (6)
and where ( > stands for averaging over time and where N is the number of adsorbates. The adsorbate-induced change in the IR reflectance is given by AR = P/IoA
,
(7)
where A is the cross-sectional area of the incident photon beam. The surface area covered by the incident beam is A0 = A/cosd, where B is the angle of incidence. The intensity of the incident IR beam is determined by the Poynting vector and is given by 10 = cEi/8a, where Eo is the amplitude of the electric field of the incident light beam. Hence, if n, = IV/A0 denotes the number of adsorbates per unit surface area, then AR=--
Note that for low adsorbate
87r nu Mrl
(J~)hc
ccosen2e2~
)
w*
coverages, 0 < 1, we can calculate, to a good approximation, without adsorbates. This gives AR to linear order in 0. For the CO/Cu(lll) system, a linear dependence of AR on 0 has been observed experimentally [lOI for 0 < 0.4.
P by using the current JII obtained
28
In classical local optics, the metal is described by the bulk dielectric function E(W) which, for copper (below the onset of interband transitions), is very well described by the Drude formula,
E(W)= 1 -
wi
w(wi- i/TB)
(9)
At low tempera.ture, the Drude relaxation time 7~ and the electron mean free path M 25 cm-l and ! M 3000 8, at T M 80 K) and in the t? = Vj7TB are very long (fi/~ present applications we can put 1/7~ = 0. It is then easy to calculate (Ji) = wiEi/87r. Substituting
this into (8) gives
The friction coefficient 9 = l/~~h, where l/~~h is the damping due to excitation of electron-hole pairs, of the parallel frustrated translation of the adsorbed molecules. As will be shown below, 7eh can be obtained from the adsorb&e-induced contribution to the DC resistivity of thin metallic films and for CO on Cu( 111) this gives ~,h NN3.9 x lo-l1 s, which, however, is rather uncertain in the film thickness and adsorbate coverage. Note the anti-absorption peak at w = wu, where the reflectivity is higher than away from resonance, This has a simple physical meaning: According to (3), vll -ti = 0 at w = wu, i.e. no relative motion occurs between the adsorbates and the collective motion of the electron gas, resulting in no adsorbate-induced energy absorption. Local optics is accurate only if w >> v~/6, where w and 6 = c/wp are the frequency and the decay length (in local optics) into the metal of the electric field associated with the incident IR light [ll]. T o see this, note that if 6 >> VFT, where T = 27r/w is the period of the external light, an electron on the Fermi surface can only move a short distance (on the scale of the decay length d of the electric field) during the time period T. Hence the electron will effectively only see the electric field at one point in space during the time period T so that mi, M eE exp(-iwt) or v M (ieE/mw) exp(-e’wt), which gives the Drude conductivity and local optics. But if 6 < vpT an electron on the Fermi surface will propagate over a distance of the order of the decay length 6, or more, during the time period T. Hence the electron will be influenced by the electric field over a large spatial region, implying nonlocal optics. That is, a contribution to the time dependence of the electric field an electron experiences during the time period T comes from the motion of the electron in the spcats’nllyvarying external electric field. To take this into account one must replace the standard local relation J(r) = nE(r)
(11)
29
between the current density and the electric field by a more general expression of the form J(r) = / $T’u(r, r’)E(r’)
(12)
To obtain this non-local relation between current density and the electric field we use an approach based on Boltzman’s equation and which was originally proposed for studing the anomalous skin effect. Let us consider a semi-infinite metal with its surface in the ey-plane and the posititive r-axis directed towards the interior of the metaL The surface is assumed to have a la,yer of adsorbates which can perform harmonic oscillations in the z-direction. As pointed out above, inside the metal (at infra,red frequencies) the paxallel electric field component is much stronger than the normal component. Hence, neglecting the normal field component and assuming that the parallel electric field is along the x-axis we can write Boltzman’s equation for the electron distribution function f(z, Q, Q, v,) in the form
e& af af -.-++-y al+
(13)
where Q is the bulk relaxation time and fo is proportional to the Fermi distribution function. Now, we assume that a fraction p of the electrons arriving at the surface are scattered specularly while the rest are scattered diffusively with the drift velocity ‘u (the velocity of adsorbate vibration in the x-direction). Hence f(z, us, r+,, vZ) must satisfy the boundary condition f(0, %, r+/, 4
= Pf(0, %, ny, -4
+ (1 - P)fo(% - II, “yr 4
where ‘uZ > 0. To obta,in the equation of motion for the adsorbate vibration, we must take into account that a relative motion between an adsorbate and the drift motion of the electrons in the metal will 1ea.d to friction due to tra.nsfer of momentum from electrons to the adsorbate. The electron momentum flux in the z-direction can be written in the form IIs2 = m
J
d3vwzf(0,
2’2, uyr 212)
(14
The friction force acting on an adsorbate is the momentum flux divided by the number of adsorbates per unit area. The equation of motion for an adsorbate vibration has the form MZ + MC4.& + rI,,/n~
= 0
(15)
From (l)-(4) the distribution function f (x, v) can be found. With this solution it is easy to evaluate the drift current induced by the external electric field &(z):
30
Finally, using this relation together with Maxwells equations it is possible to calculate the reflectivity of the a,dsorbate covered metal surface. This approach gives the following general formula for R = Ro + AR: [IZ]
(17) (18) (19) where wl = v~/a and
(20) 4d = q2-ffdy(t-;) =
where u = iq//3, f(Y) + -i7r/by.
,f3 = b/l
-
q2 -
,2;Byzy2
”
_!-
P
fJ3
bu
+
(u2
-
1) In z]
(21)
and Q = 3iw/4wl. As w/w1+ co, E+ q2 + 1 so that
iw/wl
Hence iW$l w;-w2-dw?j
so that An-+
(w; - wy
_3--- wl (l-p) 4 wp
case
(wi
- wy
+ w%+
as W/WI + 00. If we use the relation [13] 1 - p = lGn,Mq/(Snmv~) (10) as it should.
.
(22) then (22) reduces to
generated by the synchrotron source at Brookhaven, Hirschthe adsorbate-induced changes in the IR reflectivity of a Cu( 100) surface upon CO exposure. In Fig. 2, we show their results for the CO coverage 0 = 0.40 f 0.05. The quantity plotted is R(O)/R(O)= (Ro+ AR)/R, as a function of the frequency w of the IR light. Since no clustering occurs for CO on Cu( loo), for 0 << 1 the CO molecules can be considered as randomly distributed on the substrate binding sites. Using infrared radiation
mug1 et al. [7] h ave recently studied
31
The solid curve in the same figure is calculated from (17)-(21) using a jellium model for Cu with one conduction electron per Cu atom. The damping or friction coefficient 17in (Ii’)-(19) h as b een adjusted to reproduce the asymptotic reflectivity change for “large” w, which amount to a 1.23 f 0.10% reduction in the reflectivity. The resulting friction 9 = l/~~h corresponds to an electron-hole pair lifetime of the parallel frustrated CO vibration r,h = (4.6 f 1.0) x 10eL1 s, in good agreement with that deduced 1131from DC-resistivity measurements [14] on thin Cu films, 7eh a 3.9 x lo-l1 s. For the parameter ~1 in (45), we have used w1 = 500 cm-‘, which is remarkably close to the prediction of the jellium model, wl = W~VF/C NN444 cm -l. The overall a#greement between theory and experiment is satisfactory, considering that copper is not jellium.
1.ooo
R @I R (0) 0.995
0.990
0
1000 0
(cm-‘)
Fig. 2. Measured reflectivity as a function of frequency for the CO/Cu(lOO) system at the coverage 0 = 0.4. The solid curve is the background absorption calculated using the jellium model with wr = 50O~rn-~.
32
The two resonance structures in Fig. 2 at w = 285 and 345 cm-l are associated with the frustrated rotation and the C&CO stretch vibrations, respectively (see insert in Fig. 2). The parallel CO vibration occurs at [15] w = 40 cm-l, i.e. it is outside the frequency region presented in Fig. 2. The Cu-CO mode is dipole allowed (with respect to the surface normal) and gives rise to a “dip” in the reflectivity, as is usually observed for dipole-allowed adsorbate vibrations. On the other hand, the frustrated rotation of CO is dipole-forbidden, and this mode is observed only for the reasons discussed above. That is, since some motion of the CO molecule occurs parallel to the surface, some (reduced) coupling between this mode and the parallel electric current should occur, just as for a “pure” frustrated translation. Note also that the frustrated rotation gives rise to enhanced refiectiPrity at resonance; the physical origin of this effect was explained above. The reflectivity does not return to the value for the clean surface as expected for a “pure” frustrated translation in the local optical region and in the absence of inhomogeneous broadening and dephasing. But the asymmetry of the line profile is very similar to the one calculated from (18)and (19), see Fig. 1. Note that in this calculation no adjustable parameters occur. Recently Lin et al 1161 h ave measured the IR-reflectivity from CO on Ni(lO0) at room temperature. At the CO coverage na = 0.064Aa2 a very small adsorbate induced reflectivity than e was observed, -0.2 f O-2%, independent of the frequency w for w between 4OOcm- 5 and 2000cn~-~. Lin et al. used this experimental result to argue against the model presented above. However, as we will now show, the result of Lin et al. is in qualitative agreement with what is expected from theory. The theory presented above is based on the jellium model where a single free-electron like band crosses the Fermi energy. On the other hand, Ni is known to have a complicated band structure with several very flat electronic bands (d-bands) crossing the Fermi energy and interband transitions are known to occur in Ni already for tiw N 800~z-~; we may tentatively use the theory presented above below this frequency. But even in this limited frequency range Ni differ in an important way from copper in that the Drude relaxation time TB is much shorter for Ni than for Cu (at a given temperature); this again is related to the d-bands at 6~ which gives rise to a high density of states at EF into which the “free” sp-electrons can scatter (note: the d-band electrons themself contribute very little to the DC conductivity of Ni owing to their large effective mass). Hence at room temperature the mean free path in Ni is about a factor of 5 shorter than that of Cu. Assuming one free electron per metal atom with an effective mass identical to the free electron mass one can calculate 6, M 2OOA for both Ni and Cu and 1 M 3000;1 for copper at 7’ = 90K while at room temperature, 1 M 3OOw for Cu and I M 6OA for Ni. Hence, the ratio 1/6 equals w 15 for Cu at T = 90K and 1.5 and 0.3 for Cu and Ni at room temperature, respectively.
33
In fig. 3 we show the dependence of the ratio R(O)/R(O) on the parameter I/s. In all cases R(O)/R(O) --t 1 - (1 - p)” as W/WI -+ CXI(where wl M 5OOcna-’ for Cu and Ni and a = (V&)( 3/4cosl9). It is obvious that for I/S = 15 and 1.5 the background absorption is very similar in magnitude and nearly equal to that for 1/6 = 00. But for Ni at room temperature (where I/S M 0.3) the adsorbate induced change in the reflectivity is very small if w < 1.5~1, which is the only frequency region where the theory may be applied to for Ni (see above). Hence one expect a much smaller adsorbate induced contribution to the background absorption for Ni than for Cu, in qualitative agreement with the measurements of Lin et al.
1
I-(I-p)aJ 0
Fig. 3. The reflectivity as a function of the frequency for several values of the ratio 1/6 between the bulk electron mean free path and the skin depth 6. u = (?J~/c)(3/4cose).
In fig. 4 we show the nature of the absorption structures expected for parallel adsorbate vibrations with resonance frequencies at wo = 0.6~1 (as for the frustrated CO rotation on Cu(IO0)) an d a t wg = 3.6~1 and for l/6 = 10 and 0.25. The dash-dotted lines in the same figure shows the background absorption for l/6 = 10 and 0.25, i.e. the same as the two corresponding curves in fig. 3. Note that when wg increases the absorption structures associated with the parallel vibrations become more and more Lorenteian-like i.e. the asymmetry disappear, a result which is indeed expected in the local optic’s frequency
34
region (see (10)).
-_w-*
A
___-___________--____.
a--_-_
--._
+
--. --_ --. -, -_ t+ --_
-C
--__
l/S =
---
0.25
R Ko
---
_----_a
-a---------------__-_
‘1.
0.6q
‘Y %
I/S=
I-(I-p)c
‘\.
\
10
1
‘\
-\
‘\
‘\
#q-j = 3.k -\
-\
‘\
-\
--
2
-_
-w
3
k. ---
4
W/wl Fig. ‘4, Dash-dotted lines: The reflectivity as a function of the frequency for I/6 = 10 and 0.25. Solid lines: The anti-absorption resonances associated with parallel vibrations located’at wg = 0.6~1 and 3.6~1. a = (~~/c)(3/4cost9).
It is interesting to note that in a narrow frequency interval the reflectivity is higher with adsorb&es on the surface than without i.e. R(Q)/R(O) > 1. This result is only possible if ,R(O) < 1 which is indeed the case even for a “perfect” system with no bulk wave incident absorption (i.e. I. = co). To see this, let us consider an electromagnetic on a metal surface. The field will penetrate into the metal to a distance N 6 = c/wp.
35
An electron which enter this region will pick up some drift momentum and propagate “ballistically” towards the interior of the crystal as a “hot” electron. This will result in a continous transfer of energy to the metal and hence the reflectivity R will always be smaller than unity even for a perfect system at zero temperature. The theory outlined above correctly describes this background absorption and in fig. 5 we show the reflectivity R both for a perfect surface (no adsorbates, p = 1) and in the case of an adsorbate layer (diffusive surface scattering, p = 0) dash-dotted curve. The solid curves shows the reflectivity (for p = 0) in the vicinity of the resonance frequencies wu = 0.6~1, 1.6~1, 2.6~1 and 3.6~1 of four parallel vibrations. Note that the reflectivity R is always smaller than unity.
1
R
p=l
1 --
_2.6~~
_w() = 3.6L
l-c \ ‘p=O
I
1
I
I
1
2
3
4
Fig. 5 The reflectivity as a function of frequency. Dashed line: Reflectivity of a clean metal surface (0 = 0). Dash-dotted line: Reflectivity of a metal surface where the electrons scatter diffusively. Solid lines: Anti-absorption resonances for parallel adsorbate vibrations with wg = 0.6~1, 1.6~1, 2.6~1 and 3.6~1. Q = (~~7/c)(3/4cost9).
36
The problem of the IR-reflectivity discussed above is closely related with the problem of the DC resistivity of a thin metallic film. To see this we note that ohmic heating due to scattering of the conduction electrons by adsorbates can be written in the form P = ApdA0(J2)
(23)
where Ap is the adsorbate contribution film resistivity at the frequency w and where d and A0 are the thickness and the area of the metal film, respectively. Comparing (23) with (5) at w = 0 we obtain a relation between ~,h = l/p7 and Ap
so-
I
I
(a)
N
aa E, 20-
(b)
G ”
lo-
5 g
s-
0.15 na
(A-*)
Fig. 6. (a) The change in the film resistivity Ap as a function of CO coverage for the CO/Ni(lll) sy st em. (b) The variation of 6P/6na(na + 0) with the film thickness d. The straight line has the slope -1. Adopted from ref. [14]. For low adsorbate
coverages n, the resistivity
Ap is found to vary linear with na so
that AP
-
%
aP
= an,
In,=0
(25)
Hence 1 -= Gh
9s
a
In,-0
(26)
This formula was used in ref. [13] to deduce ~,_h for some different absorption systems. For example, fig. 6a shows the change in resistivity Ap as a function of the CO coverage
37
for the CO/N i ch emisorption system. For low CO coverage Ap increases linearly with na. According to (26), Ap/n, N l/d if we assume that T is independent of d as expected if the film is thick enough. This relation is well satisfied for the CO-Ni chemisorption system as shown in fig. 6b. From fig. 6b we get
and using M = 2811 (the CO mass) and n = 8.47 x 10m2Ae3 gives ~,h _.. = 1.4 x 10-lla. Similar, for CO on a copper film one obtain the e-h pair relaxation time quoted earlier.
3. Summary
and conclusion
There is in our opinion little doubt that the theory presented above is the correct explanation for why “dipole forbidden” vibrational modes have been observed in IRAS. Not only does the theory correctly describe the background absorption but even the predicted vibrational line shape agrees nicely with experimental data for the CO-Cu(100) system. But a.s an additional test of the theory we suggest that IR-measurements on the H/Cu system should be performed. It would also be interesting to repeat the measurement on the CO/Ni(lOO) system at T N 1OOK where the electron mean free path should be so long that the condition 1/6 > 1 should be satisfied below the onset ofinterband transitions. “Dipole forbidden” vibrational modes have also been observed for H on W(100) and Mo(100). It is very likely that these modes too are observed in IRAS via the indirect coupling discussed above. But in these cases the jellium model can not be used in the analysis owing to the complicated band structure (including surface states) of these metals. The theory presented above is closely connected with the concept of surface resistivity which has been found to have many interesting and useful implications for other surface physics problems as discussed in ref. [ 171and [ 181. It is interesting to speculate if the theory presented above is valid for other types of elementary excitations in addition to parallel adsorbate vibrations. We have only found one such case namely parallel vibrations of surface charge density waves, pinned by impurities or by the periodic crystal potential. As shown by Overhauser this problem is formally identical to the one studied above if the adsorbate mass M, resonance frequency wo and damping 7 in (3) are replaced by the charge density wave effective mass m*, the pinning frequency w;f and the e-h pair damping v*. Hence, in this case one would again expect to observe enhanced reflectivity at resonance, but the resonance frequency could be much higher than for parallel adsorbate vibrations.
33
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[8] B.N.J. Persson and A-1. Volokitin, Chem. Phys. Letters 185 (1991) 292. [9] B.N.J. Persson, Chem. Phys. Letters 197 (1992) 7. [lo] C.J. Hirschmugl, G.P. Williams, F.M. Hoffmann, and Y.J. Chabal, to be published; private communication. [ll] There is also a surface contribution from the nonlocality due to the abrupt change in the electric field in the surface region. But as shown in Phys. Rev. B44 (1991) 3277, if vf/w >> a th is surface contribution is negligible compared with the bulk contribution,
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in Modern Physics, ed. G.
[15] J. Ellis and J.P. Toennies, private communication. [16] K.C. Lin, R.G. Tobin, P.Dumas, C.J. Hirschmugl and G.P. Williams, Phys. Rev. B (in press). [17] B.N.J. Persson, Surf. Sci. 269/270
(1992) 103.
[18] B.N.J. Persson, J. Chem. Phys. 98 (1993) 1659.
23
INFRARED REFLECTION-ABSORPTION SPECTROSCOPY OF DIPOLE FORBIDDEN ADSORBATE VIBRATIONS
B.N.J. PERSSON AND AI. VOLOKITIN Insti tuf ftir FestkGrperforschung, Forschungszen trum Jiihch, Postfach 1913, D-52425 Jiilich, Germany
ABSTRACT We explain the origin of recent observations of so-called dipole-forbidden adsorbate vibrations in infrared-reflection-absorption spectroscopy (IRAS) of atoms and molecules adsorbed on metal surfaces. The excitation of these modes is indirectly mediated by the metal electrons and closely related to the concept of surface cesistivity. The theory is in very good agreement with the IRAS measurements of Hirschmugl et al. [Phys. Rev. Lett, 65 (1990) 4801 for CO on Cu(100) and in qualitative agreement with the measurements of Lin et al. [Phys. Rev. B, in press ] for CO on Ni(100).
1. Introduction Vibrations in adsorbates can be studied using infrared-reflection-absorption spectroscopy (IRKS), electron-energy-loss spectroscopy (EELS), or inelastic helium scattering ,(IHS). V-b I rational spectroscopy has traditionally been employed for identifying the types of bonds in molecules. Since the vibrational frequencies are affected by the nature of the adsorption bond, information about the binding sites and orientation of molecules on surfaces can often be deduced from IRAS or EELS. For example, the frequency of the C-O stretch vibration for CO adsorbed on metallic surfaces decreases with increasing coordination, and from the frequency shift alone it is often possible to deduce the binding sites on the surface. Of particularly interest are the low-frequency parallel vibrations, the so-called frustrated translations. The frequency of these modes reflects the lateral curvature, at the binding sites, of the adsorbate-substrate potential energy surface. This information is of utmost importance for the understanding of many static and dynamic properties of adsorbed layers, e.g. surface diffusion, the nature of adsorbate structures
and phase transitions in adsorbed layers. To give an example, it has been shown [l] that domain wall superstructures, which often occur at high coverage in sdsorbate systems, are usually stable only because the adsorbates along the domain walls can move away from the substrate symmetry sites in order to lower the total energy. The lineshape of adsorbate vibrations conta,ins information ambout energy transfer processes which is of fundamental importance for many surface processes such as vibrational relaxation in adsorbed molecules, chemical reaction at surfaces, surface diffusion, sticking, desorption, fluid-solid heat transfer, the Kapitza resistance, boundary lubrication, atom transfer in STM, local chemical modification with the STM and so on. Because of its high resolution (- 0.01 cm-l) IRAS is the most suitable method for studies of vibrational line shapes. In the context of IRAS from metal surfaces, it has generally been believed that only vibrational modes with a non-zero dynamical dipole moment normal to the surface can be detected. This conclusion was based on the strong screening of the parallel electric field at the surface. But recently parallel frustrated translations [H on W(100) an d on Mo( loo)] and frustrated rotations [CO on Cu( loo)] have been observed with IRAS. IHS is particularly suitable for studying the low-frequency frustrated translations, and it has been ampplied to CO on Ni( loo), Pt(lll), and Cu(100). [2,3] Until recently, the resolution of EELS was not high enough to resolve parallel frustrated translations for most adsorbates, e.g. CO. However, recently EEL spectrometers with a. resolution of better than 1 meV ha,vvebeen developed, and in an EELS study by Kisters et al. [4] all the adsorbate vibrational modes for CO on Ir(lOO) h ave been detected in off-specular EELS. In this paper we discuss in detail the IR-line shape of parallel adsorbate vibrations (frustrated translations and rotations). These modes are usually dipole-forbidden with respect to a normal electric field but have nevertheless been detected in IRAS; these measurements open up new applications for studying adsorbate vibrations. We demonstrate that the vibrational line shape of parallel a,dsorbate vibrations is closely connected to the problem of surface conductivity.
2. IR-spectroscopy
of dipole forbidden modes
When a beam of infrared radiation is incident on a metal surface covered by molecules, “dips” usually occur in the reflection spectra at those energies which correspond to vibrational excitations of the adsorbed molecules. The change in reflectivity due to the
25
adsorbed molecules is defined by A - AR =- &-R RO where R and R. are the intensity lecules, respectively.
RO
(1)
of the reflected beam with and without adsorbed mo-
Since the wavelength of the incident photons is much larger than the size of the molecules, the is usually assumed that the interaction between the radiation field and an adsorbed molecule is of the dipole fdrm Hint = -r; - E
(2)
where fi is the dipole moment operator of the molecule and E is the electric field evaluated at the site of the molecule. A beam of photons incident at the angle 6’to the surface normal can be decomposed into s- and p-polarized components. [5] Since the phase change of the s-component upon reflection from a metal surface is near K for any 0, the resultant of the incident and reflected electric fields becomes practically zero at the surface. Consequently, the dipole interaction between a s-polarized wave and the adsorbates is extremely weak. On the other hand, the normal electric field component at the surface associated with a p-polarized wa,ve is nearly twice as la.rge as that of the incoming wave, while the parallel electric field component is several orders of magnitude smaller than the normal component. Hence the intemction energy due to direct coupling between a p-polarized wave and the adsorbate dipoles will be strong only for modes with a non-zero dynamic dipole moment normal to the surface. The difference in magnitude between the normal and the parallel electric field components results in an (approximate) surface selection rule: only those uihtional modes that have a dynamic dipole rnonaent normal to the mrface are excitated in IRAS. It was therefore a surprise when formally dipole forbidden (with respect to a normal electric field) frustrated translations [II on W(lOO)] [6] and rotations [CO on Cu(loO)] [7] w h ere observed for adsorbates on metallic surfaces. In fact, these modes a,re observed as strongly as the dipole active modes even though the parallel electric field component at the surface is reduced by a factor Bll/El N LQ/L+,N 1O’2 compared with the normal electric field component and the corresponding In-intensity is reduced by the factor IJ?$/E~/~ N 10m4. The consideration above does not take into account the fact that due to the large polarizability of a metal, even a small parallel electric field component in the surface region can induce a noticeable current density in the metal. Interaction of the adsorbate vibrations with this current density can produce a noticeable change in the reflectivity. We will discuss this mechanism of indirect interaction below and we will show that the change in reflectivity due to dipole-forbidden modes can be of the same order of magnitude as that
26
associated with dipole-allowed modes. From studies of the former modes, one can obtain information about the mecha4nisms of electron surface scattering and surface conductivity. In fig. 1 we show the sharp Fano resonance for the frustrated rotation of CO adsorbed on Cu(100). [‘I] Note the peculiar anti-absorption structure a.ssociated with this mode, where, at resonance, the reflectivity is higher than awa,y from resonance. This result should be contrasted with those for modes with finite dynamical dinole moments normal to the surface, for which reflection “dips” usually occur. I
I
220
I
I
260 w(cm-l)
Fig. 1. IR-spectra of the frustrated is the result of theory, see text.
I
I
300
rotation for CO on Cu( 100). The thick dashed line
To explain the origin of the structure in Fig. 1, consider a metal surface with a low concentration of randomly distributed adsorbates. [a, 91 An incident IR light beam will induce a current in the metal. Let J]I be the component of the current parallel to the metal surface, jvst inside the metal. We can write J nevll, where VII is the parallel II = component of the electron “drift” velocity, just inside the metal. Adsorbales
on surfaces can perform
vibrations
parallel to the surface. These “fru-
27
strated translations” are usually dipole forbidden. Nevertheless, they can be excited in IR spectroscopy because they couple to the electronic current density Jll induced in the metal by the external driving field. To see this, note that the relative motion between an adsorbate and the collective motion of the electrons in the metal introduces a friction force f = --Mq(ti-vtr(l) acting on the adsorbate, where u denotes the parallel vibrational coordinate of the adsorbate and 11is the friction coefficient. This is similar to the force which acts on a body in streaming water, which, of course, depends only on the relative velocity between the body and the water. The equation of motion for u becomes Mii +
Mw$l+ Mq(li - v,,) =
0
where wu is the resonance frequency of the frustrated transla,tion. it follows that w2 - w; YI - ir = ,2 _ w; + iwrl TI The time-averaged P =
adsorbate
induced power absorption
(3)
, If VII N exp(-iwt)
is therefore
N(f e (VII- 5)) = NMq(v(;)h(w) = lVM7j(J~)h(w)/n2e2
where
h(w) =
wp up +w2q2
(w2(d -
then
(4
,
(5) (6)
and where ( > stands for averaging over time and where N is the number of adsorbates. The adsorbate-induced change in the IR reflectance is given by AR = P/IoA
,
(7)
where A is the cross-sectional area of the incident photon beam. The surface area covered by the incident beam is A0 = A/cosd, where B is the angle of incidence. The intensity of the incident IR beam is determined by the Poynting vector and is given by 10 = cEi/8a, where Eo is the amplitude of the electric field of the incident light beam. Hence, if n, = IV/A0 denotes the number of adsorbates per unit surface area, then AR=--
Note that for low adsorbate
87r nu Mrl
(J~)hc
ccosen2e2~
)
w*
coverages, 0 < 1, we can calculate, to a good approximation, without adsorbates. This gives AR to linear order in 0. For the CO/Cu(lll) system, a linear dependence of AR on 0 has been observed experimentally [lOI for 0 < 0.4.
P by using the current JII obtained
28
In classical local optics, the metal is described by the bulk dielectric function E(W) which, for copper (below the onset of interband transitions), is very well described by the Drude formula,
E(W)= 1 -
wi
w(wi- i/TB)
(9)
At low tempera.ture, the Drude relaxation time 7~ and the electron mean free path M 25 cm-l and ! M 3000 8, at T M 80 K) and in the t? = Vj7TB are very long (fi/~ present applications we can put 1/7~ = 0. It is then easy to calculate (Ji) = wiEi/87r. Substituting
this into (8) gives
The friction coefficient 9 = l/~~h, where l/~~h is the damping due to excitation of electron-hole pairs, of the parallel frustrated translation of the adsorbed molecules. As will be shown below, 7eh can be obtained from the adsorb&e-induced contribution to the DC resistivity of thin metallic films and for CO on Cu( 111) this gives ~,h NN3.9 x lo-l1 s, which, however, is rather uncertain in the film thickness and adsorbate coverage. Note the anti-absorption peak at w = wu, where the reflectivity is higher than away from resonance, This has a simple physical meaning: According to (3), vll -ti = 0 at w = wu, i.e. no relative motion occurs between the adsorbates and the collective motion of the electron gas, resulting in no adsorbate-induced energy absorption. Local optics is accurate only if w >> v~/6, where w and 6 = c/wp are the frequency and the decay length (in local optics) into the metal of the electric field associated with the incident IR light [ll]. T o see this, note that if 6 >> VFT, where T = 27r/w is the period of the external light, an electron on the Fermi surface can only move a short distance (on the scale of the decay length d of the electric field) during the time period T. Hence the electron will effectively only see the electric field at one point in space during the time period T so that mi, M eE exp(-iwt) or v M (ieE/mw) exp(-e’wt), which gives the Drude conductivity and local optics. But if 6 < vpT an electron on the Fermi surface will propagate over a distance of the order of the decay length 6, or more, during the time period T. Hence the electron will be influenced by the electric field over a large spatial region, implying nonlocal optics. That is, a contribution to the time dependence of the electric field an electron experiences during the time period T comes from the motion of the electron in the spcats’nllyvarying external electric field. To take this into account one must replace the standard local relation J(r) = nE(r)
(11)
29
between the current density and the electric field by a more general expression of the form J(r) = / $T’u(r, r’)E(r’)
(12)
To obtain this non-local relation between current density and the electric field we use an approach based on Boltzman’s equation and which was originally proposed for studing the anomalous skin effect. Let us consider a semi-infinite metal with its surface in the ey-plane and the posititive r-axis directed towards the interior of the metaL The surface is assumed to have a la,yer of adsorbates which can perform harmonic oscillations in the z-direction. As pointed out above, inside the metal (at infra,red frequencies) the paxallel electric field component is much stronger than the normal component. Hence, neglecting the normal field component and assuming that the parallel electric field is along the x-axis we can write Boltzman’s equation for the electron distribution function f(z, Q, Q, v,) in the form
e& af af -.-++-y al+
(13)
where Q is the bulk relaxation time and fo is proportional to the Fermi distribution function. Now, we assume that a fraction p of the electrons arriving at the surface are scattered specularly while the rest are scattered diffusively with the drift velocity ‘u (the velocity of adsorbate vibration in the x-direction). Hence f(z, us, r+,, vZ) must satisfy the boundary condition f(0, %, r+/, 4
= Pf(0, %, ny, -4
+ (1 - P)fo(% - II, “yr 4
where ‘uZ > 0. To obta,in the equation of motion for the adsorbate vibration, we must take into account that a relative motion between an adsorbate and the drift motion of the electrons in the metal will 1ea.d to friction due to tra.nsfer of momentum from electrons to the adsorbate. The electron momentum flux in the z-direction can be written in the form IIs2 = m
J
d3vwzf(0,
2’2, uyr 212)
(14
The friction force acting on an adsorbate is the momentum flux divided by the number of adsorbates per unit area. The equation of motion for an adsorbate vibration has the form MZ + MC4.& + rI,,/n~
= 0
(15)
From (l)-(4) the distribution function f (x, v) can be found. With this solution it is easy to evaluate the drift current induced by the external electric field &(z):
30
Finally, using this relation together with Maxwells equations it is possible to calculate the reflectivity of the a,dsorbate covered metal surface. This approach gives the following general formula for R = Ro + AR: [IZ]
(17) (18) (19) where wl = v~/a and
(20) 4d = q2-ffdy(t-;) =
where u = iq//3, f(Y) + -i7r/by.
,f3 = b/l
-
q2 -
,2;Byzy2
”
_!-
P
fJ3
bu
+
(u2
-
1) In z]
(21)
and Q = 3iw/4wl. As w/w1+ co, E+ q2 + 1 so that
iw/wl
Hence iW$l w;-w2-dw?j
so that An-+
(w; - wy
_3--- wl (l-p) 4 wp
case
(wi
- wy
+ w%+
as W/WI + 00. If we use the relation [13] 1 - p = lGn,Mq/(Snmv~) (10) as it should.
.
(22) then (22) reduces to
generated by the synchrotron source at Brookhaven, Hirschthe adsorbate-induced changes in the IR reflectivity of a Cu( 100) surface upon CO exposure. In Fig. 2, we show their results for the CO coverage 0 = 0.40 f 0.05. The quantity plotted is R(O)/R(O)= (Ro+ AR)/R, as a function of the frequency w of the IR light. Since no clustering occurs for CO on Cu( loo), for 0 << 1 the CO molecules can be considered as randomly distributed on the substrate binding sites. Using infrared radiation
mug1 et al. [7] h ave recently studied
31
The solid curve in the same figure is calculated from (17)-(21) using a jellium model for Cu with one conduction electron per Cu atom. The damping or friction coefficient 17in (Ii’)-(19) h as b een adjusted to reproduce the asymptotic reflectivity change for “large” w, which amount to a 1.23 f 0.10% reduction in the reflectivity. The resulting friction 9 = l/~~h corresponds to an electron-hole pair lifetime of the parallel frustrated CO vibration r,h = (4.6 f 1.0) x 10eL1 s, in good agreement with that deduced 1131from DC-resistivity measurements [14] on thin Cu films, 7eh a 3.9 x lo-l1 s. For the parameter ~1 in (45), we have used w1 = 500 cm-‘, which is remarkably close to the prediction of the jellium model, wl = W~VF/C NN444 cm -l. The overall a#greement between theory and experiment is satisfactory, considering that copper is not jellium.
1.ooo
R @I R (0) 0.995
0.990
0
1000 0
(cm-‘)
Fig. 2. Measured reflectivity as a function of frequency for the CO/Cu(lOO) system at the coverage 0 = 0.4. The solid curve is the background absorption calculated using the jellium model with wr = 50O~rn-~.
32
The two resonance structures in Fig. 2 at w = 285 and 345 cm-l are associated with the frustrated rotation and the C&CO stretch vibrations, respectively (see insert in Fig. 2). The parallel CO vibration occurs at [15] w = 40 cm-l, i.e. it is outside the frequency region presented in Fig. 2. The Cu-CO mode is dipole allowed (with respect to the surface normal) and gives rise to a “dip” in the reflectivity, as is usually observed for dipole-allowed adsorbate vibrations. On the other hand, the frustrated rotation of CO is dipole-forbidden, and this mode is observed only for the reasons discussed above. That is, since some motion of the CO molecule occurs parallel to the surface, some (reduced) coupling between this mode and the parallel electric current should occur, just as for a “pure” frustrated translation. Note also that the frustrated rotation gives rise to enhanced refiectiPrity at resonance; the physical origin of this effect was explained above. The reflectivity does not return to the value for the clean surface as expected for a “pure” frustrated translation in the local optical region and in the absence of inhomogeneous broadening and dephasing. But the asymmetry of the line profile is very similar to the one calculated from (18)and (19), see Fig. 1. Note that in this calculation no adjustable parameters occur. Recently Lin et al 1161 h ave measured the IR-reflectivity from CO on Ni(lO0) at room temperature. At the CO coverage na = 0.064Aa2 a very small adsorbate induced reflectivity than e was observed, -0.2 f O-2%, independent of the frequency w for w between 4OOcm- 5 and 2000cn~-~. Lin et al. used this experimental result to argue against the model presented above. However, as we will now show, the result of Lin et al. is in qualitative agreement with what is expected from theory. The theory presented above is based on the jellium model where a single free-electron like band crosses the Fermi energy. On the other hand, Ni is known to have a complicated band structure with several very flat electronic bands (d-bands) crossing the Fermi energy and interband transitions are known to occur in Ni already for tiw N 800~z-~; we may tentatively use the theory presented above below this frequency. But even in this limited frequency range Ni differ in an important way from copper in that the Drude relaxation time TB is much shorter for Ni than for Cu (at a given temperature); this again is related to the d-bands at 6~ which gives rise to a high density of states at EF into which the “free” sp-electrons can scatter (note: the d-band electrons themself contribute very little to the DC conductivity of Ni owing to their large effective mass). Hence at room temperature the mean free path in Ni is about a factor of 5 shorter than that of Cu. Assuming one free electron per metal atom with an effective mass identical to the free electron mass one can calculate 6, M 2OOA for both Ni and Cu and 1 M 3000;1 for copper at 7’ = 90K while at room temperature, 1 M 3OOw for Cu and I M 6OA for Ni. Hence, the ratio 1/6 equals w 15 for Cu at T = 90K and 1.5 and 0.3 for Cu and Ni at room temperature, respectively.
33
In fig. 3 we show the dependence of the ratio R(O)/R(O) on the parameter I/s. In all cases R(O)/R(O) --t 1 - (1 - p)” as W/WI -+ CXI(where wl M 5OOcna-’ for Cu and Ni and a = (V&)( 3/4cosl9). It is obvious that for I/S = 15 and 1.5 the background absorption is very similar in magnitude and nearly equal to that for 1/6 = 00. But for Ni at room temperature (where I/S M 0.3) the adsorbate induced change in the reflectivity is very small if w < 1.5~1, which is the only frequency region where the theory may be applied to for Ni (see above). Hence one expect a much smaller adsorbate induced contribution to the background absorption for Ni than for Cu, in qualitative agreement with the measurements of Lin et al.
1
I-(I-p)aJ 0
Fig. 3. The reflectivity as a function of the frequency for several values of the ratio 1/6 between the bulk electron mean free path and the skin depth 6. u = (?J~/c)(3/4cose).
In fig. 4 we show the nature of the absorption structures expected for parallel adsorbate vibrations with resonance frequencies at wo = 0.6~1 (as for the frustrated CO rotation on Cu(IO0)) an d a t wg = 3.6~1 and for l/6 = 10 and 0.25. The dash-dotted lines in the same figure shows the background absorption for l/6 = 10 and 0.25, i.e. the same as the two corresponding curves in fig. 3. Note that when wg increases the absorption structures associated with the parallel vibrations become more and more Lorenteian-like i.e. the asymmetry disappear, a result which is indeed expected in the local optic’s frequency
34
region (see (10)).
-_w-*
A
___-___________--____.
a--_-_
--._
+
--. --_ --. -, -_ t+ --_
-C
--__
l/S =
---
0.25
R Ko
---
_----_a
-a---------------__-_
‘1.
0.6q
‘Y %
I/S=
I-(I-p)c
‘\.
\
10
1
‘\
-\
‘\
‘\
#q-j = 3.k -\
-\
‘\
-\
--
2
-_
-w
3
k. ---
4
W/wl Fig. ‘4, Dash-dotted lines: The reflectivity as a function of the frequency for I/6 = 10 and 0.25. Solid lines: The anti-absorption resonances associated with parallel vibrations located’at wg = 0.6~1 and 3.6~1. a = (~~/c)(3/4cost9).
It is interesting to note that in a narrow frequency interval the reflectivity is higher with adsorb&es on the surface than without i.e. R(Q)/R(O) > 1. This result is only possible if ,R(O) < 1 which is indeed the case even for a “perfect” system with no bulk wave incident absorption (i.e. I. = co). To see this, let us consider an electromagnetic on a metal surface. The field will penetrate into the metal to a distance N 6 = c/wp.
35
An electron which enter this region will pick up some drift momentum and propagate “ballistically” towards the interior of the crystal as a “hot” electron. This will result in a continous transfer of energy to the metal and hence the reflectivity R will always be smaller than unity even for a perfect system at zero temperature. The theory outlined above correctly describes this background absorption and in fig. 5 we show the reflectivity R both for a perfect surface (no adsorbates, p = 1) and in the case of an adsorbate layer (diffusive surface scattering, p = 0) dash-dotted curve. The solid curves shows the reflectivity (for p = 0) in the vicinity of the resonance frequencies wu = 0.6~1, 1.6~1, 2.6~1 and 3.6~1 of four parallel vibrations. Note that the reflectivity R is always smaller than unity.
1
R
p=l
1 --
_2.6~~
_w() = 3.6L
l-c \ ‘p=O
I
1
I
I
1
2
3
4
Fig. 5 The reflectivity as a function of frequency. Dashed line: Reflectivity of a clean metal surface (0 = 0). Dash-dotted line: Reflectivity of a metal surface where the electrons scatter diffusively. Solid lines: Anti-absorption resonances for parallel adsorbate vibrations with wg = 0.6~1, 1.6~1, 2.6~1 and 3.6~1. Q = (~~7/c)(3/4cost9).
36
The problem of the IR-reflectivity discussed above is closely related with the problem of the DC resistivity of a thin metallic film. To see this we note that ohmic heating due to scattering of the conduction electrons by adsorbates can be written in the form P = ApdA0(J2)
(23)
where Ap is the adsorbate contribution film resistivity at the frequency w and where d and A0 are the thickness and the area of the metal film, respectively. Comparing (23) with (5) at w = 0 we obtain a relation between ~,h = l/p7 and Ap
so-
I
I
(a)
N
aa E, 20-
(b)
G ”
lo-
5 g
s-
0.15 na
(A-*)
Fig. 6. (a) The change in the film resistivity Ap as a function of CO coverage for the CO/Ni(lll) sy st em. (b) The variation of 6P/6na(na + 0) with the film thickness d. The straight line has the slope -1. Adopted from ref. [14]. For low adsorbate
coverages n, the resistivity
Ap is found to vary linear with na so
that AP
-
%
aP
= an,
In,=0
(25)
Hence 1 -= Gh
9s
a
In,-0
(26)
This formula was used in ref. [13] to deduce ~,_h for some different absorption systems. For example, fig. 6a shows the change in resistivity Ap as a function of the CO coverage
37
for the CO/N i ch emisorption system. For low CO coverage Ap increases linearly with na. According to (26), Ap/n, N l/d if we assume that T is independent of d as expected if the film is thick enough. This relation is well satisfied for the CO-Ni chemisorption system as shown in fig. 6b. From fig. 6b we get
and using M = 2811 (the CO mass) and n = 8.47 x 10m2Ae3 gives ~,h _.. = 1.4 x 10-lla. Similar, for CO on a copper film one obtain the e-h pair relaxation time quoted earlier.
3. Summary
and conclusion
There is in our opinion little doubt that the theory presented above is the correct explanation for why “dipole forbidden” vibrational modes have been observed in IRAS. Not only does the theory correctly describe the background absorption but even the predicted vibrational line shape agrees nicely with experimental data for the CO-Cu(100) system. But a.s an additional test of the theory we suggest that IR-measurements on the H/Cu system should be performed. It would also be interesting to repeat the measurement on the CO/Ni(lOO) system at T N 1OOK where the electron mean free path should be so long that the condition 1/6 > 1 should be satisfied below the onset ofinterband transitions. “Dipole forbidden” vibrational modes have also been observed for H on W(100) and Mo(100). It is very likely that these modes too are observed in IRAS via the indirect coupling discussed above. But in these cases the jellium model can not be used in the analysis owing to the complicated band structure (including surface states) of these metals. The theory presented above is closely connected with the concept of surface resistivity which has been found to have many interesting and useful implications for other surface physics problems as discussed in ref. [ 171and [ 181. It is interesting to speculate if the theory presented above is valid for other types of elementary excitations in addition to parallel adsorbate vibrations. We have only found one such case namely parallel vibrations of surface charge density waves, pinned by impurities or by the periodic crystal potential. As shown by Overhauser this problem is formally identical to the one studied above if the adsorbate mass M, resonance frequency wo and damping 7 in (3) are replaced by the charge density wave effective mass m*, the pinning frequency w;f and the e-h pair damping v*. Hence, in this case one would again expect to observe enhanced reflectivity at resonance, but the resonance frequency could be much higher than for parallel adsorbate vibrations.
33
REFERENCES [l] B.N.J. Persson, Surf: Sci. Rep.15 (1992) 1. [2] R. Berndt,
J.P. Toennies, and G. Wall, J. Electron Spectr. 44 (1987) 183.
[3] A.M. Lahee, J.P. Toennies and G. Wiill, Surf. Sci. 177 (1987) 371. [4] G. Kisters, J.G. Chen, S. Lehwald, and H. Ibach, Surf Sci. 245 (1991) 65. [5] L.D. Landau and E.M. Lifshitz, Electrodynamics mon Press, London, 1984).
of Continuous Media (Perga-
[S] Y.J. Chabal, Phys. R ev. Lett. 55 (1985) 845; J.E. Reutt, Y.J. Chabal, and S.B. Christman, Phys. Rev. B38 (1988) 3112. [7] C. J. Hirschmugl, G.P. Williams, Lett. 65 (1990) 480.
F.M. Hoffmann,
and Y. J. Chabal, Phys. Rev.
[8] B.N.J. Persson and A-1. Volokitin, Chem. Phys. Letters 185 (1991) 292. [9] B.N.J. Persson, Chem. Phys. Letters 197 (1992) 7. [lo] C.J. Hirschmugl, G.P. Williams, F.M. Hoffmann, and Y.J. Chabal, to be published; private communication. [ll] There is also a surface contribution from the nonlocality due to the abrupt change in the electric field in the surface region. But as shown in Phys. Rev. B44 (1991) 3277, if vf/w >> a th is surface contribution is negligible compared with the bulk contribution,
where a N lw is the width of the surface region.
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