Chapter 13 Inverse Photoemission

509

Chapter 13

INVERSE PHOTOEMISSION

P. D. JOHNSON

1.

INTRODUCTION

In this chapter we review Inverse Photoemission (IPES), the analogue of the parent technique Photoemission. Other chapters have demonstrated how the excitation of electrons by photons may be used to derive a variety of information on both the electronic and geometrical structure of different materials. With electrons being excited in photoemission, the primary requirement is that the initial state be an occupied state. In inverse photoemission an electron is added to the system and now the probed states or final states are unoccupied. Thus we review the extent to which the experience obtained in the development of photoemission may be carried over into studies of the unoccupied bands through the inverse photoemission experiment. Shown schematically in fig. 1, inverse photoemission is the process involving the emission of a photon during the radiative transition of an electron between two unoccupied states. In that the incident particle is an electron and the emitted particle a photon, inverse photoemission is generally considered as "time reversal" of the photoemission process. Such a time reversal would be strictly true only if the final states of inverse photoemission were located below the Fermi level. However considerable progress may be made if, neglecting for the moment the Fermi occupation of the electronic states, a direct comparison is made between the cross-section for the two "time-reversed transitions. Such a comparison has been made for the solid state by

'

*

Pendry and for adsorbed molecules by Johnson and Davenport. The interaction Harniltonian H' between the photons and electrons is given by

H' = (A.p+p.A)

'

+ -[ A f 2m2

where A is the vector potential of the electromagnetic radiation. In the Inverse Photoemission process photons are created and it becomes necessary to quantize the electromagnetic field. Thus the classical vector potential is replaced by a field operator A(x,t) defined by

where &(a)is the linear polarization vector whose direction depends on the photon propagation

510

f

Fig. 1. Comparison of the inverse and direct photoemission processes. (a) In IPES an electron which has coupled to an unoccupied state above E,, makes a radiative transition to an unfilled state above EF. (b) In PES an electron below EF is excited to a state above.,,E , direction q. The two operators atg,a and aq,.

either create or destroy a photon in the state q,a

respectively and V, is the normalization volume For the photon. From equations (1) and (2) it is possible, using first-order perturbation theory, to derive an expression for the differential cross-section for the emission of a photon such that

where the transition is between two electronic states I i > and I f > differing in energy by an amount f i w . The incident electron has a momentum n k and a represents the fine structure constant. A similar expression may be derived for the photoemission process and again assuming "time-reversal" it can be shown that the ratio R of the two cross-sections is given by

2

R=[?]

(4)

That is, the ratio of the inverse photoemission cross-section to the photoemission cross.

511

section is inversely related to the ratio of the square of the wavelength of the emitted particles, a reflection of the difference in available phase space for these final states. Equation (4) is derived with the assumption of complete time reversal, the matrix elements appearing in the equations describing the differential cross-section for inverse photoemission, eqn. (3),and the equivalent for photoemission being considered identical. For localized states this assumption may not be valid. In photoemission, the outgoing electron experiences a coulombic potential whereas in inverse photoemission the incoming electron is scattered by the short range potential characteristic of a "neutral" atom. Johnson and Davenport 2 have considered in detail the effect of using these different potentials in calculating the inverse photoemission crosssection into the localized level of an adsorbed molecule. Their conclusion was that the difference

Fig. 2. Comparison of the photoemission cross-section from a neutral hydrogen atom H ( dashed line ) and from a negative hydrogen ion H- ( solid line ). The cross-sections are normalized at v = 1.5~1 where v1 is the ionization potential of H-. ( Reproduced from ref. 3 ). between the two scattering potentials was most marked in the threshold region. A particularly illuminating example of this effect is provided by a comparison of the photoemission cross-

sections of the hydrogen atom, H, and the negative hydrogen ion, H ’. In fig. 2, these crosssections are shown as a function of the photon energy, scaled to the threshold energy. The final state following photoionization of the atom is an outgoing electron in the coulombic potential of the positive ion, H+; from the negative ion, the photoelectron experiences the short range potential of the atom, H. Calculation of an inverse photoemission cross-section through the straightforward application of equation (4) to these different photoemission cross-sections will result in a threshold value of infinity for the coulombic polential and zero for the short range potential I In the UV energy range characteristic of inverse photoemission, the ratio R in equation ( 4 ) typically has a value of 10-5. It is precisely for this reason that the development of the technique as a viable spectroscopy has so lagged behind the development of photoemission. Indeed, it is only with electron sources operating in the space charge limited regime that inverse photoemission has developed into its modern momentum or K-resolved form (KRIPES). Detailed in the different

512

sections of this chapter IPES has now been applied to the study of bulk band structures, surface states and adsorbate induced features on both metals and semiconductor surfaces.

2.

INSTRUMEMATION

As has been reviewed extensively elsewhere, 5 the requirements of an inverse photoemission experiment divide into two elements, the electron source and the photon detector. In particular it is the properties of the former, the electron source, that determine the overall angular or momentum resolution. The ideal electron source would provide a large current into a well focussed spot with small angular divergence. Space charge effects will place limitations on the performance that can be achieved in practice but larger currents may be obtained where the spot size or angular convergence can be sacrificed. Stoffel and Johnson 6 have described an electron source whereby electrons are first accelerated in a simple diode extraction arrangement and then decelerated through a three element lens onto the sample. This gun, fig. 3, has been shown to operate successfully in a space charge limited mode, producing a 1mm. focussed spot with angular divergence of the order of 5O. Several authors have chosen to follow an alternative and earlier design due to Erdrnan and Zipf. 7 Here the extraction source is a triode rather than diode, but again, a lens is used to decelerate and focus the electrons on to the sample.

Fig. 3. Schematic diagram of the Stoffel-Johnson electron gun design. C and A represent the diode extraction source. A,F, and 0 ( ground potential ) represent the three element lens. L = D =16mm, Q = 2.5 D and P = 1.3 D. A development of IPES was the introduction of a spin polarized electron source into the experiment. This allowed studies of magnetic materials in the same style as spin polarized photoemission experiments. A typical source of spin polarized electrons has been described in considerable detail elsewhere. 9 Briefly electrons are photoemitted by circularly polarized light from a GaAs cathode that has been exposed to cesium and oxygen to lower its workfunction. Selection rules determine whether the photoemitted electrons are polarized either parallel or anti-parallel to the axis of rotation of the light. Experiments using such a source will be described in more detail later. However for now, we note that electron sources using the photocathode enjoy the advantage of a smaller energy spread, typically 0.1 eV rather than 0.27 eV for the BaO thermal source. The photon detectors used in IPES fall into two categories, those thal can be tuned to detect

*

513

.. .._ ._--____------________ .. .. I . .

ZQ f J 0)

52

5z

< U k I 9.2

9.6

10.0 ENERGY (eV)

I 10.4

Fig. 4. (a) A typical arrangement for the use of a Geiger Muller detector in IPES. The central electrode collects the electron cascade generated by the incident photon. (b) The bandpass characteristics (-) are determined by the product of the transmission of the CaF window (---) and the photoionization cross-section of the iodine vapor ( . , . . . ) . photons of different wavelengths and those that operate at a constant photon energy, 1.e. isochromat detectors. It is the latter, because of their ease of construction and operation, that have dominated the experiment to date. Indeed, it was with the introduction of the Geiger Muller counter, fig. 4(a), into the experiment by V. Dose, 10 that the recent surge of developments in IPES began. The first Geiger Muller counters used in IPES were band pass detectors centered at 9.7 eV with an energy window of approximately 0.8 eV. This resolution was determined by the transmission properties of a CaF entrance window and the photoionization properties of the iodine gas filling the detector, fig. 4(b). Whilst this arrangement is still widely used, several groups have replaced the CaF by a SrF window altering the detected photon energy to 9.5 eV and Because these detectors are insensitive to the direction of narrowing the bandwidth to 0.4 eV. travel of the detected photon they can be conveniently combined with large collection mirrors to enhance the signal rate. This advantage is not enjoyed so easily by detectors requiring a well defined source such as the spectrographs to be described later. Several different combinations of windows and gases have been used to generate other isochromat detectors for IPES studies. Another variant has been to replace the gas by the photo-

514

sensitive surface of an electron multiplier. Indeed, by coating the first dynode of an electron multiplier with another alkali-halide, KBr, Babbe et al. 1 2 have claimed both an increase in sensitivity and in resolution. The introduction of tunable spectrographs into Inverse Photoemission has allowed experiments to be performed in a similar style to Photoemission experiments using Synchrotron Radiation. Described in greater detail elsewhere, 5 three different spectrometer or spectrograph designs have been used to date. Two instruments are conventional in arrangement, one being based on a Toroidal grating l 3 and the second a normal incidence instrument l4 based on a spherical grating. The former allows photons to be detected in a higher energy range, 20-100 eV, the latter operates at lower energies 10-20 eV.

Grating sensitive detector

(b)

Detector

LiF

Fig. 5. (a) Off-Rowland circle normal incidence spectrograph with parallel detection. (b) Refractor with a lens as the dispersing element and single channel detection. The third spectrograph, 1 5 shown in fig. 5(a), is again of the normal incidence variety but here the authors recognize that the requirements of the experiment allow the focussing or optical properties to be relaxed in one dimension. This leads to a design in which the source of photons, the sample, is placed in one chamber and the photon detector placed in a separate chamber reducing the problem of shielding for the photon sensitive surface of the detector and allowing the full range of surface experiments to be carried out in the main chamber. With an instrument of this type the overall energy resolution that can be achieved at the lower energies is typically 0.3 eV. However this figure is essentially determined by the energy spread of the electron source, the 270 meV of the BaO cathode. A variant of the tunable detector was the replacement of the grating as the dispersive element by a lens manufactured from an alkali-halide. 1 k 1 7 The basic layout of such an instrument, a "Refractor", is shown in fig. 5(b). Because of the rapidly changing refractive index for wavelengths near the transmission cut-off of the alkali halide, different wavelengths

515

are focussed at different points along the axis of the lens. Tunability is therefore achieved simply by moving the photon sensitive surface with it's defining aperture along this axis. This simple detector can be operated with reasonably good resolution but over a more limited range than the large spectrographs, a typical range being 2.0 eV. Having discussed the various experimental details we now turn in the following sections to a discussion of the different range of experiments.

3.

METALS

3.1

Bulk States: The Direct Transition

As noted in the introduction to this chapter, the inverse photoemission process involves the emission of a photon during the radiative transition of an electron between two unoccupied states. As in photoemission, momentum conservation is maintained through the intervention of the crystal lattice. Thus the photon flux emitted at an energy nu for an incident electron beam energy E may be written 18

2. Here I Pf,i I ISthe square of the momentum matrix element between unoccupied bands i and f separated by nu and ci describes the coupling probability to the initial state. The first 6 function confines the transition to the same point in k space. In common with photoemission, kll is a good

quantum number but k l is indeterminate. Therefore most of the procedures already developed for bulk band mapping in photoemission will carry over into the study of the unoccupied bands. Indeed, in that this one to one correspondence exists, it cannot be said that anything new or unexpected has been learned about the bulk bands from IPES. However we briefly review some of the experimental methodology and discuss a few of the results. The type of data recorded in an experiment will be determined by the apparatus, and in particular, the type of photon detector used. With an isochromat detector of the Geiger Muller type, the emitted photon intensity is recorded as the incident electron beam energy is swept. For a given kll, determined by the angle of incidence of the electron beam and the incident beam energy, transitions are observed at some kl restricted through the 6 function in equation (5). Alternatively the photon detector may be of the spectrograph variety with the capability of detecting photons over a range of different energies. Now spectra will be recorded at some kll given by

516

_'X_

R=

d

2"

6"

I

=@

O

I

I

6 8 ENERGY ( e V )

2

4

I

10

F=O

2

4

6

8

ENEEGY (eV)

10

Fig. 6. KRIPES data taken on Pd(ll0) as a function of 8 , the angle of incidence in the PP and E? azimuths. The incident electron beam energy was 22.5 eV relative to EF. Features labelled BB represent bulk transitions and those labelled S, are surface derived. where Ei is the incident energy with respect to the vacuum level and 0 is the angle of incidence. Ei is set to different energies and all allowed transitions are detected in parallel. Indeed, as an aside, we note that with the use of a spectrograph in IPES, it is far easier to map the unoccupied band structure at some kll # 0 than it is to do the equivalent experiment in photoemission. This reflects the fact that i n the latter experiment for a selected take-off angle each point in a spectrum corresponds to a different value of kll. As an example of bulk band mapping, we show in fig. 6,two sets of IPES spectra recorded In moving away from the center of the zone in the PX and PB azimuths of a Pd (1 10) crystal. both azimuths, transitions are observed into the unoccupied d band immediately above the Fermi level: little or no dispersion is observed ior this band. Transitions into dispersing sp bands, labelled BE, are also identified in both azimuths. We reserve our discussion of the unoccupied surface states, labelled S, until later. We show in fig. 7 a comparison between the experimentally observed peak positions and the bulk bands calculated with an interpolation scheme. 2o The latter scheme was fitted to the results of a first-principles calculation of Christensen 21 with minor adjustments to improve agreement with earlier photoemission data. 22 Aside from such studies there have also been several spin polarized inverse photoemission studies of the bulk ferromagnetic materials Ni and Fe. This latter type of experiment] reviewed

517

,OF-

8 I

\

6

v-

\

-

\

'

\

4

2

0X

-

r

Y

P A R A L L E L WAVE VECTOR

Fig. 7. Ef (kll) plot of the data of fig. 6 (solid circles) compared with the calculated dispersion for kinematically allowed direct transitions within the bulk band structure (solid lines). The projected bulk band gaps are indicated by shading. extensively elsewhere, ~ - requires 2 ~ the introduction of a spin polarized electron source as described earlier. The "spin resolved spectra N$ and NT are obtained from the raw spectra n, and nT ( photon counts with the incident spin aligned in opposite directions ) through

N = nu + (n l + pA ) T 2 and

(7)

(n, - nJ) I (nT + n,) and P is the projected component of the spin polarization of the incident beam on the sample. The first experiment of this type 8 was carried out on a N i ( l l 0 ) surface where as expected it was shown that the unoccupied bands are entirely of minority character. Figure 8 shows the spin resolved spectra, N, and NT, and the asymmetry A obtained in that experiment with the

A is the measured asymmetry

electron beam incident at different angles in the c110> azimuth. Further experiments on the bulk band structure of ferromagnetic materials have followed earlier photoemission work by

518

examining exchange splittings at different points in the zone on for instance F e ( l l 0 ) 26 and also the temperature dependence of the latter. 27 In agreement with the photoemission studies it was found that the exchange splittings showed a varying temperature dependence throughout the zone.

0.4 1 .

-0.6

0

I

2

'

..

ENERGY ABOVE EF ( e V

N

T

-I

I

1

Fig. 8. Spin polarized inverse photoemission spectra and spin asymmetry recorded from a Ni (110) surface in the el 10> azimuth for an angle of incidence of the electron beam of (a) Oo and (b) 20 . 3.2 Surface States 3.2.1. Shockley States and Image States Whilst nothing particularly new has emerged thus far from IPES studies of unoccupied bulk bands, a more significant contribution has been made through studies of the unoccupied surface slates. This stems from the observation by Johnson and Smith 28 that IPES is capable of observing a particular class of surface state derived from the long range image potential. These states are generally referred to as image stales. The observation of pre-emergent fine structure in low energy electron diffraction studies of surfaces 29 had previously lead to models invoking the existence of such states. It was postulated that at energies above the vacuum level the electrons might couple to these states causing sharp structure in the measured rdectivity of the electron beams. However more recently. the same fine structure has been interpreted in terms of interference effects between the incident and reflected beams, 30 rather than bound or stationary

519 states. The observation of image states in IPES therefore confirms the existence of bound states. Following on from the early observation of these states, their existence has repeatedly been confirmed through direct observation on a number of different surfaces. 31*32 A further development came, however, with the observation that the Rydberg series of image states display binding energies dependent on the particular crystallographic plane studied. l 7 It was shown that a simple one-dimensional potential model, the multiple reflection or phase model, 29.33 could be used to predict the binding energies of these states and further that the same model provided the link between the image states and the Shockley or crystal-derived surface states. These latter states have been the subject of a number of earlier photoemission studies 34 and more recently inverse photoemission studies. 31 The spectra in fig. 9 present an example of the observation of an image state in a KRIPES experiment. Here the spectra are recorded from a Cu(ll1)surface for various angles of incidence of the electron beam. Aside from transitions into bulk and surface states the image state is clearly seen approximately 0.8 eV below the vacuum level. Having given an introduction, we now present a more detailed description of the properties

Fig. 9. Spectra recorded from a Cu(ll1) surface as a function of the angle of incidence of the electron beam. BB represents an unoccupied bulk band, SS a Shockley surface state and IS an image state. The energy of the isochromat detector used was 11.O eV.

Energy obove EFleVI

520

of the image states before showing their relationship to the crystal-derived states through the multiple reflection model. An electron located outside of a substrate of dielectric constant c experiences a potential

V(z) =

eL (E---

4z

(E+

I)

1)

where z is the distance from the surface. This one dimensional potential is hydrogenic in form and the solution of Schrodinger's equation yields an infinite series of states converging on the vacuum level. For an infinitely repulsive metal surface ( E = 0 ) the binding energies Eb of this series have the form

0.85eV Eb = - 2 n

n = 1,2,3 ,.....

(9)

However if the condition of infinite repulsion is relaxed, wave function penetration of the substrate may be accounted for through the introduction of a "quantum defect" parameter a. Thus

If the reflectivity of the electron wave at the substrate is described by a phase change $c then for the limited energy range of the Rydberg series (eq. 9) the quantum defect parameter may be written 29

Given that $c changes from 0 to 7c on crossing a "Shockley inverted band gap, it may be anticipated from equations (10) and (11) that the binding energy of the image states will reflect the position of the vacuum level within the gap. It was the observation of this phenomena in a comparison of the n = 1 image states on the Cu that lead to a more detailed examination of the multiple (001) and Cu (111) surfaces reflection model of surface states. 2933In this model the electrons are considered to be trapped in the surface region through multiple reflection between the crystal barrier on the one hand and the surface barrier due to the image potential on the other. Using a scattering formulation Echenique and Pendry s3 demonstrated that the bound states or surface states would be given by singularities in the function

521

v=

1

1 - rcr be

9,)

x9,+

where rcei% and rbeigb are the reflectivities from the crystal and image barrier respectively. If one assumes that rc = rb = 1, then the requirement of a singularity in Y’ leads to a quantization condition for the existence of surface states $c

+

n = 1,2,3,

@b = 2x11

(13)

To quantify equation (13) further, we review the two band, nearly free electron description of the crystal band gap. Within this model the electron energies or bands are given by the solution of

I

I

n2k2 -E

2m

vg

vP

n 2(k -

g)2

2m

-E

=

o

where g is a bulk reciprocal lattice vector and Vg is the associated fourier component of the pseudopotential. At the zone boundary g/2. a band gap is opened up of width 21Vgl. Within this gap surface states may exist, characterized by a complex momentum, the imaginary component describing the decay of the states away from the surface. Goodwin 35 was the first to derive the surface state wavefunction within the nearly free electron model. If k = p + iq then the solution of eq.14 for p = 912 gives

ny 2m

=

where Eg =

(4EEg +

-1

v”,) * - (E + Eg)

n y . The corresponding wavefunction 8m

y~ = eq‘cos(pz+Q

with

n2

sin (26) = - 2rn

171

522

Matching logarithmic derivatives at the termination of the crystal zc and the image barrier leads to

Kt;lll

kt -

= p tan (pz,

+

.

6) - q

where K is the perpendicular component of the electron wavevector referenced to the crystal inner potential. The crystal termination is generally taken to be half a lattice spacing beyond the last row of atoms. The phase change Qc a 26 and thus from equation (17) spans the range from 0 to K on crossing the gap. A useful form for the phase change I$b on reflection from the asymptolic

377

0

FERMl LEVEL

( a ) cu (411)

0

FERMl LEVEL 0

s

2s

77

PHASE

Fig. 10. Energy variation of the phases (pc, Q~ and 9 = Qc + $B showing n = 1 image states IS and (a) the n = 0 crystal induced surface state (SS) for C u ( l l l ) , (b) the n = 0 surface resonance for Cu(OO1).

523

image barrier is provided by McRae and Kane, who using a expression 36

WKB approximation, derive the

with Ev - E referencing the binding energy to the vacuum level E., In fig.(lO) we show the result of applying the quantization condition, equation (12), to the copper (001) and (111) surfaces with the phases defined by equations (17) and (18). Not only is good agreement found for the binding energies of the image states but the figure shows that the condition n = 0 gives an excellent prediction for the binding energy of the Shockley type surface state at the bottom of the (111) bandgap 37 and also a surface resonance on the (001) surface. 38

Cu( I 1 1 )

7. ( n . 1 1 . )

Fig.11. Calculated charge densities of the n = 0 surface state and the n =1 image state for C u ( l l 1 ) from Ref. 39. Simple one dimensional models of the crystal-derived or Shockley states have traditionally employed a step potential at the termination of the crystal. Using wave function matching with appropriate Whittaker functions describing the electron states in the image region, Weinert et al 39 rederived the results of the multiple reflection model and from the form of the wavefunctions concluded that the quantum number n of the particular state is simply related to the number of extrerna in the wavefunction beyond the crystal boundary, fig. 11. Thus the one dimensional potential running perpendicular to the surface supports an infinite series of states in an identical fashion to the coulombic potential of the hydrogen atom. However for the latter coulombic potential n = 0 represents a non-physical solution, the wavefunction having a

524

singularity at the origin. The image potential on the other hand saturates in the surface region (see section 3.3) allowing an n = 0 lowest order solution which in the limit has an identical form to the wavefunction appropriate to the step potential. The step potential may therefore be viewed as a screened image potential and as with any short range potential the number of allowed states is finite. In a series of papers N.V. Smith and coworkers 19,40-4* have applied the phase model to a number of zone boundary surface states. Within the NFE model, the wavefunction inside the crystal for zone boundary states must now be described by four plane waves rather than two. The electron waves again make multiple reflections between the crystal potential and the one dimensional image potential. In each complete cycle, the surface barrier is approached twice and the quantization condition gives

If

is written as the average phase change on reflection from the surface barrier then (211

@ c + ~ @ b=> nn

showing that now the number of surface state solutions has doubled. The wavefunctions within the crystal may be expressed as even and odd combinations of the plane waves thus

X

-

r

PARALLEL WAVE VECTOR

-

Y

Fig. 12. E(kl1) dispersion relations for the surface features of P d ( i l 0 ) labelled Sn in fig. 6. The solid curves represent the predicted binding energies of surface states from the phase model. Shading indicates the projected bulk band gaps. The dashed curve (ET) is the electron escape threshold.

525

where at the zone boundary of the surface Brillouin zone kil = g11/2 and p, q, and 6 carry the same meaning as in equation (15). A complete analysis including detailed derivations of these different parameters has been presented by Chen and Smith. 42 As an example, we show in fig 12 the result of applying the quantization condition (eqn. 19) to the (110) surface of Pd. Several states, predicted by the model in the TX and i T azimuths, are observed experimentally (fig. 6 and ref. 19). We note that wavefunction matching with the same crystal wave functions, eqn. 21, but with a step potential rather than image potential description has also been applied by Bartynski et al. to the noble metal (110) surfaces. 43 The successes of the multi-reflection or phase model are demonstrated in Table 1 where the experimental observations and model predictions for the binding energies of surface states on different noble and transition metal surfaces are tabulated. The model predictions shown are restricted to those that have been derived using the straightforward application of equations (13) and (20) above with no attempt to adjust the form of surface potential as discussed in section 3.3 below. We now turn to a brief discussion of the effective masses observed for the image states. Because of their location well outside of the crystal potential, one assumes that these states will probably display a free electron like dispersion parallel to the surface with an effective mass of unity. However several experimental studies have suggested that in certain cases the effective mass may be considerably higher than this: m, = 1.6 for Ni(1l l ) , 5 5 Ag(001) 60 and Pt(001). 6 2 The earlier observations lead to theoretical models based on both surface corrugation 76 and on many body effects 77. However these ideas were quickly refuted in a series of papers. Several groups 58,7879 demonstrated that surface corrugation was not responsible for any observed enhancement. Indeed such a model requires an unrealisticly large corrugation potential. In several other studies, it was found that many body effects or a dynamic image ~ ~the potential lead to an enhancement of the effective mass of less than 3%. 3 9 ~ 7 9 ,On and experimental side, repetition of the original experiments on Ag (OOl), 6 1 N i ( l l 1 ) Pt(001) 6 3 has tended in all cases to reduce their experimental effective masses to values close to 1.Ome. However high resolution two-photon photoemission studies show that for certain image states located near the top of the NFE band gap, the effective mass can be higher than unity, 1.3me in the case of Ag(ll1). 6 1 The currently accepted explanation of this observation, is that the binding energy of the state represents the result of "competition" between, on the one hand, the crystal potential and on the other, the image potential. Near the edge of the bulk band gap, the surface state or image state may be expected to show a longer decay into the bulk and consequently the crystal potential will play a greater role. This is reflected in the image state displaying an effective mass similar to that of the nearby gap edge. In band gaps away from the center of the zone several of the crystal derived surface states have been found to have effective masses considerably larger than the 1.Ome. However by simply applying the phase analysis with gap edges determined from the combined interpolation scheme, N.V. Smith and coworkers 19.42,61 e e 3 have shown good agreement between predicted and experimentally observed effective masses for both image states and the crystal derived states on a number of different surfaces.

526

Table 1. Binding energies of surface states as determined experimentally and as predicted by the phase model for different critical points in the Erillouin Zone of noble and transition metal surfaces. The subscript refers to the phase model notation with 0 for crystal derived and 1 for image potential derived states. The former are referenced with respect to the Fermi level, the latter to the vacuum level (except for the c110> Y image states)

527

3.2.2

Tamm or d-type surface states.

There have been several studies of d-type unoccupied surface states on the (100) surfaces of Nb, Mo, Ta and W. Interest in these surfaces stems from the observation that the W 84 and Mo 85 surfaces undergo temperature dependent surface reconstructions. Several theories have suggested that surface states close to the Fermi level might well play a role in these reconstructions. 86 In a study of W(100) and Mo(l00) Drube et al. 8 7 identified a surface state of even symmetry, a dZ2 state, on both surfaces at the center of the zone, fig. 13. Interestingly an odd Z2 state predicted to cross the Fermi level at f FR on the W surface 88 was not observed even though a candidate for this state had previously been identified in an earlier photoemission study.

89

In

another IPES study Bartynski and Gustafsson have examined the unoccupied surface states on Ta(001). Ta has one less electron than W and thus it has been proposed that any occupied states

-

2

0

2

4

6

8

-

2

0

2

4

6

ENERGY (eV relative to E,I

Fig. 13. (a) Energy dependence of Inverse Photoemission spectra from W(OO1) at the zone center from ref. 76. The intrinsic surface state near EF and the image potential state at EF + 3.9 eV show no dispersion with k l . (b) Angular dependence along the [I101 direction (FR in the surface Brillouin zone). near the Ferrni level on W might be unoccupied on Ta. 91 In their experimental study Bartynski and Gustafsson identified a number of surface states and/or resonances on Ta but concluded that a simple rigid band shift did not result in complele overlap of the Ta and W surface features. They did however, identify a surface state at EF at the center of the zone which they associated with the "Swanson Hump" state previously observed in the photoemission study of W. 89

528 Pan et al. 92 have studied the unoccupied states on the Nb(001) surface. As in the other studies they identified an unoccupied surface state at the center of the zone of dZz character. Examining the photon energy dependence of this state, the authors found, in agreement with an earlier photoemission study of the same surface state, 93 that the wavelength dependence of the intensity closely followed the square of the amplitude of the external electric field, [E,12,,t. This observation, fig. 14, suggests that the state is highly localized in the surface region. I

I

I

1

I

I

I

I

20

22

24

26

28

8 IE#

OUI

I

Id

I6

16

PHOTON ENERGY l e v 1

Fig. 14. The intensity of the dZz type surface state at the center of the zone on Nb(001) as a function of photon energy. The experimental points are compared with the calculated Fresnel fields inside and outside of the surface.

3.3

The Surface Barrier

The multiple reflection model provides a simple description relating the binding energies of both the image states and the crystal-derived or Shockley states. These binding energies reflect the local boundary condition, which in the surface region is determined by the response of the other electrons to the presence of the electron in the surface state. In the terminology of Lang and Kohn 94 an electron induces a local charge distribution in the surface region and the centroid of this induced distribution represents the classical image plane. In modelling the surface barrier it becomes necessary to use some form of saturated image potential. Whilst the form of the image potential given by eqn. (8) is appropriate at long range, close into the surface the potential has to flow smoothly over into a value characteristic of the inner potential of the metal. Weinert et al. 39 presented a systematic exploration of the relationship between the binding energies of the surface states and the position of the image plane. Using wavefunction matching with the image plane position as a variable they found that each position of the image plane defined a unique series of binding energies for the surface states. Within the limitations of their simple model they found that fitting to the experimental observations produced image plane positions

529

closer to the "jellium-edge" than calculated in the formal first principles theory of Lang and Kohn and further a crystallographic dependence. The same conclusions were arrived at by Ortuno and Echenique 95 using a similar one dimensional model. Interestingly, a more recent first principles calculation using a non-local exchange correlation potential has also placed the image plane closer to the jellium edge. 96 The exploration of the form of the surface barrier has continued in more sophisticated analyses. Using different surface barriers, Chen and Smith 42 attempted to fit the full range of surface states, both at the zone center and the zone boundary, on a number of different crystal planes. With a NFE description of the crystal potential they concluded that caution should be exercised when presenting quantitative information on the position of the image plane or shape of the surface potential. Still more sophisticated modelling relies on the use of fully self-consistent calculations of the crystal potential. This potential is matched to the so called JJJ potential, 97 which is thought to provide an adequate description of the saturated image potential. It takes the form (in hartrees)

Y

A exp [ - p ( z - za)]

+1

A and j3 are constants determined by matching V(z) and its derivative at the reference plane z = to. The parameter X determines the range over which the barrier saturates and UO represents the bulk inner potential. Using such a model Jennings et al. 98 have fitted both the planar average potential for a number of metals determined from density functional calculations and also the LEED fine structure observed for a number of different surfaces. Smith et al 99 have also used this same model to fit photoemission and inverse photoemission data from all of the noble metal and neighboring transition metal low index surfaces. In all of these models, there appears to be general agreement on the approximate position of the image plane, which ranges from 1.5 to 2.5 a.u. from the center of the last row of atoms depending on the crystal plane. Most of the density response occurs in the low density tails of the electron profile in the vacuum region. The simplest model for this density that would include the lattice, and hence any face dependence, would be the superposition of atomic like densities. Starting from this premise, Smith et al. 99 determine the planar averaged density for a single layer of atoms and extend this to the planar averaged density from a' series of layers < p(z) >. They show this to have the form

where zj represents the jellium edge position and ,€ determines the the decay length of the density profile. Within this model therefore the density profile reflects the jellium edge position, but only as a scaling factor, and the image plane position will show some face dependence. More recently Tamura and Feder 99a have considered the use of an energy-dependent "dynamical" rather than "static" surface potential barrier. For the Pd(ll0) surface, they found that the use of such a barrier avoided some of the problems encountered by Smith et al, 99 who found it difficult to define a single unique fit to all of the surface states on the (110) surfaces.

530

3.4

Interface states and Thin Films.

As a conclusion to our discussion of IPES studies of metallic surfaces we consider in this section the results obtained from interfaces or bimetallic systems. Described in greater detail elsewhere in this book, the study of thin films has been prompted by their unique properties compared to their bulk counterparts, in such areas as catalysis 100 and magnetism. lol To date IPES studies of thin films have been limited. Drube and Himpsel lo* have reported studies of monolayer coverages of Mn and V deposited on a Ag(l11) substrate. By comparing the spectra with those obtained in an earlier study of the Mn-in-Ag spin glass 103 and also with first-principles calculations of these thin films 1°4 the authors conclude that their films were ferromagnetic and that they were observing minority spin features. However more recent calculations Io5 suggest that, certainly in the case of a Ag(001) substrate, the early transition metals prefer an antiferromagnetic rather than a ferromagnetic configuration. The authors of the latter paper suggest that on the (111) surface the situation may be more complex. A spin polarized inverse photoemission study of such systems would be capable of determining whether

ENERGY ABOVE E, (eV)

Fig. 15. Inverse photoemission spectra recorded from the clean N b ( l l 0 ) surface (dashed spectra) and the Nb surface with a monolayer of Pd (solid line spectra). The normally incident electron beam energy with respect to the Fermi level is indicated.

531

the peaks above the Fermi level are polarized, evidence of ferromagnelism, or unpolarized, indicative of a paramagnetic or antiferromagnetic structure. Frank et al. lo6 have studied the growth of Ni films on a C u ( l l 1 ) substrate. In the region of one monolayer thickness they observe a well defined peak situated at the Fermi level, which they interpret as the appearance of an unoccupied nickel d band of minority character rather than the C u ( l l 1 ) Shockley state 37 pulled to lower binding energy. They support this argument by examining the adsorption characteristics of hydrogen on the thin film. The fact that hydrogen appears to adsorb on this surface leads the authors to suggest that as in the case of nickel surfaces lo7, it is the presence of d holes at the Fermi energy that mediates the adsorption. However they observe their "unoccupied nickel d band" at,the center of the zone in contrast to the results of a first-principles calculation by Tersoff and Falicov, lo8 who suggest that it should only be observed farther out in the zone. This therefore represents another system where SPIPES might well shed more light. Thin films of palladium grown on a N b ( l l 0 ) substrate have been extensively studied using photoemission, LEED,AES and a number of other techniques. This interest originally stemmed from the observation that the hydrogen absorption characteristics of the niobium are strongly modified by the presence of the thin films. lo9 Photoemission indicates that with the formation of the Pd monolayer the valence band has a form characteristic of a noble metal in that the d bands appear to be filled. l o Indeed the monolayer is inert to the adsorption of carbon monoxide at room temperature. Inverse photoemission studies of this system by Pan et al., 82 have revealed the presence of a well defined interface state with the formation of the first monolayer. Shown in fig. 15, the state displays little or no dispersion with .kl evidence of a two dimensional state. The interpretation of it being an interface state is confirmed by comparison with the results ofboth a FLAPW slab calculation and a Pd3Nb3 multilayer calculation. These calculations, fig. 16, indicate that with the formation of the interface, the state, which was previously a surface resonance on the clean niobium, now becomes more localized in the interface. Finally we consider alkali metal overlayers. Heskett et al. have studied the adsorption and growth of Na thin films on an Al(111) substrate. 113.114 .On the clean surface these authors identify an image state, 0.54 eV below the vacuum level. With the adsorption of Na they suggest that this state is quenched and that new features appearing in the spectra represent transitions into into the unoccupied 3p band and a hybridized s-d band. In support of this argument the authors find that the dispersion they observe for these states compares favorably with the dispersion calculated for a Rb thin film by Wimmer. 115 This interpretation of the spectra has however been disputed by Lindgren and Wallden. 116 The latter authors suggest that the peaks reflect the presence of bound state resonances in the thin film. In a series of papers 117-119 they have applied the phase model of surface states to the thin film situation. Thus the quantization condition, eqn. 13, would now give

where $c and $b are as defined in eqn (13) and ,@, = kd is the phase change through a film of thickness d. Applying this model to NdAI(111). Lindgren and Wallden demonstrated that the dominant peak in the spectra could be interpreted as a bound state resonance satisfying eqn (23). The latter interpretation is appealing in that the peak in the spectra of Heskett el al. does indeed appear to be tied to the vacuum level.

532

a

3.

sub-surface

3.

interface Nb

Fig. 16. Calculated local density of states at various sites (left to right) for the N b ( l l 0 ) surface, for the commensurate Pd/Nb(llO) surface and for the bulk PdaNba(l10) multilayer. The shaded regions delineate the positions of the surface and interface peaks in the various calculations.

4.

SEMICONDUCTOR STUDIES

Inverse Photoemission has been used to identity critical points and map out the dispersion of the conduction bands in a number of semiconductors. This exercise, identical to that for bulk band GaP l z 2 , CdTe, CdS, CdSe, 123 mapping in metals, has been carried out for Si and Ge, 12O GaAs, InP, lnAs and InSb. 124 In order to interpret the data, a free electron description has generally been used to describe the initial state and for the Ill-V compounds the dispersion obtained for the conduction bands in IPES experiments has nicely complemented the dispersion obtained from the final states in earlier ARPES experiments. 125 An example is given in Fig. 17 for the conduction bands of InP in the rZKX direction. l Z 4 Again, as in the case of metallic surfaces, the ability to vary the detected photon energy allows the clear identification of surface states and surface resonances. The termination of the bulk structure of the semiconductor results in the presence of broken or dangling bands in the surface layer. The surface atoms rearrange allowing bonding/antibonding pairs to form between these half-filled broken bonds and thereby producing both occupied and unoccupied surface states. States of the latter type have been identified on Si(lO0)ZXl and Si(ll1)7X7 126 and GaP(l1O)lXl. 122 On these particular surfaces, the unoccupied surface states fall within the gap. This is not always the case and on many other surfaces hybridization with bulk bands leads to surface resonances rather than surface states. Thus surface resonances have been observed on G e ( l l 1 ) Z X l 120 S i ( l l 1 ) Z X l 120.127 and G a A s ( l l 0 ) l X l . l2I

533

Momentum nlong Ill01

Fig. 17. Comparison of the experimentally determined conduction bands of InP in the rXKX direction from IPES studies, ref. 124 (filled symbols), with those obtained in PES studies (open symbols), ref 125. These are both compared with pseudopotential calculations for bands below 7 eV (ref. 125a) and free electron bands folded back into the reduced zone above 7 eV. Recently it has been demonstrated that information on both the occupied and the unoccupied surface electronic structure may also be obtained from the Scanning Tunneling Microscope. lZ8 In this technique a fine metal tip is brought up to the surface under investigation. By varying the bias voltage applied between the tip and surface, electrons are enabled to tunnel either into or out of the different surface states. The important and interesting characteristic of this spectroscopic technique is that it provides information on the real space location of these states and thus compliments the information obtained in PES and IPES experiments which locate the states in momentum space. A number of studies of semiconductor-metal interfaces have been carried out. These include Pd on Si(l1 1)7X7,126 Cu, Ag and Au on the same surface, 129 Ti on GaAs(l1O)lXl 130 and Sb overlayers on GaAs(l10) and InP(110). l 3 I In general, with the initial deposition of the metal, new unoccupied states are induced above the Fermi level. With the formation of an intermediate compound, the unoccupied density of slates is distinctly different from that characteristic of the metal overlayer formed at high coverage. For example, in the case of Pd2S.i formed when Pd is deposited on Si 126 the IPES study was characterized by a broad band of unoccupied states 4 eV in width as opposed to the narrow peak associated with the unoccupied d bands of Pd metal or the lower density of states of the conduction band of the Si substrate. It is possible to obtain a well-ordered (1x1) overlayers by thermal annealing after room temperature deposition of Sb onto freshly cleaved GaAs(l10) and InP(110) surfaces. The results of an inverse photoemission study of these ordered overlayers are shown in fig 18

534

I

,

1

, Sb/GaAs(llO) I

I

E, = 15.6 eV

0

2

4

6

0

I

1

2

I

1

Sb/lnP(110)

E, = 16.6 eV

0

(1x1)-Sb

A

clean

4

6

8

Energy (eV relative to E),

Fig. 18. Inverse photoemission spectra from clean cleavage (triangles) and an ordered (1XI) Sb overlayer (dots) for GaAs and InP. Sb induced states are marked by arrows. The peaks above 4 eV are derived from bulk states and are unaffected by the Sb adsorption. where it will be seen that the presence of the Sb produces a well defined surface resonance at 2.1 eV above the valence-band maximum for both substrates.

5.

ADSORF'TION SYSTEMS

Inverse photoemission has been applied to the study of atomic and molecular adsorption systems spanning bath chemisorption and physisorption. The full description of the bonding of atoms and molecules to surfaces involves the Identification of both bonding and antibonding orbitals. Whilst the division between bonding and antibonding does not necessarily represent a division between occupied and unoccupied, one may assume that the bonding orbitals, the more deeply bound states, have tended to be the subject of earlier photoemission studies. On the other hand the antibonding levels are more likely to be probed in inverse photoemission studies of adsorbates. Although limited, these studies have moved from the straight forward identification of the adsorbate induced levels to the examination of the two dimensional bandstructures associated with the adsorption. Discussion of the new features above the Fermi level ranges from their identification as the antibonding component of a surface molecule complex through to the possibility of standing wave resonances formed in a planar averaged cavity induced by Ihe adsorbate between the substrate and the surface barrier. 132.133 The latter model is identical to that used in the descriplion of thin films by Lindgren and Wallden (section 3.3). 1 1 6 In the following sections we discuss oxygen chemisorption, xenon physisorption, and Ihe adsorption of diatomic molecules, all on metal substrates.

535

5.1

Oxygen chemisorption

Oxygen represents the most extensively studied atomic adsorbate in inverse photoemission. Its chemisorption on all of the low index planes of nickel 134-137 and on the (110) and (111) surfaces of copper 138 has been studied. In Figure 19, the spectra recorded from a Ni(l10) surface as a function of oxygen exposure 137 shows the emergence of a peak 3eV above the Fermi level with the formation of the (2x1) overlayer structure. A similar adsorbate induced feature is observed on the Ni(11l) surface 136,where polarization of the emitted photons or symmetry selection rules have been used to determine that the new feature has A1 symmetry. The authors therefore associated it with the oxygen 2p, orbital. However this is in disagreement with the results of an earlier study of the same system 134 where it was concluded that the state was pxpy derived or A3 Symmetry.

L 3 w = 9.7eV

0

2

4

6

8

E - E , ( eV )

Fig. 19. Normal incidence IPES isochromat spectra (9.7 eV) recorded from N i ( l l 0 ) as a function of oxygen exposure as indicated. The different LEED patterns observed for the overlayer structures are also indicated. Using the surface molecule descrlption, Desinger et al. 137 have suggested that a correlation exists between the binding energies of the occupied bonding orbitals observed in photoemission studies and the energies of the unoccupied antibonding orbitals for the same system. They show that in progressing from Ni(l11) through Ni(001) to'Ni(l10) the bonding level moves further from the Fermi level to higher binding energy whilst the antibonding level moves away from the Fermi level in the opposite direction. The observation of the unoccupied level on the Ni(001)

536

surface is required to confirm such a picture but unfortunately the predicted position has In the first coincided with a substrate bulk band transition in all studies to date. 1 3 5 v 1 3 7 ~ 1 3 9 studies 135,137 it was suggested that an adsorbate induced state of A5 symmetry. i.e., 2pxpy character, leads to an increase in the density of states above the Fermi level. However, the later spin polarized study 139 found a decrease in the density of states rather than an increase and further, found no change in the spin polarization of the unoccupied d bands immediately above the Fermi level. This latter observation argues against the presence of an additional adsorbate induced feature. Interestingly, an adsorbate induced occupied feature, immediately above the d bands, was identified in earlier photoemission studies of oxygen adsorbed on the Cu(OO1) surface 140 However, the symmetry of the new state was not identified in those in a ~ ( 2 x 2 structure. ) studies. Donath et al. 14 have performed a SPIPES study of the 0 p(2xl)/Ni(llO) system and find that the adsorbate induced peak 3 eV above the Fermi level is exchange split by 80 meV. They interpret this as an indication that the oxygen atom is itself magnetized. We will return to a discussion of this observation below. On both Cu(ll1) and Cu(llO), an oxygen induced peak has been identified in IPES studies 13* at approximately 3.0 eV above the Fermi level, similar to that found on the nickel surfaces. On the Cu(l10) surface a number of other features were identified following the formation of an ordered overlayer. However, it was suggested that most of these features might well be associated with bulk and surface derived bands from the substrate. In particular a second adsorbate induced feature 6.3 eV above the Fermi level at the center of the zone is thought to reflect the folding of X ontoy via the 2x1 surface superlattice. Chen and Smith 133 have examined the adsorption of oxygen on these surfaces within the standing wave description. Using phase analysis they model the adsorbate layer by shifting the effective image plane position outward. Figure 20 shows the results of such an analysis for clean

8

“ 4

>-

W K

Y W

2 0 1.0

0.5

0

0.5

PARALLEL WAVE VECTOR

1.0

(i-‘)

Fig. 20. E(kl1) dispersion relations from ref 133 for clean C u ( l l 1 ) and for the adsorbate system Cu(l11)/02. Open circles are the inverse photoemission data of ref. 17 on clean Cu(ll1); the photoemission data of ref 37 on clean C u ( l l 1 ) are shown as the dots near F. Solid circles are the inverse-photoemission data of ref. 137 for Cu(l11)/02.

537

C u ( 1 f f ) and Cu(111)/0. With a displacement of the image plane of 1.4 A the band assigned to the pz derived antibonding orbital in the surface molecule model now appears in the standing wave resonance description as the clean surface "n=l" image state shifted towards the Fermi level. Interestingly, within this picture, the adsorbate induced peak identified in the SPIPES study of Ni(l1O)/O as an antibonding level 141 would now be associated with a modified surface state of the substrate. Thus any exchange splitting in the peak would reflect the surface magnetization of the substrate itself rather than the magnetization of the adsorbate. From the experimental data a picture emerges of oxygen bonding to the transition metals with the formation of a well defined bonding orbital approximately 6.0 eV below the Fermi level. Such an observation finds close agreement with a calculation of the electronic structure of the ~ ( 2 x 2 )oxygen structure on Ni(001) by Liebsch. 142 That calculation gave a splitting of 7.0 eV between the bonding and antibonding levels with the unoccupied 2pz orbital further from the Fermi level than the 2pxp, orbitals. It is not clear at this stage whether these unoccupied levels are to be associated with the new peaks observed in IPES studies, typically 3 eV above the Ferrni level, or whether they are in fact much closer to the unoccupied d bands. No candidate for such an orbital has been conclusively identified on any surface studied to date.

5.2 Xenon Physisorption Because of its weak interaction with the substrate, xenon physisorption has been thought to provide an ideal test of final state screening in electron spectroscopies such as photoemission and inverse photoemission. In photoemission studies, the occupied xenon levels are observed to move to higher binding energy with the growth of each new layer. Kaindl et al. 143 have suggested that these layer dependent binding energies reflect the distance-dependent image charge screening. Such a mechanism represents a final state effect with the photohole inducing the image or screening charge in the substrate. Wandelt and co-workers have proposed an alternative model in which the binding energies of the Xe levels are determined by the layer dependent workfunction. 1 4 4 t 1 4 5 In this latter model the mechanism is an initial state effect and the final state effects are thought to be negligible. In photoemission studies both of these models may be invoked in that they both result in binding energy shifts in the same direction. In inverse photoemission on the other hand the two models would result in binding energy shifts in opposite directions. The interpretation of the IPES data has relied on comparison with photoemission and EELS data, the latter representing transitions between the occupied and unoccupied states. In two separate 1PES studies of Xe physisorption, Horn et al. 146 and Wandelt et al. 147 interpreted their data in terms of the two different models. Horn et al. 146 studying the adsorption of Xe on A u ( l l 0 ) were able to identify peaks in the multilayer spectrum by comparison with atomic spectra and EELS data. With certain assumptions about the structure in the monolayer spectrum, they concluded that their results were consistent with the image charge screening model. In a later study, Wandelt e l at. 147 adsorbed Xe multilayers on the Ru(001) surface. They interpreted their multilayer spectrum, fig. 21, in a similar fashion to the earlier study. However they concluded that their observation, peaks moving closer to the Fermi level with increasing coverage, supported the local work function model. In that the spectra from the multilayers appeared similar it would seem that it is crucial to correctly establish the binding energies appropriate to the monolayer. Unfortunately the monolayer coverage displays the weakest signal.

538

0

2

.

4

6

E-EF l e v )

8

Fig. 21. Inverse photoemission spectra recorded from a clean Ru(001) surface and the same surface following exposure to xenon. The indicated exposures correspond to 1 ML (curve b), 2 ML (curve c) and 5 ML (curve d) of physisorbed xenon. B and S designate unoccupied bulk and surface bands of the Ru, respectively. We note however that in a later paper Bertel et al. 14* have suggested that interpretation of the data may be further complicated by whether or not wetting of the substrate occurs. In the following section we return to the subject of final state screening with our discussion of molecular adsorption.

5.3 Molecular Adsorption The most studied adsorption system in surface science has been and remains the adsorption of carbon monoxide on transition metal surfaces. It is now well established that in most systems the carbon monoxide is chemisorbed on the surface in an upright or near upright configuration with the carbon atom closest to the surface. The standard models of the adsorption propose that the bonding involves the molecular 50 and 2x: orbitals both centered on the carbon atom. The former is occupied in the gas phase and the latter unoccupied. In the Blyholder model 149 these molecular orbitals are thought to bond to the metallic occupied and unoccupied d orbitals as shown

in fig. 22(a). Electrons are considered donated from the occupied 5a orbital to the d complex and this charge transfer is compensated by "back-donation'' into the unoccupied 2 r level. Avouris et al 150 have described an alternative model, the 2r resonance model, which favors a greater participation of the substrate sp continuum. In fig. 22(b) we show a molecular orbilal representation of this model. The interaction between the continuum and the unoccupied 271 orbital is thought to result in a considerable broadening of the latter and its concomitlanl partial

539

co

Metal

CO

2noo

Metal

Fig. 22. (a) The Blyholder model (ref. 149) of carbon monoxide adsorption with donation of electrons from the 50 orbital compensated for by back-donation of electrons into the molecular 271 level. (b) The 2x resonance model with increased interaction of the substrate continuum. occupancy. One essential difference that arises from these two possible bonding configurations is that with increased bonding strength the Blyholder model suggests that the unoccupied 2x orbital will move further from the Fermi level whilst the resonance model would predict the same level moving closer to the Fermi level. It is to be hoped therefore that IPES studies of the 2 x orbital will shed further light on the bonding mechanism. As we shall see however, a number of other factors potentially complicate the discussion. These include both adsorbate-adsorbate interactions and also final state effects where it is to be recognized that IPES represents, as does PES, an excited state spectroscopy. The first clear IPES observation of the unoccupied 2x orbital of CO adsorbed on a transition metal, namely the N i ( l l 1 ) surface, revealed a broad peak positioned 3 eV above the Fermi level. 1 5 1 Subsequent studies of numerous surfaces have revealed a similar but in general narrower feature. In Figure 23 we show the IPES spectrum recorded following CO adsorption on the Ni(001) surface. 152 Within the Blyholder model the carbon monoxide derived feature 4 eV above the Fermi level would correspond to the antibonding component of the metallic drr-2n band. We note in passing that to date no studies have found any structure identified as relating to the unoccupied or antibonding component of the do-5o bond. Several authors have attempted to correlate the observed energy of the 2x orbital with the bonding strength of the carbon monoxide. 77*152,153 Measured wilh respect to the Fermi level, there appear to be no obvious systematics in the observed position of the CO 2x orbital when either strongly chemisorbed on transition metals or weakly chernisorbed on the noble metal copper surfaces. However, in all cases of adsorption on metal surfaces, the 2x orbital is found below the vacuum level rather than above, as in the case of the gas phase molecule. This observation clearly contradicts the naive interpretation of the standard Blyholder model and has lead authors to look for correlations in terms of the binding energy with respect to the vacuum level. Figure 24 shows such a correlation by Johnson and Hulbert 152 where the binding energies

540

referenced with respect to the vacuum level are compared with the infra-red stretch frequencies of the different adsorption systems. 155 The latter being used as an indication of the relative bonding strength. The figure clearly shows that in moving from the gas phase GO 154 or the weak physisorption system CO/Ag, 156 through the weak chemisorption regime, GO on the copper surfaces, 77 to the stronger chernisorption systems, GO on the transition metal surfaces,l~l.152.157-159 the measured energy of the 2n orbital drops from above the vacuum level to below. As already noted, whilst bonding to the d orbitals alone will result in the 2rc orbital moving further from the Fermi level, increased interaction with the sp continuum is expected to result in the 2n moving to higher binding energy or closer to the Fermi level. Proponents of the surface resonance picture have therefore suggested that many of the observations favor their model. Indeed on one surface, namely Cu(OOl), two peaks were observed following GO adsorption and these were interpreted as the bonding-antibonding pair derived from the 2n-px interaction. 160

Fig. 23. Comparison of inverse-photoemission spectra recorded for an electron beam incident along the surface normal of (a) the clean Ni(001) surface and (b) the same surface following the adsorption of 20L of CO at 100K. The incident beam energy was 17 eV. Several authors 31.150.i5*t161,162 have noted that interpretation of the spectra may also be complicated by final state or relaxation effects. IPES is a probe of the excited state, an electron having been added to the system. For delocalized states, such as bulk bands, the perturbation introduced by this additional electron will be minimal. However in the case of molecular adsorbates, the more localized interaction will lead to relaxation effects which modify the measured final state energy. The coulombic interaction between the added electron and the other molecular electrons will lead to the affinity level or final state being at a lower binding energy

541

2

-4

1

co

CO /Ag

I I

I I

I

Fig. 24. Binding energies, with respect to Evac, of the CO 2x level plotted against the infrared stretch frequencies for the same adsorption systems. The vertical dashed lines represent from the left, the division into threefold, twofold and one fold adsorption sites. Reference sources are as follows: N2, CO (155), CO/Ag (156), C u ( l l l ) , Cu(OOl), Cu(ll0) (77),NdNi(001), P d ( l l l ) , Ni(001) (1521, Pd(001) (157), N i ( l l 0 ) (158), P t ( l l 0 ) (159). than the ground state. Indeed, as already noted, in the gas phase the measured affinity level of CO lies in the continuum above the vacuum level. When the CO molecule is brought into contact with a surface the screening provided by the metallic electrons reduces the separation between the affinity level and the ground state. It was this observation that lead Johnson and Hutbet? 152 to suggest that final state effects might well play a role in determining the observed positions of the CO 2 x orbital shown in Figure 24. Gumhalter and co-workers 162 have also discussed the role of such final state effects. They examine the effect of increased delocalization on the substrate image screening of the affinity level. Such a delocalization will result from a strengthening of the interaction between the molecule and the surface. They argue that CO adsorption on the noble metal surfaces such as copper, represents an upper limit to the image induced relaxation effects. On this basis they therefore conclude that CO adsorption on transition metal surfaces such as nickel must include initial state shifts reflecting the interaction of the 2 x orbital with the substrate sp continuum. In a recent study of CO adsorption on N i ( l l l ) , Frank et at. 163 reported the observation of a coverage dependent position for the CO 2 x level. At low coverage they identified a peak which they interpreted as the 2x level, only 1.3 eV above the Fermi level, closer than had previously been observed. At higher coverage with the formation of an ordered overlayer this peak moved further from the Fermi level and showed evidence of substructure or multiple peaks. Following an earlier study of CO on Ni(ll0) by Freund et al., 164 they suggested that the substructure reflected adsorbate-adsorbate interactions and that further it was this interaction rather than

542

final state effects that ultimately determined the observed position of the 2x level. Evidence for adsorbate-adsorbateinteractions is provided by a recent IPES study of CO on Ni(ll0). 165 Here the authors report the observation of a two dimensional bandstructure derived from the adsorbate 2~ orbitals. They suggest that their study combined with an earlier photoemission study 166 of adsorbate derived bands below E, represents the only complete study of all of the bands associated with the drr-2x interaction. Studies of the coadsorption of CO and potassium have consistently shown on all surfaces that the presence of the alkali metal results in the 2x level moving closer to the Fermi level. 77.152,167 Coadsorption is generally thought to result in increased back donation into the 2x level as evidenced by the considerable reduction in the infra red stretch frequency. 168 The shift of the 2 x level towards the Fermi level is therefore again inconsistent with the Blyholder model and implies that other interactions are taking place. Whether these interactions reflect a direct bonding between the CO and alkali metal 169 or long range electrostatic effects associated with the alkali atom 170 remains to be determined. There have been a few studies comparing the adsorption of NO and CO on different surfaces. 152.157 The two molecules differ in that gas phase NO already has an extra electron in the antibonding 2 x level. The question arises as to whether this extra electron will serve as a tag

1

I

1

1

I I 0.0

1

1

1

1

I I I ( 1.0 2.0

1

1

1

3.0

1

1

1

1

4.0

E N E R G Y ABOVE E,leV>

1

1

1

1

5.0

1

' 0

Fig. 25. Inverse photoemission spectra recorded from (a) Pd(ll1) and (b) Ni(001) following the adsorption of of NO at room temperature and 100K respectively. The incident electron beam energies were 17.0 eV with respect to the Fermi level. The 2rr orbitals are indicated by the vertical lines.

543 of the 2 x level and allow for a clearer identification of the interaction between the adsorbate and the substrate levels. To date all IPES studies of NO on transition metal surfaces have been consistent in placing the unoccupied 2 x level approximately 1.5 eV above EF. Examples are given in Figure 25 for NO adsorbed on a Ni(001) surface and a P d ( l l 1 ) surface. 152 Photoemission studies of these same adsorption systems have identified what is thought to be the occupied and 2.6 eV 172 below the Fermi level respectively. It is component of the 2~ complex 2.1 eV of interest to determine whether these latter levels are predominantly substrate drr or molecular 2 x in character ? Rogozik et al. 157 have suggested that in the ground state of the adsorbate complex, the NO 2rr level straddles the Fermi level. Interpreting the data within this framework, the peak observed in the photoemission spectra may be seen as the metallic dx component of the d n - 2 n bond. A similar picture has also been proposed in a discussion by Batra and Brundle 173 of an earlier photoemission study of NO adsorbed on Ni(001). The latter discussion was based on the results of a “ground-state’’ cluster calculation. Johnson and Hulbert 152 have presented an alternative view based on the excited state. They point out that the equivalent dx bonding component for CO adsorbed on transition metal surfaces has been identified in only a few systems 166,1748175and therefore suggest that the new feature observed in photoemission spectra may well represent emission from the predominantly molecular 2n orbital, in agreement with earlier studies. 171 By performing transition state calculations ( adding or subtracting 0.5 electron to or from the 2 1 level ) on a linear NiNO chain they find that the two final states are separated by an energy difference of the order of 5.0 eV. Thus in this picture, measurements from the two adsorbate induced features gives a measure of the effective electron - electron interaction Ueffin the presence of the metallic substrate. U,n therefore takes the values of 3.6 and 4.2 eV for Ni (001) and Pd (111) respectively. In the gas

phase, an ionization potential of 9.26 eV has been measured for NO 176 and 0.024 eV for NO- li7 giving a U,ff of 9.28 eV The difference reflecting the increased screening in the presence of the substrate. It has been noted by several authors 151.152.16Z178.179that some measure of the screening provided by the metallic substrate may be obtained by comparing IPES spectra with the results of NEXAFS of Near Edge X-ray Absorption experiments. In the latter experiment an electron is promoted from a core level, [e.g . the C 1s level] to the unoccupied 2n level by absorption of a photon of the appropriate energy. The two spectroscopies differ through the presence of the core hole. Gumhalter et al. 162 have compared the CO/Cu (110) adsorption system with gas phase CO. They find that the presence of the metallic screening reduces the effective core hole potential U from 10 eV for the gas phase to approximately 2.2 eV in the adsorbed phase. A similar Comparison for the CO/Ni(001) chemisorption system produces a value of 3.75 eV. 1 5 2 Another measure of the level or effect of metallic screening may be obtained by comparing the observed binding energies of the molecular shape resonances or bound states in the continuum. These observations are described in the next section.

5.4

Molecular Shape Resonances.

Shape resonances are thought to arise through multiple scattering of the electron within the molecular potential l80 and have been observed in both valence l e l and core level photoionization. 182 By invoking dipole selection rules, the angular dependence of the shape

544 I

Fig. 26. Observations of the molecular shape resonance for CO adsorbed on Ni(001). (a) Cross-hatched peak shows the 2 x orbital above EF measured as the final state in IPES. The individual points 4 show the IPES cross-section for observation of this orbital as a function of the incident electron beam energy with respect to EF. (b) Photoionization cross section of the CO 4 0 molecular level from ref 183. (c) Near edge structure for carbon K-edae excitation from ref. 182.

Ezl 10 20 ENERGY ABOVE EF ( e V 1

-

4

->

k z 5

I I I I

W

15

25

35

PHOTON ENERGY (eV1

I-

5

1

I I

i 0

E,

l

I

I

I

290 300 PHOTON ENERGY (eV1

I

I

310

I

I

resonance has been used. to determine the molecular orientation from both photoemission la3 and Johnson and Davenport 2 proposed that the shape resonance should be NEXAFS studies. la2 observable in Inverse Photoemission as an initial state effect rather than a final state effect as in photoemission. Thus the cross-section for observation-of the 2n level should peak at incident electron energies corresponding to coupling into the shape resonance as an initial state. The results of such a study for CO adsorbed on Ni(001) la4 are shown in fig. 26. The figure compares the intensity of the 2n level as a function of the incident beam energy in IPES studies with the shape resonances observed for the same system in valence level photoemission la3 and carbon K-edge NEXAFS studies. 182 The system is interesting in that it allows a comparison between the effective screening of a valence photohole and a core level photohole. For the valence levels the screening appears to be almost complete. Photoemission and inverse photoemission produce nearly identical values for the shape resonance position even though on the one hand the resonance is bound lo a positive ion and on the other the resonance is bound to a neutral atom. For the core level photoionization, the photohole is less well screened and the shape resource moves Closer to the Ferrni level. It would therefore appear that the level of screening or relaxation reflects the level of localization of the photohole. We note in passing that coupling of incident

545

electrons to the shape resonance as an initial channel has also now been reported in several EELS studies. 185 It has further been suggested that the position of the shape resonance may be used as an indication of the change in the interatomic bond length for molecules adsorbed on surfaces. 186 Whilst it has been clearly demonstrated that the resonance position reflects the bond length in the gas phase the above studies indicate that more caution should be exercised for the surface adsorbate where the quantitative effect of substrate screening will be difficult to determine.

6.

RESONANT INVERSE PHOTOEMISSION

The previous sections have covered a number of different experimental observations, all of which have been discussed and interpreted in terms of one electron transitions into well defined energy bands or levels. However it is well known that there is a variety of structure or peaks occurring within photoemission spectra that may be interpreted only within a framework of multi-electron excitations. 34 Such phenomena include, for instance, the observation of satellite structure or the observation of plasmon emission. It is only recently that multi-electron phenomena have been observed and identified in inverse photoemission and that as a result of the introduction of tunable photon detectors. Resonant enhancement of a radiative transition represents coupling between some discrete channel ( a plasmon or core level excitation ) and the continuum ( the direct transition ). Wendin has considered the theoretical aspects of resonant inverse photoemission. He finds that the emitted photon intensity I(E,o) given by

J

I @,w) = d% I k(w,E) ? 6(%+ 61- E) where t&co,E) is the radiative scattering amplitude, reduces to an expression of the form

Here o(E) is the cross-section for the direct radiative transition, A(E-o) the lineshape or spectral function of the discrete excitation and R(o,E) describes the resonant enhancement of the radiative capture process. Probably the most striking example of the role of many electron effects was the observation by Drube and Himpsel lee that the intensity of the IPES transition or the cross-section shows a strong enhancement when the energy of the transition corresponds to the plasma frequency of the material. Their observation was made in a study of antimony thin films grown on different substrates. The spectra, reproduced in fig. 27, show peaks associated with transitions into the unoccupied levels of the antimony and also a peak remaining at fixed photon energy, irrespective of the incident electron energy. This latter peak they identified as a plasmon peak reflecting the decay of plasrnons either directly or indirectly into photons. More importantly however, their spectra clearly show that whenever the plasmon peak coincides in energy with a direct transition, then that transition shows a dramatic enhancement of its intensity. This same phenomenon has and of Nb(001) and Nb(ll0). 92 In a study of also been reported in IPES studies of graphite leg

546

8

10

12

14

16

18

20

22

Photon Energy (eV1

Fig. 27. Inverse photoemission spectra recorded from a thin film (20 A) of Sb grown on cleaved InP(110) for various energies Ei of the normally incident electrons.. The vertical arrow marks the photons of energy nwP emiited by decaying plasmons. Resonant enhancement occurs when the direct inverse photoemission channel coincides with the plasmon channel. AI(001) no such enhancement was observed. Indeed, on that surface an intensity minimum rather than maximum was observed at the plasma frequency. This observation was simply interpreted as the "time reversal" of the surface photoeffect. In the free electron gas the longitudinal plasmon will not couple directly to the transverse field of the photon. It is only in the surface region that bulk plasmons are able to decay into photons. Further, surface plasmons will decay into photons only through the intervention of surface roughness. In their study of niobium single crystals however, Pan et al. 92 were clearly able to show that the observed phenomenon was related to bulk properties and independent of the condition of the surface. Indeed they found that the resonant behavior did not occur for either surface or interface states. They suggested that scattering from the crystal lattice could be responsible for mediating the coupling between the photons and plasmons. Such scattering would be weak in free electron materials such as aluminum but strong for the transition metals. The spectral function for the plasmon will reflect the loss function Im(-I/&) for the material. Figure 28 presents a comparison between the intensity of the direct transition observed to resonate at the plasmon frequency of niobium and the loss function for that material derived from reflectivity measurements (ref. 191). Another example of such coupling is the so called "Giant Dipole Resonance". Here the excitation of a core to bound transition represents the discrete channel. Resonant enhancement of photoemission cross-sections at photon energies corresponding to the threshold for core to bound transitions is a well studied phenomenon. The equivalent resonance has been o b s e i e d in IPES by

547

I

I

I

I

'

I

I

I

I

L

Electron Beam Enerpy w r t E,(ev)

Fig. 28. Intensity of a direct transition (.) in inverse photoemission spectra recorded from a N b ( l l 0 ) crystal as a function of the electron beam energy from ref. 92. These are compared with the loss function I m ( l / [ q ) and the surface loss function I m ( l / [ & + l [ )for niobium from ref. 191. Drube and Himpsel in a study of lnSe Iz4 and in a number of studies of the rare earths in the High T, Superconductors by Weaver and coworkers. 192

7.

The Beginning of the End or the End of the Beginning ?

After a slower start the development of inverse photoemission has progressed to the point where the technique is providing relevant information on both the traditional and new electronic structure problems comparable to that obtained in PES. An example being the recent surge of activity in the field of High T, Superconductivity. Here PES and IPES have competed equally in the development of an understanding of the electronic structure. However it is the currently much higher energy resolution capability of the former technique that has ultimately provided data capturing the imagination of a wider audience. l g 3 The ability to achieve a high energy resolution thus presents one of the more immediate challenges in the further development of IPES. The

548

problem is one of reducing the energy spread in the source whilst maintaining sufficient incident flux to allow the experiment. The majority of this chapter has been devoted to the studies of metallic systems. This is partly a reflection of the bias of the author and partly a reflection of the bias in the field as a whole. Studies of the unoccupied surface states, both crystal derived and image potential derived, have lead to a renewed interest in the correct form of the surface barrier. This represents an important property of the surface and interest will obviously continue. Other metallic systems that will receive a growing interest are the newer areas relating to magnetic problems, both surfaces and thin films. However it may also be anticipated that more activity will be devoted to studies of the conduction bands of the technologically important semiconductors. Other areas of increased activity will be the more complex systems including alloys, bimetallic interfaces and different compounds. In these systems the possibility of using the site specific resonant behavior associated with core level excitation points to the development of IPES capabilities in a photon energy range higher than that currently accessible with the normal incidence spectrographs. This latter possibility represents another area with technological challenges which if solved may well prove rewarding.

Acknowledgements The author is extremely grateful for numerous discussions over the years with Jim Davenport, Steve Hulbert, Neville Smith and Mike Weinert.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

J.B. Pendry, J. Phys. C 14 (1981) p1381. P.D. Johnson and J.W. Davenport, Phys. Rev. B 31 (1985) p7521. H.A. Bethe and E.E. Salpeter, "Quantum Mechanics of One- and Two- Electron Atoms", 1977 Plenum Publishing Corp., New York, p315-317. Earlier extensive reviews of IPES include V. Dose, Surf. Sci. Reports 5 (1985) p337; N.V. Smith and D.P. Woodruff, Prog. Surf. Sci. 21 (1986) p295; F.J. Himpsel, Comm. Cond. Mat. Phys. 12 (1986) p 199; N.V. Smith, Rep. Prog. Phys. 5 1 (1988) p1227. P.D. Johnson and S.L. Hulbert, Rev. Sci. Inst. (to be published). N.G. Stoffel and P.D. Johnson, Nucl. Inst. and Meth. A234 (1984) p230. P.W. Erdman and E.C. Zipf, Rev. Sci. Inst. 53 (1982) p225. J. Unguris, A. Seiler, R.J. Celotta, D.T. Pierce, P.D. Johnson and N.V. Smith, Phys. Rev. Lett 49 (1982) p1047. D. Pierce, R.J. Celotta, G.-C. Wang, W.N. Unertl, A. Galejs, C.E. Kuyatt and S.R. Mielczarek, Rev. Sci. Instrum. 5 1 (1980) p478. G. Denninger, V. Dose and M. Scheidt, Appl. Phys. 81 (1979) p375. V. Dose, Th. Fauster and R. Schneider, Appl. Phys. A40 (1986) p203. N. Babbe, W. Drube, I. Schafer and M. Skibowski, J. Phys. E: Sci. Instrurn. 18 (1985) p158. G. Chauvet and R. Baptist, J.Electron Spectrosc. 24 (1981) p255. Th. Fauster, D. Straub, J.J. Donelon, D. Grirnm, A. Marx and F.J. Himpsel, Rev. sci. lnst 5 6 (1986) p1212. P.D. Johnson, S.L. Hulbert, R.F. Garrett and M.R. Howells, Rev. Sci. Instrum. 57 (1986) pl324. T.T. Childs, W.A. Royer and N.V. Smith, Rev. Sci. Instrum. 55 (1984) p1613. S.L. Hulbert, P.D. Johnson, N.G. Stoffel, W.A. Royer and N.V. Smith, Phys. Rev. B 30 (1985) p6815.

549

18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.

50.

51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65.

D.P. Woodruff, N.V. Smith, P.D. Johnson and W.A. Royer, Phys. Rev. B 31 (1985)

p4046.

N.V. Smith, C.T. Chen, J.M. Tranquada and P.D. Johnson, Phys. Rev. B 38 (1988)

pl2259-12262.

N.V. Smith, Phys. Rev. B 19 (1979) p5019. N.E. Christensen, Phys. Rev. B 14 (1976) p3446. F.J. Himpsel and D.E. Eastman. Phys. Rev. B 18 (1978) p5236. V. Dose and M. Globl, Chapter 13 in "Polarized Electrons in Surface Physics", Ed. by R. Feder, World Scientific Publishing Co. Pte. Ltd. (1985). D.T. Pierce, A. Seiler, G.S. Feigerle, J.L. Pena and R.J. Celotta, J. of Mag. and Mag. Matls. 54-57 (1986) p617; A. Seiler, C.S. Feigerle, J.L. Pena, R.J. Gelotta and D.T. Pierce, Phys. Rev. B 32 (1985) p7776. M. Donath, Appl. Phys. A49 (1989) p351. H. Scheidt, M. Globl, V. Dose and J. Kirschner, Phys. Rev. Lett 51 (1983) p1688. J. Kirschner, M. Globl, V. Dose and H. Scheidt, Phys. Rev. Lett 53 (1984) p612. P.D. Johnson and N.V. Smith, Phys. Rev. B 27 (1983) p2527. E.G. Mcrae. Rev. Mod. Phys. 51 (1979) p541. R.E. Dietz, E.G. Mcrae and R.L. Campbell, Phys. Rev. Lett 45 (1980) p1280. N.V. Smith and D.P. Woodruff, Prog. Surf. Sci. 21 (1986) p295. D. Straub and F.J. Himpsel Phys. Rev. B 33 (1986) p2256. P.M. Echenique and J.B. Pendry, J. Phys. C 11 (1978) p2065. E.W. Plummer and W. Eberhardt, Adv. Chem. Phys. 49 (1982) p533. E.T. Goodwin, Proc. Camb. Phil. SOC.35 (1939) p205. E.G. Mcrae and M.L. Kane, Surf. Sci. 108 (1981) p435. S.D. Kevan, Phys. Rev. Lett. 50 (1983) p526. D.P. Woodruff, S.L. Hulbert, P.D. Johnson and N.V. Smith, Phys. Rev. B 31 (1985) p4046. M. Weinert, S.L. Hulbert and P.D. Johnson, Phys. Rev. Lett 55 (1985) p2055. N.V. Smith, Phys. Rev. B 32 (1985) p3549. R.F. Garrett and N.V. Smith Phys. Rev. B 33 (1986) p3740. C.T. Chen and N.V. Smith Phys. Rev. B 35 (1987) p5407. R.A. Bartynski, T. Gustafsson and P. Soven. Phys. Rev. B 31 (1985) p4745. D. Straub and F.J. Himpsel, Phys. Rev. B 33 (1986) p2256. W. Jacob, V. Dose, U. Kolac, Th. Fauster and A. Goldmann, Z Phys. 863 (1986) p459. K. Giesen, F. Hage, F.J. Himpsel, H.J. Reiss and W. Steinmann, Phys. Rev. B 35 (1987). p971. S.D. Kevan and R. Gaylord, Phys. Rev. B 36 (1987) p5809. A. Goldmann, V. Dose and G. Borstel, Phys. Rev. B 32 (1985) p1971. S.L. Hulbert, P.D. Johnson, N.G. Stoffel and N.V. Smith, Phys. Rev. B 32 (1985) p3451. K. Giesen, F. Hage, F.J. Himpsel, H.J. Reiss and W. Steinmann, Phys. Rev. Lett. 55 (1985) p300. P. Heimann, H. Nedderrneyer and H.R. Roloff, J. Phys. C10 (1977) L17. G.V. Hansson and S.A. Flodstrom, Phys. Rev. B 18 (1978) p1572. D.P. Woodruff, W.A. Royer and N.V. Smith, Phys. Rev. B 34 (1986) p764. F.J. Himpsel and D.E. Eastman. Phys. Rev. Lett. 41 (1978) p507. A. Goldrnann, M. Donath, W. Altmann and V. Dose, Phys. Rev. B 32 (1985) p837. S.L. Hulbert, P.D. Johnson and M. Weinert, Phys. Rev. B 34 (1986) p3670. G. Thorner, G. Borstel, V. Dose and J. Rogozik, Surf. Sci. 157 (1985) L379. S.L. Hulbert. P.D. Johnson, M. Weinert and R.F. Garrett, Phys. Rev. 6 33 (1986) p760. D. Straub and F.J. Himpsel, Phys. Rev. Lett 52 {3984) ~1922. B. Reihl, K.H. Frank and R.R. Schlitter, Phys. Rev. B 30 (1984) p7328. K. Giesen, F. Hage, F.J. Himpsel, H.J. Reiss, W. Steinmann and N.V. Smith, Phys. Rev. B 35 (1987) p975. R. Drube, V. Dose and A. Goldmann, Surf. Sci.197 (1988) p317. A.J. Viescas and P.D. Johnson, unpublished. S.D. Kevan. Phvs. Rev. B 28 (1983). 02268. M. Donath, M. Globl, B. Senftinger and V. Dose, Sol. Stat. Comrn. 60 (1986) p237.

550

66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79.

80.

81. 82. 83. 84. 85. 86. 87 88.

89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99.

99a.

100. 101.

102. 103. 104. 105. 106. 107. 108. 109. 110.

111.

W. Altmann, V. Dose and A. Goldmann. 2. Phys. 65 (19860 p171. P. Heimann, H. Miosga and H. Neddermeyer, Phys. Rev. Lett 42 (1 979) p801. R. Courths, H. Wern, U. Hau, B. Cord. V. Bachelier and S. Hufner. J. Phys F14 (1984) pl559. G. Binnig, K.H. Frank, H. Fuchs. N. Garcia, B. Reihl. H. Rohrer, F. Salvan and A.R. Williams, Phys. Rev. Lett 55 (1985). p991. R. Drube, V. Dose, H. Derks and W. Heiland, Surf. Sci.214 (1989) L253. R.A. Bartynski and T. Gustafsson, Phys. Rev. B 33 (1986)p6588. S.D. Kevan, Phys. Rev. B 28 (1983) p4822. B. Reihl and K.H. Frank, Phys. Rev. B 31 (1985) p828. B. Reihl, R.R. Schlitter and H. Neff, Phys. Rev. Lett 52 (1984) p1826. This state, previously interpreted in reference 67 as a bulk state reflecting the surface reconstruction, has been reinterpreted as a surface state by N.V. Smith, C.T. Chen, R.A. Bartynski and T. Gustafsson, Surf. Sci. Lett 227 (1990) ‘L130. N. Garcia, B. Reihl, K.H. Frank and A.R. Williams, Phys. Rev. Lett 54 (1985) p591. V. Dose, Surf. Sci. Reports 5 (1985) p337. W.L. Clinton, M.A. Esrick and W.S. Sacks, Phys. Rev. B 31 (1985) p7540. J.B. Pendry. C.G. Larsson and P.M. Echenique, Surf. Sci. 166 (1986) p57. P.M. Echenique, J. Phys. C I 8 (1985) L1133. W. Steinmann, Appl. Phys. A49 (1989) p365. A.V. Hamza and G. Kubiak, J.Vac Sci. Tech. A8 (1990) p2687. N.V. Smith, Phys. Scr. T 17 (1987) p5019. M.K. Debe and D.A. King, Phys. Rev. Lett. 39 (1977) p708. T.E. Felter, R.A. Barker and P.J. Estrup, Phys. Rev. Lett. 38 (1977) ~ 1 1 3 8 . e.g. E. Tossatti, Sol. Stat. Comrn. 25, (1978). ~ 6 3 7 ;J.E. Inglesfield, J. Phys. C12 (1979) p149; H. Krakauer. M. Posternak and A.J. Freeman, Phys. Rev. Lett. 43 (1979) pl885. W. Drube. D. Straub, F.J. Himpsel, P.Soukassian, C.L. Fu and A.J. Freeman, Phys. Rev. 8 3 4 (1986) p8989. S. Ohnishi, A.J. Freeman and E. Wimmer, Phys. Rev. 6 29 (1984) ~ 5 2 6 7 . M.I. Holmes and T. Gustafsson. Phys. Rev. Lett 47 (1981) p443. R.A. Bartynski and T. Gustafsson, Phys. Rev. B 35 (1987) p939. H. Krakauer, Phys. Rev. B. 30 (1984) p6834. X. Pan, A.J. Viescas and P.D. Johnson, Phys. Rev. 8. 40 (1989) ~ 3 4 2 5 . 6.-S. Fang, C.A. Ballentine and J.E. Erskine, Phys. Rev. B. 38 (1988) ~ 4 2 9 9 . N.D. Lang and W. Kohn, Phys. Rev. B 7 (1973) p3541. M. Ortuno and P.M. Echenique, Phys. Rev. B 34 (1986) p5199. P. Gies, Europhysics Lett.1 (1986) p661. R.O. Jones, P.J. Jennings and 0. Jepsen, Phys. Rev. B 29 (1984) p6474. P.J. Jennings, R.O. Jones and M. Weinert, Phys. Rev. B 37 (1988) ~ 6 1 1 3 . N.V. Smith, C.T. Chen and M. Weinert, Phys. Rev. B 40 (1989) ~ 7 5 6 5 . E. Tamura and R. Feder, to be published. J.W.A Sachtler, J.P. Biberian and G.A. Somorjai, Surf. Sci. 110 (1981) p43. B.T. Jonker, K.H. Walker, E. Kisker, G.A. Prim and C. Carbone, Phys. Rev. Lett. 57 (1986) p142. W. Drube and F.J. Himpsel, Phys. Rev. B 35 (1987) p4131. R.G. Jordan, W. Drube, D. Straub and F.J. Himpsel, Phys. Rev. B 33 (1986) ~ 5 2 8 0 . C.L. Fu, A.J. Freeman and T. Oguchi, Phys. Rev. Lett. 54 (1985) p2700. S. Blugel, M. Weinert and P.H. Dederichs, Phys. Rev. Lett. 60 (1988) ~ 1 0 7 7 . K.H. Frank, R. Dudde, H.-J. Sagner and W.Eberhardt, Phys. Rev. B 39 (1989) p940. W. Eberhardt, F. Greuter and E. W. Plummer, Phys. Rev. Lett. 46 (1981) p1081; F. Greuter, I. Strathy, E. W. Plumrner and W. Eberhardt, Phys. Rev. B 33 (1986) ~ 7 3 6 . J. Tersoff and L.M. Falicov. Phys. Rev. B 24 (1981) p754. M.A. Pick, J.W. Davenport, M. Strongin and G.J. Dienes, Phys. Rev. Lett. 43 (1 979) p286. M. El-Batanouny, M. Strongin and G.P. Williams, Phys. Rev. 6 2 7 (1983) ~ 4 5 8 0 . M.W. Ruckman and M. Strongin, Phys. Rev. B 29 (1984) p7105.

551

112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 125a 126. 127. 128. 129. 130. 131.

132. 133. 134. 135. 136.

137. 138. 139. 140.

141 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158.

X. Pan, P.D. Johnson, M. Weinert, R.E. Watson, J.W. Davenport, G.W. Fernando

and S.L. Hulbert, Phys. Rev. B 38 (1988) p7850. D. Heskett. K.-H Frank, E.E. Koch and H.-J Freund. Phys. Rev. B 36 (1987) p1276. D. Heskett. K.-H Frank, K. Horn, E.E. Koch, H.-J Freund, A. Baddorf, K.-D. Tsuei and E.W. Plumrner. Phys. Rev. B 37 (1988) ~ 1 0 3 8 7 . E. Wirnmer, J. Phys. F 1 3 (1983) p2313. S. A. Lindgren and L. Wallden, Phys. Rev. B 38 (1988) ~ 1 0 0 4 4 . S. A. Lindgren and L. Wallden, Phys. Rev. Lett 59 (1987) p3003. S. A. Lindgren and L. Wallden, Phys. Rev. B 38 (1988) p3060. S. A. Lindgren and L. Wallden, Phys. Rev. Lett 61 (1988) p2894. D. Straub, L. Ley and F.J. Himpsel. Phys. Rev. B 33 (1986) p2607. D. Straub, M. Skibowski and F.J. Himpsel, Phys. Rev. B 32 (1985) p5237. D. Straub, M. Skibowski and F.J. Himpsel, J. Vac. Sci. Tech. A3 (1985) p 1484 K.O. Magnusson, U.O. Karlsson, D. Straub, S.A. Flodstrom and F.J. Himpsel, Phys. Rev. B 36 (1987) p6566. W. Drube,D. Straub and F.J. Hirnpsel, Phys. Rev. B 35 (1987) ~ 5 5 6 3 . G.P. Williams, F. Cerrina. G.J. Lapeyre, J.R. Anderson, R.J. Smith and J. Hermanson, Phys. Rev. B 34 (1986) p5548. J.R. Chelikovsky and M.L. Cohen. Phys. Rev. B 14 (1976) p556. F.J. Hirnpsel and Th. Fauster, J. Vac. Sci. Tech. A2 (1984) p1484. D. Straub. L. Ley and F.J. Himpsel, Phys. Rev. Lett 54 (1985) p142. R.M. Tromp, R.J. Hamers and J.E. Demuth, Science 234 (1986) p304. J.M. Nicholls, F. Salvan and B. Reihl. Surf. Sci. 178 (1986) p10. R. Ludeke.D. Straub, F.J. Himpsel and G. Landgren, J. Vac. Sci. Tech. A 4 (1986) p874. W. Drube and FJ. Himpsel, Phys. Rev. B 37 (1988) p855. 2. Lenac, M. SunjiC , H. Conrad and M.E. Kordesh, Phys. Rev. B 36 (1987) p9500. C.T. Chen and N.V. Smith, Phys. Rev. B 40 (1989) p7487. F.J. Himpsel and Th. Fauster, Phys. Rev. Lett 49 (1982) p1583. H. Scheidt, M. Glob1 and V. Dose, Surf. Sci. 123 (1982) L728. W. Altmann, K. Dessinger, M. Donath, V. Dose, A. Goldrnann and H. Scheidt, Surf. Sci. 151 (1985) L185. K. Dessinger, V. Dose, A. Goldmann, W. Jacob and H. Scheidt, Surf. Sci 154 (1985) p695. W. Jacob, V. Dose and A. Goldmann, Appl. Phys. A41 (1986) p145. L.E. Klebanoff, R.K. Jones, D.T. Pierce and R.J. Celotta, Phys. Rev. B 36 (1987) p784. K.Y. Yu, W.E. Spicer, 1. Lindau, P. Pianetta and S.F. Lin, Surf. Sci. 57 (1976) p157; G.G. Tibbets, J.M. Burkstrand and J.C. Tracy, Phys. Rev. B 15 (1977) p3652. G. Schonhense, M. Donath, U. Kolac and V. Dose, Surf. Sci. 206 (1988) L888. A. Liebsch, Phys. Rev. B 17 (1978) p1653. G. Kaindl, T.C. Chiang, D.E. Eastman and F.J. Himpsel, Phys. Rev. Lett 45 (1980) ~ 1 8 0 8 . K. Wandelt, J. Vac. Sci. Tech. A2 (1984) p802. K. Wandelt and J. Hulse, J. Chem. Phys. 80 (1984) p1340. K. Horn, K.H. Frank, J.A. Wilder and B. Reihl, Phys. Rev. Lett 57 (1986) p1064. K. Wandelt, W. Jacob, N. Memrnel and V.Dose, Phys. Rev. Lett 57 (1986) p1643. E. Bertel, W. Jacob and V. Dose, Appl. Phys. A 44 (1987) p93. G.J. Blyholder, J. Phys. Chem. 68 (1964) p2772. Ph. Avouris, P.S.Bagus and C.J. Nelin, J. Electron Spectrosc. Relat. Phenomena 38 (1986) p269. Th. Fauster and F.J. Himpsel, Phys. Rev. B 27 (1983) p1390. P.D. Johnson and S.L. Hulbert, Phys. Rev. B 35 (1987) p9427. F.J. Himpsel, J. Phys. Chem Solids 49 (1988) p3. G.J. Schulz, Rev. Mod. Phys. 45 (1973) p423. A compilation of the infra red stretch frequencies is given in S. Ishi, Y. Ohno and B. Viswanathan, Surf. Sci. 161 (1985) p349. J.E. Dernufh, D. Schneisser and Ph. Avouris, Phys. Rev. Lett 47 (1981), p 1166 J. Rogozik, J. Kijppers and V. Dose, Surf. Sci. 148 (1985) L653. C.S. Feigerle, A. Seiler, J.L. Pena, R.J. Celotta and D.T. Pierce, Phys. Rev. Lett 56 (1 986) p2207.

552 159. 160. 161. 162. 163. 164. 165. 166 167. 168. 169 170 171. 172. 173. 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187.

188. 189. 190. 191. 192. 193.

S. Ferrer, K.H. Frank and B. Reihl, Surf. Sci. 162 (1985) p264. J. Rogozik, V. Dose, K.C. Prince, A.M. Bradshaw, P.S. Bagus. K. Hennann and Ph. Avouris, Phys. Rev. B 32 (1985) p4296. B. Gumhalter, Surf. Sci. 157 (1985) L355. B. Gumhalter, K. Wandelt and Ph. Avouris. Phys. Rev. B 37 (1988) p8048. K.H. Frank, H.-J. Sagner,E.E. Koch and W.Eberhardt, Phys. Rev. B 38 (1988) p8501. H.J. Freund, J. Rogozik, V. Dose and M. Neurnann, Surf. Sci. 175 (1986) p651. N. Memmel, G. Rangelow, E. Bertel, V. Dose, K. Kometer and N. Rosch, Phys. Rev. Lett 63 (1989) p1884. H. Kuhlenbeck, H.B. Saalfeld, M. Neumann, H. J. Freund and E.W. Plurnmer, Appl. Phys. A 44 (1987) p83; H. Kuhlenbeck, H.B. Saalfeld, U. Buskotte, M. Neurnann, H. -J. Freund and E.W. Plurnmer, Phys. Rev. B 39 (1989) p3475. C. Benndorf, E. Bertel, V. Dose, W. Jacob, N. Mernmel and J. Rogozik. Surf. Sci. 191 (1987) p455. M.P. Kishinova. G. Pirug and H.P. Bonzel, Surf. Sci. 133 (1983) p321. D. Heskett, E.W. Plurnmer. R.A. dePaola and W. Eberhardt. Phys. Rev. B 33 (1986) p5171. J.K. Norskov, S. Holloway and N.D. Lang, Surf. Sci. 137 (1984) p65. D.E. Peebles. E.L. Hardegree and J.M. White, Surf. Sci. 148 (1984) p635. H. Conrad, G. Ertl, J. Kijppers and E.E. latta, Surf. Sci. 65 (1977) p235. I.P. Batra and C.R. Brundle, Surf. Sci. 57 (1976) p12. R.J. Smith, J. Anderson and G.J. Lapeyre, Phys. Rev. B 22 (1980) p632. N.B. Brookes. A. Clarke and P.D. Johnson, Phys. Rev. Lett 63 (1989) p2764. D.W. Turner, C. Baker, A.D. Baker and C.R. Brundle, "Molecular Photoelectron Spectroscopy', (Wiley-lnterscience, London, 1970). K. P. Huber and G. Herzberg, "Constants of Diatomic Molecules", (Van NostrandReinhold, New York.1979). P.D. Johnson, H.H. Farrell and N.V. Smith, Vacuum 33 (1983) p775. Y. Jugnet, F.J. Himpsel, Ph. Avouris and E.E. Koch, Phys. Rev. Lett 53 (1984) p198. J.L. Dehmer and D. Dill, Phys. Rev. Lett. 35 (1975) p213. C.L. Allyn, T. Gustafsson and E.W. Plurnmer, Solid State Commun. 28 (1978) p85. J. Stohr and R. Jaeger, Phys. Rev. B 26 (1982) p4111. C.L. Allyn, T. Gustafsson and E.W. Plummer, Chem. Phys. Lett. 47 (1977) p127. S.L. Hulbert, Xiaohe Pan and P.D. Johnson, Phys. Rev. B 35 (1987) ~ 7 7 1 0 . e.g. T.S. Jones and N.V. Richardson, Phys. Rev. Lett 61 (1988), p 1752; P.J. Rous, E.T. Jensen and R.E. Palmer, Phys. Rev. Lett 63 (1989) p2496. J. Stohr, J.L. Gland, W. Eberhardt, D. Outka, R.J. Madix, F. Sette, R.J. Koestner and U. Dobler, Phys. Rev. Lett 51 (1983) p2414. G. Wendin and K. Nuroh, Phys. Rev. Lett 39 (1977), p 48; K. Nuroh and G. Wendin, Phys. Rev. B 24 (1981) p5533; G. Wendin, in " Giant Resonances in Atoms, Molecules and Solids", NATO AS1 Series B 151, eds. J.P. Connerade, J. -M. Esteva and R.C. Karnatak, (Plenum Press, 1987) p171. W. Drube and F.J. Himpsel, Phys. Rev. Lett 60 (1988) p140. Y. Hu, T.J. Wagener, Y. Gao, H.M. Meyer and J.H. Weaver, Phys. Rev. B 38 (1988) p3037. W. Drube, F.J. Hirnpsel and P.J. Feibelman, Phys. Rev. Lett 60 (1988) ~ 2 0 7 0 . J.H. Weaver, D.W. Lynch and C.G. Olsen, Phys. Rev. B 7 (1973) p4311. T.J. Wagener, Yongjun Hu, Y. Gao, M.B. Jost, J. H. Weaver, N.D. Spencer and K.C. Goretta, Phys. Rev. B 39 (1989), p 2928; H.M. Meyer 111, T.J. Wagener , J. H. Weaver, and D.S. Ginley, Phys. Rev. B 39 (1989) p7343. C.G. Olsen, R. Liu, A. -B. Yang, D. W. Lynch, A.J. Arko, R.S. List, B.W. Veal, Y.C. Chang, P.Z. Jiang and A.P. Paulikas, Science 245 (1989) p731.