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Spectroscopy of metal surface states by inverse photoemission
Progress in Surface Science, Vol. 42, pp. 75-88 Printed in the U.S.A. All rights reserved.
0079-6816/93 $24.00 + .00 Copyright © 1993 Pergamon Press Ltd.
Spectroscopy of Metal Surface States by Inverse Photoemission N. M e m m e l
MPi fftr Plasmaphysik, Euratom Association, W-8046 Garching, Germany
Abstract In the past decade inverse photoemission has proved to be a technique well suited to study unoccupied bulk and:surface electronic states of solids I. This paper presents a brief review focusing on the spectroscopy of surface states on metal surfaces and how these states are influenced by simple adsorbates, surface reconstructions or the presence of a ferromagnetic substmte. The experimental observations are discussed within the framework of a nearly free electron model of surface states.
Contents I. Introduction 2. Inverse Photoemission - Idea and Experiment 3. Surface State Model 4. Clean and Adsorbate Covered Surfaces 5. Reconstructed Surfaces 6. Ferromagnetic Surfaces 7. Summary and Outlook
Abbreviations Evac
vacuum energy
EF
Fermi energy
IPE
inverse photoemission
ML
monolayer
PBS
projected bulk band structure
SBZ
surface Brillouin zone
75
76
N. Memmel
1. I n t r o d u c t i o n Sixty years ago - in 1932 - Tamm 2 discovered that electrons can be confined to some region in space not only by the walls of a potential well, but also by a quantum well with one wall replaced by a semi-infinite periodic potential. Such a potential well is the simplest model of a crystalline surface. Provided the electron energy is below the vacuum level and falls into a gap of the energy spectrum of the infinite crystal - so that the electron can neither escape to the vacuum nor penetrate into the crystal - the electron forms a bound state at the surface ("surface state"). Its wave function decays exponentially into the vacuum and into the crystal. Tamm's theoretical work was soon refined and generalized by Maue 3, Goodwin, 4 Shockley 5 and others. But it took some 40 or even .50 years until metal surface states could be investigated experimentally by electron spectroscopy: occupied surface states by photoemission (1970) 6 and unoccupied surface states by inverse photoemission (1984) 7. Since then a lot of work has been devoted to the exploration of surface states and a there is a wealth of data available on surface states on clean metal surfaces8. Surface states are localized near the surface and are therefore sensitive to changes in the surface potential well. Starting from the properties of clean metal surface states, we show how modifications of the surface by simple adsorbates and/or by surface reconstruction are manifested as changes of the twodimensional surface electronic structure. Furthermore, spin-resolved measurements of surface states yield information about the magnetic behaviour of the surfaces of ferromagnetic materials.
2. I n v e r s e P h o t o e m i s s i o n - I d e a a n d E x p e r i m e n t The term inverse photoemission denotes a Bremsstrahlung experiment at electron and photon energies in the ultraviolet range. 9 An electron beam with well-defined energy and momentum is directed onto the sample. At the sample the electrons can undergo radiative transitions from their initial state with energy Ei to a lower-lying unoccupied state with a final state energy Ef (fig. I). The photons emitted in this process are energy analyzed in the detector. The energy of the final state is given by energy conservation as the difference between the known incident electron energy Ei and the measured photon energy ho~ E f = Ei - hto.
(2.1)
The existence of electronic states at various final state energies Ef can be probed in two ways: Either the incident electron energy Ei is kept fixed and the photon detection energy is varied or the the photon energy is kept fixed and the incident electron energy is swept through (isochromatic mode). Maxima in the photon count rate are observed if a final state exists whose energy Ef satisfies equation (2.1). As the final state has to be unoccupied, IPE probes states with energies above the Fermi energy EF.
Inverse PhotoemissionSpectroscopy
77
E
11~
Eva( EF ~
~ k
Fig. 1. Principle of Inverse Photoemission.
Besides energy conservation also "momentum" or wavevector conservation applies, which, in a periodic solid, reads as kf-- ki- q- G
,
(2.2)
where k i and k f denote the electron wave vector in the initial and final state, respectively: q is the wave vector of the photon and G the reciprocal lattice vector exchanged in the transition. In the ultraviolet range the photon wave vector q is three orders of magnitude smaller than the typical dimension of the Brillouin zone. The transition therefore appears as a vertical, direct transition in the reduced zone scheme of the solid's band structure (where the exchange of reciprocal lattice vectors is already included) and equation (2.2) simplifies to k f - - ki •
(2.3)
Therefore it seems quite simple to map the energy vs. wave vector dispersion Ef(kf) of the electron's final state by varying the incident momentum hki. However, upon approaching the surface the electron feels an attractive force towards the crystal and its wave vector component perpendicular to the surface is increased in an unknown way. Only the component parallel to the surface is conserved, i.e~ it is the same inside and outside the solid, and can therefore be controlled by experiment according to kll =
2/~t__~2• Eki n. sinO = ~12m. h2 (~E , - qb). sin O
where Ekin is the electron's kinetic energy, O the angle of incidence and •
(2.4) the sample work
function. The fact that only kll is directly accessible to the experiment complicates the determination of the E vs. k dispersion for hulk states. Triangulation or symmetry methods therefore have to be used for an absolute k-determination "). For the spectroscopy of surface states, however, this imposes no restrictions since these states are only two-dimensional in nature and only disperse with kl
78
N. M0mmel
The present experiments were carried out in the isochromatic mode using an Erdmann-Zipf-type electron gun II with BaO cathode and two energy selective Geiger-Miiller counters with SrF2 entrance windows and iodine (plus Ar puffer gas) filling, resulting in a detection energy of 9.4 eV. The overall resolution amounts to 0.4 eV 12. The angle of incidence O and thereby kll can be varied by rotating the sample. The two counters are mounted at fixed angles of 40 ° and 90 ° relative to the electron gun. The simultaneous use of two counters offers several advantages: First, it increases the detection efficiency; second, it delivers information about the radiation characteristic of the observed transition and thereby about the symmetry of the final state; and, third, it increases the apparent energy resolution in cases of overlapping transitions with different radiation characteristics 13. The spin-resolved measurements were carried out using the spin-polarized electron source described in Ref. 14. Basically, it consists of a negative electron affinity GaAs photocathode illuminated by a circularly polarized laser beam. The spin polarization can be reversed by reversing the helicity of the incoming laser light. A spin polarization of 30% is achieved. The beam currents are similar to those of non spin resolved electron sources. Therefore spin resolution is achieved without any loss in signal intensity.
3. S u r f a c e S t a t e C a l c u l a t i o n s The measured surface state energies are compared with calculations using a simplified version t5 of the surface state model of Echenique and Pendry 16. A nearly free electron two-band approximation is used to descripe the semi-infinite periodic crystal. In this approximation, besides the effective crystal potential V0, only a single component 2VG-cos(Gr) of the Fourier expansion of the periodic crystal potential is taken into account, which gives rise to an energy gap in the band structure of width 2VG. The values of V0 and V G are chosen such as to reproduce the position and width of the gap in the PBS of the respective substrate. In the immediate surface region (which we can think of as part of the outermost layer) we use a flat potential of depth V0 and width d, joined in the vacuum region by an image potential barrier decaying as 1/4z towards the vacuum level Evac (see fig. 2a, left). As we are mainly interested in changes of the surface state energies, e.g. due to adsorption or reconstruction, the value of d is used to fit the measured surface state energies of the clean surface. For gaps near the centre of the SBZ the reciprocal lattice vector G associated with this gap has only a component perpendicular to the surface. This effectively reduces the model to a onedimensional problem with a free-electron-like E vs. kll dispersion of the corresponding surface states. The simple model yields crystal induced surface states as well as the so-called image states, which exist owing to the long range Coulomb image potential in the vacuum region. The wave functions of crystal induced states are mainly concentrated in the surface layer, whereas image
Inverse Photoemission Spectroscopy potential induced states are mainly located a few/~ outside the crystal in the vacuum. Analogously to the hydrogen atom, the image states form a Rydberg-like series converging towards the vaccum energy Evac. For gaps near the SBZ boundaries - the ones mainly discussed in this paper - the following changes have to be considered: First, the respective reciprocal lattice vector G in this case has also a component GIt parallel to the surface. The pseudopotential V0+ 2VG.cos(Gr) inside the crystal therefore varies parallel to the surface as well. As discussed in the next section this affects the surface state dispersion. Owing to the lower symmetry at the zone boundary there exists twice the number of surface states with alternating odd and even parity with respect to the mirror operation rll ---"-rll. Furthermore, as the kinetic energy associated with the electron's momentum parallel to the surface cannot be used to overcome the vacuum potential barrier, bound surface states exist, if the energy is below the "escape threshhold" Evac + h2 . . k 2 2m '1
or
t, 2 . ( k l l _ G l l ) 2 Evac + 2"-'~
whichever is lower. Consequently, the Rydberg series of image states now converges towards this energy.
4. Clean and Adsorbate Covered Surfaces In this section we focus on the surface state dispersions and their modifications by one of the simplest adsorbate systems conceivable, viz. the adsorption of a monolayer of alkali-metal. The concepts are illustrated for the adsorption of a sodium monolayer on a Ni(110) surface. The discussion proceeds in three steps: First we discuss the properties of the clean metal surface states, then we examine the band structure of a hypothetical unsupported Na monolayer in vacuum and finally we combine the two results to the two-dimensional band structure of a Na monolayer on Ni(110). For the clean surface the experimental data, already condensed in an E vs. kit diagram, are displayed as open circles in fig. 2a (right) along the FY azimuth of the SBZ. Also shown are the PBS (grey) with the prominent gap around ~ just above EF and the calculated surface state bands (solid lines) in this gap. The experimentally observed dispersion behaviour is reproduced quite well by the model calculations: If the surface state energy is close to the "escape threshhold" (dashed lines in fig. 2, right); the dispersion is free-electron-like since the electron wave function is mainly located outside the crystal in the region with no potential corrugation parallel to the surface. If, however, the surface state energy is close to a gap boundary, the electron wave function extends appreciably into the crystal and the surface state dispersion approximates the dispersion of the bulk bands which define the gap.
79
80
N. Memmel
r
(a) N i ( l l O ) c l e a n
~
Evac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EF
J
...................... ¢--/---------------------
V
V
i-d'i
Y
~
6
-- ,:j,iiil ~i~i i i i i i i~ 4 .....iik . . . . ~ii~iiiiiiiiiiiiiii]i~i~iiiiiiiik° s :4!iiii~i!~!i~!~i:i
,,..,,
= = z
" ...............
0
:%@~i~@~!iiiiii~i~ii
(b) unsupported Na monolayer Evac . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I- 3.0A -~ I
I
Z
r
Y
p
(c) Na monolayer on Ni(llO) Evac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EF
. . . . . . . . . . . . . . . . . . . . . . f . . . . . . ~. . . . . .-~---------V0 3.2eV ~~ /~ /~ A I ½ ~
2vo/\
/\
' / \ / \ / H H
,J v
/I
I I
i
i
i
i
I
>04 i
v j -],- d,--i -j2.25A-I . i
"-"
""
!
f
6
~
z
2
0
0.5
1.0
1.5
k, (A-b Fig. 2. Model potentials (left) used for the surface state calculations and E(kll) dispersions (right) for (a) the clean Ni(110) surface, (b) an unsupported Na monolayer in vacuum and (c) a Na monolayer on Ni(i 10). Open circles denote experimental data points, solid lines the results from the surface state calculations. Dotted lines in (b) are from FLAPW calculations. The size of the experimental data points indicates the maximum intensity with which the transition is observed in any of the different detection geometries. The white (grey) background indicates the gap (allowed energy range) of the PBS of the clean surface.
Inverse PhotoemissionSpectroscopy in the second step, let us briefly consider a free Na monolayer in vacuum. The band structure of such a system as obtained from self-consistent FLAPW calculations 1"7is displayed by the dotted lines in fig. 2b, fight panel. As can immediately be seen the various bands disperse nearly freeelectron-like with only small gaps at the SBZ boundary. Indeed, the position and dispersion of these bands are nearly perfectly reproduced by the energy bands (solid lines in fig 2b, right) of the simple "one-dimensional" potential well depicted in the left part of this figurelS: A flat potential 3/~ wide (i.e. the distance between two densely packed layers in the Na bulk) and 3.2 eV deep (i.e. the effective Na potential in free electron theory), confined on both sides by image potential barriers with a vacuum energy of 3.1 eV above EF (i.e. the work function of the free Na monolayer). This illustrates that Na - and the alkali-metals in general - are excellent examples of free electron metals not only in three but also in two dimensions. Finally, to calculate the two-dimensional band structure of a Na monolayer on Ni(110) in a first approximation, we replace one of the image potential barriers of the t,nsupported monolayer by the potential representing the Ni(l 10) substrate. The resulting model potential is shown in fig. 2c, left tg. In the right part of this figure the calculated bands (solid lines) are compared with the experimental data points (open circles). The agreement is surprisingly good considering the simplicity of the model. The deviations between theory and experiment are less than 0.5 eV. The dispersion of the lowest three states in the gap is generally quite weak. This indicates that the electron wave function is roughly evenly distributed between the periodic substrate and the "onedimensional" potential region with no potential corrugation parallel to the surface, in particular the Na overlayer. In the language of the chemist these bands would therefore be termed hybrid bands originating from the surface states of the clean surface and the alkali-metal states of the free monolayer. In a number of recent publications 2° about alkali-metal overlayers on various substrates the measured alkali-metal induced bands were often, sometimes successfully, compared with the freeelectron-like bands of unsupported alkali-metal monolayers. This is in apparent contradiction to the present results, which clearly show that - at least for substrates with large band gaps in the PBS the strongly varying pseudopotential of the substrate has to be taken into account for a realistic description of the band dispersion. However, the above-mentioned experiments can also be understood in the present model since they were performed either on substrates with band gaps near F, where the simple model would also yield a free-electron-like dispersion, or on jellium-like substrates, which, owing to their small pseudopotential corrugation, only slightly affect the dispersion of the alkali-metal bands 21.
81
82
N. Memmel
5. Reconstructed Surfaces The adsorption of Na on Ni(l 10) also provides a convenient system to study the effects of surface reconstruction on the surface electronic structure. At s u b m o n o l a y e r c o v e r a g e s the adsorption of Na induces a missing row reconstruction of the Ni substrate. Owing to the large mass transport involved in the missing row reconstruction this type of reconstruction is activated and can be suppressed at low temperatures, so that both the unreconstructed and reconstructed surfaces can be prepared and directly compared with each other. The reconstructed Ni surface exhibts a series of ( I xn) reconstructions 22. In the initial stage of Na adsorption every n-th Ni row is removed and replaced by Na atoms. At intermediate Na coverages
a5 v
.=
0
2
E-EF
4
(eV)
6
0
2
E-EF
4
(eV)
6
0
2
E-E~
4
6
(eV)
Fig. 3. IPE spectra taken at the F-point of the SBZ for various coverages of Na on a cold, non reconstructed (left panel) and annealed, reconstructing Ni(110) surface (central panel). Coverages are given in fractions of a densely packed Na monolayer. Right panel: IPE spectra taken close to the Y-point of the SBZ for various coverages of hydrogen adsorbed at z 100 K on a Ni(110) surface. Coverages are given relatively to the number of Ni atoms in the outermost layer. The white (grey) background indicates the gap (allowed energy range) of the PBS of the clean surface.
Inverse PhotoemissionSpectroscopy
83
the familiar (lx2) reconstruction is observed where already every second Ni row is removed. At higher coverages only every n-th Ni row is left in place until finally at monolayer coverage all Ni rows are removed and the surface reverts to the unreconstructed structure. Figure 3 shows IPE spectra recorded at the ~ - p o i n t of the SBZ for various coverages of Na on Ni(110). The spectra in the left panel are taken on a cold (T -~ 100 K), non-reconstructed surface, the data in the central panel are from an annealed (T _>300 K) reconstructing surface. The most prominent effect of Na adsorption on the non-reconstructed surface is a continuous downward shift of the crystal induced surface state S I of the clean surface. As can be seen, this state gradually develops into the surface state S1 of the surface covered by the Na monolayer, which was already discussed in the previous section. The image state $2 is quenched in the initial stage of adsorption but reappears at lower energies upon further Na deposition. For ONa >- 0.7 a third state is seen in the spectra. The behaviour observed on the reconstructed surface is quite different. Upon the onset of reconstruction at low coverages the surface state SI is strongly attenuated and shifted to higher energies. At intermediate coverage values (0.30_
token, a decrease in the number o f Ni atoms in the outermost substrate laver - as happens during the missing row reconstruction - should increase the surface state energies. Indeed the surface states on the reconstructed surface are always observed at higher energies compared to the unreconstructed surface with the same Na coverage.
84
N. Memmel
The solid lines in fig. 4 (right) show the results of calculations where the reduction in the density of Ni atoms due to the missing row reconstruction was modelled by analog)' with the Na adsorption by shortening the periodic crystal potential linearly with the number of Ni rows removed by the reconstruction. Again the calculations describe the experimental data (solid circles) surprisingly well. Even the appearance of a fiirther surface state at the bottom of the gap is reproduced by the cal cul ations. The strange up and down movement of the state SI with increasing Na coverage can now be understood as a consequence of two opposing effects: The increase in Na coverage, which tends to lower the surface state energies, and the simultaneous decrease of Ni rows due to the reconstruction, which tries to raise the surface state energies. At low coverages the reconstruction "wins" since its onset is rather rapid. At intermediate submonolayer coverages the reconstruction is essentially unchanged (low energy electron diffraction shows a (lx2) reconstruction all the time) and the increasing Na coverage causes a downshift similar to the cold surface. Near monolayer coverage when the reconstruction is completed the Ni density in the surface layer rapidly changes
6 > ~4 !
0.0
0.5 1.0 Na coverage (ML)
0.0
0.5 1.0 Na coverage (ML)
Fig. 4. Coverage dependence of the surface state energies at ~" on a non reconstructed (left) and a reconstructing Ni(110) surface (right). Symbols denote experimental data points, thick solid lines the results of the model calulations (see text). The topmost curves display the variation of the escape threshhold Evac + h2/2m, kl12 due to the Na induced work functiom change. The white (grey) background indicates the gap (allowed energy range) of the PBS of the clean surface at Y'.
Inverse PhotoemissionSpectroscopy
85
again, leading once more to an increase in surface state energy. For the image state $2 the Na induced work function reduction is also important, leading altogether to a continous downward shift. Analogous behaviour is found on Cu( l 10) 24 and A g ( l lO) 25, where the same kind of r e construction is induced by Na adsorption. Hydrogen adsorption on Ni(I l 0) at low temperatures yields a continuous downward shift of the crystal induced surface'state (fig. 3, right panel) similar to Na adsorption on the non-reconstructed surface. Although the' N i ( l l 0 ) surface undergoes a pairing row reconstruction 2t' at hydrogen coverages above 1 ML, no significant break in the smooth downward shift of the surface state is observed at this coverage. This can be easily understood in the context of our simple lateral averaging model. The hydrogen induced pairing row reconstrtiction does not change the atomic density in the outermost layer and therefore the onset of reconstrtlction does not alter (or only slightly alters) the surface state energies, so that a continuous downward shift due to hydrogen adsorption is always observed. Upon annealing the H-covered surface a missing row reconstruction occurs and the surface states shift to higher energies 27 - as expected from the simple model. The same behaviour is also observed for hydrogen adsorption on Cu( l 10) ~ . Clearly, the pairing row reconstruction also alters the surface electronic structure. But obviously this effect is quite small and is not seen in the present experiments. The missing row reconstruction involving long range mass transport, however, changes the electronic structure quite drastically. This can best be rationalized by considering the various moments of the atomic density distribution in the outermost surface layer: Reconstructions involving long range mass transport already change the 0 th -order term (i.e. the number of atoms) whereas reconstructions that solely change the periodicity only affect higher order terms. The change in atomic density therefore has to be considered first. Then, in a second step, the consequences of the changed periodicity - backfolding of bands into the new SBZ and interaction of the backfolded with the "original" bands - can be included. In the present case the first step is already sufficient for a qualitative understanding of the observed surface state shifts.
6. Ferromagnetic Surfaces As magnetism is a collective phenomenon, the question immediately arises whether the reduced symmetry and coordination number of the atoms at the surface yield different magnetic behaviour of the outermost surface layer(s) in relation to the bulk. A further rather general question concerns the interaction of electrons with a nearby ferromagnetic sample: To what extent does an electron close to the surface of a ferromagnetic sample experience a spin dependent potential? The answer to the first question can be found by studying the spin splitting of crystal induced surface States, since the wave functions of these states peak in the outermost atomic layer, whereas an answer to the second question can be given by measuring the spin splitting of image potential induced surface states because these states are mainly located a few .~ in front the surface.
86
N. Memmel
Figure 5 shows spin resolved IPE spectra for a crystal induced surface state in the gap of the PBS close to the X-point of the Ni(110) SBZ. At X" the s-like upper band gap boundary shows an exchange splitting of ~200 meV due to hybridization with the magnetic d bands. The p-like lower edge of the band gap shows a smaller spin splitting since hybridization with the d bands is symmetry forbidden. The experimentally observed spin splitting of the surface state amounts to 170 + 30 meV 29. This value is similar to the exchange splitting of the bulk bands. We therefore conclude that the magnetization in the surface layer is not significantly different from the bulk. in particular, this experiment disproves the existence of magnetically "dead" surface layers. This has also been shown for the (001) and (111) surfaces of Ni 3°. Spin resolved IPE data for an image potential induced surface state are displayed in fig. 6. The measurements were performed on a Ni(111) surface at the F-point of the SBZ. The first member of the Rydberg-like series of images states is resolved at an energy of ~ 4.6 eV, close to the vacuum energy of 5.3 eV. As can be seen the peaks for spin-up and spin-down electrons exhibit a small, but significant energy difference. A careful analysis yields a value of 18 + 3 meV 31. This spin splitting, however, does not necessarily mean that the potential a few/~ in front of the crystal surface is spin dependent: Model calculations as described in section 3, using a spin dependent crystal potential (to
image potential surface state
crystal induced surface state
N I
Ni(! 10) FX "r-
O= 0°
O = 45 °
0
t~
2
4
6
8
,/%, |
5.0
i
J
i
i
J
6.0 7.0 E - E F (eV)
Fig. 5. Inset: Spin averaged IPE spectrum for Ni(110) near ~ . The peak at ~ 6 eV denoted by SS is due to a crystal induced surface state in the gap at 3 . Main figure: Enlarged and spin resolved plot of the crystal induced surface state emission SS.
0
2
4
6
8
4
!
4.2
4.4 4.6 E - E F (eV)
4.8
Fig. 6. Inset: Spin averaged IPE spectrum for Ni(I 11) at normal electron incidence. The feature at ~ 4.6 eV is due to a image potential surface state in the gap at F. Main figure: Enlarged and spin resolved plot of the image potential induced surface state emission IS.
Inverse PhotoemissionSpectroscopy
87
describe the spin splitting of the bulk bands correctly) but a spin independent harrier potential in front of the surface, yield a splitting of = 13 meV in reasonable agreement with experiment. The measured spin splitting of 18 _+3 meV can therefore already be explained by the small extent to which the image state wave function penetrates into the crystal. No spin dependent vacuum barrier is required to explain the measured result. This finding is also supported by calculations using the more sophisticated one-step model of inverse photoemission_~2.
Summary and Outlook Owing to their localization near the surface, surface states are sensitive probes of the solidvacuum interface. It was demonstrated that modification of the surface either chemically by adsorbates or geometrically by a surface reconstruction changes the energy position and dispersion of the surface states. Furthermore, the spin splitting of surface states was used to study the magnetic properties at and close to the surface of ferromagnetic substrates. Throughout this work surface states were mainly treated as "passive spectators" probing the surface properties. However, the question arises whether and in what cases the surface states are "active ingredients" in determining surface properties of metals such as chemical reactivity, surface geometry or surface magnetism. For example, surface or quantum well states near the Fermi level have been snggested as being responsible for adsorbate induced reconstructions 33 or for the oscillatory magnetic coupling observed in thin film epitaxy 34. Electron spectroscopies offer a promising way to elucidate the role of surface states as possible driving forces for these processes.
Acknowledgement It is a pleasure to thank E. Bertel for many stimulating discussions and to acknowledge the pleasant collaboration with U. Bischler, M. Donath, M.L. Hirschinger, F. Passek, G. Rangelov, P. Sandl and V. Dose.
88
N. Memmel
References I 2 3 4 5 6 7 8 9 lo tJ 12 J3 14 Ls l~, 17 18 19 20
21 22 23 24 25 2~, 2"7 28 29 3o 31 ?,2 33 34
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0079-6816/93 $24.00 + .00 Copyright © 1993 Pergamon Press Ltd.
Spectroscopy of Metal Surface States by Inverse Photoemission N. M e m m e l
MPi fftr Plasmaphysik, Euratom Association, W-8046 Garching, Germany
Abstract In the past decade inverse photoemission has proved to be a technique well suited to study unoccupied bulk and:surface electronic states of solids I. This paper presents a brief review focusing on the spectroscopy of surface states on metal surfaces and how these states are influenced by simple adsorbates, surface reconstructions or the presence of a ferromagnetic substmte. The experimental observations are discussed within the framework of a nearly free electron model of surface states.
Contents I. Introduction 2. Inverse Photoemission - Idea and Experiment 3. Surface State Model 4. Clean and Adsorbate Covered Surfaces 5. Reconstructed Surfaces 6. Ferromagnetic Surfaces 7. Summary and Outlook
Abbreviations Evac
vacuum energy
EF
Fermi energy
IPE
inverse photoemission
ML
monolayer
PBS
projected bulk band structure
SBZ
surface Brillouin zone
75
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N. Memmel
1. I n t r o d u c t i o n Sixty years ago - in 1932 - Tamm 2 discovered that electrons can be confined to some region in space not only by the walls of a potential well, but also by a quantum well with one wall replaced by a semi-infinite periodic potential. Such a potential well is the simplest model of a crystalline surface. Provided the electron energy is below the vacuum level and falls into a gap of the energy spectrum of the infinite crystal - so that the electron can neither escape to the vacuum nor penetrate into the crystal - the electron forms a bound state at the surface ("surface state"). Its wave function decays exponentially into the vacuum and into the crystal. Tamm's theoretical work was soon refined and generalized by Maue 3, Goodwin, 4 Shockley 5 and others. But it took some 40 or even .50 years until metal surface states could be investigated experimentally by electron spectroscopy: occupied surface states by photoemission (1970) 6 and unoccupied surface states by inverse photoemission (1984) 7. Since then a lot of work has been devoted to the exploration of surface states and a there is a wealth of data available on surface states on clean metal surfaces8. Surface states are localized near the surface and are therefore sensitive to changes in the surface potential well. Starting from the properties of clean metal surface states, we show how modifications of the surface by simple adsorbates and/or by surface reconstruction are manifested as changes of the twodimensional surface electronic structure. Furthermore, spin-resolved measurements of surface states yield information about the magnetic behaviour of the surfaces of ferromagnetic materials.
2. I n v e r s e P h o t o e m i s s i o n - I d e a a n d E x p e r i m e n t The term inverse photoemission denotes a Bremsstrahlung experiment at electron and photon energies in the ultraviolet range. 9 An electron beam with well-defined energy and momentum is directed onto the sample. At the sample the electrons can undergo radiative transitions from their initial state with energy Ei to a lower-lying unoccupied state with a final state energy Ef (fig. I). The photons emitted in this process are energy analyzed in the detector. The energy of the final state is given by energy conservation as the difference between the known incident electron energy Ei and the measured photon energy ho~ E f = Ei - hto.
(2.1)
The existence of electronic states at various final state energies Ef can be probed in two ways: Either the incident electron energy Ei is kept fixed and the photon detection energy is varied or the the photon energy is kept fixed and the incident electron energy is swept through (isochromatic mode). Maxima in the photon count rate are observed if a final state exists whose energy Ef satisfies equation (2.1). As the final state has to be unoccupied, IPE probes states with energies above the Fermi energy EF.
Inverse PhotoemissionSpectroscopy
77
E
11~
Eva( EF ~
~ k
Fig. 1. Principle of Inverse Photoemission.
Besides energy conservation also "momentum" or wavevector conservation applies, which, in a periodic solid, reads as kf-- ki- q- G
,
(2.2)
where k i and k f denote the electron wave vector in the initial and final state, respectively: q is the wave vector of the photon and G the reciprocal lattice vector exchanged in the transition. In the ultraviolet range the photon wave vector q is three orders of magnitude smaller than the typical dimension of the Brillouin zone. The transition therefore appears as a vertical, direct transition in the reduced zone scheme of the solid's band structure (where the exchange of reciprocal lattice vectors is already included) and equation (2.2) simplifies to k f - - ki •
(2.3)
Therefore it seems quite simple to map the energy vs. wave vector dispersion Ef(kf) of the electron's final state by varying the incident momentum hki. However, upon approaching the surface the electron feels an attractive force towards the crystal and its wave vector component perpendicular to the surface is increased in an unknown way. Only the component parallel to the surface is conserved, i.e~ it is the same inside and outside the solid, and can therefore be controlled by experiment according to kll =
2/~t__~2• Eki n. sinO = ~12m. h2 (~E , - qb). sin O
where Ekin is the electron's kinetic energy, O the angle of incidence and •
(2.4) the sample work
function. The fact that only kll is directly accessible to the experiment complicates the determination of the E vs. k dispersion for hulk states. Triangulation or symmetry methods therefore have to be used for an absolute k-determination "). For the spectroscopy of surface states, however, this imposes no restrictions since these states are only two-dimensional in nature and only disperse with kl
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N. M0mmel
The present experiments were carried out in the isochromatic mode using an Erdmann-Zipf-type electron gun II with BaO cathode and two energy selective Geiger-Miiller counters with SrF2 entrance windows and iodine (plus Ar puffer gas) filling, resulting in a detection energy of 9.4 eV. The overall resolution amounts to 0.4 eV 12. The angle of incidence O and thereby kll can be varied by rotating the sample. The two counters are mounted at fixed angles of 40 ° and 90 ° relative to the electron gun. The simultaneous use of two counters offers several advantages: First, it increases the detection efficiency; second, it delivers information about the radiation characteristic of the observed transition and thereby about the symmetry of the final state; and, third, it increases the apparent energy resolution in cases of overlapping transitions with different radiation characteristics 13. The spin-resolved measurements were carried out using the spin-polarized electron source described in Ref. 14. Basically, it consists of a negative electron affinity GaAs photocathode illuminated by a circularly polarized laser beam. The spin polarization can be reversed by reversing the helicity of the incoming laser light. A spin polarization of 30% is achieved. The beam currents are similar to those of non spin resolved electron sources. Therefore spin resolution is achieved without any loss in signal intensity.
3. S u r f a c e S t a t e C a l c u l a t i o n s The measured surface state energies are compared with calculations using a simplified version t5 of the surface state model of Echenique and Pendry 16. A nearly free electron two-band approximation is used to descripe the semi-infinite periodic crystal. In this approximation, besides the effective crystal potential V0, only a single component 2VG-cos(Gr) of the Fourier expansion of the periodic crystal potential is taken into account, which gives rise to an energy gap in the band structure of width 2VG. The values of V0 and V G are chosen such as to reproduce the position and width of the gap in the PBS of the respective substrate. In the immediate surface region (which we can think of as part of the outermost layer) we use a flat potential of depth V0 and width d, joined in the vacuum region by an image potential barrier decaying as 1/4z towards the vacuum level Evac (see fig. 2a, left). As we are mainly interested in changes of the surface state energies, e.g. due to adsorption or reconstruction, the value of d is used to fit the measured surface state energies of the clean surface. For gaps near the centre of the SBZ the reciprocal lattice vector G associated with this gap has only a component perpendicular to the surface. This effectively reduces the model to a onedimensional problem with a free-electron-like E vs. kll dispersion of the corresponding surface states. The simple model yields crystal induced surface states as well as the so-called image states, which exist owing to the long range Coulomb image potential in the vacuum region. The wave functions of crystal induced states are mainly concentrated in the surface layer, whereas image
Inverse Photoemission Spectroscopy potential induced states are mainly located a few/~ outside the crystal in the vacuum. Analogously to the hydrogen atom, the image states form a Rydberg-like series converging towards the vaccum energy Evac. For gaps near the SBZ boundaries - the ones mainly discussed in this paper - the following changes have to be considered: First, the respective reciprocal lattice vector G in this case has also a component GIt parallel to the surface. The pseudopotential V0+ 2VG.cos(Gr) inside the crystal therefore varies parallel to the surface as well. As discussed in the next section this affects the surface state dispersion. Owing to the lower symmetry at the zone boundary there exists twice the number of surface states with alternating odd and even parity with respect to the mirror operation rll ---"-rll. Furthermore, as the kinetic energy associated with the electron's momentum parallel to the surface cannot be used to overcome the vacuum potential barrier, bound surface states exist, if the energy is below the "escape threshhold" Evac + h2 . . k 2 2m '1
or
t, 2 . ( k l l _ G l l ) 2 Evac + 2"-'~
whichever is lower. Consequently, the Rydberg series of image states now converges towards this energy.
4. Clean and Adsorbate Covered Surfaces In this section we focus on the surface state dispersions and their modifications by one of the simplest adsorbate systems conceivable, viz. the adsorption of a monolayer of alkali-metal. The concepts are illustrated for the adsorption of a sodium monolayer on a Ni(110) surface. The discussion proceeds in three steps: First we discuss the properties of the clean metal surface states, then we examine the band structure of a hypothetical unsupported Na monolayer in vacuum and finally we combine the two results to the two-dimensional band structure of a Na monolayer on Ni(110). For the clean surface the experimental data, already condensed in an E vs. kit diagram, are displayed as open circles in fig. 2a (right) along the FY azimuth of the SBZ. Also shown are the PBS (grey) with the prominent gap around ~ just above EF and the calculated surface state bands (solid lines) in this gap. The experimentally observed dispersion behaviour is reproduced quite well by the model calculations: If the surface state energy is close to the "escape threshhold" (dashed lines in fig. 2, right); the dispersion is free-electron-like since the electron wave function is mainly located outside the crystal in the region with no potential corrugation parallel to the surface. If, however, the surface state energy is close to a gap boundary, the electron wave function extends appreciably into the crystal and the surface state dispersion approximates the dispersion of the bulk bands which define the gap.
79
80
N. Memmel
r
(a) N i ( l l O ) c l e a n
~
Evac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EF
J
...................... ¢--/---------------------
V
V
i-d'i
Y
~
6
-- ,:j,iiil ~i~i i i i i i i~ 4 .....iik . . . . ~ii~iiiiiiiiiiiiiii]i~i~iiiiiiiik° s :4!iiii~i!~!i~!~i:i
,,..,,
= = z
" ...............
0
:%@~i~@~!iiiiii~i~ii
(b) unsupported Na monolayer Evac . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I- 3.0A -~ I
I
Z
r
Y
p
(c) Na monolayer on Ni(llO) Evac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EF
. . . . . . . . . . . . . . . . . . . . . . f . . . . . . ~. . . . . .-~---------V0 3.2eV ~~ /~ /~ A I ½ ~
2vo/\
/\
' / \ / \ / H H
,J v
/I
I I
i
i
i
i
I
>04 i
v j -],- d,--i -j2.25A-I . i
"-"
""
!
f
6
~
z
2
0
0.5
1.0
1.5
k, (A-b Fig. 2. Model potentials (left) used for the surface state calculations and E(kll) dispersions (right) for (a) the clean Ni(110) surface, (b) an unsupported Na monolayer in vacuum and (c) a Na monolayer on Ni(i 10). Open circles denote experimental data points, solid lines the results from the surface state calculations. Dotted lines in (b) are from FLAPW calculations. The size of the experimental data points indicates the maximum intensity with which the transition is observed in any of the different detection geometries. The white (grey) background indicates the gap (allowed energy range) of the PBS of the clean surface.
Inverse PhotoemissionSpectroscopy in the second step, let us briefly consider a free Na monolayer in vacuum. The band structure of such a system as obtained from self-consistent FLAPW calculations 1"7is displayed by the dotted lines in fig. 2b, fight panel. As can immediately be seen the various bands disperse nearly freeelectron-like with only small gaps at the SBZ boundary. Indeed, the position and dispersion of these bands are nearly perfectly reproduced by the energy bands (solid lines in fig 2b, right) of the simple "one-dimensional" potential well depicted in the left part of this figurelS: A flat potential 3/~ wide (i.e. the distance between two densely packed layers in the Na bulk) and 3.2 eV deep (i.e. the effective Na potential in free electron theory), confined on both sides by image potential barriers with a vacuum energy of 3.1 eV above EF (i.e. the work function of the free Na monolayer). This illustrates that Na - and the alkali-metals in general - are excellent examples of free electron metals not only in three but also in two dimensions. Finally, to calculate the two-dimensional band structure of a Na monolayer on Ni(110) in a first approximation, we replace one of the image potential barriers of the t,nsupported monolayer by the potential representing the Ni(l 10) substrate. The resulting model potential is shown in fig. 2c, left tg. In the right part of this figure the calculated bands (solid lines) are compared with the experimental data points (open circles). The agreement is surprisingly good considering the simplicity of the model. The deviations between theory and experiment are less than 0.5 eV. The dispersion of the lowest three states in the gap is generally quite weak. This indicates that the electron wave function is roughly evenly distributed between the periodic substrate and the "onedimensional" potential region with no potential corrugation parallel to the surface, in particular the Na overlayer. In the language of the chemist these bands would therefore be termed hybrid bands originating from the surface states of the clean surface and the alkali-metal states of the free monolayer. In a number of recent publications 2° about alkali-metal overlayers on various substrates the measured alkali-metal induced bands were often, sometimes successfully, compared with the freeelectron-like bands of unsupported alkali-metal monolayers. This is in apparent contradiction to the present results, which clearly show that - at least for substrates with large band gaps in the PBS the strongly varying pseudopotential of the substrate has to be taken into account for a realistic description of the band dispersion. However, the above-mentioned experiments can also be understood in the present model since they were performed either on substrates with band gaps near F, where the simple model would also yield a free-electron-like dispersion, or on jellium-like substrates, which, owing to their small pseudopotential corrugation, only slightly affect the dispersion of the alkali-metal bands 21.
81
82
N. Memmel
5. Reconstructed Surfaces The adsorption of Na on Ni(l 10) also provides a convenient system to study the effects of surface reconstruction on the surface electronic structure. At s u b m o n o l a y e r c o v e r a g e s the adsorption of Na induces a missing row reconstruction of the Ni substrate. Owing to the large mass transport involved in the missing row reconstruction this type of reconstruction is activated and can be suppressed at low temperatures, so that both the unreconstructed and reconstructed surfaces can be prepared and directly compared with each other. The reconstructed Ni surface exhibts a series of ( I xn) reconstructions 22. In the initial stage of Na adsorption every n-th Ni row is removed and replaced by Na atoms. At intermediate Na coverages
a5 v
.=
0
2
E-EF
4
(eV)
6
0
2
E-EF
4
(eV)
6
0
2
E-E~
4
6
(eV)
Fig. 3. IPE spectra taken at the F-point of the SBZ for various coverages of Na on a cold, non reconstructed (left panel) and annealed, reconstructing Ni(110) surface (central panel). Coverages are given in fractions of a densely packed Na monolayer. Right panel: IPE spectra taken close to the Y-point of the SBZ for various coverages of hydrogen adsorbed at z 100 K on a Ni(110) surface. Coverages are given relatively to the number of Ni atoms in the outermost layer. The white (grey) background indicates the gap (allowed energy range) of the PBS of the clean surface.
Inverse PhotoemissionSpectroscopy
83
the familiar (lx2) reconstruction is observed where already every second Ni row is removed. At higher coverages only every n-th Ni row is left in place until finally at monolayer coverage all Ni rows are removed and the surface reverts to the unreconstructed structure. Figure 3 shows IPE spectra recorded at the ~ - p o i n t of the SBZ for various coverages of Na on Ni(110). The spectra in the left panel are taken on a cold (T -~ 100 K), non-reconstructed surface, the data in the central panel are from an annealed (T _>300 K) reconstructing surface. The most prominent effect of Na adsorption on the non-reconstructed surface is a continuous downward shift of the crystal induced surface state S I of the clean surface. As can be seen, this state gradually develops into the surface state S1 of the surface covered by the Na monolayer, which was already discussed in the previous section. The image state $2 is quenched in the initial stage of adsorption but reappears at lower energies upon further Na deposition. For ONa >- 0.7 a third state is seen in the spectra. The behaviour observed on the reconstructed surface is quite different. Upon the onset of reconstruction at low coverages the surface state SI is strongly attenuated and shifted to higher energies. At intermediate coverage values (0.30_
token, a decrease in the number o f Ni atoms in the outermost substrate laver - as happens during the missing row reconstruction - should increase the surface state energies. Indeed the surface states on the reconstructed surface are always observed at higher energies compared to the unreconstructed surface with the same Na coverage.
84
N. Memmel
The solid lines in fig. 4 (right) show the results of calculations where the reduction in the density of Ni atoms due to the missing row reconstruction was modelled by analog)' with the Na adsorption by shortening the periodic crystal potential linearly with the number of Ni rows removed by the reconstruction. Again the calculations describe the experimental data (solid circles) surprisingly well. Even the appearance of a fiirther surface state at the bottom of the gap is reproduced by the cal cul ations. The strange up and down movement of the state SI with increasing Na coverage can now be understood as a consequence of two opposing effects: The increase in Na coverage, which tends to lower the surface state energies, and the simultaneous decrease of Ni rows due to the reconstruction, which tries to raise the surface state energies. At low coverages the reconstruction "wins" since its onset is rather rapid. At intermediate submonolayer coverages the reconstruction is essentially unchanged (low energy electron diffraction shows a (lx2) reconstruction all the time) and the increasing Na coverage causes a downshift similar to the cold surface. Near monolayer coverage when the reconstruction is completed the Ni density in the surface layer rapidly changes
6 > ~4 !
0.0
0.5 1.0 Na coverage (ML)
0.0
0.5 1.0 Na coverage (ML)
Fig. 4. Coverage dependence of the surface state energies at ~" on a non reconstructed (left) and a reconstructing Ni(110) surface (right). Symbols denote experimental data points, thick solid lines the results of the model calulations (see text). The topmost curves display the variation of the escape threshhold Evac + h2/2m, kl12 due to the Na induced work functiom change. The white (grey) background indicates the gap (allowed energy range) of the PBS of the clean surface at Y'.
Inverse PhotoemissionSpectroscopy
85
again, leading once more to an increase in surface state energy. For the image state $2 the Na induced work function reduction is also important, leading altogether to a continous downward shift. Analogous behaviour is found on Cu( l 10) 24 and A g ( l lO) 25, where the same kind of r e construction is induced by Na adsorption. Hydrogen adsorption on Ni(I l 0) at low temperatures yields a continuous downward shift of the crystal induced surface'state (fig. 3, right panel) similar to Na adsorption on the non-reconstructed surface. Although the' N i ( l l 0 ) surface undergoes a pairing row reconstruction 2t' at hydrogen coverages above 1 ML, no significant break in the smooth downward shift of the surface state is observed at this coverage. This can be easily understood in the context of our simple lateral averaging model. The hydrogen induced pairing row reconstrtiction does not change the atomic density in the outermost layer and therefore the onset of reconstrtlction does not alter (or only slightly alters) the surface state energies, so that a continuous downward shift due to hydrogen adsorption is always observed. Upon annealing the H-covered surface a missing row reconstruction occurs and the surface states shift to higher energies 27 - as expected from the simple model. The same behaviour is also observed for hydrogen adsorption on Cu( l 10) ~ . Clearly, the pairing row reconstruction also alters the surface electronic structure. But obviously this effect is quite small and is not seen in the present experiments. The missing row reconstruction involving long range mass transport, however, changes the electronic structure quite drastically. This can best be rationalized by considering the various moments of the atomic density distribution in the outermost surface layer: Reconstructions involving long range mass transport already change the 0 th -order term (i.e. the number of atoms) whereas reconstructions that solely change the periodicity only affect higher order terms. The change in atomic density therefore has to be considered first. Then, in a second step, the consequences of the changed periodicity - backfolding of bands into the new SBZ and interaction of the backfolded with the "original" bands - can be included. In the present case the first step is already sufficient for a qualitative understanding of the observed surface state shifts.
6. Ferromagnetic Surfaces As magnetism is a collective phenomenon, the question immediately arises whether the reduced symmetry and coordination number of the atoms at the surface yield different magnetic behaviour of the outermost surface layer(s) in relation to the bulk. A further rather general question concerns the interaction of electrons with a nearby ferromagnetic sample: To what extent does an electron close to the surface of a ferromagnetic sample experience a spin dependent potential? The answer to the first question can be found by studying the spin splitting of crystal induced surface States, since the wave functions of these states peak in the outermost atomic layer, whereas an answer to the second question can be given by measuring the spin splitting of image potential induced surface states because these states are mainly located a few .~ in front the surface.
86
N. Memmel
Figure 5 shows spin resolved IPE spectra for a crystal induced surface state in the gap of the PBS close to the X-point of the Ni(110) SBZ. At X" the s-like upper band gap boundary shows an exchange splitting of ~200 meV due to hybridization with the magnetic d bands. The p-like lower edge of the band gap shows a smaller spin splitting since hybridization with the d bands is symmetry forbidden. The experimentally observed spin splitting of the surface state amounts to 170 + 30 meV 29. This value is similar to the exchange splitting of the bulk bands. We therefore conclude that the magnetization in the surface layer is not significantly different from the bulk. in particular, this experiment disproves the existence of magnetically "dead" surface layers. This has also been shown for the (001) and (111) surfaces of Ni 3°. Spin resolved IPE data for an image potential induced surface state are displayed in fig. 6. The measurements were performed on a Ni(111) surface at the F-point of the SBZ. The first member of the Rydberg-like series of images states is resolved at an energy of ~ 4.6 eV, close to the vacuum energy of 5.3 eV. As can be seen the peaks for spin-up and spin-down electrons exhibit a small, but significant energy difference. A careful analysis yields a value of 18 + 3 meV 31. This spin splitting, however, does not necessarily mean that the potential a few/~ in front of the crystal surface is spin dependent: Model calculations as described in section 3, using a spin dependent crystal potential (to
image potential surface state
crystal induced surface state
N I
Ni(! 10) FX "r-
O= 0°
O = 45 °
0
t~
2
4
6
8
,/%, |
5.0
i
J
i
i
J
6.0 7.0 E - E F (eV)
Fig. 5. Inset: Spin averaged IPE spectrum for Ni(110) near ~ . The peak at ~ 6 eV denoted by SS is due to a crystal induced surface state in the gap at 3 . Main figure: Enlarged and spin resolved plot of the crystal induced surface state emission SS.
0
2
4
6
8
4
!
4.2
4.4 4.6 E - E F (eV)
4.8
Fig. 6. Inset: Spin averaged IPE spectrum for Ni(I 11) at normal electron incidence. The feature at ~ 4.6 eV is due to a image potential surface state in the gap at F. Main figure: Enlarged and spin resolved plot of the image potential induced surface state emission IS.
Inverse PhotoemissionSpectroscopy
87
describe the spin splitting of the bulk bands correctly) but a spin independent harrier potential in front of the surface, yield a splitting of = 13 meV in reasonable agreement with experiment. The measured spin splitting of 18 _+3 meV can therefore already be explained by the small extent to which the image state wave function penetrates into the crystal. No spin dependent vacuum barrier is required to explain the measured result. This finding is also supported by calculations using the more sophisticated one-step model of inverse photoemission_~2.
Summary and Outlook Owing to their localization near the surface, surface states are sensitive probes of the solidvacuum interface. It was demonstrated that modification of the surface either chemically by adsorbates or geometrically by a surface reconstruction changes the energy position and dispersion of the surface states. Furthermore, the spin splitting of surface states was used to study the magnetic properties at and close to the surface of ferromagnetic substrates. Throughout this work surface states were mainly treated as "passive spectators" probing the surface properties. However, the question arises whether and in what cases the surface states are "active ingredients" in determining surface properties of metals such as chemical reactivity, surface geometry or surface magnetism. For example, surface or quantum well states near the Fermi level have been snggested as being responsible for adsorbate induced reconstructions 33 or for the oscillatory magnetic coupling observed in thin film epitaxy 34. Electron spectroscopies offer a promising way to elucidate the role of surface states as possible driving forces for these processes.
Acknowledgement It is a pleasure to thank E. Bertel for many stimulating discussions and to acknowledge the pleasant collaboration with U. Bischler, M. Donath, M.L. Hirschinger, F. Passek, G. Rangelov, P. Sandl and V. Dose.
88
N. Memmel
References I 2 3 4 5 6 7 8 9 lo tJ 12 J3 14 Ls l~, 17 18 19 20
21 22 23 24 25 2~, 2"7 28 29 3o 31 ?,2 33 34
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