Energy shift of the Cu L 3 M 4,5 M 4,5 Auger line excited by proton impact on Cu 110 : Enhanced electron correlations at the surface

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1 PHYSICAL REVIEW B VOLUME 53, NUMBER APRIL 1996-I Energy shift of the Cu L 3 M 4,5 M 4,5 Auger line excited by proton impact on Cu 110 : Enhanced electron correlations at the surface S. Parhofer Siemens AG, Corporate Research and Development, Postfach 3220, Erlangen, Germany R. Pfandzelter and M. Potthoff Humboldt-Universität zu Berlin, Institut für Physik, Invalidenstrasse 110, Berlin, Germany Received 30 November 1995 Cu L 3 M 4,5 M 4,5 Auger spectra excited by impact of 1.0-MeV protons on Cu 110 were measured. In the case of grazing incidence angles, a shift of the Auger line to higher kinetic energies was observed. This is attributed to a surface effect. The observed shift is interpreted within the Cini-Sawatzky theory. Taking into account the surface core-level shift and the surface shift of the center of gravity of the valence band only is not sufficient to explain the observed shift of the Auger line. We find evidence that the shift is partly due to a change of the on-site Coulomb interaction U at the very surface. A rough estimation shows U to be increased by less than 0.6 ev at the surface when compared with the bulk. I. INTRODUCTION Electron correlations at metal surfaces are an important subject of present research. Due to the reduced coordination number of atoms at the surface, electrons tend to be more localized when compared with the bulk. Therefore, electron correlation effects are believed to be more pronounced at the surface. This promises and has resulted in interesting and technologically important effects. 1 From the theoretical point of view, studying electron correlations at metal surfaces is by no means a trivial task. Mostly, a conventional band theory is not adequate at all, and one is forced to start from Hubbardtype model Hamiltonians. A reliable description of a particular system is inevitably based on an accurate knowledge of the typical parameters that enter the model. There is an especially urgent need for information on a priori unknown parameters characterizing the strength of electron correlations at the surface of a single crystal. As a prototype for studying correlation effects at metal surfaces, we have chosen the open 110 surface of Cu. For late 3d transition metals it is especially the on-site Coulomb interaction U among the 3d electrons that dominates essential physical properties. Up to now little has been known about the change of U when passing from the bulk to the surface. The main purpose of this paper is to show that it is possible to obtain information about the difference U between the surface and bulk values by means of highresolution proton-induced CVV Auger-electron spectroscopy AES. AES is exactly the method to investigate electroncorrelation effects, since the direct Coulomb interaction between the two remaining holes in the valence band drastically affects the Auger line shape: A strong satellite splits off on the low-energetic side of the bandlike part in the spectrum as soon as U exceeds a certain critical value roughly given by the bandwidth. 2,3 The shape of the Cu L 3 M 4,5 M 4,5 line resulting from Auger transitions in the bulk has been described successfully within the framework of the Cini- Sawatzky model. 2,4 The main spectral features have to be interpreted as satellites, and the bandlike part is nearly negligible. Here we will apply the Cini-Sawatzky model to obtain information on correlations at the very surface. Our study requires a highly surface-sensitive AES experiment: Significant deviations of U from its bulk value can only be expected in the topmost surface layer. In conventional AES, the information depth is essentially determined by the escape depth of the Auger electrons, because the primary particles kev electrons, x rays penetrate deeply into the target. The escape depths vary between several Å and several tens of Å in the range of principal Auger-electron energies, 5 which means that mainly bulk electronic properties are probed. Several attempts have been made to enhance the surface sensitivity in electron- or x-ray-induced AES to a certain degree. 6,7 A substantial improvement, however, was shown to be possible by using positrons or grazingly incident protons as primary particles, where a nearly exclusive sensitivity to the topmost surface layer could be achieved. 8,9 Whereas positron-induced AES suffers from small annihilation probabilities with inner-shell electrons, large cross sections for inner-shell ionization can be achieved in protoninduced AES simply by adjusting the beam energy. The gist of this technique is the fact that high-energetic protons that are grazingly incident upon an ideally flat surface do not penetrate into the target but are specularly reflected. Creation of Auger electrons via core-hole excitation is thus confined to atoms of the topmost surface layer. Crucial for a successful application of the method is a proper choice of the proton energy: 9 It must be high enough to enable effective core-hole excitation at the large impact parameters occurring in specular reflection, but low enough for reasons of experimental feasibility. In the present case of Cu L 3 subshell ionization, a proton beam energy of 1.0 MeV is good compromise. II. EXPERIMENT The experiments were performed at the Forschungszentrum Rossendorf in a UHV chamber pressure mbar, which is attached to a differentially pumped beamline of the 2-MeV van-de-graaff accelerator. A monoenergetic, mass-selected proton beam with an angular divergence of /96/53 15 / /$ The American Physical Society

2 S. PARHOFER, R. PFANDZELTER, AND M. POTTHOFF 53 FIG. 1. Cu L 3 M 4,5 M 4,5 Auger spectra excited by 2.6-keV electrons or 1.0-MeV protons incident upon Cu 110. The incidence angle to the surface is 20 for the electron excited spectrum first spectrum from the top and 4.0 second, 0.8 third and 0.3 fourth for the proton-excited spectra. The spectra are represented by straight line segments connecting the experimental data points. No off-line treatment was applied, and no corrections for the scattered electrons and the background were made. The zero of energy is at the Fermi energy. For clarity, the origins have been displaced vertically by arbitrary amounts. 0.1 is incident upon a Cu 110 surface at a grazing angle along a high-index lattice direction. The current density is typically 100 na/mm 2. Those electrons that are emitted by proton impact in the direction normal to the beam and nearly normal to the target surface are energy analyzed by a 150 spherical sector analyzer 100-mm mean radius with transfer lens system. The electron-energy spectra were recorded using a constant electron pass energy 50 ev and pulse-counting detection. The constant absolute energy resolution was 0.5 ev. The recording time for the electron spectra presented here was about 15 min each; the step width is usually 0.2 ev. The copper single crystal was mechanically polished and carefully oriented to a residual deviation from the 110 surface of less than 0.1. The surface was cleaned in situ by frequent cycles of mild sputtering 1 kev Ar, 20 A/cm 2, 5 min and subsequent annealing 700 K, 5 min until no more contaminations were detected by AES. The same surface preparation technique was applied beforehand in another chamber and routinely resulted in a sharp lowenergy electron-diffraction LEED pattern. The adjustment of the grazing angle is controlled by a step motor with an accuracy of 0.1. III. RESULTS In Fig. 1 we show some measured Cu L 3 M 4,5 M 4,5 Auger spectra. The spectra are represented by straight lines which connect the experimental data points; no off-line treatment was applied, and no corrections for the scattered electrons and the background were made. The electron-excited spectrum Fig. 1, first from the top shows four peaks and two shoulders, one at the low- and one at the high-energy side of the main peak. Neither the energetic positions nor the relative intensities of the spectral features change, when 1.0- MeV protons are incident at a sufficiently large angle Fig. 1, second from the top. This is reasonable, since for both electrons and protons the L 3 inner-shell ionization arises from direct Coulomb interaction between projectile and target core electron. Moreover, excitation occurs far above the threshold in both cases, and a post-collision interaction, which has been found to slightly affect the line position, 10 can be excluded. High-resolution studies of the Cu L 3 M 4,5 M 4,5 Augerelectron spectrum have already been performed by several authors using x rays or electrons as primary beams e.g., Refs. 4, 11, and 12. The spectra are the same as the spectra presented here within the experimental uncertainty. In all cases, the primary particles deeply penetrate into the target and generate Auger electrons in numerous layers under the surface. The information depth is thus mainly determined by the transport properties of the Auger electrons in the solid. In the present case, the escape depth of the Auger electrons amounts to about 13 atomic layers; 5 i.e. the percentage which comes from the topmost surface layer is negligible, and the spectra represent bulk electronic properties. In order to increase the portion of Auger electrons coming from the very surface, we decreased the incidence angle of the protons to the surface. All other experimental parameters were held constant. The Auger spectra for 0.8 and 0.3 are shown in Fig. 1 third and fourth from the top. The spectra closely resemble the spectra excited by electrons or protons at 4.0 as far as the overall shape and relative intensities of the spectral features are concerned. Yet there are two distinct changes: First and most important, the whole spectrum shifts to higher energies. Second, the widths of the spectral features are slightly increased. We note that this cannot be due to a worse energy resolution: All parameters determining the experimental energy resolution spectrometer pass energy, widths of entrance and exit slits, electron source size were held constant. In Fig. 2 we plot the energy positions of the maximum of the main peak as a function of the incidence angle. Below about 1.5, the peak gradually shifts to higher energies. The shift is maximal at the smallest incidence angles and amounts to about 0.4 ev. The same behavior is found for the two low-energy peaks albeit with larger experimental uncertainty and the high-energy peak. Here the observed maximum shifts are 0.4, 0.3, and 0.4 ev, respectively. An exact determination of line positions in Auger spectroscopy is often impeded by the background of secondary electrons and in elastically scattered Auger electrons. The background in proton-excited Auger spectra differs from electron-excited spectra due to the lack of reflected electrons. In addition, we observed a dependence of the background on the incidence angle of the protons. Auger spectra spanning a large energy range show that the portion of inelastically scattered Auger electrons is reduced when the protons are grazingly incident. In order to check to what extent the line positions are affected by the electron background, we tenta-

3 ENERGY SHIFT OF THE Cu L 3 M 4,5 M 4,5 AUGER LINE... when passing from the bulk to the surface. This is corroborated by the monotonic increase of the linewidths, so even at the smallest incidence angle the measured Auger spectrum may be considered as a superposition of surface and bulk spectra. IV. DISCUSSION FIG. 2. Energy position of the maximum of the main peak in the Cu L 3 M 4,5 M 4,5 Auger spectrum as a function of the incidence angle of 1.0-MeV protons solid circles upon a Cu 110 surface. For comparison, results for electron excitation are displayed as well open circles. The zero of energy is at the Fermi energy. tively applied two different background-removal techniques: a simple spline interpolation under the Auger peak, and a physically meaningful convolution technique. 13 We found that the effect of background corrections on the peak positions is negligible; e.g., the main peak is shifted by less than 0.05 ev. The linewidths show exactly the same characteristic dependence on the incidence angle as the line positions. For 1.5, the widths are constant; for 1.5, they gradually increase and have a maximum at the smallest angles used. For example, the full width at half maximum FWHM of the main peak increases from about 1.4 to 1.8 ev. The observed shift of the Auger line positions toward higher energies is attributed to the enhanced surface sensitivity for grazing incidence. The trajectories of protons, which are incident at a sufficiently small angle upon an ideally flat surface, are governed by correlated small-angle deflections. The protons are specularly reflected, and Auger electrons can only be excited from the top surface layer atoms. In the present case, the critical angle c for specular reflection is A real surface, however, has atomic steps, defects, and thermally elongated atoms, and therefore perfect reflection cannot be expected. This applies especially to high proton energies, where the interaction length with the surface is large. On the other hand, even beyond the regime of specular reflection i.e., c ), successive uncorrelated small-angle deflections lead to an enhanced reflection coefficient and reduced penetration depth for small incidence angles. 15 In the present case, we thus expect a gradual and monotonic enhancement of the surface sensitivity, i.e., the percentage of Auger electrons coming from the topmost layer, with decreasing incidence angle. This enhancement starts when the penetration depth falls below the escape depth of the Auger electrons. The critical angle for specular reflection should give the order of magnitude of relevant incidence angles, which is in agreement with the experimental observation. In conclusion, we thus believe that the observed shift of the Auger line positions gives a lower limit of the actual shift We now turn to the interpretation of the experimental findings. The standard Cini-Sawatzky theory 2,3 see also Ref. 16 for a completely occupied, nondegenerate valence band rigorously derives the AES intensity from a two-particle spectral density within the framework of Hubbard-type models. These include the on-site Coulomb interaction among the valence-band electrons U. In the case of strong U the Cini- Sawatzky model predicts the AES spectrum to be dominated by a sharp satellite which takes almost the whole spectral weight. For our purposes it is sufficient to concentrate on the energetic position of this satellite and its change at the surface. In the case of strong correlations the satellite position E S is given by E S,i 2T 0,i c,i U i. Here T 0 is the center of gravity of the valence band, and c denotes the energy of the core state. Note that we define c as an energy eigenvalue and not as a binding energy; the same holds for the definition of T 0. The energy zero has been chosen to coincide with the Fermi level. This implies c T 0 0, while E S 0 and U 0.) The index i refers to layers parallel to the surface. For the semi-infinite system under consideration, the one-particle quantities T 0 and c as well as the Coulomb interaction U are assumed to be layer dependent, i.e., to be dependent on the distance to the crystal surface. Within the context of the Cini-Sawatzky model, Eq. 1 may be derived from a rather simple analysis of the moments of the two-particle spectral density. 17 Alternatively, Eq. 1 becomes evident following Cini s approximation and the related discussion in Ref. 3. We notice that Eq. 1 provides a local relation between the quantities T 0, c, and U for a layer i, and the position E S,i of the satellite that is assumed to result exclusively from transitions at atoms within the same layer i. No hopping integrals occur in Eq. 1, which means that the satellite position is neither affected by the shape nor by the effective width of the layer density of states a band narrowing is expected for the topmost surface layer because of the reduced coordination number. The Coulomb interaction U in Eq. 1 accounts for the direct influence on the satellite position due to the correlations between the two excited holes in the valence band. We do not consider the Coulomb interaction between valence and core electrons: In the case of a completely occupied valence band such an interaction, and thus core-hole effects at all, are almost meaningless. 18 Therefore, in Eq. 1 T 0 is the band center of gravity referring to the ground state without core hole. To obtain information about the change of U when passing from the Cu bulk to the surface, we first have to discuss 1

4 S. PARHOFER, R. PFANDZELTER, AND M. POTTHOFF 53 a possible shift of the center of gravity of the d band T 0 T surf 0 T bulk 0 as well as a surface core-level shift SCLS c surf c bulk c. We assume that correlations that affect the line position indirectly via T 0 are well accounted for by the local-density formalism within the density-functional theory. To determine T 0, a self-consistent scalar-relativistic calculation based on the tight-binding linear muffin-tin orbitals method in the atomic-sphere approximation 19 has been performed. The method has been proven to be accurate and efficient in many applications. The Cu 110 surface is treated as a slab of finite thickness. 20 Seven inequivalent Cu layers and two inequivalent layers of empty spheres also turn out to be sufficient for convergence of the results. The center of gravity of the d- projected density of states for the topmost Cu layer is found to be 0.6 ev higher than in the bulk, T ev. 21 Since T 0 is an integral quantity, an accuracy for T 0 that is clearly better than 0.1 ev can be expected. The energetic shift of the Cu 2p level 2p has been investigated in recent experimental as well as theoretical studies Unfortunately, there are no documented data for the 110 surface to our knowledge. Nevertheless, an estimation of 2p for the 110 surface is possible when referring to trends of the SCLS for different surfaces of the same crystal: The SCLS will be stronger the more open the surface is. 25 Calculations 24 for the closed-packed 111 and for the more open 100 surface of copper yield 2p and ev, respectively, and thus confirm the above mentioned trend. Experimental values are known for the 100 surface only, and amount to 2p 0.24 ev Ref. 22 and 2p 0.22 ev, 23 which is slightly less than the theoretical result. Comparing with the 100 surface, the SCLS for the even more open 110 surface can be expected to be larger. We may thus cautiously assume 2p to be larger than 0.2 ev for the 110 surface. With these estimates for the shift of the center of gravity of the d band T 0 and for the SCLS 2p and with the experimental result for the shift of the Auger satellite position, we are able to estimate the shift of U when passing from the bulk to the surface. Following the discussion in Sec. III, the Auger line originating from transitions within the topmost surface layer shifts by more than 0.4 ev to higher kinetic energies: E S 0.4 ev. Furthermore, we have T ev and 2p 0.2 ev. According to Eq. 1, for the shift of U this means U 2 T 0 c E S 0.6 ev; the on-site Coulomb interaction is increased by less than 0.6 ev at the very surface when compared with the bulk. For the time being it is only possible to give an upper limit for U. This is mainly due to the rough estimation of the SCLS for the 110 surface. Without experimental data or reliable first-principles calculations for the 110 surface no stronger conclusion is possible. In particular, a SCLS larger than 0.2 ev is conceivable remembering the trend towards larger SCLS s for more open surfaces. On the other hand, according to our results an increased U at the surface is still implied for rather large SCLS s up to 0.8 ev. However, we also have to bear in mind that the experiment gives only a lower limit for the actual shift of the Auger line due to possible small contributions from layers below the topmost surface layer. V. SUMMARY While the surface shifts of one-particle quantities, such as the energies of the valence and the core states, are nowadays in principle available by experiments or ab initio calculations, little is known about the change of Coulomb interaction energies. We have shown AES induced by grazingly incident protons to be an efficient technique for studying effects of electron correlations at crystal surfaces. The Cu L 3 M 4,5 M 4,5 Auger line has been observed to shift by about 0.4 ev to higher kinetic energies when passing from the bulk to the 110 surface. Small contributions to the intensity originating from transitions within subsurface layers manifest themselves in an additional slight broadening of the line. The energetic difference between the line position caused by transitions exclusively within the topmost surface layer and within the bulk is therefore expected to be slightly higher than 0.4 ev. In connection with a rough estimate for the SCLS for the 110 copper surface and with a firstprinciples determination of the shift of the valence-band center of gravity, we obtained evidence of a change of the onsite Coulomb interaction U at the surface when compared with the bulk. An upper limit for the change U could be derived by applying the Cini-Sawatzky model: U is increased by less than 0.6 ev at the surface. A stronger conclusion concerning the true value of U is only possible when reliable data for the SCLS s are available. In this context an application of proton-induced AES to other low-index Cu surfaces seems to be promising. ACKNOWLEDGMENTS The authors would like to thank Dr. R. Grötzschel from the Forschungszentrum Rossendorf for hosting our experiment, and M. Mäder for technical assistance. We also thank H. Ufer from the Universität Osnabrück for performing the linear muffin-tin orbitals LMTO calculation. This work was funded by the German Federal Minister for Research and Technology BMFT, and the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich See, for example, Ultrathin Magnetic Structures, edited by J. A. C. Bland and B. Heinrich Springer, Berlin, 1994, Vols. I and II. 2 M. Cini, Solid State Commun. 24, G. A. Sawatzky and A. Lenselink, Phys. Rev. B 21, E. Antonides, E. C. Janse, and G. A. Sawatzky, Phys. Rev. B 15, J. Ferrón and E. C. Goldberg, Surf. Sci. 275, G. B. Hoflund, D. A. Asbury, C. F. Corallo, and G. R. Corallo, J. Vac. Sci. Technol. A 6, H. W. Haak, G. A. Sawatzky, and T. D. Thomas, Phys. Rev. Lett. 41, D. Mehl, A. R. Koymen, K. O. Jensen, F. Gotwald, and A. Weiss, Phys. Rev. B 41, R. Pfandzelter and J. Landskron, Phys. Rev. Lett. 70, T. Jach and C. J. Powell, Phys. Rev. Lett. 46,

5 ENERGY SHIFT OF THE Cu L 3 M 4,5 M 4,5 AUGER LINE H. H. Madden, D. M. Zehner, and J. R. Noonan, Phys. Rev. B 17, P. T. Andrews, T. Collins, and P. Weightman, J. Phys. C 19, N. Rosenberg, M. Tholomier, and E. Vicario, J. Electron. Spectrosc. Relat. Phenom. 46, The critical angle is calculated from a surface continuum potential based on Moliére interatomic potentials. 15 V. S. Remizovich, M. I. Ryazanov, and I. S. Tilinin, Zh. Eksp. Teor. Fiz. 79, Sov. Phys. JETP 52, W. Nolting, Z. Phys. B 80, W. Nolting, Grundkurs: Theoretische Physik, 7. Viel-Teilchen- Theorie Zimmermann-Neufang, Ulmen, M. Potthoff, J. Braun, W. Nolting, and G. Borstel, J. Phys. Condens. Matter 5, O. K. Andersen and O. Jepsen, Phys. Rev. Lett. 53, ; O. K. Andersen, Z. Pawlowska, and O. Jepsen, Phys. Rev. B 34, The calculation shows that within the limit of the atomic sphere approximation the relaxation of the surface has no decisive influence on T 0. T 0 is changed by less than 0.03 ev at the surface when considering an inward relaxation of 8.5% for the topmost surface layer and an outwards relaxation of 2.3% for the second layer with respect to the bulk interlayer spacing D. L. Adams, H. B. Nielsen, and J. N. Andersen, Surf. Sci. 128, H. Ufer unpublished. 22 P. S. Bagus, G. Pachioni, and F. Parmigiani, Phys. Rev. B 43, J. A. Rodriguez and D. W. Goodman, J. Phys. Chem. 95, D. Hennig private communication ; D. Hennig, M. V. Ganduglia- Pirovano, and M. Scheffler unpublished. 25 P. H. Citrin and G. K. Wertheim, Phys. Rev. B 27,