Comparison of cross sections in high resolution electron energy loss spectroscopy and infrared reflection spectroscopy

Surface Science 66 (1977) 56-66 0 North-Holland Publishing Company

COMPARfSON OF CROSS SECTIONS IN HIGH RESOLUTION ELECTRON ENERGY LOSS SPECTROSCOPY AND INFRARED REFLECTION SPECTROSCOPY

H. IBACH Institut fiir Gre~z~~c~enforschung und Vakuum~hysik der Kernforsch~ngsanla~eJiilich, D-51 70 Jiilich, Germany Received 24 January 1977

Electron energy losses and absorption of infrared radiation are both caused by the dipole moment of the surface vibration. A comparison of absolute intensities between both techniques should therefore be possrble. In this paper the appropriate formulas are derived. For the adsorption system CO on Pt(l11) which has been investigated by both techniques a perfect agreement is found. For a number of adsorbate systems the effective ionic charge is calculated from previously published electron energy loss data.

1, Introduction

Surface vibrations of adsorbates on single crystal surfaces may be studied by either infrared reflection spectroscopies [l-3] (IRS) or high resolution electron energy loss spectroscopy (ELS). .The latter technique has experienced considerable progress recently and four groups [4-91 have presented data with sufficient resolution. As Lucas and Sunjic [lo], Evans and Mills [l l] and this author have pointed out already in the earlier stages of this development both techniques, IRS and EIS, essentially deliver the same physical information. In both techniques the inelastic process is caused by the same physical entity, i.e. the vibrating surface dipole and the same selection rules apply. It is not immediately obvious why and to what extend this statement holds. We therefore wish to discuss in this paper the similarities of photon-dipole and electron-dipole interaction in some more detail. For both scattering processes theoretical relations between the cross sections and the dipole moment of the adsorbate vibrations are available. Recently the adsorption of CO on Pt(ll1) has been studied by IRS and ELS and quantitative data have been reported [ 1,I 21. A quantitative comparison of the cross sections has therefore become possible. This comparison provides a rigorous test of the present models for the photon-dipole and electron-dipole interaction and the accuracy of the currently available theoretical treatments. In this paper we therefore summarize the appropriate formulas and carry out the com56

H. Ibach / Comparison of cross sections

51

parison. The comparison will be made by calculating the effective ionic charge e*. The quantitative agreement between e * derived from IRS and ELS shows that besides the vibration spectrum itself intensity measurements provide information about an additional parameter of the adsorbate systems. This parameter, the effective ionic charge, is of considerable importance. For a layer of adsorbed atoms e* provides information about the derivative of the surface potential $ with respect to the distance r of the adsorbate layer d$/dr = e0’ e’N,,

(1)

with N, the number of adsorbate atoms per cm*. In selfconsistent first principle theories for chemisorption d@/dr is calculated easily [13] and therefore the effective ionic charge would be useful quantity for comparison between theory and experiment. In parameterized or semiempirical approaches e* would provide a reasonable quantity to which parameters could be adjusted as e* represents a collective property of the electron system. We have therefore used the present available ELS data for a variety of different adsorbates to calculate e* for these systems.

2. IRS and EL& qualitative picture In IRS the adsorption of infrared radiation due to excitation of surface vibrations of adsorbates is measured after reflection from a plane substrate (mostly metal) surface. Energy is extracted from the radiation field when the frequency of the light matches the eigenfrequency w of a dipole active oscillator and is ultimately converted to heat via the anharmonic coupling of the infrared active oscillator to all eigenmodes of the system. The interaction between the radiation and the vibrating dipole is produced by the electric field of the light exerting a force on the charge e* of the oscillator. The wavelength of light is long compared to atomic distances and the excitation will therefore be almost completely in phase for neighbouring dipoles. For a surface adsorbate lattice this is equivalent to the statement that the wavevector 4 11of the surface wave is large. Quantitatively 4 11is 411=4L sin 0,

(2)

with 4~ the wavevector of the light and 19the angle of incidence with respect to the normal. After conversion to atomic units (denoted by a circumflex in the following) 4s is 411=(137)-l

A& sin 8.

(3)

For metals the dielectric constant is rather high. Therefore the tangential component of the electric field is practically zero under any condition, while a substantial field normal to the surface exists for light reflected at grazing incidence and polarized in the plane of incidence (see section 3). Thus in IRS only the perpendicular component of a surface vibration is excited.

58

H. Ibach 1 Comparison of cross sections

While the above considerations are rather straightforward and commonplace the mechanism of electron-dipole scattering is somewhat more complicated. The picture that has emerged from rigorous quantum mechanical treatments [lO,ll] may be described as follows. When an electron approaches the surface the electric field of the electron exerts a force on dipole active oscillators. Just as in IRS and for the same reason for metals the field is practically normal to the surface. Therefore the same selection rule with respect to the orientation of the dipole oscillator applies. As a consequence of the long range nature of the coulomb field the most significant contributions to the total interaction arise during the time where the electron is still many lattice constants away from the surface. The field is then nearly homogeneous on the atomic scale and therefore mostly long wavelength surface waves are excited. The lateral extension of the electric field, however, being a function of the distance of the electron shrinks up as the electron approaches the surface. This is the reason, why unlike to IRS in EI.23 a continuous distribution of surface wave vectors is excited. In IRS the field is periodic in time. Therefore for harmonic oscillators only the fundamental frequency is excited. This is different in ELS. The total interaction time of the electron is of the order of an oscillator period. From the standpoint of the oscillator the external force therefore contains all frequencies. As a result multiple excitations with a Poisson distribution in the excitation probabilities occur [lo]. For a single adsorbate layer, however, multiple excitations of this nature are frequently unobservable as the intensities of the corresponding electron losses are too low. Although the above considerations suggest that mainly surface waves with wavevectors small compared to the reciprocal lattice vector are excited, the picture so far does not allow to estimate the value of 411where maximum excitation probability occurs. Such an estimate is provided from the alternative picture of the electron-surface wave interaction, i.e. if one considers the force that the electric field of the dipole active surface wave exerts on the electron. It then becomes immediately clear that the maximum interaction occurs when the electron behaves like a surfer, i.e. when the component of electron velocity direction of the wave matches the phase velocity

parallel’ to the propagation

It should be mentioned that this resonance condition is indeed to be found in the equations for the cross section as a resonance denominator [l]. The equivalent equation in atomic units is 6 11= fi&(2Eo)-‘~2

sin-’

with Ee the primary

B,

energy of the electron. For a typical phonon energy fiiw = 100

meV and a primary energy of 5 eV, i 11 is then for large 6 $[I= 6 x 10-3,

(5)

H. Ibach / Comparison of cross sections

while for infrared absorption

59

4 11is (eq. (3))

Gil = 2.6 X lo-‘. In both cases 4 is small compared to a reciprocal lattice vector and thus the effect of phonon dispersion has a negligible effect on the observed frequency. After these qualitative considerations that might help to some understanding of the nature of ELS in particular we now turn our attention to the quantitative description of the cross sections and their relation to the effective ionic charge e* of the adsorbate.

3. Infrared reflection

spectroscopy

A quantitative treatment of IRS has already been presented by Greenlert [l.] The resulting equations are, however, very complicated and difficult to evaluate. In this chapter we shall derive a much simpler expression which is valid for spectroscopy on metal surfaces. As starting point we use the linear approximation theory of McIntyre and Aspnes [ 14.1This is justified because the change in reflectivity due to adsorbates AR/R is always small. Furthermore, we shall consider only terms that are linear in the concentration of adsorbates. This simplification is justified as experimentally a linear relation between AR and the coverage is found [2,3.]For a three phase system (1 vacuum, 2 adsorbate layer, 3 metal) AR/R is ml -=--

8nd

m,, Ra

cos e Im f2 x

Rl

= &d

cos e Im E2 x

E3

(6)

Zq-Gg’

E3

El -E3

1 1 -

(fl/E2E3)(E2

(1/e3)(eI

+ E3) sin2e

+ E3) sin28

1’

where d is the adsorbate layer thickness, h the wavelength, and E the complex dielectric function of the three phases. The subscripts 1 and II refer to light polarized perpendicular and parallel to the plane of incidence, respectively. As ~3 becomes rather large for metals in the infrared ARJR is practically zero. The physical reason is that the electric vector perpendicular to the plane of incidence has a node on the surface and the coupling to the adsorbate layer is therefore small. In the frequency region of interest ~3 is much larger the e2. For the case of platinum e.g. f3 - - 120 + 340i at h-l = 2200 cm-‘, while for a CO layer on Pt(ll1) (at a coverage of es = 0.25), e2 = 1 t 2i in the adsorption maximum. Eq. (7) then simplifies to

The angular dependence

is valid as long as cos28 > Ie3 I -‘.

In the case of platinum

60

H. Ibach / Comparison of cross sections

this means 0 has to be smaller than 87”. For a system of harmonic E(W) = E,

+

oscillators E is

C&W: - cd2- ioy),

(9)

with O; = 4rrNe”/p, where N is the number of oscillators per cm3, e* the effective ionic charge, y a damping constant, and ~1 the reduced mass. For a narrow band eq. (9) may be replaced by 2 % E(O)=E,+-

ti =&

i

0’0- cd2 2

[6(w - we) + &(a +

00

o,)l.

The intensity of an absorption band in IR spectroscopy then easily calculated. Making use of

(10)

defined as j(Af?~/R)dw

is

(11) and neglecting terms of higher order in N (E,= 1) one derives

ARII

(12)

RI1

Nd is the surface concentration of oscillators and may be replaced by N$s with N, the number of surface sites and BS the fractional coverage. ef is the component of e* in the direction of the polarization of the light, i.e. perpendicular to the surface. Infrared experiments are usually carried out with unpolarized light. At large angles of incidence R 11is roughly equal to RI and therefore (13)

ARIR = $R,,IR,,. For convenience

we express the final equation

s

$dhG=

dh& = 4.57 X 10e6 cm d( 1IX),

in atomic units:

(14? (15)

where physical quantities in atomic units are denoted with a circumflex. This formula is accurate enough for most practical purposes and much more convenient than those previously used. For comparison or for a rough estimate of the absorption to be expected from an adsorbate layer it may be useful to relate e* also to the absorption coefficient of gases. The intensity of gas phase IR absorption bands is usually given as the integrated molar intensity 2 (units: mol- ’ P cme2) [ 151. Using eq. (10) the absorption

H. Ibach / Comparison of cross sections k for dilute systems is

coefficient

k = ;+;/~o>[+

- arj) + &(W + %)I,

and the extinction s

coefficient

(16)

K = 4nk/X integrated

over the frequency

K dw = 2no;lc.

(17)

Because the integrated 2=6X

61

1O23 f

molar intensity

A is defined as

(18)

$d;.

K is equal to A = 1.16 X lo6 (C**/fi) (Q/m01 cm*).

(19)

This refers to molecules oriented parallel to the polarization vector. As one third of the molecules is oriented parallel to one polarization direction 2 becomes ;1 = 3.87 X lo5 (C**/fi) (Q/m01 cm*).

(20)

4. Electron energy loss spectroscopy The inelastic scattering of electron from ordered surface lattices has been treated by Evans and Mills [ 11.1According to their paper the intensity of an energy loss divided by the elastic intensity is for the case of specular reflection: S = 87~&*i?&‘~

cos-‘8

F(a,B),

(21)

where Eo is the primary energy, pl the perpendicular component moment (both in atomic units) and F (a, 13)an angular term

F(a,B) =

sin*0 - 2 c0s2e 1 to*

a = I+?&,,

+ (1 + c0s2e) In 1 + -!(Y*1 ’ (

QE = Rw/2E,,

of the dipole

(22) (23)

which contains the angle 19, up to which the spectrometer accepts reflected electrons scattered slightly off the specular direction. In the derivation of eq. (21) is assumed that 9, is the same in and out of the scattering plane (circular aperture). Using fi: = (3672 h&)-r

e***/j.i,

the relative intensity S = 4tr(1836R&,)-’

(24)

S is &BS@**/ji) cos-‘8

F(a,fl).

(25)

Eq. (25) holds when the specular reflex is sharp, i.e. for well ordered surface lattices

H. Ibach / Comparison of cross sections

62

only. For disordered lattices and even for coverages where a full regular surface lattice is not completed the situation is more complicated. In general the intensity in ELS is therefore not simply linear in coverage even if e* is independent of coverage. The practical importance of this point may warrant a more detailed discussion. While a quantitative treatment is not yet available, some qualitative aspects may be understood easily. As explained in section 2 the electrons excite surface phonons with a continuous distribution of wave vectors. It is easy to see that this distribution has to be different parallel and perpendicular to the plane of incidence. Consequently the angular distribution of electrons around the specular reflex does not only depend on the polar angle 9 (measured from the direction of specular reflection) but also on the azimuth cp.The angular dependence of the differential cross section is [ 1 I] @

(4cos cpcos 8 -9~

dR ff ~--. For simplicity

dz

0:

(#+

sin 6)’ =rY2 sin2p 9;))”

-

(26)

we consider dS/dG! averaged over upin the following

a2 t y=lY; (1 + cos28)

(v2 + &)a ’

(27)

y2 = 2 sin28/(1 t ~0~~8). The averaged cross section normalized at 9 = 0 is plotted in fig. 1 versus 6/9~. As seen from fig. 1, dS/dQ falls rather rapidly in the beginning and tails off smoothly for higher 9. The dashed lines indicate the limit up to which a typical spectrometer (8, = 1 S”, E,, = 5 eV) accepts the inelastic intensity for phonon energies of 100 and 300 meV respectively. As long as most of the inelastic intensity is accepted by

Fig. 1. Differential cross section averaged over the azimuth versus 9/8~. The curves are normalized to one for 0 = 0. The dashed lines indicate the limit up to which a typical spectrometer accepts the inelastic intensity of phonon losses.

H. Ibach / Comparison of cross sections

63

the analyzer (19, > 19~) disorder affects the elastic and the inelastic intensity by approximately the same factor and the ratio S remains essentially unchanged by disorder. Unfortunately the condition 6, > 0~ is not fulfilled to a satisfying degree in many cases (fig. 1). Then for disordered surfaces S will be larger than calculated from eq. (25) and care should be taken in the analysis of intensities.

5. Application

to CO on Pt(ll1)

For the adsorption system CO on Pt(l11) both IR reflection spectra [2] and ELS [12] spectra have been reported. In IR spectroscopy a band at h-’ = 2100 cm-’ corresponding to the CO stretching vibration of CO molecules in on top position [12] is observed. At saturation the coverage is approximately 8,- 0.25 [12]. As we compare saturation intensities in IR and ELS the comparison is not impeded by the uncertainty in OS.The integrated intensity of the IR band is [2] s (Af?/R) dhG = 2.75 X 10-6, and the effective ionic charge is calculated to be e * = 0.549. This value is to be compared with the value for gaseous CO (e* = 0.65) [ 161. For the evaluation of ELS data the cut off angle r9, has to be known. In practice electron spectrometers have not a finite acceptance angle but rather a certain acceptance function j(8). For the purpose of this evaluation we take 8, as the angle where the intensity of the elastic peak has fallen off to half the maximum value. For the spectrometer used in ref. [ 121 this value is 1.5”. Using the relative intensity of the CO loss at 261 meV (= 2100 cm-‘) reported in ref. [ 121, a value of e* = 0.56 is calculated. This value is in remarkably good agreement with the value derived from IR-spectroscopy. This agreement provides additional support to the model for inelastic electron surface scattering.

6. Effective ionic charges for various systems A substantial number of systems have now been investigated by ELS. A comparison of effective ionic charges may therefore be attempted. Formula (25) allows the calculation of effective ionic charges from the ratio between inelastic and elastic intensity provided that primary energy Eo, acceptance angle 6, and the angle of incidence 0 are specified. Fortunately these specifications have been made by the previous authors [20], although it appears that most authors have not corrected the primary energy for contact potential differences. As long as the primary energy is high and the acceptance angle 8, not too small the possible error in e* is however small. For Eo = 5 eV, 6, = 1.5” and Rw = 100 meV; e.g., and error in Ee by 1 eV causes an error in e* of 9%. Furthermore for electron optical reasons a reduction in

H. Ibach / Comparison of cross sections

64

the actual primary energy causes an increase in 9, so that the effect of contact potential changes is partially compensated (compare eq. (21)). In our calculations we therefore have used the uncorrected values for Ee as specified by the authors. Recent results of Bertolini et al. [9] on adsorption of benzene on nickel have not been included. An evaluation based on the spectrum presented at the Noordwijk conference [9] would lead to unreasonable high values fore*. An estimate of the CO coverage from the intensity of the CO peak in the same spectrum, however, would also lead to the conclusion that these surfaces should have been contaminated with 10% of a monolayer of CO. This is much more than one would expect under typical experimental conditions. It may therefore be that either the magnification scale or the spectrometer specifications as given by Bertolini et al. are in error or the surface adsorbate lattice was substantially disordered. For symmetry reasons the polarization of the adsorbate vibrations is perpendicular to the surface except for C-H vibrations in adsorbed acetylene. In this case we have assumed that the effective ionic charge is the same for the C-H bending and the C-H stretching vibration. As these vibrations are perpendicular to each

Table 1 Effective ionic charges for various adsorption system calculated from the relative intensities according to eq. (2.1) (primary energy Eg and angular aperture 9, are used as specified by the authors; for adsorbed CO the high and low frequencies correspond to the carbon-oxygen and the metal-carbon stretching vibration respectively; for C2H2 the angle between the C-H group and the surface normal has been calculated under the assumption that e* is the same for bending and stretching vibration; here 0 and e* refers to a single CH unit) Adsorption system

Adsorption

W(100) + H W(lO0) + D W(100) + H W(lll)+H Si(ll1) + H W(100) + 0 Ni(lOO) + 0 Pt(lll)+CO

Bridge Bridge Top Top Top 4-fold p (2 x 2) Top Bridge

Ni+CO Pt(ll1)

Top + C2H2

300 K state

site

hw (meV)

130 93 155 160 257 15 53 258 58 230 45 256 59 95 375

Rel. intensity -~

0

e*

5.6 1.1 6.9 1 2.1 3.1 1.1 6 3.5 2.6 2.3 4.6 1.0 2.1 1.7

2 2 0.4 1 1 0.17 0.25 0.25 0.25 0.25 0.25 0.5 0.5 0.5 0.5

0.037 0.039 0.035 0.035 0.09 0.27 0.35 0.56 0.21 0.32 0.14 0.44 0.15 0.051 0.051

x x x x x x x x

x x x x x x x

1O-3 10-3 lO-4 10-3 10-3 10-3 10-2 lO-3 10-S lO-3 lO-3 lO-3 10-Z 10-S 10-4

Ref. __. ____ 5 5 5 8 16 6 7 12 12 12 12 18 18 19 19

H. Ibach / Comparison of cross sections

65

other the effective ionic charge is e*2 = e;” (bending)

t eT2 (stretching).

(28)

A comparison of the effective ionic charges in table 1 shows a reasonable consistency even in cases where data have been taken with entirely different spectrometers. For hydrogen, e.g., in on-top position on W(lll) and W(100) surfaces the same values are calculated. The comparison of hydrogen and deuterium on W(100) for which e* should be equal provides information on the general accuracy that one may expect. Further inspection of table 1 shows that e* is the highest for vibrations involving oxygen, medium for metal-carbon vibrations, and low for hydrogen. This trend is in agreement with the electronegativity differences, although the effective ionic charge for adsorbed oxygen is about a factor of two smaller than for oxide compounds. For adsorbed acetylene e* may also be compared to the value for a C-H unit that is calculated from the integrated molar intensity of gaseous acetylene [1.5] according to eq. (16) for which a value of e* = 0.061 is obtained. We conclude that high resolution electron energy loss spectroscopy has reached a stage where quantitative evaluation of intensity data has become possible. A systematic exploitation of this possibility may render new information and lead to a better understanding of chemisorption.

Acknowledgement It is a pleasure to acknowledge helpful discussions with George Comsa and the substantial suggestions that helped to improve this paper.

References [l] [2] (31 [4] [S] (61 (71 [S]

[9]

[lo]

R.G. Greenler, J. Chem. Phys. 44 (1966) 310; 50 (1969) 1963. A.M. Bradshaw and J. Pritchard, Proc. Roy. Sot. London A316 (1970) 169. R.A. Shigeishi and D.A. King, Surface Sci. 58 (1976) 379. H. Ibach, Phys. Rev. Letters 24 (1970) 1416; 27 (1971) 253; J. Vacuum Sci. Technol. 9 (1972) 713. H. Froitzheim, H. Ibach and S. Lehwald, Phys. Rev. Letters 36 (1976) 1549. H. Froitzheim, H. Ibach and S. Lehwald, Phys. Rev. B14 (1976) 1362. S. Anderson, Solid State Commun. 20 (1976) 229. C. Backx, B. Feuerbacher, B. Fitton and R.F. Willis, Surface Sci. 63 (1977) 193; C. Backx, B. Feuerbacher, R.F. Willis and B. Fitton, in: Proc. Conf. on Photoemission from Surfaces, Noordwijk, 1976. G. Dalmai-Imelik, J.C. Bertolini and J. Rousseau, Surface Sci. 63 (1977) 67; J.C. Bertolini, G, Dalmai-Imelik and J. Rousseau, in: Proc. Conf. on Photoemission from Surfaces, Noordwijk, 1976. A.A. Lucas and S. Sunjic, in: Progress in Surface Science, Vol. 2 (Pergamon, 1972) p. 75.

66

[ 111 [12] [13] [14J [IS] [16] [17] [18] [19] [20]

H. Ihach j Comparison of cross sections

E. Evans and D.L. Mills, Phys. Rev. B5 (1972) 4126. H. Froitzheim, H. Hopster, H. Ibach and S. Lehwald, Appl. Phys. 13 (1977) 147. See e.g. J. Appelbaum and D.A. Haman, Phys. Rev. Letters 34 (1975) 806. J.D.E. McIntyre and D.E. Aspnes, Surface Sci. 24 (1971) 417. L.H. Little, Infrared Spectra of Adsorbed Species (Academic Press, London, 1966) p. 382. R.A. Toth, R.H. Hunt and E.K. Plyler, J. Mol. Spectr. 32 (1969) 85. H. Froitzheim, H. Ibach and S. Lehwald, Phys. Letters A55 (1975) 247. S. Andersson, Solid State Commun. 21 (1977) 75. H. Hopster, H. Ibach, H. Froitzheim and S. Lehwald, to be published. The cut off angle 6, for the spectrometer of Backs et al. is 3’ according to private communication.