J . Phys. Chem. 1984,88, 837-848 must be to the A2 d-Rydberg state in cis-hexatriene. Further members of this series in trans-hexatriene appear at 7.35 and 7.71 eV. The magnitudes of the quantum defects calculated for these bands, 6 = 0.44 for the 6.22-eV band, -0.65 for the 5.85- and 7.08-eV bands, and -0.20 for the 6.52-, 7.35-, and 7.71-eV bands, are in full agreement with their symmetry-based assignments.I5 The only band we cannot interpret is the 6.92-eV band in trans-hexatriene. It is rather strong under optical conditions. However it, or the continuum absorption beneath it, is greatly enhanced when the optical selection rules are relaxed. If it were a Rydberg transition, we would predict an analogous transition to exist in the cis isomer. N o analogous transition is seen in the cis isomer either under optical conditions or under any other (15) M. B. Robin, "Higher Excited States of Polyatomic Molecules", Vol. I, Academic Press, New York, 1974, p 51.
837
conditions attained in this experiment. This transition remains unassigned. One other feature of the spectrum of trans-hexatriene merits attention: The previous assignment of the optically allowed, 6 = 0.05 Rydberg series as It is clear, from its optical intensity, the magnitude of its quantum defect, and the selection rules presented in Table 111, that this must be a d-Rydberg series. Thus in hexatriene, as in ethylene,] transitions occur to 3s, two 3p, and two 3d Rydberg states but which of these are active depends on the specific set of experimental conditions. The detailed assignments of each transition are currently under investigation.16 Acknowledgment. J.P.D.acknowledges support from the National Science Foundation under Grant CHE79-2650 1. (16) A. SabljiE and R. McDiarmid, manuscript in preparation.
FEATURE ARTICLE Excited States at Metal Surfaces and Their Nonradiative Relaxation Phaedon Avowis* and Bo N. J. Persson IBM Thomas J . Watson Research Center, Yorktown Heights, New York 10598 (Received: August 25, 1983; In Final Form: December 21, 1983)
We present a general overview of the spectroscopy and relaxation dynamics of vibrational and electronic excitations of molecules and atoms adsorbed on metal surfaces. We discuss briefly some experimental tools, in particular, electron energy loss spectroscopy, and present experimental illustrations of rotational, vibrational, and electronic excitations of adsorbates. For excitations at surfaces, new effective nonradiative decay paths are opened involving, for example, excitation of electron-hole pairs and phonons. For excited molecules not in direct contact with the metal substrate (or where this overlap can be neglected), the nonradiative quenching can only result from the interaction between the oscillating electric field of the excited molecule and the metal. We first discuss the "classical theory" of this coupling and point out its limitations. We then present an improved theory and compare its predictions with experimental data. For excited molecules in direct contact with the substrate, electron transfer between the molecule and the metal can often occur, and this leads in general to strongly nonadiabatic processes. We illustrate this type of decay path for both vibrational and electronic excitations. Finally, multiphonon and phase relaxation of vibrations at surfaces are briefly discussed.
1. Introduction The unique physical and chemical properties of the surfaces of solids are attracting increasing attention in both basic science and techno1ogy.I The technological uses of surface processes are numerous, the most important ones probably being industrial catalytic chemistry and the fabrication of the revolutionary new generation of microelectronic devices. Basic surface science traditionally has been concerned with structural aspects of surfaces and adsorbates and mechanistic aspects of surface reactions. In recent years, however, increasing attention is being paid to the detailed electronic structure of adsorbates and particularly to the microscopic description of surface dynamical processes. New optical and electron scattering techniques provide detailed information on the quantum states of adsorbed atoms and molecules." The excited states (vibrational, rotational, and electronic) (1) See, for example, G. A. Somorjai, 'Chemistry in Two Dimensions: Surfaces", Cornell University Press, Ithaca, NY, 198 1. (2) Ph. Avouris and J. E. Demuth, Annu. Rev. Phys. Chem., in press. (3) H. Ibach and D. L. Mills, "Electron Energy Loss Spectroscopy and Surface Vibrations", Academic Press, New York, 1982.
0022-3654/84/2088-0837$01.50/0
of adsorbates or of excited species in the vicinity of the surface are intimately involved in most dynamic surface processes and, therefore, their nature and mode of nonradiative relaxation are subjects of strong interest. All steps of a surface chemical reaction-sticking, reaction, and desorption-involve energy exchange between the adsorbate and substrate states.I Adsorbate excited states are also involved in surface photochemical proce~ses,~-' photon- and electron-stimulated desorption,8 resonance photoemis~ion,~ surface Raman scattering,I0J1 and photolu(4) R. F. Willis, Ed., 'Vibrational Spectroscopy of Adsorbates", Springer Series in Chemical Physics, Springer-Verlag, New York, 1980. (5) C. J. Chen and R. M. Osgood, Appl. Phys., A31, 171 (1983). (6) A. Nitzan and L. E. Brus, J. Chem. Phys., 75, 2205 (1981). (7) G. M. Goncher and C. B. Harris, J . Chem. Phys., 77, 3767 (1982). (8) N. H. Tolk, M. M. Traum, J. C. Tully, and T. E. Madey, Eds., "Desorption Induced by Electronic Transitions", Springer Series in Chemical Physics, Springer-Verlag, New York, 1983. (9) G. Loubriel, T. Gustafsson, L. I. Johansson, and S . J. Oh, Phys. Rev. Leu., 49, 571 (1982). (10) A Otto in "Light Scattering in Solids", M. Cardona and G. Cuntherodt, Eds., Springer-Verlag, New York, 1983.
0 1984 American Chemical Society
838 The Journal of Physical Chemistry, Vol. 88, No. 5, 1984 minescen~e.'2'~Using laser diagnostic techniques, several elegant state-testate inelastic scattering experiments from surfaces also have been performed r e ~ e n t l y . ' ~ - ~ ~ In this article we present a general view of the spectroscopy and relaxation dynamics of vibrational and electronic excitations at metal surfaces. First we discuss breifly the principles of techniques, particularly inelastic electron scattering, used to study the excitations of adsorbates. We then present spectroscopicresults illustrating some interesting and novel aspects of vibrational, rotational, and electronic excitations of adsorbates. The influence of the substrate on the intrinsic excitations of the adsorbates is described briefly and we present evidence for the occurrence of metal molecule charge-transfer (CT) excitations. In sections 4 and 5 we explore the new nonradiative decay channels opened to excited species near metal surfaces. We discuss the basis of the so-called local optical theory and its application in the "classical" description of energy transfer to the substrate via field coupling. The conditions under which the classical theory should be valid are examined. We then consider the basis of the "nonlocal" optics theory and apply it to obtain a more general theory of nonradiative relaxation involving the generation of electron-hole pairs in the metal. The accuracy of the thus derived expression for the linear response function g(qli,w), a quantity basic in the description of the energy-transfer process (and of a variety of other surface processes), is verified by comparison with inelastic electron scattering studies from clean metal surfaces. The general relaxation theory is then applied to specific vibrationally and electronically excited adsorbate systems. It is found that the relaxation of physisorbed systems is well accounted for by field coupling but that electric field coupling to the substrate cannot account for the faster decay rates of chemisorbed species. Simple theoretical models allowing for charge transfer between substrate and adsorbate are presented and applied to the vibrational relaxation of chemisorbed C O and the decay via electron tunneling to the substrate of electronically excited noble gas atoms. Finally, we will discuss briefly the decay of excitations via phonon emission and the contribution of dephasing processes to the line width of adsorbate excitations.
-
2. Spectroscopy of Adsorbates. General Discussion Excited states of adsorbates can be produced and monitored by photon or particle (e.g., electron) scattering spectroscopies. Infrared reflection-absorption spectroscopy has been used for a long time to study the vibrational spectra of adsorbates on metal surfaces with a typical resolution of 55 cm-' (0.6 meV).4 The great majority of the published optical studies involve chemisorbed CO, but recently studies of other adsorbate systems have been reported?' For strongly IR-active modes, such as the CO stretch, the sensitivity is typically a few percent of a monolayer (about 1 order of magnitude lower than that of electron energy loss spectroscopy). The point of interest here regarding IR reflection-absorption spectroscopy is that the high spectral resolution of the technique allows the measurement of the line widths of (11) Ph. Avouris and J. E. Demuth in "Surface Studies with Lasers", Springer Series in Chemical Physics, F. Aussenegg, A. Leitner, and M. E. Lippitch, Eds., Springer-Verlag, New York, 1983. (12) G. Ritchie, and E. Burstein, Phys. Rev. E, 24, 4843 (1981). (13) A. M. Glass, P. F. Liao, J. G. Bergman, and D. H. Olson, U p f .Left., 5, 368 (1980). (14) G. M. McClelland, G. D. Kubiak, H. G. Rennagel, and R. N. Zare, Phys. Reu. Lett., 46, 831 (1981). (15) A. W. Kleyn, A. C. Luntz, and D. J. Auerbach, Phys. Rev. Lett., 47, 1169 (1981). (16) F. Frenkel, J. Hager, W. Krieger, H. Walther, C. T. Campbell, G. Ertl, H. Kuipers, and J. Segner, Phys. Rev. Lett., 46, 152 (1981). (17) J. W. Hepburn, F. J. Northrup, G. L. Ogram, J. C. Polanyi, and J. M. Williamson, Chem. Phys. Left.,85, 127 (1982). (18) M. Asscher, W. L. Guthrie, T.-H. Lin, and G. A. Somorjai, Phys. Rev. Lett., 49, 76 (1982). (19) H. Zacharias, M. M. T. Lay, and P. A. Roland, Phys. Rev. Lett., 49, 1790 (1982). (20) J. Misewich, C. N. Plum, G. Blyholder, and P. L. Houston, J. Chem. Phys., 78, 4245 (1983).
(21) For a recent compilation of results see J. Darville in "Vibrations at Metal Surfaces", C. R. Brundle and H. Morawitz, Us.Elsevier, , New York, 1983.
Avouris and Persson vibrational excitations of adsorbates and can thus provide information regarding the lifetime broadening of such excitations. Electronic excitations of adsorbates can be studied ellipsometrically by using conventional light sources but the spectral range covered is quite limited.22 Synchrotron radiation eliminates the spectral range problem so that both valence and core excitations of adsorbates can be s t ~ d i e d . ~ ~ , ~ ~ The most widely used approach in the study of the spectroscopy of adsorbates is inelastic electron ~ c a t t e r i n g . ~Inelastic ,~ electron scattering is particularly suitable for surface spectroscopy. Since electrons interact strongly with matter, electron spectroscopy has a high absolute sensitivity and is intrinsically surface sensitive. The electron energy can be varied continuously so that vibrational and electronic excitations of adsorbates can be studied in the same apparatus. Electron spectroscopy is, unlike optical spectroscopy, less restricted by symmetry or spin selection rules, and under the appropriate scattering conditions essentially all the excitations of a particular system can be studied. The major tradeoff is the lower resolution of electron spectroscopy (currently 23-5 meV). This lower resolution could present a problem in some vibrational spectroscopic studies and does not allow the study of the intrinsic line shapes of vibrational excitations. For electronic excitations, on the other hand, the intrinsic width is quite large due to efficient nonradiative decay channels opened by the interaction with the metal substrate, and resolution is not a problem. Electron energy loss spectroscopy is the principal technique used to obtain the spectra shown in this p a ~ e r . ~The , ~ physical principle is quite simple: electrons generated by a filament are accelerated, energy selected by an electron monochromator, and collimated by electron optics. This nearly monoenergetic electron beam is directed toward the adsorbate-covered surface, and the elastically and inelastically scattered electrons are energy analyzed by a second electron monochromator. The experimental variables include the primary electron beam energy, Eg, and the incidence and observation angles with respect to the surface normal. The electron-adsorbate interaction mechanism can be, somewhat artifically, separated into two types-short-range and long-range scattering. In the long-range interaction mechanism the electric field from the incident electron and its image in the substrate induces dipoles on the adsorbates. The time-varying electric field from these dipoles can then scatter the incident electron inelastically, leaving the molecule in a vibrationally or electronically excited state. Only excitations which have a nonzero dynamic dipole can be observed by this long-range electron scattering mechanism. In this respect, optical excitation (e.g., IR absorption) and dipole electron scattering have the same seleciion rjles. The momentum transfer parallel to the surface qll = ki,,,- k,,, is small in dipole scattering, and therefore the scattered electrons appear close to the specular direction (emergence angle = angle of incidence) in a lobe of angular width A0 N hU/2Eg where h w is the particular excitation energy (for a discussion of dipole electron scattering from clean metal surfaces see Section 40. In the case of adsorbates on metal surfaces an additional restriction is imposed by the so-called "surface dipole" selection rule, which states that only excitations with a nonzero component of the dynamic dipole perpendicular to the metal surface can be excited by dipole scattering (electron or photon).25 The reason for this selection rule lies in the screening of the dynamic dipoles by the metallic free electrons. The image of a dipole parallel to the metal surface is also parallel to the surface and its direction is opposite to that of the original dipole so that the net dipole field is zero. The image of a perpendicular dipole on the other hand has the same direction as the original dipole, giving a net dipole twice as strong. More precisely, for a substrate characterized by a dielectric function e(u) = q(u) ie2(o),the intensity ratio ZL/Zll is given by ZL/Ill = q 2 ( w ) + e $ ( ~ ) . From ~ ~ the frequency de-
+
(22) H. J. Robota, P. M. Whitmore, and C. B. Harris, J . Chem. Phys., 76,'1692 (1982). (23) J. E. Cunningham, D. Greenlaw, and C. P. Flynn, Phys. Reu. E , 22, 717 (1'980). (24) J. Stahr and R. Jaeger, Phys. Reu. E, 26, 41 1 1 (1982). (25) G. W. Rubloff, Solid State Commun., 26, 523 (1978).
Feature Article
The Journal of Physical Chemistry, Vol. 88, No. 5, 1984 839
pendence of c(w) it can be deduced that the screening is important in the vibrational part of the spectrum but much less important for electronic excitations. The short-range electron-molecule interaction leads to ‘impact scattering” which is more difficult to describe in a general manner since it involves the details of the electronic structure of the adsorbate-substrate complex and because multiple scattering processes become important. The momentum transfers are large, and therefore the angular distribution of the scattered electrons is more isotropic. Although the contribution of impact scattering to integrated scattering cross section is comparable to or larger than that due to dipole scattering, the more isotropic angular nature of impact scattering together with the fact that measurements involve scattered electron collection over small solid angles implies that the detected flux due to impact scattering is usually much lower than that of dipole scattering in the specular direction. Impact scattering, on the other hand, allows the observation of essentially all the excitations of a system, not just the dipole-allowed one^.^,^ The surface dipole selection rule is not applicable in this case. Impact scattering does however have some interesting selection rules of its own. Recently, it has been shown that these selection rules can be used to obtain site symmetry information on the adsorbate-substrate complex.26 A different aspect of short-range scattering involves the possibility of spin exchange between the incident electron and a bound electron of the target. Exchange scattering allows the observation of excitations involving change in spin, such as singlet -triplet tran~itions.~’ A special type of short-range excitation mechanism is provided by resonance electron scattering. This mechanism has been known and utilized in the study of free atoms and molecules for some time,28but it has only recently been demonstrated in the case of adsorbate^.^^ In resonance scattering, an electron of appropriate energy is captured by an atom or molecule to form a transient negative ion. Two different electron capture mechanisms have been observed in the adsorbed phase. The first involves capture in a shape resonance. In this case the incident electron is captured in a potential well surrounding the ground-state atom or molecule. The exact shape of the potential is determined by the interplay of the repulsive (centrifugal and electron-electron Coulomb repulsion) and attractive (polarization and exchange) interactions which the incident electron senses as it approaches the target. Only a relatively narrow range of incident electron energies lead to a large amplitude for capture of the electron in the well. The is fast ( s) so that electron capture process Ii)neutn\l the negative ion has initially the nuclear configuration of the neutral. In the ion state, however, the force. field felt by the nuclei is different, and a nuclear relaxation toward the new equilibrium configuration takes place. Excitation of the adsorbate is the result of the electron emission process ~),,, namely, the ion undergoes a vertical transition (Le., the electron tunnels out of the well) back to the neutral, but not necessarily to the initial quantum state. The excitation process li) v) in the neutral adsorbate is therefore accomplished by the sequence li)nsutral I,)lon r n n e u t r a 1 and is not constrained by optical selection rules. An example of a novel type of surface excitation, observed via resonance scattering, is shown in Figure 1. The spectrum of molecular hydrogen adsorbed on a silver surface at 10 K is obtained via the 22, shape resonance and shows pure rotational transitions J” = 0 J” = 2 (-49 meV) and pure vibrational (-5 18 meV) and vibrational-rotational (-562 meV) transit i o n ~ .The ~ ~ observation of rotational excitations of adsorbed H2 provides a dramatic demonstration of unhindered motion of
- v),,
-
-
-
-
-
-
(26) N. J. DiNardo, J. E. Demuth, and Ph. Avouris, Phys. Reu. E , 27, 5832 (1983). (27) See, for example, Ph. Avouris, J. E. Demuth, D. Schmeisser, and S. D. Colson, J . Chem. Phys., 77, 1062 (1982). (28) G. J. Schulz, Rev. Mod. Phys., 45, 423 (1973). (29) J. E. Demuth, D. Schmeisser, and Ph. Avouris, Phys. Reu. Lett., 47, 1166 (1981). (30) Ph. Avouris, D. Schmeisser, and J. E. Demuth, Phys. Rev. Lett., 48, 199 (1982).
0.5
0.1”
0
0.6
0.7
ELECTRON ENERGY LOSS (eV)
Figure 1. Electron energy loss spectra as a function of H 2 exposure in langmuirs (1 langmuir = 1 X 10“ t o w s ) to a silver surface at -10 K. Off-specular scattering conditions are used (ei 42O, Bo 48’) and E , = 3 eV. The low-energy loss at -49 meV is due to a J = 0 J = 2 rotational excitation of para-H2 (adapted from ref 30).
-
I
l
l
I
I
I
I
- -
I
I
1.4
1.6
I
I
IL 0, on Ag(lll) T = IOK E,= 6 e V
0
0.2 0.4 0.6 0.8 1.0 1.2 ELECTRON
1.8 2.0
ENERGY LOSS ( e V )
Figure 2. Electron energy loss spectra of O2adsorbed on a polycrystalline Ag surface at -20 K. Electron beam energy E B = 6 eV. Overtones of ; ground state up to u = 8 and the IAn and IXP+ electronically the % excited states are observed (adapted from ref 3 1 ) .
molecules in the physisorbed state. The mobility of physisorbed molecules is of importance in the dependence of the sticking coefficient on surface coverage. A different example of resonance scattering is provided by the spectrum of a monolayer of O2on Ag(l11) at -10 K shown in Figure 2. The spectrum is obtained with 6-eV electrons which excite a Feshbach reson~nce.~’ The electron capture process in this case can be described as first involving an excitation step followed by the attachment of the incident electron to the neutral excited state to give a negative ion state (in this case a 211,). Decay of this state by electron detachment populates a very large number of overtone states in the (%,-) ground electronic state (up to u = 8) and the low-lying lAg and ‘Eg+electronically excited states Adsorbate overtone states can be used to obtain inforof 02.31 mation regarding changes in the intramolecular bonding upon a b s o r p t i ~ n . ~The ~ . ~spectrum ~ of Figure 2 clearly demonstrates the ability of inelastic electron scattering to probe highly optically ‘Agtransition. Note also forbidden excitations such as the 32[
-
(31) D. Schmeisser, J. E. Demuth, and Ph. Avouris, Phys. Reu. E, 26,4857 (1982). ( 3 2 ) Ph. Avouris and J. E. Demuth, J . Chem. Phys., 75, 5953 (1981).
840
The Journal of Physical Chemistry, Vol. 88.No. 5, 1984
Avouris and Persson Xe/Cu
T=15K EB = I5 eV
'=15K
He1(21.2eV) TWO LAYERS
/J I I
I -6
-0
I -4
I
I
J
I
-2
0
6
9
ATOMIC STATES
I IO
I
II
BINDING ENERGY (eV) ENERGY LOSS (eV) Figure 4. Left: The ultraviolet photoemission spectra of a monolayer
-
and two layers of Xe on Cu. Right: The corresponding electron energy loss spectra. Also shown are the line shape of the 5p6 5p&,6s transition and the free-Xe excitations (adapted from ref 37). I.0L
by the adsorption are usually small, 50.1 eV. Classicaly theory does not always predict correctly the magnitude or the direction of the spectral shift. As an example, we show in Figure 3 the electronic spectra of N2 adsorbed on Al( 111) at 15 K.35 Ultraviolet photoemission spectroscopy (UPS) shows that the photoionization spectrum of the adsorbed N2 is rigidly shifted with respect to the gas-phase N2 spectrum-a characteristic of physisorption. The multilayer N2 spectrum (top) shows transitions to several excited states of N2 with distinct vibronic structure. Several spin-forbidden singlet triplet excitations can be seen demonstrating the occurrence of exchange scattering. At monolayer coverage of the surface, the spectrum (bottom of Figure 3) is very similar (minimal shifts) but shows significant broadening as a result of the coupling of the excited molecule with the aluminum substrate. We will discuss this broadening in section 4g in terms of nonradiative decay induced via field coupling of the adsorbate and substrate excitations. Noble gas atoms adsorbed on metal surfaces at low temperatures provide a particularly interesting prototype system in the study of electronic excitations of adsorbates. In their ground state the noble gases have a full np6 outer shell and interact with the metal surface primarily via dispersion forces. Their electronically excited states are of a Rydberg nature, the lowest energy one having the alkali-like configuration np5(n 1)s; so, for example, an excited Xe atom looks, in terms of electronic structure, like a ground-state Cs atom. The alkalis are known to adsorb ionically on most metals, and, under appropriate conditions, excited noble gases may behave analogously so that the excited states of the adsorbed noble gases could interact strongly with the surface and may be ionic. Using optical reflectance techniques Flynn and c o - ~ o r k e r studied s ~ ~ several combinations of noble gases and metal surfaces and concluded that, while all systems show excitonic absorptions in the multilayer regime, the excitations of some systems in the mono- or submonolayer regime are not observable. Since the results of optical spectroscopy can be complicated by local field effects,39low electron energy EELS has been recently used to study the excitations of several noble gas/metal systems. In Figure 4 we show results for Xe/Cu. Since knowledge of surface coverage is essential in this experiment, the difference in final-state shifts in ultraviolet photoemission spectroscopy (UPS) was used to delineate the mono- and multilayer coverage regimes. In Figure 4a we show the UPS spectra of one- and two-layer Xe
-
7
9
It
13
ELECTRON ENERGY LOSS (eV)
Figure 3. Electron energy loss spectra of N2 on Al(111) at - 1 5 K. Electron beam energy EB = 15 eV. Upper spectrum: multilayer N2 film. Lower spectrum: monolayer coverage (adapted from ref 35).
in Figure 2 that these spin-forbidden excitations are not excessively broadened in comparison to the elastic beam width.
3. Electronic Excitations of Adsorbates a. Weakly Adsorbed Systems. In this category we include adsorbate systems whose electronic ground state is not strongly perturbed by the adsorption process (e.g., physisorption systems). However, the binding of the excited states of such systems is not in principle known. When there is no specific chemical type of interaction between the excited adsorbate and the substrate, then the commonly used classical electrodynamic theory describes the excited species-surface interaction by representing the excited adsorbate by a point dynamic dipole and considering the coupling of this dipole with its own image in the The mutual coupling of the dynamic dipoles of neighboring adsorbates is usually ignored. Under these conditions classical theory gives the magnitude of the spectral shift in terms of the oscillator strength of the transition and the dielectric properties of the metal. In this model, the direction of the shift (to higher or lower frequency) is determined solely by the dielectric properties of the metal. The electronic excitations of a variety of weakly bound adsorption systems including polyatomics (e.g., aromatic molecules on Ag(1 11)),34 diatomics (e.g., N 2 on Al( 11l))ps and noble gas atoms (e.g., Ar and Xe on Au, Cu, Ag, and A1)36J7have been studied. It was found that, in the absence of strong lateral interactions (dispersion)p8 the spectral shifts of the intrinsic excitations induced (33) See,for example, R. R. Chance, A. Prock, and R. Silky, Adv. Chem. Phys., 37, 1 (1978). (34) Ph. Avouris and J. E. Demuth, J . Chem. Phys., 75, 4783 (1981). (35) Ph. Avouris, D. Schmeisser,and J. E. Demuth, J. Chem. Phys., 79, 488 (1983). (36) J. E.Demuth, Ph. Avouris, and D. Schmeisser,Phys. Rev. Letr., 50, 600 (1983). (37) Ph. Avouris, J. E.Demuth, and N. J. DiNardo, J. Phys. (Paris), in press.
-
+
~~
(38) D. Schmeisser, C. M. Weinert, Ph. Avouris, and J. E. Demuth, Chem. Phys. Lett., in press. (39) A. Bagchi, R.G. Barrera, and B. B. Dasgupta, Phys. Reu. Left., 44, 1475 (1980).
Feature Article
,
The Journal of Physical Chemistry, Vol. 88, No. 5. 1984 841
r--PYRAZINE / Ag (Ill)
I
I
I
I
I
I
I
CO/Ni (100) T-35C En=19eV
EB=lIO e V
i
CLEAN I
I
I
0
2
4
XI000 I
I
I
I
6
8
0
12
4
ENERGY LOSS (eV) 0
2 4 6 8 1 ELECTRON LOSS ENERGY (eV)
Figure 6. Electron energy loss spectra of CO on Ni(100) at 35 "C as a function of CO exposure. E B = 19 eV (adapted from ref 41).
0
-.
Figure 5. Electron energy loss spectra of clean Ag( 111) and as a function of pyrazine exposure. Both adsorbate intrinsic and metal adsorbate charge-transfer excitations are observed (adapted from ref 34).
and in Figure 4b the corresponding electronic excitations. Also shown diagrammatically are the free-Xe atomic spectra and the line shape of the lowest energy excitation 5p6 5p:126s (J = 1 and J = 2) after background subtraction. From these spectra we see that the excitonic absorption of the Xe monolayer is clearly visible (detailed EELS studies indicate that these absorptions are seen for as low as 0.08 layer and that the integrated intensity per atom is approximately constant).36 There is also an obvious correlation of the bands in the adsorbed phase with groups of atomic excitations. We also observe that the line shape of the lowest 5p6 5p56s transition of monolayer Xe/Cu is quite symmetric with a line width (fwhm) of -0.6 eV and that the maximum of this band is blue shifted with respect to the gas-phase value by -0.2 eV. The nature of the broadening mechanism of these excitations is of significant interest, and, as well be discussed metal electron transfer. in section 5b, it involves adsorbate In addition to substrate-perturbed intrinsic (neutral) adsorbate excitations and the weakly ionic excitations of the noble gases discussed above, completely new excitations which involve charge transfer between the metal and the absorbate have been observed. An example of such a case is provided by the system pyrazine on Ag(l1 l).34 In Figure 5 we see that exposure of the silver surface to increasing amounts of pyrazine vapor results in the appearance of the intrinsic excitations of pyrazine seen on the high-energy side of the sharp plasmon-interband transition of silver at -4 eV. On the low-energy side of this feature, an onset type of transition is observed which, unlike the intrinsic pyrazine excitations, decreases in intensity with further exposures and is virtually undetectable at 4.5 langmuir where multilayers of pyrazine are formed. When the sample is annealed to -220 K, the condensed pyrazine is removed, leaving only the more strongly bound first layer, and the low-energy onset feature reappears. This low-energy transition is ascribed as involving a dynamic charge transfer from silver (sp band) to the lowest empty (T*) orbital of pyrazine. The threshold (onset) energy h a T of these charge-transfer (CT) excitations is approximately given by 4' - A - e'/&, where 4' is the work function of silver in the presence of the adsorbate, A is the electron affinity of the adsorbate, and e2/4z accounts for the imagelike interaction of the negative ion and the positive charge in the metal. The importance of these C T states in surface optical phenomena, including surface-enhanced Raman scattering, has already been discussed.lO*' b. Electronic Spectroscopy of Chemisorbed Systems. In chemisorption the molecular orbitals of the adsorbate are mixed with the metallic band states. Certain adsorbate orbitals interact
-
-
-
strongly with the metal and are responsible for the chemisorption bond, while others are little affected by the adsorption. These electronic interactions manifest themselves clearly in the photoionization spectra of the adsorbates. While the photoionization spectra of physisorbed adsorbates (e.g., N2/AI(l 11)) are rigidly shifted with respect to the gas spectra due to the nonspecificity of the interacti01-1,~~ spectra of chemisorption systems show drastic modifications. Carbon monoxide on transition-metal surfaces has been the most widely studied molecular chemisorption system. The ground-state orbital configuration of C O is K K ( 3 ~ ) ~ ( 4 a ) ~ ( 1 ~ ) ~ ( 5 aExtensive )~. photoemission studies have led to a model of the chemisorption bond between CO and transition metals which involve charge donation from the 5a C O orbital to the metal.40 The fact that the C-0 bond is weaker in the chemisorbed state and its stretching frequency is lower has been accounted for by proposing a back-donation of charge from the metal to the lowest unoccupied orbital of C O the 27r* antibonding orbital (the 5u orbital is essentially nonbonding). Therefore, both occupied and unoccupied orbitals of the isolated adsorbate can be involved in the chemisorption interaction. In Figure 6 we show the EEL spectra of C O on Ni( 100) at 300 K.41 The spectrum of the clean Ni( 100) surface shows bands at -0.7 eV (surface interband transition) and at -10.5 eV (plasmon and "parallel band" transitions). Upon exposure to C O both metallic transitions are quenched while electronic excitations of chemisorbed C O at -6 and -8.5 eV are clearly observed at higher exposures (-2 langmuirs). Similar electronic excitations of chemisorbed CO have been observed on Cu and other transition metals.41 It is intriguing that the transitions of CO on Ni (Figure 6) have the same excitation energy (but are considerably broader) states of free CO. The latter exas the transitions to the citations of free C O are due to triplet and singlet coupled 50 27r* orbital transitions, respectively. We have recently argued that the excitations of chemisorbed C O at 6 and 8 eV are in fact due to triplet and singlet coupled 55 2%* transitions where 55 and 27r* are the rehybridized orbitals of chemisorbed CO. The reasoning behind this assignment involves a correlated shift of the 55 and 2%orbitals and is discussed in detail in ref 41. In general, however, excitations of chemisorbed species are very difficult to interpret. The electronic bands are, as a result of the strong coupling with the substrate, broad and featureless and provide little information regarding their origin. 39'11
-
-
(40) See, for example, E. W. Plummer and W. Eberhardt in "Advances in Chemical Physics", Vol. 49, T. Prigogine and S. A. Rice, Eds., Wiley, New York, 1982. (41) Ph. Avouris, N. J. DiNardo, and J. E. Demuth, J . Chem. Phys., 80, 491 (1984).
(42) B. N. J. Persson, Phys. Rev. Left., 50, 1089 (1983).
842
The Journal of Physical Chemistry, Vol. 88. No. 5, 1984
4. Theoretical Modeling of the Relaxation Processes In a classical description one can consider a vibrationally or electronically excited molecule as an oscillating charge distribution which is surrounded by an oscillating electric field. This field penetrates into the metal where it can excite electron-hole pairs (and phonons) and thus quench the adsorbate excitation. Here we will study this process in some detail. We will present a general theory which is applicable to all dynamical processes at surfaces which do not involve charge transfer between the metal and the molecule. Processes involving charge transfer (considered in section 5 ) are, in general, much more complicated and depend on the details of the electronic structure of the interacting molecule-metal system. a . Response Function g(qll,w). Let a metal occupy the halfspace z > 0, and consider an arbitrary current density located in the half-space z < -d. Assume for simplicity that retardation effects can be neglected. Thus, the _electricfield from the external = current density can be written as E,,, = -VdCxt. Since V2deXt 0 for z > -d, deXtcan in this region of space be written as a superposition of evanescent plane waves
This external potential induces a current density in the metal which gives rise to an induced potential &,d(?,t). Assume that dextis weak enough so that the metal responds linearly to it. For z < 0, where V2f$ind= 0, we can then write4'
Avouris and Persson a
A
k'
ENERGY TRANSFER n w = l f ( k ' * - k 2 ) / 2 m MOMENTUM TRANSFER fiAT=fi(T-T) b
POSITIVE BACKGROUND ELECTRON DENSITY DISTRIBUTION
0
2
Figure 7. Top: In intraband transitions electrons at or below the Fermi surface are excited to states outside the Fermi sphere. This process requires an_energy_inpu_t h w = h 2 ( k R- k 2 ) / 2 m and a momentum transfer hAk = h(k'- k ) . Bottom: A schematic representation of the positive and negative charge density distributions along the normal to the surface direction according to the jellium model. g] = d1and do[1
+ g] = tdl from which one obtains the standard
textbook result46
This equation defines the linear response function q(qIl,w). It is implicitly understood that the metal can be treated as translationally invariant parallel to the surface. Equation 1 shows that the response of the metal to an external probe is entirely contained Equation 6 is not, however, completely correct. First, a real in g(qll,w) as long as we are only interested in the induced potential metal does not have a steplike surface profile along z but a profile outside the metal. A great variety of surface processes can be which varies smoothly on a microscopic scale. In addition, the described in this way including van der Waals forces between an bulk dielectric function is nonlocal. We will discuss these coratom and a metal surface, the surface photoelectric effect, friction rections to eq 6 later (section 4d), but we will first review the forces on charged particles near metal surfaces, e t ~ . ~ ~ s ~ ~ "classical" theory for the quenching of excited states, which is The application which we are interested in here involves the based on eq 3 and 6 . damping of a vibrating dipole. If the oscillating electric field from c. "Classical" Theory for Quenching of Excited States at an excited molecule, located a distance d above a metal surface, Surfaces. Consider first a free excited molecule. Let again IB) is well approximated by a dipole field at the metal, then the denote the excited state and IA) the ground state. The excited damping rate of this excitation due to interaction with the metal state can decay to the ground state, IB) IA), by emitting a is simply given by33345 photon, at a rate which is given by the classical formula
-
-( -)
1 =4 2 Tg
where ji = (BIfiIA) is the matrix element of the dipole moment operator between the ground state IA) and the excited state IB). b. Evaluation of g(qli,w) by Local Optics. We will first calculate g(q,,,w) within the theoretical framework usually called local optics which simply means that the metal-vacuum system is described by a dielectric function t given by t = t(w) in the metal ( z > 0) and t = 1 in vacuo ( z < 0). Consider now the response of this system to the external potential
3 h
f 1 3
c
(7)
-
But the total potential 4 = dent+ dindand e (d@/dz) must be continuous at the metal-vacuum interface and therefore 40[1 -
where hfl is the excitation energy, 1.1 = I(BJfiIA)Iis the dynamic dipole moment for the transition, IB) IA), and c is the velocity of light. We now consider the interaction of the excited molecule and a metal as a function of the distance d from a metal surface. In a series of elegant experiments Kuhn and Drexhage4' studied the lifetime r(d) of an electronically excited molecule as a function of d . They found that for d a,r ( d ) r0,while for d 2 c l f l oscillations in r were observed due to the interaction between the molecule and its own radiation field which is partially reflected by the metal surface. Thus, the behavior of r(d) at these distances can be explained without taking into account nonradiative energy transfer to the metal. However, this is not the case for smaller d where it is possible for the nearfield of the excited molecule to transfer energy to the metal. The excitation of the metal electrons requires conservation of energy as well as momentum (see Figure 7a). One can distinguish between three sources of the required momentum:'@(a) in the bulk the momentum needed
(43) See,for example, M. J. Mehl and W. L. Schaich, Surf. Sci., 99, 553 (1980). (44) P. J. Feibelman, Prog. Surf. Sci., 12, 287 (1982); Phys. Reu. B, 22, 3654 (1980); 12, 1319 (1975); 14, 762 (1976). (45) H. Morawitz, Phys. Rev., 187, 1792 (1969); B. N. J. Persson, J . Phys. C, 11, 4251 (1978).
(46) See,for example, J. D. Jackson, "Classical Electrodynamics", Wiley, New York, 1962, Chapter 4. (47) K. H. Drexhage, M. Fleck, H. Kuhn, F. P. Schafer, and W. Sperling, Ber. Bunsenges. Phys. Chem., 73, 1179 (1969); K. H. Drexhage, H. Kuhn, and F. P. Schafer, ibid.,72, 329 (1968). (48) B. N. J. Persson and M. Persson, Surf. Sci., 3, 609 (1980).
4ext = ,+oe~qii.fil-~liz+~~ (4) Since t is a constant for both z > 0 and z < 0, the induced potential satisfies V2&d = 0 (except at z = 0) and we can therefore write
dind=~o(-g(qll,w))e41,~',+~11~-iw~ = 6 e7qll~fll-q11z-iw~
z o
(5)
- -
Feature Article
The Journal of Physical Chemistry, Vol. 88. No. 5, 1984
can be supplied by electron-phonon or electron-impurity scattering (intraband transitions) or by the crystal potential (interband transitions); (b) from the surface potential; (c) from the spatial variation of the near field of the excited molecule. The classical theory accounts only for process a. To account for process b one must use a dielectric function which varies continuously in the surface region of the metal. To account for process c one must use a dielectric function which is nonlocal in the bulk. This aspect will be discussed further in the next section. To calculate the contribution from process a we substitute eq 6 into eq 3 to obtain
If one assumes that e(w) is well described by a Drude dielectric function
+
where wp is the bulk plasmon frequency and the relaxation time and, if w 1
f. Comparison with Experiment. It is important to know the accuracy of the expressions for Im g presented in the previous section. Fortunately, a direct experimental test is possible. It was (55) N. D. Lang and W. Kohn, Phys. Reu. B, 7, 3541 (1973).
0 0.0
0.5
I.o
k P F
Figure 8. Top: Screened dipole potential $dipole and two electron wave functions $k,(z) ( k , = O.lkF and k , = kF). both with t = tF,are shown as a function of ~ F Z . Electron density parameter r, = 3. Bottom: Relative probability p(k,) for excitation of an electron on the Fermi surface ( t = tF) as a function of k , (adapted from ref 53).
recently realized42that Img g(qll,w) can be measured directly, at least for small qlland w , by using inelastic electron scattering from clean metal surfaces. Such measurements have now been performedSZon Cu( 100) and Ni( loo), and here we will compare the predictions of the theory described in the last section with data for Cu( 100). For a more detailed discussion, see ref 5 1 and 52. Consider a beam of electrons with kinetic energy Eo = h2k2/2m, incident at an angle a on a clean metal surface. The electric field from the incident electrons penetrates iQto the metal where it can excite electron-hole pairs. Let k and k'denote the wavevectors of an incident and inelasticity scattered electrons, respectively. Thus, hGIl(gll = kll - k'lI) is the momentum transfer parallel to the surface and hw_= h2(k2- k R ) / 2 mis the corresponding energy transfer. Let P(k,k')dQl, d(hw) be the probability that an incident electron is scattered into the range of energy losses between h w and_h(w + dw) and into the solid angle dol, around the direction of k'. For small momentum transfer, ql, > 1, 18/x as x i.e., kFd >> + / w we get
by extrapolating the data in the inset to T = 0. The filled circles show the Drude contribution to AP at r w m temperature as given by AP(T = 293K) - AP(T = OK). The solid curves are theoretically predicted results for AP for process a using 1 = 147 8, and processes b c. The agreement between experiment and theory is excellent with respect to the dependence of AP on hw. The mean free path I = 147 A compares favorably with the value 125 A deduced from optical data for Cu. The absolute value of AP deviates by only 35% from the theoretical result and, as will be seen below, the deviation is on the average less than 20% over a range of impact energies. The dependence of AP on the incident electron energy is shown in Figure 9b where experimental data for h w = 0.1 eV and T = 293 K are shown. The solid curves correspond to the calculation contributions from processes a + b c, b + c, and b, respectively. The Drude contribution, process a, at T = 293 K was calculated by using the mean free path 1 = 147 A found above. The agreement between experiment and theory (the T = 293 K data (open circles) should be compared with processes a b c is very good, as regards the dependence of AP on the incident electron energy, the absolute value of AP, and the relative magnitude of the Drude contribution. The importance of the contribution c is obvious from Figure 9b. g . Electron-Hole Pair Quenching of Excited States at Surfaces. In the last section we have demonstrated that the expression for Im g given in section 4e is quite accurate, at least for Cu( 100). It is thus meaningful to use this expression in discussing the lifetime of vibrational excitations and of low-lying electronic excitations of molecules at surfaces and this is the topic of this section. It should be noted here that the same problem has been considered by Korzeniewski et al.,56who used the jellium approximation for the metal and computed the dielectric response within the random phase approximation.
which has the same dependence on w and d as Fb. It is interesting now to compare the classical Drude contribution to the damping rate, as given by eq 19, with the contribution from processes b + c as given by eq 20 and 22 (assuming that kFd >> wF/w). Obviously both are linear in w but they have a different distance dependence; (l/T)a a &3 while ( 1 / 7 ) b + c 0: &4. For a r, = 2.67 jellium (representing cu) one has = 0.5 and wF/wp = 0.7 so that Fb/Fa= (6[wp/8wF)kFl/k&= 0.51/d. Thus, process b dominates over process a already for d 5 70 A. Here we have taken 1 = 145 A as obtained in section 4 for Cu at infrared 100 frequencies. Since the mean free path I is very long ( I A) in all of the noble metals for frequencies below the onset of interband transitions from the d band, it follows that processes b c will dominate over process a in a large distance region (e.g., d 5 50 A). experiments of the kind discussed in section 4c are at present being performed to test these prediction^.^' The theory, as presented above, is not directly applicable to the calculation of the dipole contribution to the quenching of excited states in adsorbed molecules because the theory is limited to processes which involve small q,l(and thus large d since qll 1 1 4 . However, the corrections arising from the larger qll components have been estimated and the resulting modified quenching rate equation will now be applied to two systems: (a) the nonradiative decay of the C-0 stretching vibration for C O chemisorbed on Cu(100) and (b) the nonradiative decay of the electronically excited C3n, state of N, physisorbed on Al(111) at 15 K. By infrared reflection-absorption studies of the line width of the C 4 stretch on Cu(loo), the vibrational lifetime was estimated s while the dipole theory (accounting to bes8 T~~~~N 1.3 X
(56) G. Korzeniewski, T. Maniv, and H. Metiu, Chem. Phys. Lett., 73, 212 (1980); J . Chem. Phys., 76, 1564 (1982).
cation.
+
+
+ +
wF W 1 F c = 18 - - w p kFd
-
+
-
(57) C. B. Harris, private communication; W. Crasse, private communi-
846
The Journal of Physical Chemistry, Vol. 88, No. 5, 1984
for all processes a-c) gives T~~ = 1.7 X lo-'' s. Thus, the theory involving dipole (field) coupling can only account for about 10% of the observed damping rate. Similar conclusions can be reached by considering the vibrations of other chemisorbed species such as N2/Pt( 111). In chemisorption systems there is a strong overlap of the adsorbate and substrate wave functions and, as we will show in section 5a, the observed decay rate, which is faster than predicted by the field coupling theory, is most likely associated with local charge rearrangements (charge oscillations between the metal and the C O molecule). Let us now consider the system N2/AI(1 11). As already discussed (section 3a) photoemission studies of this system show no significant pertubation of the ground-state electronic structure of N2upon adsorption. In addition, the lag* orbital involved in the low-energy electronic excitations is below cF (in the presence of a valence hole) so that electron tunneling from the adsorbate to empty conduction band states of the metal (a mechanism which as we will see is important in the quenching of excited noble gases) cannot occur. The lifetime of the C 3 n , excited state obtained ~ 5 X s.35 The lifetime from line-width studies is T , , ~= calculated by using the gas-phase value for the dynamic dipole moment p(C311, B311g), hw = 3.7 eV, and a reasonable value for the molecule-image plane separation (1 A) is -5.5 X s,35 in excellent agreement with the experimental value. It should be noted however that, if only process a is considered (as in the classical theory), then the predicted decay rate is 10 times lower than the observed value.
-
-
5. Quenching of Excitations via Charge Transfer The field coupling studied in section 4 is the only possible coupling between a molecule and a metal if there is no direct overlap between them. This is the case, for example, if the molecule is separated from the metal via an inert layer, e.g., an oxide layer. However, a molecule chemisorbed on the metal surface will share some of its electrons with the metal, and for such systems one would in general expect charge transfer to have a strong influence on a variety of dynamical processes such as quenching of vibrational or electronic excitation^,^'*^^ dissociation reactions,m and sticking.61 Here we will illustrate this with two examples, namely, the quenching of the C-O stretching vibration of C O on Cu( 100) and the quenching of excited noble gas atoms on metal surfaces (e.g., Xe/Cu). a. Quenching of the C - 0 Stretching Vibration of Chemisorbed CO. It was pointed out in section 4g that dipole coupling can only account for only 10% of the observed damping rate of the C-0 stretching vibration of C O adsorbed on Cu(100). We will now show that the main part of the damping is associated with local charge rearrangements which depend on the nature of the COCu( 100) chemisorption bond. Consider a molecule with an affinity level t, approaching a metal surface. As the molecule comes near the metal the originally sharp level ea may broaden by interaction with the metal, Le., tunneling of electrons between the orbital la) and the metal gives the level a finite lifetime. Furthermore, the level will be shifted toward lower energies in a way which is correlated with the effective electron potential of the clean metal surface.62 Considering both effects, the resulting resonance state may be located in the vicinity of the Fermi energy and thus be partly filled. This is schematically illustrated in the case of the C O molecule in Figure 10, where the affinity level is a low-lying level with some 2a* character (see also discussion in section 3b). If there is such ( 5 8 ) R. Ryberg in "Vibrations at Surfaces", R. Caudano, J. M. Gilles, and A. A. Lucas, Eds., Plenum, New York, 1982, p 307; Surf. Sci., 114, 627 (1982). (59) B. N. J. Persson and M. Persson, Solid Sfafe Commun., 36, 175 (1980). (60) J. E. Demuth, H. Ibach, and S. Lehwald, Phys. Rev. Lett., 40, 1044 (1978); B. N. J. Persson and R. Ryberg, ibid., 48, 549 (1982). (61) J. K. Norskov and B. I. Lundquist, Surf. Sci., 89, 251 (1979); R. Brako and D. M. Newns, Solid State Commun., 33, 713 (1980); K. Schonhammer and 0. Gunnarsson, 2. Pfiys. B, 38, 127 (1980). (62) See,for example, H. Hjelmberg, B. I. Lundquist, and J. K. Norskov, Phys. Scr., 20, 192 (1972).
Avouris and Persson
/'
I
/
I
27r* FREE
/
GO
CHEMISORBED
co
Figure 10. Schematic diagram illustrating the lowering of the energy, broadening and partial filling by charge transfer from the metal of the 2?r* level of CO as the molecule approaches the metal surface.
an adsorbate-induced resonance state at the Fermi energy (eF), then, as the molecule is vibrating, this resonance will move up and down in energy around cF, In the case of the C O molecule, as the C-0 bond length is increased, the affinity level will move toward lower energies, since 2a* is an antibonding orbital. Since the Fermi level remains fixed, electrons must flow from the metal to the affinity level and back to the metal as the bond becomes compressed again. Associated with this charge rearrangement is a (frictional-like) damping of the vibrational motion. A rough description of this damping process can be obtained by using a model Hamiltonian of the Newns-Anderson type:
+ Xkt k U k ' U k
H = Eo(Q)U+U
-k C(v,k(Q)a'Uk k
+ hc)
(23)
where Q is the displacement associated with a vibrational mode of the molecule, is the energy of the molecular level calculated for a fixed Q, t k is a set of energy levels for the electrons in the metal, and Vuk(Q)describes the hopping of an electron between the molecule and the metal. Since the amplitude of the vibrational motion is small, it is reasonable to expand t, and v,k to first order in Q
€,(e)
Substituting these expressions back into eq 23 we obtain terms such as t.I(O)a+aQ which will couple the electronic degrees of freedom with the vibrational degrees of freedom, allowing for the vibrational motion to decay to its ground state while simultaneously exciting an electron-hole pair in the metal. Using first-order perturbation theory and assuming that the shape of the resonance derived from level la) is Lorentzian, we obtain the following simple expression for the damping rate: 59 1 / = ~ 2aQ(6n,)z
(25)
where 6n, is the fluctuation of the number of electrons in the orbital la) during one vibration. To apply this formula to calculate the lifetime T of the C - 0 stretching vibration for CO adsorbed on Cu( 100) requires that we know 6n,. This quantity can be estimated as follows. In IR and electron energy loss studies of CO on Cu( 100)63964it was found that the dynamical dipole moment of the C-O stretching vibration is p = 0.2 D. Gas-phase CO, on the other hand, has p = 0.1 D. We make the assumption that the increase, A p = 0.1 D, in the dynamic dipole moment of chemisorbed CO is due to the oscillating charge between the metal and the 2a* orbital. By assuming that this charge is about equally divided among the carbon and oxygen atoms (Le., qc = qo) we can write Ap = qc(do (63) B. N. J. Persson and R. Ryberg, Phys. Reu. B, 24, 6954 (1981). (64) S. Anderson and B. N. J. Persson, Phys. Reu. Len.,45, 1421 (1980).
The Journal of Physical Chemistry, Vol. 88, No. 5, I984 841
Feature Article
i l
where c I and c2 are orbital energies, U 1and U12are Coulomb repulsion terms involving two electrons in level 1 or one electron in 1 and the other in 2, respectively, and u is an image screening term. The decay rate of the excited state via the tunneling process can then be expressed by a Golden Rule formula: ( l /7)electron
transfer
(2T/h)cIvk126(c2 +
= (2*/h)(lvkI2)P(C2 +
RESONANT ELECTRON TRANSFER
COUPLING VIA THE ELECTRIC FIELD
Figure 11. (a) Schematic illustration of the tunneling process of the excited electron in level 12) of the adsorbate to the empty level Ik) of the metal. (b) Coupling of adsorbate and substrate excitations via the E field.
+
dc) where do and dc are the distances of the centers of the oxygen and carbon atoms from the static image plane of the metal, respectively. These distances can be obtained easily, since from LEED measurements we know the corresponding distance to the first Cu lattice plane65 and the distance of this lattice plane to the image plane has been calculated by Lang and K ~ h n Thus, .~~ do = 1.35 8, and dc = 0.2 8, so for AH N 0.1 D we obtain qc E 0.016e. Therefore, the fluctuation in the number of electrons in the 2 ~ orbital * is estimated to be 8n N 0.03. Since the 2 ~ * orbital is degenerate and can hold four electrons, eq 25 should ~ 2 ~ R [ 4 ( 6 n / 4 ) ~=] ~ R ( 6 n ) ~ / 2The . C-0 be written as 1 / = vibrational frequency is R = 4 X 1014s-I and with 8n = 0.03 we obtain T(theory) = 1.8 X s. This value is in good agreement with the experimental lifetime T(expt1) = (3 A 1) X s obtained from the vibrational line-width studies.5s As a second example we can consider the case of N2 adsorbed on Pt( 11 1). From the measurements by Shigeishi et a1.66on this system one can calculate the dynamic dipole moment for the N-N stretching vibration to be p = 0.08 D. Since a free N2 molecule has zero dynamic dipole moment we will assume that the observed dynamic dipole moment for chemisorbed N 2 is due entirely to charge fluctuation between the N 2 2 ~ orbital * and the metal surface. We can then estimate the charge fluctuation 8nZn.= 0.02. Therefore, since the vibration frequency of the N-N mode is R = 4.5 X lOI4 SKI,we obtain T(theory) ;= 4 X s, which should be compared with the experimental lifetime T(expt1) ;= 1.8 X s. Again a reasonably good agreement between experiment and this simple model is found. b. Quenching of Electronically Excited States via Charge Transfer. Whenever there is overlap between the metal substrate and adsorbate wave functions, the possibility of a new decay path involving charge transfer rather than energy transfer is opened. This process in relation to the quenching of electronically excited states has been treated recently by using an Anderson-Newns model Hamilt~nian.~’ Here we will present only a simple qualitative discussion. Consider a molecule with two (nondegenerate) electronic levels 1 and 2. Level 1 is doubly occupied (spin t and 4) in the ground state while level 2 is located above the Fermi level and is thus empty. Next, consider what happens when one electron is excited from level 1 to level 2. Due to the positive hole in level 1, level 2 will be pulled down in energy and may end up either above or below the Fermi energy of the substrate. Assume first that the level ends up above the Fermi energy. The excited state is coupled to the metal via a coupling element Vkand therefore can decay via resonant electron transfer (tunneling) from level 2 to an orbital Ik) in the unoccupied part of the metal conduction band as is schematically shown in Figure 11. Energy conservation demands that the following condition (in the limit vk 0) be met for this process to occur: - UI - v €2 - € 1 - UI + u12 > CF (26)
-
(65) S. Anderson and J. Pendry, Phys. Reo. Lett., 5, 3115 (1978). (66) R. A. Shigeishi and D. A. King, Surf. Sci., 62, 379 (1977). (67) B. N. J. Persson and Ph. Avouris, J . Chem. Phys., 79,5156 (1983).
u12
k
u 1 2
”
+ - €k)
+ 0)
(27)
where p ( t ) is the density of unoscupied levels of the metal and (Ivkl’) the angular average (in k space) of lVkI2. v k depends on the overlap of the substrate and adsorbate wave functions and, since the metal wave functions decay roughtly exponentially away from the metal surface, we expect (ll/kI2) e-Od where d is the separation between the metal surface and the orbital 12) and /3 2(2m(cF + 4 - tk)/h)’/*(4 is the work function and tF the Fermi energy). Now consider the case where level 2 ends up below the Fermi level. In this case resonant electron transfer 12) Ik) is forbidden by the Pauli principle and the decay can be described by the field coupling model discussed earlier (of course field coupling will be present even if 12) is above cF). For excited noble gas atoms on metal surfaces (see discussion in section 3a), e.g., Xe on Au, inequality 26 is satisfied. The line widths of the np6 nps(n 1)s transitions are of the order of 0.5 eV. Density functional calculations on noble gas atoms on jellium surfaces by Lang et aL6*also give line widths of 1 eV. On the other hand, the line widths that we calculate for decay via field coupling are about 1 order of magnitude smaller, e.g., -0.02 eV for Xe(5p56s) on A u . ~ ’Therefore, we conclude that for excited noble gas atoms on metals the dominant decay path involves tunneling of the excited electron to the empty conduction band states of the substrate. It is likely that, whenever this decay route is energetically possible (see inequality 26), it will dominate over the decay path involving field coupling of the adsorbate and substrate excitations. However, since wave-function overlap is required, this mechanism represents a short-range interaction and even thin dielectric layers between the surface and the adsorbate may eliminate this decay path. In the case of the noble gases the theory, in agreement with the experiment, predicts symmetric line shapes. However, in general quite asymmetric line shapes may result as an outcome of the electron-transfer pro~ess.~’
-
-
-
-
+
-
6. Multiphonon and Phase Relaxation We close this work with a short discussion of vibrational energy and phase relaxation involving substrate phonons. A vibrationally or electronically excited adsorbate can, in principle, decay to the ground state by exciting either electron-hole pairs or substrate phonons. The latter process is however ineffective if the adsorbate vibrational frequency R is much higher than the maximum phonon frequency of the metal wo. For example, the C-0 stretching frequency on Ni(100) is hR N 0.25 eV while hwo N 0.03 eV. Thus, at least eight substrate phonons must be excited in order to conserve energy, and such high-order multiphonon processes have a small probability. As a rule of thumb, for each additional phonon needed the relaxation rate is reduced by a factor of 1.5-2 orders.69 In the case of low-frequency vibrations, however (e.g., the vibration of oxygen in the 0 ~ ( 2 x 2 Ni(100) ) system where f l / w o 5 1) decay via substrate phonon excitation is expected to be the dominant decay path. Recently, in an elegant experiment by Chiang et al.,’O the line width of the Ni-CO vibration for CO/Ni( 100) at 300 K was determined to be 15 cm-I. In this 1.3 so that the Ni-CO vibration can decay via case O / w o emission of two phonons. Using a Morse potential to describe the Ni-CO energy curve, a simple perturbation theory analysis’l
-
-
-
(68) N. D. Lang, A. R. Williams, F. J. Himpsel, B. Reihl, and D. E. Eastman, Phys. Reu. E , 26, 1728 (1982). (69) V. P. Zhdanov and K. I . Zamaraev, Caral. Rev.-Sei. Eng., 24, 313 (1982). (70) S. Chiang, R. G. Tobin, and P. L. Richards, to be submitted for publication. (71) B. N. J. Persson, to be submitted for publication.
848
The Journal of Physical Chemistry, Vol. 88. No. 5, 1984
-
gives lifetime broadening (fwhm) for two- and three-phonon decay of -42 and 1.5 cm-I, respectively. This simple calculation does therefore suggest that the dominant decay mechanism of the Ni-CO vibration and M-CO vibrations in general may involve phonon emission.72 Let us now consider dephasing contributions to observed line widths. In a vibrational spectroscopy experiment (e.g., IR absorption-reflection), the spectral signal A(w) can be expressed as A(w)
a
JImdt (u(t) u(0))eiw'
where u ( t ) is the vibrational coordinate and where the bracket denotes a thermal average. There are two ways by which the correlation function ( u ( r ) u ( 0 ) ) can decay with increasing time: (i) vibrational energy relaxation results from the decay of the amplitude ( u 2 ( t ) ) as t while (ii) elastic scattering of phonons (or electron-hole pairs) by the adsorbate vibration destroys the definite phase relationship between u ( t ) and u(0) and leads to the decay of the correlation function (u(t) u ( 0 ) ) while ( u * ( t ) ) remains constant as t -, The contribution from dephasing via phonon scattering to the line widths of N i x 0 and Ni C-0 modes at 300 K has been calculated'' to be very small, 1 and -2 X cm-', respectively. This contribution will be even smaller at lower temperatures and will vanish at T = 0 K. Finally, consider inhomogeneous broadening. In the absence of lateral interaction between the adsorbed molecules, binding to different coordination sites on a single-crystal surface does not lead to inhomogeneous broadening, because the binding energy differences between such sites are large so that discrete bands are produced. For example, for C O on Ni( 100) the on-top site has v(C-0) = 2065 cm-' and v(Ni-C) = 480 cm-l while the bridge-bonded site has v(C-0) = 1930 cm-' and v(Ni-C) = 360 Inhomogeneous broadening can arise, however, as a result of lateral (e.g., dipole-dipole) interactions among adsorbates in
--
-
-
(72) For a more complete discussion on decay via photon excitation see, for example: J. C. Tully, Annu. Reu. Phys. Chem., 61, 319 (1980); G. Korzeniewski, E. Hood,and H. Metiu, J . Vuc. Sci. Technol.,20, 594 (1982). (73) S. Anderson, Solid Srare Commun., 21, 75 (1977).
Avouris and Persson inhomogeneous (e.g., incomplete) overlayers. For example, the dipole-dipole interaction has been shown to give rise to a contribution of about 4 cm-' to the line width of the C-0 stretch for C O on Cu(100) at low coverage. It should be noted that experimental studies of C O on single crystals and evaporated Ni films find quite similar line ~ i d t h s , 'indicating ~ that the homogeneous broadening (=20 cm-l) dominates over the inhomogeneous broadening.
Outlook There is no doubt that the study of surface dynamical processes will be an area of increasing activity in the future. The development of new laser diagnostic techniques such as femtosecond laser technology will allow the real time monitoring of dynamical processes at surfaces such as vibrational energy relaxation. Light-induced processes at metal surfaces are of significant chemical interest, particularly photochemistry of core-excited states of adsorbates. These states decay via very fast Auger processes and have the potential of selective bond breaking and also binding site selectivity. There is need for better theoretical understanding of the nature and strength of the interaction of excited states and surfaces. Studies using the time-dependent, self-consistent field formalism are particularly desirable. The state-to-state energy and chemically inelastic particlesurface scattering studies promise to provide very valuable information on the details of particlesurface interactions. Realistic trajectory calculations are required in order to make connection between the theories of nonradiative relaxation of species at surfaces (described here) and relaxation in the scattering process. Molecular dynamics calculations coupled with accurate ab initio calculations of the adsorption potential should provide this link. Acknowledgment. We thank S. Anderson, J. E. Demuth, N. J. DiNardo, R. Ryberg, and D. Schmeisser, who have contributed to various parts of the work described in this article, and whose comments were very helpful. It is also a pleasure to acknowledge interesting discussions with N . D. Lang, A. R. Williams, J. C. Tully, and R. Walkup. (74) R. B. Bailey, T. Iri, and P. L. Richards, Sur5 Sci., 100,626 (1980).
