Appl. Phys. A 59, 479-486 (1994)
Applied ,o,,°, P h y s i c s A -Surfaces ' © Springer-Verlag 1994
Quantization of electronic states on metal surfaces Th. Fauster Sektion Physik, Universitht Miinchen, Schellingstrasse 4, D-80799 Miinchen, Germany (Fax: 49-89/2180-3391, E-maih
[email protected]) Received 16 May 1994 / Accepted 8 July 1994
Abstract. An electron in front of a metal surface experiences an attractive force due to the induced image charge. Band gaps in the band structure can prevent a penetration into the metal along certain directions. The Coulomb-like potential supports bound states in front of the surface which correspond to a hydrogen atom in one dimension. These image states can be measured with high resolution by twophoton photoemission. The adsorption of metals modifies the states. If the electrons can penetrate into the metal, quantumwell states can develop corresponding to standing waves in the overlayer. Image states on small islands show the quantization effects due to the lateral localization. The spectrosopy of image states by two-photon photoemission permits the investigation of growth and morphology of deposited metal layers, a well as the illustration of fundamental quantummechanical effects.
The factor 4 in the denominator of this image potential arises because the electron and the image charge are separated by a distance 2z. Band gaps can exist even in a metal along certain directions. This means that the electron cannot penetrate into the metal. It is trapped in front of the surface if its energy is below Evac so it cannot overcome the vacuum barrier. The situation corresponds to the Coulomb problem in one dimension and the resulting image states form a series of bound states (numbered by n) converging towards Evac with energies [1]
PACS: 73.20.At, 73.20.Dx, 79.60.Dp
E(n) = Evac - 0.85 e V / n 2 , n = 1 , 2 , . . . .
Quantization of electronic states is always related to a localization of the electron. The quantum-mechanical description of the motion of a free electron gives the same energy as classical mechanics. In this paper, the case of electrons localized more than 2 N outside a metal surface is being considered. This localization arises from the attraction of the electrons to the metal surface which can be described by the concept of an image charge. The quantum-mechanical treatment of this situation leads to image states which are only loosely bound. It will be shown that these states can provide test electrons to study various properties of surfaces.
1 Introductory remarks
1.1 Image states An electron in front of a metal surface induces an electric field identical to the one produced by an opposite charge placed at the same distance z inside the metal (Fig. 1). The attractive force e2 1 F ( z ) - 4rre0 (2z) 2 ' (1)
due to the image charge, can be derived from a Coulomblike potential approaching the vacuum energy Eva c for large distances:
V(z)
e2 = Ew~
1
4tee0 4z
(2)
(3)
The binding energies of the states are reduced by a factor of 16 compared to the hydrogen atom. The wave functions are obtained from the radial part of the wave function for the hydrogen atom multiplied by z and expanded by a factor of 4 [2, 3]. The maximum of the wave function for the n = 1(2) state is more than 2 (10) }k away from the surface (Fig. 1).
1.2 Two-photon photoemission Image states on metal surfaces have been detected first in inverse photoemission experiments [4, 5]. The limited energy resolution prevented the clear identification of the series of states (3) so far [6]. The experimental technique with the best energy resolution and surface sensitivity for the study of image states is two-photon photoelectron spectroscopy (Fig. 2). A photon is used to excite an electron out of an occupied state below EF into the image state. A second photon excites the electron above Evac. It can then leave the surface and its energy and direction can be measured by conventional techniques of electron spectroscopy. An energy resolution better than 25 meV has been achieved [7, 8]. The low-energy cutoff of the spectrum at the top of Fig. 2 corresponds to electrons leaving the sample with negligible kinetic energy and can be used to determine the work function ~ = Evac - EF of
480
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Fig. 3. Two-photon photoemission spectra from Ag(100) measured at two different photon energies. The enlarged portion of the upper spectrum shows the n = 4 state as a shoulder
image potential 10k,
20~,
Fig. 1. Top: The electric field of an electron in front of a metal surface can be described by the concept of an image charge. Bottom: The corresponding attractive image potential leads to a series of bound states if the electron cannot penetrate into the metal along certain directions due to a band gap. For the lowest two states, the square of the wave function is shown
system for the first and second excitation step, respectively [7]. In this paper, only electrons traveling along the direction parallel to the surface normal will be considered. The motion of the electron parallel to the surface is essentially free and can be described by an effective mass close to the freeelectron mass [9, 11].
2 Clean surfaces
° °
Evac .... ] E(n) 2hv
EF Fig. 2. Schematic energy diagram for the excitation steps in two-photon photoemission. Spectra record the emitted electrons as a function of their kinetic energy
the sample [9]. Because /~vac is the reference level for the image states, the simultaneous and accurate measurement of the work function is convenient and important. Two-photon photoemission is a second-order process and has an intensity comparable to regular photoemission from thermally occupied states ,-~ 0.2 eV above EF [10]. The high photon intensities needed are obtained from the frequencydoubled (2hu) and the fundamental (hu) wave of a dye-laser
Two-photon photoemission spectra taken on a Ag(100) surface with two different photon energies are presented in Fig. 3 [7]. The existence of a series of peaks is obvious in both spectra. The bottom spectrum shows two peaks, whereas the top spectrum shows three resolved peaks and a shoulder at the high-energy side of the third peak assigned to the n = 4 image state. Contributions from even higher members of the image-state series cannot be excluded. In order to detect these states, photon energies close to the work function (4.43 eV for Ag(100) [7]) are necessary which explains the absence of these structures in the bottom spectrum of Fig. 3. The energies of the peaks deviate considerably from the prediction of (3) with the largest deviation for the n = 1 state which is 0.53 eV below Evac instead of 0.85 eV. The energies of the series of states can be described, however, by a slight modification to (3):
E(n)=Evac-0.85 e V / ( n + a ) 2 , n = l , 2 , . . . .
(4)
A quantum defect a = 0.26 gives an excellent description of the experimental data of Fig. 3. The deviation from the simple model of (3) is also seen for other surfaces and materials in Fig. 4. For all clean surfaces, the series of states can be described extremely well by (4) with an appropriate choice of the quantum defect a [9]. There is no dependence on the surface structure such as fcc(111) vs (100) surfaces.
Quantization of electronic states on metal surfaces
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Energy relative to Evac (eV) Fig. 4. Two-photonphotoemissionspectra for various surfaces. The different energies relative to Evac depend on the energetic position relative to the band gaps, as illustrated in the rightpanel
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band gap has a node at the surface so it can be matched to the solution analogous to the hydrogen atom. For energetic positions lower in the band gap, the wave function has a finite amplitude which changes the boundary condition at the surface. This gives different solutions with reduced binding energy, as illustrated in Fig. 5. The maximum of the wave function moves further away from the surface plane into a region of a weaker image potential resulting in a reduced binding energy. The quantum defect changes from zero to 1/2 across the gap (top to bottom) [12]. For most surfaces, the band-gap parameters obtained from the bulk-band structure give the correct energies of the image states [9, 10]. An exception occurs for ferromagnetic surfaces [13, 14] which might be due to the neglect of many-body effects [9, 10]. It should be noted that from the line width of spectra such as presented in Fig. 4, the lifetime of the image states can be determined. The results agree well with the direct measurements by time-resolved experiments [15, 16]. The lifetime of image states is about one order of magnitude larger than the lifetime of bulk states and is influenced by the penetration of the wave function into the bulk [3]. Other contributions identified by experimental studies are the decay into unoccupied surface states or d bands [9, 16].
image potential
Fig. 5. Wave functionof n = 1 image states as a function of their energetic position relative to the band gap. The matching conditions at the surface push the maximumaway from the surface leadingto a decrease in binding energy going from the top to the bottom of the band gap
The binding energies rather depend on the energetic position of the image states within the band gap, as illustrated in the right column of Fig. 4. An image state near the top of the band gap lag(111) and Cu(111)] has a binding energy close to 0.85 eV, as predicted by (3), whereas an image state near the center of the gap [Ag(100) and Pd(111)] has a binding energy around 0.55 eV. An image state close to the bottom of the band gap would be expected on Pd(100) which has not been measured yet by two-photon photoemission. In the derivation of (3), the penetration of the wave function into the bulk has been neglected (Fig. 1). For energies within the band gap, solutions decaying exponentially into the bulk exist, and the solution in the vacuum region has to be matched at the surface. This is illustrated in Fig. 5, which shows that the bulk solution for energies at the top of the
3 Metal
overlayers
In the preceding section the experimental proof of the existence of image-states series on clean metal surfaces was presented. The somewhat surprising result was that the energies of these states depend on the energetic position relative to the band gap. Apart from the value of the work function, this is dominated by a property of the bulk-band structure. In this section modifications of the surface and their consequences on the image states will be studied. For metal overlayers on a metal substrate, the concept of the image charge can certainly be maintained and image states can exist. Keeping in mind the importance of the band gap on the energy of the image states, the discussion can be separated for overlayer materials which have or do not have a band gap in the relevant energy range.
3.1 A u / P d ( l l l ) The first case occurs for Au on Pd(111) [17]. There is a large band gap around .Eva c for Pd, whereas the upper edge of the band gap for Au is ~ 2 eV below Evac (Fig. 7). The vacuum energy [18-20] as well as the energy of the first image state relative to EF [18, 2, 21] are very similar for P d ( l l l ) and Au(111). Consequently, only small variations of these quantities with coverage are expected. Due to the small lattice mismatch (~ 5%) between the two fcc materials, epitaxial growth is expected. At room temperature a layer-by-layer growth has been reported [22, 23] with pseudomorphic Au layers for coverages up to 3 MonoLayers (ML) [24]. A series of spectra for Pd(111) with Au coverages ranging from 0 to 10 ML is shown in Fig. 6. The data are plotted relative to EF. The work function is given to the right of each spectrum and shows little variation. For a rough surface, a reduced work function is expected [25]. The observed
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(5)
In first-order perturbation theory, the energy correction as a function of coverage can be estimated. The system of j layers of Ag on Pd can be regarded as an Ag crystal whose potential VAg is changed to the Pd potential Vpd after j layers (Fig. 10). Above 2 ML, the energies of the n = 1 states are just below the upper edge of the Ag band gap [18], and the wave function for a thick Ag film can be approximated (cf. Fig. 5) by ~b(z) = exp(z/A)
sin(Trz/d)
,z < 0 .
(6)
For Ag(111), the layer separation d is 2.36 ~k and the decay length A can be estimated to 6.1 ML [12, 18]. Using the parameters for a periodic potential from [18] a perturbation energy of ('//)[Vpd -- VAg]~ ) / (2/)12/)) = 2.6 eV e x p ( - 2 j / A )
(7)
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3.5 Fig. 10. Energy diagram and wave function of the first image state for Ag on Pd(111). The energy correction can be estimated from perturbation theory by replacing the Ag potential "by the Pd potential outside the Ag layers is obtained. This expression predicts the energy correction to decay on a length scale of A/2 = 3.0 ML, which is in good agreement with the experimental value. The prefactors differ by a factor of ten, which arises because only the wave function inside the metal (6) has been evaluated. The proper normalization of the complete wave function results in a 10% probability to find the electron inside the crystal. This number agrees with theoretical estimates [16], but is relatively uncertain because it depends on the difference of the potential parameters. It should be noted that this constitutes an example for using perturbation theory to obtain the wave function from the energy corrections. More sophisticated calculations reproduce very well the experimental values for any completed layers [18, 28].
4.0 E-EF
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Fig. 11. Two-photonphotoemission spectra for 1 ML Ag on Pd(111) deposited at 90 K and after heating to the indicated temperaturesfor 60 s. The energy scale is relative to EF energies 2hu have to be lower than the work function to avoid one-photon photoemission [9]. At lower temperatures, the mobility of the Ag atoms is reduced, and a change of the growth mode to three-dimensional islands occurs, as sketched in the bottom of Fig. 11. The intensity ratio of the peaks corresponding to different layer heights is roughly 1:2, as expected for diffusion-limited growth [31]. The spectra show pronounced changes after heating the sample for 60 s to the temperatures given in Fig. 11 and subsequent cooling down to 90 K for the measurements. After heating just above room temperature, the series at lower energies has disappeared and only electrons from one-layerthick Ag areas are observed. The spectrum for 373 K is similar to the one where 1 ML of Ag is deposited at room temperature (cf. Fig. 8). The Ag atoms have covered the open Pd(111) patches and the Ag film forms a smooth layer.
3.3 Surface morphology The preceding sections demonstrated how image states depend on surface properties such as the band gap and the work function. These-properties have to be interpreted as local quantities if the surface becomes inhomogeneous. In the following, the influence of a changed surface morphology on the image states will be studied. An easy way to vary the growth mode in metal-on-metal epitaxy is by changing the substrate temperature or heating the deposited films. As an example, spectra for 1.0 ML of Ag on P d ( l l l ) are presented in Fig. 11. The lowest spectrum for deposition at 90 K shows two series of image states and looks similar to the one for 1.35 ML of Ag on Pd(111) in Fig. 8. The series at lower energy comes from two-layerthick Ag areas, and the other from one-layer-thick areas. Because the coverage is l ML, also patches which are not covered by Ag must exist on the surface. The image states of the clean Pd(111) substrate are not seen in Fig. 11, because they lie above the measured vacuum energy, The photon
For heating temperatures above 500 K, the image state gets broader and shifts to higher energy. At about 600 K, one narrow peak is observed which does not shift in energy up to about 750 K. Due to the narrow symmetric line shape, it must be an image state on a homogeneous surface. Because its energy is between the values for 1 ML of Ag and clean Pd, it must be due to a surface alloy. Support for an incorporation of Ag atoms into the Pd surface comes from the observation that the temperature is well below the desorption temperature of 1100 K for Ag from Pd(111), and that Ag atoms two- and three-layers deep in the fcc Pd(111) structure were identified by photoelectron forward-scattering experiments for samples heated to 700 K [24, 29]. The stable surface alloy is observed between 600 K and 750 K for coverages up to 16 ML. The energies of the image states are always higher than the corresponding values for completed layers after deposition at room temperature and indicate a Ag concentration of the surface alloy increasing with the initial Ag coverage [18].
485
Quantization of electronic states on metal surfaces
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3.8 4.0 4.2 4.4 4.6 0 50 100 150 E- E F ( eV ) Island diameter (~,) Fig. 12, Two-photon photoemission spectra for various amounts of Ag on Pd(111) deposited at 90 K (left). The energy shift relative to a smooth film (dashed line) is due to the lateral localization of the image state. From the experimental data, distributions of the coverage by islands of various diameters are derived (right). The integral over the curves corresponds to the coverage given in the left-hand panel. The mean area of the islands is proportional to the coverage (top right)
For annealing temperatures above 750 K, the image state shifts further in the direction of the clean P d ( l l l ) surface. The Ag evaporates or gets incorporated deeper into the bulk. At about 1200 K, the image states and the work function of the clean P d ( l l l ) surface are observed [18].
3.4 Islands The most important result obtained from the data for Ag on P d ( l l l ) is that the image-state series for the bare Pd substrate and Ag layers of different height can be easily distinguished due to their different energies. This has been used in the preceding section to identify the growth of threedimensional islands at low temperatures. The concept of the local work function leads to the unambiguous assignment of electrons to patches of different Ag coverage. This means that they are localized laterally on the surface in addition to the perpendicular direction. The following questions arise: What is the minimum size of an island which can support image states and can effects of the lateral localization be observed? The experimental answer to these questions requires the preparation of small Ag islands, which can be achieved for small coverages deposited at low temperatures. In the lefthand panel of Fig. 12, spectra for Ag coverages between 0.25 and 0.7 ML adsorbed at 9 0 K are shown [32]. A shift of up to 0.2eV to higher energy compared to the case of a smooth 1 ML Ag film (top spectrum and dashed line in
Ag
Fig. 13. Energy shift (dotted line) and the wave function for a image state localized on a small Ag island
Fig. 12) is observed. The shift decreases with increasing coverage and can be further reduced by heating (spectrum for 273 K in Fig. 12). The width of the peaks is larger than for image states on homogeneous surfaces and the line shape is asymmetric with a tail at the high-energy side. At these low coverages, no significant occupation of two-layer-high islands is expected [31], and there is no intensity to the left of the peaks (cf. Fig. 11). The energy shifts are due to the lateral confinement of the image-state electrons on the Ag islands. This situation is illustrated in Fig. 13. For an electron localized in the lateral dimension, the wave function is shown by the thin solid line in Fig. 13. The bottom of the potential well is given by the energy of the n = 1 image state for one layer of Ag on P d ( l l l ) . The well has a finite height limited by the energy of the n = 1 state for clean P d ( l l l ) . This choice of the parameters for the potential well yields the correct limiting values for vanishing and infinite island diameter d. The energy of a particle in a square infinitely high box of area d 2 is A E = 2h27r2/ 2 m d 2
.
(8)
Islands on hexagonal substrates are not expected to be squares, but the energy shift is indirectly proportional to the area for other shapes as well with a different proportionality factor in (8). The energy shift for localization in one dimension on a stripe of width d is half the value given in (8). This implies that (8) holds within a factor of the order of two even for islands of fractal or ramified shape, as observed by scanning tunneling microscopy [33, 34]. The finite depth of the potential well leads to a smaller prefactor in (8). This correction depends only weakly on the island shape and is valid for the energy shifts used in this work, which are small compared to the well depth. The consequence of (8) is that the island area can be derived from the energy shift and that the shape of the spectra in Fig. 12 reflects the distribution of island areas. Using a least-squares-fit procedure, the distribution of the islands' sizes has been obtained from the experimental spectra [32]. Circular islands have been assumed and the potential well of finite depth shown in Fig. 13 has been used. The distributions of the coverages by islands of various diameters are shown in the right-hand panel of Fig. 12. The solid lines in the lefthand panel show the fits of the model to the experimental data. The distributions are normalized so that the area under the curve is proportional to the coverage. For Ag adsorbed on P d ( l l l ) at 90K, the mean island diameter is about 7 (14) Ag atoms for coverages of 0.25 (0.70) ML. After heating of the Ag film, the islands become larger, as illustrated in Fig. 12 for the 0.70 ML film. A broad distribution with a mean value of ,,~ 100 N is seen after annealing to 273 K for 60 s. The start of the distributions at ~ 10 )k diameter
486 is determined by the energy range of the experimental data and does not lead to any unphysical shape o f the curves. The smallest islands observed by s c a n n i n g t u n n e l i n g microscopy studies for metal-on-metal systems are of similar diameter [34, 33] which corresponds roughly to islands consisting of seven close-packed atoms. For the data at 90 K, the height of the distributions is almost i n d e p e n d e n t of coverage and the m e a n area of the islands grows proportionally to the coverage (Fig. 12, top right). This b e h a v i o r can be explained if the density of nucleation centers is c o n s t a n t (in the coverage range studied here) and fixed by the experimental conditions such as evaporation rate and temperature. F r o m the slope of the solid line, the density o f n u c l e a t i o n centers at 90 K is obtained to 7 x 1012 c m -~. This corresponds to a diffusion length of ~ 2 0 N , in agreement with other works [33, 34].
4 Conclusions The examples in the article have illustrated that electrons in image states are localized in front of metal surfaces, and how they can be used to probe the properties of the surface. For clean surfaces, i n f o r m a t i o n on the b a n d gaps is obtained. For overlayer systems, localization in the overlayer or on small islands can be observed. The image-state electrons are coupled only w e a k l y to the electronic states of the sample and are not i n v o l v e d in any b o n d i n g . This permits the identification of the localization effects in an unperturbed way. For the experimental investigation of image states, a technique with high energy resolution and low b a c k g r o u n d is provided by t w o - p h o t o n photoemission. These methods constitute a u n i q u e possibility to study the m o r p h o l o g y of surfaces and the growth of thin films through the spectroscopy of electronic states. I have benefitted from the excellent experimental work and the ideas of N. Fischer, R. Fischer, S. Schuppler, and W. Wallauer. Professor W. Steinmann gave me the opportunity to continue the work on two-photon photoemission. I express my gratitude to all these people. This work has been supported by the Deutsche Forschungsgemeinschaft (SFB 338).
Acknowledgements.
References 1. P. M. Echenique, J. B. Pendry: J. Phys. C 11, 2065 (1978) 2. D. Straub, F. J. Himpsel: Phys. Rev..13 33, 2256 (1986)
Th. Fauster 3. P. M. Echenique, J. B. Pendry: Prog. Surf. Sci. 32, 111 (1990) 4. V. Dose, W. Altmann, A. Goldmann, U. Kolac, J. Rogozik: Phys. Rev. Lett. 52, 1919 (1984) 5. D. Straub, F. J. Himpsel: Phys. Rev. Lett. 52, 1922 (1984) 6. F. J. Himpsel: Phys. Rev. B 43, 13394 (1991) 7. S. Schuppler, N. Fischer, T. Fauster, W. Steinmann: Appl. Phys. A 51, 322 (1990) 8. D. F. Padowitz, W. R. Merry, R. E. Jordan, C. B. Harris: Phys. Rev. Lett. 69, 3583 (1992) 9. W. Steinmann, T. Fauster: In Laser Spectroscopy and Photochemistry on Metal Surfaces, ed. by H. L. Dai, W. Ho (World Scientific, Singapore 1994) 10. T. Fauster: Prog. Surf. Sci. 46, 177 (1994) 11. K. Giesen, F. Hage, F. J. Himpsel, H. J. RieB, W. Steinmann, N. V. Smith: Phys. Rev. B 35, 975 (1987) 12. N. V. Smith: Phys. Rev. B 32, 3549 (1985) 13. S. Schuppler, N. Fischer, W. Steinmann, R. Schneider, E. Bertel: Phys. Rev. B 42, 9403 (1990) 14. R. Fischer, N. Fischer, S. Schuppler, T. Fauster, F. J. Himpsel: Phys. Rev. B 46, 9691 (1992) 15. R.W. Schoenlein, J. G. Fujimoto, G. L. Eesley, T. W. Capehart: Phys. Rev. Lett. 61, 2596 (1988) 16. S. Schuppler, N. Fischer, T. Fauster, W. Steinmann: Phys. Rev. B 46, 13539 (1992); Phys. Rev, B 47, 10058 (1993) (erratum) 17. R. Fischer, T. Fauster, W. Steinmann: Phys. Rev. Lett. (1994) (submitred) 18. R. Fischer, S. Schuppler, N. Fischer, T. Fauster, W. Steinmann: Phys. Rev. Lett. 70, 654 (1993) 19. G. V. Hansson, S. A. Flodstr6m: Phys. Rev. B 18, 1572 (1978) 20. F. Meier, D. Pescia: Phys. Rev. Lett. 47, 374 (1981) 21. D. P. Woodruff, W. A. Royer, N. V. Smith: Phys. Rev. B 34, 764 (1986) 22. Y. Kuk, L. C. Feldman, P. J. Silverman: Phys. Rev. Lett. 50, 511 (1983) 23. R. C. Jaklevic: Phys. Rev. B 30, 5494 (1984) 24. B. Eisenhut: Wachstum und Struktur diinner Silber- und Gold-Filme auf Palladium (111)- und Silber (111)-Oberflfichen. Dissertation. Universit~it Mfinchen, Miinchen (1992) 25. K. Wandelt: In Thin Metal Films and Gas Chemisorption, ed. by P. WiBmann (Elsevier, Amsterdam 1987) p. 280 26. Y. Kuk, L. C. Feldman, P. J. Silverman: J. Vac. Sci. Technol. A 1, 1060 (1983) 27. Chr. ReuB, W. Wallauer, T. Fauster, W. Steinmann: Unpublished 28. T. Fauster: Appl. Phys. A (1994) (in press) 29. B. Eisenhot, J. Stober, G. Rangelov, T. Fauster: Phys. Rev. B 47, 12980 (1993) 30. N. Fischer, S. Schuppler, R. Fischer, T. Fauster, W. Steinmann: Phys. Rev. B 47, 4705 (1993) 31. C. Argile, G. E. Rhead: Surf. Sci. Rep. 10, 277 (1989) 32. R. Fischer, T. Fauster, W. Steinmann: Phys. Rev. B 48, 15496 (1993) 33. R. Q. Hwang, C. Giinther, S. Schr/Sder, S. Gtinther, E. Kopatzki, R. J. Behm: J. Vac. Sci. Technol. A 10, 1970 (1992) 34. H. Roeder, H. Brune, J.-P. Bucher, K. Kern: Surf. Sci. 298, 121 (1993)
